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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Mar. Sci.</journal-id>
<journal-title>Frontiers in Marine Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Mar. Sci.</abbrev-journal-title>
<issn pub-type="epub">2296-7745</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fmars.2023.1149938</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Marine Science</subject>
<subj-group>
<subject>Review</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Review of algorithms estimating export production from satellite derived properties</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>J&#xf6;nsson</surname>
<given-names>Bror F.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="author-notes" rid="fn001">
<sup>*</sup>
</xref> <uri xlink:href="https://loop.frontiersin.org/people/1486388"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Kulk</surname>
<given-names>Gemma</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/185421"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Sathyendranath</surname>
<given-names>Shubha</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/373399"/>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>Earth Observation Science &amp; Applications, Plymouth Marine Laboratory</institution>, <addr-line>Plymouth</addr-line>, <country>United Kingdom</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>National Centre for Earth Observation, Plymouth Marine Laboratory</institution>, <addr-line>Plymouth</addr-line>, <country>United Kingdom</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>Edited by: Jeremy Werdell, National Aeronautics and Space Administration, United States</p>
</fn>
<fn fn-type="edited-by">
<p>Reviewed by: Monique Messi&#xe9;, Monterey Bay Aquarium Research Institute (MBARI), United States; Greg M. Silsbe, University of Maryland, College Park, United States</p>
</fn>
<fn fn-type="corresp" id="fn001">
<p>*Correspondence: Bror F. J&#xf6;nsson, <email xlink:href="mailto:brj@pml.ac.uk">brj@pml.ac.uk</email>
</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>21</day>
<month>08</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>10</volume>
<elocation-id>1149938</elocation-id>
<history>
<date date-type="received">
<day>23</day>
<month>01</month>
<year>2023</year>
</date>
<date date-type="accepted">
<day>06</day>
<month>07</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 J&#xf6;nsson, Kulk and Sathyendranath</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>J&#xf6;nsson, Kulk and Sathyendranath</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>Whereas the vertical transport of biomass from productive surface waters to the deep ocean (the biological pump) is a critical component of the global carbon cycle, its magnitude and variability is poorly understood. Global-scale estimates of ocean carbon export vary widely, ranging from &#x223c;5 to &#x223c;20 Gt C y <sup>&#x2013; 1</sup> due to uncertainties in methods and unclear definitions. Satellite-derived properties such as phytoplankton biomass, sea surface temperature, and light attenuation at depth provide information about the oceanic ecosystem with unprecedented coverage and resolution in time and space. These products have been the basis of an intense effort over several decades to constrain different biogeochemical production rates and fluxes in the ocean. One critical challenge in this effort has been to estimate the magnitude of the biological pump from satellite-derived properties by establishing how much of the primary production is exported out of the euphotic zone, a flux that is called export production. Here we present a review of existing algorithms for estimating export production from satellite-derived properties, available <italic>in-situ</italic> datasets that can be used for testing the algorithms, and earlier evaluations of the proposed algorithms. The satellite-derived products used in the algorithm evaluation are all based largely on the Ocean Colour Climate Change Initiative (OC-CCI) products, and carbon products derived from them. The different resources are combined in a meta-analysis.</p>
</abstract>
<kwd-group>
<kwd>carbon export</kwd>
<kwd>biological pump</kwd>
<kwd>satellite oceanography</kwd>
<kwd>ocean color</kwd>
<kwd>net community production</kwd>
<kwd>biogeochemistry</kwd>
<kwd>algorithms</kwd>
</kwd-group>
<contract-sponsor id="cn001">European Space Agency<named-content content-type="fundref-id">10.13039/501100000844</named-content>
</contract-sponsor>
<counts>
<fig-count count="10"/>
<table-count count="5"/>
<equation-count count="20"/>
<ref-count count="88"/>
<page-count count="18"/>
<word-count count="9304"/>
</counts>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-in-acceptance</meta-name>
<meta-value>Ocean Observation</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1" sec-type="intro">
<label>1</label>
<title>Introduction</title>
<p>The recirculation of major nutrients and carbon in the ocean is strongly controlled by the vertical export of particulate organic matter from the surface ocean to the ocean&#x2019;s interior (<xref ref-type="fig" rid="f1">
<bold>Figure 1</bold>
</xref> and e.g. <xref ref-type="bibr" rid="B29">Falkowski et&#xa0;al., 1998</xref>; <xref ref-type="bibr" rid="B68">Sabine et&#xa0;al., 2004</xref>; <xref ref-type="bibr" rid="B35">Honjo et&#xa0;al., 2008</xref>; <xref ref-type="bibr" rid="B75">Siegel et&#xa0;al., 2022</xref>). Marine phytoplankton transform CO<sub>2</sub> to organic carbon via photosynthesis with light as the energy source (<xref ref-type="bibr" rid="B26">Eppley, 1972</xref>; <xref ref-type="bibr" rid="B32">Geider et&#xa0;al., 1998</xref>), a critical biological process that is the foundation of most marine ecosystems (<xref ref-type="bibr" rid="B69">Sarmiento and Bender, 1994</xref>; <xref ref-type="bibr" rid="B59">Pauly and Christensen, 1995</xref>). The resulting chemical energy bound as organic carbon is used in marine food webs to build other types of biomass and as energy for autotrophic and heterotrophic organisms. While the carbon fixation by phytoplankton (or Primary Production, PP) in marine ecosystems is of vital significance (e.g. <xref ref-type="bibr" rid="B60">Platt et&#xa0;al., 1989</xref>; <xref ref-type="bibr" rid="B59">Pauly and Christensen, 1995</xref>; <xref ref-type="bibr" rid="B30">Fasham, 2003</xref>; <xref ref-type="bibr" rid="B48">Marinov et&#xa0;al., 2008</xref>; <xref ref-type="bibr" rid="B16">Chavez et&#xa0;al., 2011</xref>), there has been a longstanding debate about how to quantify its magnitude (<xref ref-type="bibr" rid="B60">Platt et&#xa0;al., 1989</xref>; <xref ref-type="bibr" rid="B66">Quay and Karl, 2010</xref>; <xref ref-type="bibr" rid="B22">Duarte et&#xa0;al., 2013</xref>; <xref ref-type="bibr" rid="B86">Williams et&#xa0;al., 2013</xref>). Methods to observe or infer different components of primary production have been developed (<xref ref-type="bibr" rid="B6">Bender et&#xa0;al., 1987</xref>; <xref ref-type="bibr" rid="B19">Cullen, 2001</xref>; <xref ref-type="bibr" rid="B30">Fasham, 2003</xref>) that are valid over varying spatial and temporal domains (<xref ref-type="bibr" rid="B4">Balch et&#xa0;al., 2022</xref>), and there are significant differences in how different researchers define biological production (<xref ref-type="bibr" rid="B85">Williams, 1993</xref>; <xref ref-type="bibr" rid="B19">Cullen, 2001</xref>). Most of the biomass generated by PP in the euphotic (sunlit) zone is consumed by heterotrophs and remineralized in the upper ocean. The remaining part is called Net Community Production (NCP) and if aggregated over sufficiently large temporal and spatial scales, they equate to Export Production (EP). Organic carbon resulting from EP is transported to deeper waters by, among other pathways, the downward vertical flux of Particulate or Dissolved Organic Carbon (POC, DOC), often referred to as the &#x201c;biological pump&#x201d; (BCP, <xref ref-type="bibr" rid="B82">Volk and Hoffert, 1985</xref>). See <xref ref-type="bibr" rid="B75">Siegel et&#xa0;al. (2022)</xref> for an exhaustive discussion about the Biological Carbon Pump (BCP) and other processes that sequester carbon from the surface ocean to deeper waters. As with PP, the understanding of the magnitude and spatiotemporal variability of the biological pump remains limited (<xref ref-type="bibr" rid="B13">Burd et&#xa0;al., 2010</xref>; <xref ref-type="bibr" rid="B9">Britten and Primeau, 2016</xref>).</p>
<fig id="f1" position="float">
<label>Figure&#xa0;1</label>
<caption>
<p>Conceptual model of the relationships between different terms describing carbon fluxes in the Ocean. Each term is defined in the text and <xref ref-type="table" rid="T1">
<bold>Table&#xa0;1</bold>
</xref>.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1149938-g001.tif"/>
</fig>
<p>Satellite-based ocean color products have provided an unprecedented resource to study ocean biogeochemistry and biological oceanography with high spatiotemporal resolution and coverage (<xref ref-type="bibr" rid="B33">Groom et&#xa0;al., 2019</xref>; <xref ref-type="bibr" rid="B49">McClain et&#xa0;al., 2022</xref>) and significant effort has been allocated to also assess the biological pump from space with limited success (<xref ref-type="bibr" rid="B75">Siegel et&#xa0;al., 2022</xref>). One critical challenge has been to quantify community respiration (<xref ref-type="bibr" rid="B84">Westberry et&#xa0;al., 2012</xref>) and to establish the ratio of PP that is exported out from the euphotic zone (<xref ref-type="bibr" rid="B9">Britten and Primeau, 2016</xref>; <xref ref-type="bibr" rid="B73">Siegel et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B75">Siegel et&#xa0;al., 2022</xref>). The large uncertainties associated with satellite-based EP products has led to global-scale estimates of ocean carbon export that vary from &#x223c; 5 to 20 Gt C y<sup>&#x2013; 1</sup> (<xref ref-type="bibr" rid="B25">Dunne et&#xa0;al., 2007</xref>; <xref ref-type="bibr" rid="B34">Henson et&#xa0;al., 2011</xref>; <xref ref-type="bibr" rid="B42">Laws et&#xa0;al., 2011</xref>; <xref ref-type="bibr" rid="B73">Siegel et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B75">Siegel et&#xa0;al., 2022</xref>).</p>
<sec id="s1_1">
<label>1.1</label>
<title>Fluxes and relationships</title>
<p>The main approach to estimate EP from remotely sensed products is based on empirical correlations identified from regression analysis of <italic>in-situ</italic> observations of vertical POC fluxes in combination with properties that can be derived from satellite (e.g. <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al., 2015</xref>). This method has so far generated algorithms with arguably limited ability to predict EP (e.g. <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al., 2015</xref>; <xref ref-type="bibr" rid="B58">Palevsky et&#xa0;al., 2016</xref>). The many challenges to estimate export fluxes from satellite-derived properties are further complicated by differences and inconsistencies in how EP and export fluxes are defined and quantified. We will describe the most common definitions in the following sections and summarize them in <xref ref-type="table" rid="T1">
<bold>Table 1</bold>
</xref>.</p>
<table-wrap id="T1" position="float">
<label>Table&#xa0;1</label>
<caption>
<p>Different terms associated with Biological Production that are relevant for algorithm development.</p>
</caption>
<table frame="hsides">
<tbody>
<tr>
<td valign="top" align="left">Gross Primary Production</td>
<td valign="top" align="left">GPP</td>
<td valign="top" align="left">Total production of organic carbon by autrotrophs</td>
</tr>
<tr>
<td valign="top" align="left">Net Primary Production</td>
<td valign="top" align="left">NPP</td>
<td valign="top" align="left">GPP less losses to respiration by autrotrophs</td>
</tr>
<tr>
<td valign="top" align="left">Net Community Production</td>
<td valign="top" align="left">NCP</td>
<td valign="top" align="left">GPP less all community respiration in the defined system</td>
</tr>
<tr>
<td valign="top" align="left">Export Production</td>
<td valign="top" align="left">EP</td>
<td valign="top" align="left">NCP integrated over sufficient time and space to satisfy dynamic steady state conditions. The part of biological production in the euphotic zone that is exported to deeper waters.</td>
</tr>
<tr>
