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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Environ. Sci.</journal-id>
<journal-title>Frontiers in Environmental Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Environ. Sci.</abbrev-journal-title>
<issn pub-type="epub">2296-665X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1198856</article-id>
<article-id pub-id-type="doi">10.3389/fenvs.2023.1198856</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Environmental Science</subject>
<subj-group>
<subject>Review</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Applications of biogeochemical models in different marine environments: a review</article-title>
<alt-title alt-title-type="left-running-head">Ismail and Al-Shehhi</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fenvs.2023.1198856">10.3389/fenvs.2023.1198856</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Ismail</surname>
<given-names>Kaltham A.</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/2309749/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Al-Shehhi</surname>
<given-names>Maryam R.</given-names>
</name>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1281485/overview"/>
</contrib>
</contrib-group>
<aff>
<institution>Department of Civil</institution>, <institution>Infrastructure and Environmental Engineering</institution>, <institution>Khalifa University</institution>, <addr-line>Abu Dhabi</addr-line>, <country>United Arab Emirates</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/44644/overview">Marta Sebastian</ext-link>, Institut de Ci&#xe8;ncies del Mar, Spain</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/31357/overview">Peter Leslie Croot</ext-link>, University of Galway, Ireland</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2291947/overview">Cristina Schultz</ext-link>, Northeastern University, United States</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Maryam R. Al-Shehhi, <email>maryamr.alshehhi@ku.ac.ae</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>28</day>
<month>08</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>11</volume>
<elocation-id>1198856</elocation-id>
<history>
<date date-type="received">
<day>02</day>
<month>04</month>
<year>2023</year>
</date>
<date date-type="accepted">
<day>11</day>
<month>08</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 Ismail and Al-Shehhi.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Ismail and Al-Shehhi</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>Marine biogeochemical models are an effective tool for formulating hypothesis and gaining mechanistic understanding of how an ecosystem functions. This paper presents a comprehensive review of biogeochemical models and explores their applications in different marine ecosystems. It also assesses their performance in reproducing key biogeochemical components, such as chlorophyll-a, nutrients, carbon, and oxygen cycles. The study focuses on four distinct zones: tropical, temperate, polar/subpolar, and high nutrient low chlorophyll (HNLC). Each zone exhibits unique physical and biogeochemical characteristics, which are defined and used to evaluate the models&#x2019; performance. While biogeochemical models have demonstrated the ability to simulate various ecosystem components, limitations and assumptions persist. Thus, this review addresses these limitations and discusses the challenges and future developments of biogeochemical models. Key areas for improvement involve incorporating missing components such as viruses, archaea, mixotrophs, refining parameterizations for nitrogen transformations, detritus representation, and considering the interactions of fish and zooplankton within the models.</p>
</abstract>
<kwd-group>
<kwd>marine biogeochemistry</kwd>
<kwd>tropical</kwd>
<kwd>subtropical</kwd>
<kwd>polar</kwd>
<kwd>carbon cycle</kwd>
<kwd>biogeochemical models</kwd>
<kwd>chlorophyll-a</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Biogeochemical Dynamics</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Marine biogeochemistry concerns the interactions between physical, geological, chemical, and biological processes that influence the cycling of key elements and organisms within the oceans, along the ocean floor and water column, and between the ocean and the atmosphere (<xref ref-type="bibr" rid="B1">Achterberg, 2014</xref>). Carbon (C) is one of the primary elements in marine biogeochemistry owing to its importance in both the Earth&#x2019;s climate and living organisms. The other important elements considered include nitrogen, oxygen, phosphorous, silicon, and iron. When these become limiting in the marine environment, they affect the growth of phytoplankton and consequently of zooplankton that graze them (<xref ref-type="bibr" rid="B55">Dutkiewicz et al., 2020</xref>). Phytoplankton play a critical role in the biogeochemical cycling through their carbon and nutrient fixation during the photosynthesis process (<xref ref-type="bibr" rid="B179">Munhoven, 2013</xref>),whereas, zooplankton consume phytoplankton as one of their primary sources of food and process a significant portion of carbon and nutrients (<xref ref-type="bibr" rid="B80">Ford et al., 2018</xref>). Thus, modelling the biogeochemistry of the ocean is an important step toward understanding its primary productivity and eutrophication, as well as the cycling and variability of nutrients (<xref ref-type="bibr" rid="B161">Malone and Newton, 2020</xref>). The availability of nutrients along with other physical factors such as light and temperature drives ocean&#x2019;s primary productivity (<xref ref-type="bibr" rid="B80">Ford et al., 2018</xref>). However, the excessive/unbalanced enrichment of water with nutrients (eutrophication) can result in accelerating growth of phytoplankton yielding to unfavourable disturbance to the balance of organisms in the water as well as water quality (<xref ref-type="bibr" rid="B161">Malone and Newton, 2020</xref>). Therefore, over the last two&#xa0;decades, marine biogeochemical models have been developed and widely utilized to explore how primary production responds to physical environment disturbances (e.g., El Nino, surface light, temperature increase) at a variety of temporal and spatial scales. Many of these models have originated from the pioneering efforts carried out by Steele in 1958 (<xref ref-type="bibr" rid="B225">Steele, 1958</xref>). In his plankton-based model, the assumption was made that the mixed layer is biologically homogeneous, with physical mixing rates (due to factors like wind, tides, and currents) being faster than the growth rate of organisms. The assumption of a homogeneous mixed layer may not hold for deep mixed layers, like the northeast Atlantic Ocean, where increased depth leads to greater light limitation instead of nutrient limitation. Phytoplankton growth occurs near the surface, where light is abundant despite the deep mixed layer. Thus, physical mixing alone cannot overcome the density differences between nutrient-rich deep water and the surface layer. As a result, nutrient depletion may occur in the surface layer, which can restrict organism growth and decrease primary production rates. Hence, Riley revised Steele&#x2019;s model by assuming that the depth of the euphotic zone fluctuates with chlorophyll-a (Chl-<italic>a</italic>) content (Chl-<italic>a</italic> influences depth of PAR through shading) rather than being fixed arbitrarily (<xref ref-type="bibr" rid="B205">Riley, 1965</xref>). It is important to note that light attenuation is also influenced by other particles and water properties within the water column, which can contribute to the overall light availability for photosynthetic activity. Riley&#x2019;s model also assumes an increase in the carbon: Chl-<italic>a</italic> ratio with the decrease in nutrient availability. More recently, most of the new models have used nitrogen as fundamental currency and accounted for a simplified food web that distinguishes phytoplankton and zooplankton, along with a regeneration network that incorporates detritus, dissolved organic nitrogen, and several nutrients. The classical NPZD (Nutrients, Phytoplankton, Zooplankton, and Detritus) approach, developed by <xref ref-type="bibr" rid="B65">Fasham et al. (1990)</xref>., is one of the earliest and most widely cited biogeochemical models. These main four compartments include biotic (e.g., phytoplankton, zooplankton) and abiotic (e.g., ammonium, nitrate, dissolved organic/inorganic carbon (DOC/DIC), particulate organic carbon (POC)) elements) (<xref ref-type="bibr" rid="B210">Sarmiento et al., 1993</xref>).The simplest form of NPZD is presented in Equations <xref ref-type="disp-formula" rid="e1">1</xref>&#x2013;<xref ref-type="disp-formula" rid="e4">4</xref>.<disp-formula id="e1">
