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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"><?xmltex \makeatother\@nolinetrue\makeatletter?>
  <front>
    <journal-meta><journal-id journal-id-type="publisher">BG</journal-id><journal-title-group>
    <journal-title>Biogeosciences</journal-title>
    <abbrev-journal-title abbrev-type="publisher">BG</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Biogeosciences</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1726-4189</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/bg-17-55-2020</article-id><title-group><article-title><?xmltex \hack{\vspace{5mm}}?>Oceanic <inline-formula><mml:math id="M1" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> outgassing and biological production hotspots<?xmltex \hack{\break}?> induced by pre-industrial river loads of nutrients and carbon<?xmltex \hack{\break}?> in a global modeling approach</article-title><alt-title>Oceanic <inline-formula><mml:math id="M2" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> outgassing and biological production hotspots</alt-title>
      </title-group><?xmltex \runningtitle{Oceanic {$\chem{CO_{{2}}}$} outgassing and biological production hotspots}?><?xmltex \runningauthor{F.~Lacroix et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1 aff2">
          <name><surname>Lacroix</surname><given-names>Fabrice</given-names></name>
          <email>fabrice.lacroix@mpimet.mpg.de</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Ilyina</surname><given-names>Tatiana</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-3475-4842</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Hartmann</surname><given-names>Jens</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-1878-9321</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Ocean in the Earth System, Max Planck Institute for Meteorology, Hamburg, Germany</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Department of Geoscience, Environment and Society (DGES), Université Libre de Bruxelles, Brussels, Belgium</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Institute for Geology, Center for Earth System Research and Sustainability, University of Hamburg, Hamburg, Germany</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Fabrice Lacroix (fabrice.lacroix@mpimet.mpg.de)</corresp></author-notes><pub-date><day>6</day><month>January</month><year>2020</year></pub-date>
      
      <volume>17</volume>
      <issue>1</issue>
      <fpage>55</fpage><lpage>88</lpage>
      <history>
        <date date-type="received"><day>23</day><month>April</month><year>2019</year></date>
           <date date-type="rev-request"><day>25</day><month>April</month><year>2019</year></date>
           <date date-type="rev-recd"><day>4</day><month>November</month><year>2019</year></date>
           <date date-type="accepted"><day>11</day><month>November</month><year>2019</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2020 Fabrice Lacroix et al.</copyright-statement>
        <copyright-year>2020</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/17/55/2020/bg-17-55-2020.html">This article is available from https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020.html</self-uri><self-uri xlink:href="https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020.pdf">The full text article is available as a PDF file from https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020.pdf</self-uri>
      <abstract><title>Abstract</title>
    <p id="d1e138">Rivers are a major source of nutrients, carbon and  alkalinity to the global ocean.
In this study, we firstly estimate pre-industrial riverine loads of nutrients, carbon and alkalinity based on a hierarchy of weathering and terrestrial organic matter export models, while identifying
regional hotspots of the riverine exports. Secondly, we implement the riverine loads into a global ocean biogeochemical model to describe their implications for oceanic nutrient concentrations,
net primary production (NPP) and air–sea <inline-formula><mml:math id="M3" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> fluxes
globally, as well as in an analysis of coastal regions. Thirdly, we quantitatively assess the
terrestrial origins and the long-term fate of riverine carbon in the ocean.
We quantify annual bioavailable pre-industrial riverine loads
of 3.7 Tg P, 27 Tg N, 158 Tg Si and 603 Tg C delivered to the ocean globally. We thereby identify the tropical Atlantic catchments (20 % of global C),
Arctic rivers (9 % of global C) and Southeast Asian rivers (15 % of global C)
as dominant suppliers of carbon for the ocean.
The riverine exports lead to a simulated net global oceanic <inline-formula><mml:math id="M4" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> source of 231 Tg C yr<inline-formula><mml:math id="M5" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> to the atmosphere, which is mainly caused by inorganic carbon (source of 183 Tg C yr<inline-formula><mml:math id="M6" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)
and by organic carbon (source of 128 Tg C yr<inline-formula><mml:math id="M7" 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>) riverine loads. Additionally, a sink of 80 Tg C yr<inline-formula><mml:math id="M8" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> is caused by the enhancement of the biological carbon uptake from dissolved
inorganic nutrient inputs from rivers and the resulting alkalinity production.
While large outgassing fluxes are simulated mostly in proximity to major river mouths, substantial outgassing fluxes can be found further offshore, most prominently in the tropical Atlantic.
Furthermore, we find evidence for the interhemispheric transfer of carbon in the model; we detect a larger relative outgassing flux (49 % of global riverine-induced outgassing)
in the Southern Hemisphere in comparison to the hemisphere's relative
riverine inputs (33 % of global C inputs), as well as an outgassing flux of 17 Tg C yr<inline-formula><mml:math id="M9" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in the Southern Ocean.
The addition of riverine loads in the model leads to a strong NPP increase in the tropical west Atlantic, Bay of Bengal and the East
China Sea (<inline-formula><mml:math id="M10" display="inline"><mml:mo lspace="0mm">+</mml:mo></mml:math></inline-formula>166 %, <inline-formula><mml:math id="M11" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>377 % and <inline-formula><mml:math id="M12" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>71 %, respectively).
On the light-limited Arctic shelves, the NPP is not strongly sensitive to riverine loads, but the <inline-formula><mml:math id="M13" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> flux is strongly altered regionally due to substantial dissolved inorganic and organic
carbon supplies to the region.
While our study confirms that the ocean circulation remains the main driver for biogeochemical distributions in the open ocean, it reveals the necessity to consider riverine inputs
for the representation of heterogeneous features in the coastal ocean and to represent riverine-induced pre-industrial carbon outgassing in the ocean.
It also underlines the need to consider long-term <inline-formula><mml:math id="M14" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> sources from volcanic and shale oxidation fluxes in order to close the framework's atmospheric carbon budget.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

      <?xmltex \hack{\newpage}?>
<?pagebreak page56?><sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e279">Rivers deliver substantial amounts of carbon (C), phosphorus (P), nitrogen (N), silicon (Si), iron (Fe) and alkalinity (Alk)
to the ocean <xref ref-type="bibr" rid="bib1.bibx97 bib1.bibx98 bib1.bibx29 bib1.bibx15 bib1.bibx108 bib1.bibx16" id="paren.1"/>.
In the ocean, these compounds undergo biogeochemical transformations and are ultimately either buried in the sediment or are outgassed
to the atmosphere <xref ref-type="bibr" rid="bib1.bibx37 bib1.bibx95 bib1.bibx7 bib1.bibx102 bib1.bibx24 bib1.bibx63" id="paren.2"/>. In global ocean biogeochemistry models, riverine
inputs and their contributions to the oceanic cycling of C have been strongly simplified or even completely omitted. In this study, we attempt to improve the understanding of the long-term
effects of riverine loads in the ocean by firstly estimating the magnitudes of biogeochemical riverine
loads for the pre-industrial time period and secondly by assessing
their long-term implications for marine biogeochemical cycles in a global ocean model.</p>
      <p id="d1e288">Natural riverine C and nutrients originate from the weathering of the lithosphere and from organic matter exports of the terrestrial biosphere <xref ref-type="bibr" rid="bib1.bibx70" id="paren.3"/>.
Weathering directly releases nutrients (P, Si and Fe) that can be taken up by the
terrestrial ecosystems or exported directly to aquatic systems <xref ref-type="bibr" rid="bib1.bibx52" id="paren.4"/>. In these ecosystems, these nutrients are reported to enhance the carbon uptake
due to their limitation of the biological primary production <xref ref-type="bibr" rid="bib1.bibx30 bib1.bibx34" id="paren.5"/>.
During the weathering process, Alk and dissolved inorganic C (DIC) are released, while <inline-formula><mml:math id="M15" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is drawn down from the atmosphere <xref ref-type="bibr" rid="bib1.bibx4 bib1.bibx81 bib1.bibx51" id="paren.6"/>. Spatially explicit
weathering models could potentially be used to provide the weathering release yields of nutrients, Alk and C (e.g., <xref ref-type="bibr" rid="bib1.bibx52" id="altparen.7"/>), as well as to quantify the weathering-induced drawdown
of atmospheric <inline-formula><mml:math id="M16" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in Earth system models (ESMs, <xref ref-type="bibr" rid="bib1.bibx70 bib1.bibx51 bib1.bibx52 bib1.bibx92" id="altparen.8"/>). These approaches rely on estimating chemical weathering rates as a 1st-order function
of hydrology, lithology, rates of physical erosion, soil properties and temperature <xref ref-type="bibr" rid="bib1.bibx4 bib1.bibx51 bib1.bibx52" id="paren.9"/>.</p>
      <p id="d1e335">The terrestrial biosphere also provides C and nutrients (P, N, Si and Fe) to rivers. This happens dominantly through organic matter exports <xref ref-type="bibr" rid="bib1.bibx81 bib1.bibx98 bib1.bibx90" id="paren.10"/>.
The formation of organic matter through biological primary production on land consumes atmospheric <inline-formula><mml:math id="M17" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx70" id="paren.11"/>.
Then, dissolved and particulate organic matter can be mobilized in soils
and peatlands through leaching and physical erosion, and exported to freshwaters. While the natural P and Fe within the terrestrial organic matter originate from weathering, C and N mostly originate from atmospheric fixation <xref ref-type="bibr" rid="bib1.bibx81 bib1.bibx42" id="paren.12"/>.</p>
      <p id="d1e358">Dissolved inorganic nutrients enhance the biological primary production
in the ocean, which results in a net uptake of atmospheric <inline-formula><mml:math id="M18" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx110" id="paren.13"/>. In turn, riverine inputs of DIC result in C outgassing in the ocean (e.g., <xref ref-type="bibr" rid="bib1.bibx51" id="altparen.14"/>).
The remineralization of terrestrial organic matter provided by rivers releases DIC and nutrients to the ocean. The composition of this organic matter and the timescales of its degradation in the ocean
have however been open questions for over
2 decades <xref ref-type="bibr" rid="bib1.bibx59 bib1.bibx53 bib1.bibx21 bib1.bibx64" id="paren.15"/>.
In the case of terrestrial dissolved organic matter (tDOM), its reported degradation during its transit in rivers induces high C to nutrients ratios of its loadings to the ocean
(i.e., <inline-formula><mml:math id="M19" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> weight ratios of over 500, <xref ref-type="bibr" rid="bib1.bibx79 bib1.bibx98" id="altparen.16"/>),
which is likely due to the preference
of organic matter rich in nutrients for bacterial metabolic activities
<xref ref-type="bibr" rid="bib1.bibx53" id="paren.17"/>.
The degradation of tDOM is suggested to cause C outgassing in the coastal ocean due to its large release of DIC and low release of nutrients to the water column <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx85 bib1.bibx1" id="paren.18"/>.
Although the previous degradation of tDOM in rivers implies low biological reactivity of tDOM in the ocean, tDOM
is not a major constituent of organic mixtures in open ocean seawater or in sediment pore water <xref ref-type="bibr" rid="bib1.bibx59 bib1.bibx53 bib1.bibx11" id="paren.19"/>. It is thus reactive to a certain degree in the ocean,
with recent studies suggesting the abiotic breakdown of tDOM as a possible explanatory mechanism <xref ref-type="bibr" rid="bib1.bibx35 bib1.bibx1" id="paren.20"/>. In the case of riverine particulate organic matter (POM), stronger gaps of
knowledge exist <xref ref-type="bibr" rid="bib1.bibx21" id="paren.21"/>. Riverine POM has however been reported to affect
the coastal ocean biogeochemistry regionally by controlling the availability of nutrients through its remineralization <xref ref-type="bibr" rid="bib1.bibx37 bib1.bibx24 bib1.bibx104" id="paren.22"/>.
Furthermore, a substantial proportion of weathered P is exported to the ocean bound to iron-manganese oxide and hydroxide particle surfaces
(Fe-P, <xref ref-type="bibr" rid="bib1.bibx22" id="altparen.23"/>). Within
the ocean, a fraction of P in Fe-P is thought to be desorbed and thus converted to bioavailable dissolved inorganic phosphorus (DIP).</p>
      <?pagebreak page57?><p id="d1e420">Pre-industrial P and N riverine loads likely strongly differed to their present-day loads due to dramatic anthropogenic perturbations of inputs to freshwaters
during the 20th century <xref ref-type="bibr" rid="bib1.bibx98 bib1.bibx16" id="paren.24"/>.
Riverine exports of P and N are also suggested to have already been perturbed prior to 1850 due to
increased soil erosion from land-use changes, due to fertilizer use in agriculture and due to sewage sources <xref ref-type="bibr" rid="bib1.bibx74 bib1.bibx36 bib1.bibx16" id="paren.25"/>.
Since global modeling
studies of the climate are usually initialized for 1850 <xref ref-type="bibr" rid="bib1.bibx39" id="paren.26"/> or 1900 <xref ref-type="bibr" rid="bib1.bibx18" id="paren.27"/>, these exports from non-natural sources should also be taken into account in initial
pre-industrial model simulations. While anthropogenic perturbations of C and Si have also been reported in published literature,
they are less substantial at the global scale than for P and N <xref ref-type="bibr" rid="bib1.bibx98 bib1.bibx90 bib1.bibx71 bib1.bibx72" id="paren.28"/>.</p>
      <p id="d1e438">Until now, riverine point sources of biogeochemical compounds have been omitted or poorly represented
in global ocean biogeochemical models, despite being suggested to strongly impact the biogeochemistry of coastal regions <xref ref-type="bibr" rid="bib1.bibx37 bib1.bibx102 bib1.bibx24" id="paren.29"/> and being
suggested to cause a pre-industrial source of atmospheric <inline-formula><mml:math id="M20" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in the ocean <xref ref-type="bibr" rid="bib1.bibx95 bib1.bibx7 bib1.bibx43 bib1.bibx91" id="paren.30"/>. This background <inline-formula><mml:math id="M21" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> outgassing flux of 0.2 to 0.8 Gt C yr<inline-formula><mml:math id="M22" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> is significant in the context of the present-day oceanic C uptake of around 2.3 Gt C yr<inline-formula><mml:math id="M23" 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> <xref ref-type="bibr" rid="bib1.bibx58" id="paren.31"/>.
In a modeling study, <xref ref-type="bibr" rid="bib1.bibx7" id="text.32"/> derived terrestrial C loads from an erosion model and analyzed the oceanic outgassing caused by these C inputs.
The impacts of riverine nutrients and Alk were however not considered, and C was only added to the ocean as DIC thus omitting terrestrial organic matter dynamics in the ocean.
<xref ref-type="bibr" rid="bib1.bibx23" id="text.33"/> analyzed the impacts of present-day riverine loads on the oceanic NPP in an ocean biogeochemical model covering the Atlantic Ocean for an analysis period of 10 years, a time period that
likely does not suffice to assess their long-term
implications on the biogeochemistry of basin areas remote to land.
<xref ref-type="bibr" rid="bib1.bibx12" id="text.34"/> added present-day biogeochemical riverine loads to an global ocean model to focus on their implications for global opal export distributions, ignoring other
impacts of the riverine inputs in the model.
Also in a global ocean model, <xref ref-type="bibr" rid="bib1.bibx18" id="text.35"/>
quantified the coastal anthropogenic <inline-formula><mml:math id="M24" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> uptake, but the impacts caused by biogeochemical riverine loads were not represented.
To our knowledge, a study has yet to give a comprehensive overview of the magnitudes of pre-industrial riverine exports and
their long-term implications for the global oceanic biogeochemical cycling in a 3-D model.  An initial ocean state that considers pre-industrial
riverine supplies has not been achieved in a global ocean model, which would be needed to investigate the temporal impacts associated with their perturbations.
Past ocean model studies have also not represented the composition and oceanic dynamics of terrestrial organic matter, which differs from oceanic organic matter. Furthermore, it is often unclear under which criteria the
Alk supplies to the ocean were constrained in many global ocean models.
Regional coastal responses to the addition biogeochemical riverine loads have not been assessed at the global scale until now, largely
due to the incapability of the global ocean models to represent plausible continental shelf areas in the past <xref ref-type="bibr" rid="bib1.bibx12" id="paren.36"/>.</p>
      <p id="d1e524">To address the knowledge gaps listed above we did the following.
<list list-type="order"><list-item>
      <p id="d1e529">We implement a representation of pre-industrial riverine loads into
a global ocean biogeochemical model, considering both weathering and non-weathering sources of nutrients, C and Alk. We compare our estimates with a wide range of published literature values, while also
determining regions of disproportionate contributions to global terrestrial exports.</p></list-item><list-item>
      <p id="d1e533">We assess the implications of riverine inputs for oceanic net primary production (NPP) and air–sea <inline-formula><mml:math id="M25" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> fluxes globally, as well as regionally in an analysis of shallow shelf regions.</p></list-item><list-item>
      <p id="d1e548">We evaluate the origins and fate of riverine C quantitatively, while assessing the balance between the land C uptake and the oceanic C outgassing in the individual models.
This balance of the land C uptake
and its oceanic outgassing is then used to assess the potential implementation of riverine fluxes in a fully coupled land–atmosphere–ocean setting.</p></list-item></list></p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methods</title>
      <p id="d1e559">To address the objectives of this study, we derived the most relevant pre-industrial (1850) riverine loads of biogeochemical compounds to the ocean in dependence of pre-industrial ESM variables.
The derived riverine loads were then incorporated into a global ocean biogeochemical model in order to assess their global and regional impacts in the ocean. In order to quantify
the response of coastal regions to the riverine supplies, we also defined 10 regions with ocean depths of less than 250 m for analysis.</p>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Deriving pre-industrial riverine loads</title>
      <p id="d1e569">We focused on the riverine exports of P, N, Si, Fe, C and Alk at the global scale.
The river catchments were defined by using the largest 2000 catchments of the Hydrological Discharge (HD) model <xref ref-type="bibr" rid="bib1.bibx44 bib1.bibx46" id="paren.37"/>, a component of the Max Planck Institute Earth System Model (MPI-ESM). They
were derived from the runoff flow directions of the model at a horizontal resolution of 0.5<inline-formula><mml:math id="M26" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>.
The exorheic river catchments (catchments which discharge into the ocean) were considered to be catchments which had river mouths at a distance of less than 500 km to the coastline in the HD model.
Catchments with larger distances were considered to be endorheic catchments (catchments which do not discharge into the ocean). The biogeochemical compound yields in these catchments were assumed to be retained
permanently, whereas the riverine exports of exorheic catchments were added to the ocean.</p>
      <p id="d1e584">We considered both weathering as well as non-weathering sources of P, N, Si, Fe, C and Alk to river catchments (Fig. <xref ref-type="fig" rid="Ch1.F1"/>). These were derived, if possible, from spatially explicit models.
Within the catchments, we accounted for transformations of P, N and Fe to organic matter through biological productivity on land and in rivers.
These transformations were derived from globally fixed ratios with respect to organic C.
The<?pagebreak page58?> organic C in tDOM and POM was, in turn, assumed to ultimately originate from terrestrial
biological <inline-formula><mml:math id="M27" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> uptake <xref ref-type="bibr" rid="bib1.bibx70" id="paren.38"/>
and was therefore not subtracted from the catchment DIC pools. Additionally, a fraction of the catchment P was also assumed to have been adsorbed to Fe-P. Everything considered, rivers deliver terrestrial
organic matter (tDOM and POM), inorganic compounds (DIP, Fe-P, DIN, DSi, DFe and DIC) and Alk to the ocean in our approach (Fig. <xref ref-type="fig" rid="Ch1.F1"/>).</p>
      <p id="d1e605">The surface runoff, surface temperature and precipitation data used to drive the weathering release and land export models were obtained from the output of a coupled MPI-ESM
pre-industrial simulation <xref ref-type="bibr" rid="bib1.bibx39" id="paren.39"/>. We thereby used the annual 100 year means of pre-industrial
data computed at a horizontal grid resolution of 1.875<inline-formula><mml:math id="M28" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. The runoff data were scaled by a factor of 1.59 to account for the runoff model bias with regard to
global estimations <xref ref-type="bibr" rid="bib1.bibx33" id="paren.40"/>, a factor that is discussed in Appendix B.</p>
<sec id="Ch1.S2.SS1.SSS1">
  <label>2.1.1</label><title>Terrestrial dissolved and particulate organic matter characteristics</title>
      <p id="d1e630">We assumed that the pre-industrial loads of tDOM
and POM did not strongly differ to their present-day loads at the global scale. <xref ref-type="bibr" rid="bib1.bibx98" id="text.41"/>, who modeled
anthropogenic perturbations to riverine loads for 1970 and 2000, only simulated small changes in global POC and DOC loads over this time period.
<xref ref-type="bibr" rid="bib1.bibx90" id="text.42"/> suggest a total anthropogenic perturbation of the global riverine C export to the ocean of around 10 %, for which we did not account in this study.</p>
      <p id="d1e639">The riverine loads of tDOM and POM were therefore directly derived from the DOC and POC river loads
for the reference year 1970 (NEWS2), assuming no change between this time segment and the pre-industrial time period. These organic loads were determined from the models of <xref ref-type="bibr" rid="bib1.bibx47" id="text.43"/> and <xref ref-type="bibr" rid="bib1.bibx14" id="text.44"/>.
The <xref ref-type="bibr" rid="bib1.bibx47" id="text.45"/> model quantifies the DOC catchment yields as a function of runoff, wetland area and consumptive water use. <xref ref-type="bibr" rid="bib1.bibx14" id="text.46"/> describe the POC catchment yields
as a function of catchment suspended solids yields, which depend on grassland and wetland areas, precipitation, slope and lithology.</p>
      <p id="d1e654">The tDOM and POM exports were assumed to consist of globally constant fractions of organic C, P, N and Fe.
The tDOM <inline-formula><mml:math id="M29" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratio was based on a <inline-formula><mml:math id="M30" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> mole ratio of <inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:mn mathvariant="normal">2583</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> derived from <xref ref-type="bibr" rid="bib1.bibx79" id="text.47"/> and <xref ref-type="bibr" rid="bib1.bibx22" id="text.48"/>. The tDOM total <inline-formula><mml:math id="M32" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> mole ratio was chosen to be <inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:mn mathvariant="normal">16</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>, in order to
represent the same <inline-formula><mml:math id="M34" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratio as of the organic matter export to the sediment in the ocean biogeochemistry model,
which was also the reasoning for choosing the <inline-formula><mml:math id="M35" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">P</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow></mml:math></inline-formula> mole ratio of <inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">3.0</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">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. The <inline-formula><mml:math id="M37" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow></mml:math></inline-formula> mole ratio of tDOM was therefore <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:mn mathvariant="normal">2583</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">16</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">3.0</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">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>.
The <inline-formula><mml:math id="M39" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratio of riverine POM is highly uncertain, but global <inline-formula><mml:math id="M40" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> mole ratios from observational data (56–499) <xref ref-type="bibr" rid="bib1.bibx79 bib1.bibx88 bib1.bibx22" id="paren.49"/> suggest a much closer ratio
to the production and export ratios of oceanic organic matter (mole <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">122</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>, <xref ref-type="bibr" rid="bib1.bibx105" id="altparen.50"/>) than for tDOM. Due to this and current gaps of knowledge on the composition of riverine POM,
we chose the same <inline-formula><mml:math id="M42" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow></mml:math></inline-formula> ratio as of oceanic POM (<inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:mn mathvariant="normal">122</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">16</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">3.0</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">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><label>Figure 1</label><caption><p id="d1e926"><bold>(a)</bold> Table of sources of nutrient, carbon and alkalinity inputs to river catchments and <bold>(b)</bold> scheme of origins and transformations of the catchment compounds, as well as biogeochemical processes in the ocean
in our framework.
The abbreviations are: Inorg. Comp.: Inorganic Compounds, tDOM: terrestrial dissolved organic matter, POM: particulate organic matter, DIP: dissolved inorganic phosphorus, Fe-P: iron-bound phosphorus, DIN: dissolved inorganic nitrogen, DSi: dissolved silica, DFe: dissolved iron, DIC: dissolved inorganic carbon, Alk: alkalinity.</p></caption>
            <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020-f01.png"/>