<td valign="top" align="left">Export Flux</td>
<td valign="top" align="left">EFlux</td>
<td valign="top" align="left">Permanent flux of particulate carbon over a depth horizon below the euphotic zone</td>
</tr>
<tr>
<td valign="top" align="left">ef-ratio</td>
<td valign="top" align="left">ef-ratio</td>
<td valign="top" align="left">The ratio between new or export production and NPP in a steady state system.</td>
</tr>
<tr>
<td valign="top" align="left">Export Efficiency</td>
<td valign="top" align="left">Ef</td>
<td valign="top" align="left">The ratio of NPP that is exported across a vertical horizon.</td>
</tr>
</tbody>
</table>
</table-wrap>
<sec id="s1_1_1">
<label>1.1.1</label>
<title>Gross primary production</title>
<p>GPP is the total rate of carbon production by autotrophic organisms before correction for losses due to excretion or respiration, or in other words the gross conversion of inorganic carbon to its organic state (<xref ref-type="bibr" rid="B19">Cullen, 2001</xref>; <xref ref-type="bibr" rid="B30">Fasham, 2003</xref>) by autotrophs. GPP can in theory be derived from first principles (e.g. <xref ref-type="bibr" rid="B40">Lawrenz et&#xa0;al., 2013</xref>, and references).</p>
</sec>
<sec id="s1_1_2">
<label>1.1.2</label>
<title>Net primary production</title>
<p>NPP is the net rate at which autotrophic organisms assimilate carbon. This is normally defined as GPP minus the fraction used by primary producers for cellular respiration and maintenance. (<xref ref-type="bibr" rid="B6">Bender et&#xa0;al., 1987</xref>; <xref ref-type="bibr" rid="B60">Platt et&#xa0;al., 1989</xref>; <xref ref-type="bibr" rid="B85">Williams, 1993</xref>; <xref ref-type="bibr" rid="B5">Behrenfeld and Falkowski, 1997</xref>; <xref ref-type="bibr" rid="B19">Cullen, 2001</xref>; <xref ref-type="bibr" rid="B30">Fasham, 2003</xref>). NPP is also the portion of carbon fixation from photosynthesis that is available to heterotrophic organisms in the ecosystem (<xref ref-type="bibr" rid="B16">Chavez et&#xa0;al., 2011</xref>). NPP has primarily been measured <italic>in-situ</italic> using the <sup>14</sup>C method developed by <xref ref-type="bibr" rid="B55">Nielsen (1952)</xref>, where collected samples are incubated with a known amount of radioactive <sup>14</sup>C-bicarbonate that labels the dissolved inorganic carbon pool (e.g. <xref ref-type="bibr" rid="B61">Platt and Jassby, 1976</xref>; <xref ref-type="bibr" rid="B6">Bender et&#xa0;al., 1987</xref>; <xref ref-type="bibr" rid="B19">Cullen, 2001</xref>; <xref ref-type="bibr" rid="B30">Fasham, 2003</xref>). Other approaches to estimate NPP are based on measuring changes of O<sub>2</sub> in light-dark incubations and different isotopic methods (e.g. <sup>18</sup>O <sup>13</sup>C, <xref ref-type="bibr" rid="B6">Bender et&#xa0;al., 1987</xref>; <xref ref-type="bibr" rid="B19">Cullen, 2001</xref>; <xref ref-type="bibr" rid="B16">Chavez et&#xa0;al., 2011</xref>). Typically, the shorter the duration of the incubation method (of order 1 hour), the more the measurement is considered to approach GPP. Longer incubations (order 10 hours) lead to estimates of NPP.</p>
<p>One major development has been the ability to estimate PP from satellite-derived properties (e.g. <xref ref-type="bibr" rid="B28">Eppley et&#xa0;al., 1985</xref>; <xref ref-type="bibr" rid="B62">Platt et&#xa0;al., 1988</xref>; <xref ref-type="bibr" rid="B71">Sathyendranath et&#xa0;al., 1991</xref>; <xref ref-type="bibr" rid="B5">Behrenfeld and Falkowski, 1997</xref>; <xref ref-type="bibr" rid="B31">Friedrichs et&#xa0;al., 2009</xref>), providing depth-integrated estimates with unprecedented spatial resolution and coverage. Note that, in principle, the method of Platt and Sathyendranath, based on short (1-2h) photosynthesis-irradiance experiment, may be considered to estimate GPP, whereas the method of Behrenfeld and colleagues, based on <italic>in situ</italic> incubation of one day, approaches NPP. A common approach to quantify PP in the surface ocean from satellite derived properties is based on a concept where stocks of carbon biomass or chlorophyll are combined with auxiliary properties to estimate rates of photosynthesis (e.g. <xref ref-type="bibr" rid="B62">Platt et&#xa0;al., 1988</xref>; <xref ref-type="bibr" rid="B5">Behrenfeld and Falkowski, 1997</xref>; <xref ref-type="bibr" rid="B2">Arrigo et&#xa0;al., 1998</xref>; <xref ref-type="bibr" rid="B83">Westberry et&#xa0;al., 2008</xref>). Another approach is to use Inherent Optical Properties (IOPs) to estimate NPP by combining satellite-based proxies for energy absorption in the water column with inferences of the efficiency when absorbed energy is converted into carbon biomass (<xref ref-type="bibr" rid="B1">Antoine et&#xa0;al., 1996</xref>; <xref ref-type="bibr" rid="B44">Lee et&#xa0;al., 1996</xref>; <xref ref-type="bibr" rid="B77">Smyth et&#xa0;al., 2005</xref>; <xref ref-type="bibr" rid="B76">Silsbe et&#xa0;al., 2016</xref>).</p>
</sec>
<sec id="s1_1_3">
<label>1.1.3</label>
<title>Net community production</title>
<p>NCP represents the net increase of biomass or carbon in the ecosystem of interest, or NPP minus community respiration of all heterotrophs (<xref ref-type="bibr" rid="B85">Williams, 1993</xref>; <xref ref-type="bibr" rid="B19">Cullen, 2001</xref>; <xref ref-type="bibr" rid="B30">Fasham, 2003</xref>). NCP estimates must be constrained to a defined domain in time and space to be of practical use. A method that aggregates results over the mixed layer can provide diametrically different results for a specific region compared with one that includes the part of the photic zone below the base of the mixed layer or parts of the mesopelagic. Likewise, NCP over short timescales should be interpreted very differently than annual averages (<xref ref-type="bibr" rid="B30">Fasham, 2003</xref>).</p>
</sec>
<sec id="s1_1_4">
<label>1.1.4</label>
<title>Export production</title>
<p>Export Production (EP, <xref ref-type="bibr" rid="B41">Laws, 1991</xref>) is the net production of organic carbon above a specified horizon and is assumed to be equivalent with NCP when the system is in steady-state and all temporal lags are accounted for. EP is an important property for the global carbon cycle by constraining the sequestration of organic carbon to deeper waters. EP is by definition only valid over significantly longer timescales than any processes directly controlling production and respiration. Hence, it is not possible to directly convert <italic>In-situ</italic> measurements of mixed layer NCP to EP since the newly-produced biomass might be consumed before it can be exported to the aphotic zone. It is also not yet possible to derive mechanistic relationships between EP satellite-based products. EP serves as the upper bound for transport of POC from the euphotic zone to the bathypelgic (e.g. <xref ref-type="bibr" rid="B60">Platt et&#xa0;al., 1989</xref>; <xref ref-type="bibr" rid="B73">Siegel et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B75">Siegel et&#xa0;al., 2022</xref>).</p>
</sec>
<sec id="s1_1_5">
<label>1.1.5</label>
<title>Export flux</title>
<p>If EP reflects the aggregated production of carbon above a depth horizon available for export to deeper waters, Eflux represents the direct or indirect measurement of this transport. Eflux is defined as the flux of material over a depth horizon and normally quantified via sediment traps (<xref ref-type="bibr" rid="B24">Dunne et&#xa0;al., 2005</xref>; <xref ref-type="bibr" rid="B11">Buesseler et&#xa0;al., 2007</xref>) or by measuring the reduction of particle-reactive <sup>234</sup>Th in comparison to its longer-lived parent <sup>238</sup>U in the water column (e.g. <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al., 2018</xref>, and references therein). The <sup>234</sup>Th method determines the downward flux of POC by integrating the deficit of <sup>234</sup>Th in the upper water column and couples it to the POC/<sup>234</sup>Th ratio in sinking particles. Samples can be collected with much higher vertical resolution than traps, allowing for the estimation of POC flux at or very near Z<sub>eu</sub> without the need for a common reference depth. In contrast to EP, Eflux can be estimated across any temporal or spatial scale. Factors controlling the regional, temporal, and depth variations of POC/<sup>234</sup>Th ratios are however poorly understood (<xref ref-type="bibr" rid="B64">Puigcorbe et&#xa0;al., 2020</xref>). Other sources of uncertainty arise from neglecting physical processes and the necessary assumption of steady state in the Th isotope system (<xref ref-type="bibr" rid="B12">Buesseler et&#xa0;al., 2006</xref>).</p>
</sec>
<sec id="s1_1_6">
<label>1.1.6</label>
<title>Export efficiency</title>
<p>The fraction of PP that is exported out of the euphotic zone (EP/NPP) can be described as the carbon export efficiency (Ef). This is a non-dimensional ratio that describes how inefficient the ecosystem is in retaining carbon in the upper layer of the ocean. The more efficient the pelagic ecosystem is, the more inefficient the carbon export is, to the point where all carbon is recycled, and no carbon will be exported (<xref ref-type="bibr" rid="B10">Buesseler, 1998</xref>).</p>
</sec>
<sec id="s1_1_7">
<label>1.1.7</label>
<title>e-ratio</title>
<p>A special case of Ef is the e-ratio, or the flux of particulate organic carbon at the base of the euphotic zone divided by NPP, (<xref ref-type="bibr" rid="B52">Murray et&#xa0;al., 1996</xref>).</p>
</sec>
<sec id="s1_1_8">
<label>1.1.8</label>
<title>f-ratio</title>
<p>
<xref ref-type="bibr" rid="B27">Eppley and Peterson (1979)</xref> characterized export efficiency as the ratio of New to Total photosynthetic production, or the f-ratio. This idea is based on the concept of distinguishing NPP driven by nitrogen compounds originating from different processes in the ecosystem. New production is fueled by nutrients (usually NO<sub>3</sub> <sup>&#x2013;)</sup> recently introduced to the euphotic zone (either from deeper waters or via lateral processes) (<xref ref-type="bibr" rid="B23">Dugdale and Goering, 1967</xref>) in contrast to production from rapidly recycled compounds such as ammonium. Export production would then be equal to New production if the system is in a steady state and all transformations between ammonium and NO<sub>3</sub> <sup>&#x2013;</sup> occur outside the euphotic zone (<xref ref-type="bibr" rid="B42">Laws et&#xa0;al., 2011</xref>).</p>
<p>The f-ratio was originally believed to be significant by being directly related to Ef, but this interpretation relied on the assumption that nitrification mainly occur below the euphotic zone, something that more recent measurements have questioned (<xref ref-type="bibr" rid="B21">Dore and Karl, 1996</xref>; <xref ref-type="bibr" rid="B88">Yool et&#xa0;al., 2007</xref>). <xref ref-type="bibr" rid="B60">Platt et&#xa0;al. (1989)</xref> also suggested that elevated new production is directly driven by perturbations in the physical forcing which challenges a necessary assumption of steady state.</p>
</sec>
<sec id="s1_1_9">
<label>1.1.9</label>
<title>ef-ratio</title>
<p>
<xref ref-type="bibr" rid="B43">Laws et&#xa0;al. (2000)</xref> combined the e- and f-ratios to an ef-ratio based on the assumption that new production should balance export production if a system is in steady-state. This ratio makes it possible to combine measurements of new and export production.</p>
</sec>
<sec id="s1_1_10">
<label>1.1.10</label>
<title>pe-ratio</title>
<p>A more precise definition of the e-ratio is the pe-ratio, or &#x201c;the ratio between the export of rapidly sinking particulate matter (particle export) and the total production of organic matter by photosynthesis (primary production)&#x201d; (<xref ref-type="bibr" rid="B52">Murray et&#xa0;al., 1996</xref>; <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al., 2005</xref>). The pe-ratio shows similar spatial patterns as the f-ratio on global scales, especially when identifying eutrophic and oligotrophic regions.</p>
</sec>
</sec>
<sec id="s1_2">
<label>1.2</label>
<title>Structure of the review</title>