<mml:math id="m1">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>D</mml:mi>
<mml:mi>I</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="italic">Uptake</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>R</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>s</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>
<disp-formula id="e2">
<mml:math id="m2">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>I</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>m</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>g</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
<disp-formula id="e3">
<mml:math id="m3">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>Z</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>g</mml:mi>
<mml:mi>Z</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>h</mml:mi>
<mml:mi>Z</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
<disp-formula id="e4">
<mml:math id="m4">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mi mathvariant="normal">P</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mi mathvariant="normal">Z</mml:mi>
<mml:mi mathvariant="normal">P</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">D</mml:mi>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>
</p>
<p>Where dDIN/dt, dP/dt, dZ/dt, and dD/dt are rate of change of nutrient, phytoplankton, zooplankton, and detritus respectively. DIN is the dissolved inorganic nutrient. Uptake is the rate at which phytoplankton consumes nutrients. Remineralisation is the rate at which organic matter is breaking down into nutrients. I is growth rate of phytoplankton due to light and nutrient availability. m is phytoplankton mortality rate. g is zooplankton grazing rate on phytoplankton. h is zooplankton mortality rate. mP and hZP are the rate of detritus generation due to phytoplankton and zooplankton mortality respectively. r is the rate at which detritus (D) is remineralized into nutrients.</p>
<p>The most applied form of nutrient uptake by phytoplankton is the Michaelis-Menten/Monod saturation function, which relates phytoplankton&#x2019;s growth rates to the concentration of a limiting nutrient (<xref ref-type="bibr" rid="B176">Monod, 1949</xref>). However, Droop approach (<xref ref-type="bibr" rid="B51">Droop, 1973</xref>; <xref ref-type="bibr" rid="B50">Droop, 1983</xref>) suggested that the growth rate is more likely dependent on cells&#x2019; internal rather than the external concentration of nutrients, and cells could absorb more nutrients than are required for growth (luxury uptake of nutrients) (<xref ref-type="bibr" rid="B113">John and Flynn, 2000</xref>; <xref ref-type="bibr" rid="B33">Cherif and Loreau, 2010</xref>). Hence, the growth of phytoplankton can be described by a function of internal concentration (quota model-(<xref ref-type="bibr" rid="B51">Droop, 1973</xref>; <xref ref-type="bibr" rid="B50">Droop, 1983</xref>)). In addition, it is argued that the growth rate is determined by the most limiting process, either light limitation or nutrient uptake, permitting for switching between the two (<xref ref-type="bibr" rid="B81">Franks, 2002</xref>).</p>
<p>Recently developed ocean biogeochemical models with increased complexity can accommodate more than 70 state variables (<xref ref-type="bibr" rid="B78">Follows et al., 2007</xref>) (<xref ref-type="fig" rid="F1">Figure 1</xref>). In addition to these models, several other biogeochemical models have focused on the inorganic carbon cycle. For instance, the Hamburg model of the oceanic carbon cycle (HAMOCC) was initially a pure inorganic carbon cycle model and was utilized to evaluate both the inorganic carbon cycle and the ocean model residence time properties (<xref ref-type="bibr" rid="B159">Maier-Reimer and Hasselmann, 1987</xref>). The Hadley Centre Ocean Carbon Cycle (HadOCC) model which was primarily developed for global climate studies is another example of a carbon cycle model which incorporates the full suite of biogeochemical processes (<xref ref-type="bibr" rid="B40">Cox et al., 2000</xref>).</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Schematic representation of the ocean biogeochemical models varying in complexity from the most basic NPZ form to those with more state variables and processes (high complexity). The labelled rectangular boxes are model variables, and processes are represented by arrows. Sediment interactions are represented which is comprised of different approaches.</p>
</caption>
<graphic xlink:href="fenvs-11-1198856-g001.tif"/>
</fig>
<p>Despite the importance of phytoplankton in carbon fixation in the surface ocean, direct measurements of their carbon biomass are rare, and that multiple factors, including physical processes and microbial activity, contribute to carbon export and remineralization in the oceanic carbon cycle (<xref ref-type="bibr" rid="B107">Hood et al., 2006</xref>). Chlorophyll (Chl-<italic>a</italic>) which is a pigment present in phytoplankton to photosynthesize is commonly used to estimate phytoplankton biomass. Chlorophyll has distinctive optical properties (<xref ref-type="bibr" rid="B157">Macintyre et al., 2000</xref>) and is controlled by a complex interplay of physiologic, oceanographic, and ecological ocean factors (<xref ref-type="bibr" rid="B235">Sverdrup, 1953</xref>; <xref ref-type="bibr" rid="B267">Wroblewski et al., 1988</xref>). Furthermore, the relationship between chlorophyll concentration and phytoplankton biomass is nonlinear and the ratio of chlorophyll to biomass varies by an order of magnitude under photoacclimation (<xref ref-type="bibr" rid="B68">Fennel, 2003</xref>; <xref ref-type="bibr" rid="B41">Cullen, 2015</xref>). Several biogeochemical models (<xref ref-type="bibr" rid="B177">Moore et al., 2002</xref>; <xref ref-type="bibr" rid="B7">Aumont and Bopp, 2006</xref>; <xref ref-type="bibr" rid="B79">Follows et al., 2007</xref>; <xref ref-type="bibr" rid="B255">Vichi et al., 2007</xref>), although not all of them, use a parameterization of photoacclimation to take into account changes in the phytoplankton biomass to chlorophyll ratio (<xref ref-type="bibr" rid="B87">Geider et al., 1997</xref>).</p>
<p>Along with Chl-<italic>a</italic> as being an important state variable in the biogeochemical models, macronutrients such as nitrogen, phosphorous, silica (necessary for diatom phytoplankton), and micronutrient iron play a significant role in phytoplankton growth and Chl-<italic>a</italic> production. These nutrients exist in the oceans with varying concentrations due to a variety of factors including regional variations in nutrient sources, physical processes like ocean currents and mixing, biological uptake and recycling, the impact of atmospheric deposition, and terrestrial runoff. In addition, seasonal fluctuations, upwelling events, and nutrient limitation regimes (<xref ref-type="bibr" rid="B48">Anderson et al., 2002</xref>; <xref ref-type="bibr" rid="B219">Smith, 2006</xref>; <xref ref-type="bibr" rid="B44">Davis et al., 2015</xref>; <xref ref-type="bibr" rid="B273">Yang et al., 2017</xref>) can have an impact on nutrient availability, which increases the geographical and temporal variability in nutrient concentrations across oceanic regions. Due to the increase of anthropogenic activities, coastal ecosystems receive high levels of nitrogen and phosphorous leading to eutrophication. Excessive nutrient enrichment can result in algal blooms (Chl-<italic>a</italic> concentrations above 40&#xa0;g&#xa0;L<sup>-1</sup>) (<xref ref-type="bibr" rid="B36">Clarke et al., 2009</xref>). Ecosystems in various regions, such as the Baltic Sea (<xref ref-type="bibr" rid="B251">Vahtera et al., 2007</xref>; <xref ref-type="bibr" rid="B206">R&#xf6;nnberg and Bonsdorff, 2016</xref>), Chesapeake Bay (<xref ref-type="bibr" rid="B180">Murphy et al., 2022</xref>), and the Gulf of Mexico (<xref ref-type="bibr" rid="B195">Rabalais et al., 2002</xref>), have experienced imbalances due to eutrophication, including oxygen depletion, loss of biodiversity, and negative effects on fish and shellfish populations.</p>