          </fig>

</sec>
<sec id="Ch1.S2.SS1.SSS2">
  <label>2.1.2</label><title>Phosphorus</title>
</sec>
<sec id="Ch1.S2.SS1.SSSx1" specific-use="unnumbered">
  <title>P weathering yields</title>
      <p id="d1e955">We derived the P weathering yields from a spatiotemporal model <xref ref-type="bibr" rid="bib1.bibx52" id="paren.51"/>, which quantifies the P weathering release in relation to the <inline-formula><mml:math id="M44" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SiO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and cation release
induced by weathering. The
model was originally calibrated for the extensive data set of 381 river catchments
of the Japanese Archipelago with runoff and lithological characteristics <xref ref-type="bibr" rid="bib1.bibx49" id="paren.52"/> being used as sole model variables. The model was then corrected for temperature and soil shielding effects
at the global scale <xref ref-type="bibr" rid="bib1.bibx52" id="paren.53"/>:
              <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M45" display="block"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">Prelease</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:munder><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">lith</mml:mi></mml:mrow></mml:munder><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>⋅</mml:mo><mml:mi>q</mml:mi><mml:mo>⋅</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">Prelease</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the chemical weathering rate of P per area (t km<inline-formula><mml:math id="M47" 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> yr<inline-formula><mml:math id="M48" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>), <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is an empirical factor
representing the rate of P weathering of the lithology <inline-formula><mml:math id="M50" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M51" display="inline"><mml:mi>q</mml:mi></mml:math></inline-formula> is the surface runoff (mm yr<inline-formula><mml:math id="M52" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>),
<inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is a lithology-dependent temperature function and <inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is a parameter to account for soil shielding.</p>
      <p id="d1e1145">The lithology types consisted of 16 lithological classes from the global lithological database GliM <xref ref-type="bibr" rid="bib1.bibx50" id="paren.54"/>.
The lithology-dependent factor <inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> represents the chemical weathering rate factor for <inline-formula><mml:math id="M56" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SiO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M57" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> cations (<inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SiO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Cat</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) multiplied with the relative
P content (<inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi mathvariant="normal">Prel</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>):
              <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M60" display="block"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi mathvariant="normal">P</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SiO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Cat</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi mathvariant="normal">Prel</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e1271">The parameters <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SiO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mi mathvariant="normal">Cat</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi mathvariant="normal">Prel</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> for each lithology <inline-formula><mml:math id="M63" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> can be found in <xref ref-type="bibr" rid="bib1.bibx52" id="text.55"/>.</p>
      <p id="d1e1324">The temperature correction function <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is an Arrhenius relationship for basic (rich in iron and magnesium) and acid (high silica content) lithological
classes, with activation energies normalized to the average temperature of the calibration catchments of the study <xref ref-type="bibr" rid="bib1.bibx52" id="paren.56"/>. For acid rock lithologies, an activation energy of
60 kJ mol<inline-formula><mml:math id="M65" 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>  was assumed, whereas for basic rock types 50 kJ mol<inline-formula><mml:math id="M66" 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> was used. Carbonate lithologies do not have a temperature correction function due to the absence
of a clear relationship to field data, as well as due to uncertainties in the mechanisms of a temperature effect on carbonate weathering <xref ref-type="bibr" rid="bib1.bibx52 bib1.bibx93" id="paren.57"/>.</p>
      <p id="d1e1372">A soil shielding factor <inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was considered to represent the inhibition of weathering by certain types of soils. These soils, which have low physical erosion rates, develop a chemically<?pagebreak page59?> depleted thick layer, shielding them from
water supply and thus partly preventing the weathering of the soil aggregates <xref ref-type="bibr" rid="bib1.bibx101" id="paren.58"/>.
An average soil shielding factor of 0.1 was estimated for the soils Ferrasols, Acrisols, Nitisols, Lixisols, Histosols and Gleysols while performing a calibration at the global scale in <xref ref-type="bibr" rid="bib1.bibx52" id="text.59"/>.</p>
</sec>
<sec id="Ch1.S2.SS1.SSSx2" specific-use="unnumbered">
  <title>Non-weathering P sources</title>
      <p id="d1e1398">Since the P cycle was already perturbed in the assumed pre-industrial state (1850) due to anthropogenic activities <xref ref-type="bibr" rid="bib1.bibx74 bib1.bibx36 bib1.bibx16" id="paren.60"/>, we also accounted for P sources other than weathering (P<inline-formula><mml:math id="M68" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi mathvariant="normal">nw</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>).
Similarly to <xref ref-type="bibr" rid="bib1.bibx16" id="text.61"/>, we derived the non-weathering catchment source of P as the sum of fertilizer (P<inline-formula><mml:math id="M69" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi mathvariant="normal">fert</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>), sewage (P<inline-formula><mml:math id="M70" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi mathvariant="normal">sew</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>) and allochthonous P inputs (P<inline-formula><mml:math id="M71" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi mathvariant="normal">alloch</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>):
              <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M72" display="block"><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">P</mml:mi><mml:mrow><mml:mi mathvariant="normal">nw</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">P</mml:mi><mml:mrow><mml:mi mathvariant="normal">fert</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">P</mml:mi><mml:mrow><mml:mi mathvariant="normal">sew</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">P</mml:mi><mml:mrow><mml:mi mathvariant="normal">alloch</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e1521">P<inline-formula><mml:math id="M73" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi mathvariant="normal">fert</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> was the P input to river catchments originating from the agricultural application of fertilizers, manure and organic matter (1.6 Tg P yr<inline-formula><mml:math id="M74" 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> globally, from <xref ref-type="bibr" rid="bib1.bibx16" id="altparen.62"/>); P<inline-formula><mml:math id="M75" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi mathvariant="normal">sew</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>
was the P input from sewage (0.1 Tg P yr<inline-formula><mml:math id="M76" 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> globally, <xref ref-type="bibr" rid="bib1.bibx83" id="altparen.63"/>) and P<inline-formula><mml:math id="M77" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi mathvariant="normal">alloch</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represented allochthonous organic matter P inputs (1 Tg P yr<inline-formula><mml:math id="M78" 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>, which were simplified as vegetation
in floodplains in <xref ref-type="bibr" rid="bib1.bibx16" id="altparen.64"/>). All of these P inputs were estimated for year 1900 due to previous estimates not being available to our knowledge.
Since our framework was developed with the aim of being used in ESMs, we assumed soil equilibrium since this is the initial state criteria used in state-of-the-art model simulations.
Therefore, P exports due to perturbations of organic matter erosion in soils were not considered.
The global distribution of anthropogenic P inputs (agricultural <inline-formula><mml:math id="M79" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> sewage) to catchments was assumed to be the same as the distribution of contemporary anthropogenic P inputs, which
were derived from the NEWS2 study:
              <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M80" display="block"><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">P</mml:mi><mml:mrow><mml:mi mathvariant="normal">ant</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">P</mml:mi><mml:mrow><mml:mi mathvariant="normal">ant</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">global</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">DIP</mml:mi><mml:mrow><mml:mtext>ant-pd</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="normal">DIP</mml:mi><mml:mrow><mml:mtext>ant-pd</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="normal">global</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where P<inline-formula><mml:math id="M81" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi mathvariant="normal">ant</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">global</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> is the global sum of anthropogenic P inputs to catchments, whereas DIP<inline-formula><mml:math id="M82" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mtext>ant-pd</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and DIP<inline-formula><mml:math id="M83" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mtext>ant-pd</mml:mtext><mml:mo>,</mml:mo><mml:mi mathvariant="normal">global</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> are<?pagebreak page60?> anthropogenic inputs from the NEWS2 study (1970) for every catchment and their global sum, respectively.
Regarding the allochthonous P inputs, we assumed the same global distribution as for the organic matter yields. Both of these distributions are shown and discussed in the Supplement S1.1 and S1.2.</p>
</sec>
<sec id="Ch1.S2.SS1.SSSx3" specific-use="unnumbered">
  <title>P river loads</title>
      <p id="d1e1724">For each catchment, we estimated the annual P exports of the individual catchments (P<inline-formula><mml:math id="M84" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi mathvariant="normal">total</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>) as the sum of the catchment weathering yields (P<inline-formula><mml:math id="M85" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi mathvariant="normal">w</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>)
and of non-weathering catchment P inputs (P<inline-formula><mml:math id="M86" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi mathvariant="normal">nw</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>):
              <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M87" display="block"><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">P</mml:mi><mml:mrow><mml:mi mathvariant="normal">total</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">P</mml:mi><mml:mrow><mml:mi mathvariant="normal">w</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">P</mml:mi><mml:mrow><mml:mi mathvariant="normal">nw</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e1813">P<inline-formula><mml:math id="M88" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi mathvariant="normal">total</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> was then fractionated into inorganic P (IP<inline-formula><mml:math id="M89" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">catch</mml:mi></mml:msub></mml:math></inline-formula>) and organic P bound within tDOM (DOP) and POM (POP), which were assumed to have been taken up
on land or in freshwaters by the biology at the prescribed fixed organic <inline-formula><mml:math id="M90" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratio.
The remaining catchment P was assumed to be IP<inline-formula><mml:math id="M91" display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">catch</mml:mi></mml:msub></mml:math></inline-formula>:
              <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M92" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">IP</mml:mi><mml:mi mathvariant="normal">catch</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">P</mml:mi><mml:mrow><mml:mi mathvariant="normal">total</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">DOP</mml:mi><mml:mrow><mml:mi mathvariant="normal">total</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">POP</mml:mi><mml:mrow><mml:mi mathvariant="normal">total</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">catch</mml:mi></mml:mrow></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
            The IP was thereafter fractionated into DIP and Fe-P (IP bound to iron-manganese oxide and hydroxide) at a ratio <inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">inorg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (DIP : Fe-P <inline-formula><mml:math id="M94" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula>,
approximated from the pre-industrial global export estimates of <xref ref-type="bibr" rid="bib1.bibx22" id="altparen.65"/>) and (<inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">inorg</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>):
              <disp-formula id="Ch1.E7" content-type="numbered"><label>7</label><mml:math id="M97" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="normal">DIP</mml:mi><mml:mi mathvariant="normal">catch</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">inorg</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">IP</mml:mi><mml:mi mathvariant="normal">catch</mml:mi></mml:msub></mml:mrow></mml:math></disp-formula>
            and
              <disp-formula id="Ch1.E8" content-type="numbered"><label>8</label><mml:math id="M98" display="block"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">Fe</mml:mi><mml:mo>-</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow><mml:mi mathvariant="normal">catch</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">inorg</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">IP</mml:mi><mml:mi mathvariant="normal">catch</mml:mi></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
            We did not consider detrital particulate inorganic P exports from the physical weathering of rock. This P is not
bioavailable in rivers or in the coastal ocean due to strong covalent bonds of the detrital mineral structures <xref ref-type="bibr" rid="bib1.bibx22" id="paren.66"/>.</p>
</sec>
<sec id="Ch1.S2.SS1.SSS3">
  <label>2.1.3</label><title>Nitrogen and iron</title>
      <p id="d1e2034">The N inputs to river catchments were derived from a globally fixed mole <inline-formula><mml:math id="M99" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratio of <inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:mn mathvariant="normal">16</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx105" id="paren.67"/> with regard to P inputs for all species (<inline-formula><mml:math id="M101" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">DIN</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">IP</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M102" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> in tDOM and <inline-formula><mml:math id="M103" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> in POM).
In published literature, higher <inline-formula><mml:math id="M104" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratios for all riverine species exports are suggested, with <xref ref-type="bibr" rid="bib1.bibx16" id="text.68"/> simulating
a pre-industrial <inline-formula><mml:math id="M105" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> mole ratio of <inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:mn mathvariant="normal">21</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> and <xref ref-type="bibr" rid="bib1.bibx109" id="text.69"/> reporting higher <inline-formula><mml:math id="M107" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratios of over <inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:mn mathvariant="normal">16</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> in a synthesis of measurements in major rivers.
However, denitrification in river estuaries, which is not taken into account in the mentioned studies, also removes N (3–10 Tg N yr<inline-formula><mml:math id="M109" 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>, <xref ref-type="bibr" rid="bib1.bibx97" id="altparen.70"/>).
According to our calculations, this estuarine N sink could reduce the <inline-formula><mml:math id="M110" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratio of the global exports to around <inline-formula><mml:math id="M111" display="inline"><mml:mrow><mml:mn mathvariant="normal">16</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> (Supplement S1.3).
For Fe, we used a <inline-formula><mml:math id="M112" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">P</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow></mml:math></inline-formula> mole ratio of <inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">3.0</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">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, which is the <inline-formula><mml:math id="M114" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Fe</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> export ratio of organic matter in the ocean biogeochemistry model, to quantify Fe inputs to catchments for all species (<inline-formula><mml:math id="M115" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">IP</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">DFe</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M116" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">P</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow></mml:math></inline-formula> in tDOM and <inline-formula><mml:math id="M117" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">P</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow></mml:math></inline-formula> in POM).
The iron of the Fe-P iron-manganese oxides and hydroxides was not considered to be bioavailable.</p>
</sec>
<sec id="Ch1.S2.SS1.SSS4">
  <label>2.1.4</label><title>Dissolved inorganic carbon and alkalinity</title>
      <p id="d1e2298">The DIC and Alk weathering release, as well as the drawdown of atmospheric <inline-formula><mml:math id="M118" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> induced by weathering, were quantified according to the studies of <xref ref-type="bibr" rid="bib1.bibx51" id="text.71"/> and <xref ref-type="bibr" rid="bib1.bibx41" id="text.72"/>.
Weathering reactions cause an uptake of atmospheric <inline-formula><mml:math id="M119" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and a release of DIC as <inline-formula><mml:math id="M120" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> during carbonate weathering
              <disp-formula id="Ch1.E9" content-type="numbered"><label>9</label><mml:math id="M121" display="block"><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mi mathvariant="italic">&gt;</mml:mi><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mn mathvariant="normal">2</mml:mn><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:mrow></mml:math></disp-formula>
            and silicate weathering
              <disp-formula id="Ch1.E10" content-type="numbered"><label>10</label><mml:math id="M122" display="block"><mml:mtable rowspacing="0.2ex" columnspacing="1em" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">Mg</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SiO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mn mathvariant="normal">4</mml:mn><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mn mathvariant="normal">4</mml:mn><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mi mathvariant="italic">&gt;</mml:mi><mml:mrow class="chem"><mml:mn mathvariant="normal">2</mml:mn><mml:msup><mml:mi mathvariant="normal">Mg</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mn mathvariant="normal">4</mml:mn><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SiO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d1e2487">The Eqs. (9) and (10) dictate the release of 1 mol <inline-formula><mml:math id="M123" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> (thus 1 mol DIC and 1 mol Alk)
for each mole of <inline-formula><mml:math id="M124" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>
taken up during the weathering of silicate lithologies, and of
2 mol <inline-formula><mml:math id="M125" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> (thus 2 mol DIC and 2 mol Alk) for the uptake of each mole of <inline-formula><mml:math id="M126" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> drawn down during the weathering of carbonate lithologies.</p>
      <p id="d1e2538">The release equations from <xref ref-type="bibr" rid="bib1.bibx51" id="text.73"/> and <xref ref-type="bibr" rid="bib1.bibx41" id="text.74"/> quantify the lithology (<inline-formula><mml:math id="M127" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula>) dependent <inline-formula><mml:math id="M128" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> weathering release as a function of surface runoff (<inline-formula><mml:math id="M129" display="inline"><mml:mi>q</mml:mi></mml:math></inline-formula>), temperature (<inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>),
soil shielding <inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and a
weathering parameter <inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mi mathvariant="normal">C</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>:
              <disp-formula id="Ch1.E11" content-type="numbered"><label>11</label><mml:math id="M133" display="block"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:munder><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">lith</mml:mi></mml:mrow></mml:munder><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>⋅</mml:mo><mml:mi>q</mml:mi><mml:mo>⋅</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e2685">The parameter <inline-formula><mml:math id="M134" display="inline"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mo>,</mml:mo><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is dependent on the weathering rate of the lithology and the composition of the lithology.</p>
      <p id="d1e2706">The catchment DIC and Alk catchment loads were the <inline-formula><mml:math id="M135" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> weathered annually within the catchments, assuming conservation of
Alk along the land–ocean continuum <xref ref-type="bibr" rid="bib1.bibx4" id="paren.75"/>. We therefore assumed a <inline-formula><mml:math id="M136" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">DIC</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">Alk</mml:mi></mml:mrow></mml:math></inline-formula> loads ratio of <inline-formula><mml:math id="M137" 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>, without considering additional DIC sources from
respiration of organic matter in soil pore water, groundwater or in rivers. River observational data however show
that the riverine <inline-formula><mml:math id="M138" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and total DIC mole exports rarely deviate by more than
10 % <xref ref-type="bibr" rid="bib1.bibx81 bib1.bibx6" id="paren.76"/>.</p>
</sec>
<?pagebreak page61?><sec id="Ch1.S2.SS1.SSS5">
  <label>2.1.5</label><title>Silica</title>
      <p id="d1e2775">To quantify the global spatial distribution of riverine DSi exports, we used the model developed by <xref ref-type="bibr" rid="bib1.bibx15" id="text.77"/>:
              <disp-formula id="Ch1.E12" content-type="numbered"><label>12</label><mml:math id="M139" display="block"><mml:mtable rowspacing="0.2ex" class="split" columnspacing="1em" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">DSiO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mi mathvariant="normal">prec</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mi>ln⁡</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">prec</mml:mi><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mi mathvariant="normal">volc</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mi mathvariant="normal">volc</mml:mi></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mi mathvariant="normal">bulk</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mi mathvariant="normal">bulk</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>b</mml:mi><mml:mi mathvariant="normal">slope</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:mi mathvariant="normal">slope</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
            where <inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">DSiO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the export of DSi (Tg <inline-formula><mml:math id="M141" display="inline"><mml:mrow class="chem"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SiO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula> yr<inline-formula><mml:math id="M142" 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> km<inline-formula><mml:math id="M143" 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>), ln(prec) is the natural logarithm
of the precipitation (mm d<inline-formula><mml:math id="M144" 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>), volc is the area fraction covered by volcanic lithology (no dimension), bulk is the bulk density of the soil (Mg m<inline-formula><mml:math id="M145" 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>), slope is the
average slope (m km<inline-formula><mml:math id="M146" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>), and
<inline-formula><mml:math id="M147" display="inline"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mi mathvariant="normal">prec</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M148" display="inline"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mi mathvariant="normal">volc</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M149" display="inline"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mi mathvariant="normal">bulk</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M150" display="inline"><mml:mrow><mml:msub><mml:mi>b</mml:mi><mml:mi mathvariant="normal">slope</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are the regression coefficients estimated in <xref ref-type="bibr" rid="bib1.bibx15" id="text.78"/>.
For the precipitation, we used the pre-industrial model output from the MPI-ESM, whereas the volcanic area originated from <xref ref-type="bibr" rid="bib1.bibx28" id="text.79"/>, the soil density from <xref ref-type="bibr" rid="bib1.bibx8" id="text.80"/> and <xref ref-type="bibr" rid="bib1.bibx9" id="text.81"/>, and
the average slope from the Global Agro-Ecological Zones database <xref ref-type="bibr" rid="bib1.bibx32" id="paren.82"/>. The exports were aggregated for the HD model catchment areas. The loads that
were generated by applying the <xref ref-type="bibr" rid="bib1.bibx15" id="text.83"/> model were also converted
to teragrams silicon (Tg Si) and are given accordingly in our study. We approximated the weathering release of Si using this DSi model output, therefore assuming that sinks of Si on land or in rivers are compensated by sources
from these ecosystems (a further equilibrium assumption). We also neglected the riverine exports of particulate Si originating from physical erosion.</p>
</sec>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Ocean model setup</title>
<sec id="Ch1.S2.SS2.SSS1">
  <label>2.2.1</label><title>Ocean biogeochemistry</title>
