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<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" xml:lang="en" dtd-version="3.0" article-type="research-article"><?xmltex \bartext{Research article}?>
  <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-19-4129-2022</article-id><title-group><article-title>Accounting for non-rainfall moisture and temperature improves litter decay
model performance in a fog-dominated dryland system</article-title><alt-title>Non-rainfall moisture improves litter decay models</alt-title>
      </title-group><?xmltex \runningtitle{Non-rainfall moisture improves litter decay models}?><?xmltex \runningauthor{J.~R.~Logan et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1 aff2">
          <name><surname>Logan</surname><given-names>J. Robert</given-names></name>
          <email>loganja3@msu.edu</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Todd-Brown</surname><given-names>Kathe E.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-3109-8130</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Jacobson</surname><given-names>Kathryn M.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Jacobson</surname><given-names>Peter J.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Vogt</surname><given-names>Roland</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff2">
          <name><surname>Evans</surname><given-names>Sarah E.</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>W. K. Kellogg Biological Station, Hickory Corners, MI, USA</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Department of Integrative Biology, Michigan State University, East
Lansing, MI, USA</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Department of Environmental Engineering Sciences, University of
Florida, Gainesville, FL, USA</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Department of Biology, Grinnell College, Grinnell, IA, USA</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Institute of Meteorology, Climatology and Remote Sensing, University
of Basel, Basel, Switzerland</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">J. Robert Logan (loganja3@msu.edu)</corresp></author-notes><pub-date><day>6</day><month>September</month><year>2022</year></pub-date>
      