<p>Eutrophication can cause frequent hypoxia or anoxia (<xref ref-type="bibr" rid="B184">Officer et al., 1984</xref>; <xref ref-type="bibr" rid="B181">Naqvi et al., 2000</xref>; <xref ref-type="bibr" rid="B222">Soetaert and Middelburg, 2009</xref>) emphasizing the need for biogeochemical models in monitoring water quality and alerting ecosystem managers of pollution incidents (<xref ref-type="bibr" rid="B69">Fennel et al., 2019</xref>). These models simulate and predict fluctuations in water quality indicators, considering primary production, oxygen levels, and nutrient dynamics. By utilizing field observations and real-time monitoring data, these models can provide valuable insights to mitigate ecological imbalances promptly (<xref ref-type="bibr" rid="B189">Piehl et al., 2022</xref>).</p>
<p>In addition to macronutrients, iron is a major limiting nutrient in high latitudes seas, such as the subarctic Pacific Ocean, Southern Ocean, and southern Indian Ocean (<xref ref-type="bibr" rid="B174">Miller et al., 1991</xref>; <xref ref-type="bibr" rid="B178">Moore et al., 2004</xref>; <xref ref-type="bibr" rid="B99">Hamilton et al., 2020</xref>). In many regions, the atmosphere serves as the primary source of iron, which is transported as aerosols and often associated with soil dust (<xref ref-type="bibr" rid="B83">Fung et al., 2000</xref>; <xref ref-type="bibr" rid="B211">Sarthou et al., 2003</xref>). However, Iron sources can vary in different regions, including coastal Antarctica. It is essential to note that dust is not the predominant source of iron in all regions. In coastal areas, such as coastal Antarctica, diverse sources, including glacial melt and diagenesis, are considered to understand the origins of iron (<xref ref-type="bibr" rid="B90">Gerringa et al., 2012</xref>; <xref ref-type="bibr" rid="B218">Sherrell et al., 2018</xref>; <xref ref-type="bibr" rid="B47">Dinniman et al., 2020</xref>). Dissolved oxygen is another crucial state variable in ocean biogeochemical models, impacting the ecological and biogeochemical structure of marine ecosystems (<xref ref-type="bibr" rid="B265">Wilson et al., 2019</xref>). Oxygen depletion and hypoxia can occur due to factors like nutrient loading and insufficient oxygen replenishment. In regions where oxygen levels decrease significantly, known as hypoxic regions, the intensification of hypoxia leads to denitrification and the formation of oxygen minimum zones (OMZs) (<xref ref-type="bibr" rid="B230">Stramma et al., 2010</xref>; <xref ref-type="bibr" rid="B231">Stramma et al., 2009</xref>; <xref ref-type="bibr" rid="B229">Stramma et al., 2008</xref>; <xref ref-type="bibr" rid="B122">Karstensen et al., 2008</xref>; <xref ref-type="bibr" rid="B144">Levin and Breitburg, 2015</xref>; <xref ref-type="bibr" rid="B133">Lachkar et al., 2016</xref>; <xref ref-type="bibr" rid="B130">Lachkar et al., 2019</xref>; <xref ref-type="bibr" rid="B132">Lachkar et al., 2020</xref>; <xref ref-type="bibr" rid="B145">Levin, 2018</xref>; <xref ref-type="bibr" rid="B98">Gr&#xe9;goire et al., 2021</xref>). Coastal zones or upwelling regions are typical locations for these hypoxic regions in the ocean (<xref ref-type="bibr" rid="B93">Gobler and Baumann, 2016</xref>).</p>
<p>Biogeochemical models have been used in various ecosystems of the world ocean, and for the purpose of our study, we have classified the regions into four distinct zones: tropical, temperate, polar/subpolar, and HNLC. The tropical zone spans approximately 40% of the Earth&#x2019;s surface, stretching from the Tropics of Cancer (latitude 23.5&#xb0;N) to the Tropic of Capricorn (latitude 23.5&#xb0;S) (<xref ref-type="bibr" rid="B252">Val et al., 2023</xref>). The zone is primarily defined by consistently high temperatures with a sea surface temperature above 20&#xb0;C and an abundance of sunlight, which leads to high primary production and nutrient cycling. However, there may be some variation in precipitation patterns, humidity levels, and cloud cover across different regions within the tropical zone, which can influence local climate conditions (<xref ref-type="bibr" rid="B151">L&#xf8;nborg et al., 2021</xref>). However, temperate regions are those with latitudes from 35&#xb0; to 50&#xb0; North and South and is marked by moderate sea surface temperatures and seasonal variations in nutrient availability and primary production (<xref ref-type="bibr" rid="B151">L&#xf8;nborg et al., 2021</xref>). In tropical coastal waters, sea surface temperatures typically range between 20&#xb0;C and 32&#xb0;C. Temperate coastal waters, on the other hand, have a wider temperature range, ranging from 0&#xb0;C to 25&#xb0;C, with greater seasonal variation than tropical locations. Although seasonal variations are still noticeable in tropical coastal waters, they are not primarily driven by temperature (<xref ref-type="bibr" rid="B63">Eyre and Balls, 1999</xref>). The polar/subpolar zone is covering the Arctic and Antarctic regions (the areas between 60 degrees and the poles) and is defined by low sea surface temperatures usually range from &#x2212;1&#xb0;C and 14.7&#xb0;, sea ice cover, and limited sunlight, leading to low primary production and nutrient cycling (<xref ref-type="bibr" rid="B216">Schultz, 1995</xref>). Finally, the HNLC (High Nutrient Low Chlorophyll) zones are regions where the abundance of phytoplankton biomass (or Chl-<italic>a</italic>) is low and almost constant, and macronutrients, in particular nitrates, are never considerably depleted (<xref ref-type="bibr" rid="B60">Edwards et al., 2004</xref>). These regions constitute more than 20% of the global ocean (<xref ref-type="bibr" rid="B165">Martin et al., 1994</xref>) and is found in areas where iron availability is low and limits the growth of phytoplankton, which are the base of the marine food web. The HNLC zones are found in areas of the Southern Ocean, the equatorial Pacific, and parts of the North Pacific and North Atlantic, <xref ref-type="fig" rid="F2">Figure 2</xref>.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>World ocean map with the indicated climatic zones presented in this study. The symbols on the map indicate regions where biogeochemical modeling studies, discussed in the review, have been conducted. Boxes with dashed outline are regions where HNLC zone mentioned in the text.</p>
</caption>
<graphic xlink:href="fenvs-11-1198856-g002.tif"/>
</fig>
<p>Herein, we describe existing biogeochemical models used to study various ecosystems for the present state in the global oceans at the regional and global scale, and assess their performance, strengths, uncertainties and limitations in estimating several biochemical components, including Chl-<italic>a</italic>, macronutrients (e.g., nitrate, phosphate, silicate), micronutrients (iron), carbon and oxygen cycles. This paper begins with a section that describes different modelling approaches, components, assumptions and structure. Then, the assessment of applications of these models in different ecosystems of the global oceans are discussed.</p>
</sec>
<sec id="s2">
<title>2 Biogeochemical modelling approaches</title>
<p>The existing biogeochemical models are categorized herein by their different level of complexity in terms of the number of phytoplankton functional types (PFTs), different forms of inorganic and organic matter, physics, and deep sediments incorporation.</p>
<sec id="s2-1">
<title>2.1 Classical NPZD approach</title>
<p>The classical NPZD approach is an improvement of the NPZ (<xref ref-type="bibr" rid="B284">Evans et al., 1985</xref>; <xref ref-type="bibr" rid="B81">Franks, 2002</xref>) which considers a single variable for each compartment (nutrients - phytoplankton - zooplankton - detritus, sometimes including a different compartment for bacteria) neglecting the differences between the different biological types (<xref ref-type="bibr" rid="B65">Fasham et al., 1990</xref>; <xref ref-type="bibr" rid="B66">Fasham, 1993</xref>; <xref ref-type="bibr" rid="B168">McGillicuddy et al., 1995b</xref>). In this approach, nitrogen is typically considered a limiting nutrient because it is a necessary component of chlorophyll, nucleic acids, and proteins, all of which are important for the growth of phytoplankton and photosynthesis (<xref ref-type="bibr" rid="B147">Liefer et al., 2019</xref>). Also, compared to other nutrients, nitrogen availability is frequently limited, which can have an adverse effect on the entire food web by limiting phytoplankton development (<xref ref-type="bibr" rid="B22">Bristow et al., 2017</xref>). The detritus component accounts for the organic matter pool, which is derived from faecal materials, the fraction non-assimilated by grazing zooplankton and phytoplankton decay. The detritus is recycled by bacteria and degraded to dissolved organic nitrogen, or digested by zooplankton (<xref ref-type="bibr" rid="B142">Leles et al., 2016</xref>). The process through which autotrophic organisms, including phytoplankton, produce organic matter by converting sunlight and nutrients into biomass referred as primary production. Contrarily, in secondary production, organic matter is consumed by heterotrophic creatures like zooplankton, which graze on primary producers or consume other organisms.</p>