      <p id="d1e3025">The Max Planck Institute Ocean Model (MPIOM, <xref ref-type="bibr" rid="bib1.bibx62" id="altparen.84"/>), which was used to simulate oceanic physics, is a <inline-formula><mml:math id="M151" display="inline"><mml:mi>z</mml:mi></mml:math></inline-formula> coordinate global circulation model. It solves primitive equations under the
hydrostatic and Boussinesq approximation on a C-grid with a free surface for every model time step (1 h). The grid configuration used in this study (GR15)
consists of a bipolar grid with one pole over the Antarctic and one over Greenland. It resolves the ocean horizontally at around 1.5<inline-formula><mml:math id="M152" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and through 40 unevenly spaced vertical layers with increasing thicknesses at greater depths. The flow fields of the MPIOM dictate
the advection, mixing and diffusion of biogeochemical compounds in the ocean. The atmospheric surface boundary data, as well as river freshwater model inputs, which are used to drive MPIOM here, originate from the
Ocean Model Intercomparison Project (OMIP, <xref ref-type="bibr" rid="bib1.bibx94" id="altparen.85"/>). The atmospheric forcing data set is a mean annual cycle for atmospheric parameters at a daily time step constructed from ECMWF
reanalysis project ERA-40 data. For the freshwater forcing climatology,
the HD model was driven with the ERA-40 atmospheric data <xref ref-type="bibr" rid="bib1.bibx45" id="paren.86"/>.</p>
      <p id="d1e3053">The Hamburg Ocean Carbon Cycle model (HAMOCC) simulates the inorganic carbon chemistry, biological transformations, nutrient cycling and gas dynamics in
the oceanic water column, sediment and at the air–sea interface. The model core along with its equations are described in <xref ref-type="bibr" rid="bib1.bibx57" id="text.87"/>,
but we also accounted for more recent modifications explained in <xref ref-type="bibr" rid="bib1.bibx78" id="text.88"/>. These included incorporating dynamic
nitrogen fixation by cyanobacteria <xref ref-type="bibr" rid="bib1.bibx87" id="paren.89"/>,
following recommendations of the OMIP protocol <xref ref-type="bibr" rid="bib1.bibx86" id="paren.90"/> and including nitrogen deposition according to the Coupled Model Intercomparison Project 6 (CMIP6) database (<uri>https://esgf-node.llnl.gov/projects/input4mips/</uri>, last access: 17 December 2019).
The pools of the model consist of DIP, DIN, DFe, <inline-formula><mml:math id="M153" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, DSi, DIC, Alk, opal, calcium carbonate (<inline-formula><mml:math id="M154" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), phytoplankton (PHY), cyanobacteria (CYA), dissolved organic material (DOM)
and particulate organic material (POM) (Appendix <xref ref-type="fig" rid="App1.Ch1.S1.F10"/>).</p>
      <p id="d1e3096">The inorganic carbon chemistry is based on <xref ref-type="bibr" rid="bib1.bibx76" id="text.91"/>, with adjustments in the calculation of chemical constants as described in the OMIP protocol <xref ref-type="bibr" rid="bib1.bibx86" id="paren.92"/>. Total
DIC and total Alk are thereby prognostic tracers from which the carbonate species are determined diagnostically. Total DIC includes all carbonate species and total
Alk includes carbonate as well as borate alkalinity.</p>
      <p id="d1e3105">The dynamics of organic matter cycling in the ocean are based on an NPZD (nutrients, phytoplankton, zooplankton, detritus/POM) model extended with pools for DOM and cyanobacteria.
The phytoplankton growth follows Michaelis–Menten kinetics
as a function of temperature, light and nutrient availability. A constant ratio
(<inline-formula><mml:math id="M155" display="inline"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">P</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">122</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">16</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">3.0</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">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, <xref ref-type="bibr" rid="bib1.bibx105" id="altparen.93"/>) dictates the composition of all oceanic organic matter.
Both oceanic DOM and POM are advected according to the ocean physics, and the POM also sinks as a function of depth <xref ref-type="bibr" rid="bib1.bibx77" id="paren.94"/>. The aerobic remineralization of organic matter
takes place when the <inline-formula><mml:math id="M156" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentration is above a threshold, whereas at low enough <inline-formula><mml:math id="M157" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentrations, denitrification and sulfate reduction can take place.
Furthermore, the phytoplankton produce opal shells when dissolved silica is available, and <inline-formula><mml:math id="M158" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> shells when dissolved silica is depleted.
The <inline-formula><mml:math id="M159" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and opal shells sink at constant rates.</p>
      <p id="d1e3208">HAMOCC also contains a 12-layer sediment module that simulates the same remineralization and dissolution processes as in the water column for sediment constituents <xref ref-type="bibr" rid="bib1.bibx54" id="paren.95"/>.
The sediment consists of a fraction of pore water, which contains dissolved inorganic compounds (e.g., DIC and DIP).
POM, <inline-formula><mml:math id="M160" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and
opal fluxes from the water column are deposited to the top sediment layer. There is a diffusive inorganic compound flux at the water-sediment interface and a particulate flux from the
bottom layer to a diagenetically consolidated burial layer.</p>
      <?pagebreak page62?><p id="d1e3225">Dust is added through atmospheric deposition according to input fields of <xref ref-type="bibr" rid="bib1.bibx75" id="text.96"/>. The model considers the dynamics of <inline-formula><mml:math id="M161" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M162" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M163" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>O and <inline-formula><mml:math id="M164" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and their exchange
at the ocean–atmosphere interface. Since we modeled
a pre-industrial state in this study, we used
constant atmospheric concentrations for <inline-formula><mml:math id="M165" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> of 278 ppmv <xref ref-type="bibr" rid="bib1.bibx31" id="paren.97"/>.</p>
</sec>
<sec id="Ch1.S2.SS2.SSS2">
  <label>2.2.2</label><title>Treatment of the river loads in the ocean biogeochemistry model</title>
      <p id="d1e3298">The biogeochemical riverine loads were added to the ocean surface layer in HAMOCC constantly over the whole year.
The locations of major river mouths were manually corrected on a case-to-case basis for large rivers in order to reproduce the same locations as of the OMIP freshwater inputs.</p>
      <p id="d1e3301">The riverine dissolved inorganic compounds (DIC, Alk, DIP, DIN, DSi, DIC, DFe) were added to the HAMOCC in their species pools.
We added 80 % of P contained in the riverine Fe-P to the oceanic DIP pool in order for the amount of bio-available Fe-P to be comparable to the estimated range given in <xref ref-type="bibr" rid="bib1.bibx22" id="text.98"/> (1.1–1.5 Tg P yr<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>).
The rest of the Fe-P pool was considered to be unreactive in the ocean.
The riverine POM was added to the oceanic POM pool in HAMOCC.</p>
      <p id="d1e3319">For tDOM, we extended HAMOCC with a new model tracer that was characterized by the described <inline-formula><mml:math id="M167" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">Fe</mml:mi></mml:mrow></mml:math></inline-formula> mole ratio. tDOM was mineralized as a function of
the tDOM concentration at a rate constant <inline-formula><mml:math id="M168" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant="normal">rem</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">tDOM</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and of an oxygen limitation factor (<inline-formula><mml:math id="M169" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Γ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>), which decreases the maximum potential remineralization rate
depending on the <inline-formula><mml:math id="M170" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentration:
              <disp-formula id="Ch1.E13" content-type="numbered"><label>13</label><mml:math id="M171" display="block"><mml:mrow><mml:mi mathvariant="normal">dtDOM</mml:mi><mml:mo>/</mml:mo><mml:mi mathvariant="normal">d</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant="normal">rem</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">tDOM</mml:mi></mml:mrow></mml:msub><mml:mo>⋅</mml:mo><mml:mi mathvariant="normal">tDOM</mml:mi><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">Γ</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
            Since a large fraction of tDOM delivered by rivers is already strongly degraded, it is to a certain extent
resistant to microbial degradation in the ocean <xref ref-type="bibr" rid="bib1.bibx59 bib1.bibx111" id="paren.99"/>. We therefore assumed a slightly lower remineralization rate constant of tDOM (<inline-formula><mml:math id="M172" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mi mathvariant="normal">rem</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">tDOM</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) compared to oceanic DOM (0.003 versus 0.008 d<inline-formula><mml:math id="M173" 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 oceanic DOM).
This rate constant is within the range provided for the Louisiana shelf in <xref ref-type="bibr" rid="bib1.bibx35" id="text.100"/> (0.001–0.02 d<inline-formula><mml:math id="M174" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>),
and we also compared open ocean tDOM concentrations to the limitedly available observational data in Supplement S2.2.
The <inline-formula><mml:math id="M175" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> limitation function used (<inline-formula><mml:math id="M176" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Γ</mml:mi><mml:mrow><mml:mi>O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) was the same as the function used for oceanic DOM, which is described in <xref ref-type="bibr" rid="bib1.bibx78" id="text.101"/>.</p>
</sec>
<sec id="Ch1.S2.SS2.SSS3">
  <label>2.2.3</label><title>Pre-industrial ocean biogeochemistry model simulations</title>
      <p id="d1e3511">We performed two ocean model simulations in order to assess the impacts of biogeochemical riverine fluxes in terms of their magnitudes and locations: REF and RIV.</p>
      <p id="d1e3514">REF was performed using the standard model version until now (for instance in <xref ref-type="bibr" rid="bib1.bibx78" id="altparen.102"/>), which was lacking in terms of its representation of
riverine inputs: Biogeochemical inputs were added to the entire surface ocean in order to compensate for sediment burial losses at the global scale.
This was done with the reasoning that in HAMOCC, biogeochemical inputs are needed in order to maintain a stable ocean state, since the burial loss in the sediment induces a loss of <inline-formula><mml:math id="M177" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, opal and POM. Without these model inputs, ocean
biogeochemical pool inventories would thrive to zero. In order to maintain a state close to equilibrium in the standard model version (REF), inputs representing the redissolution of <inline-formula><mml:math id="M178" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (added in a mole
<inline-formula><mml:math id="M179" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Alk</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:math></inline-formula> ratio of <inline-formula><mml:math id="M180" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>),
inputs of DSi and
inputs of oceanic DOM were therefore added homogeneously per area to the entire surface ocean in the magnitudes of the global sediment losses. Therefore, the inputs were almost solely added to the open surface ocean,
since it covers 94 % of the total ocean area in the model (see Supplement S5).
REF was performed for 5000 years, where burial fluxes were computed
approximately every 1000 years. The fluxes resulting from these calculations were added to the ocean at every model time step.</p>
      <p id="d1e3566">The simulation RIV replaced the homogeneous inputs of <inline-formula><mml:math id="M181" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Alk</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:math></inline-formula>, DSi and oceanic DOM to the ocean surface computed from burial losses with riverine inputs of DIP, Fe-P, DIN, DSi, DFe, DIC, Alk, tDOM and POM, which were
derived in the described approach. The major
differences to the REF simulation originate from the geographic locations of the inputs, the magnitudes of C loads to the ocean,
as well as from the riverine mole ratios of <inline-formula><mml:math id="M182" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">Alk</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:math></inline-formula> in comparison to the <inline-formula><mml:math id="M183" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> burial compensation inputs (<inline-formula><mml:math id="M184" 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> for RIV and <inline-formula><mml:math id="M185" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> for REF) and of tDOM (<inline-formula><mml:math id="M186" display="inline"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2583</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>) in comparison to the oceanic DOM inputs
(<inline-formula><mml:math id="M187" display="inline"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">122</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>). Since the riverine inputs to the ocean were fully constrained by our calculations in RIV,
long simulations were needed to equilibrate both the water column and the sediment to the new biogeochemical inputs. We performed a simulation for 4000 years
first, including both the water column and sediment model components. Once particulate fluxes to the sediment were approximately stable, we used the 100-year mean of these fluxes to perform
a 10 000-year simulation of the sediment sub-model.
The resulting sediment state was then coupled back to the water column for a simulation of 2000 more years.</p>
      <p id="d1e3671">We used REF as a reference simulation in order to compare RIV to, which enabled us to compare the impacts
of riverine loads at plausible pre-industrial magnitudes and locations (RIV) to REF, where the vast majority of inputs were added directly to the open ocean.
For the analysis of the resulting ocean biogeochemistry,
we used the last 100-year means of RIV and REF.</p>
</sec>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Definitions of coastal regions for analysis</title>
      <p id="d1e3683">To investigate the impacts of riverine exports on coastal regions, we selected 10 shallow shelf regions characterized by large riverine loads that cover a variety of latitudes (Table <xref ref-type="table" rid="Ch1.T1"/>).
The shelves were defined to have depths of less than 250 m. The cutoff sections perpendicular to the coast were done according to MARgins and CATchments Segmentation (MARCATS) <xref ref-type="bibr" rid="bib1.bibx65" id="paren.103"/>,
except for the Beaufort Sea,<?pagebreak page63?> Laptev Sea, North Sea and Congo shelf, where
we used the COastal Segmentation and related CATchments (COSCATs) definitions
<xref ref-type="bibr" rid="bib1.bibx82" id="paren.104"/> due to the vastness of their MARCATS segmentations.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e3697">Comparison of the surface areas (<inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> m<inline-formula><mml:math id="M189" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>) of selected coastal regions with depths of under 250 m in the ocean model setup
and in the segmentation approaches. The comparisons were done with the MARCATS <xref ref-type="bibr" rid="bib1.bibx65" id="paren.105"/> or
COSCATs (Beaufort Sea, Laptev Sea, North Sea, Congo shelf, <xref ref-type="bibr" rid="bib1.bibx82" id="altparen.106"/>). The shelf classes were defined as in <xref ref-type="bibr" rid="bib1.bibx65" id="text.107"/>.</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="left"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Coastal regions</oasis:entry>
         <oasis:entry colname="col2">Major rivers</oasis:entry>
         <oasis:entry colname="col3">Model</oasis:entry>
         <oasis:entry colname="col4">MARCATS/</oasis:entry>
         <oasis:entry colname="col5">Shelf class</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">area</oasis:entry>
         <oasis:entry colname="col4">COSCAT area</oasis:entry>
         <oasis:entry colname="col5"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">1. Beaufort Sea (BS)</oasis:entry>
         <oasis:entry colname="col2">Mackenzie</oasis:entry>
         <oasis:entry colname="col3">269</oasis:entry>
         <oasis:entry colname="col4">274</oasis:entry>
         <oasis:entry colname="col5">Polar</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2. Laptev Sea (LS)</oasis:entry>
         <oasis:entry colname="col2">Lena</oasis:entry>
         <oasis:entry colname="col3">397</oasis:entry>
         <oasis:entry colname="col4">326</oasis:entry>
         <oasis:entry colname="col5">Polar</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">3. North Sea (NS)</oasis:entry>
         <oasis:entry colname="col2">Rhine</oasis:entry>
         <oasis:entry colname="col3">499</oasis:entry>
         <oasis:entry colname="col4">871</oasis:entry>
         <oasis:entry colname="col5">Marginal sea</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">4. Sea of Okhotsk (OKH)</oasis:entry>
         <oasis:entry colname="col2">Amur</oasis:entry>
         <oasis:entry colname="col3">245</oasis:entry>
         <oasis:entry colname="col4">992</oasis:entry>
         <oasis:entry colname="col5">Marginal sea</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">5. East China Sea (CSK)</oasis:entry>
         <oasis:entry colname="col2">Yangtze, Huang He</oasis:entry>
         <oasis:entry colname="col3">731</oasis:entry>
         <oasis:entry colname="col4">1299</oasis:entry>
         <oasis:entry colname="col5">Tropical</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">6. Bay of Bengal (BEN)</oasis:entry>
         <oasis:entry colname="col2">Ganges</oasis:entry>
         <oasis:entry colname="col3">245</oasis:entry>
         <oasis:entry colname="col4">230</oasis:entry>
         <oasis:entry colname="col5">Indian margin</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">7. Southeast Asia (SEA)</oasis:entry>
         <oasis:entry colname="col2">Mekong</oasis:entry>
         <oasis:entry colname="col3">1795</oasis:entry>
         <oasis:entry colname="col4">2318</oasis:entry>
         <oasis:entry colname="col5">Indian margin</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">8. Tropical west Atlantic (TWA)</oasis:entry>
         <oasis:entry colname="col2">Amazon, Orinoco</oasis:entry>
         <oasis:entry colname="col3">448</oasis:entry>
         <oasis:entry colname="col4">517</oasis:entry>
         <oasis:entry colname="col5">Tropical</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">9. Congo shelf (CG)</oasis:entry>
         <oasis:entry colname="col2">Congo</oasis:entry>
         <oasis:entry colname="col3">53</oasis:entry>
         <oasis:entry colname="col4">38</oasis:entry>
         <oasis:entry colname="col5">Tropical</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">10. South America (SAM)</oasis:entry>
         <oasis:entry colname="col2">Paraná</oasis:entry>
         <oasis:entry colname="col3">1553</oasis:entry>
         <oasis:entry colname="col4">1230</oasis:entry>
         <oasis:entry colname="col5">Subpolar</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Pre-industrial rivers loads</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Global weathering release</title>
      <p id="d1e3981">The weathering release models provide global annual means for the pre-industrial weathering release of P, Si,
DIC and Alk
(Table <xref ref-type="table" rid="Ch1.T2"/>), as well as their spatial distributions (Fig. <xref ref-type="fig" rid="Ch1.F2"/>). The calculated global P release is
1.34 Tg P yr<inline-formula><mml:math id="M190" 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> when considering the runoff scaling factor of 1.59,
which fits within the P release range of 0.8–4 Tg P yr<inline-formula><mml:math id="M191" 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> reported in published literature <xref ref-type="bibr" rid="bib1.bibx22 bib1.bibx112 bib1.bibx41 bib1.bibx52" id="paren.108"/>.
While the <xref ref-type="bibr" rid="bib1.bibx52" id="text.109"/> and <xref ref-type="bibr" rid="bib1.bibx41" id="text.110"/> estimates (1.1 and 0.8–1.2 Tg P yr<inline-formula><mml:math id="M192" 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>, respectively) originate from the same weathering model as is used here, the 1.9 Tg P yr<inline-formula><mml:math id="M193" 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>
value reported
in <xref ref-type="bibr" rid="bib1.bibx112" id="text.111"/> was constructed by upscaling measurement data points.
In a further study, <xref ref-type="bibr" rid="bib1.bibx22" id="text.112"/> provide a quantification of the prehuman phosphorus cycle while distinguishing between land–ocean fluxes from shale-erosion as well as from weathering.
The reported total prehuman riverine P export with a weathering source is given by averaging non-detrital P species concentrations from unpolluted rivers and multiplying them with global
runoff estimates, thereby yielding an estimate of 2.5–4.0 Tg P yr<inline-formula><mml:math id="M194" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.
Both estimates that originate from the upscaling of river measurements are therefore higher than the P weathering fluxes provided in the modeling approach in this study, in <xref ref-type="bibr" rid="bib1.bibx41" id="text.113"/> and in <xref ref-type="bibr" rid="bib1.bibx52" id="text.114"/>, which suggests
further effort might be needed to constrain the global P weathering release more accurately.</p>
      <p id="d1e4071">For Si, we model a global release of 168 Tg Si yr<inline-formula><mml:math id="M195" 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>. This is within the range estimated by
<xref ref-type="bibr" rid="bib1.bibx15" id="text.115"/> (158–199 Tg Si yr<inline-formula><mml:math id="M196" 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>), who used the same
model while using present-day observational data to drive the model for precipitation. Our estimate is also comparable to
the 173 Tg Si yr<inline-formula><mml:math id="M197" 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> value reported by <xref ref-type="bibr" rid="bib1.bibx29" id="text.116"/>.</p>
      <p id="d1e4116">The modeled DIC and Alk release amount to 374 Tg C yr<inline-formula><mml:math id="M198" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and 37.8 Teq yr<inline-formula><mml:math id="M199" 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> globally, which also take into account the runoff scaling factor.
By extrapolating from measurement data of 60 large river catchments, <xref ref-type="bibr" rid="bib1.bibx79" id="text.117"/>
suggests that the global DIC export to the ocean is around 380 Tg yr<inline-formula><mml:math id="M200" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and
originates directly from
weathering. Further modeling studies also provide similar weathering release estimates of 260 to 300 Tg C yr<inline-formula><mml:math id="M201" 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> <xref ref-type="bibr" rid="bib1.bibx13 bib1.bibx4" id="paren.118"/>. The atmospheric <inline-formula><mml:math id="M202" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> drawdown induced
by weathering is directly related to the weathering release of DIC, since silicate weathering draws down 1 mole of <inline-formula><mml:math id="M203" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> per mole <inline-formula><mml:math id="M204" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, and
carbonate weathering
draws down 0.5 mol of <inline-formula><mml:math id="M205" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> per mole <inline-formula><mml:math id="M206" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> released (Eqs. <xref ref-type="disp-formula" rid="Ch1.E9"/> and <xref ref-type="disp-formula" rid="Ch1.E10"/>).
While we model a <inline-formula><mml:math id="M207" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> drawdown flux of 280 Tg C yr<inline-formula><mml:math id="M208" 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> induced by weathering, drawdown
fluxes of 220–440 Tg C yr<inline-formula><mml:math id="M209" 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> are reported in published literature <xref ref-type="bibr" rid="bib1.bibx38 bib1.bibx5 bib1.bibx51 bib1.bibx41" id="paren.119"/>.
The results imply that, of the 374 Tg C yr<inline-formula><mml:math id="M210" 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> DIC released by weathering,
280 Tg C yr<inline-formula><mml:math id="M211" 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> originates from atmospheric C drawdown,
while the rest originates from the weathering DIC release from the carbonate lithology (94 Tg C yr<inline-formula><mml:math id="M212" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e4317">Global pre-industrial weathering release of P, Si, DIC and Alk, as well as <inline-formula><mml:math id="M213" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> drawdown,
modeled in this study and previously estimated in published literature.</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="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Species</oasis:entry>
         <oasis:entry colname="col2">Modeled</oasis:entry>
         <oasis:entry colname="col3">Estimates</oasis:entry>
         <oasis:entry colname="col4">Source</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">weathering</oasis:entry>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">release</oasis:entry>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">P release (Tg yr<inline-formula><mml:math id="M214" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">1.34</oasis:entry>
         <oasis:entry colname="col3">0.8–4.0</oasis:entry>
         <oasis:entry colname="col4">Compton et al. (2000), Wang et al. (2009)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">Hartmann et al. (2014), Goll et al. (2014)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Si release (Tg yr<inline-formula><mml:math id="M215" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">168</oasis:entry>
         <oasis:entry colname="col3">158–200</oasis:entry>
         <oasis:entry colname="col4">Beusen et al. (2009), Dürr et al. (2011)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">Tréguer and De La Rocha (2013)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">DIC release (Tg yr<inline-formula><mml:math id="M216" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">374</oasis:entry>
         <oasis:entry colname="col3">260–550</oasis:entry>
         <oasis:entry colname="col4">Berner et al. (1983), Amiotte Suchet et al. (1995)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">Mackenzie et al. (1998), Hartmann et al. (2009)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Alk release (Teq yr<inline-formula><mml:math id="M217" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">37.6</oasis:entry>
         <oasis:entry colname="col3">–</oasis:entry>
         <oasis:entry colname="col4">–</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M218" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> drawdown (Tg yr<inline-formula><mml:math id="M219" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">280</oasis:entry>
         <oasis:entry colname="col3">220–440</oasis:entry>
         <oasis:entry colname="col4">Gaillardet et al. (1999), Amiotte-Suchet et al. (2003)</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">Hartmann et al. (2009), Goll et al. (2014)</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><label>Figure 2</label><caption><p id="d1e4586">Weathering release yields of <bold>(a)</bold> P (kg P km<inline-formula><mml:math id="M220" 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>), <bold>(b)</bold> Si (t Si km<inline-formula><mml:math id="M221" 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>) and <bold>(c)</bold> DIC (t C km<inline-formula><mml:math id="M222" 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>).</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020-f02.png"/>