      <volume>19</volume>
      <issue>17</issue>
      <fpage>4129</fpage><lpage>4146</lpage>
      <history>
        <date date-type="received"><day>16</day><month>January</month><year>2022</year></date>
           <date date-type="rev-request"><day>14</day><month>February</month><year>2022</year></date>
           <date date-type="rev-recd"><day>6</day><month>June</month><year>2022</year></date>
           <date date-type="accepted"><day>9</day><month>June</month><year>2022</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2022 J. Robert Logan et al.</copyright-statement>
        <copyright-year>2022</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022.html">This article is available from https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022.html</self-uri><self-uri xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022.pdf">The full text article is available as a PDF file from https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e155">Historically, ecosystem models have treated rainfall as
the primary moisture source driving litter decomposition. In many arid and
semi-arid lands, however, non-rainfall moisture (fog, dew, and water vapor)
plays a more important role in supporting microbial activity and carbon
turnover. To date though, we lack a robust approach for modeling the role of
non-rainfall moisture in litter decomposition. We developed a series of
simple litter decay models with different moisture sensitivity and
temperature sensitivity functions to explicitly represent the role of
non-rainfall moisture in the litter decay process. To evaluate model
performance, we conducted a 30-month litter decomposition study at 6 sites
along a fog and dew gradient in the Namib desert, spanning almost an eightfold
difference in non-rainfall moisture frequency. Litter decay rates in the
field correlated with fog and dew frequencies but not with rainfall. Including
either temperature or non-rainfall moisture sensitivity functions improved
model performance, but the combination of temperature and moisture
sensitivity together provided more realistic estimates of litter
decomposition than relying on either alone. Model performance was similar
regardless of whether we used continuous moisture sensitivity functions
based on relative humidity or a simple binary function based on the presence
of moisture, although a Gaussian temperature sensitivity outperformed a
monotonically increasing <inline-formula><mml:math id="M1" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> temperature function. We demonstrate that
explicitly modeling non-rainfall moisture and temperature together is
necessary to accurately capture litter decay dynamics in a fog-affected
dryland system and provide suggestions for how to incorporate non-rainfall
moisture into existing Earth system models.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e178">Drylands play an important part in the global carbon cycle, but we still
lack a strong understanding of carbon cycling in these systems.
Historically, ecosystem models have underestimated dryland litter
decomposition rates (Parton et al., 2007; Adair et
al., 2008). This is partly because the models are driven by rainfall,
assuming little to no decay between precipitation events. While rainfall
pulses play a large role in dryland systems (Noy-Meir,
1973; Seely and Louw, 1980), considering rain alone does not fully capture
litter decomposition in these systems. This may be partially because much
decomposition occurs at and above the soil surface, and aboveground litter
decomposition is less sensitive to large rain pulses than belowground
decay (Austin, 2011;
Jacobson and Jacobson, 1998). Abiotic processes including photodegradation,
aeolian erosion, and thermal degradation that drive aboveground litter
decomposition can degrade litter regardless of moisture conditions
(Austin, 2011) and rain events as little as 1 mm can
facilitate microbial activity (Collins et al., 2008).
Finally, non-rainfall moisture (NRM: fog, dew, and water vapor) can support
substantial biotic decomposition of plant litter, even in the absence of
rain (Jacobson et
al., 2015; Dirks et al., 2010; Wang et al., 2017; Logan et al., 2021). These
findings demonstrate that carbon and nutrient cycling in drylands are not
restricted to precipitation pulses and that NRM is a crucial driver of
dryland biogeochemical cycles. As our understanding of the importance of NRM
in arid and semi-arid ecosystems evolves, we need to update our conceptual
and predictive models to incorporate these important drivers of ecosystem
processes.</p>
      <p id="d1e181">Despite growing recognition of NRM's importance, current litter decay models
do not explicitly account for its ability to support decomposition. This is
partly because field-based studies of NRM-driven decomposition are scarce
and so far, have mostly focused on documenting single cases and
understanding mechanisms. Recent studies have shown that the rate of
NRM-driven decomposition depends on many factors including the frequency of
humid conditions (Evans et al., 2020), the composition of
decomposer communities (Logan et al., 2021;
Wenndt et al., 2021), and interactions with other processes, such as
photodegradation
(Wang
et al., 2015; Gliksman et al., 2017; Logan et al., 2022). These insights
have been very helpful in demonstrating that NRM-driven decomposition occurs
and identifying its various mechanisms. However, before we can incorporate
NRM into mechanistic Earth system models, we need multiyear studies that
quantify the relationship between NRM and mass loss across a range of
environmental conditions (Bonan et al., 2013), something
that has not been done to date.</p>
      <p id="d1e184">One recent attempt to model NRM-driven decomposition has shed light on this
challenge. Evans et al. (2020) developed a model that
treated decomposition as a pulse process that could be triggered by either
rain or NRM when conditions met a given criterion (i.e., when relative
humidity was above a given threshold or when dew was present as determined
by a leaf wetness sensor). They found that accounting for NRM produced mass
loss estimates that were considerably higher than those from a rain-only
model and that these new estimates were within the range observed in the
field. This approach showed that NRM can improve mass loss estimates, but it
included several simplifying assumptions that need to be tested before NRM
can be incorporated into models more generally. First, the authors modeled
annual mass loss by measuring instantaneous respiration rates and scaling
them up to annual time scales. This showed that the NRM-driven biotic
activity on the scale of individual events can be used to estimate long-term
mass loss rates over several months, albeit with wide error estimates. A
better approach would be to validate model predictions by formally
integrating rates of mass loss at multiple sites and in multiyear field
studies (Bonan et al., 2013). Studies where NRM meteorology
and decomposition are both measured and quantifiably linked to one another
are currently lacking.</p>
      <p id="d1e187">Second, their model treated decomposition as essentially a pulse process
that could be triggered by either rainfall or NRM, but responded similarly
to both (in other words, as long as the threshold condition was met,
decomposition was considered to be “on”). While rainfall and NRM may
induce similar decomposition rates for a similar moisture level, this
approach does not allow the possibility of continuous responses. For
example, CO<inline-formula><mml:math id="M2" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> fluxes are strongly correlated with litter moisture
content (Jacobson et al., 2015), which varies
with relative humidity (Tschinkel, 1973; Dirks et al.,
2010), so a sensitivity function that allows instantaneous decay rates to
vary depending on the magnitude of the NRM event may be more appropriate
than a simple threshold trigger.</p>
      <p id="d1e200">Finally, their model did not include
temperature dependence, despite decomposition being highly sensitive to
temperature in almost all terrestrial systems (Sierra,
2012; Sierra et al., 2015). Relative humidity is closely linked to air
temperature, and average temperature during NRM events is often considerably
lower than during rain events (Logan et al., 2021).
Developing more powerful NRM-driven litter decay models may therefore
require incorporating continuous moisture responses and temperature
sensitivities to accurately capture decomposition dynamics, although to date
these remain untested.</p>
      <p id="d1e203">We set out to determine whether incorporating NRM into a simple litter decay
model improved model performance in an NRM-dominated system. We tested
multiple potential relationships between meteorological variables and litter
decay rates in an attempt to parameterize a model of NRM-driven
decomposition. We had two main objectives:
<list list-type="order"><list-item>
      <p id="d1e208">Use a novel dataset to evaluate multiple methods of modeling litter
decomposition as a function of NRM.</p></list-item><list-item>
      <p id="d1e212">Determine how important temperature sensitivity is in NRM-driven litter
decomposition models.</p></list-item></list>
Since existing studies examining decomposition under different moisture regimes
are limiting (Jacobson et al., 2015;
Evans et al., 2020), we draw upon literature on soil organic matter
decomposition and rainfall-driven litter decomposition to identify potential
moisture and temperature sensitivity functions (Sierra et
al., 2015). To evaluate models, we conducted a 30-month, multisite litter
decomposition study that spanned an eightfold magnitude of NRM frequency.
By placing litter across this gradient and making continuous meteorological
measurements alongside mass loss, we were able to quantify the relationship
between NRM and litter decay on a multiyear time scale for the first time.
Finally, we used a Bayesian-Monte Carlo approach to parameterize mass loss
models using several temperature and moisture sensitivity functions and used
model selection criteria to identify the best models.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Empirical measurements</title>
      <p id="d1e231">We conducted our study in the central Namib desert in western Namibia. The
Namib desert is a coastal fog desert, with a steep NRM gradient across a
narrow geographic range
(Eckardt et al.,
2013). Rain is scarce in the Namib desert and NRM is expected to be responsible for
the vast majority of litter decomposition (Evans et al.,
2020). We leveraged the FogNet weather array, a network of meteorological