<p>With this review we have aimed to assess how different published algorithms that use satellite-derived properties to calculate EP perform. Our approach has been to leverage already existing evaluation studies where different models have been compared with each other, and only directly compare algorithms or validation datasets when no existing information is available. Earlier studies evaluating EP algorithms each use slightly varying approaches and were often conducted to compare newly developed algorithms with already existing ones. We address these differences by performing a kind of meta-analysis where different evaluations and validation datasets are compared together with the respective algorithms. We have followed the guidelines for systematic reviews prescribed in <xref ref-type="bibr" rid="B38">Khan et&#xa0;al. (2003)</xref> when applicable.</p>
<p>The review begins with a brief description of existing EP algorithms, followed by a presentation of different datasets that can be useful for the evaluation satellite-based EP algorithms. Next, we discuss earlier studies that evaluates EP algorithms, including our own comparison where we use the <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>; <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref>, and <xref ref-type="bibr" rid="B50">Mouw et&#xa0;al. (2016a)</xref> datasets to assess the different EP algorithms. Finally, we discuss the different evaluations and provide a recommendation about which algorithm to use.</p>
</sec>
</sec>
<sec id="s2">
<label>2</label>
<title>Export production algorithms</title>
<p>A number of different approaches to constrain and scale EP using different satellite derived properties have been proposed over the years. Most algorithms are developed to provide some kind of export efficiency ratio that then can be scaled with PP estimates to generate properties that are comparable to observations of EP. It is not well defined if either satellite-derived PP products or EP algorithms are assuming that the biological production is defined as GPP, NPP, or something in between, while this is not always clear from <italic>in-situ</italic> measurements either (<xref ref-type="bibr" rid="B4">Balch et&#xa0;al., 2022</xref>). As a result, we use the term PP to designate primary production without specifying if it is GPP or NPP. All relationships except for those of <xref ref-type="bibr" rid="B7">Betzer et&#xa0;al. (1984)</xref>; <xref ref-type="bibr" rid="B57">Pace et&#xa0;al. (1987)</xref>, and the re-parametrization of <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref> by <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref> are designed to provide global estimates of EP. Terms used in the the algorithms are summarized in <xref ref-type="table" rid="T2">
<bold>Table 2</bold>
</xref>.</p>
<table-wrap id="T2" position="float">
<label>Table&#xa0;2</label>
<caption>
<p>Input and output parameters for the different algorithms.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="top" colspan="3" align="left">Input parameters</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">chl</td>
<td valign="top" align="left">Chlorophyll</td>
<td valign="top" align="left">mg m<sup>&#x2013; 3</sup>
</td>
</tr>
<tr>
<td valign="top" align="left">SST</td>
<td valign="top" align="left">Sea Surface Temperature</td>
<td valign="top" align="left">&#xb0;C</td>
</tr>
<tr>
<td valign="top" align="left">PP</td>
<td valign="top" align="left">Gross or Net Primary Production</td>
<td valign="top" align="left">mg C m<sup>&#x2013; 2&#xa0;d &#x2013; 1</sup>
</td>
</tr>
<tr>
<td valign="top" align="left">Z</td>
<td valign="top" align="left">Depth level across which to calculate export</td>
<td valign="top" align="left">m</td>
</tr>
<tr>
<td valign="top" align="left">Z<sub>eu</sub>
</td>
<td valign="top" align="left">Depth of the euphotic zone</td>
<td valign="top" align="left">m</td>
</tr>
<tr>
<th valign="top" colspan="3" align="left">Output parameter</th>
</tr>
<tr>
<td valign="top" align="left">EP</td>
<td valign="top" align="left">Export Production</td>
<td valign="top" align="left">mg C m<sup>&#x2013; 2&#xa0;d &#x2013; 1</sup>
</td>
</tr>
</tbody>
</table>
</table-wrap>
<sec id="s2_1">
<label>2.1</label>
<title>Eppley and Peterson, 1979</title>
<disp-formula>
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<disp-formula>
<label>(2)</label>
<mml:math display="block" id="M2">
<mml:mrow>
<mml:mi>E</mml:mi>
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<p>
<xref ref-type="bibr" rid="B27">Eppley and Peterson (1979)</xref>&#x2019;s seminal paper is to our knowledge the first study that suggested a quantitative relationship between PP and EP. They base their algorithm solely on PP, with two different scaling factors if the magnitude of PP is above or below 200 mg C m<sup>-2</sup> d<sup>-1</sup>.</p>
</sec>
<sec id="s2_2">
<label>2.2</label>
<title>Suess, 1980</title>
<disp-formula>
<label>(3)</label>
<mml:math display="block" id="M3">
<mml:mrow>
<mml:mi>E</mml:mi>
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<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0.0238</mml:mn>
<mml:mi>z</mml:mi>
<mml:mo>+</mml:mo>
<mml:mn>0.212</mml:mn>
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<p>
<xref ref-type="bibr" rid="B80">Suess (1980)</xref> uses one scaling factor for PP and adds a depth dependency as to predict organic carbon flux at any depth across a depth horizon below the base on the euphotic zone. The algorithm was derived from sediment trap data.</p>
</sec>
<sec id="s2_3">
<label>2.3</label>
<title>Betzer et al., 1984</title>
<disp-formula>
<label>(4)</label>
<mml:math display="block" id="M4">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>P</mml:mi>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>0.0409</mml:mn>
<mml:mi>P</mml:mi>
<mml:msup>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mn>1.41</mml:mn>
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</mml:msup>
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<mml:mrow>
<mml:msup>
<mml:mi>z</mml:mi>
<mml:mrow>
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</mml:mrow>
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<p>The <xref ref-type="bibr" rid="B7">Betzer et&#xa0;al. (1984)</xref> relationship was derived from on <sup>14</sup>C based PP and POC flux observations using a free-drifting sediment trap at 900&#xa0;m. The trap was deployed at four locations between 12&#xb0;N and 6&#xb0;S at 153&#xb0;W in the Pacific Ocean.</p>
</sec>
<sec id="s2_4">
<label>2.4</label>
<title>Pace et al., 1987</title>
<disp-formula>
<label>(5)</label>
<mml:math display="block" id="M5">
<mml:mrow>
<mml:mi>E</mml:mi>
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<mml:mi>P</mml:mi>
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<mml:mn>1.000</mml:mn>
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<p>
<xref ref-type="bibr" rid="B57">Pace et&#xa0;al. (1987)</xref> expanded on <xref ref-type="bibr" rid="B80">Suess (1980)</xref> by including the vertical flux of both POC and particulate organic nitrogen (PON) based on <italic>in-situ</italic> observations from the Vertical Transport and Exchange (VERTEX) program in the north-east Pacific Ocean.</p>
</sec>
<sec id="s2_5">
<label>2.5</label>
<title>Baines et al., 1994</title>
<disp-formula>
<label>(6)</label>
<mml:math display="block" id="M6">
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</mml:mrow>
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<mml:mo>+</mml:mo>
<mml:mn>0.30</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>log</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>l</mml:mi>
<mml:mo>+</mml:mo>
<mml:mn>0.27</mml:mn>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>log</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi>C</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>l</mml:mi>
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<mml:mo stretchy="false">)</mml:mo>
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</mml:msup>
</mml:mrow>
</mml:msup>
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</mml:math>
</disp-formula>
<p>The algorithm of <xref ref-type="bibr" rid="B3">Baines et&#xa0;al. (1994)</xref> is derived from a relationship between the e-ratio, PP, Efluxes, and the depth of the euphotic zone. All three variables are independently predicted from Chl with an R<sup>2</sup> o<italic>f</italic> 0.54 &#x2013; 0.90.</p>
</sec>
<sec id="s2_6">
<label>2.6</label>
<title>Laws et al., 2000</title>
<disp-formula>
<label>(7)</label>
<mml:math display="block" id="M7">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>P</mml:mi>
<mml:mo>=</mml:mo>
<mml:mi>P</mml:mi>
<mml:mi>P</mml:mi>
<mml:mo>&#xb7;</mml:mo>
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<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>0.62</mml:mn>
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<mml:mo stretchy="false">)</mml:mo>
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<p>This algorithm is based on a relationship between Ef, SST, and the f-ratio derived from data in Table&#xa0;3 of <xref ref-type="bibr" rid="B43">Laws et&#xa0;al. (2000)</xref>. We use the equation as described by <xref ref-type="bibr" rid="B34">Henson et&#xa0;al. (2011)</xref>.</p>
</sec>
<sec id="s2_7">
<label>2.7</label>
<title>Dunne et al., 2005</title>
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<mml:mtext>&#xa0;</mml:mtext>
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</mml:mrow>
</mml:mtd>
<mml:mtd columnalign="left">
<mml:mrow>
<mml:mtext>if&#x2009;</mml:mtext>
<mml:mi>E</mml:mi>
<mml:mi>f</mml:mi>
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</mml:mrow>
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<mml:mtr columnalign="left">
<mml:mtd columnalign="left">
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</mml:mrow>
</mml:mtd>
<mml:mtd columnalign="left">
<mml:mrow>
<mml:mtext>if&#x2009;</mml:mtext>
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<mml:mi>f</mml:mi>
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</mml:mrow>
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<mml:mtr columnalign="left">
<mml:mtd columnalign="left">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:mtd>
<mml:mtd columnalign="left">
<mml:mrow>
<mml:mtext>otherwise</mml:mtext>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mrow>
</mml:mrow>
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</disp-formula>
<p>
<xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> is based on trap and <sup>234</sup>Th observations together with PP from <inline-formula>
<mml:math display="inline" id="im1">
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<mml:mi>H</mml:mi>
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</mml:mrow>
</mml:msup>
<mml:mi>C</mml:mi>
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</inline-formula> incubations at different depths, SST, Zeu, and Chl. Ef is constrained to fall between 0.04 and 0.72 (<xref ref-type="bibr" rid="B24">Dunne et&#xa0;al., 2005</xref>; <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al., 2015</xref>).</p>
</sec>
<sec id="s2_8">
<label>2.8</label>
<title>Henson et al., 2011</title>
<disp-formula>
<label>(11)</label>
<mml:math display="block" id="M11">
<mml:mrow>
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<mml:mi>P</mml:mi>
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<p>The <xref ref-type="bibr" rid="B34">Henson et&#xa0;al. (2011)</xref> model is parameterized to estimate export at the 100&#xa0;m depth horizon. (<xref ref-type="bibr" rid="B34">Henson et&#xa0;al., 2011</xref>; <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al., 2015</xref>).</p>
</sec>
<sec id="s2_9">
<label>2.9</label>
<title>Laws et al., 2011</title>
<p>The algorithms in Laws et al. (2011) is a further development of <xref ref-type="bibr" rid="B43">Laws et al., 2000</xref>. They introduce two relationships: which is equation 2 in in <xref ref-type="bibr" rid="B42">Laws et al. (2011)</xref>, and</p>
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<mml:mrow>
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<mml:mi>S</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
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</mml:mrow>
<mml:mo>&#xb7;</mml:mo>
<mml:mi>P</mml:mi>
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<mml:mn>0.43</mml:mn>
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</disp-formula>
<p>Equation 12 is based on contours in <xref ref-type="fig" rid="f2">
<bold>Figure&#xa0;2</bold>
</xref> of <xref ref-type="bibr" rid="B43">Laws et&#xa0;al. (2000)</xref> and evaluated in <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref>, both equations 12 and 13 are evaluated in <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>.</p>
