<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing with OASIS Tables v3.0 20080202//EN" "journalpub-oasis3.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" dtd-version="3.0"><?xmltex \makeatother\@nolinetrue\makeatletter?>
  <front>
    <journal-meta>
<journal-id journal-id-type="publisher">BG</journal-id>
<journal-title-group>
<journal-title>Biogeosciences</journal-title>
<abbrev-journal-title abbrev-type="publisher">BG</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Biogeosciences</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1726-4189</issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>

    <article-meta>
      <article-id pub-id-type="doi">10.5194/bg-13-3397-2016</article-id><title-group><article-title>Estimate of changes in agricultural terrestrial nitrogen pathways and
ammonia emissions from 1850 to present in the<?xmltex \hack{\newline}?> Community Earth System Model</article-title>
      </title-group><?xmltex \runningtitle{Estimate of changes in agricultural terrestrial nitrogen pathways}?><?xmltex \runningauthor{S.~Riddick et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff2 aff7">
          <name><surname>Riddick</surname><given-names>Stuart</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3 aff6">
          <name><surname>Ward</surname><given-names>Daniel</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Hess</surname><given-names>Peter</given-names></name>
          <email>pgh25@cornell.edu</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Mahowald</surname><given-names>Natalie</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Massad</surname><given-names>Raia</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Holland</surname><given-names>Elisabeth</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Department of Biological and Environmental Engineering, Cornell
University, Ithaca, NY, USA</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Centre for Atmospheric Science, Department of Chemistry, University
of Cambridge, Cambridge, UK</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Department Earth and Atmospheric Sciences, Cornell University, Ithaca, NY, USA</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>INRA, AgroParisTech, UMR1402 ECOSYS, 78850 Thiverval-Grignon,
France</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Pacific Centre for Environment and Sustainable Development,
University of the South Pacific, Suva, Fiji</institution>
        </aff>
        <aff id="aff6"><label>a</label><institution>now at: Atmospheric and Oceanic Sciences, Princeton University,
Princeton, USA</institution>
        </aff>
        <aff id="aff7"><label>b</label><institution>now at: Department of Civil and Environmental Engineering, Princeton University, Princeton, NY, USA</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Peter Hess  (pgh25@cornell.edu)</corresp></author-notes><pub-date><day>13</day><month>June</month><year>2016</year></pub-date>
      
      <volume>13</volume>
      <issue>11</issue>
      <fpage>3397</fpage><lpage>3426</lpage>
      <history>
        <date date-type="received"><day>12</day><month>August</month><year>2015</year></date>
           <date date-type="rev-request"><day>28</day><month>September</month><year>2015</year></date>
           <date date-type="rev-recd"><day>6</day><month>May</month><year>2016</year></date>
           <date date-type="accepted"><day>12</day><month>May</month><year>2016</year></date>
      </history>
      <permissions>
<license license-type="open-access">
<license-p>This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/3.0/">http://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions><self-uri xlink:href="https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016.html">This article is available from https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016.html</self-uri>
<self-uri xlink:href="https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016.pdf">The full text article is available as a PDF file from https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016.pdf</self-uri>


      <abstract>
    <p>Nitrogen applied to the surface of the land for agricultural purposes
represents a significant source of reactive nitrogen (N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula>) that can be emitted
as a gaseous N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> species, be denitrified to atmospheric nitrogen (N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>), run off
during rain events or form plant-useable nitrogen in the soil. To investigate
the magnitude, temporal variability and spatial heterogeneity of nitrogen
pathways on a global scale from sources of animal manure and synthetic
fertilizer, we developed a mechanistic parameterization of these pathways
within a global terrestrial land model, the Community Land Model (CLM).
In this first model version the parameterization emphasizes an explicit
climate-dependent approach while using highly simplified representations of
agricultural practices, including manure management and fertilizer
application. The climate-dependent approach explicitly simulates the
relationship between meteorological variables and biogeochemical processes to
calculate the volatilization of ammonia (NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>), nitrification and runoff
of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> following manure or synthetic fertilizer application. For the year
2000, approximately 125 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> is applied as manure and
62 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> is applied as synthetic fertilizer. We estimate the
resulting global NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions are 21 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> from manure
(17 % of manure production) and 12 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> from fertilizer
(19 % of fertilizer application); reactive nitrogen runoff during rain
events is calculated as 11 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> from manure and
5 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> from fertilizer. The remaining nitrogen from manure
(93 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) and synthetic fertilizer (45 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) is
captured by the canopy or transferred to the soil nitrogen pools. The
parameterization was implemented in the CLM from 1850 to 2000 using a
transient simulation which predicted that, even though absolute values of all
nitrogen pathways are increasing with increased manure and synthetic
fertilizer application, partitioning of nitrogen to NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions from manure
is increasing on a percentage basis, from 14 % of nitrogen applied in 1850
(3 Tg NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) to 17 % of nitrogen applied in 2000
(21 Tg NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>). Under current manure and synthetic
fertilizer application rates we find a global sensitivity of an additional
1 Tg NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> (approximately 3 % of manure and fertilizer) emitted per
year per <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C of warming. While the model confirms earlier estimates of
nitrogen fluxes made in a range of studies, its key purpose is to provide a
theoretical framework that can be employed within a biogeochemical model,
that can explicitly respond to climate and that can evolve and improve with
further observation.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

      <?xmltex \hack{\newpage}?>
<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p>Nitrogen is needed by all living things for growth. However, it is
relatively inert in its most abundant form, diatomic nitrogen (N<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and
needs to be converted to a form of reactive nitrogen (N<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> before it can
be used by most plants for growth (Visek, 1984). Supplying sufficient
N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> for maximum crop yield is a major concern in agriculture. In
preindustrial times N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> demand was partly solved with the use of animal
manure and seabird guano as well as crop rotation and the use of nitrogen-fixing crops   (Smil, 2000). However, by the early 20th century the
supply of these N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> sources could not match the demands of an increasing
population and the Haber–Bosch process of creating synthetic N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> was
developed  (Galloway et al., 2004).</p>
      <p>The use of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> to improve crop yield has become an environmental concern
as N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> in synthetic fertilizer and manure cascades through the soil,
water and the atmospheric nitrogen cycles. Plants can readily use applied
N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> for plant growth; however, N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> washed off fields or volatilized
as gas can reduce ecosystem biodiversity through acidification and
eutrophication (Sutton et al., 2013). Increased N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> in the hydrosphere
can lead to the subsequent degradation of riverine and near-shore water
quality as the water becomes more acidic and the growth of primary producers
blooms  (Turner and Rabalais, 1991; Howarth et al., 2002), which can
alter the local interspecies competition and biodiversity  (Sutton et al.,
2012). Reactive nitrogen emissions into the atmosphere impact air quality
through the ozone generation associated with the emissions of nitrogen oxide
(e.g., Hudman et al., 2010) and the contribution of ammonia (NH<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> to
aerosol formation (e.g., Gu et al., 2014). Nitrogen cycling also impacts
climate through the stimulation of plant growth and the associated increase
in carbon storage; through the associated emissions of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O, a strong
greenhouse gas; through emissions of nitrogen oxides and the associated
ozone production; and through the emissions of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>, with its potential
to cool the climate through aerosol formation  (e.g., Adams et al., 2001).</p>
      <p>As a result of their dependence on environmental conditions, N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula>
pathways following manure or synthetic fertilizer application are likely to
change as the climate changes. This study describes a
biogeochemically consistent process-driven parameterization suitable for use
in Earth system models for simulating N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> flows following the
addition of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> as manure or synthetic fertilizer. The
parameterization is evaluated against local measurements of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> fluxes
and against global NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> flux estimates. This parameterization allows
simulations of the coupling between the nitrogen cycle and climate to
explicitly include NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions and the N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> runoff from manure and
synthetic fertilizer application. To our knowledge, no Earth system model
has yet to explicitly predict changing nitrogen pathways from manure and
synthetic fertilizer in response to climate. We note at the outset that the
representation of agricultural processes is highly simplified in the initial
model version described here.</p>
      <p>Sources of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> largely fall into two categories: “new” sources, created
by chemical and biological processes, and those that are “recycled”, such as
manure excretion by animals. The largest natural new N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> creation is by
biological nitrogen fixers found in the ocean, biological nitrogen fixers on
land, and as the by-product of lightning estimated at 140 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 50 %,
58 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 50 % and 5 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 50 %,
respectively (Fowler et al., 2013). The dominant
anthropogenic sources of new N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> are Haber–Bosch-derived fertilizer
(estimated at 120 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 10 % in 2005), the burning of
fossil fuels (30 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 10 % in 2000), and a further
60 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 30 % (ca. 2005) from biological nitrogen fixers
grown for human consumption, such as legumes (Fowler et al., 2013). Since
preindustrial times, anthropogenic N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> creation has increased from
15 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> to the present estimate of 210 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> (Galloway et
al., 2004; Fowler et al., 2013).</p>
      <p>Animal manure is used to stimulate plant growth in agriculture. It contains
N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> recycled from the soil produced when animals eat plants. A
comprehensive increase in livestock population is estimated to have
increased global manure production from 21 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in 1850 to the
present estimate of 141 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>  (Holland et al., 2005). It is
suggested that this increase in recycled N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> production speeds up the
decay and processing of plant biomass, releasing different N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> products
to the atmosphere when compared to natural decay processes  (Davidson,
2009).</p>
      <p>Projections of agricultural activity (Bodirsky et al., 2012) suggest
continued increases in the application of synthetic fertilizers until the
mid-21st century (and possibly beyond) concurrent with increases in
manure production   (Tilman et al., 2001). In addition to the increased use
of organic and synthetic fertilizers in the future, NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions are
expected to increase because of the impact of changing climate on nitrogen
biogeochemistry  (Tilman et al., 2001; Skjøth and Geels, 2013; Sutton et
al., 2013). Skjøth and Geels (2013) predict increases in future NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions of up to 60 % over Europe by 2100, largely due to increased
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions with temperature. Sutton et al. (2013) predict future
temperature increases may enhance global NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions by up to
approximately 40 % assuming a 5 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C warming. In addition to future
changes in climate-induced NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> volatilization from manure and synthetic
fertilizer application, future changes in agro-management practices, soil
microbiological processes and nitrogen runoff may also be expected.</p>
      <p>Current estimates of the direct forcing of nitrate aerosols present as
ammonium nitrate encompass the range from <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.03 to <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.41Wm<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
in the ACCMIP (Atmospheric Chemistry and Climate Model
Intercomparison Project) (Shindell et al., 2013) and AeroCom Phase II (Myhre
et  al., 2013) simulations. With a future reduction in sulfate emissions the
relative importance of nitrate aerosols is expected to dominate the direct
aerosol forcing by 2100, with a resulting increase in radiative forcing of up
to a factor of 8.6 over what it would have been without accounting for nitrate aerosols (Hauglustaine et
al., 2014). These estimates do not consider the impact of climate change on
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions.</p>
      <p>Modeling studies calculating NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emission from manure and synthetic fertilizer
have broadly fallen into two categories: models that use empirically derived
agriculturally based emission factors and more complex process-based models.
Global emissions have almost been universally estimated using the former
approach. Emission factors were used by Bouwman et al. (1997) to estimate
global NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions in 1990 of 54 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, with an emission of
21.6 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> from domestic animals  (Bouwman et al., 1997). Beusen
et al. (2008) also used emission factors to estimate global NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emission from agricultural livestock (21 Tg N yr<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and synthetic
fertilizers (11 Tg N yr<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> in 2000; Bouwman et al. (2013) estimated
emissions of 34 Tg NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> on agricultural land, with 10 Tg NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
from animal housing. A number of more recent global
models have included emission factors explicitly as a function of
temperature (e.g., Huang et al., 2012; Paulot et al., 2014). Paulot et al. (2014)
estimate current global NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions of 9.4 Tg yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for
synthetic fertilizer and 24 Tg yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for manure.</p>
      <p>Alternatively, process-based or mechanistic models have been developed that
estimate N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> flows, equilibria and transformations between different
nitrogen species as well as N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> emissions from synthetic fertilizer and
manure. Process models have been used on the field to regional scale, but
not on the global scale. These models generally do not simulate the runoff
of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula>. For example, Génermont and Cellier (1997) simulate the
emissions of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>(g) to the atmosphere after considering the physical
and chemical equilibria and transfer of Nr species (NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>(g),
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>(aq), and NH<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>(aq)) in the soil. The resulting model is used
to calculate the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions from synthetic fertilizer over France
within the air quality model, Chimere (Hamaoui-Laguel et al., 2014). Other
examples include Pinder et al. (2004), who describe a process model of
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions from a dairy farm, while Li et al. (2012) describe a
farm-scale process model of the decomposition and emission of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> from
manure.</p>
      <p>The overall goal of this paper is to describe and analyze a global model
capable of simulating nitrogen pathways from manure and synthetic fertilizer
added to the surface of the land under changing climatic conditions. The
model will allow for a better global quantification of the climate, health and
environmental impacts of a changing nitrogen cycle under climate change. The
resulting model is designed out of necessity for use within an Earth system
model so as to simulate the interactions between the climate and the carbon
and nitrogen cycles. Section 2 presents the overall methodology used here
including a detailed description of the process model used to calculate
climate-dependent nitrogen pathways. Section 3 analyzes the model and
includes a comparison of simulated vs. site level measurements of
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> fluxes, an analysis of the globally heterogeneous nitrogen pathways
from applied manure and synthetic fertilizer over a range of climatic
regimes, model predictions for changes in nitrogen pathways from 1850 to
present and the sensitivity of the results to model parameters. Section 4
gives our conclusions.</p>
</sec>
<sec id="Ch1.S2">
  <title>Methods</title>
      <p>In this section we describe a process model for the flow of agricultural
nitrogen (FAN) that simulates NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions and other N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> flows
from applied manure and synthetic fertilizer applications, including their
spatial and temporal variations, within an Earth system model, the Community
Earth System Model 1.1 (CESM1.1). The FAN process model developed here
simulates the incorporation of manure and fertilizer N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> into soil
organic matter and soil nitrogen pools (Chambers et al., 1999), its
volatilization as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> to the atmosphere and the direct runoff of
N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> from the surface (Fig. 1). The model is global in nature, is
designed to conserve carbon and nitrogen, and responds to changes in climate.
It is designed to provide an interface between the application of manure and
synthetic fertilizer and the nitrogen cycling developed within the Community
Land Model 4.5 (CLM4.5), the land component of the CESM.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><caption><p>Schematic of the addition of the FAN (flow of agricultural nitrogen)
process model to the CESM nitrogen cycle. Some minor pathways are not shown.
Soil nitrogen pools and plant nitrogen exist in CLM4.5. Urine nitrogen
(N<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mtext>urine</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is directly input to the TAN pool, while fecal matter is split
into three parts that decompose into the TAN pool at a rate determined by
their C : N ratio (N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>available</mml:mtext></mml:msub></mml:math></inline-formula>, N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>resistant</mml:mtext></mml:msub></mml:math></inline-formula>, N<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mtext>unavailable</mml:mtext></mml:msub><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:math></inline-formula>
Manure nitrogen that does not mineralize (N<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mtext>unavailable</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is added to the
soil organic nitrogen pool. Nitrogen applied as synthetic fertilizer is
added to the N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>fertilizer</mml:mtext></mml:msub></mml:math></inline-formula> pool where it decomposes into the TAN pool.
Losses from the TAN pool include ammonia (NH<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> emission (into
CAM-chem), nitrogen runoff (into the RTM), nitrate (NO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
formation and diffusion to the soil nitrogen pools.</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016-f01.png"/>