stations throughout the central Namib desert that is part of the Southern
African Science Service Centre for Climate Change and Adaptive Land
Management (SASSCAL; <uri>http://www.sasscalweathernet.org/</uri>, last access: 1 July 2022) and maintained
by the Gobabeb Namib Research Institute (<uri>https://www.gobabeb.org/</uri>, last access: 1 July 2022) (Fig. A1 in the Appendix). Each station measures air temperature, relative humidity, wind speed
and direction, soil temperature, leaf wetness state, rainfall, and fog
precipitation on a Juvik fog screen. The sites are all located within 70 km
of one another but span an order of magnitude in NRM frequency: wet
conditions (fog or dew) occur for 3.1 % of the period (quantified by hours
wet) at the driest site and 25.3 % at the wettest; a   characterization
of meteorology across these sites was part of this study. Weather data were
recorded once per minute and converted to hourly averages for analysis.</p>
      <p id="d1e240">At six sites, we deployed senesced tillers of <italic>Stipagrostis sabulicola</italic> to monitor mass loss. <italic>S. sabulicola</italic> is the
dominant grass in the Namib Sand Sea with widely distributed congenerics
across Africa and Asia
(Roth-Nebelsick et
al., 2012; GrassBase – The Online World Grass Flora, 2021). Since
litter-associated fungal communities can respond differently to NRM based on
their history of exposure to different moisture regimes
(Logan et al., 2021), we collected all tillers from the same
site (Gobabeb) so the initial fungal community would be the same. To avoid
potential microclimate effects of traditional litter bags (Xie,
2020), we measured mass loss by placing tillers in litter racks, custom-made
wooden frames designed to hold grass tillers while keeping them completely
exposed to ambient solar radiation and moisture conditions (Fig. A2)
(Evans et al., 2020; Logan et al., 2021). Every 6 months for 30 months (19 January 2018 to 12 August 2020; 936 days in total),
we collected a subset of 10 tillers at each site and weighed them. Tillers
were destructively harvested at each time point; so in our final dataset,
each tiller was weighed prior to deployment and once again when it was
collected.</p>
      <p id="d1e249">Precolonization is a very important step in standing-litter decomposition
since it can “prime” litter to be more ready to degrade once it reaches
the soil surface; this contributes to changes in litter decay rates over
time. To assess the effects of NRM on litter decomposition throughout the
decay process, we deployed litter at two stages of decay. Categories were
based on previous observations of <italic>S. sabulicola</italic> decay in situ in the Namib desert
(Logan et al., 2021). Early-stage tillers were tillers that
had senesced in the preceding 2 months, had no visible fungal growth, and
had visibly intact cuticles (Fig. A2). Late-stage tillers were harvested
from upright plants that had likely been standing for at least 1 year
post-senescence and were characterized by coverings of light and
dark pigmented fungi and a cracked cuticle that was considerably more
permeable to water. Previous work found similar measures of gross litter
quality (including C <inline-formula><mml:math id="M3" display="inline"><mml:mo>:</mml:mo></mml:math></inline-formula> N ratios, total lignin, and lignin <inline-formula><mml:math id="M4" display="inline"><mml:mo>:</mml:mo></mml:math></inline-formula> N content) between
litter at these two stages, and found that the primary difference between
the two is the level of fungal colonization and state of cuticle
degradation, with late-stage tillers harboring much larger fungal
communities (Logan et al., 2021). Since we only collected
standing grass litter that had not yet fallen over, our terminology of
“early” and “late” does not reflect the entire decomposition process but
is meant to highlight relative successional differences between the litter
stages based on time since senescence and saprophytic community size.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Model description</title>
      <p id="d1e277">To model the effect of NRM on litter decomposition, we began by modeling
decay rates using a simple exponential model of the form:
            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M5" display="block"><mml:mrow><mml:mi>M</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>eff</mml:mtext></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>t</mml:mi></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:mi>M</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is mass at time <inline-formula><mml:math id="M7" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is initial mass, and <inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>eff</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the
effective litter decay constant. This approach captures typical litter decay
dynamics, with a rapid initial decay phase followed by slower mass loss over
time, but does not differentiate between slow and rapid litter pools. We
determined an effective decay rate for each site and litter stage, plotting
this as a function of the total NRM time and accumulated rainfall at that
site.</p>
      <p id="d1e361">This approach, whereby we fit a separate effective decay rate for sites with
different climates, is a common approach to describe how litter
decomposition varies under different climatic conditions
(Zhang et al., 2008). However, because it treats mass loss as
solely dependent on the decay rate and time, this approach does not
explicitly include temperature or moisture. To determine how moisture and
temperature influenced litter decay, we incorporated NRM and temperature
dependence by allowing them to modify an intrinsic litter decay
(<inline-formula><mml:math id="M10" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>int</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> term, which represents the rate of litter decay under ideal,
non-limiting conditions according to
            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M11" display="block"><mml:mrow><mml:mi>M</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>int</mml:mtext></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>t</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>h</mml:mi><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>g</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M12" display="inline"><mml:mrow><mml:mi>h</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:mi>g</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are sensitivity functions for NRM and temperature,
respectively. Unlike the simple model described by Eq. (1), in this
model, the litter decay rate (<inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>int</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the maximum rate under ideal
temperature and moisture conditions, which is then modified downward by the
sensitivity functions (with the exception of <inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> temperature
sensitivity function that allows increasing decomposition above a reference
temperature); see next section for sensitivity functions. This allowed us to
test specific hypothesized relationships between moisture and litter decay
rates, both within and between sites depending on how we choose to fit the
parameters (i.e., separate fits for each site or global parameter estimates).
Using a one-pool model allowed us to simplify the intrinsic decay component
of the model and focus on the effect of different temperature and moisture
sensitivities. We discretized the model using hourly meteorological data,
calculating the rate of mass loss for each hour as:
            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M16" display="block"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mi>t</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi>k</mml:mi><mml:mtext>int</mml:mtext></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>g</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi>h</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Sensitivity functions</title>
      <p id="d1e561">Since litter decomposition can occur in response to dew and fog
(Jacobson et al., 2015) or water vapor under
humid conditions even in the absence of liquid water
(Dirks et al., 2010), we tested separate sensitivity
functions based on either relative humidity levels, or based on a
measurement of the presence of liquid water. Sensitivity functions are
presented in Table 1 and shown in Fig. 1. The threshold model is binary,
allowing decomposition to happen at the intrinsic litter decay rate if and
only if relative humidity is above a specified threshold (<inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>T</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. This
simple approach has yielded mass loss estimates similar to those previously measured in the field (Evans et al., 2020). To account for
possible saturation at high relative humidities, we also evaluated a
logistic sensitivity model that allows the rate of decomposition potential
to slow as relative humidity approaches 100 %. The exponential moisture
model allows decomposition rates to increase exponentially with relative
humidity, reflecting the relationship between litter moisture content and
relative humidity that is often seen in both controlled
(Tschinkel, 1973) and field conditions (Dirks
et al., 2010). Each moisture sensitivity function was normalized to 1 when
relative humidity was 100 %. Finally, we tested a fourth function based on
the presence or absence of moisture as measured by a leaf wetness sensor, in
which decomposition occurred at the intrinsic decay rate when the wetness
sensors were wet and not at all when conditions were dry. Previous work
showed that relative humidity can accurately predict leaf wetness state
(Sentelhas
et al., 2008; Evans et al., 2020), so we expected this model to perform
similarly to the threshold model.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e579">Temperature and NRM sensitivity functions included in the
models. Each curve shows one parameter combination chosen by random
sampling using a normal distribution around a specified set of priors as
identified in Table 2 (<inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">895</mml:mn></mml:mrow></mml:math></inline-formula> 230 total combinations). The
wetness moisture function has no parameter and is simply the proportion of
time during each hour that the leaf wetness sensor detected the presence of
moisture.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022-f01.png"/>