        </fig>

      <p id="d1e4641">We observe hotspots that contribute disproportionately
to the weathering release yields, with the Amazon, Southeast Asia
as well as northern Europe and Siberia acting as strong sources of weathering (Fig. <xref ref-type="fig" rid="Ch1.F2"/>).
The disproportionate importance of these regions for the global weathering release is largely due to wet and/or warm climates, as well as to their lithological characteristics <xref ref-type="bibr" rid="bib1.bibx4 bib1.bibx38 bib1.bibx49" id="paren.120"/>.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Global riverine loads in the context of published estimates</title>
      <p id="d1e4657">In our modeling framework, the global pre-industrial riverine exports to the ocean amount to 3.7 Tg P yr<inline-formula><mml:math id="M223" 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>, 27 Tg N yr<inline-formula><mml:math id="M224" 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>, 158 Tg Si yr<inline-formula><mml:math id="M225" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and 603 Tg C yr<inline-formula><mml:math id="M226" 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>,
whereas 0.3 Tg P, 2.2 Tg N, 10 Tg Si and 19 Tg C are retained in endorheic catchments. The fraction of Fe-P assumed to not desorb in the coastal ocean was also subtracted from the global loads (0.2 Pg P yr<inline-formula><mml:math id="M227" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3" specific-use="star"><?xmltex \currentcnt{3}?><label>Table 3</label><caption><p id="d1e4723">Comparison of modeled global riverine loads (Model. global loads) with previous estimates (Tg yr<inline-formula><mml:math id="M228" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>). The total loads thereby exclude particulate inorganic loads,
except for the 1970 POP estimate, which includes all particulate P compounds from the
NEWS2 study. Fe-P only
considers all particulate P (PP) that is assumed to be desorbed in the ocean. The PP value from the NEWS2 study considers both
POP as well as particulate inorganic phosphorus. </p></caption><oasis:table frame="topbot"><oasis:tgroup cols="6">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="left" colsep="1"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="left"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Species</oasis:entry>
         <oasis:entry colname="col2">Model.</oasis:entry>
         <oasis:entry colname="col3">Estimates</oasis:entry>
         <oasis:entry colname="col4">Species</oasis:entry>
         <oasis:entry colname="col5">Model.</oasis:entry>
         <oasis:entry colname="col6">Estimates</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">global</oasis:entry>
         <oasis:entry colname="col3">and</oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5">global</oasis:entry>
         <oasis:entry colname="col6">and</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">load</oasis:entry>
         <oasis:entry colname="col3">source</oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5">load</oasis:entry>
         <oasis:entry colname="col6">source</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">P [Tg P yr<inline-formula><mml:math id="M244" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>]</oasis:entry>
         <oasis:entry colname="col2">3.7</oasis:entry>
         <oasis:entry colname="col3">4–4.8 (prehuman)<inline-formula><mml:math id="M245" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">N [Tg N yr<inline-formula><mml:math id="M246" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>]</oasis:entry>
         <oasis:entry colname="col5">27</oasis:entry>
         <oasis:entry colname="col6">19–21 (pre-industrial)<inline-formula><mml:math id="M247" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">2 (1900)<inline-formula><mml:math id="M248" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">37 (1970)<inline-formula><mml:math id="M249" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">7.6 (1970)<inline-formula><mml:math id="M250" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">DIP</oasis:entry>
         <oasis:entry colname="col2">0.5</oasis:entry>
         <oasis:entry colname="col3">0.3–0.5 (prehuman)<inline-formula><mml:math id="M251" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">DIN</oasis:entry>
         <oasis:entry colname="col5">3.4</oasis:entry>
         <oasis:entry colname="col6">2.4 (pre-industrial)<inline-formula><mml:math id="M252" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">1.1 (1970)<inline-formula><mml:math id="M253" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">14 (1970)<inline-formula><mml:math id="M254" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">DOP</oasis:entry>
         <oasis:entry colname="col2">0.1</oasis:entry>
         <oasis:entry colname="col3">0.2 (prehuman)<inline-formula><mml:math id="M255" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">DON <inline-formula><mml:math id="M256" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> PON</oasis:entry>
         <oasis:entry colname="col5">24</oasis:entry>
         <oasis:entry colname="col6">19 (pre-industrial)<inline-formula><mml:math id="M257" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">0.6 (1970)<inline-formula><mml:math id="M258" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6">23 (1970)<inline-formula><mml:math id="M259" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">POP</oasis:entry>
         <oasis:entry colname="col2">2.2</oasis:entry>
         <oasis:entry colname="col3">0.9 (prehuman)<inline-formula><mml:math id="M260" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">5.9 (PP, 1970)<inline-formula><mml:math id="M261" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">C [Tg C yr<inline-formula><mml:math id="M262" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>]</oasis:entry>
         <oasis:entry colname="col5">603</oasis:entry>
         <oasis:entry colname="col6">450–950 (present day)<inline-formula><mml:math id="M263" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">8</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">9</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">10</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">11</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Fe-P</oasis:entry>
         <oasis:entry colname="col2">0.8</oasis:entry>
         <oasis:entry colname="col3">1.1–1.5 (prehuman)<inline-formula><mml:math id="M264" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4">DIC</oasis:entry>
         <oasis:entry colname="col5">366</oasis:entry>
         <oasis:entry colname="col6">260–550 (present day)<inline-formula><mml:math id="M265" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">12</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">13</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">14</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">–</oasis:entry>
         <oasis:entry colname="col4">DOC</oasis:entry>
         <oasis:entry colname="col5">134</oasis:entry>
         <oasis:entry colname="col6">130–250 (present day)<inline-formula><mml:math id="M266" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">9</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">15</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">POC</oasis:entry>
         <oasis:entry colname="col5">103</oasis:entry>
         <oasis:entry colname="col6">100–140 (present day)<inline-formula><mml:math id="M267" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">9</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">DSi (Tg Si yr<inline-formula><mml:math id="M268" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">158</oasis:entry>
         <oasis:entry colname="col3">158–200 (present day)<inline-formula><mml:math id="M269" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">4</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">5</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e4738"><inline-formula><mml:math id="M229" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx22" id="text.121"/>. <inline-formula><mml:math id="M230" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx16" id="text.122"/>.
<inline-formula><mml:math id="M231" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> NEWS2 <xref ref-type="bibr" rid="bib1.bibx98" id="paren.123"/>. <inline-formula><mml:math id="M232" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx15" id="text.124"/>. <inline-formula><mml:math id="M233" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">5</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx29" id="text.125"/>. <inline-formula><mml:math id="M234" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx108" id="text.126"/>.
<inline-formula><mml:math id="M235" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx42" id="text.127"/>. <inline-formula><mml:math id="M236" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">8</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx61" id="text.128"/>. <inline-formula><mml:math id="M237" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx81" id="text.129"/>. <inline-formula><mml:math id="M238" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx91" id="text.130"/>. <inline-formula><mml:math id="M239" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">11</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx90" id="text.131"/>.
<inline-formula><mml:math id="M240" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">12</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx13" id="text.132"/>.
<inline-formula><mml:math id="M241" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">13</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx4" id="text.133"/>. <inline-formula><mml:math id="M242" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">14</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx73" id="text.134"/>. <inline-formula><mml:math id="M243" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">15</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx21" id="text.135"/>.</p></table-wrap-foot></table-wrap>

      <p id="d1e5541">In the following, we compare the magnitudes of the modeled pre-industrial riverine exports of P, N, Si and C, as well as of their fractionations, with a wide range of estimates found in published literature (Table <xref ref-type="table" rid="Ch1.T3"/>).
This was done in comparison to pre-industrial estimates directly, as well as to 1970 estimates by the NEWS2 study, in order to assess the modeled loads in the context of present-day estimations.</p>
      <p id="d1e5547">The modeled global P loads are slightly below the P export estimate range of 4–4.7 Tg P yr<inline-formula><mml:math id="M270" 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> reported in <xref ref-type="bibr" rid="bib1.bibx22" id="text.136"/>, which was constructed by scaling measured catchment P
loads of pristine rivers to the global
river freshwater discharge (thus prehuman). A recent modeling study by <xref ref-type="bibr" rid="bib1.bibx16" id="text.137"/>, which takes P retention processes in rivers into account, suggests a lower global load of
2 Tg P yr<inline-formula><mml:math id="M271" 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 the year 1900. The 1970 estimate (7.6 Tg P yr<inline-formula><mml:math id="M272" 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>) provided by the NEWS2 study, which considers substantial anthropogenic P inputs,
nevertheless suggests a steep 20th century increase in the global P export to the ocean when considering all three pre-industrial estimates.
The modeled DIP export to the ocean (0.5 Tg P yr<inline-formula><mml:math id="M273" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) is situated at the top range of the prehuman estimates (0.3–0.5 Tg  yr<inline-formula><mml:math id="M274" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) and well below estimates for the year
1970 (1.1 Tg P yr<inline-formula><mml:math id="M275" 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>).
A direct fractionation of the global P flux to DIP, DOP and POP is not provided in the <xref ref-type="bibr" rid="bib1.bibx16" id="text.138"/> study.
Furthermore, we estimate similar global loads of DOP to <xref ref-type="bibr" rid="bib1.bibx22" id="text.139"/> (around 0.1 and 0.2 Tg P yr<inline-formula><mml:math id="M276" 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>,<?pagebreak page64?> respectively). The modeled DOP value is also much lower than the 1970 DOP estimate (0.6 Tg P yr<inline-formula><mml:math id="M277" 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>),
which is realistic due to the human-caused increase of DOP loads during the 20th century <xref ref-type="bibr" rid="bib1.bibx98" id="paren.140"/>.
The modeled POP global load is larger than the estimate of <xref ref-type="bibr" rid="bib1.bibx22" id="text.141"/>, which could be due to the POM <inline-formula><mml:math id="M278" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratio of 122:1 chosen in our study.
Strong uncertainties exist in the global <inline-formula><mml:math id="M279" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratios for riverine POM, with <xref ref-type="bibr" rid="bib1.bibx80" id="text.142"/> suggesting a mole ratio of around 56 <inline-formula><mml:math id="M280" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula>, whereas <xref ref-type="bibr" rid="bib1.bibx88" id="text.143"/> estimate a ratio of around 499, which would strongly affect
the results given here.
The particulate P load given in the NEWS2 study
is vastly higher than the POP load modeled in our study, but a large fraction of the estimate is likely detrital particulate P, which we do not account for in the present study.
The modeled Fe-P (1.0 Tg P yr<inline-formula><mml:math id="M281" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) is slightly below the range estimated in <xref ref-type="bibr" rid="bib1.bibx22" id="text.144"/> (1.5–3.0 Tg P yr<inline-formula><mml:math id="M282" 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>). However, the
assumed reactive fraction of the
Fe-P loads (0.8 Tg P yr<inline-formula><mml:math id="M283" 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>) here is close to how much Fe-P is suggested to be desorbed in the coastal ocean in <xref ref-type="bibr" rid="bib1.bibx22" id="text.145"/> (1.1–1.5 Tg P yr<inline-formula><mml:math id="M284" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>).</p>
      <p id="d1e5764">Despite our simplified assumption of N loads being directly coupled to P loads, the modeled global N load is situated within the prehuman and contemporary
land–ocean N load estimates modeled in <xref ref-type="bibr" rid="bib1.bibx42" id="text.146"/> (21 and 40 Tg N yr<inline-formula><mml:math id="M285" 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>, respectively). The modeled annual DIN load (3.4 Tg N)
is slightly higher than the prehuman load given in the <xref ref-type="bibr" rid="bib1.bibx42" id="text.147"/> study (2.4 Tg N yr<inline-formula><mml:math id="M286" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>). In <xref ref-type="bibr" rid="bib1.bibx16" id="text.148"/>, the global pre-industrial N load is suggested to be lower (19 Tg N yr<inline-formula><mml:math id="M287" 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>)
due to
in-stream retention and removal of N.</p>
      <?pagebreak page66?><p id="d1e5813">Since we assume that the change in the global DSi load over the 20th century is small, we directly compare our modeled pre-industrial DSi load estimate with present-day DSi load estimates from published literature.
The modeled global load of DSi is 158 Tg Si yr<inline-formula><mml:math id="M288" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in our framework, which is situated at the low end of the present-day estimate range of 158–200 Tg Si yr<inline-formula><mml:math id="M289" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.
The NEWS2 study used the same <xref ref-type="bibr" rid="bib1.bibx15" id="text.149"/> DSi export model forced with present-day observational precipitation data. <xref ref-type="bibr" rid="bib1.bibx29" id="text.150"/> and <xref ref-type="bibr" rid="bib1.bibx108" id="text.151"/> upscaled
from discharge-weighted DSi concentrations at river mouths.  Substantial amounts of particulate Si are suggested to be delivered to the ocean, yet it is not clear how much of it is dissolvable in the ocean <xref ref-type="bibr" rid="bib1.bibx108" id="paren.152"/>,
and, therefore, particulate Si is not considered in our study.
The effects from contemporary increases in river damming on global DSi loads are also uncertain. Increased damming could have increased the global
silica retention in rivers <xref ref-type="bibr" rid="bib1.bibx60 bib1.bibx71" id="paren.153"/>. Therefore, the global pre-industrial DSi load to the ocean could potentially have been larger than for the present day, but quantifying the
implications of damming for the
in-stream retention of DSi, as well as of suggested increased DSi inputs from weathering and from the terrestrial biosphere (e.g., <xref ref-type="bibr" rid="bib1.bibx40" id="altparen.154"/>) escape the scope of this study.</p>
      <p id="d1e5859">In our study, we also assumed that the pre-industrial C loads of all species were the same as for the present day.
While the C retention along the land–ocean continuum might have
increased during the 20th century,
enhanced soil erosion through changes in land use might have also increased the C inputs to the freshwater systems, leaving question marks on the magnitude of the net anthropogenic perturbation <xref ref-type="bibr" rid="bib1.bibx90 bib1.bibx72" id="paren.155"/>.
The modeled total C, DIC, DOC and POC fluxes agree with the present-day estimate ranges shown in Table <xref ref-type="table" rid="Ch1.T3"/> but are also situated at the lower end of these ranges. The organic C loads,
which originate directly from the NEWS2 study, are particularly low.</p>
      <p id="d1e5867">The large spreads of the riverine export estimates
underline difficulties in constraining pre-industrial riverine fluxes. Even for the present day, <xref ref-type="bibr" rid="bib1.bibx16" id="text.156"/> note large differences between the simulated loads of their study and the previous
global modeling study NEWS2.
In turn, upscaling from point measurements are often based on data collected by <xref ref-type="bibr" rid="bib1.bibx79" id="text.157"/> for the pre-1980 time period without taking into account more recent river measurement data. They also rely on the assumption of a linear
relationship between riverine discharge and compound loads.
While we acknowledge a certain degree of uncertainty in the numbers provided
in this study, the modeling approach chosen nevertheless leads to global pre-industrial riverine loads that are in line with
what was suggested previously and
constitutes a framework that could be incorporated within state-of-the-art Earth system models.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Hotspots of riverine loads</title>
      <p id="d1e5884">We observe several regions of disproportionate contributions to global riverine loads (Fig. <xref ref-type="fig" rid="Ch1.F3"/>, Table <xref ref-type="table" rid="Ch1.T4"/>), with a distribution largely following spatial patterns of the weathering
release.
Our framework reveals large differences between the riverine exports from the Northern Hemisphere and from the Southern Hemisphere.
The Northern Hemisphere thereby accounts for an annual riverine C input of 404 Tg C to the ocean, vastly dominating
the global loads (67 % of global riverine C), while the Southern Hemisphere delivers 199 Tg C (33 % global riverine C).</p>
      <p id="d1e5891">Rivers that drain into the tropical Atlantic basin consist of a major fraction of the global oceanic biogeochemical supply (Table <xref ref-type="table" rid="Ch1.T4"/>). This is due to major rivers
of the South American continent debouching into the ocean basin, as well
as considerable exports provided by West African rivers. According to our framework, the annual C loads of the seven largest rivers debouching in the basin (Orinoco, Amazon, São Francisco, Paraíba do Sul, Volta, Niger and Congo) amount to
123 Tg C (fractionated into 58 Tg DIC, 44 Tg DOC, 21 Tg POC), which consists of around 20 % with respect to global riverine C exports. These regional C loads agree very well
with estimated values derived from monthly data of
<xref ref-type="bibr" rid="bib1.bibx6" id="text.158"/> (53 Tg DIC, 46 Tg DOC). Of these major rivers, the pre-industrial Amazon river provides the largest input of biogeochemical tracers to the ocean
(modeled annual loads of 0.07 Tg DIP, 0.5 Tg DIN, 15.2 Tg DSi, 33.2 Tg DIC, 28.3 Tg DOC Tg, 17.1 Tg POC), which compare well with the present-day data (0.22 Tg DIP, 17.8 Tg DSi,
32.7 Tg DIC, 29.1 Tg DOC, <xref ref-type="bibr" rid="bib1.bibx6" id="altparen.159"/>). For the other catchments debouching in the tropical Atlantic, the modeled DIC loads are close to estimated values for the Congo, Orinoco and Niger, but are overestimated for the smaller catchments of the Paraíba, Volta
and São Francisco. Calculating the regional sum of the modeled pre-industrial and estimated present-day DIP loads reveals a much lower pre-industrial load (<inline-formula><mml:math id="M290" display="inline"><mml:mrow><mml:mn mathvariant="normal">81.8</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> g P yr<inline-formula><mml:math id="M291" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)
with respect to the total present-day load (<inline-formula><mml:math id="M292" display="inline"><mml:mrow><mml:mn mathvariant="normal">276</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> g P yr<inline-formula><mml:math id="M293" 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>), suggesting a realistic increase of <inline-formula><mml:math id="M294" display="inline"><mml:mrow><mml:mn mathvariant="normal">194</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> g P yr<inline-formula><mml:math id="M295" 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> due to anthropogenic perturbations.</p>
      <p id="d1e5984">Although less substantial in the context of global loads,
major Arctic rivers (Yukon, Mackenzie, Ob, Lena, Yenisei) provide a large C supply to the Arctic Ocean, with a dominant fraction of the C load consisting of DIC. In our framework, these rivers provide 37.5 Tg DIC (10 % of global
DIC), 14.4 Tg DOC (11 % of global DOC) and 4.4 Tg POC annually to the Arctic Ocean. The total riverine
C loads to the Arctic therefore amount to 56 Tg C yr<inline-formula><mml:math id="M296" 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>, thus 9 % of global C loads.
The DIC, DOC and POC load levels are comparable to estimates of 29 Tg DIC yr<inline-formula><mml:math id="M297" 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> <xref ref-type="bibr" rid="bib1.bibx106" id="paren.160"/>, 17 Tg DOC yr<inline-formula><mml:math id="M298" 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> <xref ref-type="bibr" rid="bib1.bibx89" id="paren.161"/>
and 5 Tg POC <xref ref-type="bibr" rid="bib1.bibx27" id="paren.162"/>. Total Arctic DIP loads (<inline-formula><mml:math id="M299" display="inline"><mml:mrow><mml:mn mathvariant="normal">40.8</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> g P yr<inline-formula><mml:math id="M300" 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>) derived from our modeling approach are slightly higher
with regard to the published literature estimate of <inline-formula><mml:math id="M301" display="inline"><mml:mrow><mml:mn mathvariant="normal">35.8</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> g P yr<inline-formula><mml:math id="M302" 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>. DIP inputs from anthropogenic sources are considered to be small for Arctic catchments <xref ref-type="bibr" rid="bib1.bibx98" id="paren.163"/>,
which explains why the modeled pre-industrial
DIP loads are of similar magnitudes to observed DIP loads for the present day. Modeled Arctic DIC and DIP loads, which are strongly affected by inputs from the weathering models used in this study,
are slightly larger with respect to published literature estimates, suggesting that the runoff scaling factor of 1.59 that we applied within the weathering models might be too high for this region.
Certain factors, such as the effects of permafrost on weathering rates, which could impact the dynamics of weathering in the region, also remain enigmatic <xref ref-type="bibr" rid="bib1.bibx52" id="paren.164"/>.</p>
      <?pagebreak page67?><p id="d1e6094">Southeast Asian rivers also provide large loads of biogeochemical tracers to the ocean. The Huang He, Brahmaputra–Ganges, Yangtze, Mekong, Irrawaddy and Salween rivers, which have catchment areas characterized by warm and humid climates,
provide 92.4 Tg C yr<inline-formula><mml:math id="M303" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> to the ocean (15 % of global C loads). We observe vastly elevated DIP levels for the present-day estimates (<inline-formula><mml:math id="M304" display="inline"><mml:mrow><mml:mn mathvariant="normal">76.4</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> g P yr<inline-formula><mml:math id="M305" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) with
regards to our modeled pre-industrial loads (<inline-formula><mml:math id="M306" display="inline"><mml:mrow><mml:mn mathvariant="normal">299</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> g P yr<inline-formula><mml:math id="M307" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>). The NEWS2 study
suggests a strong present-day perturbation of the DIP loads due to
anthropogenic inputs to the region's catchments <xref ref-type="bibr" rid="bib1.bibx98" id="paren.165"/>, which can plausibly explain these differences.</p>
      <p id="d1e6168">The Indo-Pacific islands have been identified as a region with much higher weathering yields than the global average <xref ref-type="bibr" rid="bib1.bibx52" id="paren.166"/>. Although this region only
accounts for around 2 % of the global land surface, it provides 7 % (39 Tg) of C and most notably 10 % of the global POC (10 Tg C) delivered by rivers to the ocean annually, making the region
a stronger terrestrial source of POC than all Arctic catchments. Thus, the POM mobilization through soil erosion is likely a major driver of land–sea carbon exports in the region.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><label>Figure 3</label><caption><p id="d1e6176">Modeled annual river loads of DIP <bold>(a)</bold>, DSi <bold>(b)</bold>, DIC <bold>(c)</bold>, Alk <bold>(d)</bold>, DOM <bold>(e)</bold> and POM <bold>(f)</bold>.</p></caption>
          <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020-f03.png"/>