      </fig>

      <p>Nitrogen pathways subsequent to the application of manure or synthetic
fertilizer depend on the complex interaction between both human and natural
processes. In particular they depend on the biology and physics of the
applied substrate, agricultural practices and climate. Bottom-up emission
inventories with specified emission factors that take into account the
animal feed, the type of animal housing, if any, and the field application of
the synthetic fertilizer or manure (e.g., Bouwman et al., 1997) are
generally used in global chemistry and chemistry–climate applications. For
example, this type of emission inventory (e.g., Lamarque et al., 2010) was
used in the Atmospheric Chemistry and Climate Model Intercomparison Project
(ACCMIP) (Lamarque et al., 2013a) for assessing historical and future
chemistry–climate scenarios and in assessing nitrogen deposition (Lamarque
et al., 2013b) with implications for the carbon cycle. However, these
inventories include very simplified representations of the effect of climate
on emissions, for example, by grouping countries into industrial or
developing categories (Bouwman et al., 1997). A seasonal emission dependence
is not implicit in these bottom-up inventories although sometimes an
empirical relationship is applied (e.g., Adams et al., 2001; also see
Skjøth et al., 2011).</p>
      <p>In the first application of the model described here we take the opposite
tact. We have minimized the description of agricultural practices, and
instead emphasize the physically based climate-dependent biogeochemistry of
manure and synthetic fertilizer decomposition and the resultant nitrogen
pathways. While traditional bottom-up NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emission inventories reflect
regional differences in agro-management practices and the resulting regional
differences in NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions, they do not account for physically based
geographical and meteorological influences, including temperature,
atmospheric mixing and rainfall. However, these influences are accounted for
in the parameterization described below. As with regional differences in
agro-management practices, meteorological impacts may also induce large
regional and interannual variations in NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions. For example,
increasing the ground temperature from 290 to 300 K   (at a pH of
7) increases the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions by a factor of 3 (see Sect. 2.2.6).</p>
      <p>We recognize in this first application that we are simplifying many
important agro-management processes. First, we assume that all synthetic
fertilizer is urea and the pH of the soil is given. Different applied
synthetic fertilizers have a strong impact on the pH of the soil–fertilizer
mixture with the overall emission factor very dependent on the pH (Whitehead
and Raistrick, 1990). Urea is the most commonly used synthetic fertilizer
accounting for over 50 % of the global nitrogenous synthetic fertilizer
usage (Gilbert et al., 2006) and has one of the highest emission factors for
commonly used synthetic fertilizers (Bouwman et al., 1997). Emission factors
for other types of fertilizers can be significantly smaller. Thus the
estimates here for fertilizer NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions may be considered as an
upper estimate. Second, we do not account for manure management practices.
Instead we assume all manure is continuously spread onto fields. In a global
study Beusen et al. (2008) considered four primary pathways for manure
nitrogen: (i) manure nitrogen lost from the system (14 % of the manure
nitrogen, range 5–26 %), (ii) manure nitrogen excreted in animal houses
followed by storage and subsequent spreading onto croplands (35 % of
manure nitrogen; range 24–51 %), (iii) manure nitrogen excreted in
animal houses followed by storage and subsequent spreading onto pasture
lands (7% of manure nitrogen; range 3–11 %), and (iv) manure nitrogen
excreted by grazing animals onto pastures (44 % of manure nitrogen; range
29–59 %). Of the 42 % of manure nitrogen excreted in housing, 20 %
(range: 12–28%) is emitted as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> from housing and storage
facilities (Beusen et al., 2008). An additional 15–23 % of the remaining
manure nitrogen is emitted as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> (range: 11–30 %) after it is spread
onto crop or pasture land. Of the 44 % of manure nitrogen excreted by
grading animals on pasture land 11–12 % (range 6–17 %) is emitted as
ammonia. Considering these various pathways the overall emission factor for
manure nitrogen is estimated as 19 % in Beusen et al. (2008) (compare with
17 % in this study). Third, we do not account for specific fertilizer
application techniques. For example, the soil incorporation of manure leads
to a 50 % reduction in NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions compared to soil broadcasting
(Bouwman et al., 2002). We recognize that there are large spreads in all
these ranges and that regional practices may alter these numbers, although
large errors may be unavoidable due to insufficient characterization of
regional agro-management practices.</p>
      <p>In the present application we also simplify the representation of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
fluxes to the atmosphere. The aerodynamic resistances used to compute the
flux of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> to the atmosphere are calculated with CLM4.5, but due
to the configuration of the CLM they are not calculated at the plant function
type (PFT) level. Instead, the canopy capture of the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> flux is
calculated as a global number. The high spatial heterogeneity of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions may preclude an accurate local representation of exchange
processes on the approximately 2 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 2<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> grid cell used here,
although even on similar coarse resolutions Zhu et al. (2015) show the
implementation of a bidirectional scheme has significant global and
pronounced regional impacts. Nevertheless, the simulation of dynamic
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions, as described below, with NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions responding
to temperature on the model time step is a first step towards more accurately
coupling terrestrial NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> fluxes with the atmosphere.</p>
      <p>A number of requirements are necessary to model NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions following
synthetic fertilizer or manure application within an Earth system model,
specifications that are not necessary in more traditional formulations. (1) The
model must be global in nature to characterize global interactions
between applied N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> and climate. (2) The model must conserve nitrogen.
In particular the nitrogen associated with manure does not add new nitrogen
to the system, but merely represents a recycling of available nitrogen.
Artificial sources or sinks of nitrogen may have serious repercussions,
especially when simulating the global nitrogen cycle on the timescale of
centuries. (3) The model must be able to simulate the changing impact of
climate on the fate of manure and synthetic fertilizer N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula>. In
particular, NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions are sensitive to both temperature and the
water content of the soil. In addition, the runoff of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> is likely to
change under climate change. The process model developed here is capable of
simulating the physics of changing nitrogen pathways under a changing
climate.</p>
      <p>An ideal model would incorporate a globally explicit representation of
agro-management practices, including manure treatment (housing, storage and
spreading) and fertilizer application (e.g., see Sutton et al., 2013). It
would also include an explicit representation of the bidirectional exchange
of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> between the land and atmosphere, including the incorporation of
PFT dependent canopy deposition and aerodynamic resistances. While the model
developed here captures many of the regional and global features seen in
models based on emission factors, here we emphasize the importance of
regional and climatic changes in meteorology.</p>
<sec id="Ch1.S2.SS1">
  <title>Relation between the FAN process model and the CESM1.1</title>
      <p>The parameterization developed here acts as the interface between specified
manure and synthetic fertilizer application and the CESM1.1. The CESM1.1
simulates atmospheric, ocean, land and sea ice processes, linked together
using a coupler, and includes a land and ocean carbon cycle (Hurrell et al.,
2013; Lindsay et al., 2014). The CESM participates in the Climate Model
Intercomparison Project (CMIP5) and has been extensively evaluated in the
literature (see Hurrell et al., 2013). The land model within the CESM1.1, CLM 4.5, includes representation of surface energy and water fluxes,
hydrology, phenology, and the carbon cycle (Lawrence et al., 2007; Oleson et
al., 2008). CLM4.5 retains the basic properties of the previous model
version (CLM4), which has been extensively tested and evaluated by many
studies at the global  (Lawrence et al., 2007; Oleson et al., 2008;
Randerson et al., 2009) and the site  (Stoeckli et al., 2008; Randerson et
al., 2009) scale. CLM4.5 includes improvements to better simulate: (1) water
and momentum fluxes at the Earth's surface; (2) carbon and nitrogen dynamics
within soils and (3) precipitation runoff rates (Koven et al., 2013).
CLM4.5 simulations can be forced by meteorology (as done here), or as a part
of a coupled carbon–climate model (Lawrence et al., 2007; Oleson et al.,
2008). The current version of the carbon model is an improved version of the
coupled carbon–climate model used in Keppel-Aleks et al. (2013), Lindsay et
al. (2014) and Thornton et al. (2009). The carbon model includes a nitrogen
limitation on land carbon uptake, described in Thornton et al. (2007, 2009).
Further improvements have been made to the below ground carbon cycle, as
well as other elements of the land model in order to improve its performance
(e.g., Koven et al., 2013; Lawrence et al., 2012). The impact of increases in
nitrogen deposition (from fossil fuels, fires and
agriculture; Lamarque et al., 2010) have been evaluated (Thornton et al.,
2007, 2009) and extensively compared to observations (e.g.,
Thomas et al., 2013).</p>
      <p>As described in Koven et al. (2013), CLM4.5 simulates the basic flows of
N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> within soils following the Century N model (Parton et al., 1996,
2001; Del Grosso et al., 2000), including the processes of nitrification,
denitrification, and emissions of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> and N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> and the loss of
N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> from leaching and runoff. CLM4.5 also simulates the transfer of
N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> between soils and vegetation, and the loss of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> from fire.
Sources of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> within CLM4.5 are from biological nitrogen fixation
and from surface deposition. The process model developed here adds an
additional source of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> to CLM4.5, the addition of synthetic
fertilizer. It also adds an additional pathway whereby N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> is recycled:
the creation and application of manure (Fig. 1).</p>
      <p>The relation between nitrogen cycling within the FAN process model developed
here and that within the atmospheric, land and river components of the
Community Earth System Model (CESM1.1) is given in Fig. 1. In this first
study the subsequent fate of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> from synthetic fertilizer or manure
application after it is incorporated into the soil organic matter or the
soil nitrogen pools of CLM4.5 is not considered (see Fig. 1). As
described in more detail below, synthetic fertilizer and manure are not applied to
particular PFTs (e.g., pasture or grassland) within CLM4.5. This is
because soil related properties including soil nitrogen are not specified at
the PFT level within CLM4.5, but instead are specified at the column
level that includes many PFTs. In practice we expect that the impact of this
contamination across PFTs will be small since the major N-application
regions (central US, northern India, eastern China) are not PFT-diverse but
contain almost exclusively crop and grass PFTs.</p>
      <p>Note that as a first approximation the model described here does not
simulate the direct emission loss of species other than NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>.
Atmospheric emission losses of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O or N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> (and potentially
NO<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mi>x</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>  are simulated in CLM4.5 (Koven
et al., 2013), the land component model of the CESM1.1, “downstream” from
the pathways explicitly considered here. In addition, the fate of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula>
emitted into the atmosphere as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> directly from synthetic fertilizer
or manure is handled by the atmospheric chemistry component of the CESM
(CAM-chem) and is not considered here (Fig. 1). The runoff of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula>
from manure or synthetic fertilizer nitrogen pools has been coupled to the
river transport model (RTM) in Nevison et al. (2016) (Fig. 1) but is
also not considered here.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <title>FAN process model</title>
      <p>A schematic of the overall model is given in Fig. 1. All the equations and
variables used in the model are presented in the Appendix. The assumptions
used in constructing this model are detailed below where appropriate.
Sensitivity to model parameters is given in Sect. 3.4. The N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula>
pathways are calculated separately for manure and synthetic fertilizer.
While this model assumes that synthetic fertilizer application and manure
application can take place in the same approximately 2 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 2<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>
grid cell, we assume that manure and synthetic fertilizer are not applied in the
exactly the same place. Therefore the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions, the nitrogen
incorporation into soil pools, and the nitrogen runoff are separately
calculated for manure and synthetic fertilizer in each column. This means
that the total ammoniacal nitrogen (TAN) pools (consisting of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>(g),
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>(aq), and NH<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> for manure and synthetic fertilizer are
discrete and hence the nitrogen pathways are not combined.</p>
      <p>The application rate and geographical distribution used for manure and
synthetic fertilizer application is taken from the synthetic fertilizer
application and manure production data sets developed in Potter et al. (2010).
These data sets are valid for ca. 2000 for synthetic fertilizer and 2007
for manure (Potter et al., 2010). As discussed above we assume that manure
is continuously spread onto fields, by-passing the use of animal houses and
storage. Manure and synthetic fertilizer is assumed to be spread across all
PFTs in CLM4.5, as these share a common nitrogen pool. Future model
versions will refine these initial assumptions.</p>
      <p>To adequately model the conversion from manure to TAN it is necessary to
separate the manure into four different pools depending on the decomposition
timescales (Sects. 2.2.1 and 2.2.2 and Fig. 1). A similar strategy was
adopted by Li et al. (2012) for manure and is commonly used in simulating
litter decomposition. Synthetic fertilizer N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> is added to one pool,
whereafter it decomposes into the TAN pool (Fig. 1). Once in the TAN pool
N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> (1) washes off during rain events  (Brouder et al., 2005); (2) volatilizes
as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> (Sutton et al., 1994; Nemitz et al., 2000),
whereafter it is redeposited onto the canopy (not shown) or enters the
atmospheric flow; (3) nitrifies to form nitrate (NO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (Stange
and Neue, 2009); or (4) is incorporated into the soil nitrogen pools.
Nitrate, in turn, becomes incorporated into the soil (Fig. 1). A number of
other smaller loss processes are not explicitly simulated.</p>
      <p>Manure must be added to the model in such a manner as to conserve nitrogen
(Fig. 1). Here, we assume animals consume carbon and nitrogen from plants
and then subsequently excrete this as manure. Within the CLM, carbon and
nitrogen in the plant-leaf pool is thus converted to carbon and nitrogen in
manure, conserving overall carbon and nitrogen.   The conversion rate from
carbon and nitrogen in plants to that in manure is set to equal the rate of
manure production. The external data set of Potter (2010) gives the rate of
N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> production from animals, and thus allows us to specify the nitrogen
flows. The specified C to N ratio in the plant-leaf pool determines the
associated carbon flows due to ruminant consumption of plant material. The
input manure production rate from animals implicitly includes that produced
from transported feed. Thus the subsequent NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emission rate includes
the nitrogen contained in transported feed grown elsewhere. Here we make the
simplification that the consumption rate of plant matter to balance the
manure production is local. That is, we do not explicitly consider the
import of animal feed to match the carbon and nitrogen flows associated with
manure production. While this is not entirely consistent, the development of
the requisite data set for feedstock flows from 1850–2000 is outside the
scope of this study. We do not know of an Earth system model that does
consider the anthropogenic import of nitrogen or carbon. This inconsistency
could produce cases where there is insufficient local plant material to
balance the overall manure and urine production, but this is generally not
the case. The parameterization also ignores export of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> in ruminant
products such as milk and protein, and other N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> losses, which could
create an additional source of uncertainty.</p>
<sec id="Ch1.S2.SS2.SSS1">
  <title>Manure and urine</title>
      <p>Prescribed manure (including urine) is input at a constant annual rate
<inline-formula><mml:math display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">applied</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> into the
manure nitrogen pools depending on latitude and
longitude. It is assumed that a fraction (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>u</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.5) of nitrogen
excreted is urine, with the remaining 50 % excreted as fecal matter
(Gusman and Mariño, 1999). In practice the fraction of nitrogen excreted
as urine is highly variable and depends on the type of animal feed and other
parameters (Jarvis et al., 1989). The excreted urine is directly added to
the TAN pool (g N m<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. This is consistent with urea forming the
dominant component of urine N and the subsequent rapid conversion of urea to
ammoniacal form (Bristow et al., 1992). Feces are composed of matter with
varying carbon to nitrogen ratios that take different times to decompose
depending on how easily they can be digested by microbes<inline-formula><mml:math display="inline"><mml:mo>.</mml:mo></mml:math></inline-formula> Excreted feces are
assumed to form three different pools (g m<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> depending on their rate
of mineralization (e.g., Gusman and Mariño, 1999): (1) we assume a fraction
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>un</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 5 % is excreted as unavailable nitrogen (N<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mtext>unavailable</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,
the lignin component of manure where the nitrogen remains immobilized by
bacteria (C : N ratio &gt; 25 : 1); (2) a fraction <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>r</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 45 % goes
to the resistant pool (N<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mtext>resistant</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, which forms the cellulose component
of manure (C : N ratio ca. 15 : 1), which forms TAN relatively slowly; (3) and a
fraction <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>a</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 50 % goes to the available pool (N<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mtext>available</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> that
is readily available to form TAN (N<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mtext>available</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. In reality the fractions
within each of these broadly defined pools will be dependent on the type of
animal and the type of feed.</p>
      <p><?xmltex \hack{\newpage}?>The equations governing the three manure pools (see Fig. 1) are