        </fig>

      <p id="d1e600">To model temperature dependence, we tested two common temperature
sensitivity functions: a <inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> model and a Gaussian distribution.
<inline-formula><mml:math id="M20" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> sensitivity is a monotonically increasing function that is used to
model many biological process including litter decomposition
(Sierra et al., 2015). Each increase of 10 <inline-formula><mml:math id="M21" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C above
a reference temperature (<inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>ref</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, often the site's mean temperature),
results in an acceleration of the process in question by a given amount,
called the <inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> coefficient. To account for possible negative
temperature dependence above an optimum temperature (<inline-formula><mml:math id="M24" 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>, we also
tested a Gaussian temperature sensitivity function. A Gaussian function is
often particularly well suited for describing aggregated responses of entire
communities (Low-Décarie et al., 2017), as is the case
for the fungal communities on our tillers (Logan et al.,
2021). Temperature sensitivity was normalized to 1 at <inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>opt</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> in the
Gaussian model and <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>ref</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> in the <inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> model. We tested each
combination of moisture and temperature functions (as well as moisture-only
and temperature-only versions) for a total of 15 different model structures
and 895 230 model-parameter combinations.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e707">Moisture and temperature sensitivity functions. The first
three moisture functions are based on relative humidity and the fourth is
based on leaf wetness state. Moisture functions are normalized to 1 at
100 % relative humidity and temperature sensitivity functions are
normalized to 1 at <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>ref</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and
<inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>opt</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. “RH” is relative humidity.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="120pt"/>
     <oasis:colspec colnum="4" colname="col4" align="justify" colwidth="150pt"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Class</oasis:entry>
         <oasis:entry colname="col2">Name</oasis:entry>
         <oasis:entry colname="col3">Model</oasis:entry>
         <oasis:entry colname="col4">Parameters</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Moisture</oasis:entry>
         <oasis:entry colname="col2">Threshold</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M30" display="inline"><mml:mi>h</mml:mi></mml:math></inline-formula>(RH) <inline-formula><mml:math id="M31" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> if (RH <inline-formula><mml:math id="M32" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>T</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>T</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M35" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> relative humidity threshold</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Moisture</oasis:entry>
         <oasis:entry colname="col2">Exponential</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M36" display="inline"><mml:mi>h</mml:mi></mml:math></inline-formula>(RH) <inline-formula><mml:math id="M37" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">2</mml:mn><mml:mfrac><mml:mrow><mml:mn mathvariant="normal">100</mml:mn><mml:mo>-</mml:mo><mml:mtext>RH</mml:mtext></mml:mrow><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mn mathvariant="normal">0.5</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:mfrac></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mn mathvariant="normal">0.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M40" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> RH value at half saturation point</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Moisture</oasis:entry>
         <oasis:entry colname="col2">Logistic</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M41" display="inline"><mml:mi>h</mml:mi></mml:math></inline-formula>(RH) <inline-formula><mml:math id="M42" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M43" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mi>r</mml:mi></mml:msup><mml:mo>(</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mn mathvariant="normal">0.5</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mn mathvariant="normal">100</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mi>r</mml:mi></mml:msup><mml:mo>(</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mn mathvariant="normal">0.5</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:mtext>RH</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M44" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M45" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> logistic growth rate <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mn mathvariant="normal">0.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M47" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> RH value at half saturation point</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Moisture</oasis:entry>
         <oasis:entry colname="col2">Wetness</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M48" display="inline"><mml:mi>h</mml:mi></mml:math></inline-formula>(LWS) <inline-formula><mml:math id="M49" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> leaf wetness state</oasis:entry>
         <oasis:entry colname="col4">None</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Temp.</oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> model</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:mi>g</mml:mi><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msubsup><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mtext>ref</mml:mtext></mml:msub><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> coefficient <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>ref</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M54" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> reference temperature</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Temp.</oasis:entry>
         <oasis:entry colname="col2">Gaussian</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:mi>g</mml:mi><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn><mml:msup><mml:mfenced open="(" close=")"><mml:mfrac><mml:mrow><mml:mi>T</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mtext>opt</mml:mtext></mml:msub></mml:mrow><mml:mtext>SD</mml:mtext></mml:mfrac></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">SD <inline-formula><mml:math id="M56" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> standard deviation <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>opt</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M58" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> optimal temperature</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e1223">To understand the nature of the different models and compare them across a
range of conditions, we performed two model runs. First, we explored a large
parameter space to determine how parameters interact with one another across
a wide range of hypothetical conditions. This included parameter values
outside of realistic ranges (for example, relative humidity thresholds from
5 % to 99 % and an intrinsic litter turnover time from 0.1 to 100 years). This
allowed us to see how parameters interacted with each other within the
different models and explore general properties of each model. Next, to
assess which models performed best under realistic conditions, we
constrained the parameter space to more accurately reflect real world
parameter values. For this model run, we determined optimal values for each
parameter based on laboratory and field incubations and then randomly varied
parameter combinations around these values; see next section for details.
Parameter definitions as well as constrained values used in the second model
run are reported in Table 2. Figure 1 shows the range of temperature and
moisture sensitivities we used in the constrained model run.</p>
      <p id="d1e1226">We used the Akaike information criterion (AIC) to compare the constrained
models to one another to determine which was the best fit to the data. AIC
is a model selection criterion that rewards goodness of fit based on a log
likelihood function while penalizing models with greater parameters to
reduce overfitting biases (Aho et al., 2014). We report AIC
values for all combinations of models from the constrained parameter run to
compare model performance under realistic scenarios.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e1232">Parameter definitions and values used to constrain the
second model run to realistic conditions. Values were randomly varied around
means and standard deviations shown, with “<inline-formula><mml:math id="M59" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula>” denoting the number of
iterations used for each parameter (<inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">895</mml:mn></mml:mrow></mml:math></inline-formula> 230 total
model-parameter combinations). For <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>opt</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, and SD, models were run with two standard
deviations (i.e., twice the value shown below).</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="justify" colwidth="58pt"/>
     <oasis:colspec colnum="2" colname="col2" align="justify" colwidth="112pt"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="80pt"/>
     <oasis:colspec colnum="4" colname="col4" align="justify" colwidth="60pt"/>
     <oasis:colspec colnum="5" colname="col5" align="justify" colwidth="123pt"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Parameter</oasis:entry>
         <oasis:entry colname="col2">Definition</oasis:entry>
         <oasis:entry colname="col3">Model (type)</oasis:entry>
         <oasis:entry colname="col4">Value</oasis:entry>
         <oasis:entry colname="col5">Justification</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Log<inline-formula><mml:math id="M63" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:math></inline-formula> turnover time (<inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">Intrinsic turnover time (i.e., <?xmltex \hack{\hfill\break}?>turnover time under ideal temperature and moisture conditions)</oasis:entry>
         <oasis:entry colname="col3">All</oasis:entry>
         <oasis:entry colname="col4">1 <inline-formula><mml:math id="M65" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1 year <?xmltex \hack{\hfill\break}?>(<inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">Estimated from maximum <?xmltex \hack{\hfill\break}?>respiration rate from previous <?xmltex \hack{\hfill\break}?>studies</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"><inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>ref</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Reference temperature for <?xmltex \hack{\hfill\break}?> <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>  function</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (temp)</oasis:entry>
         <oasis:entry colname="col4">12.3 <inline-formula><mml:math id="M70" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C</oasis:entry>
         <oasis:entry colname="col5">Mean temperature when wet</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"><inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2"><inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> sensitivity</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (temp)</oasis:entry>
         <oasis:entry colname="col4">2.38 <inline-formula><mml:math id="M74" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.292 <inline-formula><mml:math id="M75" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C <?xmltex \hack{\hfill\break}?>(<inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">Temperature incubations (Fig. 2)</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"><inline-formula><mml:math id="M77" 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="col2">Optimum temperature for <?xmltex \hack{\hfill\break}?>Gaussian distribution</oasis:entry>
         <oasis:entry colname="col3">Gaussian (temp)</oasis:entry>
         <oasis:entry colname="col4">29.7 <inline-formula><mml:math id="M78" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2.37 <inline-formula><mml:math id="M79" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C <?xmltex \hack{\hfill\break}?>(<inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">Temperature incubations (Fig. 2)</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">SD</oasis:entry>
         <oasis:entry colname="col2">SD around <inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mtext>opt</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> for <?xmltex \hack{\hfill\break}?>Gaussian distribution</oasis:entry>
         <oasis:entry colname="col3">Gaussian (temp)</oasis:entry>
         <oasis:entry colname="col4">6.59 <inline-formula><mml:math id="M82" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 3.02 <inline-formula><mml:math id="M83" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C <?xmltex \hack{\hfill\break}?>(<inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">Temperature incubations (Fig. 2)</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"><inline-formula><mml:math id="M85" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mn mathvariant="normal">0.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">RH value where moisture <?xmltex \hack{\hfill\break}?>sensitivity is 50 % of maximum</oasis:entry>
         <oasis:entry colname="col3">Exponential, <?xmltex \hack{\hfill\break}?>logistic (NRM)</oasis:entry>
         <oasis:entry colname="col4">90 <inline-formula><mml:math id="M86" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 10 % <?xmltex \hack{\hfill\break}?>(<inline-formula><mml:math id="M87" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">Range of humidity conditions <?xmltex \hack{\hfill\break}?>during which NRM typically<?xmltex \hack{\hfill\break}?>occurs (Evans et al., 2020)</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"><inline-formula><mml:math id="M88" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>T</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">RH value above which <?xmltex \hack{\hfill\break}?>decomposition is “on”</oasis:entry>
         <oasis:entry colname="col3">Simple threshold <?xmltex \hack{\hfill\break}?>(NRM)</oasis:entry>
         <oasis:entry colname="col4">90 <inline-formula><mml:math id="M89" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 10 % <?xmltex \hack{\hfill\break}?>(<inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">Range of humidity conditions <?xmltex \hack{\hfill\break}?>during which NRM typically <?xmltex \hack{\hfill\break}?>occurs (Evans et al., 2020)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M91" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">Rate of logistic growth <?xmltex \hack{\hfill\break}?></oasis:entry>
         <oasis:entry colname="col3">Logistic (NRM)</oasis:entry>
         <oasis:entry colname="col4">1 <inline-formula><mml:math id="M92" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1 <?xmltex \hack{\hfill\break}?>(<inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">Smaller values approximated a <?xmltex \hack{\hfill\break}?>straight line; higher values resembled the simple threshold model</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><title>Constraining parameter space</title>
      <p id="d1e1806">We parameterized the models using a brute force approach where we randomized
parameter inputs to represent conditions seen in the field (Table 2) and
then selected the model-parameter combinations with the lowest AIC scores.
To constrain temperature parameters, we performed a laboratory incubation of <italic>S. sabulicola</italic>
tillers. We varied the temperature from 10 to 35 <inline-formula><mml:math id="M94" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C in 5 <inline-formula><mml:math id="M95" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C
steps, allowing litter to equilibrate for 60 min before measuring
respiration. We sprayed eight tillers with sterile deionized water until
they were saturated to stimulate fungal activity and placed them in 55 mL
acrylic tubes connected to a LI-8100A gas analyzer (LI-COR Biosciences,
Lincoln, NE, USA), measuring mean flux during 3 min incubations. To
measure the response of the specific fungal communities associated with
litter used in the field study, all tillers used in the laboratory incubation were
collected at Gobabeb, the same site where litter in the mass loss experiment
was collected.</p>
      <p id="d1e1830">To calculate <inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, we excluded the measurements at 35 <inline-formula><mml:math id="M97" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (when
response becomes negative) and then used the <inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> function in the
<italic>respirometry</italic> package in R to calculate a separate <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> value for each tiller
(Birk, 2021; R Core Team, 2020). For the reference
temperature, we used the mean temperature when leaf wetness sensors were
“wet” across all sites (12.3 <inline-formula><mml:math id="M100" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C). This value was fairly constant
among sites, varying by less than 0.9 <inline-formula><mml:math id="M101" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (Fig. A3). For the
Gaussian temperature sensitivity parameters, we used the “optim” function in
R to find the optimum temperature (<inline-formula><mml:math id="M102" 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> and standard deviation (SD)
around the optimum after normalizing flux rates to the maximum rate measured
for each tiller (R Core Team, 2020).</p>
      <p id="d1e1910">The turnover time represents the litter's intrinsic decay rate under ideal
temperature and moisture conditions and is equivalent to the inverse of
<inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>int</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, the exponential parameter in the decay function. To place a lower
boundary on this value, we examined previous studies that measured
respiration from <italic>S. sabulicola</italic> under wet conditions and extrapolated to estimate a
minimum turnover time (in years) under ideal, non-limiting conditions.
Jacobson et al. (2015) reported respiration
rates from wet <italic>S. sabulicola</italic> tillers as high as 1.5 <inline-formula><mml:math id="M104" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>g CO<inline-formula><mml:math id="M105" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>-C g<inline-formula><mml:math id="M106" 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> L h<inline-formula><mml:math id="M107" 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>, corresponding to an intrinsic turnover time of <inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.63</mml:mn></mml:mrow></mml:math></inline-formula> years, assuming 50 % of plant litter mass is carbon. This is within
the range of intrinsic turnover rates reported for other grasses
(Zhang et al., 2008). We therefore used a turnover time with a
mean of 1 year around a log-normal distribution. We varied the logistic
growth parameter (<inline-formula><mml:math id="M109" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula>) of the logistic moisture sensitivity function around a
value of 1, because at much lower values it began to resemble a straight line
(i.e., no longer logistic sensitivity) and at higher values it converged on
the simple threshold model.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Meteorological conditions and temperature incubations</title>
      <p id="d1e2005">Moisture conditions varied substantially among the sites. Duration of
wetness during the study period (as determined by leaf wetness sensors)
ranged from 672 h (3.1 % of total hours) at the driest site (Garnet
Koppie) to 5672 h (25.3 % of total hours) at the wettest site
(Kleinberg). Drier sites tended to be warmer; mean temperature when dry was
2.3 <inline-formula><mml:math id="M110" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C warmer at the warmest site (Garnet Koppie) than at the
coolest site (Kleinberg) (Table 3). Temperatures during NRM events were
lower and less variable than temperatures during dry periods (Table 3). Wet
conditions almost never occurred when temperatures were above 20 <inline-formula><mml:math id="M111" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C at any site (Fig. A3). Average relative humidity differed among the sites
and was correlated with hours of wetness. Rainfall occurred at all sites
during the study period, ranging from 26.4–64.2 mm, but did not correlate
with NRM frequency. The optimum temperature for respiration in the
incubations was 30 <inline-formula><mml:math id="M112" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C, with flux rate dropping at 35 <inline-formula><mml:math id="M113" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C
(Fig. 2).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e2046">Temperature sensitivity of respiration from
<italic>S. sabulicola</italic> tillers in a laboratory incubation, used
to constrain temperature parameters (mean <inline-formula><mml:math id="M114" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1 S.E.M., <inline-formula><mml:math id="M115" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:math></inline-formula>). Flux rate is normalized to the rate at 30 <inline-formula><mml:math id="M116" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C. Tillers were
sprayed with deionized water until saturated and respiration was measured at
5 <inline-formula><mml:math id="M117" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C intervals.</p></caption>
          <?xmltex \igopts{width=227.622047pt}?><graphic xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022-f02.png"/>