</sec>
<sec id="s2-2">
<title>2.2 Improving nitrogen and carbon flux and adding other elements</title>
<p>Modifications have been made in the classical NPZD approaches to improve the estimation of nitrogen and carbon flux (<xref ref-type="bibr" rid="B73">Fennel et al., 2006</xref>), with the addition of variable Chl-<italic>a</italic> and introducing a nitrogen-based nutrient-phytoplankton-heterotroph model which is of intermediate complexity with respect to Fasham&#x2019;s and McGillicuddy&#x2019;s models (<xref ref-type="bibr" rid="B65">Fasham et al., 1990</xref>; <xref ref-type="bibr" rid="B167">McGillicuddy et al., 1995a</xref>). Although nitrate is considered one of the most important limiting nutrients for the growth of phytoplankton biomass and primary production in open ecosystems; in some locations, such as the equatorial Pacific, North Pacific, and the Southern Ocean, nitrate (NO<sub>3</sub>) levels may exceed 4&#xa0;&#xb5;M (central Pacific) and phytoplankton biomass is low (<xref ref-type="bibr" rid="B32">Chai et al., 1996</xref>). The high nitrate and low Chl-<italic>a</italic> (HNLC) conditions observed in these regions are commonly associated with limited iron availability (<xref ref-type="bibr" rid="B143">Leonard et al., 1999</xref>; <xref ref-type="bibr" rid="B190">Pitchford and Brindley, 1999</xref>; <xref ref-type="bibr" rid="B253">Venables and Moore, 2010</xref>).</p>
<p>Nevertheless, in high-latitude areas, other factors besides the iron deficiency may also inhibit phytoplankton growth. Low temperatures (<xref ref-type="bibr" rid="B204">Rhee and Gotham, 1981</xref>), imbalanced nutritional stoichiometry (<xref ref-type="bibr" rid="B89">Gerhard et al., 2022</xref>), short days and prolonged cloud cover (<xref ref-type="bibr" rid="B34">ChrEilertsen and Degerlund, 2010</xref>), and grazing pressure (<xref ref-type="bibr" rid="B42">Dale et al., 1999</xref>) from higher trophic levels are some examples of these constraints. <xref ref-type="bibr" rid="B143">Leonard et al., 1999</xref> accounted for iron limitation (nutrient compartment) in his extended NPZD model with the employment of nine compartments. The model incorporated iron partitioning into new iron and regenerated iron, as well as dissolved iron bioavailability in the marine environment. Following these developments, Galbraith developed the Biogeochemistry with Light Iron Nutrients and Gases (BLING) model, also based on NPZD (<xref ref-type="bibr" rid="B84">Galbraith et al., 2009</xref>). This model employs a specific approach to isolate the global impact of iron on two major features of photosynthesis: maximum light-saturated photosynthesis rates and photosynthetic efficiency. The model uses sophisticated parameterizations or algorithms to separate and quantify the impact of iron on these distinct components. These sophisticated formulations take into account various factors and processes, such as iron uptake mechanisms, iron limitation effects, and biochemical reactions, to provide a detailed understanding of how iron affects photosynthetic process. The model also considers an implicit representation (without explicitly modeling it as a separate parameter or variable) of the growth rate of phytoplankton.</p>
<p>The proportion of the main elements in most biogeochemical models is commonly described with a constant elemental ratio (stoichiometry): 106&#xa0;C (carbon):16&#xa0;N (nitrogen):1&#xa0;P (phosphorous) (<xref ref-type="bibr" rid="B201">Redfield, 1933</xref>). This ratio is the most widely used stoichiometric reference for planktonic nutrient limitation (<xref ref-type="bibr" rid="B191">Ptacnik et al., 2010</xref>). Hence, biogeochemical models may consider simple growth formulations with constant C: Nutrients stoichiometry or neglect photo-acclimation by considering a constant Chl:C ratio. The classical Michaelis Menten equations are the simplest representation of phytoplankton growth (<xref ref-type="bibr" rid="B176">Monod, 1949</xref>) assuming a constant stoichiometric ratio between nitrogen, phosphorous, and carbon (<xref ref-type="bibr" rid="B201">Redfield, 1933</xref>; <xref ref-type="bibr" rid="B105">Ho et al., 2003</xref>; <xref ref-type="bibr" rid="B193">Quigg et al., 2003</xref>; <xref ref-type="bibr" rid="B194">Quigg et al., 2011</xref>; <xref ref-type="bibr" rid="B76">Finkel et al., 2006</xref>; <xref ref-type="bibr" rid="B76">Finkel et al., 2006</xref>). The Redfield ratio has been modified to take into account observed differences from the conventional ratio. As study by (<xref ref-type="bibr" rid="B3">Anderson and Sarmiento, 1994</xref>) have been conducted to analyse nutrient data and evaluate the variability of nutrient ratios under different conditions in several regions. Their research emphasizes the significance of taking into account context-specific elements that can affect nutrient stoichiometry, such as nutrient availability, microbial community composition, and ecological interactions Biogeochemical models that incorporate these modified formulations of the Redfield ratio use specific units (nitrogen, phosphorus, or carbon currency) to represent phytoplankton biomass and these models can generally be utilized for global scale studies (<xref ref-type="bibr" rid="B7">Aumont and Bopp, 2006</xref>; <xref ref-type="bibr" rid="B78">Follows et al., 2007a</xref>; <xref ref-type="bibr" rid="B56">Dutkiewicz et al., 2009</xref>). On the other hand (<xref ref-type="bibr" rid="B50">Droop, 1983</xref>), has more advanced and complex growth formulations which account for the dynamics of phytoplankton cell internal quota (<xref ref-type="bibr" rid="B125">Klausmeier et al., 2004</xref>; <xref ref-type="bibr" rid="B21">Bougaran et al., 2010</xref>; <xref ref-type="bibr" rid="B16">Bernard, 2011</xref>; <xref ref-type="bibr" rid="B160">Mairet et al., 2011</xref>; <xref ref-type="bibr" rid="B257">Wang et al., 2022</xref>). Thus, phytoplankton biomass in Droop&#x2019;s model (<xref ref-type="bibr" rid="B50">Droop, 1983</xref>) is represented by at least two state variables, typically carbon and nitrogen currency. Different versions of Droop&#x2019;s model have been embedded and utilized in 1D (<xref ref-type="bibr" rid="B135">Lancelot et al., 2000</xref>; <xref ref-type="bibr" rid="B2">Allen et al., 2002</xref>; <xref ref-type="bibr" rid="B141">Lefe et al., 2003</xref>; <xref ref-type="bibr" rid="B175">Mongin et al., 2003</xref>; <xref ref-type="bibr" rid="B19">Blackford et al., 2004</xref>; <xref ref-type="bibr" rid="B208">Salihoglu et al., 2008</xref>) and 3D (<xref ref-type="bibr" rid="B236">Tagliabue and Arrigo, 2005</xref>; <xref ref-type="bibr" rid="B255">Vichi et al., 2007</xref>; <xref ref-type="bibr" rid="B254">Vichi and Masina, 2009</xref>; <xref ref-type="bibr" rid="B256">Vogt et al., 2010</xref>) marine biogeochemical models. In these models, Chl-<italic>a</italic> dynamics can be also defined with various levels of complexity. The ratio of Chl: C can be constant (non-photo-acclimation), or prognostic with a dynamic behaviour (<xref ref-type="bibr" rid="B77">Flynn and Flynn, 1998</xref>; <xref ref-type="bibr" rid="B86">Geider et al., 1998</xref>; <xref ref-type="bibr" rid="B207">Ross and Geider, 2009</xref>) or diagnostic with an empirical (<xref ref-type="bibr" rid="B16">Bernard, 2011</xref>) and mechanistic relationships (<xref ref-type="bibr" rid="B88">Geider and Platt, 1986</xref>; <xref ref-type="bibr" rid="B49">Doney et al., 1996</xref>; <xref ref-type="bibr" rid="B18">Bissett et al., 1999</xref>). These approaches vary in terms of their level of complexity, assumptions, and underlying mechanisms employed. The constant Chl:C ratio method is the simplest, assuming no acclimation or variation in Chl-<italic>a</italic> concentration. Prognostic techniques enable dynamic modifications of the Chl-<italic>a</italic>:C ratio, capturing phytoplankton&#x2019;s adaptation to changing environmental conditions. Both empirical and mechanistic diagnostic techniques estimate Chl-<italic>a</italic> content based on observational or mechanistic correlations, respectively, without explicitly modelling the physiological processes. Each method provides information about the regulation of Chl-<italic>a</italic> dynamics and their ecological implications in marine ecosystems.</p>