                  <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mtext>dN</mml:mtext><mml:mtext>available</mml:mtext></mml:msub><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mtext>a</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>applied</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mtext>a</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mtext>available</mml:mtext></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E1"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>m</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mtext>available</mml:mtext></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mtext>dN</mml:mtext><mml:mtext>resistant</mml:mtext></mml:msub><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mtext>r</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>applied</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mtext>r</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mtext>resistant</mml:mtext></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E2"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>m</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mtext>resistant</mml:mtext></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E3"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mtext>dN</mml:mtext><mml:mtext>unavailable</mml:mtext></mml:msub><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mtext>un</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>applied</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>m</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mtext>unavailable</mml:mtext></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">applied</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the amount of manure
applied (g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>a</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>r</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>un</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are the
fractions of manure applied to each pool; and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (s<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are temperature-dependent
mineralization rates of these manure pools and into soil nitrogen pools. The decay
constants, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, are
measured as the fast and slow decomposition rates for biosolids added to
various soils and incubated at 25 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (Gilmour et al., 2003), where a
two-component decay model accurately fits approximately 73 % of the samples
incubated. The decay timescales for manure in the available and resistant
pools at 25 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C are 48  and 667 days, respectively. The
temperature dependence of the decay constants is derived from a fit of
temperature-dependent mineralization rates (see Appendix A) (Vigil and Kissel,
1995) corresponding to a <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn>10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> value of 3.66. To prevent the manure pools from
building up over long timescales we assume that manure is incorporated into
soils with a time constant of 365 days with a mechanical rate constant
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. This timescale is consistent with the base
bioturbation rate of 1 cm<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> assumed in Koven et al. (2013)
and a typical length scale of 1 cm. The sensitivity of the subsequent
nitrogen pathways to this timescale is small (Sect. 3.4). Note that
nitrogen in the N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>unavailable</mml:mtext></mml:msub></mml:math></inline-formula> pool does not mineralize and is thus only
incorporated into soil organic matter on the timescale determined by
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. We assume that nitrogen prior to conversion
to TAN comprises a range of insoluble organic compounds that do not wash
away or otherwise volatilize.</p>
</sec>
<sec id="Ch1.S2.SS2.SSS2">
  <title>Synthetic fertilizer</title>
      <p>Synthetic fertilizer nitrogen is added to the N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>fertilizer</mml:mtext></mml:msub></mml:math></inline-formula> pool
(g N m<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (Fig. 1) at a rate <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">applied</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (g N m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> that depends on geography and time. The amount of nitrogen
within the synthetic fertilizer pool is subsequently released into the TAN
pool at the rate <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (s<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>:
              <disp-formula id="Ch1.E4" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">dN</mml:mi><mml:mi mathvariant="normal">fertilizer</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">applied</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mi mathvariant="normal">fertilizer</mml:mi></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
            Here we assume all synthetic fertilizer is urea. We set the decay timescale
of urea fertilizer to be 2.4 days, consistent with the decay rate measured in
Agehara and Warncke (2005) for temperatures from 15 to 20 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C. In a
series of experiments Agehara and Warncke (2005) show that 75 % of the
urea hydrolyzes in a week at temperatures from 10 to 25 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C without a
significant dependence on temperature especially for temperatures above 15
to 20 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C.</p>
      <p>The timing for synthetic fertilizer application is determined internally within the CLM4.5 crop model (Levis et al., 2012) as the spring planting date for corn. Note, however, that except for the determining the timing of fertilizer application, the crop model is not used. We use the planting date for corn since the CLM4.5 crop model only specifically includes
corn, soybean and temperate cereals and the planting date for corn lies
between the earlier planting date for temperate cereal crops and the later
planting of soy. The date for fertilizer application is determined for each
grid point location using the surface temperature-based criteria developed
by Levis et al. (2012) for simulating the planting date of corn: the 10-day
running mean temperature, 10-day running mean daily minimum temperature and
growing degree days must all surpass fixed threshold values (283.15 and
279.15 K and 50 days, respectively) before planting can take place.
Fertilizer application dates can have a large influence on the seasonality
of the emissions (e.g., see Paulot et al., 2014) and the subsequent flows of
N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> (Sect. 3.4). Future applications will assume more complete
algorithms for fertilizing the spectrum of crops, as well as multiple
fertilizer applications and double cropping. A global accounting of
fertilization practices and application techniques (e.g., fertilizer
injection) nevertheless remains a considerable source of uncertainty in a
global simulation of the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions from agriculture.</p>
</sec>
<sec id="Ch1.S2.SS2.SSS3">
  <title>Total ammoniacal nitrogen (TAN)</title>
      <p>We consider two TAN pools (g N m<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, one for the nitrogen produced from
synthetic fertilizer N<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mtext>TAN</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> the other for nitrogen from manure
N<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mtext>TAN</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The budget for the manure and synthetic fertilizer TAN pools
respectively is given by

                  <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mtext>TAN</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mtext>u</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>applied</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mtext>r</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mtext>resistant</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mtext>a</mml:mtext></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mtext>available</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mtext>run</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msubsup><mml:mi>K</mml:mi><mml:mi>D</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E5"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mtext>TAN</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mtext>TAN</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>f</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mtext>fertilizer</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mtext>run</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msubsup><mml:mi>K</mml:mi><mml:mi>D</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msubsup></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E6"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mspace linebreak="nobreak" width="1em"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mtext>TAN</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              Here <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">run</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (g N m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
is the loss of nitrogen by runoff from the manure or synthetic
fertilizer TAN pool; <inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi>K</mml:mi><mml:mi>D</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> (s<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the
loss rate of nitrogen to the soil nitrogen pools; <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>  (g N m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions from the
manure and fertilizer TAN pools, respectively, to the atmosphere; and
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>  (g N m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are the loss of nitrogen
through nitrification from the manure and synthetic fertilizer TAN
pools. The formulation of each of these terms is given below. Inputs into
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">TAN</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> pool are from the fraction
(<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>u</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> of applied manure as urine <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">applied</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>),
and from the decomposition of the nitrogen
within the available and resistant manure pools. Input into the
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">TAN</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> pool is from the synthetic
fertilizer pool.</p>
</sec>
<sec id="Ch1.S2.SS2.SSS4">
  <title>Runoff of nitrogen to rivers</title>
      <p>The immediate runoff of fertilizer and manure nitrogen to rivers from the
manure and fertilizer TAN pools is derived from the runoff rate of water (<inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>)
(m s<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> in the CLM multiplied by concentration of nitrogen in the TAN
water pool:
              <disp-formula id="Ch1.E7" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">run</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>R</mml:mi><mml:mo>×</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">TAN</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
            The value of <inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> is calculated within the CLM and is a function of
precipitation, evaporation, drainage and soil saturation. The amount of
water within the TAN pool (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>water</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is needed to convert
N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>TAN</mml:mtext></mml:msub></mml:math></inline-formula> (g N m<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> to a concentration (g N m<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. An
expression for <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
is given in Sect. 2.2.9. It should be emphasized
that this is the immediate runoff of manure and synthetic fertilizer
nitrogen from the TAN pools. Subsequent loss of nitrogen derived from manure
and synthetic fertilizer application occurs following the nitrogen transfer
to the soil pools, but is not tracked in these simulations. Additional
hydrological losses will also occur following the deposition of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
volatilized to the atmosphere. These losses are also not tracked in the
current simulation.</p>
      <p>Initially, we attempted to use the runoff parameterization based on the
global Nutrient Export from Watersheds 2 (NEWS 2) model (Mayorga et al.,
2010), where runoff is also parameterized in terms of <inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>. However, the amount
of nitrogen that runs off in NEWS 2 is represented in terms of the annual
nitrogen initially applied to the land and thus is not directly related to
the amount of nitrogen in the TAN pool.</p>
</sec>
<sec id="Ch1.S2.SS2.SSS5">
  <title>Diffusion through soil</title>
      <p>Nitrogen is assumed to diffuse from the TAN pool to the soil pools.
Génermont and Cellier (1997) represent the diffusion coefficient of
ammonium through soils as dependent on soil water content, soil porosity,
temperature and an empirical diffusion coefficient of ammonium in free water
(see Appendix A). For example, assuming a temperature of 21 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C, a soil
porosity of 0.5 and a soil water content of 0.2 the resulting diffusion
coefficient is approximately 0.03 cm<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> day<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, in reasonable
agreement with measurements in Canter et al. (1996). Here we assume a
typical length scale of 1.0 cm to convert the diffusion rate to a timescale.
The resulting diffusion of ammoniacal nitrogen is added to preexisting
nitrogen pools in CLM4.5 and is not further tracked.</p>
</sec>
<sec id="Ch1.S2.SS2.SSS6">
  <title>Flux of ammonia to the atmosphere</title>
      <p>The flux of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> to the atmosphere is
calculated from the difference between the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentration at the
surface (NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>(g), g m<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> of the TAN pool and the free-atmosphere
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentration (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">χ</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, g m<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> divided
by the aerodynamic (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>a</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and boundary layer (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>b</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> resistances
(Nemitz et al., 2000; Loubet et al., 2009, Sutton et al., 2013).
              <disp-formula id="Ch1.E8" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mtext>(g)</mml:mtext><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">χ</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></disp-formula>
            The calculation of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>(g) is given below. For compatibility with the
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emission parameterization we compute average values of <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>a</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>b</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>
over each CLM soil column, which may contain several PFTs. We specify
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">χ</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to be 0.3 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, representative
of concentrations over low-activity agricultural sites (Zbieranowski and
Aherne, 2012). Continental NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentrations between 0.1 and
10 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> have been reported by Zbieranowski and Aherne (2012) and Heald
et al. (2012). A concentration of 0.3 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> is intermediate
between concentrations at low to moderate pollution sites as diagnosed in
GEOS-chem (Warner et al., 2016). The sensitivity to this parameter is small
as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>(g)  is usually very large (Sect. 3.4). While Eq. (8) allows
for negative emissions (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mtext>g</mml:mtext><mml:mo>)</mml:mo><mml:mo>&lt;</mml:mo><mml:msub><mml:mi mathvariant="italic">χ</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> or deposition of atmospheric
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> onto the soil we disallow negative emissions in the
current simulations. In future studies the atmospheric concentration of
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> will be calculated interactively by coupling the FAN model to the
atmospheric chemistry component of the CESM (CAM-chem), thus allowing the
dynamics of the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> exchange between the soil, the atmosphere and
vegetation to be captured (e.g., Sutton et al., 2013).</p>
      <p>A large fraction of the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emitted to the atmosphere is assumed
captured by vegetation. The amount emitted to the atmosphere is given by
              <disp-formula id="Ch1.E9" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:msub><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mtext>atm</mml:mtext></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">capture</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">capture</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is set to 0.6. Plant recapture
of emitted NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> is often reported to be as high as 75 % (Harper et
al., 2000; Nemitz et al., 2000; Walker et al., 2006; Denmead et al., 2008;
Bash et al., 2010). Using seabird nitrogen on different substrates (rock,
sand, soil and vegetation) inside a chamber, Riddick (2012) found NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
recapture to be 0 % on rock, 32 % on sand, 59 % on soil and 73 % on
vegetation. We set <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">capture</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to 0.6 as a
mid-point between the value for soil (when the crops are planted) and when
crops are fully grown (Wilson et al., 2004). Bouwman et al. (1997) also used
canopy capture to estimate emissions with the captured fraction ranging from
0.8 in tropical rainforests to 0.5 in other forests to 0.2 for all other
vegetation types, including grasslands and shrubs. Bouwman et al. (1997)
omitted canopy capture over arable lands and intensively used grasslands.
Overall, the deposition of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> onto the canopy (or even the soil
surface) is poorly constrained (e.g., see Erisman and Draaijers, 1995) and
often ignored in model simulations. In reality canopy capture is not
constant but depends on surface characteristics and boundary layer
meteorology. Variations in canopy capture will induce temporal and regional
variations in NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions. Explicitly including canopy capture
fraction allows a differentiation between biogeochemical pathways in future
studies. In the future, when the model is fully coupled with the atmospheric
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> cycle a compensation point approach would be desirable for
calculating the net NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions, but this is outside the scope of the
present study.</p>
      <p>It is assumed that the nitrogen in the TAN pool is in equilibrium between
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>(g) (g m<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>(aq) (g N m<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and NH<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>(aq)
(g N m<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The equilibrium that governs the speciation of these species
is determined by the Henry's law coefficient (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>H</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>H</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is a
measure of the solubility of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> in water, and the disassociation
constant of NH<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> in water (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>   (mol L<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (e.g.,
Sutton et al., 1994):

                  <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E10"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">g</mml:mi><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mover><mml:mo>⟷</mml:mo><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:mover><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E11"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo><mml:mover><mml:mo>⟷</mml:mo><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mover><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              Combining these two expressions NH<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">g</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> can be expressed as a function of the total TAN (e.g., Pinder et al., 2004, although note their different units for
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>:
              <disp-formula id="Ch1.E12" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">g</mml:mi><mml:mo>)</mml:mo><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">TAN</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub><mml:mfenced open="[" close="]"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mfenced><mml:mo>/</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where [H<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>+</mml:mo></mml:msup></mml:math></inline-formula>] is the hydrogen ion concentration in mol L<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. Both
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> are temperature-dependent. As temperature and pH increase the concentration of
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">g</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>  increases. The pH of the solution
depends on the type of soil, the exposure of the manure to air, and the type of
fertilizer used and may change with the aging of the manure or synthetic
fertilizer. In Eghball et al. (2000) the majority of the reported
measurements of pH for beef cattle feedlot manure are between 7 and 8,
although in one case a pH of 8.8 was measured. The recommended pH for
various crops ranges from approximately 5.8 to 7.0 depending on the crop
(e.g., <uri>http://onondaga.cce.cornell.edu/resources/soil-ph-for-field-crops</uri>). For
now we simply set the pH of the solution to 7 for both the synthetic
fertilizer and manure TAN pools. Sensitivity to pH is explored in Sect. 3.4.</p>
</sec>
<sec id="Ch1.S2.SS2.SSS7">
  <?xmltex \opttitle{Conversion of TAN to NO${}_{{3}}{}^{{-}}$}?><title>Conversion of TAN to NO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula></title>
      <p>The flux of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> from the TAN pool to NO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> by
nitrification (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> was adapted from Stange
and Neue (2009) for the gross nitrification rates in response to fertilization
of a surface with manure or synthetic fertilizer. In particular, Stange and
Neue (2009) fit measured gross nitrification rates to an expression using a
maximal nitrification rate, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mtext>max</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g N kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> h<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, modified
by a soil temperature response function (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>) and a soil moisture response
function (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>M</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>) (Stange and Neue, 2009). However, since <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mtext>max</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is fit
from their experimental data, the dependence of the nitrification rate on
the ammonium concentration is not explicitly included in the formulation of
Stange and Neue (2009). We have remedied this by setting the maximum
nitrification rate (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mtext>max</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> in the formulation of (Stange and Neue,
2009) to be consistent with the
formulation in Parton et al. (2001):
              <disp-formula id="Ch1.E13" content-type="numbered"><mml:math display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{8.0}{8.0}\selectfont$\displaystyle}?><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn>2.</mml:mn><mml:msub><mml:mi>r</mml:mi><mml:mtext>max</mml:mtext></mml:msub><mml:msub><mml:mi>N</mml:mi><mml:mtext>water</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mtext>N</mml:mtext><mml:msub><mml:mtext>H</mml:mtext><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mtext>(g)</mml:mtext><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mtext>H</mml:mtext></mml:msub><mml:mfenced close="]" open="["><mml:msup><mml:mrow class="chem"><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msup></mml:mfenced><mml:mo>/</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mtext>g</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mi mathvariant="normal">Π</mml:mi><mml:mo>(</mml:mo><mml:mi>M</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mtext>g</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>  and <inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Π</mml:mi><mml:mo>(</mml:mo><mml:mi>M</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are functions of soil temperature and moisture and the
ammonium concentration is assumed to be in equilibrium with the other forms
of ammoniacal nitrogen and is thus expressed in terms of pH,
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>(g) (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:math></inline-formula>) and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mtext>max</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is equal to
1.16 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mo>-</mml:mo></mml:msup><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p>
</sec>
<sec id="Ch1.S2.SS2.SSS8">
  <title>Nitrate</title>
      <p>The rate of change of the nitrate pool is given by
              <disp-formula id="Ch1.E14" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mtext>dN</mml:mtext><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msubsup><mml:mi>K</mml:mi><mml:mi>D</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msubsup><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
            The source of nitrate ions is nitrification from the TAN pool. Nitrate is
lost to the soil nitrate pool through diffusion. Nitrate leaching is not
explicitly taken into account in the current model as the diffusion of
nitrate into the soil pools occurs very rapidly. The loss of nitrate through
runoff and leaching can, however, occur within the CLM, but is not tracked
in the current simulations. Nitrate ions diffuse significantly faster than
the NH<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> ions because they are not subject to immobilization by
negatively charged soil particles  (Mitsch and Gosselink, 2007). Diffusion
rates used in this study are derived from the same formulation as assumed
for the diffusion of ammonium (e.g., see Jury et al., 1983) with a different
base diffusion rate. The summary of measurements given in Canter et
al. (1996), where both the diffusion of ammonium and nitrate were measured in
the same soil types and wetness, suggest the base diffusion rate of
NO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> is approximately 13 times faster than that of ammonium.</p>
</sec>
<sec id="Ch1.S2.SS2.SSS9">
  <title>TAN and manure water pools</title>
      <p>The evolution of the TAN manure and synthetic fertilizer water pools
depends on the water added during manure or synthetic fertilizer application
and the subsequent evolution of the water in the pools. The equations for
the manure and synthetic fertilizer water are