        </fig>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3" specific-use="star"><?xmltex \currentcnt{3}?><label>Table 3</label><caption><p id="d1e2098">Summary of meteorological conditions at each site during
the study showing mean temperature when dry, mean temperature when wet, wet
hours during the entire study period (as determined by leaf wetness
sensors), the proportion of total time when conditions were wet, accumulated
rainfall during the study period, and mean relative humidity throughout the
study period. Temperature ranges in parentheses report the middle 95 % of
data. Mean temperatures apply to the time period used in this study but
should not be used to infer mean annual temperatures for each site since the
study lasted 2.5 years and therefore data from January–August are represented more
than September–December. Full names for sites are included in Fig. A1.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="7">
     <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:thead>
       <oasis:row>
         <oasis:entry colname="col1">Site</oasis:entry>
         <oasis:entry colname="col2">Temp<inline-formula><mml:math id="M118" display="inline"><mml:msub><mml:mi/><mml:mtext>dry</mml:mtext></mml:msub></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col3">Temp<inline-formula><mml:math id="M119" display="inline"><mml:msub><mml:mi/><mml:mtext>wet</mml:mtext></mml:msub></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">Wet hours</oasis:entry>
         <oasis:entry colname="col5">Proportion of time wet</oasis:entry>
         <oasis:entry colname="col6">Rain</oasis:entry>
         <oasis:entry colname="col7">Mean relative humidity</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">(<inline-formula><mml:math id="M120" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)</oasis:entry>
         <oasis:entry colname="col3">(<inline-formula><mml:math id="M121" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)</oasis:entry>
         <oasis:entry colname="col4">(h)</oasis:entry>
         <oasis:entry colname="col5">(%)</oasis:entry>
         <oasis:entry colname="col6">(mm)</oasis:entry>
         <oasis:entry colname="col7">(%)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">GK</oasis:entry>
         <oasis:entry colname="col2">22.4 (12.67–32.34)</oasis:entry>
         <oasis:entry colname="col3">12.2 (6.88–19.17)</oasis:entry>
         <oasis:entry colname="col4">674</oasis:entry>
         <oasis:entry colname="col5">3.0 %</oasis:entry>
         <oasis:entry colname="col6">61.8</oasis:entry>
         <oasis:entry colname="col7">37.5</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">GB</oasis:entry>
         <oasis:entry colname="col2">22.2 (11.35–33.42)</oasis:entry>
         <oasis:entry colname="col3">12.4 (6.24–17.91)</oasis:entry>
         <oasis:entry colname="col4">1645</oasis:entry>
         <oasis:entry colname="col5">7.3 %</oasis:entry>
         <oasis:entry colname="col6">64.2</oasis:entry>
         <oasis:entry colname="col7">44.8</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">S8</oasis:entry>
         <oasis:entry colname="col2">21.4 (10.92–32.49)</oasis:entry>
         <oasis:entry colname="col3">11.7 (5.66–17.4)</oasis:entry>
         <oasis:entry colname="col4">1930</oasis:entry>
         <oasis:entry colname="col5">8.6 %</oasis:entry>
         <oasis:entry colname="col6">26.4</oasis:entry>
         <oasis:entry colname="col7">46.9</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">VF</oasis:entry>
         <oasis:entry colname="col2">21.7 (11.75–32.37)</oasis:entry>
         <oasis:entry colname="col3">12 (6.34–16.38)</oasis:entry>
         <oasis:entry colname="col4">2214</oasis:entry>
         <oasis:entry colname="col5">9.9 %</oasis:entry>
         <oasis:entry colname="col6">33.7</oasis:entry>
         <oasis:entry colname="col7">50.2</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MK</oasis:entry>
         <oasis:entry colname="col2">22 (12.73–32.09)</oasis:entry>
         <oasis:entry colname="col3">12.6 (8.00–16.59)</oasis:entry>
         <oasis:entry colname="col4">2810</oasis:entry>
         <oasis:entry colname="col5">12.5 %</oasis:entry>
         <oasis:entry colname="col6">44.5</oasis:entry>
         <oasis:entry colname="col7">53.6</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">KB</oasis:entry>
         <oasis:entry colname="col2">20.1 (11.01–30.91)</oasis:entry>
         <oasis:entry colname="col3">12.4 (6.69–17.07)</oasis:entry>
         <oasis:entry colname="col4">5672</oasis:entry>
         <oasis:entry colname="col5">25.3 %</oasis:entry>
         <oasis:entry colname="col6">56.6</oasis:entry>
         <oasis:entry colname="col7">67.7</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Litter mass loss</title>
      <p id="d1e2369">In general, mass loss was greater at sites with more NRM
and lower at sites with less NRM (Figs. 3, A7). There was a significant
three-way interaction between litter stage, site, and time (Table A1 in Appendix).
Within each site, early-stage and late-stage litter decomposed at comparable
rates for the first 18 months, but diverged after that depending on the site
(Fig. 3). After 24 months at the 2 driest sites, early-stage litter lost
more mass than late-stage litter. At the four wettest sites however,
late-stage litter experienced the greater mass loss (Fig. 3).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e2374">Mass loss for early-stage (yellow) and late-stage (gray)
tillers at each site (mean <inline-formula><mml:math id="M122" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1 S.E.M.). Percentage values in the
bottom of each panel show the average proportion of time throughout the
study period that the site has liquid water, as determined by a leaf wetness
sensor. Note: tillers did not actually increase in mass; the apparent
increase at some time points in some panels is merely a result of variation
among tillers, since we destructively harvested tillers at each time point
and could therefore not take repeated measurements of each tiller.</p></caption>
          <?xmltex \igopts{width=327.206693pt}?><graphic xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022-f03.png"/>