<p>Other complexities have been added to the simple NPZD model, including 1) dissolved organic nitrogen in order to allow for a comprehensive representation of a significant nitrogen pool, particularly in regions where high primary productivity is observed (<xref ref-type="bibr" rid="B106">Hood et al., 2001</xref>; <xref ref-type="bibr" rid="B52">Druon et al., 2010</xref>), 2) oxygen cycle which is known to be an essential component to represent the oxygen minimum zone caused by excessive denitrification (<xref ref-type="bibr" rid="B181">Naqvi et al., 2000</xref>; <xref ref-type="bibr" rid="B38">Codispoti et al., 2001</xref>).</p>
</sec>
<sec id="s2-3">
<title>2.3 Increasing the biological complexity</title>
<p>Unlike the simple NPZD, more complex models include different phytoplankton functional types (PFTs) and at least 15 state variables (e.g., <xref ref-type="bibr" rid="B94">Gregg, 2000</xref>; <xref ref-type="bibr" rid="B96">Gregg et al., 2003</xref>; <xref ref-type="bibr" rid="B178">Moore et al., 2004</xref>; <xref ref-type="bibr" rid="B140">Le Qu&#xe9;r&#xe9; et al., 2005</xref>; <xref ref-type="bibr" rid="B56">Dutkiewicz et al., 2009</xref>; <xref ref-type="bibr" rid="B227">Stock et al., 2014b</xref>; <xref ref-type="bibr" rid="B266">Wright et al., 2021</xref>; <xref ref-type="bibr" rid="B154">Luo et al., 2022</xref>). Considering a range of plankton groups and increasing the number of variables allows for a more thorough assessment of ecological interactions. <xref ref-type="table" rid="T2">Table 2</xref> provides a summary of the models presented in this section, emphasizing their key characteristics and improvements. Here, we expand on the interpretation of each model improvement and discuss the relevance of increasing the number of variables.</p>
<p>The incorporation of Plankton Functional Types (PFTs) in biogeochemical models has been pursued to improve the accuracy of marine ecosystem representations (<xref ref-type="bibr" rid="B5">Anderson, 2005</xref>). Notably, the integration of additional complexity beyond NPZD models presents challenges, including limited understanding of ecology, data constraints, and the need to consolidate diversity within functional groups (<xref ref-type="bibr" rid="B5">Anderson, 2005</xref>). This approach is exemplified in biogeochemical models such as ERSEM (European Regional Seas Ecosystem Model) versions 1 and 2 (<xref ref-type="bibr" rid="B14">Baretta et al., 1995</xref>; <xref ref-type="bibr" rid="B15">Baretta-Bekker et al., 1997</xref>; <xref ref-type="bibr" rid="B19">Blackford et al., 2004</xref>). ERSEM adopts a functional role-based classification of biotic groups, categorizing phytoplankton as producers, bacteria as decomposers, and zooplankton as consumers, employing a general lower trophic approach. This approach is similar to the functional roles in an NPZD model, where each component has specific functions within the nutrient dynamics and planktonic community interactions. However, what distinguishes ERSEM from other NPZD models is its comprehensive integration of ecosystem-specific processes and interactions, allowing for a more tailored representation of biotic groups and their functions. The division of the food web into three functional categories is based on traits, including silica uptake, maximum growth rate, and nutrient affinity. The ERSEM model was initially applied to the North Sea to study the seasonal cycling of nutrients (i.e., nitrogen, phosphorous, silica, carbon). ERSEM was later modified to produce the Biogeochemical Flux Model (BFM), which accounts for the Chemical Functional Families (CFFs) in the state variables. The CFFs is split into living, non-living, and inorganic states (<xref ref-type="bibr" rid="B255">Vichi et al., 2007</xref>).</p>
<p>The Pelagic Interactions Scheme for Carbon and Ecosystem Studies (PISCES) is another example of a simple PFT model adapted from HAMOCC (<xref ref-type="bibr" rid="B9">Aumont et al., 2003</xref>) and extensively and widely applied in more than a hundred studies directly or indirectly (<xref ref-type="bibr" rid="B8">Aumont et al., 2015</xref>) The NASA Ocean Biogeochemical Model (NOBM) is a PFT model coupled with the Ocean-Atmosphere Spectral Irradiance Model (OASIM) (<xref ref-type="bibr" rid="B97">Gregg, 2001</xref>; <xref ref-type="bibr" rid="B95">Gregg et al., 2009</xref>) and is capable of simulating global-scale biogeochemical cycles. Additionally, the PlankTOM model describes the lower trophic level of marine ecosystems and has various extensions with different numbers of PFTs (<xref ref-type="bibr" rid="B140">Le Qu&#xe9;r&#xe9; et al., 2005</xref>; <xref ref-type="bibr" rid="B129">Kwiatkowski et al., 2014</xref>).</p>
<p>The Model of Ecosystem Dynamics, nutrient Utilization, Sequestration and Acidification (MEDUSA) includes the biogeochemical cycles of iron, silicon, and nitrogen as well as small and large plankton size classes (<xref ref-type="bibr" rid="B275">Yool et al., 2011</xref>; <xref ref-type="bibr" rid="B276">2013</xref>). MEDUSA focuses on the biological sequestration of carbon in the deep ocean. Similarly, the Tracers of Phytoplankton with Allometric Zooplankton (TOPAZ), developed by <xref ref-type="bibr" rid="B53">Dunne et al., 2010</xref>, focuses on simulating the interactions among phytoplankton and allometric zooplankton, emphasizing their roles within the ecosystem dynamics.This model has been implemented in several studies (<xref ref-type="bibr" rid="B116">Jung, et al., 2019a</xref>; <xref ref-type="bibr" rid="B24">Bronselaer et al., 2020</xref>; <xref ref-type="bibr" rid="B217">Sharada et al., 2020</xref>) and extended in the Carbon, Ocean Biogeochemistry and Lower Trophics (COBALT) model, which improves the planktonic food web dynamics resolution to examine the influence of climate on the flow of energy from phytoplankton to fish (<xref ref-type="bibr" rid="B226">Stock et al., 2014a</xref>). Since the planktonic food web representation in TOPAZ is highly idealized due to an implicit representation of zooplankton and bacteria, COBALT addressed these limitations by including three explicit zooplankton groups and bacteria with a mechanistic parametrization of the impacts of these groups on the biogeochemistry (<xref ref-type="bibr" rid="B227">Stock et al., 2014b</xref>).</p>
<p>The DARWIN biogeochemical model is a more complex PFT model allowing for several different configurations and number of PFTs. It is initially developed to study <italic>Prochlorococcus</italic> species (<xref ref-type="bibr" rid="B79">Follows et al., 2007b</xref>) and later applied to global distributions of phytoplankton (<xref ref-type="bibr" rid="B58">Dutkiewicz et al., 2015</xref>; <xref ref-type="bibr" rid="B150">Lo et al., 2019</xref>). Nevertheless, the Regulated Ecosystem Model (REcoM) is based on a functional group approach (<xref ref-type="bibr" rid="B213">Schourup-Kristensen et al., 2014</xref>) and has also been commonly used in the Southern Ocean studies (<xref ref-type="bibr" rid="B238">Taylor et al., 2013</xref>; <xref ref-type="bibr" rid="B152">Losch et al., 2014</xref>; <xref ref-type="bibr" rid="B102">Hauck and V&#xf6;lker, 2015</xref>).</p>
<p>The complexity of the aforementioned PFT models depends on the number of the independent elements, processes parameterization (e.g., shape of functional responses, number of parameters, linear vs. nonlinear) along with the number of PFTs considered (<xref ref-type="bibr" rid="B80">Ford et al., 2018</xref>). As the number of PFTs increases, the complexity of the model increases as well. Generally, adding complexity to the model does not necessarily improve the model&#x2019;s performance as the addition of complexity will require validation of each component of the ecosystem. Even under ideal circumstances, biogeochemical observations are lacking for full spatiotemporal coverage. As a result, the validity of additional processes is sometimes simply determined by how much they contribute to certain quantities like the total chlorophyll content (<xref ref-type="bibr" rid="B80">Ford et al., 2018</xref>). These studies comparing models of varying complexity have typically concluded that increasing model complexity does not always result in an increase in model skill (<xref ref-type="bibr" rid="B82">Friedrichs et al., 2007</xref>; <xref ref-type="bibr" rid="B127">Kriest et al., 2010</xref>; <xref ref-type="bibr" rid="B259">Ward et al., 2013</xref>; <xref ref-type="bibr" rid="B129">Kwiatkowski et al., 2014</xref>; <xref ref-type="bibr" rid="B269">Xiao and Friedrichs, 2014</xref>).</p>