<fig id="f2" position="float">
<label>Figure&#xa0;2</label>
<caption>
<p>Lagrangian experiment locations in the <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref> study. CCE drifter tracks (blue box, upper right). CRD drifter tracks (green box, lower left). Image from <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref>.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1149938-g002.tif"/>
</fig>
</sec>
<sec id="s2_10">
<label>2.10</label>
<title>Westberry et al., 2012</title>
<disp-formula>
<label>(14)</label>
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</mml:math>
</disp-formula>
<p>
<xref ref-type="bibr" rid="B84">Westberry et&#xa0;al. (2012)</xref> uses a number of empirical relationships between PP and respiration (R) to assess NCP and EP. Part of their analysis is to generate regional PP-R relationships by dividing available observations into broad latitudinal zones with different nutrient dynamics.</p>
</sec>
<sec id="s2_11">
<label>2.11</label>
<title>Siegel et al., 2014</title>
<disp-formula>
<label>(15)</label>
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<label>(19)</label>
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<p>
<xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref> algorithm divides EP is to different size classes based on the assumed ability to assess the community structure of phytoplankton assemblages via satellite-derived properties. The different terms are specified as follows: <italic>AlgEP</italic> is the total vertical flux of sinking algal cells and aggregates and <italic>FecEP</italic> is the total vertical flux of sinking fecal material released from zooplankton grazers. <inline-formula>
<mml:math display="inline" id="im2">
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mi>A</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>g</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the fraction of microphytoplankton production that sinks out of the base of the euphotic zone (assumed by <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref> to be 0.1) and <italic>PP<sub>M</sub>
</italic> is the PP of microphytoplankton. <inline-formula>
<mml:math display="inline" id="im3">
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
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<mml:mi>e</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>M</mml:mi>
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</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula>
<mml:math display="inline" id="im4">
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
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<mml:mi>c</mml:mi>
<mml:mi>S</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the fractions of grazing on microphytoplankton and smaller (&lt;20 <inline-formula>
<mml:math display="inline" id="im5">
<mml:mi>&#x3bc;</mml:mi>
</mml:math>
</inline-formula> m) phytoplankton, respectively, that contribute to fecal matter export from the euphotic zone (assumed by <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref> to be 0.3 and 0.1, respectively). <italic>G<sub>M</sub>
</italic> and <italic>G<sub>S</sub>
</italic> are the grazing rates on microphytoplankton and small phytoplankton and are derived from phytoplankton mass balance budgets.</p>
</sec>
<sec id="s2_12">
<label>2.12</label>
<title>Li &amp; Cassar, 2016</title>
<disp-formula>
<label>(20)</label>
<mml:math display="block" id="M20">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>P</mml:mi>
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<mml:mrow>
<mml:mn>8.57</mml:mn>
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</mml:mrow>
<mml:mrow>
<mml:mn>17.9</mml:mn>
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</mml:mrow>
</mml:math>
</disp-formula>
<p>The <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref> model was developed using a Genetic Programing approach to statistically optimize the <xref ref-type="bibr" rid="B43">Laws et&#xa0;al. (2000)</xref> and <xref ref-type="bibr" rid="B34">Henson et&#xa0;al. (2011)</xref> relationships using O<sub>2</sub>/Ar-based NCP estimates.</p>
</sec>
</sec>
<sec id="s3">
<label>3</label>
<title>
<italic>In situ</italic> data for evaluation</title>
<p>The <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> compilation of <italic>in-situ</italic> pe-ratios is based on 122 field observations from approximately 40 oceanographic studies with global distribution. The dataset includes estimates of PP, Chl a, New Production, nutrients, oxygen or carbon based estimates of EP, particle export estimates based on sinking flux from sediment traps and/or <sup>234</sup>Th, and the carbon-to-chlorophyll ratio. Physical parameters include mixed layer temperature and the depth of the euphotic zone (minimum of the 1% light level or sampling zone), The data coverage is presented in <xref ref-type="fig" rid="f3">
<bold>Figure&#xa0;3</bold>
</xref>. They find that, In general, pe-ratios are high (&gt;0.4) in the Polar regions, moderate (0.3&#x2013;0.4) in coastal regions and open ocean regions supporting phytoplankton blooms, and low (0.05&#x2013;0.2) elsewhere. The data can be accessed as supplementary information to the <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> publication.</p>
<fig id="f3" position="float">
<label>Figure&#xa0;3</label>
<caption>
<p>Locations of <italic>in-situ</italic> POC flux observations presented in <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>, (orange markers), <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref>, (green markers) and <xref ref-type="bibr" rid="B50">Mouw et&#xa0;al. (2016a)</xref>; <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref>, blue markers for observations shallower than 200 meters, purple for observations deeper than 200 meters).</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1149938-g003.tif"/>
</fig>
<p>The <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref> datasets are based on 32 Lagrangian process studies where shallow-drifting sediment traps were combined with <sup>238</sup>U-<sup>234</sup> Th measurements to quantify EP (<xref ref-type="bibr" rid="B11">Buesseler et&#xa0;al., 2007</xref>). These Lagrangian studies where conducted between 2 and 5 days either within in the California Current Ecosystem (CCE) Long Term Ecological Research (LTER) or the Costa Rica Dome (CRD) FLUx and Zinc Experiments (FLUZiE) programs. Drifters were drogued at 15&#xa0;m depth and tracked by satellite with either experimental incubation bottles or VERTEX-style sediment traps attached below (<xref ref-type="bibr" rid="B79">Stukel et&#xa0;al., 2013</xref>). This experimental setup allowed for simultaneous measurement of carbon export, food web processes (PP, protozoan grazing, mesozooplankton grazing, size-spectra of phytoplankton community), and net changes of <italic>in-situ</italic> Chl. The datasets consist of observations from 7 cruises (<xref ref-type="fig" rid="f2">
<bold>Figure&#xa0;2</bold>
</xref>) and can be located via the acknowledgments section of <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref> or as supplementary information to the publication.</p>
<p>The <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref> algorithm development and evaluation used a global dataset of mixed layer O<sub>2</sub>/Ar based NCP estimates either from discrete samples analyzed in the lab or continuous underway measurements (<xref ref-type="bibr" rid="B67">Reuer et&#xa0;al., 2007</xref>; <xref ref-type="bibr" rid="B14">Cassar et&#xa0;al., 2009</xref>; <xref ref-type="bibr" rid="B36">J&#xf6;nsson et&#xa0;al., 2013</xref>). NCP can be derived from O<sub>2</sub>/Ar measurements by assuming a mass balance of biological O<sub>2</sub> in the mixed layer. Oxygen saturation at the ocean surface is influenced by biological (i.e., PP) and physical processes (e.g., bubble injection and temperature changes). Ar and O<sub>2</sub> have similar temperature dependencies (<xref ref-type="bibr" rid="B18">Craig and Hayward, 1987</xref>). Combined with their similar solubilities, they have almost equivalent responses to processes such as temperature or air pressure change and bubble-mediated gas exchange. As such, oxygen concentration due to physical processes can be accounted for with measurements of the O<sub>2</sub>/Ar saturation state.</p>
<p>The dataset contains observations from 1999 to 2009 (n = 689,566) averaged to a 0.083&#xb0; &#xd7; 0.083&#xb0; grid, yielding n=14,795 samples with a mean coefficient of variation (CV) of 0.12 per gridcell (<xref ref-type="fig" rid="f4">
<bold>Figure&#xa0;4</bold>
</xref>). The O<sub>2</sub>/Ar super saturation is converted to an NCP proxy using QSCAT/NCEP blended wind speeds (<xref ref-type="bibr" rid="B67">Reuer et&#xa0;al., 2007</xref>). Samples with negative NCP are removed due to potential biases associated with vertical mixing of O<sub>2</sub>-undersaturated waters (<xref ref-type="bibr" rid="B67">Reuer et&#xa0;al., 2007</xref>; <xref ref-type="bibr" rid="B36">J&#xf6;nsson et&#xa0;al., 2013</xref>). Note that positive NCP values may also be biased by vertical mixing where vertical mixing brings O<sub>2</sub>-undersaturated water to the surface and the estimates should be regarded as lower bounds on the true NCP. Conversely, positive biases in NCP could occur in regions with high biological O<sub>2</sub> below the mixed layer (e.g., deep chlorophyll maximum). Because of these uncertainties, O<sub>2</sub>/Ar NCP data below 1.0 mmol O<sub>2</sub> m<sup>2</sup> d <sup>&#x2013; 1</sup> are removed from the dataset. Additional uncertainties and biases (e.g., gas exchange parameterization and lack of steady state in biological O<sub>2</sub> in the mixed layer) are further discussed in <xref ref-type="bibr" rid="B36">J&#xf6;nsson et&#xa0;al. (2013)</xref>. Data access is described in <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>.</p>
<fig id="f4" position="float">
<label>Figure&#xa0;4</label>
<caption>
<p>Global map of O2/Ar measurements from <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>. Samples with positive values are color coded. Samples with negative values are shown using a gray scale. Image from <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1149938-g004.tif"/>
</fig>
<p>The <xref ref-type="bibr" rid="B50">Mouw et&#xa0;al. (2016a)</xref> dataset consists of Particulate Organic Carbon (POC) flux estimated from sediment traps and <sup>234</sup>Th compiled across the global ocean including six long-term time series locations. The data set contains 15,792 individual POC flux estimates at 674 unique locations collected between 1976 and 2012 (<xref ref-type="fig" rid="f3">
<bold>Figure&#xa0;3</bold>
</xref>). Where available, the flux of other minerals is also reported. Of the observations across the globe, 85% are concentrated in the Northern Hemisphere, time series sites accounts for 36% of the data, while 71% of the data are measured at &#x2265;500 m with the most common deployment depths between 1000 and 1500&#xa0;m. The dataset is archived in the PANGAEA data repository (<xref ref-type="bibr" rid="B51">Mouw et&#xa0;al., 2016b</xref>).</p>
<p>The <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref> dataset is based on observations from sediment traps at depths less than 200 meters and <sup>234</sup>Th measurements converted to POC flux at Zeu. The data is selected to represent different sampling methodologies and spatiotemporal scales, and totals 1,719 observations from 1984 to 2014.</p>
<p>The <xref ref-type="bibr" rid="B64">Puigcorbe et&#xa0;al. (2020)</xref> dataset does not include POC flux observations but POC/<sup>234</sup>Th ratios that can be indirectly used to constrain EP and evaluate EP models. The collection contains of 9,318 measurements with a global coverage collected between 1989 and 2018 from the surface to &gt; 5500&#xa0;m, and divided into three size fractions (&#x223c;&lt; 0.7 <italic>&#xb5;</italic>m, &#x223c; 1&#x2013;50 <italic>&#xb5;</italic>m, &#x223c;&gt; 50 <italic>&#xb5;</italic>m). The data has an uneven distribution with some areas highly sampled (e.g., China Sea, Bermuda Atlantic Time Series station) while others regions are sparsely covered (the south-eastern Atlantic, the south Pacific, and the south Indian Oceans). The dataset is archived in the PANGAEA data repository (<xref ref-type="bibr" rid="B63">Puigcorbe, 2019</xref>).</p>