        </fig>

      <p id="d1e2390">When we used a simple exponential decay model without temperature and
moisture sensitivity (Eq. 1), the effective decay rate at each site was
correlated with NRM duration but not with accumulated rainfall (Fig. 4).
Late-stage litter (i.e., tillers with more well-established fungal
communities) responded more strongly to NRM than did early-stage litter; for
every additional 1000 h of wetness at a site, the effective decay rate
increased by 0.0043 yr<inline-formula><mml:math id="M123" 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 early-stage litter and 0.014 yr<inline-formula><mml:math id="M124" 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
late-stage litter (Fig. 4).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e2420">Effective decay rate calculated without explicit
temperature or NRM sensitivity (Eq. 1) relative to NRM frequency and
accumulated rainfall during the study period. Among sites, decay rate
constant was strongly correlated with the proportion of time that a site
experienced NRM conditions (early-stage: <inline-formula><mml:math id="M125" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.87</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M126" display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.007</mml:mn></mml:mrow></mml:math></inline-formula>, slope <inline-formula><mml:math id="M127" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:mn mathvariant="normal">4.311</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">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>; late-stage: <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.80</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.02</mml:mn></mml:mrow></mml:math></inline-formula>, slope <inline-formula><mml:math id="M131" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:mn mathvariant="normal">1.421</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) but was uncorrelated with total rainfall
(early-stage: <inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M134" display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.87</mml:mn></mml:mrow></mml:math></inline-formula>; late-stage: <inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.14</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M136" display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.46</mml:mn></mml:mrow></mml:math></inline-formula>).</p></caption>
          <?xmltex \igopts{width=176.407087pt}?><graphic xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022-f04.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Model parameter space exploration</title>
      <p id="d1e2597">For the three NRM sensitivity functions based on relative humidity,
parameter values showed a tradeoff between turnover time and RH thresholds
(Fig. 5): parameter combinations with the lowest AIC scores featured either
slow turnover times and a low RH threshold (bottom right of plots) or faster
turnover times and high RH thresholds (upper middle of plots). When we fit
parameters separately for each site instead of globally, AIC values
improved, but the actual values of the best parameter combinations did not
change (Fig. A4). Similarly, fitting parameters separately to early-stage and
late-stage tillers did not produce different optimal parameter values (Fig. A5).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e2602">Parameter fits for the first model run showing parameter
combinations across a wide range of hypothetical conditions. <bold>(a)</bold> The
three humidity-based NRM functions showing the relationship between turnover
time (<inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>int</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) and relative humidity
threshold (<inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>T</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mn mathvariant="normal">0.5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>). Colors
represent log<inline-formula><mml:math id="M140" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:math></inline-formula> AIC scores; models with better fit to
the data have lower scores. <bold>(b)</bold> Parameter estimation for the leaf
wetness-based moisture function showing log<inline-formula><mml:math id="M141" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:math></inline-formula> AIC as a
function of turnover time (<inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>int</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>).
Plots have different numbers of points because of different numbers of
temperature parameters that were tested (the Gaussian temperature function
has two, the <inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>  function has one, and the bottom
plot has no temperature parameters, only early-stage and late-stage tiller
combinations).</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022-f05.png"/>

        </fig>

      <p id="d1e2699">Models that included <inline-formula><mml:math id="M144" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> temperature sensitivity converged on slower
intrinsic decay rates (i.e., longer turnover times) than those using a
Gaussian temperature sensitivity or temperature-independent model (Fig. 5).
The wetness sensitivity functions yielded an optimal litter turnover time of
2.5 years under a moisture-only and <inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> temperature sensitivity model
(Fig. 5). Using a Gaussian temperature sensitivity yielded a faster intrinsic
decay with an optimal turnover time of 0.5–1.5 years.</p>
</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><title>Model performance comparison</title>
      <p id="d1e2732">Models that included NRM sensitivity had better fits than the simple
litter decay model, but the best models included both NRM and temperature
sensitivity (Fig. 6). While model fit improved (AIC scores were lower)
whenever NRM sensitivity was included, the degree to which NRM sensitivity
improved the model fit depended on the temperature sensitivity function. In
particular, models with Gaussian temperature sensitivity performed better
than those with <inline-formula><mml:math id="M146" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> sensitivity or no temperature sensitivity, a
finding consistent with the fall off in decay seen in the incubations (Fig. 2). Surprisingly, after controlling for temperature response, each of the
four moisture functions had similar AIC scores, with no single moisture
model performing appreciably better than the others (Fig. 6).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e2748">Frequency distribution of model performance
(log<inline-formula><mml:math id="M147" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:math></inline-formula> AIC scores) for each model combination of
temperature and moisture sensitivities. Each observation represents one
parameter combination after constraining as described in Table 2. Lower
log<inline-formula><mml:math id="M148" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:math></inline-formula> AIC scores denote better model fit to the data.
This figure only shows models constrained using realistic parameter
estimates described in Table 2 (<inline-formula><mml:math id="M149" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">895</mml:mn></mml:mrow></mml:math></inline-formula> 230).</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022-f06.png"/>