        </fig>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T4" specific-use="star"><?xmltex \currentcnt{4}?><label>Table 4</label><caption><p id="d1e6207">Regional hotspots of riverine C loads (Tg C yr<inline-formula><mml:math id="M308" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) and DIP loads (<inline-formula><mml:math id="M309" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> g P yr<inline-formula><mml:math id="M310" 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>) compared with regional estimates.  Modeled DIP from our approach represents pre-industrial fluxes, whereas the DIP literature estimates
are from present-day data and are strongly affected by anthropogenic perturbations.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="9">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right" colsep="1"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:colspec colnum="9" colname="col9" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Hotspots</oasis:entry>
         <oasis:entry namest="col2" nameend="col5" align="center" colsep="1">Modeled </oasis:entry>
         <oasis:entry namest="col6" nameend="col9" align="center">Estimates </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">DIC</oasis:entry>
         <oasis:entry colname="col3">DOC</oasis:entry>
         <oasis:entry colname="col4">POC</oasis:entry>
         <oasis:entry colname="col5">DIP</oasis:entry>
         <oasis:entry colname="col6">DIC</oasis:entry>
         <oasis:entry colname="col7">DOC</oasis:entry>
         <oasis:entry colname="col8">POC</oasis:entry>
         <oasis:entry colname="col9">DIP</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col9">Tropical Atlantic </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Amazon</oasis:entry>
         <oasis:entry colname="col2">33.2</oasis:entry>
         <oasis:entry colname="col3">28.2</oasis:entry>
         <oasis:entry colname="col4">17.1</oasis:entry>
         <oasis:entry colname="col5">73</oasis:entry>
         <oasis:entry colname="col6">32.7<inline-formula><mml:math id="M321" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">29<inline-formula><mml:math id="M322" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">6.1<inline-formula><mml:math id="M323" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col9">221<inline-formula><mml:math id="M324" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Congo</oasis:entry>
         <oasis:entry colname="col2">9</oasis:entry>
         <oasis:entry colname="col3">5.6</oasis:entry>
         <oasis:entry colname="col4">1.2</oasis:entry>
         <oasis:entry colname="col5">2.3</oasis:entry>
         <oasis:entry colname="col6">13<inline-formula><mml:math id="M325" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">10.58<inline-formula><mml:math id="M326" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">2.0<inline-formula><mml:math id="M327" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col9">18 <inline-formula><mml:math id="M328" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Paraíba</oasis:entry>
         <oasis:entry colname="col2">2.4</oasis:entry>
         <oasis:entry colname="col3">0.5</oasis:entry>
         <oasis:entry colname="col4">0.4</oasis:entry>
         <oasis:entry colname="col5">&lt; 0.1</oasis:entry>
         <oasis:entry colname="col6">0.3<inline-formula><mml:math id="M329" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">0.10<inline-formula><mml:math id="M330" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">–</oasis:entry>
         <oasis:entry colname="col9">0.6<inline-formula><mml:math id="M331" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Volta</oasis:entry>
         <oasis:entry colname="col2">3</oasis:entry>
         <oasis:entry colname="col3">0.5</oasis:entry>
         <oasis:entry colname="col4">0.5</oasis:entry>
         <oasis:entry colname="col5">0.1</oasis:entry>
         <oasis:entry colname="col6">0.1<inline-formula><mml:math id="M332" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">0.13<inline-formula><mml:math id="M333" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">–</oasis:entry>
         <oasis:entry colname="col9">7.0<inline-formula><mml:math id="M334" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Niger</oasis:entry>
         <oasis:entry colname="col2">1.1</oasis:entry>
         <oasis:entry colname="col3">1.5</oasis:entry>
         <oasis:entry colname="col4">0.9</oasis:entry>
         <oasis:entry colname="col5">1.0</oasis:entry>
         <oasis:entry colname="col6">2.2<inline-formula><mml:math id="M335" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">0.43<inline-formula><mml:math id="M336" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">0.8<inline-formula><mml:math id="M337" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col9">7.5<inline-formula><mml:math id="M338" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">São Francisco</oasis:entry>
         <oasis:entry colname="col2">6</oasis:entry>
         <oasis:entry colname="col3">2.9</oasis:entry>
         <oasis:entry colname="col4">0.2</oasis:entry>
         <oasis:entry colname="col5">2.4</oasis:entry>
         <oasis:entry colname="col6">0.5<inline-formula><mml:math id="M339" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">0.35<inline-formula><mml:math id="M340" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">–</oasis:entry>
         <oasis:entry colname="col9">0.5<inline-formula><mml:math id="M341" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Orinoco</oasis:entry>
         <oasis:entry colname="col2">3.3</oasis:entry>
         <oasis:entry colname="col3">4.8</oasis:entry>
         <oasis:entry colname="col4">1.1</oasis:entry>
         <oasis:entry colname="col5">2.9</oasis:entry>
         <oasis:entry colname="col6">5.0 <inline-formula><mml:math id="M342" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">3.9<inline-formula><mml:math id="M343" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">1.7<inline-formula><mml:math id="M344" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col9">21.4<inline-formula><mml:math id="M345" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Total</oasis:entry>
         <oasis:entry colname="col2">58</oasis:entry>
         <oasis:entry colname="col3">44</oasis:entry>
         <oasis:entry colname="col4">21</oasis:entry>
         <oasis:entry colname="col5">81.8</oasis:entry>
         <oasis:entry colname="col6">53</oasis:entry>
         <oasis:entry colname="col7">46</oasis:entry>
         <oasis:entry colname="col8">–</oasis:entry>
         <oasis:entry colname="col9">276</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col9">Arctic </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Mackenzie</oasis:entry>
         <oasis:entry colname="col2">4.5</oasis:entry>
         <oasis:entry colname="col3">1.7</oasis:entry>
         <oasis:entry colname="col4">0.4</oasis:entry>
         <oasis:entry colname="col5">6.0</oasis:entry>
         <oasis:entry colname="col6">6.29<inline-formula><mml:math id="M346" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">1.4<inline-formula><mml:math id="M347" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">–</oasis:entry>
         <oasis:entry colname="col9">1.5<inline-formula><mml:math id="M348" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Yukon</oasis:entry>
         <oasis:entry colname="col2">3.1</oasis:entry>
         <oasis:entry colname="col3">6.1</oasis:entry>
         <oasis:entry colname="col4">0.9</oasis:entry>
         <oasis:entry colname="col5">3.8</oasis:entry>
         <oasis:entry colname="col6">4.45<inline-formula><mml:math id="M349" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">1.7<inline-formula><mml:math id="M350" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">–</oasis:entry>
         <oasis:entry colname="col9">1.9<inline-formula><mml:math id="M351" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Lena</oasis:entry>
         <oasis:entry colname="col2">12.7</oasis:entry>
         <oasis:entry colname="col3">2.0</oasis:entry>
         <oasis:entry colname="col4">1.1</oasis:entry>
         <oasis:entry colname="col5">8.23</oasis:entry>
         <oasis:entry colname="col6">5.82<inline-formula><mml:math id="M352" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">5.83<inline-formula><mml:math id="M353" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">0.47<inline-formula><mml:math id="M354" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col9">4.4<inline-formula><mml:math id="M355" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Yenisei</oasis:entry>
         <oasis:entry colname="col2">8.6</oasis:entry>
         <oasis:entry colname="col3">2.0</oasis:entry>
         <oasis:entry colname="col4">1.2</oasis:entry>
         <oasis:entry colname="col5">8.8</oasis:entry>
         <oasis:entry colname="col6">6.96<inline-formula><mml:math id="M356" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">4.69<inline-formula><mml:math id="M357" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">0.17<inline-formula><mml:math id="M358" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col9">7.9<inline-formula><mml:math id="M359" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Ob</oasis:entry>
         <oasis:entry colname="col2">8.6</oasis:entry>
         <oasis:entry colname="col3">2.6</oasis:entry>
         <oasis:entry colname="col4">0.8</oasis:entry>
         <oasis:entry colname="col5">14.1</oasis:entry>
         <oasis:entry colname="col6">5.90<inline-formula><mml:math id="M360" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">3.05<inline-formula><mml:math id="M361" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">0.3-0.6<inline-formula><mml:math id="M362" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col9">20.4<inline-formula><mml:math id="M363" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Total</oasis:entry>
         <oasis:entry colname="col2">37.5</oasis:entry>
         <oasis:entry colname="col3">14.4</oasis:entry>
         <oasis:entry colname="col4">4.4</oasis:entry>
         <oasis:entry colname="col5">40.8</oasis:entry>
         <oasis:entry colname="col6">29.4</oasis:entry>
         <oasis:entry colname="col7">16.7</oasis:entry>
         <oasis:entry colname="col8">1.09</oasis:entry>
         <oasis:entry colname="col9">35.8</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry namest="col1" nameend="col9">Southeast Asia </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Ganges</oasis:entry>
         <oasis:entry colname="col2">7.7</oasis:entry>
         <oasis:entry colname="col3">5.8</oasis:entry>
         <oasis:entry colname="col4">15.6</oasis:entry>
         <oasis:entry colname="col5">21.3</oasis:entry>
         <oasis:entry colname="col6">4.2<inline-formula><mml:math id="M364" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">1.4<inline-formula><mml:math id="M365" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">1.7<inline-formula><mml:math id="M366" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col9">165<inline-formula><mml:math id="M367" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Irrawaddy</oasis:entry>
         <oasis:entry colname="col2">2.5</oasis:entry>
         <oasis:entry colname="col3">6.1</oasis:entry>
         <oasis:entry colname="col4">0.9</oasis:entry>
         <oasis:entry colname="col5">4.6</oasis:entry>
         <oasis:entry colname="col6">10.8<inline-formula><mml:math id="M368" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">0.89<inline-formula><mml:math id="M369" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">3.25<inline-formula><mml:math id="M370" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col9">8.7<inline-formula><mml:math id="M371" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Salween</oasis:entry>
         <oasis:entry colname="col2">0.7</oasis:entry>
         <oasis:entry colname="col3">0.3</oasis:entry>
         <oasis:entry colname="col4">0.7</oasis:entry>
         <oasis:entry colname="col5">0.8</oasis:entry>
         <oasis:entry colname="col6">8.4<inline-formula><mml:math id="M372" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">0.26<inline-formula><mml:math id="M373" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">2.9<inline-formula><mml:math id="M374" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col9">1.9<inline-formula><mml:math id="M375" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Mekong</oasis:entry>
         <oasis:entry colname="col2">4.4</oasis:entry>
         <oasis:entry colname="col3">2.1</oasis:entry>
         <oasis:entry colname="col4">3.1</oasis:entry>
         <oasis:entry colname="col5">7.2</oasis:entry>
         <oasis:entry colname="col6">4.5<inline-formula><mml:math id="M376" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">–</oasis:entry>
         <oasis:entry colname="col8">–</oasis:entry>
         <oasis:entry colname="col9">0.9<inline-formula><mml:math id="M377" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">8</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Huang He</oasis:entry>
         <oasis:entry colname="col2">3.6</oasis:entry>
         <oasis:entry colname="col3">0.5</oasis:entry>
         <oasis:entry colname="col4">0.3</oasis:entry>
         <oasis:entry colname="col5">8.3</oasis:entry>
         <oasis:entry colname="col6">1.3<inline-formula><mml:math id="M378" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">0.1<inline-formula><mml:math id="M379" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">6.3<inline-formula><mml:math id="M380" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col9">5.0<inline-formula><mml:math id="M381" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Yangtze</oasis:entry>
         <oasis:entry colname="col2">23</oasis:entry>
         <oasis:entry colname="col3">3.5</oasis:entry>
         <oasis:entry colname="col4">1.7</oasis:entry>
         <oasis:entry colname="col5">29.9</oasis:entry>
         <oasis:entry colname="col6">24<inline-formula><mml:math id="M382" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col7">2.1<inline-formula><mml:math id="M383" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">6<inline-formula><mml:math id="M384" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col9">92<inline-formula><mml:math id="M385" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Xi</oasis:entry>
         <oasis:entry colname="col2">8.6</oasis:entry>
         <oasis:entry colname="col3">0.9</oasis:entry>
         <oasis:entry colname="col4">0.4</oasis:entry>
         <oasis:entry colname="col5">4.3</oasis:entry>
         <oasis:entry colname="col6">–</oasis:entry>
         <oasis:entry colname="col7">4.6<inline-formula><mml:math id="M386" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col8">–</oasis:entry>
         <oasis:entry colname="col9">25<inline-formula><mml:math id="M387" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Total</oasis:entry>
         <oasis:entry colname="col2">50.5</oasis:entry>
         <oasis:entry colname="col3">19.2</oasis:entry>
         <oasis:entry colname="col4">22.7</oasis:entry>
         <oasis:entry colname="col5">76.4</oasis:entry>
         <oasis:entry colname="col6">–</oasis:entry>
         <oasis:entry colname="col7">–</oasis:entry>
         <oasis:entry colname="col8">–</oasis:entry>
         <oasis:entry colname="col9">299</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry namest="col1" nameend="col9">Indo-Pacific islands </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Total</oasis:entry>
         <oasis:entry colname="col2">19.4</oasis:entry>
         <oasis:entry colname="col3">10.2</oasis:entry>
         <oasis:entry colname="col4">10.1</oasis:entry>
         <oasis:entry colname="col5">24.7</oasis:entry>
         <oasis:entry colname="col6">–</oasis:entry>
         <oasis:entry colname="col7">–</oasis:entry>
         <oasis:entry colname="col8">–</oasis:entry>
         <oasis:entry colname="col9">–</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e6245"><inline-formula><mml:math id="M311" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">1</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx6" id="text.167"/>. <inline-formula><mml:math id="M312" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>
<xref ref-type="bibr" rid="bib1.bibx17" id="text.168"/>. <inline-formula><mml:math id="M313" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx106" id="text.169"/>. <inline-formula><mml:math id="M314" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx89" id="text.170"/>. <inline-formula><mml:math id="M315" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">5</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx27" id="text.171"/>. <inline-formula><mml:math id="M316" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx68" id="text.172"/>. <inline-formula><mml:math id="M317" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">7</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx69" id="text.173"/>.
<inline-formula><mml:math id="M318" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">8</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx114" id="text.174"/>. <inline-formula><mml:math id="M319" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx107" id="text.175"/>. <inline-formula><mml:math id="M320" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msup></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx98" id="text.176"/>.</p></table-wrap-foot></table-wrap>