<p>
<xref ref-type="bibr" rid="B15">Ceballos-Romero et&#xa0;al. (2022)</xref> provide a comprehensive dataset of<sup>234</sup>Th measurements sampled across the global ocean between 1967 and 2018. The compilation includes a total of 56 631 data points together with appropriate metadata including geographic location, date, and sample depth. When available, water temperature, salinity, <sup>238</sup>U (over 18 200 data points), and particulate organic nitrogen is included. Data source and method information (including <sup>238</sup>U and <sup>234</sup>Th) is also detailed along with valuable information for future data analysis such as bloom stage and steady-/non-steady-state conditions at the sampling moment. While not directly applicable in this study, this dataset provides a valuable resource for future EP algorithm development and evaluation.</p>
</sec>
<sec id="s4">
<label>4</label>
<title>Algorithm evaluations</title>
<p>The instrumental <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> study provided not only relationships between PP or Chl and EP that are widely used in ecosystem modeling, but also comparisons of a variety of empirical parameterizations with the data synthesis described in section 3.1. The observed pe-ratios were combined with <italic>in-situ</italic> observations of mixed layer temperature, depth-integrated chlorophyll, depth-integrated PP, new production, particle export, depth of the euphotic zone (minimum of the 1% light level or sampling zone), and the carbon-to-chlorophyll ratio. They found that the <xref ref-type="bibr" rid="B27">Eppley and Peterson (1979)</xref>, (<xref ref-type="fig" rid="f5">
<bold>Figure&#xa0;5A</bold>
</xref>) algorithm has the lowest coefficient of determination (9%), which they attributed to the parameterization relying on the integral of PP alone. The <xref ref-type="bibr" rid="B3">Baines et&#xa0;al. (1994)</xref>, (<xref ref-type="fig" rid="f5">
<bold>Figure&#xa0;5B</bold>
</xref>) algorithm added euphotic zone depth in addition to the depth-integral of PP and was able to account for a higher fraction of the variance (38%), while not improving the relative uncertainty (64%). A different approach was used by <xref ref-type="bibr" rid="B3">Baines et&#xa0;al. (1994)</xref>, (<xref ref-type="fig" rid="f5">
<bold>Figure&#xa0;5C</bold>
</xref>) where chlorophyll concentrations were utilized as the predictive variable. Their parameterization was able to account for a slightly higher variance (40%) while also decreasing the relative uncertainty (46%), but showed a strong bias to low values at higher pe-ratios. <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> found that the <xref ref-type="bibr" rid="B43">Laws et&#xa0;al. (2000)</xref>, (<xref ref-type="fig" rid="f5">
<bold>Figure&#xa0;5D</bold>
</xref>) algorithm succeeded in reproducing large-scale structures in the data and accounted for nearly half of the variance (47%), while decreasing the relative error to 43%. The major shortcoming of this algorithm was in reproducing variability in pe-ratios at high temperatures. <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> suggested that &#x201c;a weaker temperature dependence for phytoplankton and bacterial metabolism than for zooplankton metabolism&#x201d; accounts for this misfit.</p>
<fig id="f5" position="float">
<label>Figure&#xa0;5</label>
<caption>
<p>Comparison of particle export ratio estimates by <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> of various models described in section 2 using data described in section 3.1. Panels <bold>(A-D)</bold> show results based on algorithms described in sections 2.1, 2.3, 2.5, and 2.6, and panels <bold>(E, F)</bold> the two algorithms described in section 2.7. Symbols are grouped by temperature into less than 14&#xb0;C (crosses) and greater than 14&#xb0;C (dots). Image from <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1149938-g005.tif"/>
</fig>
<p>The algorithm developed by <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>, (<xref ref-type="fig" rid="f5">
<bold>Figures&#xa0;5E, F</bold>
</xref>) provided a reasonable fit to the compiled dataset of observations, with an R<sup>2</sup> of 58% and a relative uncertainty of 33%. The algorithm had low skill in areas with the highest pe-ratios and sites with a combination of very high pe-ratios and low to moderate PP. This discrepancy if compensated for using biomass instead of PP improved R<sup>2</sup> to 61% with a relatively low relative error (35%). <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> explained this improvement with biomass integrating ecosystem processes better over time than PP.</p>
<p>
<xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref> evaluated a number of algorithms described in section 2 by matching O<sub>2</sub>/Ar- derived NCP observations (see section 3.3) with satellite derived 8-day 0.083&#xb0; &#xd7; 0.083&#xb0; SeaWiFS Chl and PAR, VGPM NPP, and AVHRR SST. The standard SeaWiFS Chl algorithm was shown to underestimate [Chl] by a factor of 2 to 3 in the Southern Ocean at the time when <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref> conducted the evaluation (<xref ref-type="bibr" rid="B37">Kahru and Mitchell, 2010</xref>) and were improved by using a blending scheme presented by <xref ref-type="bibr" rid="B37">Kahru and Mitchell (2010)</xref>. VGPM NPP was based on the recalculated Chl data product. Phytoplankton size composition was derived using <xref ref-type="bibr" rid="B46">Li et&#xa0;al. (2013)</xref> and VGPM NPP for the algorithm developed by <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref>, together with the other parameters as presented in <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref>. See <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref> for more detailed descriptions of the data sources.</p>
<p>
<xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref> used the satellite-derived data to calculate export production for the <xref ref-type="bibr" rid="B27">Eppley and Peterson (1979)</xref>; <xref ref-type="bibr" rid="B7">Betzer et&#xa0;al. (1984)</xref>; <xref ref-type="bibr" rid="B3">Baines et&#xa0;al. (1994)</xref>; <xref ref-type="bibr" rid="B43">Laws et&#xa0;al. (2000)</xref>; <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>; <xref ref-type="bibr" rid="B42">Laws et&#xa0;al. (2011)</xref>; <xref ref-type="bibr" rid="B84">Westberry et&#xa0;al. (2012)</xref>, and <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref> algorithms. They also used the data together with observed O<sub>2</sub>/Ar- NCP to develop the <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref> algorithm. The main assumption here was that the O2/Ar-NCP is a valid proxy for EP. One could expect <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref> to outperform the other algorithms since the observational dataset was used to train the algorithm, but this was not the case (<xref ref-type="fig" rid="f6">
<bold>Figure&#xa0;6</bold>
</xref>). Instead, all EP predicting algorithms showed surprisingly similar results. <xref ref-type="bibr" rid="B27">Eppley &amp; Peterson (1979)</xref>; <xref ref-type="bibr" rid="B7">Betzer et&#xa0;al. (1984)</xref>, and <xref ref-type="bibr" rid="B3">Baines et&#xa0;al. (1994)</xref> showed almost identical distributions in the regressions against observations with R<sup>2</sup>s between 0.58 and 0.65. The algorithms of <xref ref-type="bibr" rid="B27">Eppley &amp; Peterson (1979)</xref> and <xref ref-type="bibr" rid="B7">Betzer et&#xa0;al. (1984)</xref> in particular tended to overestimate low NCP values. The different <xref ref-type="bibr" rid="B43">Laws et&#xa0;al. (2000)</xref>; <xref ref-type="bibr" rid="B42">Laws et&#xa0;al. (2011)</xref> algorithms all provided a smaller spread around the 1:1 line and a slightly better R<sup>2</sup> (0.64-0.7). The algorithms of <xref ref-type="bibr" rid="B43">Laws et&#xa0;al. (2000)</xref> also overestimated low NCP, while the algorithm of <xref ref-type="bibr" rid="B42">Laws et&#xa0;al. (2011)</xref>; (Equation 12 and 13) showed symmetrical distributions. The <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> algorithm, on the other hand, tended to underestimate NCP. This tendency was even greater for <xref ref-type="bibr" rid="B84">Westberry et&#xa0;al. (2012)</xref> and <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref>, which also showed among the lowest R<sup>2</sup>s (0.62 and 0.55, respectively). This is particularly surprising for the algorithm of <xref ref-type="bibr" rid="B84">Westberry et&#xa0;al. (2012)</xref>, which was developed using a framework that was based on the assumption of NCP being a good general proxy for EP. The two algorithms developed by <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref> showed, as expected, a good skill in predicting O<sub>2</sub>/Ar-NCP. Their Support Vector Regression (SVR) approach had the highest R<sup>2</sup>, but seemed to have a floor where values below a certain threshold were not being predicted. This could be a consequence of how the SVR was configured. The fact that all approaches showed similar and relatively good skills in predicting O<sub>2</sub>/Ar- NCP and EP is surprising, as the various algorithms model different components of the biological pump.</p>
<fig id="f6" position="float">
<label>Figure&#xa0;6</label>
<caption>
<p>Comparison of satellite algorithms of carbon export production by <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>. O<sub>2</sub>/Ar-derived NCP was converted to C using a stoichiometry of O<sub>2</sub>/C=1.4 (<xref ref-type="bibr" rid="B41">Laws, 1991</xref>). Samples with O<sub>2</sub>/Ar-NCP estimates&lt;1.0 mmol O<sub>2</sub> m<sup>2</sup> d<sup>-1</sup> were excluded. Phytoplankton size composition was derived using <xref ref-type="bibr" rid="B46">Li et&#xa0;al. (2013)</xref> and VGPM NPP for the algorithm developed by <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref>, together with the other parameters as presented in <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref>. Image from <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1149938-g006.tif"/>
</fig>
<p>The <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref> EP algorithm comparison is based on a Lagrangian approach where <italic>in-situ</italic> rates of NPP, EP and auxiliary parameters were observed concurrently in a water mass. They do this by compiling results from Lagrangian process studies in the North Eastern Pacific Ocean (see <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al., 2015</xref>, and section 3.2 for details). One main advantage of this approach is the ability to disentangle errors associated with inaccuracies of remote sensing products (e.g., PP, Chl, and SST) and errors associated with the model used to estimate EP. Their intention was not to conduct a definitive comparison of competing satellite algorithms, but rather to begin a process that assess and hopefully improves the different assumptions and parameterizations in current satellite algorithms, especially <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref>.</p>
<p>Satellite algorithms for EP are generally designed to predict export at either Z<sub>eu</sub> or 100 meters. While the observations used by <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref> were within 30&#xa0;m of Z<sub>eu</sub>, they scaled all data to Z<sub>eu</sub> using the ambient PAR at the depth of sampling. All EP algorithms were evaluated using <italic>in-situ</italic> input properties (e.g., SST, Chl, PP) as the goal was not to assess the corresponding satellite products. All water column rates and standing stock measurements were depth integrated, except when models made explicit reference to sea surface values, for methodological reasons. <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref> noted that <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> and <xref ref-type="bibr" rid="B42">Laws et&#xa0;al. (2011)</xref> are parametrized to predict total EP including active transport by diel vertically migrating organisms and passive export of DOC, leading to a positive bias since sediment traps and <sup>234</sup>Th only measure POC fluxes. <xref ref-type="bibr" rid="B79">Stukel et&#xa0;al. (2013)</xref> estimated that the active transport by diel migration is about 19% of the total sinking flux in the CCE region, providing a lower constraint on this bias.</p>