</sec>
<sec id="s2-4">
<title>2.4 The addition of several classes of organic matter and bacteria</title>
<p>Bacteria play a key role in their contribution in the microbial loop, particularly in the recycling of dissolved organic matter (DOM) and provide a linkage between the higher trophic level and the dynamics of DOM (<xref ref-type="bibr" rid="B187">Pauer et al., 2014</xref>). In biogeochemical models studying dissolved organic matter (DOM) dynamics, various classes of organic matter, along with chemical elements and Plankton Functional Types (PFTs), have been incorporated. DOM is divided into three distinct pools based on its lability: labile DOM, semi-labile DOM, and refractory DOM. Labile DOM consists of organic molecules with a lifespan ranging from minutes to days. Semi-labile DOM undergoes decomposition over a period of 1&#x2013;20 years and typically accumulates above a seasonal or permanent pycnocline. Refractory DOM, the most abundant component, exhibits the longest residence time in the water column, persisting for tens of thousands of years (<xref ref-type="bibr" rid="B29">Carlson and Hansell, 2015</xref>; <xref ref-type="bibr" rid="B186">Osterholz et al., 2015</xref>).</p>
<p>The ratios of DOC:DON vary among different DOM pools. The refractory DOM pool has a ratio of 3511:202, whereas the labile DOM pool has a ratio of 199:20 (<xref ref-type="bibr" rid="B108">Hopkinson and Vallino, 2005</xref>). These ratios indicate the relative amounts of dissolved organic carbon to dissolved organic nitrogen within each pool. It is essential to consider these ratios when incorporating DOM dynamics into biogeochemical models.</p>
<p>DOM in the oceans is an important input to the biogeochemical cycle, with the ocean&#x2019;s DOC pool serving as the biosphere&#x2019;s largest storage facility for reduced organic carbon (<xref ref-type="bibr" rid="B100">Hansell et al., 2009</xref>). Labile and, to a lesser extent, semi-refractory pools are driven by microbial reactions. In the microbial loop, the DOC-bacteria pathway constitutes a primary mechanism through which primary production is eitherrespired to CO<sub>2</sub>, directed to higher trophic levels, or transformed into refractory compounds. However, the refractory DOC is transported deep into the ocean (<xref ref-type="bibr" rid="B4">Anderson, 1999</xref>; <xref ref-type="bibr" rid="B118">Kahler and Koeve, 2001</xref>).</p>
<p>The aforementioned different forms of organic matter have been incorporated into some biogeochemical models. For instance, the semi-labile DOC and semi-labile dissolved organic nitrogen (DON) have been included in biogeochemical models that focus on regions known of their high primary productivity, particularly coastal and continental shelves regions (<xref ref-type="bibr" rid="B52">Druon et al., 2010</xref>; <xref ref-type="bibr" rid="B72">Fennel, 2010</xref>; <xref ref-type="bibr" rid="B271">Xue et al., 2013</xref>). These areas are potential sites for sediment denitrification and organic carbon transport to the open ocean (<xref ref-type="bibr" rid="B45">Devol and Christensen, 1993</xref>; <xref ref-type="bibr" rid="B199">Rao et al., 2007</xref>; <xref ref-type="bibr" rid="B74">Fennel et al., 2008</xref>; <xref ref-type="bibr" rid="B52">Druon et al., 2010</xref>). Another study by <xref ref-type="bibr" rid="B212">Schartau et al. (2007)</xref> considered the labile DOM exudation and extracellular POC formation. This process occurs during the growth of phytoplankton in which the assimilation of dissolved inorganic carbon (DIC) by phytoplankton is exuded as DOC, which is simultaneously converted into extracellular POC. A significant proportion of extracellular POC is available as transparent exopolymer particles (TEP), which consist mainly of dissolved polysaccharides (PCHO). PCHO exudation is associated with high consumption of DIC that is not directly measurable from the use of dissolved inorganic nitrogen (DIN), a phenomenon known as carbon overconsumption (<xref ref-type="bibr" rid="B244">Toggweiler, 1993</xref>).</p>
</sec>
<sec id="s2-5">
<title>2.5 Benthic-pelagic coupling</title>
<p>Sediment processes have been also integrated into the pelagic biogeochemical models to investigate the impact of atmospheric conditions on the ecosystem dynamics, the distribution of sediments processes in the water column, and the nitrogen budget derivation (<xref ref-type="bibr" rid="B221">Soetaert et al., 2001</xref>; <xref ref-type="bibr" rid="B223">2000</xref>; <xref ref-type="bibr" rid="B6">Arthur et al., 2016</xref>; <xref ref-type="bibr" rid="B62">Ehrnsten et al., 2019</xref>; <xref ref-type="bibr" rid="B124">Kearney et al., 2020</xref>). The lack of sediment regeneration of nutrients in the biogeochemical model may lead to underestimating primary productivity (<xref ref-type="bibr" rid="B149">Liu et al., 2007</xref>). Adding a representation of marine sediment in biogeochemical models is important, particularly in shallow water regions like shelves, where strong vertical mixing occurs. This inclusion helps to accurately account for nutrient recycling from sediments to surface waters, preventing the underestimation of productivity (<xref ref-type="bibr" rid="B276">Yool et al., 2013</xref>). However, it is crucial to emphasize that in many models, sediment is represented as a boundary condition with simplistic representation, and even global models that address diagenesis frequently lack a thorough representation of the benthic ecosystem.</p>
<p>While incorporating sediment interactions in biogeochemical models is important to understand the linkages between sediment diagenetic processes and the global carbon cycle (<xref ref-type="bibr" rid="B172">Middelburg, 2018</xref>; <xref ref-type="bibr" rid="B220">Snelgrove et al., 2018</xref>), many models use an oversimplified representation of sediment. Several regional models have been developed to examine specific areas of the ocean at different timescales, yielding important insights into biogeochemical processes. These models such as (<xref ref-type="bibr" rid="B223">Soetaert et al., 2000</xref>) and the Ecological ReGional Ocean Model with vertically resolved sediments (ERGOM SED 1.0) (<xref ref-type="bibr" rid="B196">Radtke et al., 2019</xref>) also add to the discussion of sediment representation and its effects on oceanic and coastal ecosystems. For example, in a coastal environment (<xref ref-type="bibr" rid="B202">Reed et al., 2011</xref>), investigated the dynamics of sedimentary phosphorus and the development of bottom-water hypoxia. Furthermore, the relationship between sediment dynamics and biogeochemical cycling was examined by (<xref ref-type="bibr" rid="B196">Radtke et al., 2019</xref>).</p>
<p>Marine sediments representation in the biogeochemical model can be parametrized using a meta-model that is based on the downward fluxes of organic matter (<xref ref-type="bibr" rid="B173">Middelburg et al., 1996</xref>), a sediment box module which uses simple 1D or 2D submodules in the pelagic model to represent a simple interaction of the water column with the sedimentary pools (<xref ref-type="bibr" rid="B276">Yool et al., 2013</xref>), or multilayer sediment modules with chemically active sediment layers (<xref ref-type="bibr" rid="B103">Heinze and Maier-Reimer, 1999</xref>). Most of the biogeochemical models utilize sediment box modules or meta-models to examine eutrophication (<xref ref-type="bibr" rid="B31">Cerco et al., 2006</xref>; <xref ref-type="bibr" rid="B222">Soetaert and Middelburg, 2009</xref>; <xref ref-type="bibr" rid="B70">Fennel et al., 2011</xref>) or hypoxia in several regions, such as Tokyo Bay (<xref ref-type="bibr" rid="B224">Sohma et al., 2008</xref>), the Baltic Sea (<xref ref-type="bibr" rid="B202">Reed et al., 2011</xref>) and the North Sea (<xref ref-type="bibr" rid="B136">Lancelot et al., 2005</xref>; <xref ref-type="bibr" rid="B171">Meire et al., 2013</xref>).</p>
</sec>
</sec>
<sec id="s3">
<title>3 Applications of biogeochemical models</title>