</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Implications for the global ocean biogeochemistry</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>The ocean state – an increased biogeochemical coastal sink</title>
      <p id="d1e7737">In the ocean simulations, the magnitudes of oceanic nutrient inputs (P, N and Si) do not strongly differ between REF and RIV (Table <xref ref-type="table" rid="Ch1.T5"/>). This implies that in REF, the
amounts of P, N and Si added to maintain a plausible ocean biogeochemical state were similar to what is derived in our approach to estimate pre-industrial riverine exports.
Despite slightly larger P and N inputs in RIV than in REF, RIV simulates
lower global surface dissolved P and N concentrations, and lower global NPP.
The coastal ocean therefore must act as an increased biogeochemical sink in RIV, since the produced organic matter reaches the shallow coastal sea floor
faster than in the open ocean, which allows for less
time for the organic matter to be remineralized within the water column. This is confirmed by the increased organic matter flux to the global coastal sediment (defined as areas with less than 250 m depths),
with an increase from 0.18 Gt C yr<inline-formula><mml:math id="M388" 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> (REF) to 0.25 Gt C yr<inline-formula><mml:math id="M389" 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> (RIV).
The global coastal POM deposition range given in a review by <xref ref-type="bibr" rid="bib1.bibx63" id="text.177"/> shows a large degree of uncertainty (0.19–2.20 Gt C yr<inline-formula><mml:math id="M390" 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>),
but nevertheless hints that the coastal POM deposition flux is possibly improved in RIV.</p>
      <p id="d1e7781">While Alk inputs were also added at nearly the same levels in REF as in the calculated riverine loads of RIV, the global C inputs are on the other hand increased by almost 100 % in RIV in comparison to REF.
The inorganic (366 Tg C yr<inline-formula><mml:math id="M391" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) and
organic (237 Tg C yr<inline-formula><mml:math id="M392" 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>) C inputs
in RIV show stronger agreement with the
riverine inorganic (260–550 Tg C yr<inline-formula><mml:math id="M393" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)
and organic C (270–350 Tg C yr<inline-formula><mml:math id="M394" 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>) global load estimates found in literature <xref ref-type="bibr" rid="bib1.bibx79 bib1.bibx4 bib1.bibx73 bib1.bibx81 bib1.bibx51 bib1.bibx98 bib1.bibx21 bib1.bibx90" id="paren.178"/>,
signifying an improvement in the model's C inputs with respect to REF.
These higher C inputs also result in a net long-term outgassing flux (231 Tg C yr<inline-formula><mml:math id="M395" 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>), which is suggested in literature for the pre-industrial time period and is absent in REF.
The net outgassing largely originates from higher <inline-formula><mml:math id="M396" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">DIC</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">Alk</mml:mi></mml:mrow></mml:math></inline-formula> ratios of the riverine inputs (<inline-formula><mml:math id="M397" 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>) than is exported through the net <inline-formula><mml:math id="M398" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> production (<inline-formula><mml:math id="M399" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula>), as well as higher <inline-formula><mml:math id="M400" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratios of tDOM inputs (<inline-formula><mml:math id="M401" display="inline"><mml:mrow><mml:mn mathvariant="normal">2583</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>) than is exported in the
oceanic organic ratio (<inline-formula><mml:math id="M402" display="inline"><mml:mrow><mml:mn mathvariant="normal">122</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>). Both of these imbalances between oceanic input and export ratios lead to an increase of the <inline-formula><mml:math id="M403" display="inline"><mml:mrow class="chem"><mml:mi>p</mml:mi><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M404" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> outgassing in the long term (see Appendix C2).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T5" specific-use="star"><?xmltex \currentcnt{5}?><label>Table 5</label><caption><p id="d1e7959">Comparison of global oceanic inputs and global ocean biogeochemical state variables for REF and RIV. Additionally, we compare the modeled global mean surface DIP, DIN and DSi
concentrations with World Ocean Atlas 2013 (WOA) surface layer means. OMZs: oxygen minimum zones.</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="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right" colsep="1"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <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 rowsep="1">
         <oasis:entry colname="col1">Variables</oasis:entry>
         <oasis:entry colname="col2">REF</oasis:entry>
         <oasis:entry colname="col3">RIV</oasis:entry>
         <oasis:entry colname="col4">Variables</oasis:entry>
         <oasis:entry colname="col5">REF</oasis:entry>
         <oasis:entry colname="col6">RIV</oasis:entry>
         <oasis:entry colname="col7">WOA</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col3" colsep="1">Open ocean and river inputs </oasis:entry>
         <oasis:entry namest="col4" nameend="col7">Global ocean variables </oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">P (Tg P yr<inline-formula><mml:math id="M405" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">3.49</oasis:entry>
         <oasis:entry colname="col3">3.7</oasis:entry>
         <oasis:entry colname="col4">NPP (Gt C yr<inline-formula><mml:math id="M406" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">48.87</oasis:entry>
         <oasis:entry colname="col6">47.09</oasis:entry>
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">N (Tg N yr<inline-formula><mml:math id="M407" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">25.2</oasis:entry>
         <oasis:entry colname="col3">27</oasis:entry>
         <oasis:entry colname="col4">Air–sea <inline-formula><mml:math id="M408" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> flux (Gt C yr<inline-formula><mml:math id="M409" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M410" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.05</oasis:entry>
         <oasis:entry colname="col6">0.18</oasis:entry>
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Si (Tg Si)</oasis:entry>
         <oasis:entry colname="col2">115</oasis:entry>
         <oasis:entry colname="col3">158</oasis:entry>
         <oasis:entry colname="col4">Organic export 90 m (Gt C yr<inline-formula><mml:math id="M411" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">6.84</oasis:entry>
         <oasis:entry colname="col6">6.47</oasis:entry>
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Alk (Tg <inline-formula><mml:math id="M412" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> yr<inline-formula><mml:math id="M413" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">416</oasis:entry>
         <oasis:entry colname="col3">366</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M414" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> export 90 m (Gt C yr<inline-formula><mml:math id="M415" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">0.66</oasis:entry>
         <oasis:entry colname="col6">0.61</oasis:entry>
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Inorganic C (Tg C yr<inline-formula><mml:math id="M416" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">208</oasis:entry>
         <oasis:entry colname="col3">366</oasis:entry>
         <oasis:entry colname="col4">Surface DIC (mM C)</oasis:entry>
         <oasis:entry colname="col5">1.94</oasis:entry>
         <oasis:entry colname="col6">1.94</oasis:entry>
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Organic C (Tg C yr<inline-formula><mml:math id="M417" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">106</oasis:entry>
         <oasis:entry colname="col3">237</oasis:entry>
         <oasis:entry colname="col4">Surface DIP (<inline-formula><mml:math id="M418" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>M P)</oasis:entry>
         <oasis:entry colname="col5">0.439</oasis:entry>
         <oasis:entry colname="col6">0.413</oasis:entry>
         <oasis:entry colname="col7">0.48</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">Surface DIN (<inline-formula><mml:math id="M419" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>M N)</oasis:entry>
         <oasis:entry colname="col5">3.90</oasis:entry>
         <oasis:entry colname="col6">3.76</oasis:entry>
         <oasis:entry colname="col7">5.04</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">Surface DSi (<inline-formula><mml:math id="M420" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>M Si)</oasis:entry>
         <oasis:entry colname="col5">13.6</oasis:entry>
         <oasis:entry colname="col6">14.6</oasis:entry>
         <oasis:entry colname="col7">7.5</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">OMZs volume (km<inline-formula><mml:math id="M421" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">2.61</oasis:entry>
         <oasis:entry colname="col6">2.45</oasis:entry>
         <oasis:entry colname="col7"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e8415">The simulated global mean surface DIP and DIN concentrations are lower in RIV than in the observational data of the World Ocean Atlas 2013 (WOA) (0.439 and 0.480 <inline-formula><mml:math id="M422" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>M DIP and 3.90 and 5.04 <inline-formula><mml:math id="M423" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>M DIN
respectively; WOA, <xref ref-type="bibr" rid="bib1.bibx19" id="altparen.179"/>), whereas the global mean surface DSi concentration is higher than in the global concentration derived from the WOA data set (13.6 and 7.5 <inline-formula><mml:math id="M424" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi></mml:mrow></mml:math></inline-formula>M DSi).
The WOA data set is constructed from present-day observations of
an ocean state that might already be perturbed by a substantial increase in riverine P and especially N loads, whereas
the model shows pre-industrial concentrations.
Considering the stronger anthropogenic increase in DIN riverine loads (e.g., <xref ref-type="bibr" rid="bib1.bibx98" id="altparen.180"/>) could plausibly shrink some of the disagreement with the WOA data set in the case of oceanic DIN concentrations.
A large part of the DIN underestimation in the model is however most likely due to notably large
tropical Pacific oxygen minimum zones, which cause a large DIN sink due to denitrification. Furthermore,
the lower surface concentrations of DIP and DIN compared to those found in the WOA data set suggest that the coastal sink
of biogeochemical compounds might be too large, meaning that the exports of P and N to the open ocean might be too low in the model. Nevertheless, the surface <inline-formula><mml:math id="M425" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">DIN</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">DIP</mml:mi></mml:mrow></mml:math></inline-formula> ratio in RIV is slightly improved in comparison to REF with respect to WOA data,
which is most likely
due to the shrinking of the tropical Pacific oxygen minimum zone, induced by reduced nutrient supplies to the region, and the corresponding decrease in denitrification.</p>
      <p id="d1e8461">The DIP and DIN underestimation bias with respect to the WOA data set are also reflected
in the spatial distributions of the surface concentrations (Fig. <xref ref-type="fig" rid="Ch1.F4"/>), in which the DIN concentrations are notably underestimated in most major basins.
The spatial patterns of differences with regard to WOA data are similar for RIV and for REF (Appendix D, Figs. <xref ref-type="fig" rid="App1.Ch1.S4.F12"/>, <xref ref-type="fig" rid="App1.Ch1.S4.F13"/>, <xref ref-type="fig" rid="App1.Ch1.S4.F14"/>), suggesting that the physical ocean features
are the dominant drivers of the nutrient distributions in the open ocean and of their bias (see also Supplement S5). Prominent spatial bias of
both REF and RIV are underestimated surface DIP and DIN concentrations in the Southern Ocean,
overestimated DSi concentrations in the Southern Ocean, and overestimated DIP concentrations in the
tropical gyres.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><label>Figure 4</label><caption><p id="d1e8474">Surface DIP <bold>(a, d, g)</bold>, DIN <bold>(b, e, h)</bold> and DSi <bold>(c, f, i)</bold> concentrations in WOA observations <bold>(a, b, c)</bold>, RIV <bold>(d, e, f)</bold> and their differences RIV-WOA <bold>(g, h, i)</bold>.</p></caption>
          <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020-f04.png"/>

        </fig>

</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Riverine-induced NPP hotspots</title>
      <p id="d1e8510">The open ocean regions with the highest NPP rates in REF remain the most dominant areas
of NPP in RIV (Fig. <xref ref-type="fig" rid="Ch1.F5"/>a, b), which also confirms the major importance of the ocean physics in dictating spatial patterns of the global NPP. In comparison to REF,
substantial enhancements of the NPP are simulated near major river mouths in RIV. In proximity to river mouths in lower latitudes,
the uptake of nutrients by the phytoplankton occurs efficiently due to favorable light conditions, thus
adding to
the local organic matter stock (Fig. <xref ref-type="fig" rid="Ch1.F5"/>c, d). This can be observed on the shallow shelves of the western tropical Atlantic,
where major nutrient supplies are provided
(see Sect. 3.3). Moreover, the NPP is increased in<?pagebreak page69?> certain semi-enclosed seas such as the Caribbean Sea, the Baltic Sea, the Black Sea and the Yellow Sea, where satellite observational data
also suggest high chlorophyll concentrations <xref ref-type="bibr" rid="bib1.bibx10" id="paren.181"/>.</p>
      <p id="d1e8520">In the tropical Atlantic, tropical Pacific, North Pacific and Southern Ocean, the NPP is decreased in RIV with respect to REF, signaling that stabilizing ocean biogeochemical
inventories with open ocean inputs, as was done in REF, also led to a slight artificial enhancement
of the NPP in these regions. The decrease in the equatorial Pacific could partly be explained by the characteristics of South American river systems,
which almost solely debouch into the Atlantic basin (Fig. <xref ref-type="fig" rid="Ch1.F7"/>). Although
Southeast Asian rivers deliver substantial biogeochemical loads to the ocean, the export of the biogeochemical compounds from eastern Asian coastal systems to the open Pacific is likely inefficient,
with modeled salinity profiles of the East China Sea
suggesting little mixing with the open ocean (Supplement S4). Currents parallel to the coast could be a key reason explaining this inefficient export <xref ref-type="bibr" rid="bib1.bibx56" id="paren.182"/>.
The decrease in the equatorial Pacific NPP is also likely responsible for most of the shrinking of the global oxygen minimum zone volume (Table <xref ref-type="table" rid="Ch1.T5"/>).</p>
      <p id="d1e8530">The Arctic Ocean does not undergo a noticeable increase in NPP, despite high nutrient concentrations in the basin in RIV. This can be explained by the region's light limitation over most of the year,
as well as the presence of sea ice coverage,
which both inhibit
the primary production<?pagebreak page70?> especially during winter. In the entire basin, the nutrient concentrations are much higher than what is suggested in the WOA database. In <xref ref-type="bibr" rid="bib1.bibx12" id="text.183"/>, where riverine nutrient inputs
were added to the ocean according to the NEWS2 study, similarly high concentrations of DSi were found in the Arctic.
Furthermore, <xref ref-type="bibr" rid="bib1.bibx48" id="text.184"/> suggest that in the Arctic Ocean, nutrients
limit phytoplankton growth in the late summer. Although the Arctic NPP in RIV and REF is substantially higher in the summer than in other seasons, the NPP is never nutrient limited for the vast majority of the ocean basin.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><label>Figure 5</label><caption><p id="d1e8542">Depth integrated annual NPP <bold>(a, b)</bold> and total annually accumulated organic matter concentration <bold>(c, d)</bold> in the surface layer in the RIV simulation and RIV – REF.</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020-f05.png"/>

        </fig>

</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><?xmltex \opttitle{Riverine-induced {$\protect\chem{CO_{{2}}}$} Outgassing}?><title>Riverine-induced <inline-formula><mml:math id="M426" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> Outgassing</title>
      <p id="d1e8577">The addition of riverine C loads causes a simulated net oceanic <inline-formula><mml:math id="M427" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> source of 231 Tg C yr<inline-formula><mml:math id="M428" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> to the atmosphere (Table <xref ref-type="table" rid="Ch1.T5"/>).
While the hotspots of the riverine-induced C outgassing are regions in proximity to major river mouths
(Fig. <xref ref-type="fig" rid="Ch1.F6"/>b),
a widespread, albeit weaker, outgassing signal can be observed in open ocean basins. The largest outgassing fluxes are found in the Atlantic and Indo-Pacific (31 % and 43 % of global outgassing flux respectively),
which is due to large riverine C supplies from tropical
Atlantic and Southeast Asian catchments (see Sect. 3.2).
In the Southern Ocean, we observe an outgassing flux of 17 Tg yr<inline-formula><mml:math id="M429" 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> when comparing RIV to REF, which is almost 10 % of the global riverine-caused outgassing.
The riverine-induced outgassing is 113 Tg yr<inline-formula><mml:math id="M430" 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> (49 % of the global outgassing flux) in the Southern Hemisphere, despite riverine C exports of the hemisphere contributing to only 199 Tg (33 %)
of annual C loads to the ocean. This implies the presence of an oceanic interhemispheric transfer of
riverine C from the Northern Hemisphere to the Southern Hemisphere (Fig. <xref ref-type="fig" rid="Ch1.F6"/>c).
This interhemispheric transfer of C in the ocean has been a topic of discussion in literature, with studies
of <xref ref-type="bibr" rid="bib1.bibx7" id="text.185"/> and <xref ref-type="bibr" rid="bib1.bibx91" id="text.186"/> also suggesting
a transport of C between latitudinal regions of the ocean that compensates for the heterogeneous distribution  of riverine C inputs.</p>
      <p id="d1e8640">The Arctic rivers (Lena, Mackenzie, Yenisei, Ob, Oder, Yukon) also provide C to their respective shelves, which causes a net outgassing of riverine C on the Laptev shelf and in the Beaufort Sea (2.2  and
2.3 Tg C yr<inline-formula><mml:math id="M431" 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>, respectively).
The impacts of riverine C loads on the Arctic shelves can also be observed in the present-day coastal ocean <inline-formula><mml:math id="M432" display="inline"><mml:mrow class="chem"><mml:mi>p</mml:mi><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> data set of <xref ref-type="bibr" rid="bib1.bibx67" id="text.187"/>, in which very high <inline-formula><mml:math id="M433" display="inline"><mml:mrow class="chem"><mml:mi>p</mml:mi><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values
are reported near river mouths (&gt; 400 ppm).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><label>Figure 6</label><caption><p id="d1e8686">Annual pre-industrial air–sea <inline-formula><mml:math id="M434" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> flux of <bold>(a)</bold> RIV, <bold>(b)</bold> RIV-REF, and <bold>(c)</bold> contributions of the Northern Hemisphere and Southern Hemisphere to riverine C loads and oceanic riverine C outgassing.
A positive flux in  <bold>(a)</bold> and  <bold>(b)</bold> describes an outgassing flux from the ocean to the atmosphere, whereas a
negative flux is a flux from the atmosphere to the ocean.</p></caption>
          <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020-f06.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Impacts of riverine loads on coastal region</title>
      <p id="d1e8731">With respect to the 10 shallow shelf regions chosen for this study (Table <xref ref-type="table" rid="Ch1.T1"/>), the catchments of the low latitude regions (5 CSK, 6 BEN, 7 SEA, 8 TWA, 9 CG) provide substantially
more C and nutrients to the coastal ocean than the high latitude regions in our framework (Fig. <xref ref-type="fig" rid="Ch1.F7"/>), although the
differing size of the coastal regions and of their catchments
may play a strong role in explaining these differences. The tropical west Atlantic (8 TWA) has the largest riverine supplies of biogeochemical compounds, which are largely provided by the Amazon and Orinoco rivers.
In the tropical regions of the Bay of Bengal (6 BEN) and Southeast Asia (7 SEA), the fraction of C delivered as
POC is substantially higher than for the rest of the regions (Fig. <xref ref-type="fig" rid="Ch1.F7"/>b). Furthermore, in the high latitude regions (1 BS, 2 LS, 3 NS, 10 SAM), DIC loads are the major source of riverine C,
whereas for the other regions, organic C
is the largest contributor to the regional C load. The higher importance of DIC loads for the Arctic C supplies can also be observed in
Table <xref ref-type="table" rid="Ch1.T4"/>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><label>Figure 7</label><caption><p id="d1e8744">Modeled riverine <bold>(a)</bold> P (TP) and N (TN), and <bold>(b)</bold> C (DIC, DOC and POC) exports to selected coastal regions. TP and TN are the total P and N from the sum of their riverine dissolved inorganic loads
(DIP, DIN) and of their riverine organic loads (P and N within tDOM and POM).
DOC and POC are the C loads within riverine tDOM and POM, respectively.</p></caption>
        <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020-f07.png"/>

      </fig>

      <p id="d1e8759">In RIV, major coastal ocean NPP increases of 166 %, 377 % and 71 % for the tropical west Atlantic (3 TWA), Bay of Bengal (5 BEN) and East China Sea (6 CSK), respectively, are simulated,
in comparison to REF (Fig. <xref ref-type="fig" rid="Ch1.F8"/>b). The availability of light, as
well as the large riverine supplies of nutrients to these regions (Table <xref ref-type="table" rid="Ch1.T4"/> in Sect. 3.2),
provides optimal conditions to enhance the biological production.
Surprisingly, the Southeast Asian shelf (6 SEA) does not undergo a large relative increase in its regional NPP
despite considerable riverine inputs to the region and favorable climatic conditions for biological production in the region. This, on the one hand, is due to the large area of the defined region (<inline-formula><mml:math id="M435" display="inline"><mml:mrow><mml:mn mathvariant="normal">1795</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> m<inline-formula><mml:math id="M436" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>),
which reduces the impact of the riverine loads per area. On the other hand, there is a larger
connection area to the open ocean due to not sharing a coastal<?pagebreak page72?> border with a continent, which implies a larger open ocean exchange, thus the influence of the riverine supplies is likely to be less significant than contributions from
open ocean supplies.
In turn, the Congo shelf (9 CG) has a very small surface area (<inline-formula><mml:math id="M437" display="inline"><mml:mrow><mml:mn mathvariant="normal">53</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> m<inline-formula><mml:math id="M438" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>) due to a steep coastal slope (Supplement S4).
The NPP in the region is however already one of the highest of the chosen regions in REF, indicating that the region is already strongly supplied with nutrients from open ocean inflows. The relative impact caused by the addition
of riverine inputs is therefore minor.</p>
      <p id="d1e8816">On the temperate shelf regions, where a stronger seasonal cycle of the light limitation takes place, the NPP in the North Sea (2 NS) is only weakly enhanced when comparing RIV to REF (<inline-formula><mml:math id="M439" display="inline"><mml:mo lspace="0mm">+</mml:mo></mml:math></inline-formula>2 %). In the South American (10 SAM) and Sea of Okhotsk (4 OKH) regions
substantial NPP increases due to the addition of riverine inputs are also not simulated. Although the NPP is strongly enhanced in the direct proximity to the Paraná river (Fig. <xref ref-type="fig" rid="Ch1.F5"/>b), the vastness of the South American
shelf (<inline-formula><mml:math id="M440" display="inline"><mml:mrow><mml:mn mathvariant="normal">1553</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">9</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> m<inline-formula><mml:math id="M441" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>)
also makes the region less sensitive to riverine inputs. In published literature, the nutrient supply which drives the NPP on the Patagonian shelf is also confirmed to be strongly controlled by
open ocean inflows, and river supplies are suggested to only have a limited influence in the region <xref ref-type="bibr" rid="bib1.bibx99" id="paren.188"/>.</p>
      <p id="d1e8855">The Arctic shelf regions also do not undergo a strong NPP increase in RIV with respect to REF (8 % and 5 % increases for the Beaufort Sea, 1 BS, and Laptev Sea, 2.LS, respectively).
We however do not consider a seasonality of the riverine inputs. Larger inputs of nutrients
in months of larger discharge from April to June <xref ref-type="bibr" rid="bib1.bibx68" id="paren.189"/>  could cause a more efficient usage of the riverine nutrients on the shelves, since the
light availability is higher and the sea ice coverage is reduced during these months.</p>
      <p id="d1e8861">An increase in <inline-formula><mml:math id="M442" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> outgassing due to the increased C inputs is simulated in all regions in RIV. In the Arctic regions (Beaufort Sea
and Laptev Sea), the relative change in the air–sea <inline-formula><mml:math id="M443" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> flux is very pronounced,
whereas the impact
is generally not as strong in the lower latitude regions due to the enhancement of the biological DIC uptake caused by riverine nutrient inputs. The tropical west Atlantic is an exception to this latitudinal pattern, since the large riverine C supplies
also cause a substantial change in the <inline-formula><mml:math id="M444" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> flux of the region.
In the North Sea, we observe an enhancement of C outgassing induced by riverine loads, but the region remains a substantial pre-industrial sink of atmospheric <inline-formula><mml:math id="M445" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in RIV,
as is still suggested for the present day by <xref ref-type="bibr" rid="bib1.bibx66" id="text.190"/>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><label>Figure 8</label><caption><p id="d1e8913"><bold>(a)</bold> Global map of the 10 chosen coastal regions with depths of less than 250 m, <bold>(b)</bold> pre-industrial annual NPP per area and <bold>(c)</bold> <inline-formula><mml:math id="M446" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> flux in the given regions (g C m<inline-formula><mml:math id="M447" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> yr<inline-formula><mml:math id="M448" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>).
In <bold>(c)</bold>, a positive flux means a flux from the ocean to the atmosphere.</p></caption>
        <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020-f08.png"/>