        </fig>

      <p id="d1e2787">Including temperature sensitivity alone (without NRM) did not improve model
fit as well as modeling only NRM sensitivity (without temperature). All of
the NRM-only models (Fig. 6, bottom row) had better fits than temperature-only models (Fig. 6, right column), although each showed a wide
range depending on the specific parameter combinations. In fact, an
unconstrained model with <inline-formula><mml:math id="M150" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> temperature sensitivity but no moisture
sensitivity converged on an optimal <inline-formula><mml:math id="M151" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> value <inline-formula><mml:math id="M152" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>, indicating a
negative temperature dependence of litter decomposition (Fig. A6), the
opposite of what we observed in the temperature incubations.</p>
      <p id="d1e2823">When we compared one of the best models that included temperature and NRM
sensitivity (specifically, a Gaussian temperature function and an
exponential moisture function) to a simple decay model that had no
temperature or NRM sensitivity but varied effective decay rate among sites
(Eq. 1), we found that the temperature and NRM model performed better
(Fig. 7). The Gaussian exponential model had lower AIC scores and the slope
of the observed vs. predicted values was closer to 1, yielding more
realistic mass loss predictions (0.85 for Gaussian exponential model, 0.71
for simple decay model).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e2828"><bold>(a)</bold> Fit of the model using Gaussian temperature
sensitivity and exponential moisture sensitivity vs. a simple exponential
decay model (without temperature or NRM sensitivity) in which
<inline-formula><mml:math id="M153" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>eff</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is allowed to vary
independently for each site (lower log<inline-formula><mml:math id="M154" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:math></inline-formula> AIC scores
denote better model fits). The simple decay model depicted here differs from
the one in Fig. 6 because this one uses
<inline-formula><mml:math id="M155" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>eff</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>  and is not constrained to the
same set of parameters. <bold>(b, c)</bold> Model  predictions for
the best version of the Gaussian exponential model versus the simple decay
model with site-specific <inline-formula><mml:math id="M156" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>eff</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values. Solid lines are the best fit lines and dotted lines are the ideal
<inline-formula><mml:math id="M157" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> line.</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022-f07.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Discussion</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Model performance</title>
      <p id="d1e2913">Decomposition is a crucial component of Earth system models and NRM is an
important moisture source in arid and mesic grasslands worldwide. In a first
attempt at modeling NRM-driven decomposition, Evans et al. (2020) compared litter decay rates in a hyperarid and a
mesic grassland, showing that decay rates are faster when NRM is more
frequent. We build on this work by demonstrating a scalable quantification
of the relationship between NRM, temperature, and litter decay rates. Doing
so is an important step to improving Earth system models, which must be
validated with field measurements made under realistic conditions
(Bonan et al., 2013). Using a 30-month, multisite field
experiment, we show that explicitly accounting for both temperature and
NRM sensitivity improved a litter decay model in an
NRM-affected system.</p>
      <p id="d1e2916">While incorporating either NRM sensitivity or temperature dependence
improved model performance, it was the inclusion of both that led to the
largest improvement. Decomposition temperature sensitivity often depends
on moisture conditions (Petraglia et al., 2019). For example,
in soils, temperature typically increases decay rates when moisture is
abundant, but higher temperatures can dry out soils, slowing decomposition
(Bear et al., 2014). Similarly, in our system, NRM
increases litter moisture content (Jacobson et
al., 2015), but fog and dew only form at cooler temperatures, when
decomposition is slower; once temperatures get high enough (in this case,
above 20 <inline-formula><mml:math id="M158" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C; Fig. A3), wet conditions soon cease, making the
positive effects of temperature moot. We find that this nuance about NRM
gives rise to unrealistic predictions when models include only one type of
sensitivity but not the other. For example, in our unconstrained model run,
a model with only temperature dependence, but no NRM sensitivity, converged
on a <inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> temperature sensitivity <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>, indicating negative
temperature dependence (Fig. A6), even though incubation data clearly show a
positive relationship across the range of conditions tillers experience in
the field (Fig. 2). This shows that both temperature and NRM sensitivity were
needed to realistically capture litter decay dynamics under NRM conditions,
lest one mask the effects of the other, yielding unrealistic results.</p>
      <p id="d1e2949">The choice of temperature sensitivity function is often very important in
modeling biological processes and can lead to quite different predictions
(Low-Décarie et al., 2017). We found that model
performance was better using a Gaussian rather than a <inline-formula><mml:math id="M161" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> temperature
sensitivity function. Surprisingly, we found that the different NRM
sensitivity functions, including both continuous and threshold functions,
described litter decay dynamics similarly well. While the threshold,
logistic, and wetness moisture sensitivity functions share a general form in
which decomposition rates increase substantially above a specific relative
humidity value, the exponential function simulates gradually increasing
decay rates at different relative humidity values. In this sense, the
exponential function more accurately mimics the moisture absorption curves
seen in field and laboratory studies (Dirks et al.,
2010; Evans et al., 2020; Tschinkel, 1973). Despite these differences,
however, each of these functions led to similar model performance. This
suggests that while explicitly including sensitivity to NRM is important,
the specific manner in which moisture is represented in the model may be
less important. NRM-explicit litter decay models in the future may be able
to represent NRM with fewer parameters by adopting a simple threshold
approach, eliminating the need to parameterize multiple moisture components.
Since relative humidity is a standard meteorological measure (unlike leaf
wetness), future models should be able to use existing data sources to
incorporate NRM, eliminating the need to collect additional data with
specialized instrumentation (Evans et al., 2020).</p>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Litter properties</title>
      <p id="d1e2971">By deploying both recently senesced and precolonized litter, we were able
to study the effect of NRM on litter decomposition at early and late stages
in the decay process. The fact that early-stage litter decomposed faster
than late-stage litter at the two driest sites is likely because early in
the decay process decomposer communities are small and photodegradation of
the cuticle is a more important contributor to mass loss than microbial
decomposition (Logan et al., 2022). As a result,
decomposition becomes more sensitive to moisture later in the decay process.
Once fungal communities were well established (as on later-stage tillers),
litter decomposition was more sensitive to moisture availability, which is
why late-stage tillers decomposed faster at the wetter sites (Fig. 3). By
deploying litter at different stages of decay across a wide moisture
gradient, we showed that sensitivity of litter decomposition to NRM appears
to increase over time.</p>
      <p id="d1e2974">Surprisingly, early-stage and late-stage litter had similar relative humidity
thresholds for decomposition even though older litter tends to absorb more
water during fog and dew events (Logan et al., 2022). In the
absence of rain, litter moisture content rarely reaches biologically
significant levels until relative humidity reaches at least 70 %–80 %
(Dirks et al., 2010; Evans et al., 2020;
Tschinkel, 1973), but this depends on several factors including the
permeability of the litter to water, the amount of time it spends in humid
conditions, and the decomposer community's sensitivity to moisture
(Tschinkel, 1973; Logan et al., 2021, 2022). While
the simple threshold-based moisture function performed very well in this
study, future studies will likely need to parameterize the moisture
threshold to fit the dominant litter type in their locales.</p>
      <p id="d1e2977">Despite converging on the same parameter values, model fits were much better
for late-stage litter than for early-stage litter (Fig. A5). This could
reflect the fact that the larger fungal communities on late-stage tillers
enable them to respond to moisture more strongly than early-stage tillers,
which do not yet have a large enough decomposer community to have a strong
biological response to NRM. This is consistent with the results from our
simple decay model (without explicit temperature and moisture sensitivity),
which showed that effective litter decay rates for late-stage tillers were
3.3 times more sensitive to changes in NRM frequency than early-stage
tillers (Fig. 4). Since the major differences between the early-stage and
late-stage tillers used in this study are their degree of prior fungal
colonization and their ability to absorb water, this reinforces the
importance of fungal communities as mediators of decomposition response to
NRM (Logan et al., 2021) and suggests that plant litter
properties related to moisture absorption may influence NRM sensitivity
(Logan et al., 2022). Examining whether these properties
have the same influence on NRM-driven decay of other plant species may
increase the generalizability of the response functions we present here.</p>
</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Incorporating into existing Earth system models</title>
      <p id="d1e2988">Developing models that realistically predict carbon turnover is a multistep
process that requires determining a model structure, parameterizing, and
accounting for external forcings (Luo et al., 2015). Our goal
was to compare several potential structures for modeling NRM-driven litter
decomposition, but fully incorporating NRM sensitivity into existing Earth
system models will require additional work. This includes identifying the
appropriate temporal resolution at which to model NRM events. The time steps
used by Earth system models have shortened considerably over the last two
decades, to the point where processes that were once represented monthly are
now modeled on hourly time scales or less
(Sokolov et al., 2018; Bolker et al., 1998;
Bonan et al., 2013). We used hourly averages of minute data to describe
decomposition rates, but do not yet know what temporal resolution is
necessary to fully capture NRM events. Future studies can compare estimates
using minute data (that have the benefit of capturing the wetting and drying
dynamics of litter at the start and end of NRM events) to daily time scales,
that can estimate NRM-driven decomposition from daily mean relative
humidity. In the case of longer (daily) time scales, temperature dependence
may be best determined using the minimum daily temperature instead of mean
temperature, since minimum temperatures are likely to occur at night when
NRM is most common. Of course, these methods will require additional
testing, but since our models were relatively insensitive to the specific
nuances of how NRM was modeled, any of several approaches may be appropriate
depending on the structure of the decomposition model in use.</p>
      <p id="d1e2991">We used relative humidity and leaf wetness sensor data to parameterize our
moisture sensitivity functions but other methods of modeling moisture may
work as well. Many ecosystem models treat soil water content (which
regulates soil organic matter decomposition) as related to the ratio of rain
to evapotranspiration (Necpálová et al., 2015). If
NRM-driven decomposition can be captured by proxies constructed from
evaporation, minimum temperature, and other values already included in
carbon submodels, it may be easier to incorporate this novel process into
existing modeling approaches. Fortunately, relative humidity is measured at
meteorological stations worldwide and extensive data are available. Even in
regions with data gaps, methods exist to estimate relative humidity from
temperature datasets (Gunawardhana et al., 2017) and these
can be incorporated into Earth system models to include NRM sensitivity
without the need to collect additional data.</p>
      <p id="d1e2994">While our study focused exclusively on aboveground litter decay, NRM may
have other effects on decomposition later in the decay process as well.
NRM-driven decomposition removes carbon from the system before it reaches
the soil surface, decreasing inputs to belowground pools. Additionally, NRM
may accelerate belowground decomposition rates once litter is incorporated
into the soil by promoting the development of larger (and specialized)
microbial communities early in the decay process
(Logan et al., 2021; Jacobson et al.,
2015). Such soil-litter mixing often increases litter decomposition in
dryland systems
(Barnes et al.,
2015, 2012; Hewins et al., 2013). Even more broadly, there are other
processes for which models ignore the role of NRM that affect carbon
cycling, like stimulating plant growth, and suppressing wildfires
(Weathers, 1999; Emery et al., 2018). To improve our
understanding of NRM-driven decomposition, studies can test the role of
NRM-driven decomposition on both aboveground and belowground litter to
identify how NRM affects linkages between these two pools.</p>
      <p id="d1e2997">NRM's role in litter decay has been observed in a wide range of ecosystems
including Mediterranean shrublands (Gliksman et al.,
2018; Dirks et al., 2010), salt-marshes (Newell et al., 1985),
hyperarid deserts (Logan et al., 2021), and temperate
steppes (Wang et al., 2017). One study found that NRM played
a substantial role even a mesic prairie with mean annual precipitation of
897 mm (Evans et al., 2020), suggesting that NRM is important
even when rainfall is relatively frequent. Our contribution does not therefore demonstrate the importance of NRM to litter decomposition in general, but
shows that the frequency of NRM events strongly predicts litter mass loss
across a wide range of moisture conditions and that this can be easily
modeled using readily available moisture data. Although this study was
conducted at the dry end of an aridity gradient, it still represented an
eightfold magnitude of NRM frequency, showing that NRM can be easily
incorporated into litter decay models. Explicitly incorporating NRM into
models in mesic systems, where rainfall plays a greater role, will likely
require including both rainfall and NRM sensitivity functions to identify
the relative role of each as rainfall increases.</p>
</sec>
<sec id="Ch1.S4.SS4">
  <label>4.4</label><title>Limitations</title>
      <p id="d1e3008">Since our goal was to present a first attempt at incorporating NRM into
litter decay models in an NRM-dominated ecosystem, we had to make several
simplifications that likely underestimated litter decay rates. First, we
only looked at standing dead litter not litter at the soil surface. Standing
litter often decomposes faster than litter lying at the soil surface
(Liu et al., 2015; Gliksman et al., 2018) and represents
an important and, until recently, overlooked source of carbon turnover in
drylands (Wang et al., 2017). While we did not look at litter
at the soil surface, surface litter absorbs atmospheric moisture
(Tschinkel, 1973) and may respond similarly to NRM, although to
date no models we know of have looked at this across a range of NRM
conditions, suggesting important avenues for future work.</p>
      <p id="d1e3011">Secondly, we focused only on coarse tillers not leafy material. In laboratory
incubations, Jacobson et al. (2015) found
that at high humidity the water content of <italic>S. sabulicola</italic> tillers (like those we used)
increased slowly, reaching only 10.5 % after 2 h, with no detectable
CO<inline-formula><mml:math id="M162" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> flux. In contrast, fine leaves reached a moisture content of
30.3 % and exhibited a flux rate of 0.99 <inline-formula><mml:math id="M163" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>g CO<inline-formula><mml:math id="M164" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>-C g L<inline-formula><mml:math id="M165" 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> min<inline-formula><mml:math id="M166" 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> after 2 h. In a field study, Evans et al. (2020) showed that gravimetric moisture content of <italic>S. sabulicola</italic> tillers
could reach 0.35 g H<inline-formula><mml:math id="M167" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O g L<inline-formula><mml:math id="M168" 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> while leafy material could
absorb as much as 1.45 g H<inline-formula><mml:math id="M169" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>O g L<inline-formula><mml:math id="M170" 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> during NRM events,
resulting in considerably higher respiration rates for leaves. Similarly,
windblown detritus (litter that has become physically disconnected from the
plant) makes up a considerable proportion of total litter mass in the Namib desert (Seely and Louw, 1980) and can absorb substantial water under
humid conditions (Tschinkel, 1973). As a result, actual rates of
NRM-driven decomposition across the whole landscape are likely higher than
what we report here.</p>
      <p id="d1e3113">Finally, we focused only on the meteorological drivers of litter
decomposition, although others factors play important roles as well.
Photodegradation (Austin and Vivanco, 2006; King
et al., 2012), macrodetritivore activity (Louw and Seely,
1982), and soil-litter mixing
(Hewins et al., 2013; Lee
et al., 2014) are all important drivers of litter decomposition in drylands.
Since our goal was to quantify the relationship between NRM and litter
turnover, we focused solely on NRM, but future studies can build on this
work by combining our approach with other existing models. For instance,
photodegradation can interact with NRM to accelerate carbon turnover,
especially of standing litter (Wang et al., 2017;
Logan et al., 2022), and accounting for photodegradation improves litter
decay models (Chen et al., 2016; Adair et al.,
2017). Combining these other mechanisms with the relative humidity-based
litter decay model we present here may reveal additional interactions that
can be validated by field studies. The fact that we were able to describe a
large degree of litter decomposition by using a simple relative
humidity-based and temperature-based model, however, demonstrates that NRM
plays an important role in the litter decay process across a wide range of
environmental conditions.</p>
</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions</title>
      <p id="d1e3126">We show that the frequency of NRM is a major predictor of
litter decomposition, and for the first time used data from a multisite
field study to develop temperature and NRM sensitivity functions for a
litter decay model. Temperature and moisture regimes are changing as a
result of anthropogenic climate change (Byrne and O'Gorman,
2016) and our ability to predict how ecosystems respond depends, in part, on
how well we can link biogeochemical cycles to their environmental drivers.
NRM and rainfall are often controlled by different climatic drivers and may
therefore respond differently under future climate change
(Haensler et al., 2011; Dai,
2013; Forthun et al., 2006). By modeling the contribution of NRM to
decomposition, in addition to that of rainfall, we can better predict how
drylands will respond to changing moisture regimes, increasing our ability
to manage these globally important systems.</p>
</sec>