<p>
<xref ref-type="fig" rid="f7">
<bold>Figure&#xa0;7</bold>
</xref> shows the resulting comparisons between satellite algorithms and <italic>in-situ</italic> measurements. At a first look, it seems that no algorithm performed significantly better or worse than any other. <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> and <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref> had R<sup>2</sup> coefficients of determination of 0.37, whereas the R<sup>2</sup> for <xref ref-type="bibr" rid="B34">Henson et&#xa0;al. (2011)</xref> and <xref ref-type="bibr" rid="B42">Laws et&#xa0;al. (2011)</xref> were 0.27. <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref> re-parameterized <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref> using their <italic>in-situ</italic> observations and improved the R<sup>2</sup> to 0.38. It should be noted that all algorithms have been developed and parameterized to function in a global setting in all physical, chemical, and biological settings. This study <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref> performed a comparison in one specific region with a small subset of ecosystem dynamics and conditions.</p>
<fig id="f7" position="float">
<label>Figure&#xa0;7</label>
<caption>
<p>Comparison between satellite algorithms and <italic>in-situ</italic> measurements by <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref>. <bold>(A)</bold> <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref> vs sediment-trap-(circles and diamonds) and <sup>234</sup>Th-derived (squares and triangles) measurements. Circles and squares are based on results using microscopy to determine the fraction of microphytoplankton. <bold>(B&#x2013;D)</bold> <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>; <xref ref-type="bibr" rid="B42">Laws et&#xa0;al. (2011)</xref>, and <xref ref-type="bibr" rid="B34">Henson et&#xa0;al. (2011)</xref> algorithms, respectively, with circles showing sediment trap data and squares showing <sup>234</sup>Th data. All panels show export normalized to the base of the Z<sub>eu</sub>, except panel D, which shows export at 100m. Green diamonds show arithmetic mean of predicted and measured export for each quartile of the measurements (35-85, 85-125, 125-205, and 205-560 mg C m<sup>-2</sup> d<sup>-1</sup> for base of Z<sub>eu</sub>; 18-65, 65-89, 89-140, and 140-300 mg C m<sup>-2</sup> d<sup>-1</sup> for 100m). Dashed lines depict a 1:1 relationship. Error bars show one standard error (for <italic>in-situ</italic> measurements) and propagation of measurement standard error through satellite algorithms (for predictions). Image from <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref>.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1149938-g007.tif"/>
</fig>
<p>
<xref ref-type="bibr" rid="B65">Puigcorbe et&#xa0;al. (2017)</xref> compared <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>; <xref ref-type="bibr" rid="B42">Laws et&#xa0;al. (2011)</xref>, and <xref ref-type="bibr" rid="B34">Henson et&#xa0;al. (2011)</xref> using PP estimates from three different satellite-derived primary production models and a regional dataset of POC fluxes based on <sup>234</sup>Th from the North Western Atlantic Ocean. They found that <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> and <xref ref-type="bibr" rid="B42">Laws et&#xa0;al. (2011)</xref> were closest to the observations but showed a 3-fold difference and no clear trends. <xref ref-type="bibr" rid="B34">Henson et&#xa0;al. (2011)</xref> consistently provided lower export estimates than the observations. Their explanation is that a stronger dependency on temperature by <xref ref-type="bibr" rid="B34">Henson et&#xa0;al. (2011)</xref> leads to low export fluxes (&#xa1; 2 mmol C m<sup>&#x2212;2</sup> d <sup>&#x2212;1</sup>) throughout the study area. They also observe a significant overestimation of EP by <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> in their equatorial domain and that <xref ref-type="bibr" rid="B42">Laws et&#xa0;al. (2011)</xref> seems to underestimate EP both in the northern half of their oligotrophic domain and at several riverine stations.</p>
</sec>
<sec id="s5">
<label>5</label>
<title>Evaluating the different EP models using three <italic>in situ</italic> databases</title>
<p>The evaluations described so far are all promoting a new algorithm (<xref ref-type="bibr" rid="B24">Dunne et&#xa0;al., 2005</xref>; <xref ref-type="bibr" rid="B45">Li and Cassar, 2016</xref>) or re-parameterizing an existing algorithm (<xref ref-type="bibr" rid="B78">Stukel et&#xa0;al., 2015</xref>). While the different approaches are thorough and the results consistent between the three studies, we believe it worthwhile to evaluate the different algorithms from a neutral starting point. For this, we use the published dataset of POC fluxes by <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>; <xref ref-type="bibr" rid="B50">Mouw et&#xa0;al. (2016a)</xref>; <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref>, and <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref>. We matched the <xref ref-type="bibr" rid="B50">Mouw et&#xa0;al. (2016a)</xref>; <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref> and <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref> data with monthly satellite-derived SST from the Group for High Resolution Sea Surface Temperature/Operational Sea Surface Temperature and Ice Analysis (<xref ref-type="bibr" rid="B81">UKMO, 2005</xref>, GHRSST/OSTIA), Chl and Kd<sub>490</sub> from Ocean Colour Climate Change Initiative (<xref ref-type="bibr" rid="B70">Sathyendranath, 2021</xref>, OC-CCI), and PP from the Biological Pump and Carbon Exchange Processes project (<xref ref-type="bibr" rid="B39">Kulk et&#xa0;al., 2021</xref>, BICEP). It should be noted that different satellite-based PP products vary considerably (<xref ref-type="bibr" rid="B8">Bisson et&#xa0;al., 2018</xref>; <xref ref-type="bibr" rid="B75">Siegel et&#xa0;al., 2022</xref>), which can affect the calculated EP estimates <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref>. We found, however, that different PP products had only a limited influence on the skill of the EP algorithms evaluated in this study and we therefore chose to only present results based on one PP product.</p>
<p>We begin by calculating global EP flux estimates averaged over the years 1998&#x2013;2020 for all algorithms using the earlier mentions satellite-derived products (all values presented in <xref ref-type="table" rid="T3">
<bold>Table&#xa0;3</bold>
</xref>). The flux estimates are between 1 and 140 Gt C y<sup>&#x2212;1</sup>, a much larger range of uncertainty than normally presented for EP. If only algorithms with one of the top three skills scores in any of our evaluations (red colors in <xref ref-type="table" rid="T3">
<bold>Tables&#xa0;3</bold>
</xref>, <xref ref-type="table" rid="T4">
<bold>4</bold>
</xref>, <xref ref-type="table" rid="T5">
<bold>5</bold>
</xref>) are included, the range is 1&#x2013;9 Gt C y<sup>&#x2212;1</sup>, This result is more in line with earlier published estimates (<xref ref-type="bibr" rid="B25">Dunne et&#xa0;al., 2007</xref>; <xref ref-type="bibr" rid="B34">Henson et&#xa0;al., 2011</xref>; <xref ref-type="bibr" rid="B42">Laws et&#xa0;al., 2011</xref>; <xref ref-type="bibr" rid="B73">Siegel et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B75">Siegel et&#xa0;al., 2022</xref>).</p>
<table-wrap id="T3" position="float">
<label>Table&#xa0;3</label>
<caption>
<p>Performance metrics for different export production models evaluated using the <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> dataset.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="top" align="left">Algorithm</th>
<th valign="top" align="center">R<sup>2</sup>
</th>
<th valign="top" align="center">MAE</th>
<th valign="top" align="center">RMSE</th>
<th valign="top" align="center">MAPE</th>
<th valign="top" align="center">sMAPE</th>
<th valign="top" align="center">Bias</th>
<th valign="top" align="center">Global flux (Gt C y<sup>-1</sup>)</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B27">Eppley and Peterson (1979)</xref>
</td>
<td valign="top" align="center">0.09</td>
<td valign="top" align="center">0.99</td>
<td valign="top" align="center">1.20</td>
<td valign="top" align="center">0.74</td>
<td valign="top" align="center">0.45</td>
<td valign="top" align="center">0.99</td>
<td valign="top" align="center">20</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B80">Suess (1980)</xref>
</td>
<td valign="top" align="center">0.36</td>
<td valign="top" align="center">0.82</td>
<td valign="top" align="center">1.01</td>
<td valign="top" align="center">0.62</td>
<td valign="top" align="center">0.40</td>
<td valign="top" align="center">0.82</td>
<td valign="top" align="center">15</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B7">Betzer et&#xa0;al. (1984)</xref>
</td>
<td valign="top" align="center">-4.11</td>
<td valign="top" align="center">2.76</td>
<td valign="top" align="center">2.84</td>
<td valign="top" align="center">1.43</td>
<td valign="top" align="center">1.75</td>
<td valign="top" align="center">2.76</td>
<td valign="top" align="center">1.2</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B57">Pace et&#xa0;al. (1987)</xref>
</td>
<td valign="top" align="center">0.52</td>
<td valign="top" align="center">0.71</td>
<td valign="top" align="center">0.87</td>
<td valign="top" align="center">0.32</td>
<td valign="top" align="center">0.34</td>
<td valign="top" align="center">0.71</td>
<td valign="top" align="center">4.9</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B3">Baines et al. (1994)</xref>
</td>
<td valign="top" align="center">-12.57</td>
<td valign="top" align="center">4.59</td>
<td valign="top" align="center">4.63</td>
<td valign="top" align="center">2.65</td>
<td valign="top" align="center">1.03</td>
<td valign="top" align="center">4.59</td>
<td valign="top" align="center">140</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B43">Laws et&#xa0;al. (2000)</xref>
</td>
<td valign="top" align="center">0.71</td>
<td valign="top" align="center">0.53</td>
<td valign="top" align="center">0.67</td>
<td valign="top" align="center">0.32</td>
<td valign="top" align="center">0.31</td>
<td valign="top" align="center">0.53</td>
<td valign="top" align="center">6</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>
</td>
<td valign="top" align="center">0.86</td>
<td valign="top" align="center">0.39</td>
<td valign="top" align="center">0.47</td>
<td valign="top" align="center">0.24</td>
<td valign="top" align="center">0.23</td>
<td valign="top" align="center">0.39</td>
<td valign="top" align="center">2.0</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B34">Henson et&#xa0;al. (2011)</xref>
</td>
<td valign="top" align="center">-0.19</td>
<td valign="top" align="center">1.24</td>
<td valign="top" align="center">1.37</td>
<td valign="top" align="center">0.60</td>
<td valign="top" align="center">0.91</td>
<td valign="top" align="center">1.24</td>
<td valign="top" align="center">1.7</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B42">Laws et al. (2011)</xref>
</td>
<td valign="top" align="center">0.69</td>
<td valign="top" align="center">0.55</td>
<td valign="top" align="center">0.70</td>
<td valign="top" align="center">0.30</td>
<td valign="top" align="center">0.30</td>
<td valign="top" align="center">0.55</td>
<td valign="top" align="center">7.1</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B42">Laws et al. (2011)</xref>
</td>
<td valign="top" align="center">0.40</td>
<td valign="top" align="center">0.82</td>
<td valign="top" align="center">0.97</td>
<td valign="top" align="center">0.37</td>
<td valign="top" align="center">0.43</td>
<td valign="top" align="center">0.82</td>
<td valign="top" align="center">5.9</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B84">Westberry et&#xa0;al. (2012)</xref>
</td>
<td valign="top" align="center">0.10</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">1.19</td>
<td valign="top" align="center">0.69</td>
<td valign="top" align="center">0.44</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">27</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>
</td>
<td valign="top" align="center">0.74</td>
<td valign="top" align="center">0.52</td>