                  <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mtext>d</mml:mtext><mml:msub><mml:mi>N</mml:mi><mml:mtext>water</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mtext>w</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>applied</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>relax</mml:mtext></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E15"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mspace linebreak="nobreak" width="1em"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mtext>water</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mtext>water</mml:mtext></mml:msub><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">d</mml:mi></mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mtext>water</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mtext>w</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>applied</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>relax</mml:mtext></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E16"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mspace linebreak="nobreak" width="1em"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mspace width="1em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="1em"/><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mtext>water</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mtext>water</mml:mtext></mml:msub><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              These equations include a source of water
(<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> added as a fraction of the synthetic
fertilizer or manure applied and a relaxation term
<inline-formula><mml:math display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, s<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> to the soil water
(<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>) calculated in
the CLM for the top 5 cm of soil. <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
explicitly takes into account the modification of the water pool due to
rainfall, evaporation and the diffusion of water in the soil layers. We
assume the TAN pool equilibrates with water within the top 5 cm of the soil
with a rate of 3 days<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. The solution is insensitive to this parameter
within the ranges examined of 1 to 10 days<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> (Sect. 3.4). The water
content of manure applied to fields depends on the animal, its feedstock and
on agricultural practices. Here we assume cattle manure is added as a slurry
with a dry fraction of 74.2 g kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and a nitrogen content of 1.6 g kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>,
resulting in 5.7 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> m water applied per gram of
manure nitrogen applied (Sommer and Hutchings, 2001). In the case of
synthetic fertilizer we assume urea is added as a liquid spread, where water
added is calculated from the temperature-dependent solubility of urea in
water (UNIDO and IFDC, 1998).</p>
</sec>
</sec>
<sec id="Ch1.S2.SS3">
  <title>Model spin-up and forcing</title>
      <p>Two different types of model simulations were conducted using CLM4.5: a
present-day control simulation (1990–2004) and a historical simulation
(1850–2000). The resolution used in these simulations is 1.9<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>
latitude by 2.5<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> longitude.</p>
<sec id="Ch1.S2.SS3.SSS1">
  <title>Present-day control simulation</title>
      <p>This simulation uses the manure and synthetic fertilizer input as given in
Potter et al. (2010). Forcing at the atmospheric boundary is set to the Qian
et al. (2006) reanalysis for solar input, precipitation, temperature, wind
and specific humidity. The simulation is run for 15 model years
(1990–2004), with the last 10 years of the simulation used for analysis. The
spin-up period allows for the more decomposition resistant N pools to
approach a steady state with respect to the loss from mechanical
incorporation into the soil.</p>
</sec>
<sec id="Ch1.S2.SS3.SSS2">
  <title>Historical simulation</title>
      <p>The historical simulation uses transient forcing conditions (accounting for
changes in atmospheric CO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>, nitrogen deposition, aerosol deposition and
land use change forcings) and the Qian et al. (2006) atmospheric forcing
data set. Quality 6-hourly meteorological data sets for the period prior to
1948 do not exist. Therefore from 1850 to 1973 CLM4.5 is driven by
recycled meteorological data, using meteorological data from the 1948–1973
time period. During this time long-term temperature changes were small:
the statistically significant long-term changes in temperature (outside of
natural variability) occur after 1973. After 1973 the meteorological data are
not recycled but are valid for the year applied.</p>
      <p>The temporal distribution of manure and synthetic fertilizer application
from 1850–2000 is specified by applying the temporal distribution of Holland
et al. (2005) to the base values as calculated in Potter et al. (2010). Due
to the lack of detailed information on the geography of historical manure and
synthetic fertilizer we use the scaled spatial distribution from Potter et al. (2010).
We assume manure production has changed from 26.3 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
in 1860 to 125 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in 2000  (Holland et al., 2005; Potter et
al., 2010), but we acknowledge that these temporal changes are uncertain. Synthetic
fertilizer was first used in the 1920s, with use increasing to 62 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in 2000.</p><?xmltex \hack{\newpage}?>
</sec>
</sec>
</sec>
<sec id="Ch1.S3">
  <title>Results</title>
<sec id="Ch1.S3.SS1">
  <title>Model evaluation</title>
      <p>To evaluate model output, measurements of the percentage of applied nitrogen
that was emitted as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>v</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> from the literature were compared against
corresponding model predictions. The model predictions are obtained from the
present-day control simulation. The percent-volatilized NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> was used as
a metric because it can be compared across time, irrespective of the absolute
amount of nitrogen applied to the surface. To be able to compare emissions
to published measurements, we require field studies with published data on
nitrogen excretion rates, NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions, ground temperature, location,
and date of measurement. Given all of these requirements we found that only
a small selection of publications had sufficient data.</p>
      <p>For the manure emissions, 44 measurements in a range of climates
(temperatures from 1.4 to 28 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) and a range of
livestock management methods (commercial beef cattle feed yard, dairy cows
grazing on ryegrass, beef cattle grazing on ryegrass and dairy cattle
grazing on pasture land) were used (Supplement Table S1). Each <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>v</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>
reported by the measurement campaign was compared against the <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>v</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> at the
corresponding grid cell in the model. For the synthetic fertilizer scenario,
10 measurements in a range of latitudes (43<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S to 50<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N)
over a range of land use surfaces (pasture, sown crops, turf and forest)
were used (Table S2). Each total annual <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>v</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> reported by the
measurement campaign was compared against the annual <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>v</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> of the
corresponding grid cell.</p>
<sec id="Ch1.S3.SS1.SSS1">
  <?xmltex \opttitle{Nitrogen volatilized as NH${}_{{3}}$ from manure}?><title>Nitrogen volatilized as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> from manure</title>
      <p>There is a general increase in <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>v</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> with temperature, in both the
model and measurements (Fig. 2). However, temperature is not the only
factor in determining NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions, where wind speed, water
availability and below ground soil properties can also effect NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emission. This is particularly demonstrated by the measurements of
Todd et al. (2007) at temperatures less than 5 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C where the measured emissions
are higher than those predicted at higher temperatures (e.g., Bussink,
1992). It is also worth noting that the model predicts the emissions of Todd
et al. (2007) at lower temperatures with relative success.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><caption><p>Comparison of model to measurements for percentage of nitrogen lost as
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions from manure for a range of studies (see
Table S1). Symbol color indicates temperature at which the emissions occurred;
shape gives the study.</p></caption>
            <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016-f02.pdf"/>

          </fig>

      <p>The agreement between measured and modeled <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>v</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> from manure appears
reasonable, with an <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.76 that is significant at the 99.9 %
confidence level. On closer inspection, the model appears to agree best with
measurements made on grassland and differs considerably with measurements
made by both campaigns for beef cattle feedlots in Texas, where beef cattle
feedlots are commercial operations to prepare livestock for slaughter and
comprise thousands of animals contained in a pen. This is perhaps not
surprising, as the parameterization developed here explicitly represents
emissions from manure spreading as opposed to the more managed conditions in
feedlots.</p>
</sec>
<sec id="Ch1.S3.SS1.SSS2">
  <?xmltex \opttitle{Nitrogen volatilized as NH${}_{{3}}$ from synthetic fertilizer}?><title>Nitrogen volatilized as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> from synthetic fertilizer</title>
      <p>The comparison between measured and modeled annual average <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>v</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>
from synthetic fertilizer applied to a range of land use types is weak, with
an <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of 0.2 that is significant at the 90 % confidence level
(Fig. 3). The lowest emissions in the model and measurements tend to be
associated with the higher latitudes of both hemispheres. There does not
appear to be any noticeable bias with land use type where the model
estimates are both higher and lower than measured values of <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mtext>v</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> for
surfaces covered in turf, pasture land and crops. The fact that the <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>
for the synthetic fertilizer measurements is lower than the <inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of the
manure measurements is potentially caused by differences between actual
farming practices and model assumptions.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><caption><p>Comparison of model to measurements for percentage of nitrogen
lost as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions from synthetic fertilizer (see
Table S2) for a range of studies. Symbol color gives the latitude at which the emissions occurred;
symbol shape gives the study and type of synthetic fertilizer application.</p></caption>
            <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016-f03.pdf"/>

          </fig>

</sec>
<sec id="Ch1.S3.SS1.SSS3">
  <title>Nitrogen runoff</title>
      <p>In this study we simulate the direct nitrogen runoff from the manure and
synthetic fertilizer TAN pools, but do not track the resulting nitrogen
flows. These flows are tracked, however, in Nevison et al. (2016), where the
nitrogen runoff from manure and synthetic fertilizer pools is routed into
the river transport model (RTM) (Dai and Trenberth, 2002; Branstetter and
Erickson III, 2003) within the CESM. Nevison et al. (2016) assume
denitrification occurs within the simulated rivers at a rate inversely
proportional to the river depth (amounting to approximately 30 % of the
nitrogen inputs on average) and compare the simulated dissolved inorganic
nitrogen (DIN) export at the river mouths against measurements (Van Drecht
et al., 2003) following Global NEWS (Mayorga et al., 2010). The simulated
DIN export is nearly unbiased for six identified rivers with high human
impact: the Columbia, Danube, Mississippi, Rhine, Saint Lawrence and
Uruguay. Explicit comparisons against the Mississippi River show that the
amplitude and seasonality of the simulated N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> runoff is in reasonable
agreement with the measurements. While the comparison in Nevison et al. (2016)
gives confidence that the runoff is reasonably simulated, the
complications in simulating river runoff preclude tight model constraints.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><caption><p>Simulated NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions from synthetic fertilizer application
from 1995 to 2004 for the present-day control simulation. Simulated emissions
(kg N ha<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> yr<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> as <bold>(a)</bold> an annual average,
<bold>(c)</bold> January–February–March
average, <bold>(d)</bold> April–May–June average, <bold>(e)</bold> July–August–September
average, and <bold>(f)</bold> October–November–December
average.  Panel <bold>(b)</bold> shows simulated emissions as a percent of annual synthetic fertilizer
application.</p></caption>
            <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016-f04.png"/>

          </fig>

</sec>
</sec>
<sec id="Ch1.S3.SS2">
  <title>Global nitrogen pathways: present day</title>
<sec id="Ch1.S3.SS2.SSS1">
  <title>Geography of nitrogen inputs</title>
      <p>Global maps of nitrogen input from synthetic fertilizer and manure
application during the present-day simulation are given in Potter et
al. (2010) and are not repeated here. Heavy synthetic fertilizer use generally
occurs in the upper Midwest of the US (mostly east of 100<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W and
north of 40<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N), western Europe (mostly west of 20<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E and
north of 40<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N), the northern part of India and much of northeastern
and north central China. High manure usage coincides with the areas of heavy
synthetic fertilizer use but is more widespread extending across much of
eastern South America from 20–40<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S and across Africa at
approximately 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><caption><p>As in Fig. 4 but for manure application.</p></caption>
            <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016-f05.png"/>

          </fig>

<?xmltex \hack{\newpage}?>
</sec>
<sec id="Ch1.S3.SS2.SSS2">
  <title>Geography of nitrogen losses</title>
      <p>There are strong geographical differences in the loss pathways of nitrogen
following manure or synthetic fertilizer application. The importance of the
various loss pathways from the TAN pool (the amount nitrogen volatilized as
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>, runoff, nitrified or diffused directly into the soil, Figs. 4–8)
is dependent on temperature, precipitation and soil moisture. In hot, arid
climates, the percentage volatilized is high (Figs. 4 and 5). For example,
regions of high NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> volatilization of applied manure N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> approach
50 % across the southwest US and Mexico, eastern South America, central
and southern Africa, parts of Australia, and across southern Asia from India
to Turkey (Fig. 5). The absolute highest emissions of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> from
applied synthetic fertilizer and from applied manure approach 20 kg N ha<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
over hot regions with high applications, e.g., the Indian subcontinent and parts of China (Figs. 4 and 5). Ammonia emissions from manure
are more broadly distributed globally than those of synthetic fertilizer
with high NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions not only over the synthetic fertilizer
hotspots, characterized by heavy application of both synthetic fertilizer
and manure but also over southeastern South America and central Africa. For
the most part, the largest synthetic fertilizer NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions occur
during April–June, reflecting the single fertilization date used in this
study as calculated in the CLM for corn. While Paulot et al. (2014) also
show the maximum synthetic fertilizer emissions generally occur from
April–June, they obtain relatively higher emissions than simulated here
during the other seasons. This is likely due to differences in the assumed
timing of applied synthetic fertilizer: Paulot et al. (2014) consider three
different synthetic fertilizer applications for each crop as well as a wide
variety of crops. The seasonal emission distribution of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions
from manure is broader than that of synthetic fertilizer but with maximum
emissions usually occurring in April–June or July–September. The simulated
geographical and seasonal NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emission distribution from manure is in
broad agreement with Paulot et al. (2014).</p>
      <p>Runoff of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> from applied synthetic fertilizer and manure TAN pools, as
well as nitrification and diffusion into the soil, depends on precipitation
and soil moisture. High manure and synthetic fertilizer N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> runoff from
the TAN pools (see Fig. 6) occurs particularly across parts of China,
Europe (particularly the northern parts) and the east central US. The
global hotspot for simulated N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> runoff from the TAN pools is China,
where runoff approaches 20 kg N ha<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for nitrogen applied as
either manure or synthetic fertilizer. In general the importance of runoff
as a nitrogen loss pathway becomes more important in the wetter and cooler
regions. In contrast, over India and Spain the agricultural nitrogen input
is high, but the runoff is relatively low. In these regions with high
temperatures (and dry conditions) NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> volatilization is the preferred
pathway for nitrogen losses from the TAN pool.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><caption><p>Simulated runoff of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> from synthetic fertilizer and manure
TAN pools for the present-day (1995–2004) control simulation. Simulated
runoff (kg N ha<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> yr<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> as an annual average for <bold>(a)</bold> synthetic
fertilizer, <bold>(c)</bold> manure. Simulated as <bold>(b)</bold> percent of annual synthetic
fertilizer application, <bold>(d)</bold> percent of annual manure application.</p></caption>
            <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016-f06.png"/>

          </fig>

      <p>The percent of the TAN pool nitrified or diffused directly into the soil
(see Figs. 7 and 8) also tends to be largest in wetter and cooler regions.
The amount of nitrogen nitrified has an optimal temperature of 28 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C
and tends to occur more rapidly under moist conditions; the diffusion of
nitrogen into the soil is also promoted under wet conditions.</p>
</sec>
<sec id="Ch1.S3.SS2.SSS3">
  <title>Regional and global accounting of nitrogen losses</title>
      <p>As nitrogen cascades through the environment it can be emitted as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
or runoff or leached at many different stages. Here we only examine the
losses directly from manure or fertilizer TAN pools. Globally, the direct
loss of applied nitrogen to the atmosphere as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> is similar for manure
and synthetic fertilizer (17 % for manure, 19 % for synthetic
fertilizer; see Fig. 9). Our global estimates of the percent of manure and
synthetic fertilizer volatilized as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> are similar to Bouwman et al. (2002)
and Beusen et al. (2008), although our estimate for synthetic
fertilizer volatilization as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> is somewhat high. Bouwman et al. (2002) estimate 19–29 %
of applied manure and 10–19 % of applied
synthetic fertilizer volatilizes as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>; Beusen et al. (2008) conclude
15–23 % of applied manure is lost as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> (including losses from
housing and storage, grazing and spreading) and 10–18 % of applied
synthetic fertilizer is lost.</p>
      <p>We calculate the global direct runoff from manure or fertilizer TAN pools
as 8 % for manure N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> and 9 % for synthetic fertilizer (Fig. 9).
Bouwman et al. (2013) find that 23 % of deposited N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> (comprised of
synthetic fertilizer, manure and atmospheric nitrogen deposition) runs off,
higher than our estimate. However, our estimate only includes the direct
runoff from the TAN pool. Additional nitrogen is lost downstream from the
TAN pool due to runoff and leaching from the soil nitrogen pools or
following NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emission and re-deposition.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F7" specific-use="star"><caption><p>As in Fig. 6 but for simulated nitrification.</p></caption>
            <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016-f07.png"/>

          </fig>

      <p>Our simulations assume a large fraction of emitted nitrogen is captured by
the canopy, where canopy capture accounts for 25.5 % of manure losses and
30 % of synthetic fertilizer losses (Fig. 9). The nitrogen captured by
the canopy may have a number of fates. First, Sparks (2009) posits that foliar nitrogen uptake could more readily influence plant growth than uptake from soils since it is a direct addition of N
to plant metabolism. As such
it would decrease plant demand on soil uptake and thus conserve the soil
nitrogen reservoirs. Secondly, nitrogen uptake by the plants, even if not
directly used in plant metabolism, may redeposit onto the surface with
litterfall. Finally, it may be emitted back to the atmosphere from plants.
The latter process can be represented through a compensation point model
between the atmosphere, the ground and stomata (e.g., Massad et al., 2010).
A full accounting of this requires the simulation to be fully coupled with
the atmosphere and soil chemistry and biogeochemistry, which is beyond the
scope of the present study.</p>
      <p>In the case of synthetic fertilizer the direct diffusion of TAN N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> into
the soil pool (22 %) is larger than nitrification (17 %); for manure it
is just the opposite: the nitrification (29 %) is larger than the direct
diffusion (14 %) (Fig. 9). In practice, as simulated here, this makes
little difference as the diffusion of nitrate into the soil pool occurs very
rapidly, an order of magnitude faster than the diffusion of nitrogen from
the TAN pool. Thus, NO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> is directly incorporated into the soil
nitrate pool without any subsequent loss. It should also be noted that a small percentage
of manure is mechanically stirred into the soil organic nitrogen pools.
Accounting for the N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> diffused from the TAN pool into the soil pools,
and assuming the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions captured by the canopy, as well as the
ammonium nitrified to NO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> that also ends up in the soil pools, we find
that globally 75 % of manure nitrogen and 71 % of synthetic fertilizer
nitrogen ends up in the soil nitrogen or soil organic nitrogen pools.
Emitted NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> may also end up in the soil nitrogen pools downstream of
the emissions. Of course, once in these soil pools, there may be subsequent
losses of nitrogen due to runoff and leaching or emissions, but these are
not calculated in this initial study.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F8" specific-use="star"><caption><p>As in Fig. 6 but for flux of TAN nitrogen to the soil.</p></caption>
            <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016-f08.png"/>