      </fig>

</sec>
<sec id="Ch1.S6">
  <label>6</label><title>Origins and fate of riverine carbon</title>
      <p id="d1e8974">In our simplified model framework (Fig. <xref ref-type="fig" rid="Ch1.F9"/>), we quantify the land sources of riverine C (1–3),
its riverine transfer to the ocean (4) and the long-term fate of the riverine C in the ocean (5–10). While the terrestrial
fluxes are derived from the weathering and organic matter export models, the fluxes of the riverine C in the ocean
are derived from RIV–REF differences of the ocean simulation. The long-term oceanic <inline-formula><mml:math id="M449" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> flux is furthermore decomposed to illustrate the contributions of riverine inorganic and organic C inputs
to the oceanic outgassing flux in a
model equilibrium analysis.
The detailed calculations of the land and ocean fluxes are shown and explained in detail in the Appendix C (C1 for terrestrial and C2 for oceanic fluxes).</p>
      <p id="d1e8990">In our framework, the global pre-industrial terrestrial uptake of atmospheric C and its export to rivers as DIC amounts to 529 Tg C yr<inline-formula><mml:math id="M450" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. The sink consists of 280 Tg C yr<inline-formula><mml:math id="M451" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> from
the drawdown
induced by weathering (1) and of 249 Tg C yr<inline-formula><mml:math id="M452" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> from the terrestrial biological uptake (3).
During the
weathering process, 94 Tg C yr<inline-formula><mml:math id="M453" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> is moreover<?pagebreak page73?> released from the lithology through carbonate weathering (2).
During silicate weathering, all the C released originates from atmospheric <inline-formula><mml:math id="M454" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. The terrestrial biological uptake (3) is derived from the net global export of organic
C to the ocean. It therefore implicitly takes into account the net land biological uptake and its export to freshwaters, as well as all net sinks and sources in river systems.
A total of 603 Tg C yr<inline-formula><mml:math id="M455" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> is transferred laterally to the ocean (4) while taking into consideration
an endorheic catchment loss of 19 Tg C yr<inline-formula><mml:math id="M456" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p>
      <?pagebreak page74?><p id="d1e9077">In the ocean, riverine inputs of C cause a long-term net annual atmospheric source of 231 Tg C yr<inline-formula><mml:math id="M457" 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> (Table <xref ref-type="table" rid="Ch1.T5"/>). We propose a decomposition of this long-term <inline-formula><mml:math id="M458" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>
flux into sources and sinks induced by the inputs of the riverine compounds (Appendix C2).
Assuming model equilibrium, the oceanic outgassing flux can be decomposed into
a source from riverine inorganic C inputs (183 Tg C yr<inline-formula><mml:math id="M459" 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>, 5), a source from terrestrial organic C (128 Tg C yr<inline-formula><mml:math id="M460" 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>, 6)
and a sink caused by the enhancement of the biological production
prompted by the addition of dissolved inorganic nutrients and its associated
alkalinity production (69 Tg C yr<inline-formula><mml:math id="M461" 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>, 7). We also calculate a sink due to disequilibrium at the atmosphere–water column interface in the model (11 Tg C yr<inline-formula><mml:math id="M462" 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>, Dr1).
The production and the downwards export
of <inline-formula><mml:math id="M463" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and POM within the ocean
lead to simulated sediment deposition fluxes of 188 Tg C yr<inline-formula><mml:math id="M464" 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 <inline-formula><mml:math id="M465" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (inorg. C flux,  8) and of 582 Tg C yr<inline-formula><mml:math id="M466" 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 POM (org. C flux,  9).
The dissolution of <inline-formula><mml:math id="M467" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and the remineralization of POM
within the sediment lead to a DIC flux of 385 Tg C yr<inline-formula><mml:math id="M468" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> from the sediment pore water to the water column. The net C flux at the sediment interface (<inline-formula><mml:math id="M469" display="inline"><mml:mrow><mml:mn mathvariant="normal">8</mml:mn><mml:mo>+</mml:mo><mml:mn mathvariant="normal">9</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula>) is therefore a burial flux of
385 Tg C yr<inline-formula><mml:math id="M470" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.
The calculated equilibrium C burial flux, which is the difference between the riverine C inputs and the equilibrium <inline-formula><mml:math id="M471" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> outgassing (<inline-formula><mml:math id="M472" display="inline"><mml:mrow><mml:mn mathvariant="normal">4</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn><mml:mo>+</mml:mo><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:math></inline-formula>), is 361 Tg C yr<inline-formula><mml:math id="M473" 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>,
which implies that there is a deviation of 24 Tg C yr<inline-formula><mml:math id="M474" 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> (Dr2)
towards the sediment. With the simulated C burial (385 Tg C yr<inline-formula><mml:math id="M475" 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>) deviating from the calculated equilibrium state C burial (361 Tg C yr<inline-formula><mml:math id="M476" 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>). Similar deviations from the equilibrium states at the atmosphere–water column and water column–sediment interfaces suggest that the model disequilibrium, which is likely due to the
long timescales of the processes taking place in the sediment, translates relatively efficiently into
a perturbation of the <inline-formula><mml:math id="M477" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> flux at the atmosphere–water column interface.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9" specific-use="star"><?xmltex \currentcnt{9}?><label>Figure 9</label><caption><p id="d1e9346">Origins and oceanic fate of riverine C in our framework (Tg C yr<inline-formula><mml:math id="M478" 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>). (1) Atmospheric C uptake through weathering.
(2) Carbonate weathering C flux from the lithology. (3) Net land biological C uptake (derived directly from riverine organic C exports). (4) Total riverine C exports. (5) Oceanic C outgassing from riverine DIC (i.e., inorganic C)
inputs.
(6) Oceanic C outgassing resulting from riverine tDOM inputs. (7) Oceanic C uptake due to the enhanced primary production by dissolved inorganic nutrients and the corresponding alkalinity production. (8) Simulated inorganic
C deposition (i.e., <inline-formula><mml:math id="M479" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> to the sediment. (9) Simulated net organic C (i.e., POM) deposition to sediment. (10) Diffusive DIC flux from the sediment pore water back to the water column.
Given are simulated fluxes by the terrestrial and ocean models, except when <inline-formula><mml:math id="M480" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula> is stated, meaning that the fluxes were calculated assuming
model equilibrium.
Dr1 and Dr2 are the calculated drifts between the simulated oceanic C fluxes and the calculated equilibrium fluxes (derived from model equations, Appendix C2) for
the ocean–atmosphere and ocean–sediment interfaces, respectively.
See Appendix C for the calculation of all fluxes.
</p></caption>
        <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020-f09.png"/>

      </fig>

      <p id="d1e9387">The simulated riverine-induced oceanic <inline-formula><mml:math id="M481" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> outgassing flux of 231 Tg C yr<inline-formula><mml:math id="M482" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> is consistent with the estimate range of 200–400 Tg C yr<inline-formula><mml:math id="M483" 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> given in <xref ref-type="bibr" rid="bib1.bibx95" id="text.191"/>, who derived an annual
global riverine C load of 300–500 Tg C, and with <xref ref-type="bibr" rid="bib1.bibx61" id="text.192"/> and <xref ref-type="bibr" rid="bib1.bibx43" id="text.193"/>, who suggest a slightly higher natural <inline-formula><mml:math id="M484" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> outgassing flux of 450 Tg C yr<inline-formula><mml:math id="M485" 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>. A recent study by <xref ref-type="bibr" rid="bib1.bibx91" id="text.194"/>
proposes both
riverine C loads and oceanic C outgassing of 780 Tg C yr<inline-formula><mml:math id="M486" 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>.
It is however unclear if and how the oceanic carbon removal of the riverine C through sediment burial was considered in the study.</p>
      <p id="d1e9473">Furthermore, we observe an imbalance in the calculated pre-industrial land uptake and the oceanic outgassing of atmospheric <inline-formula><mml:math id="M487" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in our approach, with the land uptake outweighing the oceanic outgassing
(combined net atmospheric sink of 299 Tg C yr<inline-formula><mml:math id="M488" 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>).
Accounting for further sources of atmospheric <inline-formula><mml:math id="M489" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> such as volcanic emissions and shale oxidation would therefore be necessary
to achieve a stable atmospheric carbon budget in a fully coupled land–ocean–atmosphere setting, since ESMs assume constant pre-industrial atmospheric <inline-formula><mml:math id="M490" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> levels.
For instance, <xref ref-type="bibr" rid="bib1.bibx84" id="text.195"/> suggest long-term volcanic annual emissions in the
range of 80–160 Tg C yr<inline-formula><mml:math id="M491" 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>, whereas
<xref ref-type="bibr" rid="bib1.bibx20" id="text.196"/> estimate a long-term volcanic outgassing flux as high as that of silicate weathering drawdown. In our approach, the modeled silicate weathering <inline-formula><mml:math id="M492" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> drawdown is
196 Tg C yr<inline-formula><mml:math id="M493" 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>. Additionally to the volcanic <inline-formula><mml:math id="M494" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions, the global atmospheric <inline-formula><mml:math id="M495" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> land source from the oxidation of organic carbon in shale of around
100 Tg C yr<inline-formula><mml:math id="M496" 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> given by <xref ref-type="bibr" rid="bib1.bibx95" id="text.197"/> would then be approximately close the atmospheric carbon budget in our framework.</p>
</sec>
<sec id="Ch1.S7">
  <label>7</label><title>Approach advantages and limitations</title>
<sec id="Ch1.S7.SS1">
  <label>7.1</label><title>Rivers in an Earth system model setting</title>
      <p id="d1e9616">Our approach, which quantifies riverine exports as
a function of the climate variables precipitation, surface runoff and temperature can potentially be used to estimate land–ocean exports in an ESM setting.
Since we establish a baseline for the pre-industrial state of the ocean while considering riverine loads, our study could also be used to assess oceanic impacts of
perturbations of riverine loads due to temporal changes in weathering rates <xref ref-type="bibr" rid="bib1.bibx40" id="paren.198"/>,
or due to increased
anthropogenic P and N inputs to catchments <xref ref-type="bibr" rid="bib1.bibx98 bib1.bibx16" id="paren.199"/>.</p>
      <p id="d1e9625">This study however also relies on strong assumptions in order to perform simulations at the global scale, although improvements within the framework are possible.
For one, the weathering mechanisms, the processing uptake of nutrients by the terrestrial biology, the representation of hydrological flow characteristics, as well as
transformation processes and retention in rivers could all be represented more realistically.
We notably assumed a fixed riverine <inline-formula><mml:math id="M497" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> mole ratio of <inline-formula><mml:math id="M498" display="inline"><mml:mrow><mml:mn mathvariant="normal">16</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> for all species and all catchments in this study. Riverine <inline-formula><mml:math id="M499" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratios are suggested to exceed this ratio at the global scale
(<inline-formula><mml:math id="M500" display="inline"><mml:mrow><mml:mn mathvariant="normal">29</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> by <xref ref-type="bibr" rid="bib1.bibx98" id="altparen.200"/> and <inline-formula><mml:math id="M501" display="inline"><mml:mrow><mml:mn mathvariant="normal">21</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> by <xref ref-type="bibr" rid="bib1.bibx16" id="altparen.201"/>), but
denitrification in estuaries could compensate the excess of N with regard to a <inline-formula><mml:math id="M502" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratio of <inline-formula><mml:math id="M503" display="inline"><mml:mrow><mml:mn mathvariant="normal">16</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> (see Supplement S1.3). Denitrification in estuaries is impossible to represent in the ocean model due to grid
resolution constraints. Furthermore, we assume a similar spatial
distribution of pre-industrial anthropogenic P inputs as for the present day. While the chosen spatial distribution agrees well with the distribution of other approaches (Supplement S1),
we acknowledge a large degree of
uncertainty both in the magnitudes of the pre-industrial anthropogenic inputs as well as in their distributions.</p>
</sec>
<sec id="Ch1.S7.SS2">
  <label>7.2</label><title>Dynamics of terrestrial organic matter in the ocean</title>
      <p id="d1e9727">The composition of terrestrial organic matter and its fate in the ocean have been strongly debated in the past. Recent work shows that despite its low biological reactivity, tDOM can be mineralized
by abiotic processes such
as photodegradation in the
ocean <xref ref-type="bibr" rid="bib1.bibx35 bib1.bibx85 bib1.bibx1" id="paren.202"/>, despite already having been strongly degraded during its transit in rivers. The global magnitude of the degradation of tDOM in the ocean is however strongly uncertain.
Few studies in the past have addressed the composition of
POM, although it is also thought to be efficiently remineralized in the coastal ocean sediment <xref ref-type="bibr" rid="bib1.bibx53 bib1.bibx21" id="paren.203"/>. While the C loads from POM are the lowest loads of all C compounds considered in this study, a
differing <inline-formula><mml:math id="M504" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratio to the one chosen in this study could affect the modeled riverine-induced C outgassing flux in the ocean.</p>
      <?pagebreak page75?><p id="d1e9748">Rates of remineralization processes have been suggested to be higher in the coastal ocean than in the open ocean (e.g., <xref ref-type="bibr" rid="bib1.bibx63" id="altparen.204"/>). Using a higher coastal
organic matter remineralization rate in the sediment module of HAMOCC could potentially
reduce the coastal biogeochemical sink described in this study and increase the offshore export of biogeochemical compounds.</p>
</sec>
<sec id="Ch1.S7.SS3">
  <label>7.3</label><title>Arctic Ocean</title>
      <p id="d1e9762">Simulated nutrient concentrations are particularly high in the Arctic Ocean with regard to WOA data, suggesting
that this region with strong riverine inputs might be poorly represented
in the HAMOCC.
Difficulties to represent the region could be due to fine circulation features. For instance, outflows through narrow passages have been shown to be affected by model resolution <xref ref-type="bibr" rid="bib1.bibx3" id="paren.205"/>.
The simulated sea ice coverage in our study, which is around 85 % for the Laptev Sea during the whole year on average, could be overestimated. Moreover, the NPP in the region might be underestimated
due to photosynthesis taking place under ice, in ice ponds and over extended daytime periods in
the summer months <xref ref-type="bibr" rid="bib1.bibx26 bib1.bibx100" id="paren.206"/>, all of which are not represented in HAMOCC.</p>
</sec>
</sec>
<sec id="Ch1.S8" sec-type="conclusions">
  <label>8</label><title>Summary and conclusions</title>
      <p id="d1e9780">In this study, we account for weathering and non-weathering inputs to river catchments to quantify global annual pre-industrial loads of 3.7 Tg P, 27 N, 168 Tg DSi and 603 Tg C to the ocean. These loads are consistent with published literature estimates, although
we acknowledge a
certain degree of uncertainty regarding their magnitudes.
While we omit the in-stream retention of P during its riverine transport, which reduces the global P exports
to the ocean <xref ref-type="bibr" rid="bib1.bibx16" id="paren.207"/>,
our estimate of the global pre-industrial P export to the ocean is comparable in magnitude to an estimation that determines riverine P exports by upscaling
from pristine river measurements <xref ref-type="bibr" rid="bib1.bibx22" id="paren.208"/>.</p>
      <p id="d1e9789">We identify the tropical Atlantic catchments, the Arctic Ocean, Southeast Asia and Indo-Pacific islands as regions of dominant contributions of riverine supplies to the ocean. These four regions account
for over 51 % of land–ocean C exports in total, with tropical Atlantic catchments
supplying around 20 % of C to the ocean globally. We also observe that the contributions of different C species differ between the regions. Most prominently, the C supply of the Indo-Pacific
islands is dominated by particulate organic C loads, which have been identified to be more strongly controlled by extreme hydrological events than other C species <xref ref-type="bibr" rid="bib1.bibx55" id="paren.209"/>.</p>
      <?pagebreak page76?><p id="d1e9795">In the ocean model, riverine inputs of C lead to a net global oceanic outgassing flux of 231 Gt C yr<inline-formula><mml:math id="M505" 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>, a comparable value with regards to previous estimates of 200–450 Tg C yr<inline-formula><mml:math id="M506" 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>
<xref ref-type="bibr" rid="bib1.bibx95 bib1.bibx61 bib1.bibx43" id="paren.210"/>. This outgassing flux can be decomposed into two source terms caused by inorganic C inputs (183 Tg C yr<inline-formula><mml:math id="M507" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) and organic C inputs (128 Tg C yr<inline-formula><mml:math id="M508" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>),
and a net sink term (80 Tg C yr<inline-formula><mml:math id="M509" 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>) caused by
the enhanced biological C uptake due to riverine inorganic nutrient supplies, corresponding alkalinity production and a slight model drift in alkalinity.
The magnitude of the outgassing is however strongly dependent on the magnitude of riverine C loads. In our framework, both riverine C loads and their induced oceanic C outgassing are thereby situated within
the lower range of estimates.</p>
      <p id="d1e9862">We find evidence of a substantial oceanic interhemispheric transport of riverine
C from the Northern Hemisphere to the Southern Hemisphere, with a larger relative C outgassing flux simulated over the Southern Hemisphere (49 % of global outgassing) than its relative riverine C loads (36 % of global C loads).
We also show that the Southern Ocean outgasses 17 Tg of riverine C, despite not having a direct riverine source of C, meaning that riverine C is transported within the ocean interior to the Southern Ocean in the model.
This interhemispheric transfer of riverine C in the ocean has previously been suggested to contribute to the pre-industrial
Southern Ocean source of atmospheric <inline-formula><mml:math id="M510" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> for the pre-industrial time frame <xref ref-type="bibr" rid="bib1.bibx96 bib1.bibx7 bib1.bibx43 bib1.bibx91" id="paren.211"/>. Here, we show that riverine C exports derived from state-of-the-art land export models
confirm the larger contribution of the Northern Hemispheric terrestrial C supply to the ocean. Part of this uneven terrestrial C supply is then compensated by the transport of C within the ocean and is outgassed remotely.</p>
      <p id="d1e9880">Our results help identify
oceanic regions that are sensitive to riverine fluxes. Riverine-induced changes in the regional NPP are mostly found in coastal regions, but substantial riverine-caused <inline-formula><mml:math id="M511" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> outgassing can also be observed in the open ocean of the
tropical Atlantic. In general, we show latitudinal differences
in the sensitivity of the NPP and of the <inline-formula><mml:math id="M512" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> fluxes to the riverine inputs in various coastal regions. While a high sensitivity in the NPP is found in the tropics and subtropics, with
the tropical west Atlantic, the Bay of Bengal and the East China Sea showing large NPP increases of 166 %, 377 % and 71 %, respectively, the relative changes in the regional <inline-formula><mml:math id="M513" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> fluxes are mostly larger at higher latitudes. For instance, the Laptev Sea and
the Bay of Beaufort become atmospheric sources of 2.2  and 2.3 Tg C yr<inline-formula><mml:math id="M514" 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> respectively, despite being sinks of atmospheric <inline-formula><mml:math id="M515" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> without accounting for riverine inputs.
While our analysis revolves around the implications of pre-industrial riverine loads,
regions that show strong responses to the riverine loads in this study might also be strongly affected by anthropogenic perturbations of riverine exports.</p>
      <p id="d1e9939">Deriving riverine exports as a function of ESM
variables enables
a representation of the riverine loop; starting from the terrestrial uptake of C to its riverine export and ending with its long-term outgassing in the ocean or export to the oceanic sediment.
In order to implement the framework into a coupled land–atmosphere–ocean setting such as an ESM, the atmospheric pre-industrial budget would have to be balanced. We emphasize the need to consider
long-term terrestrial <inline-formula><mml:math id="M516" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> sources originating from long-term volcanic activity and from shale oxidation in order to compensate for imbalances between the terrestrial
C sink and the oceanic C source in our framework.</p>
      <p id="d1e9953">Throughout this study, we find global heterogeneity in the spatial features of weathering fluxes, riverine loads and their implications for the ocean biogeochemistry. We confirm that considering
riverine exports to the ocean is central when assessing the biogeochemistry of coastal regions, but also find implications for certain open ocean regions (i.e., the tropical Atlantic). Our study also shows the necessity to account
for the river-induced oceanic C outgassing in ocean
biogeochemistry models, since our conservative estimate
consists of around 10 % of the magnitude of the present-day oceanic C uptake.</p>
</sec>

      
      </body>
    <back><notes notes-type="codedataavailability"><title>Code and data availability</title>

      <p id="d1e9960">Code, primary data and scripts needed to reproduce the analyses presented in this study are
archived by the Max Planck Institute for Meteorology and are available upon request (publications@mpimet.mpg.de).</p>
  </notes><app-group>
        <supplementary-material position="anchor"><?pagebreak page77?><p id="d1e9964">The supplement related to this article is available online at: <inline-supplementary-material xlink:href="https://doi.org/10.5194/bg-17-55-2020-supplement" xlink:title="pdf">https://doi.org/10.5194/bg-17-55-2020-supplement</inline-supplementary-material>.<?xmltex \hack{\clearpage}?></p></supplementary-material>
        </app-group><app-group>

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

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.S1.F10"><?xmltex \currentcnt{A1}?><label>Figure A1</label><caption><p id="d1e9983"><bold>(a)</bold> Scheme of model compartments in HAMOCC, modified from <xref ref-type="bibr" rid="bib1.bibx57" id="text.212"/> and <bold>(b)</bold> scheme of the organic dynamics taking place in the model. The most central model parameters can be found in the Supplement S2.</p></caption>
        <?xmltex \hack{\textwidth\hsize}?>
        <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020-f10.png"/>

      </fig>

<?xmltex \hack{\clearpage}?>
</app>

<?pagebreak page78?><app id="App1.Ch1.S2">
  <?xmltex \currentcnt{B}?><label>Appendix B</label><title>Runoff, temperature and precipitation</title>
      <p id="d1e10012">The weathering yields provided in this study are dependent on the MPI-ESM spatial representation of pre-industrial surface runoff, surface temperature and precipitation (Fig. <xref ref-type="fig" rid="App1.Ch1.S2.F11"/>a, b, c).</p>
      <p id="d1e10017">Previous work by <xref ref-type="bibr" rid="bib1.bibx41" id="text.213"/> describes the MPI-ESM performing well when estimating surface temperatures at single grid cells with regard to observations. The global precipitation in MPI-ESM is
slightly higher than the global precipitation that is reported in the Global Precipitation Climatology Project (GCPC) <xref ref-type="bibr" rid="bib1.bibx2" id="paren.214"/>, which is discussed along with spatial biases of the precipitation in <xref ref-type="bibr" rid="bib1.bibx103" id="text.215"/>. Most notably, the precipitation is too strong over extratropical
land surface and too little over tropical land surface. Runoff is less well reproduced globally. For the given time period of the simulation used in this study, the global runoff is
23 496 km<inline-formula><mml:math id="M517" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> yr<inline-formula><mml:math id="M518" 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>.
This is significantly lower than the global runoff estimations of
36 600–38 300 km<inline-formula><mml:math id="M519" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> yr<inline-formula><mml:math id="M520" 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> <xref ref-type="bibr" rid="bib1.bibx33 bib1.bibx25" id="paren.216"/>. The difficulty of representing several processes that control the runoff, such as evapotranspiration and condensation,
is also reflected in the large range of global runoff means of other Earth system models, which range from 23 000 to 42 500 km<inline-formula><mml:math id="M521" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> yr<inline-formula><mml:math id="M522" 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> <xref ref-type="bibr" rid="bib1.bibx41" id="paren.217"/>.</p>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.S2.F11"><?xmltex \currentcnt{B1}?><label>Figure B1</label><caption><p id="d1e10101">Modeled pre-industrial <bold>(a)</bold> surface runoff (mm a<inline-formula><mml:math id="M523" 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>), <bold>(b)</bold> surface temperature (<inline-formula><mml:math id="M524" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) and <bold>(c)</bold> precipitation (mm a<inline-formula><mml:math id="M525" 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>) annual means.</p></caption>
        <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020-f11.png"/>