<td valign="top" align="center">0.64</td>
<td valign="top" align="center">0.38</td>
<td valign="top" align="center">0.30</td>
<td valign="top" align="center">0.52</td>
<td valign="top" align="center">8.7</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>All EP values are log-transformed. Higher is better for R<sup>2</sup> while lower is better for the other metrics. Red colors denote the three algorithms with highest skill according to each metric. The final column contains global flux estimates averaged over the years 1998&#x2013;2020 using each respective algorithm and satellite-derived data described in the text.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T4" position="float">
<label>Table&#xa0;4</label>
<caption>
<p>Performance metrics for different export production models evaluated using the <xref ref-type="bibr" rid="B50">Mouw et&#xa0;al. (2016a)</xref>; <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref> dataset.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="top" align="left">Algorithm</th>
<th valign="top" align="center">R<sup>2</sup>
</th>
<th valign="top" align="center">MAE</th>
<th valign="top" align="center">RMSE</th>
<th valign="top" align="center">MAPE</th>
<th valign="top" align="center">sMAPE</th>
<th valign="top" align="center">Bias</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B27">Eppley and Peterson (1979)</xref>
</td>
<td valign="top" align="center">-2.79</td>
<td valign="top" align="center">2.01</td>
<td valign="top" align="center">2.30</td>
<td valign="top" align="center">0.74</td>
<td valign="top" align="center">0.49</td>
<td valign="top" align="center">2.01</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B80">Suess (1980)</xref>
</td>
<td valign="top" align="center">-2.10</td>
<td valign="top" align="center">1.76</td>
<td valign="top" align="center">2.08</td>
<td valign="top" align="center">0.66</td>
<td valign="top" align="center">0.44</td>
<td valign="top" align="center">1.76</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B7">Betzer et&#xa0;al (1984)</xref>
</td>
<td valign="top" align="center">-0.66</td>
<td valign="top" align="center">1.28</td>
<td valign="top" align="center">1.52</td>
<td valign="top" align="center">0.40</td>
<td valign="top" align="center">0.46</td>
<td valign="top" align="center">1.28</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B57">Pace et&#xa0;al (1987)</xref>
</td>
<td valign="top" align="center">-0.18</td>
<td valign="top" align="center">0.79</td>
<td valign="top" align="center">1.29</td>
<td valign="top" align="center">0.33</td>
<td valign="top" align="center">0.24</td>
<td valign="top" align="center">0.79</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B3">Baines et al. (1994)</xref>
</td>
<td valign="top" align="center">-11.29</td>
<td valign="top" align="center">3.94</td>
<td valign="top" align="center">4.10</td>
<td valign="top" align="center">1.37</td>
<td valign="top" align="center">0.76</td>
<td valign="top" align="center">3.94</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B43">Laws et&#xa0;al. (2000)</xref>
</td>
<td valign="top" align="center">-1.44</td>
<td valign="top" align="center">1.23</td>
<td valign="top" align="center">1.98</td>
<td valign="top" align="center">0.56</td>
<td valign="top" align="center">0.34</td>
<td valign="top" align="center">1.23</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>
</td>
<td valign="top" align="center">-0.10</td>
<td valign="top" align="center">0.90</td>
<td valign="top" align="center">1.33</td>
<td valign="top" align="center">0.36</td>
<td valign="top" align="center">0.32</td>
<td valign="top" align="center">0.90</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B34">Henson et&#xa0;al. (2011)</xref>
</td>
<td valign="top" align="center">-0.64</td>
<td valign="top" align="center">1.10</td>
<td valign="top" align="center">1.63</td>
<td valign="top" align="center">0.45</td>
<td valign="top" align="center">0.38</td>
<td valign="top" align="center">1.10</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B42">Laws et al. (2011)</xref>
</td>
<td valign="top" align="center">-1.39</td>
<td valign="top" align="center">1.30</td>
<td valign="top" align="center">1.96</td>
<td valign="top" align="center">0.58</td>
<td valign="top" align="center">0.36</td>
<td valign="top" align="center">1.30</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B42">Laws et al. (2011)</xref>
</td>
<td valign="top" align="center">-0.70</td>
<td valign="top" align="center">0.98</td>
<td valign="top" align="center">1.65</td>
<td valign="top" align="center">0.46</td>
<td valign="top" align="center">0.30</td>
<td valign="top" align="center">0.98</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B84">Westberry et&#xa0;al. (2012)</xref>
</td>
<td valign="top" align="center">-3.60</td>
<td valign="top" align="center">2.27</td>
<td valign="top" align="center">2.54</td>
<td valign="top" align="center">0.83</td>
<td valign="top" align="center">0.53</td>
<td valign="top" align="center">2.27</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>
</td>
<td valign="top" align="center">-1.47</td>
<td valign="top" align="center">1.45</td>
<td valign="top" align="center">1.99</td>
<td valign="top" align="center">0.63</td>
<td valign="top" align="center">0.40</td>
<td valign="top" align="center">1.45</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Only observations between 100 and 200 meters are included and all EP values are log-transformed. Higher is better for R<sup>2</sup> while lower is better for the other metrics. Red colors denote the three algorithms with highest skill according to each metric.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T5" position="float">
<label>Table&#xa0;5</label>
<caption>
<p>Performance metrics for different Export Production models evaluated using the <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref> dataset.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="top" align="left">Algorithm</th>
<th valign="top" align="center">R<sup>2</sup>
</th>
<th valign="top" align="center">MAE</th>
<th valign="top" align="center">RMSE</th>
<th valign="top" align="center">MAPE</th>
<th valign="top" align="center">sMAPE</th>
<th valign="top" align="center">Bias</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B27">Eppley and Peterson (1979)</xref>
</td>
<td valign="top" align="center">-1.47</td>
<td valign="top" align="center">1.63</td>
<td valign="top" align="center">1.94</td>
<td valign="top" align="center">0.60</td>
<td valign="top" align="center">0.39</td>
<td valign="top" align="center">1.63</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B80">Suess (1980)</xref>
</td>
<td valign="top" align="center">-1.06</td>
<td valign="top" align="center">1.45</td>
<td valign="top" align="center">1.77</td>
<td valign="top" align="center">0.54</td>
<td valign="top" align="center">0.36</td>
<td valign="top" align="center">1.45</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B7">Betzer et&#xa0;al (1984)</xref>
</td>
<td valign="top" align="center">-2.46</td>
<td valign="top" align="center">1.88</td>
<td valign="top" align="center">2.30</td>
<td valign="top" align="center">0.50</td>
<td valign="top" align="center">0.66</td>
<td valign="top" align="center">1.88</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B57">Pace et&#xa0;al (1987)</xref>
</td>
<td valign="top" align="center">-0.30</td>
<td valign="top" align="center">0.98</td>
<td valign="top" align="center">1.41</td>
<td valign="top" align="center">0.34</td>
<td valign="top" align="center">0.28</td>
<td valign="top" align="center">0.98</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B3">Baines et al. (1994)</xref>
</td>
<td valign="top" align="center">-7.48</td>
<td valign="top" align="center">3.24</td>
<td valign="top" align="center">3.49</td>
<td valign="top" align="center">1.11</td>
<td valign="top" align="center">0.63</td>
<td valign="top" align="center">3.24</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B43">Laws et&#xa0;al. (2000)</xref>
</td>
<td valign="top" align="center">-0.32</td>
<td valign="top" align="center">0.92</td>
<td valign="top" align="center">1.40</td>
<td valign="top" align="center">0.37</td>
<td valign="top" align="center">0.25</td>
<td valign="top" align="center">0.92</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>
</td>
<td valign="top" align="center">-0.99</td>
<td valign="top" align="center">1.29</td>
<td valign="top" align="center">1.67</td>
<td valign="top" align="center">0.38</td>
<td valign="top" align="center">0.41</td>
<td valign="top" align="center">1.29</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B34">Henson et&#xa0;al. (2011)</xref>
</td>
<td valign="top" align="center">-0.62</td>
<td valign="top" align="center">1.25</td>
<td valign="top" align="center">1.56</td>
<td valign="top" align="center">0.39</td>
<td valign="top" align="center">0.39</td>
<td valign="top" align="center">1.25</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B42">Laws et al. (2011)</xref>
</td>
<td valign="top" align="center">-0.38</td>
<td valign="top" align="center">0.97</td>
<td valign="top" align="center">1.43</td>
<td valign="top" align="center">0.39</td>
<td valign="top" align="center">0.26</td>
<td valign="top" align="center">0.97</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B42">Laws et al. (2011)</xref>
</td>
<td valign="top" align="center">-0.36</td>
<td valign="top" align="center">0.95</td>
<td valign="top" align="center">1.42</td>
<td valign="top" align="center">0.35</td>
<td valign="top" align="center">0.27</td>
<td valign="top" align="center">0.95</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B84">Westberry et&#xa0;al. (2012)</xref>
</td>
<td valign="top" align="center">-2.00</td>
<td valign="top" align="center">1.83</td>
<td valign="top" align="center">2.14</td>
<td valign="top" align="center">0.67</td>
<td valign="top" align="center">0.43</td>
<td valign="top" align="center">1.83</td>
</tr>
<tr>
<td valign="top" align="left">
<xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>
</td>
<td valign="top" align="center">-0.44</td>
<td valign="top" align="center">1.06</td>
<td valign="top" align="center">1.46</td>
<td valign="top" align="center">0.42</td>
<td valign="top" align="center">0.28</td>
<td valign="top" align="center">1.06</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>All EP values are log-transformed. Higher is better for R<sup>2</sup> while lower is better for the other metrics. Red colors denote the three algorithms with highest skill according to each metric.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>
<xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> does not report any information about sampling dates, which means that we are not able to match satellite-derived properties to the dataset. Instead, we rely on properties included in the dataset (n=125), all which we believe to be based on <italic>in-situ</italic> observations. There is 487 satellite matchups for <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref> observations between 100 and 200 meter, and 1,058 matchups for <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref>. All observations used in the comparisons are shown in <xref ref-type="fig" rid="f3">
<bold>Figure&#xa0;3</bold>
</xref>. The three datasets covers similar regions, but do not necessarily include the same observations. This is to be expected since our use of the <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref> and <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref> datasets are limited to the time of ocean color satellite coverage (1998 to present) whereas the <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> dataset has a cutoff some years before publication. <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref> have several long transects included that are not part of <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref>.</p>
<p>When visually comparing <italic>in-situ</italic> POC fluxes with predicted EP calculated using the <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>; <xref ref-type="bibr" rid="B43">Laws et&#xa0;al. (2000)</xref>, and <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref> algorithms (<xref ref-type="fig" rid="f8">
<bold>Figures&#xa0;8</bold>
</xref>&#x2013;<xref ref-type="fig" rid="f10">
<bold>10</bold>