          </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9"><caption><p>Global fate of TAN Nr applied as synthetic fertilizer <bold>(a)</bold> or as
manure <bold>(b)</bold>. NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions are split between those to the atmosphere
and those captured by the canopy.</p></caption>
            <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016-f09.png"/>

          </fig>

      <p>The global percentages given above change appreciably when examined over
subsets of countries (Fig. 10). For example, over all developed countries
the percentage of emissions of manure and synthetic fertilizer TAN as
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> (13 %) is substantially smaller than for developing countries
(21 %). These differences can be largely explained by the fact that
developing countries tend to be located in warmer climates than developed
countries (e.g., see Bouwman et al., 2002). Bouwman (2002) calculated
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/></mml:mrow></mml:msub></mml:math></inline-formula>emission factors for manure of 21 and 26 % for developed
and industrialized countries, respectively and for synthetic fertilizer of
7 and 18 %, respectively.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10" specific-use="star"><caption><p>As in Fig. 9 but for fate of TAN nitrogen by country and region.
Countries are split between developed countries and developing countries.</p></caption>
            <?xmltex \igopts{width=284.527559pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016-f10.png"/>

          </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F11"><caption><p>Comparison of manure (red) and synthetic fertilizer (blue)
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions or combined manure and synthetic fertilizer emissions
(green) (Tg N yr<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> for various inventories (see text for details) and
regions: <bold>(a)</bold> global, <bold>(b)</bold> China, <bold>(c)</bold> Europe and <bold>(d)</bold> US. Emissions from this study
are labeled as “Riddick”.</p></caption>
            <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016-f11.pdf"/>

          </fig>

      <p>In our simulations 16  and 9 % of applied agricultural nitrogen is
emitted as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> in the US and the European Union, respectively. The
direct runoff of nitrogen accounts for 9  and 14 % of the losses of
agricultural nitrogen in the US and the European Union, respectively.
Nitrogen runoff is favored in the cooler moister climate of Europe. However,
note the large contrast between India and China, where for India NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions are 27 % of the applied N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> with very little runoff, whereas
for China the runoff and emissions are approximately equal (13 and
10 %, respectively).</p>
</sec>
<sec id="Ch1.S3.SS2.SSS4">
  <title>Comparison to other emissions inventories</title>
      <p>Figure 11 gives a comparison of manure and synthetic fertilizer NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions from the FAN process model for the year 2000 to various emission
inventories. These inventories rely on emission factors depending on animal
husbandry, types of synthetic fertilizer usage and other details of
agricultural practices. Only the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emission inventory of
Huang et al. (2012) for China and that of Paulot et al. (2014) explicitly account for temperature
to modify their emission factors; the inventory of Paulot et al. (2014) also
uses wind speed to modify the emission factors. The inventories of Paulot et
al. (2014) for 2005–2008, Beusen et al. (2008) for 2000, and EDGAR v4.2
(European Commission JRC and PBL, 2011) for 2005–2008 are global inventories. The EDGAR inventory does not
strictly separate the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions into those from manure and synthetic
fertilizer, so we simply show the overall NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions from both manure
and synthetic fertilizer. Over the US we also give an estimate for synthetic
fertilizer NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> from 1995 (Goebes et al., 2003) and for NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions from animal agricultural operations (US EPA, 2004). Over the China
region, emission estimates are from Huang et al. (2012) for 2006 and Streets
et al. (2003) for 2000. Over Europe, results using the Greenhouse Gas and Air
Pollution Interactions and Synergies (GAINS) model are given (Klimont and
Brink, 2004) as reported in Paulot et al. (2014).</p>
      <p>Globally all inventories give approximately the same overall NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions of 30–35 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. The global apportionment of emissions
between manure and synthetic fertilizer in this study is in approximately
the ratio of 2 : 1, roughly consistent with that of Paulot et al. (2014) and
Beusen et al. (2008). In this study the overall NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions are
high over the US compared to the other inventories: the manure NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions are close to the estimate of other inventories, while the synthetic
fertilizer emissions are higher. The European and Chinese NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions
estimated in this study are on the low side of the other inventories. Over
Europe the current parameterization underestimates the manure emissions
compared to the other studies while the synthetic fertilizer emissions are
somewhat high. The EDGAR emission estimate is somewhat higher than the other
estimates over Europe, although this may depend on exactly what is assumed for the
boundary of the European region. Over China our synthetic fertilizer
emissions are similar to those of Huang et al. (2012), but we underestimate
the manure NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions compared to the other inventories. Of the
three regions examined all inventories suggest the Chinese emissions are
highest.</p>
</sec>
<sec id="Ch1.S3.SS2.SSS5">
  <title>Site-specific simulated pathways</title>
      <p>The hourly time series of the fate of applied nitrogen from manure and
synthetic fertilizer at a single site better illustrates the relationship
between the different nitrogen flow pathways and the local meteorology
(Fig. 12). The large fluctuations in the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions and the
resultant implications for atmospheric chemistry also demonstrate the
desirability of emissions that respond on hourly timescales to
meteorological conditions. The site shown in Fig. 12 is near the Texas
panhandle. It experiences several large rain events and surface temperatures
ranging from 0 to 18 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C over a period of about 2 months during the
spring season examined. The response of the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions to the
diurnal temperature range is clearly evident. Near the beginning of the
examined period the nitrogen losses of manure TAN due to NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
volatilization are initially small, comparable with the diffusive loss to
the soil pools and somewhat less than the loss due to nitrification. The
loss by nitrification and the diffusion from the TAN manure pool remain roughly
constant throughout the period examined, although both processes show some
response to precipitation. Note in particular that the diffusive loss reaches a
maximum near 21 May, presumably caused by the increased water content in the
soil due to the prior rain event. With the rise in temperatures towards the
end of the period, the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emission loss of manure N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> becomes
the dominant loss pathway and the TAN manure pool decreases. Closer
inspection suggests, however, that the large increase in the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions towards the end of the period cannot solely be attributed to
temperature but must also be attributed to decreased water in the TAN pool
as the soil dries. The latter process increases the concentration of
nitrogen species within the TAN pool. The TAN manure pool is punctuated by
sharp declines, associated with precipitation and increased runoff (Fig. 12c).
Synthetic fertilizer TAN responds similarly during this period but is
clearly impacted by the temporal application of synthetic fertilizer. The
decrease in the synthetic fertilizer TAN pool occurs on a timescale of
approximately a week, consistent with the timescale used in the
MASAGE_NH3 model (Paulot et al., 2014).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F12" specific-use="star"><caption><p>Site-specific pathways for nitrogen budget at 35<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N and
100<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W, near the Texas panhandle. Panels show <bold>(a)</bold> the temperature
(<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) and precipitation (mm s<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> used to force the CLM, <bold>(b)</bold> the
manure (solid) and synthetic fertilizer TAN pools (dashed) (gN m<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,
and the four major loss pathways (g N m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> from <bold>(c)</bold> the manure
TAN pool <bold>(d)</bold> the synthetic fertilizer TAN pool. Loss pathways: NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions, red; runoff, orange; nitrification, green; and diffusion to the soil,
blue.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016-f12.png"/>

          </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F13" specific-use="star"><caption><p>Applied nitrogen and nitrogen losses for the historical
simulation in Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for <bold>(a)</bold> manure and <bold>(c)</bold> synthetic fertilizer.
Nitrogen losses from the TAN pool as a percentage of applied nitrogen for
the historical simulation for <bold>(b)</bold> manure and <bold>(d)</bold> synthetic fertilizer. The
losses from the TAN pool are divided into emission losses of ammonia to the
atmosphere (gold diamond), runoff (green diamond) and loss to the soil.
Loss to the soil is divided into that due to canopy loss (asterisk) (see
Sect. 3.2.3), direct diffusive loss (cross) and nitrification (plus).</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/3397/2016/bg-13-3397-2016-f13.png"/>