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

<app id="App1.Ch1.S1">
  <?xmltex \currentcnt{A}?><label>Appendix A</label><title/>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.S1.F8"><?xmltex \currentcnt{A1}?><?xmltex \def\figurename{Figure}?><label>Figure A1</label><caption><p id="d1e3141">Location of the six FogNet sites used in this study. All
samples were collected from dunes of the Namib Sand Sea at Gobabeb.
Background image © Google Earth.</p></caption>
        <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022-f08.jpg"/>

      </fig>

<?xmltex \hack{\clearpage}?><?xmltex \floatpos{h!}?><fig id="App1.Ch1.S1.F9"><?xmltex \currentcnt{A2}?><?xmltex \def\figurename{Figure}?><label>Figure A2</label><caption><p id="d1e3153"><bold>(a)</bold> Example of a litter rack used instead of litter bag.
The “rungs” of the “ladders” are <italic>Stipagrostis sabulicola</italic> stems <inline-formula><mml:math id="M171" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> cm in diameter and 9 cm long.
<bold>(b)</bold> Living <italic>S. sabulicola</italic> hummock growing in the
dunes. <bold>(c)</bold> Dead <italic>S. sabulicola</italic> tillers like those
used in this study. <bold>(d)</bold> Close up image of a recently senesced (early-stage)
tiller with intact  cuticles and little fungal growth. <bold>(e)</bold> Close up image of a
late-stage tiller with cracked cuticle surface and substantial colonization
by dark pigmented fungi.</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022-f09.jpg"/>

      </fig>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.S1.F10"><?xmltex \currentcnt{A3}?><?xmltex \def\figurename{Figure}?><label>Figure A3</label><caption><p id="d1e3201">Frequency distributions of temperature when wet (turquoise)
and dry (red) at the six sites during the study.</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022-f10.png"/>

      </fig>

<?xmltex \hack{\clearpage}?><?xmltex \floatpos{h!}?><fig id="App1.Ch1.S1.F11"><?xmltex \currentcnt{A4}?><?xmltex \def\figurename{Figure}?><label>Figure A4</label><caption><p id="d1e3215">Parameter fits for the humidity-based moisture models
using <bold>(a)</bold> global parameters that were fitted across sites, and <bold>(b)</bold> site-specific parameters. Colors represent AIC scores with purple denoting
lower values and yellow denoting higher values. The left panel is identical
to Fig. 3 in the main text.</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022-f11.png"/>

      </fig>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.S1.F12"><?xmltex \currentcnt{A5}?><?xmltex \def\figurename{Figure}?><label>Figure A5</label><caption><p id="d1e3234"><bold>(a)</bold> Parameter fits for the humidity-based models for late-stage litter (left) and early-stage litter (right). Colors represent
AIC scores with purple denoting lower values and yellow denoting higher
values. <bold>(b)</bold> Model fits for the wetness-based models, color-coded by litter
stage (this is identical to the right panel of Fig. 5, but color coded to
show differences in litter stage).</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022-f12.png"/>

      </fig>

<?xmltex \hack{\clearpage}?><?xmltex \floatpos{h!}?><fig id="App1.Ch1.S1.F13"><?xmltex \currentcnt{A6}?><?xmltex \def\figurename{Figure}?><label>Figure A6</label><caption><p id="d1e3254"><bold>(a)</bold> Parameter estimation plot of
<inline-formula><mml:math id="M172" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> coefficient for an
<inline-formula><mml:math id="M173" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>-only model run (i.e., with no NRM sensitivity)
showing model fit is best for <inline-formula><mml:math id="M174" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values below 1. <bold>(b)</bold> Estimated <inline-formula><mml:math id="M175" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> sensitivity curves based on optimal
value determined from <bold>(a)</bold>.</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022-f13.png"/>

      </fig>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.S1.F14"><?xmltex \currentcnt{A7}?><?xmltex \def\figurename{Figure}?><label>Figure A7</label><caption><p id="d1e3320">Photos of litter racks from each
site (from driest on the left to wettest on the right) after 18 months in
the field. The dark color on the racks from the wetter sites is from
dark-pigmented fungal growth on both the tillers and the wooden frames after
exposure to frequent NRM events.</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/19/4129/2022/bg-19-4129-2022-f14.jpg"/>

      </fig>

<?xmltex \floatpos{h!}?><table-wrap id="App1.Ch1.S1.T4"><?xmltex \hack{\hsize\textwidth}?><?xmltex \currentcnt{A1}?><label>Table A1</label><caption><p id="d1e3335">ANOVA table of general mass loss model showing three-way interaction between time, site, and litter stage.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Source</oasis:entry>
         <oasis:entry colname="col2">SS</oasis:entry>
         <oasis:entry colname="col3">D<inline-formula><mml:math id="M176" display="inline"><mml:mi>f</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M177" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M178" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula></oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Days</oasis:entry>
         <oasis:entry colname="col2">1.46 <inline-formula><mml:math id="M179" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M180" 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="col3">1</oasis:entry>
         <oasis:entry colname="col4">19.3</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M181" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.001</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Site</oasis:entry>
         <oasis:entry colname="col2">1.72 <inline-formula><mml:math id="M182" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M183" 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="col3">5</oasis:entry>
         <oasis:entry colname="col4">0.454</oasis:entry>
         <oasis:entry colname="col5">0.81</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Litter Stage</oasis:entry>
         <oasis:entry colname="col2">2.51 <inline-formula><mml:math id="M184" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M185" 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></oasis:entry>
         <oasis:entry colname="col3">1</oasis:entry>
         <oasis:entry colname="col4">0.331</oasis:entry>
         <oasis:entry colname="col5">0.57</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Days <inline-formula><mml:math id="M186" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> Site</oasis:entry>
         <oasis:entry colname="col2">6.28 <inline-formula><mml:math id="M187" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M188" 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></oasis:entry>
         <oasis:entry colname="col3">5</oasis:entry>
         <oasis:entry colname="col4">0.166</oasis:entry>
         <oasis:entry colname="col5">0.97</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Days <inline-formula><mml:math id="M189" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> Litter Stage</oasis:entry>
         <oasis:entry colname="col2">2.66 <inline-formula><mml:math id="M190" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M191" 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="col3">1</oasis:entry>
         <oasis:entry colname="col4">3.51</oasis:entry>
         <oasis:entry colname="col5">0.06</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Site <inline-formula><mml:math id="M192" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> Litter Stage</oasis:entry>
         <oasis:entry colname="col2">2.05 <inline-formula><mml:math id="M193" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M194" 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="col3">5</oasis:entry>
         <oasis:entry colname="col4">0.542</oasis:entry>
         <oasis:entry colname="col5">0.74</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Days <inline-formula><mml:math id="M195" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> Site <inline-formula><mml:math id="M196" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> Litter Stage</oasis:entry>
         <oasis:entry colname="col2">1.55 <inline-formula><mml:math id="M197" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math id="M198" 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="col3">5</oasis:entry>
         <oasis:entry colname="col4">4.09</oasis:entry>
         <oasis:entry colname="col5">0.001</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Residuals</oasis:entry>
         <oasis:entry colname="col2">0.199</oasis:entry>
         <oasis:entry colname="col3">263</oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

<?xmltex \hack{\clearpage}?>
</app>
  </app-group><notes notes-type="codedataavailability"><title>Code and data availability</title>

      <p id="d1e3712">Data and code used in this paper are available as an R Markdown file at
<uri>https://github.com/loganja3/NRM-Gradient-Project</uri> (Logan and Brown, 2022).</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e3721">JRL, SEE, PJJ, and KMJ conceived the study. JRL designed the study and
conducted fieldwork. JRL and KTB developed the model code and performed the
simulations. PJJ and KMJ performed the laboratory incubations. RV collected and
processed meteorological data. JRL conducted data analysis and statistics
and prepared the manuscript with contributions from all co-authors.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e3727">The contact author has declared that none of the authors has any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e3733">Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e3739">We would like to thank the staff at the Gobabeb Namib Research Institute,
the Namibian Ministry of Environment and Tourism, the National Botanical
Research Institute, and the National Commission on Research, Science and
Technology (permit number RPIV000102017) for their permission and support
for this study. Special thanks to Martin Handjaba at Gobabeb for fieldwork in support of this project and to Lukas Mendel for assistance with
laboratory incubations. The Southern African Science
Service Centre for Climate Change and Adaptive Land Management provided the
initial funding to establish the FogNet weather network and it is currently
maintained by funding from the University of Basel. This work was also
supported in part through computational resources and services provided by
the Institute for Cyber-Enabled Research at Michigan State University. Thank
you to the participants at the 2014 FogLife Colloquium, in particular Mary
Seely and Theo Wassenaar, for their contributions in helping generate ideas
for this project from the start. Finally, thank you to the Evans Lab, the
KBS Writing Group and two reviewers for their feedback on earlier versions
of this manuscript. This paper is KBS contribution number 2303.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e3744">Funding was provided by the U.S. National Science Foundation’s Graduate Research Fellowship Program, the W. K. Kellogg Biological Station at Michigan State University, Grinnell College, and the taxpayers of the United States and Michigan.</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e3750">This paper was edited by Akihiko Ito and reviewed by two anonymous referees.</p>
  </notes><ref-list>
    <title>References</title>

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