</xref>) we see similar patterns. Comparing the <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> algorithm in its corresponding <italic>in-situ</italic> dataset results, as expected, in the same correlation as reported by the paper. A more interesting finding is that the two other algorithms have similarly good skill in predicting EP. The main exception is a slight offset from the 1:1 line by <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>. When using <italic>in-situ</italic> POC flux from <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref> dataset together with matched satellite properties, we see quite different results where neither observations from deep waters (purple markers) nor data from shallow water at less than 200&#xa0;m depth (blue markers) are predicted particularly well. The main issue seems to be that low observed values are not predicted as low values by the algorithm, which results in EP being significantly overestimated compared to observations. Here, the relationship between POC flux and EP based on the <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> dataset could arguably act as an upper constraint when applying the algorithms to the <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref> dataset. We find a less coherent pattern when <italic>in-situ</italic> POC flux from <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref> is plotted against EP from the three algorithms. The distribution of values in <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref> is trending higher than <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref>, but EP predicted by <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> falls within the same range for both <italic>in-situ</italic> datasets, leading to a notable underestimation by the algorithm. This pattern can be found for <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>, but is less pronounced, whereas <xref ref-type="bibr" rid="B43">Laws et&#xa0;al. (2000)</xref> generates EP predictions that are quite symmetrically distributed around the 1:1 line. Figures for the other algorithms can be found in the <xref ref-type="supplementary-material" rid="SM1">
<bold>Supplementary Materials</bold>
</xref>.</p>
<fig id="f8" position="float">
<label>Figure&#xa0;8</label>
<caption>
<p>Observed POC flux and EP calculated using the <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> algorithm. <italic>In-situ</italic> observations are from <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>, orange markers) <xref ref-type="bibr" rid="B50">Mouw et&#xa0;al. (2016a)</xref>; <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref>, (blue markers for observations shallower than 200 meters and purple for observations deeper than 200 meters), and <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref>, (green markers).</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1149938-g008.tif"/>
</fig>
<fig id="f9" position="float">
<label>Figure&#xa0;9</label>
<caption>
<p>Observed POC flux and EP calculated using the <xref ref-type="bibr" rid="B43">Laws et&#xa0;al. (2000)</xref> algorithm. <italic>In-situ</italic> observations are from <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>, (orange markers) <xref ref-type="bibr" rid="B50">Mouw et&#xa0;al. (2016a)</xref>; <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref>, (blue markers for observations shallower than 200 meters and purple for observations deeper than 200 meters), and <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref>, (green markers).</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1149938-g009.tif"/>
</fig>
<fig id="f10" position="float">
<label>Figure&#xa0;10</label>
<caption>
<p>Observed POC flux and EP calculated using the <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref> algorithm. <italic>In-situ</italic> observations are from <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>, (orange markers) <xref ref-type="bibr" rid="B50">Mouw et&#xa0;al. (2016a)</xref>; <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref>, (blue markers for observations shallower than 200 meters and purple for observations deeper than 200 meters), and <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref>, (green markers).</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1149938-g010.tif"/>
</fig>
<p>Finally, we compare log transformed predictions of EP from the different satellite-based models to <italic>in-situ</italic> observations of POC flux using a number of metrics: coefficient of determination (R<sup>2</sup>, <xref ref-type="bibr" rid="B87">Wright, 1921</xref>), Mean Absolute Error (MAE, <xref ref-type="bibr" rid="B17">Chicco et&#xa0;al., 2021</xref>), Root Mean Square Error (RMSE, <xref ref-type="bibr" rid="B54">Nevitt and Hancock, 2000</xref>), Mean Absolute Percent Error (MAPE, <xref ref-type="bibr" rid="B53">Myttenaere et&#xa0;al., 2016</xref>), symmetric Mean Absolute Percentage Error (sMAPE <xref ref-type="bibr" rid="B47">Makridakis, 1993</xref>), and Bias. Please see <xref ref-type="bibr" rid="B17">Chicco et&#xa0;al. (2021)</xref> and <xref ref-type="bibr" rid="B72">Seegers et&#xa0;al. (2018)</xref> for a more detailed discussion about each metric and their utility. All values are presented in <xref ref-type="table" rid="T3">
<bold>Tables&#xa0;3</bold>
</xref>&#x2013;<xref ref-type="table" rid="T5">
<bold>5</bold>
</xref>. We find that most models have limited to very limited skill when evaluated with R2 against the <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref> or <xref ref-type="bibr" rid="B8">Bisson et&#xa0;al. (2018)</xref> datasets, whereas several models perform better with <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref>; <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>, and <xref ref-type="bibr" rid="B43">Laws et&#xa0;al. (2000)</xref> at the top, when comparing predicted EP to <italic>in-situ</italic> POC fluxes in <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> dataset using <italic>in-situ</italic> properties only. These results are in accordance with the earlier presented visual comparisons. The other metrics show similar patterns.</p>
</sec>
<sec id="s6">
<label>6</label>
<title>Discussion and conclusions</title>
<p>The EP algorithms described here assume different definitions of export efficiency, are based on different products for deriving PP from satellite products (who themselves have different assumptions about PP), and are developed using different <italic>in-situ</italic> datasets. Still, the skill of predicting export production is surprisingly similar among the different algorithms. Both the <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> and <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref> algorithm evaluations showed that their own model provides the best results, which is not too surprising since they were developed using the evaluation data. The advantage is, however, modest for <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> and insignificant for <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>. The <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref> evaluation used a Lagrangian <italic>in-situ</italic> dataset collected with the <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref> algorithm in mind and performed a re-parameterization of said algorithm, but only achieved a modest improvement in skill measured as <italic>R</italic>
<sup>2</sup>. The authors argued that other statistical methods are more useful to evaluate EP algorithms and <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref> showed a larger improvement by those metrics.</p>
<p>There is only a slight correlation between how complex an algorithm is and how well it performs. <xref ref-type="bibr" rid="B74">Siegel et&#xa0;al. (2014)</xref> is arguably the most complex approach and showed good results in the <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref> study, but was performing rather poorly in <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>. The simplest approach is by <xref ref-type="bibr" rid="B27">Eppley and Peterson (1979)</xref>, which is the only algorithm evaluated that uses PP as the sole independent input feature. It performed worse than other algorithms in <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> but reasonably well in <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>. This might suggest that SST is a more important factor when estimating carbon fluxes at depth than EP from the euphotic zone.</p>
<p>We find that using the <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref> dataset together with satellite-derived properties provide a poor correlation between observed POC flux and predicted EP for the <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> algorithm, the reason for this is not entirely clear. Some possible explanations are problems with the satellite-derived products used or differences in how the <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> and <xref ref-type="bibr" rid="B51">Mouw et&#xa0;al. (2016b)</xref> datasets represent the global ocean. Another possible reason is (we assume) that all properties used in the <xref ref-type="bibr" rid="B24">Dunne et&#xa0;al. (2005)</xref> dataset are specifically sampled in connection to the POC flux observations. One could expect a better connection between surface processes and thermocline fluxes when observed over appropriate temporal and spatial scales. This suggestion would also explain the good correlations found by <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al. (2015)</xref> and <xref ref-type="bibr" rid="B45">Li and Cassar (2016)</xref>, the latter by not relying of thermocline fluxes in the evaluation.</p>
<p>A future step to better understand the contrasting results seen in this study is to re-evaluate all models with all available datasets. It is a reasonable assumption that empirical relationships between available satellite-derived products and EP differ significantly between different regions of the ocean (<xref ref-type="bibr" rid="B71">Sathyendranath et&#xa0;al., 1991</xref>; <xref ref-type="bibr" rid="B78">Stukel et&#xa0;al., 2015</xref>; <xref ref-type="bibr" rid="B9">Britten and Primeau, 2016</xref>; <xref ref-type="bibr" rid="B45">Li and Cassar, 2016</xref>). Recent syntheses of <italic>in-situ</italic> observations within the BICEP and EXPORTS projects have created the potential to re-parametrize existing algorithms and to perform new regression analyses on regional scales. An alternative promising approach to estimate EP from space is to use satellite-derived properties for data assimilation in biogeochemical models. Two recent examples are studies by <xref ref-type="bibr" rid="B20">DeVries and Weber (2017)</xref> and <xref ref-type="bibr" rid="B56">Nowicki et&#xa0;al. (2022)</xref> where they quantify the biological pump by using satellite and oceanographic tracer observations to constrain rates and patterns of organic matter production, export, and remineralization in an inverse model framework.</p>
</sec>
<sec id="s7" sec-type="author-contributions">
<title>Author contributions</title>
<p>BJ: Conceptualization, design of the work, literature review, draft, and revision of the text. GK: Conceptualization and revision of the text. SS: Funding and conceptualization. All authors contributed to the article and approved the submitted version.</p>
</sec>
</body>
<back>
<sec id="s8" sec-type="funding-information">
<title>Funding</title>
<p>Funding for this work was provided by the European Space Agency project "Biological Pump and Carbon Exchange Processes (BICEP)" and by the Simons Collaboration on Computational Biogeochemical Modeling of Marine Ecosystems (CBIOMES) (549947 SS). Additional support from the National Centre for Earth Observations of the UK is acknowledged.</p>
</sec>
<sec id="s9" sec-type="COI-statement">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec id="s10" sec-type="disclaimer">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<sec id="s11" sec-type="supplementary-material">
<title>Supplementary material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fmars.2023.1149938/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/fmars.2023.1149938/full#supplementary-material</ext-link>
</p>
<supplementary-material xlink:href="DataSheet_1.pdf" id="SM1" mimetype="application/pdf"/>
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