          </fig>

</sec>
</sec>
<sec id="Ch1.S3.SS3">
  <title>Global nitrogen pathways: historical</title>
      <p>Historical nitrogen pathways are simulated since 1850 in a simulation with
changing climate and changing application amounts. These simulations do not
include changing agricultural practices, for example changes in animal
housing and storage, changes in animal diet and explicit changes in land use.
All of these changes may substantially alter the nitrogen loss pathways.
Thus the results must be treated with caution.</p>
      <p>The nitrogen produced as manure increases in the historical simulation from
21 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in 1850 to 125 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in 2000 (Fig. 13). In
1900 we estimate that 37 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula> of manure is produced, similar to the
Bouwman et al. (2013) estimate of 35 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. Emissions of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
from applied manure increase from approximately 3 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in 1850
(14.3 % of the manure produced) to 22 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in 2000 (17.6 % of
the applied manure). On the other hand, the percentage of manure nitrogen
that is nitrified decreases from 33 to 27 % since the preindustrial period.
Note that the year 2000 emissions in the historical simulation differ
slightly from the year 2000 emissions reported in the present-day control
simulation, as the latter consists of the average emissions from 1995 to 2004.</p>
      <p>Synthetic fertilizer nitrogen application has increased dramatically since
the 1960s, with an estimated 62 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> applied as synthetic
fertilizer in 2000. We estimate that the volatilization of synthetic fertilizer
as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> is 12 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in 2000 (19 % of that applied).
The percent of synthetic fertilizer nitrogen volatized to the atmosphere as
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> in 1920 was 8 %. On the other hand, the percentage of synthetic
fertilizer that is lost through runoff decreased since the preindustrial period by
8 %. These changes can be explained by the fact the runoff of synthetic
fertilizer can act to completely drain the TAN synthetic fertilizer pool
when the application rate is small.</p>
      <p>In part the historical emission increases in NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> can also be explained by
changes in climate. The globally averaged temperature has warmed by approximately
1 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C since the preindustrial period. In a sensitivity experiment the temperature was
artificially increased by 1 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C in the rate equations governing the
nitrogen pathways following manure and synthetic fertilizer application.
Under current manure and synthetic fertilizer application rates we find that
globally an additional 1 Tg NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> is emitted from the manure and
synthetic fertilizer pools per degree of warming. The resulting manure
emissions increase by 4 % and the synthetic fertilizer emissions by 3 %
per degree of warming.</p>
</sec>
<sec id="Ch1.S3.SS4">
  <title>Sensitivity tests</title>
      <p>We have conducted a large number of sensitivity tests to evaluate the effect
of changes in individual model parameters on NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions. The various
parameters may covary, of course, with nonlinear impacts on the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions; however, we have not attempted to evaluate these effects. The
sensitivity tests for manure are given in Table 1, and those for synthetic
fertilizer in Table 2. The sensitivity tests are labeled with a number
denoting the sensitivity parameter perturbed and a letter denoting whether
the test is with respect to manure emissions (<inline-formula><mml:math display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula>) or synthetic fertilizer
emissions (<inline-formula><mml:math display="inline"><mml:mi>f</mml:mi></mml:math></inline-formula>). In each case we give the percent change in NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions
due to the parameter change and the relative emission change with respect to
the relative parameter change (the sensitivity). Rationale for the assumed
parameter bounds is given in the Supplement.</p>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T1" specific-use="star"><caption><p>Manure sensitivity tests.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="10">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:colspec colnum="9" colname="col9" align="right"/>
     <oasis:colspec colnum="10" colname="col10" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Exper.<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Parameter<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">Value<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">NH<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">4</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Run<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">5</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col6">Soil<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col7">Nitrif.<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col8">Canopy<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">8</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula>NH<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">9</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula><?xmltex \hack{\hfill\break}?>%</oasis:entry>  
         <oasis:entry colname="col10">Sens.<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>10</mml:mn></mml:msup></mml:math></inline-formula>    % <inline-formula><mml:math display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> %</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">Control<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>11</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2"/>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4">19.5</oasis:entry>  
         <oasis:entry colname="col5">10.2</oasis:entry>  
         <oasis:entry colname="col6">15.2</oasis:entry>  
         <oasis:entry colname="col7">32.3</oasis:entry>  
         <oasis:entry colname="col8">29.2</oasis:entry>  
         <oasis:entry colname="col9"/>  
         <oasis:entry colname="col10"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX1m</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>m</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">100 d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">16.6</oasis:entry>  
         <oasis:entry colname="col5">9.1</oasis:entry>  
         <oasis:entry colname="col6">13.6</oasis:entry>  
         <oasis:entry colname="col7">41.8</oasis:entry>  
         <oasis:entry colname="col8">24.8</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>15</oasis:entry>  
         <oasis:entry colname="col10">0.20</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX2m</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>m</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">750 d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">20.8</oasis:entry>  
         <oasis:entry colname="col5">10.7</oasis:entry>  
         <oasis:entry colname="col6">16</oasis:entry>  
         <oasis:entry colname="col7">25.9</oasis:entry>  
         <oasis:entry colname="col8">31.2</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10">0.06</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX3m</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math display="inline"><mml:mn mathvariant="normal">1</mml:mn></mml:math></inline-formula> d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">19.5</oasis:entry>  
         <oasis:entry colname="col5">10.2</oasis:entry>  
         <oasis:entry colname="col6">15.3</oasis:entry>  
         <oasis:entry colname="col7">32.2</oasis:entry>  
         <oasis:entry colname="col8">29.2</oasis:entry>  
         <oasis:entry colname="col9">0</oasis:entry>  
         <oasis:entry colname="col10">0.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX4m</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">10 d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">19.4</oasis:entry>  
         <oasis:entry colname="col5">10.3</oasis:entry>  
         <oasis:entry colname="col6">15.2</oasis:entry>  
         <oasis:entry colname="col7">32.4</oasis:entry>  
         <oasis:entry colname="col8">29.1</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10">0.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX5m</oasis:entry>  
         <oasis:entry colname="col2">pH</oasis:entry>  
         <oasis:entry colname="col3">6</oasis:entry>  
         <oasis:entry colname="col4">8.0</oasis:entry>  
         <oasis:entry colname="col5">16.6</oasis:entry>  
         <oasis:entry colname="col6">23.9</oasis:entry>  
         <oasis:entry colname="col7">45.8</oasis:entry>  
         <oasis:entry colname="col8">12.0</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>59</oasis:entry>  
         <oasis:entry colname="col10">4.1</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX6m</oasis:entry>  
         <oasis:entry colname="col2">pH</oasis:entry>  
         <oasis:entry colname="col3">8</oasis:entry>  
         <oasis:entry colname="col4">29.6</oasis:entry>  
         <oasis:entry colname="col5">3.7</oasis:entry>  
         <oasis:entry colname="col6">5.1</oasis:entry>  
         <oasis:entry colname="col7">23.5</oasis:entry>  
         <oasis:entry colname="col8">44.4</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn>52</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10">3.6</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX7m</oasis:entry>  
         <oasis:entry colname="col2">pH</oasis:entry>  
         <oasis:entry colname="col3">data set<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>12</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">15.0</oasis:entry>  
         <oasis:entry colname="col5">13.8</oasis:entry>  
         <oasis:entry colname="col6">18.4</oasis:entry>  
         <oasis:entry colname="col7">36.8</oasis:entry>  
         <oasis:entry colname="col8">22.5</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>23</oasis:entry>  
         <oasis:entry colname="col10"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX8m</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>capture</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">0.4</oasis:entry>  
         <oasis:entry colname="col4">29.2</oasis:entry>  
         <oasis:entry colname="col5">10.2</oasis:entry>  
         <oasis:entry colname="col6">15.2</oasis:entry>  
         <oasis:entry colname="col7">32.3</oasis:entry>  
         <oasis:entry colname="col8">19.5</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn>50</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1.3</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX9m</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>capture</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">0.8</oasis:entry>  
         <oasis:entry colname="col4">9.7</oasis:entry>  
         <oasis:entry colname="col5">10.2</oasis:entry>  
         <oasis:entry colname="col6">15.2</oasis:entry>  
         <oasis:entry colname="col7">32.3</oasis:entry>  
         <oasis:entry colname="col8">38.9</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>50</oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2.2</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX10m</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">χ</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">0.1 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">20.0</oasis:entry>  
         <oasis:entry colname="col5">9.9</oasis:entry>  
         <oasis:entry colname="col6">14.7</oasis:entry>  
         <oasis:entry colname="col7">31.8</oasis:entry>  
         <oasis:entry colname="col8">30.0</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.04</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX11m</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">χ</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"><?xmltex \hack{\hfill\break}?>1 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">18.2</oasis:entry>  
         <oasis:entry colname="col5">11.1</oasis:entry>  
         <oasis:entry colname="col6">16.4</oasis:entry>  
         <oasis:entry colname="col7">33.5</oasis:entry>  
         <oasis:entry colname="col8">27.3</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>7</oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.03</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX12m</oasis:entry>  
         <oasis:entry colname="col2">H<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O depth</oasis:entry>  
         <oasis:entry colname="col3">10 cm</oasis:entry>  
         <oasis:entry colname="col4">16.0</oasis:entry>  
         <oasis:entry colname="col5">7.7</oasis:entry>  
         <oasis:entry colname="col6">20.7</oasis:entry>  
         <oasis:entry colname="col7">37.9</oasis:entry>  
         <oasis:entry colname="col8">24.1</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>18</oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.18</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX13m</oasis:entry>  
         <oasis:entry colname="col2">H<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O depth</oasis:entry>  
         <oasis:entry colname="col3">2 cm</oasis:entry>  
         <oasis:entry colname="col4">23.1</oasis:entry>  
         <oasis:entry colname="col5">13.4</oasis:entry>  
         <oasis:entry colname="col6">8.2</oasis:entry>  
         <oasis:entry colname="col7">27.1</oasis:entry>  
         <oasis:entry colname="col8">34.6</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn>18</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.31</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX14m</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi>D</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>×</mml:mo><mml:mn>0.5</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">20.7</oasis:entry>  
         <oasis:entry colname="col5">11.6</oasis:entry>  
         <oasis:entry colname="col6">9.4</oasis:entry>  
         <oasis:entry colname="col7">33.8</oasis:entry>  
         <oasis:entry colname="col8">31.0</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.12</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX15m</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi>D</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>×</mml:mo><mml:mn>2.0</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">17.8</oasis:entry>  
         <oasis:entry colname="col5">8.5</oasis:entry>  
         <oasis:entry colname="col6">22.9</oasis:entry>  
         <oasis:entry colname="col7">30.4</oasis:entry>  
         <oasis:entry colname="col8">26.8</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>9</oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.09</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX16m</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mtext>max</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>×</mml:mo><mml:mn>0.5</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">20.7</oasis:entry>  
         <oasis:entry colname="col5">11.0</oasis:entry>  
         <oasis:entry colname="col6">16.7</oasis:entry>  
         <oasis:entry colname="col7">27.0</oasis:entry>  
         <oasis:entry colname="col8">31.1</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.12</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX17m</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mtext>max</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>×</mml:mo><mml:mn>2.0</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">17.5</oasis:entry>  
         <oasis:entry colname="col5">9.0</oasis:entry>  
         <oasis:entry colname="col6">13.0</oasis:entry>  
         <oasis:entry colname="col7">40.5</oasis:entry>  
         <oasis:entry colname="col8">26.3</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>10</oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.10</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX18m</oasis:entry>  
         <oasis:entry colname="col2">manure comp<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>13</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4">15.4</oasis:entry>  
         <oasis:entry colname="col5">8.4</oasis:entry>  
         <oasis:entry colname="col6">12.5</oasis:entry>  
         <oasis:entry colname="col7">23.8</oasis:entry>  
         <oasis:entry colname="col8">23.1</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>21</oasis:entry>  
         <oasis:entry colname="col10"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p><inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula> Control experiment. <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> Parameter changed from default
values. <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> New parameter value. <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula> NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions
(Tg N yr<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">5</mml:mn></mml:msup></mml:math></inline-formula> Runoff (Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>). <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula> Diffusion to soil
(Tg N yr<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula> Nitrification (Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>). <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">8</mml:mn></mml:msup></mml:math></inline-formula> Canopy
capture (Tg N yr<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:math></inline-formula> Percent change in NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions due to parameter change
(%). <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>10</mml:mn></mml:msup></mml:math></inline-formula> Percent change in NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions per % change in parameter
value <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>11</mml:mn></mml:msup></mml:math></inline-formula> Control simulation. <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>12</mml:mn></mml:msup></mml:math></inline-formula> Soil pH from the ISRIC-WISE
data set (Batjes, 2005). <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>13</mml:mn></mml:msup></mml:math></inline-formula> Change in manure composition to urine 41 %,
available 21 %, unavailable 25 %, and resistant 13 %.</p></table-wrap-foot></table-wrap>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T2" specific-use="star"><caption><p>Fertilizer sensitivity tests.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="10">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:colspec colnum="9" colname="col9" align="right"/>
     <oasis:colspec colnum="10" colname="col10" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Exper.<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Parameter<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">Value<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">NH3<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Run<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">5</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col6">Soil<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col7">Nitrif.<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col8">Canopy<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">8</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math></inline-formula>NH<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">9</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula><?xmltex \hack{\hfill\break}?>%</oasis:entry>  
         <oasis:entry colname="col10">Sens.<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>10</mml:mn></mml:msup></mml:math></inline-formula>   % <inline-formula><mml:math display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> %</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">Control<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>11</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2"/>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4">10.9</oasis:entry>  
         <oasis:entry colname="col5">5.3</oasis:entry>  
         <oasis:entry colname="col6">12.3</oasis:entry>  
         <oasis:entry colname="col7">9.8</oasis:entry>  
         <oasis:entry colname="col8">16.3</oasis:entry>  
         <oasis:entry colname="col9"/>  
         <oasis:entry colname="col10"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX3f</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">1 d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">11.3</oasis:entry>  
         <oasis:entry colname="col5">5.6</oasis:entry>  
         <oasis:entry colname="col6">11.6</oasis:entry>  
         <oasis:entry colname="col7">9.0</oasis:entry>  
         <oasis:entry colname="col8">17.0</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.06</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX4f</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">10 d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">10.1</oasis:entry>  
         <oasis:entry colname="col5">4.7</oasis:entry>  
         <oasis:entry colname="col6">13.7</oasis:entry>  
         <oasis:entry colname="col7">10.9</oasis:entry>  
         <oasis:entry colname="col8">15.1</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>7</oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.03</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX5f</oasis:entry>  
         <oasis:entry colname="col2">pH</oasis:entry>  
         <oasis:entry colname="col3">6</oasis:entry>  
         <oasis:entry colname="col4">4.4</oasis:entry>  
         <oasis:entry colname="col5">8.5</oasis:entry>  
         <oasis:entry colname="col6">17.7</oasis:entry>  
         <oasis:entry colname="col7">17.5</oasis:entry>  
         <oasis:entry colname="col8">6.5</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>60</oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn>4.2</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX6f</oasis:entry>  
         <oasis:entry colname="col2">pH</oasis:entry>  
         <oasis:entry colname="col3">8</oasis:entry>  
         <oasis:entry colname="col4">18.4</oasis:entry>  
         <oasis:entry colname="col5">1.5</oasis:entry>  
         <oasis:entry colname="col6">4.1</oasis:entry>  
         <oasis:entry colname="col7">2.8</oasis:entry>  
         <oasis:entry colname="col8">27.6</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn>69</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn>4.8</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX7f</oasis:entry>  
         <oasis:entry colname="col2">pH</oasis:entry>  
         <oasis:entry colname="col3">data set<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>12</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">9.4</oasis:entry>  
         <oasis:entry colname="col5">6.6</oasis:entry>  
         <oasis:entry colname="col6">13.5</oasis:entry>  
         <oasis:entry colname="col7">10.9</oasis:entry>  
         <oasis:entry colname="col8">14.1</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>14</oasis:entry>  
         <oasis:entry colname="col10"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX8f</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>capture</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">0.4</oasis:entry>  
         <oasis:entry colname="col4">16.3</oasis:entry>  
         <oasis:entry colname="col5">5.3</oasis:entry>  
         <oasis:entry colname="col6">12.3</oasis:entry>  
         <oasis:entry colname="col7">9.8</oasis:entry>  
         <oasis:entry colname="col8">10.9</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn>50</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1.2</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX9f</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>capture</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">0.8</oasis:entry>  
         <oasis:entry colname="col4">5.4</oasis:entry>  
         <oasis:entry colname="col5">5.3</oasis:entry>  
         <oasis:entry colname="col6">12.3</oasis:entry>  
         <oasis:entry colname="col7">9.8</oasis:entry>  
         <oasis:entry colname="col8">21.7</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>50</oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2.1</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX10f</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">χ</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">0.1 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">10.9</oasis:entry>  
         <oasis:entry colname="col5">5.2</oasis:entry>  
         <oasis:entry colname="col6">12.3</oasis:entry>  
         <oasis:entry colname="col7">9.8</oasis:entry>  
         <oasis:entry colname="col8">16.3</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10">0.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX11f</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">χ</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">1 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">10.8</oasis:entry>  
         <oasis:entry colname="col5">5.3</oasis:entry>  
         <oasis:entry colname="col6">12.4</oasis:entry>  
         <oasis:entry colname="col7">9.9</oasis:entry>  
         <oasis:entry colname="col8">16.1</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>1</oasis:entry>  
         <oasis:entry colname="col10">0.0</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX12f</oasis:entry>  
         <oasis:entry colname="col2">H<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O depth</oasis:entry>  
         <oasis:entry colname="col3">10 cm</oasis:entry>  
         <oasis:entry colname="col4">9.0</oasis:entry>  
         <oasis:entry colname="col5">4.0</oasis:entry>  
         <oasis:entry colname="col6">15.2</oasis:entry>  
         <oasis:entry colname="col7">12.9</oasis:entry>  
         <oasis:entry colname="col8">13.4</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>17</oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.17</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX13f</oasis:entry>  
         <oasis:entry colname="col2">H<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O depth</oasis:entry>  
         <oasis:entry colname="col3">2 cm</oasis:entry>  
         <oasis:entry colname="col4">12.9</oasis:entry>  
         <oasis:entry colname="col5">6.8</oasis:entry>  
         <oasis:entry colname="col6">8.3</oasis:entry>  
         <oasis:entry colname="col7">7.2</oasis:entry>  
         <oasis:entry colname="col8">19.3</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn>18</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.31</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX14f</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi>D</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>×</mml:mo><mml:mn>0.5</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">11.8</oasis:entry>  
         <oasis:entry colname="col5">6.1</oasis:entry>  
         <oasis:entry colname="col6">7.6</oasis:entry>  
         <oasis:entry colname="col7">11.3</oasis:entry>  
         <oasis:entry colname="col8">17.7</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.17</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX15f</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi>D</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>×</mml:mo><mml:mn>2.0</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">9.6</oasis:entry>  
         <oasis:entry colname="col5">4.2</oasis:entry>  
         <oasis:entry colname="col6">18.3</oasis:entry>  
         <oasis:entry colname="col7">7.9</oasis:entry>  
         <oasis:entry colname="col8">14.4</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>12</oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.12</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX16f</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mtext>max</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>×</mml:mo><mml:mn> 0.5</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">11.8</oasis:entry>  
         <oasis:entry colname="col5">5.8</oasis:entry>  
         <oasis:entry colname="col6">13.7</oasis:entry>  
         <oasis:entry colname="col7">5.5</oasis:entry>  
         <oasis:entry colname="col8">17.7</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.17</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX17f</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mtext>max</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>×</mml:mo><mml:mn> 2.0</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">9.4</oasis:entry>  
         <oasis:entry colname="col5">4.4</oasis:entry>  
         <oasis:entry colname="col6">10.3</oasis:entry>  
         <oasis:entry colname="col7">16.3</oasis:entry>  
         <oasis:entry colname="col8">14.2</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>14</oasis:entry>  
         <oasis:entry colname="col10"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.14</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX18f</oasis:entry>  
         <oasis:entry colname="col2">Fert. date<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>13</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4">8.4</oasis:entry>  
         <oasis:entry colname="col5">8.6</oasis:entry>  
         <oasis:entry colname="col6">15.5</oasis:entry>  
         <oasis:entry colname="col7">8.6</oasis:entry>  
         <oasis:entry colname="col8">12.6</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>23</oasis:entry>  
         <oasis:entry colname="col10"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX19f</oasis:entry>  
         <oasis:entry colname="col2">Fert. rate<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>14</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4">11.3</oasis:entry>  
         <oasis:entry colname="col5">5.6</oasis:entry>  
         <oasis:entry colname="col6">11.5</oasis:entry>  
         <oasis:entry colname="col7">9.1</oasis:entry>  
         <oasis:entry colname="col8">17.0</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">EX20f</oasis:entry>  
         <oasis:entry colname="col2">Fert decomp.<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>15</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4">10.5</oasis:entry>  
         <oasis:entry colname="col5">4.9</oasis:entry>  
         <oasis:entry colname="col6">12.9</oasis:entry>  
         <oasis:entry colname="col7">10.5</oasis:entry>  
         <oasis:entry colname="col8">15.7</oasis:entry>  
         <oasis:entry colname="col9"><inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>4</oasis:entry>  
         <oasis:entry colname="col10"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p><inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula> Control experiment. <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> Parameter changed from default
values.
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> New parameter value. <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula> NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions (Tg N yr<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">5</mml:mn></mml:msup></mml:math></inline-formula> Runoff (Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>). <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula> Diffusion to soil (Tg N yr<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula> Nitrification (Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>). <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">8</mml:mn></mml:msup></mml:math></inline-formula> Canopy capture
(Tg N yr<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:math></inline-formula> Percent change in NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions due to parameter change
(%). <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>10</mml:mn></mml:msup></mml:math></inline-formula> Percent change in NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions per % change in parameter
value. <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>11</mml:mn></mml:msup></mml:math></inline-formula> Control simulation. <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>12</mml:mn></mml:msup></mml:math></inline-formula> Soil pH from the ISRIC-WISE
data set (Batjes, 2005). <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>13</mml:mn></mml:msup></mml:math></inline-formula> Change in fertilizer date to 20 March (NH) and
20 September (SH). <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>14</mml:mn></mml:msup></mml:math></inline-formula> Applying fertilizer over 20 days. <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>15</mml:mn></mml:msup></mml:math></inline-formula> Assuming fast release
ammonium nitrate decay of fertilizer.</p></table-wrap-foot></table-wrap>