<p>The aforementioned models have been applied to resolve biochemical components including Chl-<italic>a</italic>, macronutrients (nitrogen, phosphorous, silica), micronutrients (iron), carbon and oxygen in different regions of the world&#x2019;s ocean. Here, we will focus on the application of these biogeochemical models in four zones as described in the introduction section. Detailed assessments of the capabilities of these models along with their complexity through the addition of more components are provided here and summarized in <xref ref-type="table" rid="T1">Table 1</xref>. Further, the common statistical metrics for model assessment used in the analysed studies are illustrated in <xref ref-type="table" rid="T2">Table 2</xref>. To provide a comprehensive analysis of the model performance, Taylor diagrams (<xref ref-type="bibr" rid="B237">Taylor, 2001</xref>) are employed in various biogeochemical modelling studies. Taylor Diagrams are graphical tools that show several model performance metrics at the same time, providing an illustration of the model&#x2019;s ability to capture observed data patterns. They can assist in comparing and ranking various models based on correlation, root mean square error, and standard deviation (<xref ref-type="bibr" rid="B114">Jolliff et al., 2009</xref>). We have added also a graphical illustration of the model&#x2019;s performance separated for each zone along with their temporal scale and type of observational data used to validate the model variables, see <xref ref-type="fig" rid="F3">Figures 3</xref>&#x2013;<xref ref-type="fig" rid="F7">7</xref>.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Overview of the biogeochemical models reviewed in this work showing their model approach, physical model, resolution, Nutrient/element cycling, the number of the living/non-living components and sediments formulation.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Ocean</th>
<th rowspan="2" align="center">Zone</th>
<th rowspan="2" align="center">Model approach</th>
<th rowspan="2" align="center">Physical model</th>
<th colspan="2" align="center">Resolution&#x2a;</th>
<th colspan="6" align="center">Nutrient/element cycling&#x2a;</th>
<th colspan="6" align="center">Living/non-living components</th>
<th rowspan="2" align="center">Sediments</th>
</tr>
<tr>
<th align="center">Vertical layers</th>
<th align="center">Horizontal</th>
<th align="center">Fe</th>
<th align="center">N</th>
<th align="center">P</th>
<th align="center">Si</th>
<th align="center">O<sub>2</sub>
</th>
<th align="center">C</th>
<th align="center">&#x23; of phytoplankton</th>
<th align="center">&#x23; of zooplankton</th>
<th align="center">&#x23; of detritus</th>
<th align="center">&#x23; of bacteria</th>
<th align="center">DOM</th>
<th align="center">POM</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Global</td>
<td align="left"/>
<td align="center">NOBM<sup>1</sup>
</td>
<td align="center">GCM</td>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="center">4</td>
<td align="center">1</td>
<td align="center">2</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Global</td>
<td align="left"/>
<td align="center">HAMOCC5<sup>2</sup>
</td>
<td align="center">LSG</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="center" style="background-color:#FFCC00">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">1</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">Balance</td>
</tr>
<tr>
<td align="center">Global</td>
<td align="left"/>
<td align="center">ERSEM<sup>3</sup>
</td>
<td align="center">GOTM</td>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="center" style="background-color:#FFF2CC">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">4</td>
<td align="center">3</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">Meta-mod</td>
</tr>
<tr>
<td align="center">Global</td>
<td align="left"/>
<td align="center">Moore<sup>4</sup>
</td>
<td align="center">CCSM</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="center" style="background-color:#FFF2CC">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">4</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">Meta-mod</td>
</tr>
<tr>
<td align="center">Global</td>
<td align="left"/>
<td align="center">Moore<sup>5</sup>
</td>
<td align="center">CCSM</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="center" style="background-color:#FFF2CC">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">4</td>
<td align="center">1</td>
<td align="center">2</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Global</td>
<td align="left"/>
<td align="center">PlankTOM<sup>6</sup>
</td>
<td align="center">NEMO</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">3</td>
<td align="center">2</td>
<td align="center">7</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Global</td>
<td align="left"/>
<td align="center">PISCES<sup>7</sup>
</td>
<td align="center">NEMO</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="center" style="background-color:#FFCC00">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">3</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">Meta-mod</td>
</tr>
<tr>
<td align="center">Global</td>
<td align="left"/>
<td align="center">DARWIN<sup>8</sup>
</td>
<td align="center">MITgcm</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="center" style="background-color:#FFCC00">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center">8</td>
<td align="center">2</td>
<td align="center">2</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">Meta-mod</td>
</tr>
<tr>
<td align="center">Global</td>
<td align="left"/>
<td align="center">PlankTOM<sup>9</sup>
</td>
<td align="center">NEMO</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">6</td>
<td align="center">3</td>
<td align="center">3</td>
<td align="center">1</td>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Global</td>
<td align="left"/>
<td align="center">PISCES<sup>10</sup>
</td>
<td align="center">NEMO</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">2</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">Meta-mod</td>
</tr>
<tr>
<td align="center">Global</td>
<td align="left"/>
<td align="center">Moore<sup>11</sup>
</td>
<td align="center">NCAR-CSM1</td>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FFCC00">&#x2b;</td>
<td align="center">4</td>
<td align="center">1</td>
<td align="center">2</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Global</td>
<td align="left"/>
<td align="center">TOPAZ/PISCES<sup>12</sup>
</td>
<td align="center">NEMO</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center">TOPAZ:3 PISCES: 2</td>
<td align="center">PISCES:2</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Atlantic</td>
<td align="center">Tropical</td>
<td align="center">Fasham<sup>13</sup>
</td>
<td align="center">MOM</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Atlantic</td>
<td align="center">Subtropical</td>
<td align="center">Fasham<sup>14</sup>
</td>
<td align="center">ROMS</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#2F5496"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Atlantic</td>
<td align="center">Subtropical</td>
<td align="center">Fasham<sup>15</sup>
</td>
<td align="center">ROMS</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">4</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Atlantic</td>
<td align="center">Subtropical</td>
<td align="center">Fasham<sup>16</sup>
</td>
<td align="center">ROMS</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#2F5496"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">2</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Atlantic</td>
<td align="center">Subtropical</td>
<td align="center">BFM<sup>17</sup>
</td>
<td align="center">OGCM-MED16</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="left"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">4</td>
<td align="center">4</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Atlantic</td>
<td align="center">Subtropical</td>
<td align="center">ERSEM<sup>18</sup>
</td>
<td align="center">POM</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">4</td>
<td align="center">3</td>
<td align="left"/>
<td align="center">1</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Atlantic</td>
<td align="center">Subtropical</td>
<td align="center">ERSEM<sup>19</sup>
</td>
<td align="center">POM</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="left"/>
<td align="center" style="background-color:#FFCC00">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">4</td>
<td align="center">3</td>
<td align="left"/>
<td align="center">1</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Indian</td>
<td align="center">Tropical</td>