      </fig>

      <p id="d1e10154"><?xmltex \hack{\newpage}?>The spatial patterns in the CMIP5 simulation are however comparable with the annual runoff patterns reported in <xref ref-type="bibr" rid="bib1.bibx33" id="text.218"/>, with high surface runoff observed in the Amazon basin, West Africa, Indo-Pacific islands,
Southeast Asia, eastern North America,
northern Europe as well as in Siberia. Due to the strong underestimation of the model regarding the runoff
in relation to the combined runoff mean of <xref ref-type="bibr" rid="bib1.bibx33" id="text.219"/> and <xref ref-type="bibr" rid="bib1.bibx25" id="text.220"/>,
we conclude that a scaling factor of 1.59
is necessary to represent runoff plausibly at the global scale. The global runoff from OMIP, which provides freshwater to the ocean model, is however
more plausible (32 542 km<inline-formula><mml:math id="M526" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> yr<inline-formula><mml:math id="M527" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) and was therefore not scaled. We scaled the model runoff to the global runoff estimation from <xref ref-type="bibr" rid="bib1.bibx33" id="text.221"/> and not
to the OMIP runoff, since scaling to the OMIP runoff still led to lower global P and <inline-formula><mml:math id="M528" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">DIC</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">Alk</mml:mi></mml:mrow></mml:math></inline-formula> release values than were reported in literature estimates.</p><?xmltex \hack{\clearpage}?>
</app>

<?pagebreak page79?><app id="App1.Ch1.S3">
  <?xmltex \currentcnt{C}?><label>Appendix C</label><title>Derivation of carbon fluxes in the simplified coupled system</title>
<sec id="App1.Ch1.S3.SS1">
  <label>C1</label><title>Terrestrial fluxes</title>
      <p id="d1e10220"><list list-type="order">
            <list-item>

      <p id="d1e10225">Carbonate and silicate weathering cause a terrestrial uptake of 280 Tg C yr<inline-formula><mml:math id="M529" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> from the atmosphere according to the weathering model simulations (Table <xref ref-type="table" rid="Ch1.T2"/>).</p>
            </list-item>
            <list-item>

      <p id="d1e10245">Carbonate mineral weathering causes a lithological C release flux of 94 Tg C yr<inline-formula><mml:math id="M530" 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> DIC, as shown in Sect. 3.2.</p>
            </list-item>
            <list-item>

      <p id="d1e10263">Carbon contained in terrestrial organic matter exports originates from the atmosphere <xref ref-type="bibr" rid="bib1.bibx81" id="paren.222"/>.
The net C uptake by the terrestrial and riverine biology is therefore the same as the lateral organic C export, which we derived from NEWS2 <xref ref-type="bibr" rid="bib1.bibx98" id="paren.223"/> DOC and POC exports. The
net atmospheric C uptake by the terrestrial biology, while taking into account all respiration processes on land and in rivers, is the sum of the lateral POC and DOC exports (249 Tg C yr<inline-formula><mml:math id="M531" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>).</p>
            </list-item>
            <list-item>

      <p id="d1e10287">The global riverine C export to the ocean consists of the sum of weathering and organic matter C exports (623 Tg C yr<inline-formula><mml:math id="M532" 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>) minus a loss term due to endorheic river retention
(19 Tg C yr<inline-formula><mml:math id="M533" 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>). This results
in the global riverine C export of 603 Tg C yr<inline-formula><mml:math id="M534" 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> (values are rounded).</p>
            </list-item>
          </list></p>
</sec>
<sec id="App1.Ch1.S3.SS2">
  <label>C2</label><title>Long-term ocean fluxes</title>
      <p id="d1e10336">In the model, riverine loads cause oceanic C outgassing due to the inputs of inorganic C and tDOM, while the inputs of dissolved inorganic nutrients cause a sink of atmospheric C through their enhancement of
the biological C uptake. Increased primary production thereby also produces alkalinity, which also potentially causes an uptake of atmospheric C.</p>
      <p id="d1e10339">Inorganic C is delivered to the ocean by rivers as 1 mol DIC and 1 mol alkalinity, which represent the supply of <inline-formula><mml:math id="M535" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, and it is exported from the ocean as <inline-formula><mml:math id="M536" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, which accounts for 0.5 mol DIC per 1 mol alkalinity,
leaving a surplus of 0.5 mol DIC
and 0 mol alkalinity when balancing over the oceanic inputs and exports. Increasing the oceanic DIC pool without increasing the alkalinity directly increases the dissolved <inline-formula><mml:math id="M537" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentrations, which in turn causes outgassing:
            <disp-formula id="App1.Ch1.S3.E14" content-type="numbered"><label>C1</label><mml:math id="M538" display="block"><mml:mrow><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow><mml:mo>=</mml:mo><mml:mi mathvariant="italic">&gt;</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e10434">Equilibrium model outgassing caused by riverine inorganic C inputs is therefore 0.5 fold of the riverine DIC loads.</p>
      <p id="d1e10437">Outgassing from organic matter inputs results from the high <inline-formula><mml:math id="M539" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratio of tDOM. tDOM, in contrary to POM, is not exported to the sediment. It is mineralized in the ocean, providing dissolved inorganic compounds
in the <inline-formula><mml:math id="M540" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratio of <inline-formula><mml:math id="M541" display="inline"><mml:mrow><mml:mn mathvariant="normal">2583</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">16</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>, but the subsequent uptake of the released inorganic compounds happens at a <inline-formula><mml:math id="M542" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">N</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratio of <inline-formula><mml:math id="M543" display="inline"><mml:mrow><mml:mn mathvariant="normal">122</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">16</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>, resulting in a DIC overshoot.
Since the net alkalinity over the entirety of Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S3.E15"/>) is also constant, the DIC increase causes a <inline-formula><mml:math id="M544" display="inline"><mml:mrow class="chem"><mml:mi>p</mml:mi><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> increase (<inline-formula><mml:math id="M545" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula> simplified equation):
            <disp-formula id="App1.Ch1.S3.E15" content-type="numbered"><label>C2</label><mml:math id="M546" display="block"><mml:mtable columnspacing="1em" class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:msup><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mn mathvariant="normal">2583</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">PN</mml:mi><mml:mn mathvariant="normal">16</mml:mn></mml:msub></mml:mrow><mml:mo>*</mml:mo></mml:msup></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mi mathvariant="italic">&gt;</mml:mi><mml:mn mathvariant="normal">2583</mml:mn><mml:mi mathvariant="normal">DIC</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">DIP</mml:mi><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mn mathvariant="normal">16</mml:mn><mml:mi mathvariant="normal">DIN</mml:mi></mml:mrow><mml:mo>+</mml:mo><mml:mo>*</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mi mathvariant="italic">&gt;</mml:mi><mml:msup><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mn mathvariant="normal">122</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">PN</mml:mi><mml:mn mathvariant="normal">16</mml:mn></mml:msub></mml:mrow><mml:mo>*</mml:mo></mml:msup><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2461</mml:mn><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d1e10623">The organic outgassing caused by organic matter inputs is therefore <inline-formula><mml:math id="M547" display="inline"><mml:mrow><mml:mn mathvariant="normal">2461</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">2583</mml:mn></mml:mrow></mml:math></inline-formula> multiplied with tDOM carbon loads.</p>
      <p id="d1e10638">The riverine loads of DIP and DIN on the other hand cause C uptake through their enhancement of the biological primary production. <inline-formula><mml:math id="M548" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">DIC</mml:mi><mml:mo>:</mml:mo><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is thereby removed, thus sinking <inline-formula><mml:math id="M549" display="inline"><mml:mrow class="chem"><mml:mi>p</mml:mi><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M550" display="inline"><mml:msup><mml:mi/><mml:mo>*</mml:mo></mml:msup></mml:math></inline-formula> simplified equation):
            <disp-formula id="App1.Ch1.S3.E16" content-type="numbered"><label>C3</label><mml:math id="M551" display="block"><mml:mrow><mml:mi mathvariant="normal">DIP</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">16</mml:mn><mml:mi mathvariant="normal">DIN</mml:mi><mml:mo>+</mml:mo><mml:mo>*</mml:mo><mml:mo>+</mml:mo><mml:mn mathvariant="normal">122</mml:mn><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mi mathvariant="italic">&gt;</mml:mi><mml:msup><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mn mathvariant="normal">122</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">PN</mml:mi><mml:mn mathvariant="normal">16</mml:mn></mml:msub></mml:mrow><mml:mo>*</mml:mo></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d1e10726">The resulting C uptake from the equation is therefore 122-fold the mole DIP inputs.
Additionally, alkalinity is produced in Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S3.E16"/>). The uptake of DIN (assuming nitrate and not ammonium,as is done in HAMOCC) and DIP through primary production
causes a net alkalinity increase
by a factor of <inline-formula><mml:math id="M552" display="inline"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">Alk</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">17</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx113" id="paren.224"/>.  In model equilibrium, the produced alkalinity must also be exported through Eq. (<xref ref-type="disp-formula" rid="App1.Ch1.S3.E14"/>). This alkalinity is exported in
a <inline-formula><mml:math id="M553" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">Alk</mml:mi></mml:mrow></mml:math></inline-formula> ratio of <inline-formula><mml:math id="M554" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula>, meaning an uptake of 0.5 DIC per mol alkalinity exported. The C uptake enhancement from the alkalinity increase is therefore the <inline-formula><mml:math id="M555" display="inline"><mml:mrow><mml:mn mathvariant="normal">17</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> multiplied with the (bioavailable) DIP loads.</p>
      <p id="d1e10794">With the help of these equations, the fluxes of riverine C in the ocean of Fig. <xref ref-type="fig" rid="Ch1.F9"/> were calculated.
<list list-type="custom"><list-item><label>5.</label>
      <p id="d1e10801">According to the <inline-formula><mml:math id="M556" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> export equation (Eq. <xref ref-type="disp-formula" rid="App1.Ch1.S3.E14"/>), half of the riverine DIC input is exported to the sediment as <inline-formula><mml:math id="M557" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and
the other half is outgassed as <inline-formula><mml:math id="M558" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in model equilibrium state. The contribution of outgassing caused by inorganic C in the ocean is therefore 0.5-fold the DIC inputs (366 Tg C yr<inline-formula><mml:math id="M559" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)
and therefore 183 Tg C yr<inline-formula><mml:math id="M560" 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> assuming model equilibrium.</p></list-item><list-item><label>6.</label>
      <p id="d1e10865">tDOM input <inline-formula><mml:math id="M561" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> rations vastly exceed the oceanic sediment export <inline-formula><mml:math id="M562" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratios of organic matter, which causes model equilibrium outgassing
in the ocean. Equation (<xref ref-type="disp-formula" rid="App1.Ch1.S3.E15"/>) shows that for every mol tDOM supplied to the ocean, in model equilibrium
<inline-formula><mml:math id="M563" display="inline"><mml:mrow><mml:mn mathvariant="normal">122</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">2583</mml:mn></mml:mrow></mml:math></inline-formula> of C is exported to the sediment, and <inline-formula><mml:math id="M564" display="inline"><mml:mrow><mml:mn mathvariant="normal">2461</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">2583</mml:mn></mml:mrow></mml:math></inline-formula> of C increases the dissolved <inline-formula><mml:math id="M565" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> pool, which is outgassed in the long term. The equilibrium outgassing is therefore the tDOM carbon load (134 Tg C yr<inline-formula><mml:math id="M566" 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>) multiplied
by <inline-formula><mml:math id="M567" display="inline"><mml:mrow><mml:mn mathvariant="normal">2461</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">2583</mml:mn></mml:mrow></mml:math></inline-formula>, which results in 128 Tg C yr<inline-formula><mml:math id="M568" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. In the case of POM, since the <inline-formula><mml:math id="M569" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow></mml:math></inline-formula> ratio of the riverine input (<inline-formula><mml:math id="M570" display="inline"><mml:mrow><mml:mn mathvariant="normal">122</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>) is the same as the ratio of the export to the sediment in the ocean,
there is no effect on the long-term equilibrium C outgassing flux.</p></list-item><list-item><label>7.</label>
      <p id="d1e10991">Since P has no further sinks or sources in the model other than riverine inputs and sediment burial as organic matter, in model equilibrium the
same amount of P supplied by rivers is buried in the sediment.
When DIP is taken up by the biology and transformed to organic matter, carbon is also taken up in a mole ratio of <inline-formula><mml:math id="M571" display="inline"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">C</mml:mi><mml:mo>:</mml:mo><mml:mi mathvariant="normal">P</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">122</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>. Accounting for this uptake through the biological production enhancement by DIP inputs (including
all bioavailable DIP) from rivers (1.4 Tg P yr<inline-formula><mml:math id="M572" 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>)
results in the uptake of 67 Tg C yr<inline-formula><mml:math id="M573" 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> through the biological enhancement.
Furthermore, when DIP and DIN are transformed to organic matter, an alkalinity increase of 17 mol mol<inline-formula><mml:math id="M574" 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> DIP uptake takes place (Eq. <xref ref-type="disp-formula" rid="App1.Ch1.S3.E16"/>, <xref ref-type="bibr" rid="bib1.bibx113" id="altparen.225"/>).
This increase in alkalinity causes the further uptake
uptake and export
of 2 Tg C yr<inline-formula><mml:math id="M575" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, resulting in a total sink of 69 Tg C yr<inline-formula><mml:math id="M576" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p></list-item><list-item><label>Dr1.</label>
      <p id="d1e11082">We attribute the difference between the equilibrium <inline-formula><mml:math id="M577" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> flux of 242 Tg C yr<inline-formula><mml:math id="M578" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and the modeled net <inline-formula><mml:math id="M579" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> flux of 231 Tg C yr<inline-formula><mml:math id="M580" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> (<inline-formula><mml:math id="M581" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">11</mml:mn></mml:mrow></mml:math></inline-formula> Tg C yr<inline-formula><mml:math id="M582" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>)
to the small surface alkalinity increase in the model simulations due to slight disequilibrium over the analysis time period.</p></list-item><list-item><label>8.</label>
      <p id="d1e11155">The simulated global particulate inorganic C sediment deposition flux in HAMOCC is 188 Tg C yr<inline-formula><mml:math id="M583" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p></list-item><list-item><label>9.</label>
      <p id="d1e11171">The simulated global organic C sediment deposition flux in HAMOCC model is 582 Tg C yr<inline-formula><mml:math id="M584" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p></list-item><list-item><label>10.</label>
      <p id="d1e11187">The modeled global DIC flux from the sediment back to the water, which originates from DIC release due to POM remineralization and <inline-formula><mml:math id="M585" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution in the sediment, is 385 Tg C yr<inline-formula><mml:math id="M586" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p></list-item><list-item><label>Dr2.</label>
      <p id="d1e11214">In model equilibrium, the net sediment burial C flux is the total riverine C inputs of 603 Tg C yr<inline-formula><mml:math id="M587" 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> (4) subtracted by the equilibrium outgassing of 242 Tg C yr<inline-formula><mml:math id="M588" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> (<inline-formula><mml:math id="M589" display="inline"><mml:mrow><mml:mn mathvariant="normal">5</mml:mn><mml:mo>+</mml:mo><mml:mn mathvariant="normal">6</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:math></inline-formula>),
which results in
361 Tg C yr<inline-formula><mml:math id="M590" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. The simulated net C burial flux in the simulations of 385 Tg C yr<inline-formula><mml:math id="M591" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> (<inline-formula><mml:math id="M592" display="inline"><mml:mrow><mml:mn mathvariant="normal">8</mml:mn><mml:mo>+</mml:mo><mml:mn mathvariant="normal">9</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula>) deviates from the calculated
model burial equilibrium flux. Therefore, the drift at the sediment–ocean interface is 24 Tg C yr<inline-formula><mml:math id="M593" 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> (385–361 Tg C yr<inline-formula><mml:math id="M594" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) and is in the direction of
the sediment.</p></list-item></list></p><?xmltex \hack{\clearpage}?>
</sec>
</app>

<?pagebreak page81?><app id="App1.Ch1.S4">
  <?xmltex \currentcnt{D}?><label>Appendix D</label><title>Comparison of surface nutrient distributions</title>

      <?xmltex \floatpos{h!}?><fig id="App1.Ch1.S4.F12"><?xmltex \currentcnt{D1}?><label>Figure D1</label><caption><p id="d1e11334">DIP concentrations in OBS (WOA observations), REF and RIV.</p></caption>
        <?xmltex \hack{\textwidth\hsize}?>
        <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020-f12.png"/>

      </fig>

<?xmltex \hack{\clearpage}?><?xmltex \floatpos{h!}?><fig id="App1.Ch1.S4.F13"><?xmltex \currentcnt{D2}?><label>Figure D2</label><caption><p id="d1e11348">Dissolved silica (DSi) concentrations in OBS (WOA observations), REF and RIV.</p></caption>
        <?xmltex \hack{\textwidth\hsize}?>
        <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020-f13.png"/>

      </fig>

<?xmltex \hack{\clearpage}?><?xmltex \floatpos{h!}?><fig id="App1.Ch1.S4.F14"><?xmltex \currentcnt{D3}?><label>Figure D3</label><caption><p id="d1e11363">Nitrate (DIN) concentrations in OBS (WOA observations), REF and RIV.</p></caption>
        <?xmltex \hack{\textwidth\hsize}?>
        <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://bg.copernicus.org/articles/17/55/2020/bg-17-55-2020-f14.png"/>

      </fig>

<?xmltex \hack{\clearpage}?>
</app>
  </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e11380">FL developed the model code,
and performed the experiments. All co-authors contributed to the analysis and preparation of the manuscript.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e11386">The authors declare that they have no conflict of interest.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e11392">All simulations were performed at the German Climate Computing Center (DKRZ). The research leading to these results has received funding from the European Union's Horizon 2020 research and innovation
program under the Marie Skłodowska-Curie grant agreement no. 643052 (C-CASCADES project). We acknowledge the constructive comments and suggestions received
from Pierre Regnier, Irene Stemmler, Katharina Six and Philip Pika.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e11397">This research has been supported by the C-CASCADES (grant no. 643052).<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>The article processing charges for this open-access <?xmltex \hack{\newline}?> publication were covered by the Max Planck Society.</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e11408">This paper was edited by Jack Middelburg and reviewed by two anonymous referees.</p>
  </notes><ref-list>
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    <!--<article-title-html>Oceanic CO<sub>2</sub> outgassing and biological production hotspots induced by pre-industrial river loads of nutrients and carbon in a global modeling approach</article-title-html>
<abstract-html><p>Rivers are a major source of nutrients, carbon and  alkalinity to the global ocean.
In this study, we firstly estimate pre-industrial riverine loads of nutrients, carbon and alkalinity based on a hierarchy of weathering and terrestrial organic matter export models, while identifying
regional hotspots of the riverine exports. Secondly, we implement the riverine loads into a global ocean biogeochemical model to describe their implications for oceanic nutrient concentrations,
net primary production (NPP) and air–sea CO<sub>2</sub> fluxes
globally, as well as in an analysis of coastal regions. Thirdly, we quantitatively assess the
terrestrial origins and the long-term fate of riverine carbon in the ocean.
We quantify annual bioavailable pre-industrial riverine loads
of 3.7&thinsp;Tg P, 27&thinsp;Tg N, 158&thinsp;Tg Si and 603&thinsp;Tg C delivered to the ocean globally. We thereby identify the tropical Atlantic catchments (20&thinsp;% of global C),
Arctic rivers (9&thinsp;% of global C) and Southeast Asian rivers (15&thinsp;% of global C)
as dominant suppliers of carbon for the ocean.
The riverine exports lead to a simulated net global oceanic CO<sub>2</sub> source of 231&thinsp;Tg C&thinsp;yr<sup>−1</sup> to the atmosphere, which is mainly caused by inorganic carbon (source of 183&thinsp;Tg C&thinsp;yr<sup>−1</sup>)
and by organic carbon (source of 128&thinsp;Tg C&thinsp;yr<sup>−1</sup>) riverine loads. Additionally, a sink of 80&thinsp;Tg C&thinsp;yr<sup>−1</sup> is caused by the enhancement of the biological carbon uptake from dissolved
inorganic nutrient inputs from rivers and the resulting alkalinity production.
While large outgassing fluxes are simulated mostly in proximity to major river mouths, substantial outgassing fluxes can be found further offshore, most prominently in the tropical Atlantic.
Furthermore, we find evidence for the interhemispheric transfer of carbon in the model; we detect a larger relative outgassing flux (49&thinsp;% of global riverine-induced outgassing)
in the Southern Hemisphere in comparison to the hemisphere's relative
riverine inputs (33&thinsp;% of global C inputs), as well as an outgassing flux of 17&thinsp;Tg C&thinsp;yr<sup>−1</sup> in the Southern Ocean.
The addition of riverine loads in the model leads to a strong NPP increase in the tropical west Atlantic, Bay of Bengal and the East
China Sea (+166&thinsp;%, +377&thinsp;% and +71&thinsp;%, respectively).
On the light-limited Arctic shelves, the NPP is not strongly sensitive to riverine loads, but the CO<sub>2</sub> flux is strongly altered regionally due to substantial dissolved inorganic and organic
carbon supplies to the region.
While our study confirms that the ocean circulation remains the main driver for biogeochemical distributions in the open ocean, it reveals the necessity to consider riverine inputs
for the representation of heterogeneous features in the coastal ocean and to represent riverine-induced pre-industrial carbon outgassing in the ocean.
It also underlines the need to consider long-term CO<sub>2</sub> sources from volcanic and shale oxidation fluxes in order to close the framework's atmospheric carbon budget.</p></abstract-html>
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