      <p>Except for changes in the canopy capture parameter (EX8m/f, EX9m/f) and
changes in the timing or composition of manure or synthetic fertilizer
inputs (EX18m, EX18f, EX19f, EX20f), changes in the sensitivity parameters
directly change the nitrogen cycling within the TAN pool (as described
below). For the most part the synthetic fertilizer and manure TAN pools
respond similarly to the parameter changes. Note also that, except for EX18m,
where the amount of nitrogen input into the TAN pools is reduced, the total
input and loss of nitrogen from the TAN pools remain the same for all
sensitivity experiments. In general, the sensitivity of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions
to the imposed parameter changes are within the range of <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>20 %, with
many processes within the range of <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula>10 %. The sensitivity to the
mechanical mixing of manure into the soil pools (EX1m, EX2m), the adjustment
timescale for the water pool (EX3, EX4), the diffusion rate into the soil
pools (EX14, EX15), the assumed depth of the water pool (EX12, EX13) and the
maximum nitrification rate (EX16, EX17) all impact NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions by
less than 20 %. The sensitivity to the assumed background NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
concentration is also low (EX10, EX11).</p>
      <p>The NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions are most sensitive to changes in pH (EX5, EX6, EX7).
The NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions decreased by approximately 60 % when the pH is
decreased from 7 to 6 and increased by 50 to 70 % (for manure and
synthetic fertilizer, respectively) when the pH is increased from 7 to 8. We
also test the sensitivity of the emissions to the spatially explicit pH
input from the ISRIC-WISE data set (Batjes, 2005), with a global pH average of
6.55 (EX7). The spatially explicit pH reduced the manure NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions from
the control simulation by 23 % and the synthetic fertilizer NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions by 14 %. Changes in pH also have a large impact on
nitrification. Increased pH reduces
<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and thus
the rate of conversion of <inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup><mml:mo>(</mml:mo><mml:mi mathvariant="normal">aq</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> to NO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>. The effect of pH on the rate
constant for nitrification is not included in the current parameterization.
Parton et al. (2001) suggest this effect is small, between a pH of 6 and 8,
varying only on the order of 15 %. Changes in pH also result in marked
changes in the runoff and soil diffusion due to the large changes in
emissions and nitrification: a low pH acts to increase the flux of nitrogen
through these loss pathways, while a high pH acts to decrease them.</p>
      <p>Emissions are also highly sensitive to changes in canopy capture (i.e., the
parameter  <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>capture</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) as shown in EX8 and EX9. Decreasing the fraction captured by the
canopy by a factor of 2 increases the emissions by approximately a factor of
3. Changes in this fraction modify the fixed ratio between the amount of
nitrogen captured by the canopy and that emitted to the atmosphere. Of
course, the nitrogen captured in the canopy can further impact the nitrogen
budget, but this impact is not simulated here.</p>
      <p>The NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions are somewhat sensitive to the depth of the assumed
water pool (EX12, EX13). Smaller depths (less water) give higher
concentrations of all the constituents within the TAN pool resulting in
higher NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions (Eqs. 7 and 12) and larger nitrogen runoff
(see Sect. 2.2.4). Larger depths (more water) have the opposite effect.
The diffusion of nitrogen into the soil is somewhat sensitive to changes in
the assumed water depth as the coefficient of diffusion is proportional to
the water content to the <inline-formula><mml:math display="inline"><mml:mrow><mml:mn>10</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula> power (see Appendix A).</p>
      <p>We conducted various sensitivities to synthetic fertilizer application.
Early synthetic fertilizer application decreases NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions due to
their strong temperature dependence and increase the susceptibility of the
TAN pool to runoff. An early fertilization date (set to 20 March  in the
Northern Hemisphere or 20 September  in the Southern Hemisphere) decreases the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions by 23 %
and increases the nitrogen runoff from the TAN pool by 62 % (EX18f). To
investigate the sensitivity to the application rate of synthetic fertilizer,
synthetic fertilizer was applied over 20 days as opposed to the single-day
application assumed in the default version of the model (EX19f). This did
not have a significant impact on the emissions. The assumed synthetic
fertilizer type in the default version of the model (urea) was replaced with
ammonium nitrate fertilizer in EX20f. Whereas urea is converted to NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
rather slowly, the conversion of ammonium nitrate is rapid (in the
sensitivity test the resulting nitrogen is assumed to be instantaneously
released into the TAN pool with no changes in pH). However, the emissions
are not particularly sensitive to this change. This is in contrast to
differences in volatilization rates of different synthetic fertilizers given
in Bouwman (2002). Whitehead and Raistrick (1990) show that one of the
primary differences between the addition of urea vs. ammonium nitrate
fertilizer is in the effect of the fertilizer on the soil pH, an effect that
we do not consider in this study. In particular urea increases the soil pH
and thus the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions.</p>
      <p>Finally, we test the impact of manure composition on the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions
(EX18m). The composition of manure nitrogen excreted by animals depends in
part on the digestibility of the feed, which can vary in both time and
space. To investigate this uncertainty we varied the composition of the
manure assumed in the default model version (50 % urine, 25 % available,
22.5 % resistant and 2.5 % unavailable) to the less soluble N excreta
from dairy cattle in sensitivity simulation EX18m (41 % urine, 21 %
available, 25 % unavailable and 13 % resistant; Smith, 1973). This
decreased the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions by 21 % demonstrating an important
sensitivity to the composition of manure and urine.</p>
      <p>It is important to emphasize that these sensitivity simulations only test
the parameter sensitivity within the imposed model. In particular, the
sensitivities to various farming practices are generally extraneous to the
model assumptions with some exceptions. The sensitivities to synthetic
fertilizer or manure input assumptions are tested in simulations EX18m,
EX18f, EX19f, and EX20f; sensitivities to the water depth which may crudely
represent some of the impacts of plowing manure or synthetic fertilizer into
the soil are examined in EX12 and EX13; and finally, modifications to soil pH are
tested in EX5, EX6 and EX7.</p>
</sec>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <title>Discussion and conclusions</title>
      <p>In this paper we develop a process-oriented model that predicts the climate-dependent pathways of reactive nitrogen applied as manure or synthetic
fertilizer onto the surface of the land. It is also capable of taking into
account the resulting biogeochemical cycling of nitrogen. Continued
population growth will likely result in an increased application of
synthetic fertilizers with concurrent increases in manure production in the
future (Davidson, 2012). Climate is an important determinant in the ultimate
fate of this applied nitrogen, important in determining the resulting
emissions of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> and other reactive nitrogen gases, in the runoff of
the applied nitrogen, its nitrification and its incorporation into the soil
organic and inorganic nitrogen pools. The fate of the resultant applied
nitrogen may act to acerbate climate change through the formation of
N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O, or perhaps mitigate climate change through increased carbon
fertilization and the increased formation of aerosols.</p>
      <p>Both natural and anthropogenic processes control agricultural NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions. Previous global NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emission estimates have relied on
detailed information on agricultural practices including domestic animal
type, animal housing and the field application of synthetic fertilizer or
manure (e.g., Bouwman et al., 1997) but have minimized the representation of
meteorological processes. In some cases the resulting emission factors have
implicitly included temperature dependence by using different emission
factors for industrial and developing countries (e.g., Bouwman et al. 1997),
although recently some inventories have explicitly included empirical
emission factors that vary with temperature (Paulot et al., 2014; Huang et
al., 2012). Here, we take the opposite tact by constructing a model where
the N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> pathways and in particular the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions following
manure and synthetic fertilizer application are explicitly driven by climate
but where the explicit representation of most agricultural practices is
minimized.</p>
      <p>In this study the global emissions of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> due to manure and fertilizer
nitrogen sources are similar to other recent inventories, with 21 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
emitted as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> from manure nitrogen and 12 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
emitted from synthetic fertilizer for present-day conditions. Strong regional differences in emissions
captured by the bottom up inventories are also simulated. Moreover, we are
able to simulate the interannual, seasonal and diurnal changes in NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions critical for air pollution applications (e.g., see de Meij et al.,
2006). It is perhaps important to note that the impact of nitrogen emissions
on the global carbon budget has generally made use of previous emission
inventories without explicit seasonal or diurnal dependence of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions and with a rather minimal representation of the geographic
meteorological dependence.</p>
      <p>The model developed here uses a process-level approach to estimate nitrogen
pathways from synthetic fertilizer and manure application. It is suitable
for use within an Earth system model to estimate the resulting NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions, nitrogen runoff, and the incorporation of the nitrogen into soil
organic and inorganic matter. The modeled N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> pathways dynamically
respond to climatic variation; for example, (1) the breakdown timescale of
manure and fertilizer into TAN depends on temperature; (2) the formation of
NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> gas from the TAN pool is highly temperature-sensitive, with the rate
of formation described by the temperature dependence of the thermodynamic
Henry and dissociation equilibria for NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> (Nemitz et al., 2000); (3) the
rate of nitrification of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> within the TAN pool, determined by the
rate at which ammonium ions are oxidized by nitrifying bacteria to form
nitrate ions  (Abbasi and Adams, 1998), is controlled by environmental
factors such as soil temperature and soil moisture; and (4) the runoff of
N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> is determined by the precipitation. Predictions for direct nitrogen
runoff from fertilizer and manure nitrogen pools and the incorporation of
nitrogen into soil pools from applied fertilizer and manure nitrogen are
some of the first made by a global process-level model.</p>
      <p>Manure is not a new nitrogen source but rather contains recycled N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> from soil
nitrogen produced when animals eat plants. Therefore, to conserve nitrogen
within an Earth system model, the application of manure determines the
consumption of plant matter by animals. Specifically, the model calculates
the amount of nitrogen and carbon needed for a given manure application and
subtracts it from the plant leaf pools within the CLM. The manure production
may speed up the decay and processing of plant biomass, releasing different
N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> products to the atmosphere than natural decay  (Davidson, 2009).</p>
      <p>The climate dependency incorporated into the model suggests that the
pathways of nitrogen added to the land are highly spatially and temporally
heterogeneous. An examination of nitrogen loss pathways at a point over
Texas shows the variation in the nitrogen pathways on a variety of
timescales with changes in temperature, precipitation and soil moisture.
Globally, NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> volatilization is highest in the tropics. The percentage
of manure nitrogen volatilized to NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> in this study show a large range
in both developing countries (average of 20 %; maximum: 36 %) and
industrialized countries (average of 12 %; maximum: 39 %). The model
also predicts spatial and temporal variability in the amount of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
volatilized from synthetic fertilizers, ranging from 14 % (maximum 40 %)
in industrialized countries to 22 % (maximum 40 %) in developing
countries. In comparison, the EDGAR database uses the emission factors based
on Bouwman et al. (2002), where 21  and 26 % of manure is converted
into NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> in industrialized and developing countries, respectively.
Nitrogen runoff from the manure and synthetic fertilizer TAN pools is
highest in areas of high N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> application and high rainfall, such as
China, North America and Europe. Despite high nitrogen input rates we
simulate low nitrogen runoff in India and Spain, for example. We also
simulate climate-dependent pathways for the diffusion of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> into the
soil inorganic nitrogen pools and the nitrification of ammonium to nitrate.</p>
      <p>Historically we predict emissions of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> from applied manure to have
increased from approximately 3 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in 1850 to 22 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
in 2000, while the volatilization of fertilizer reaches
12 Tg N yr<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in 2000. The NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emission factors increase by
approximately 3.4 % for manure applications and 11 % for synthetic
fertilizer applications over this historical period (1930 to 2000 for
fertilizer). Under current manure and synthetic fertilizer application rates
we find that globally an additional 1 Tg NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> is emitted from the manure
and synthetic fertilizer pools per degree of warming. Percentage-wise this
increases manure emissions by 4 % and synthetic fertilizer emissions by
3 % per degree of temperature increase.</p>
      <p>The NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions appear reasonable when compared to other inventories
on the global scale, as well as when compared to the local-scale measurements
of manure and synthetic fertilizer (Figs. 2 and 3), although these latter
comparisons highlight the difficulty in making global-scale assumptions
about surface parameters and farming methodology. The biggest disagreement
with the manure emission measurements is from beef cattle feedlots in Texas.
On the whole the model performs best when estimating NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> manure
emissions from cows on grassland. Despite the issues described above, this
model gives reasonable NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emission predictions given the limited
global information available on the grazing land of agricultural animals.
Measurements of nitrogen runoff from rivers heavily impacted by
anthropogenic nitrogen input also compare favorably with simulated results
using the river transport model within the CESM (Nevison et al., 2016).</p>
      <p>The assumption of simplified farming practices made here may be acceptable
in many locations as more complex farming methods are rarely employed in the
developing world. While the Food and Agriculture Organization  (FAO, 2005)
suggests over 75 % of the global agricultural land uses traditional
farming methods, one of the largest sources of uncertainty in this study is
associated with the simplification of agricultural practices. A number of
future model improvements are necessary in the next-generation model.
<list list-type="order"><list-item>
      <p>More realistic representation of manure management practices. While there is a
wide range of variation in animal housing and storage practices, the unique
set of emission factors entailed in animal housing and storage should be
incorporated in the next-generation model.</p></list-item><list-item>
      <p>A better representation of
nitrogen transport throughout the soil column and the resulting NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
generation. This would allow a differentiation between NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions
resulting from grazing, where urine is rapidly incorporated into the soil
column, vs. the emissions resulting from the spreading of manure slurry.
It would also allow a representation of fertilizer injection or mixing into
the soil column and the transport of nitrogen into the soil column in
association with water transport.</p><?xmltex \hack{\newpage}?></list-item><list-item>
      <p>Representation of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> emissions
from different synthetic fertilizer types. Different types of synthetic
fertilizer have rather different emission factors. As shown by Whitehead and
Raistrick (1990) many of these differences can be represented by the impact
of the fertilizer on soil pH.</p></list-item><list-item>
      <p>A full biogeochemical coupling of the FAN
process model to the overall biogeochemistry within the CESM. This would
allow the nitrogen introduced through agricultural practices to impact the
overall model biogeochemistry and allow a more thorough investigation of the
flows of agricultural nitrogen.</p></list-item><list-item>
      <p>A full coupling between the NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>
emissions represented by the FAN process model and the atmospheric chemistry
model through a PFT-dependent compensation point approach. The applied
nitrogen should be added explicitly to the CLM crop model or to pasture land
where appropriate.</p></list-item></list></p>
      <p>The increased use of synthetic fertilizer and growing livestock populations
has increased N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> flows to both the atmosphere and oceans to
unprecedented levels with a marked effect on the environment. We have
provided a first estimate of globally distributed temporal changes in
nitrogen pathways from manure and synthetic fertilizer inputs in response to
climate. This is relevant to current studies investigating the ecosystem
effects of N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>r</mml:mtext></mml:msub></mml:math></inline-formula> and, in particular, how adding synthetic fertilizer to
farmland affects the ocean and the atmosphere and impacts climate. The model
predicts vastly different nitrogen pathways depending on the region the
inputs are applied. Scenarios predicting future synthetic fertilizer use and
livestock populations suggest large increases in nitrogen added to the land
surface from both sources  (Tilman et al., 2001; Skjøth and Geels, 2013),
with an important component sensitive to climate change. The volatilization
of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> increases exponentially with temperature, suggesting future
emission increases are likely. However, increases in temperature may surpass
the optimal temperature at which certain biological processes occur, slowing
the process. Washout pathways are also likely to change, not only with
climate but also with increases in nitrogen loading. Future applications of this
model will investigate the tight coupling between nitrogen, agriculture and
climate.</p><?xmltex \hack{\clearpage}?>
</sec>

      
      </body>
    <back><app-group>

<app id="App1.Ch1.S1">
  <title/>

<?xmltex \floatpos{h!}?><table-wrap id="App1.Ch1.T1"><?xmltex \hack{\hsize\textwidth}?><caption><p>Description of model variables and equations.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.78}[.78]?><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="justify" colwidth="100pt"/>
     <oasis:colspec colnum="2" colname="col2" align="justify" colwidth="68pt"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="41pt"/>
     <oasis:colspec colnum="4" colname="col4" align="justify" colwidth="210pt"/>
     <oasis:colspec colnum="5" colname="col5" align="justify" colwidth="100pt"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Description</oasis:entry>  
         <oasis:entry colname="col2">Symbol</oasis:entry>  
         <oasis:entry colname="col3">Unit</oasis:entry>  
         <oasis:entry colname="col4">Value used or equation</oasis:entry>  
         <oasis:entry colname="col5">Reference</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">  
         <oasis:entry namest="col1" nameend="col5" align="center">Prognostic Variables </oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Pool of nitrogen from applied manure that easily forms TAN</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mtext>available</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">dN</mml:mi><mml:mi mathvariant="normal">available</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">applied</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mtext>a</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mi mathvariant="normal">available</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>m</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">available</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Pool of nitrogen from applied manure that is resistant to forming TAN</oasis:entry>  
         <oasis:entry colname="col2">N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>resistant</mml:mtext></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">dN</mml:mi><mml:mi mathvariant="normal">resistant</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">applied</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mi mathvariant="normal">resistant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>
<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>m</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">resistant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Pool of nitrogen from applied manure that does not form TAN</oasis:entry>  
         <oasis:entry colname="col2">N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>unavailable</mml:mtext></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">dN</mml:mi><mml:mi mathvariant="normal">unavailable</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">un</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">applied</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>m</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">unavailable</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Pool of nitrogen from applied  fertilizer</oasis:entry>  
         <oasis:entry colname="col2">N<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>fertilizer</mml:mtext></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">dN</mml:mi><mml:mi mathvariant="normal">fertilizer</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">applied</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>f</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mtext>N</mml:mtext><mml:mi mathvariant="normal">fertilizer</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Pool of nitrogen in TAN<?xmltex \hack{\hfill\break}?>pool from manure</oasis:entry>  
         <oasis:entry colname="col2">N<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mtext>TAN</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">TAN</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">u</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">applied</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mtext>r</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mi mathvariant="normal">resistant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mtext>a</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mi mathvariant="normal">available</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mtext>w</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mi mathvariant="normal">TAN</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:msubsup><mml:mi>K</mml:mi><mml:mi>D</mml:mi><mml:mrow><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msubsup><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mi mathvariant="normal">TAN</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:msub><mml:mtext>NO</mml:mtext><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Pool of nitrogen in TAN pool from fertilizer</oasis:entry>  
         <oasis:entry colname="col2">N<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mtext>TAN</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">TAN</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula>
<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>f</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">fertilizer</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mtext>w</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mi mathvariant="normal">TAN</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:msubsup><mml:mi>K</mml:mi><mml:mi>D</mml:mi><mml:mrow><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msubsup><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mi mathvariant="normal">TAN</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:msub><mml:mtext>NO</mml:mtext><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Pool of surface NO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mrow><mml:msub><mml:mtext>NO</mml:mtext><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">dN</mml:mi><mml:mrow><mml:mi mathvariant="normal">N</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:msub><mml:mtext>NO</mml:mtext><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msubsup><mml:mi>K</mml:mi><mml:mi>D</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msubsup><mml:mo>×</mml:mo><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Pool of manure/fertilizer water in TAN pool</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">m</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula>
<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">applied</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Pool of manure/fertilizer water in TAN pool</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math display="inline"><mml:mi>f</mml:mi></mml:math></inline-formula>)</oasis:entry>  
         <oasis:entry colname="col3">m</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">applied</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
<?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry namest="col1" nameend="col5" align="center">Variables from CLM </oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Ground temperature</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">K</oasis:entry>  
         <oasis:entry colname="col4">Taken from model</oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Runoff</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">m s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">Taken from model</oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Aerodynamic resistance</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>a</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">s m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">Taken from model</oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Boundary layer resistance</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>b</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">s m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">Taken from model</oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Water in soil</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mi>M</mml:mi></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">m</oasis:entry>  
         <oasis:entry colname="col4">Taken from the model (top 5 cm of soil)</oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry namest="col1" nameend="col5" align="center">Diagnostic Variables </oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Available manure<?xmltex \hack{\hfill\break}?>decomposition</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>a</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>a</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>a1</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>  (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Gilmour et al. (2003); Vigil and Kissel (1995)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Resistant   manure <?xmltex \hack{\hfill\break}?>decomposition</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>r</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>r</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>a2</mml:mtext></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mi>R</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Gilmour et al. (2003); Vigil and Kissel (1995)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Temperature dependence <?xmltex \hack{\hfill\break}?>for <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>a</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>r</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>R</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">N/A</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi mathvariant="normal">r</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mi>exp⁡</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mi mathvariant="normal">r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn>273.15</mml:mn><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">(Vigil and Kissel, 1995)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Surface runoff   flux</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">run</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">run</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>R</mml:mi><mml:mo>×</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mi mathvariant="normal">TAN</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">NH<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> loss rate <?xmltex \hack{\hfill\break}?>to soil pool</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi>K</mml:mi><mml:mi>D</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi>K</mml:mi><mml:mi>D</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:msup><mml:mi>l</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:msubsup><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi mathvariant="normal">w</mml:mi><mml:mrow><mml:mn>10</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msubsup><mml:mo>/</mml:mo><mml:msup><mml:mi mathvariant="italic">φ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="italic">κ</mml:mi><mml:mrow><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow><mml:mi mathvariant="normal">aq</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Génermont and Cellier<?xmltex \hack{\hfill\break}?>(1997)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">NO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> loss rate <?xmltex \hack{\hfill\break}?>to soil pool</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi>K</mml:mi><mml:mi>D</mml:mi><mml:mrow><mml:msub><mml:mtext>NO</mml:mtext><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi>K</mml:mi><mml:mi>D</mml:mi><mml:mrow><mml:msub><mml:mtext>NO</mml:mtext><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:msup><mml:mtext>l</mml:mtext><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:msubsup><mml:mi mathvariant="normal">Θ</mml:mi><mml:mtext>w</mml:mtext><mml:mrow><mml:mn>10</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msubsup><mml:mo>/</mml:mo><mml:msup><mml:mi mathvariant="italic">φ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo><mml:msubsup><mml:mi mathvariant="italic">κ</mml:mi><mml:mrow><mml:msub><mml:mtext>NO</mml:mtext><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mi mathvariant="normal">aq</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Génermont and Cellier <?xmltex \hack{\hfill\break}?>(1997)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Base vertical diffusion for <?xmltex \hack{\hfill\break}?>TAN pool</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">κ</mml:mi><mml:mrow><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow><mml:mi mathvariant="normal">aq</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">κ</mml:mi><mml:mrow><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow><mml:mi mathvariant="normal">aq</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:mn>9.8</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>10</mml:mn></mml:mrow></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mn>1.03</mml:mn><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn>273.15</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Génermont and Cellier <?xmltex \hack{\hfill\break}?>(1997)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Base vertical diffusion for <?xmltex \hack{\hfill\break}?>NO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> pool</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">κ</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mi mathvariant="normal">aq</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">κ</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mi mathvariant="normal">aq</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:mn>1.3</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mn>1.03</mml:mn><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn>273.15</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Génermont and Cellier <?xmltex \hack{\hfill\break}?>(1997)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Water Content</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mtext>w</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mtext>w=</mml:mtext></mml:msub><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mi>H</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Flux of nitrogen lost as NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> for manure (<inline-formula><mml:math display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula>) or fertilizer (<inline-formula><mml:math display="inline"><mml:mi>f</mml:mi></mml:math></inline-formula>)</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mtext>(g)</mml:mtext><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">χ</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Nemitz et al. (2000; Loubet et al. (2009); Sutton et al. (2013))</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

<?xmltex \hack{\clearpage}?><?xmltex \hack{\addtocounter{table}{-1}}?><?xmltex \floatpos{h!}?><table-wrap id="App1.Ch1.T2"><caption><p>Continued.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.78}[.78]?><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="justify" colwidth="95pt"/>
     <oasis:colspec colnum="2" colname="col2" align="justify" colwidth="68pt"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="41pt"/>
     <oasis:colspec colnum="4" colname="col4" align="justify" colwidth="230pt"/>
     <oasis:colspec colnum="5" colname="col5" align="justify" colwidth="117pt"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Description</oasis:entry>  
         <oasis:entry colname="col2">Symbol</oasis:entry>  
         <oasis:entry colname="col3">Unit</oasis:entry>  
         <oasis:entry colname="col4">Value used or equation</oasis:entry>  
         <oasis:entry colname="col5">Reference</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">Flux of NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> to atmosphere</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">F</mml:mi><mml:mrow><mml:msub><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mtext>atm</mml:mtext></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:msub><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mtext>atm</mml:mtext></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">capture</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">e.g., Wilson et al. (2004)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>(g) in equilibrium with the TAN manure (<inline-formula><mml:math display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula>) or fertilizer (<inline-formula><mml:math display="inline"><mml:mi>f</mml:mi></mml:math></inline-formula>) pool</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">g</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">g</mml:mi><mml:mo>)</mml:mo><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mi mathvariant="normal">TAN</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub><mml:mfenced open="[" close="]"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mfenced><mml:mo>/</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Derived from  Sutton et al. <?xmltex \hack{\hfill\break}?>(1994)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Henry's law constant for NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>4.59</mml:mn><mml:mo>(</mml:mo><mml:msup><mml:mi mathvariant="normal">K</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:msup><mml:mi>exp⁡</mml:mi><mml:mrow><mml:mn>4092</mml:mn><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Sutton et al. (1994)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Dissociation equilibrium constant for <?xmltex \hack{\hfill\break}?>NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>(aq)</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">mol L<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>5.67</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>10</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mi mathvariant="normal">exp</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>6286</mml:mn><mml:mfenced close=")" open="("><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub></mml:mfenced></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Sutton et al. (1994)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Flux of nitrogen from TAN to NO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> pool</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn>2.</mml:mn><mml:msub><mml:mi mathvariant="normal">r</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">g</mml:mi><mml:mo>)</mml:mo><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub><mml:mfenced open="[" close="]"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mfenced><mml:mo>/</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mtext>NH</mml:mtext><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mfrac><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mi mathvariant="normal">Σ</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:mi mathvariant="normal">Π</mml:mi><mml:mo>(</mml:mo><mml:mi>M</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Stange and Neue (2009); Parton et al. (2001)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Soil temperature function</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">Σ</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>g</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Σ</mml:mi><mml:mfenced close=")" open="("><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mfenced><mml:mo>=</mml:mo><mml:msup><mml:mfenced close=")" open="("><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">opt</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mrow><mml:msub><mml:mi mathvariant="normal">a</mml:mi><mml:mi mathvariant="normal">Σ</mml:mi></mml:msub></mml:mrow></mml:msup><mml:mi mathvariant="normal">exp</mml:mi><mml:mfenced open="(" close=")"><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">Σ</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">opt</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">opt</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced></mml:mfenced></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Stange and Neue (2009)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Soil moisture response function</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>M</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="normal">Π</mml:mi><mml:mfenced close=")" open="("><mml:mi>M</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:msup><mml:mfenced open="(" close=")"><mml:mo>[</mml:mo><mml:mo>(</mml:mo><mml:mi>M</mml:mi><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">water</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:mi>h</mml:mi><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">soil</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>]</mml:mo><mml:mo>/</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mi mathvariant="normal">crit</mml:mi></mml:msub></mml:mfenced><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Stange and Neue (2009)</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Water : N ratio in applied fertilizer</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> g<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mn>0.466</mml:mn><mml:mo>×</mml:mo><mml:mn>0.66</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mn>0.0239</mml:mn><mml:mo>×</mml:mo><mml:mfenced close=")" open="("><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">g</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mn>273</mml:mn></mml:mfenced></mml:mrow></mml:msup></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">UNIDO and IFDC (1988)</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry namest="col1" nameend="col5" align="center">Parameters </oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Flux of manure nitrogen applied to the surface</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>applied</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>(m)</oasis:entry>  
         <oasis:entry colname="col3">g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">Spatial distribution from Potter et al. (2010); annual temporal distribution from Holland et al. (2005)</oasis:entry>  
         <oasis:entry colname="col5">Potter et al. (2010); Holland et al. (2005)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Flux of fertilizer nitrogen applied to the surface</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mtext>applied</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>f</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">Spatial distribution from Potter et al. (2010); annual temporal distribution from Holland et al. (2005)</oasis:entry>  
         <oasis:entry colname="col5">Potter et al. (2010); Holland et al. (2005)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Fractions of nitrogen in manure/urine</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>u</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>a</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>r</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>un</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">N/A</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>u</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.5, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>a</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.25, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>r</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.225, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>un</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.025</oasis:entry>  
         <oasis:entry colname="col5">Gusman and Mariño (1999)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Mechanical incorporation of manure into soil</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>m</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>m</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> (365 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 86400)<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">see Koven et al. (2013)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Fertilizer   decomposition</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>f</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>f</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 4.83 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Agehara and Warncke (2005)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Water : N ratio in applied manure</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> g<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn>5.67</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Sommer and Hutchings (2001)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Relaxation rate of TAN water pool to soil water pool</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">relax</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula>(3 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 86400)<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Empirical factors <?xmltex \hack{\hfill\break}?>for <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>a</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">r</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>a1</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>a2</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>a1</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 8.94 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>a2</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 6.38 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Gilmour et al. (2003)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Empirical factors <?xmltex \hack{\hfill\break}?>for <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>r</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mtext>r1</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mtext>r2</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">K<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mtext>r1</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.0106, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>t</mml:mi><mml:msub><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.12979 K<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Vigil and Kissel (1995)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Length scale</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mi>l</mml:mi></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">m</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:mi>l</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> m</oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Soil porosity</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">ϕ</mml:mi></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Depth of soil water pool</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">m</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:mi>H</mml:mi><mml:mo>=</mml:mo><mml:mn>5.0</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Atmospheric NH<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> concentration</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">χ</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">g m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">χ</mml:mi><mml:mi mathvariant="normal">a</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.3</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mtext>g</mml:mtext><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Zbieranowski and<?xmltex \hack{\hfill\break}?>Aherne (2012)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Fraction of ammonia emissions capture by <?xmltex \hack{\hfill\break}?>canopy</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">capture</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi mathvariant="normal">capture</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.7</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">e.g., see Wilson et al. (2004)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Concentration of hydrogen ions</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:mo>[</mml:mo><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>]</mml:mo></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">mol L<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:mfenced open="[" close="]"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mfenced><mml:mo>=</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Reference Temperature</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">K</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">ref</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>298.15</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Sutton et al. (1994)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Maximum rate of nitrification</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">s<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1.16</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5">Parton et al. (2001)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Optimal temperature of microbial activity</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mtext>opt</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">K</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mtext>opt</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 301</oasis:entry>  
         <oasis:entry colname="col5">Stange and Neue (2009)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Maximum temperature of microbial activity</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mo>max⁡</mml:mo></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">K</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mo>max⁡</mml:mo></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 313</oasis:entry>  
         <oasis:entry colname="col5">Stange and Neue (2009)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Empirical factor</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">Σ</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>a</mml:mi><mml:mi mathvariant="normal">Σ</mml:mi></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 2.4</oasis:entry>  
         <oasis:entry colname="col5">Stange and Neue (2009)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Sharp parameter of the function</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:mi>b</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 2</oasis:entry>  
         <oasis:entry colname="col5">Stange and Neue (2009)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Critical water content of soil</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mtext>crit</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">g g<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> soil</oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mtext>crit</mml:mtext></mml:msub><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> 0.12</oasis:entry>  
         <oasis:entry colname="col5">Stange and Neue (2009)</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">Density of soil</oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">soil</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col3">kg m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">soil</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1050.</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col5"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

<?xmltex \hack{\clearpage}?><supplementary-material position="anchor"><p><bold>The Supplement related to this article is available online at <inline-supplementary-material xlink:href="http://dx.doi.org/10.5194/bg-13-3397-2016-supplement" xlink:title="pdf">doi:10.5194/bg-13-3397-2016-supplement</inline-supplementary-material>.</bold></p></supplementary-material>
</app>
  </app-group><ack><title>Acknowledgements</title><p>We wish to thank the reviewers. Also, Farhan Nuruzzaman and Jae Hee Hwang
for preparation of input data sets. Thanks also to Sam Levis, Dave Lawrence
and Gordon Bonan at NCAR for their input to model processes and colleagues
at Cornell University, Ben Brown-Steiner and Raj Paudel, for their help
running the model. This project was supported by NSF project number ETBC
#10216.<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>
Edited by:  A. Neftel</p></ack><ref-list>
    <title>References</title>

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    <!--<article-title-html>Estimate of changes in agricultural terrestrial nitrogen pathways and
ammonia emissions from 1850 to present in the Community Earth System Model</article-title-html>
<abstract-html><p class="p">Nitrogen applied to the surface of the land for agricultural purposes
represents a significant source of reactive nitrogen (N<sub>r</sub>) that can be emitted
as a gaseous N<sub>r</sub> species, be denitrified to atmospheric nitrogen (N<sub>2</sub>), run off
during rain events or form plant-useable nitrogen in the soil. To investigate
the magnitude, temporal variability and spatial heterogeneity of nitrogen
pathways on a global scale from sources of animal manure and synthetic
fertilizer, we developed a mechanistic parameterization of these pathways
within a global terrestrial land model, the Community Land Model (CLM).
In this first model version the parameterization emphasizes an explicit
climate-dependent approach while using highly simplified representations of
agricultural practices, including manure management and fertilizer
application. The climate-dependent approach explicitly simulates the
relationship between meteorological variables and biogeochemical processes to
calculate the volatilization of ammonia (NH<sub>3</sub>), nitrification and runoff
of N<sub>r</sub> following manure or synthetic fertilizer application. For the year
2000, approximately 125 Tg N yr<sup>−1</sup> is applied as manure and
62 Tg N yr<sup>−1</sup> is applied as synthetic fertilizer. We estimate the
resulting global NH<sub>3</sub> emissions are 21 Tg N yr<sup>−1</sup> from manure
(17 % of manure production) and 12 Tg N yr<sup>−1</sup> from fertilizer
(19 % of fertilizer application); reactive nitrogen runoff during rain
events is calculated as 11 Tg N yr<sup>−1</sup> from manure and
5 Tg N yr<sup>−1</sup> from fertilizer. The remaining nitrogen from manure
(93 Tg N yr<sup>−1</sup>) and synthetic fertilizer (45 Tg N yr<sup>−1</sup>) is
captured by the canopy or transferred to the soil nitrogen pools. The
parameterization was implemented in the CLM from 1850 to 2000 using a
transient simulation which predicted that, even though absolute values of all
nitrogen pathways are increasing with increased manure and synthetic
fertilizer application, partitioning of nitrogen to NH<sub>3</sub> emissions from manure
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(3 Tg NH<sub>3</sub> yr<sup>−1</sup>) to 17 % of nitrogen applied in 2000
(21 Tg NH<sub>3</sub> yr<sup>−1</sup>). Under current manure and synthetic
fertilizer application rates we find a global sensitivity of an additional
1 Tg NH<sub>3</sub> (approximately 3 % of manure and fertilizer) emitted per
year per °C of warming. While the model confirms earlier estimates of
nitrogen fluxes made in a range of studies, its key purpose is to provide a
theoretical framework that can be employed within a biogeochemical model,
that can explicitly respond to climate and that can evolve and improve with
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