<td align="center">Fasham<sup>20</sup>
</td>
<td align="center">OGCM</td>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left" style="background-color:#B4C6E7"/>
<td align="left"/>
<td align="center" style="background-color:#FFF2CC">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Indian</td>
<td align="center">Tropical</td>
<td align="center">ERSEM<sup>21</sup>
</td>
<td align="center">Princeton/Mellor&#x2013;Yamada</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#B4C6E7"/>
<td align="left"/>
<td align="center" style="background-color:#FFF2CC">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">4</td>
<td align="center">3</td>
<td align="center">2</td>
<td align="center">1</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Indian</td>
<td align="center">Tropical</td>
<td align="center">McCreary<sup>22</sup>
</td>
<td align="center">Four-layer model</td>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left"/>
<td align="center" style="background-color:#FFF2CC">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Indian</td>
<td align="center">Tropical</td>
<td align="center">Fasham<sup>23</sup>
</td>
<td align="center">MOM</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left"/>
<td align="center" style="background-color:#FFF2CC">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Indian</td>
<td align="center">Tropical</td>
<td align="center">PISCES<sup>24</sup>
</td>
<td align="center">NEMO</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="center" style="background-color:#FFCC00">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">3</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Indian</td>
<td align="center">Tropical</td>
<td align="center">PISCES<sup>25</sup>
</td>
<td align="center">NEMO</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">3</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Indian</td>
<td align="center">Tropical</td>
<td align="center">McCreary<sup>26</sup>
</td>
<td align="center">Six-layer model</td>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">2</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Indian</td>
<td align="center">Tropical</td>
<td align="center">Fasham<sup>27</sup>
</td>
<td align="center">ROMS</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="left"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="left"/>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Indian</td>
<td align="center">Tropical</td>
<td align="center">ERSEM<sup>28</sup>
</td>
<td align="center">GOTM</td>
<td align="left" style="background-color:#2F5496"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="center">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center">4</td>
<td align="center">3</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Indian</td>
<td align="center">Tropical</td>
<td align="center">Fasham<sup>29</sup>
</td>
<td align="center">ROMS</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#2F5496"/>
<td align="left"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="left"/>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="left"/>
<td align="left"/>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Indian</td>
<td align="center">Tropical</td>
<td align="center">PISCES<sup>30</sup>
</td>
<td align="center">ROMS</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="center" style="background-color:#FFCC00">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">3</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Indian</td>
<td align="center">Tropical</td>
<td align="center">NOBM<sup>31</sup>
</td>
<td align="center">OGCM</td>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">4</td>
<td align="center">1</td>
<td align="center">3</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Indian</td>
<td align="center">Tropical</td>
<td align="center">TOPAZ<sup>32</sup>
</td>
<td align="center">MOM</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="center" style="background-color:#FFF2CC">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">3</td>
<td align="left"/>
<td align="center">1</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">Sed-Box</td>
</tr>
<tr>
<td align="center">Indian</td>
<td align="center">Tropical</td>
<td align="center">Fasham<sup>33</sup>
</td>
<td align="center">ROMS</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="left"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="left"/>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Southern</td>
<td align="center">HNLC</td>
<td align="center">PlankTOM<sup>34</sup>
</td>
<td align="center">NEMO</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FFCC00">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">6</td>
<td align="center">3</td>
<td align="center">3</td>
<td align="center">1</td>
<td align="left"/>
<td align="left"/>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Southern</td>
<td align="center">HNLC</td>
<td align="center">NOBM<sup>35</sup>
</td>
<td align="center">OGCM</td>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">4</td>
<td align="center">1</td>
<td align="center">3</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Southern</td>
<td align="center">HNLC</td>
<td align="center">DARWIN<sup>36</sup>
</td>
<td align="center">MITgcm</td>
<td align="left" style="background-color:#2F5496"/>
<td align="left" style="background-color:#2F5496"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">2</td>
<td align="center">2</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Southern</td>
<td align="center">HNLC</td>
<td align="center">PISCES<sup>37</sup>
</td>
<td align="center">NEMO</td>
<td align="left" style="background-color:#2F5496"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="center" style="background-color:#FFCC66">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">2</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Southern</td>
<td align="center">Polar</td>
<td align="center">DARWIN<sup>38</sup>
</td>
<td align="center">MITgcm</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">6</td>
<td align="center">2</td>
<td align="left"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Southern</td>
<td align="center">Polar</td>
<td align="center">Chai<sup>39</sup>
</td>
<td align="center">ROMS</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#2F5496"/>
<td align="center" style="background-color:#FFCC00">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">1</td>
<td align="left"/>
<td align="left"/>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Southern</td>
<td align="center">HNLC</td>
<td align="center">TOPAZ<sup>40</sup>
</td>
<td align="center">ESM2M</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">3</td>
<td align="left"/>
<td align="center">2</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">Sed-Box</td>
</tr>
<tr>
<td align="center">Arctic</td>
<td align="center">Polar</td>
<td align="center">PISCES<sup>41</sup>
</td>
<td align="center">MITgcm</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">2</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Arctic</td>
<td align="center">Polar</td>
<td align="center">21 biogeochemical models<sup>42</sup> <sup>c)</sup>
</td>
<td align="center">-</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="center">Arctic</td>
<td align="center">Polar</td>
<td align="center">REcoM2<sup>43</sup>
</td>
<td align="center">FESOM</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="center">&#x2b;</td>
<td align="center" style="background-color:#FFCC00">&#x2b;</td>
<td align="left"/>
<td align="center" style="background-color:#FFCC00">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">2</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Arctic</td>
<td align="center">Polar</td>
<td align="center">BLING<sup>44</sup>
</td>
<td align="center">NEMO</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Arctic</td>
<td align="center">Polar</td>
<td align="center">DARWIN<sup>45</sup>
</td>
<td align="center">MITgcm</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">5</td>
<td align="center">2</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Pacific</td>
<td align="center">Tropical</td>
<td align="center">Leonard<sup>46</sup>
</td>
<td align="center">OGCM</td>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">Model-layer</td>
</tr>
<tr>
<td align="center">Pacific</td>
<td align="center">Tropical</td>
<td align="center">Chai<sup>47</sup>
</td>
<td align="center">ROMS</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">2</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">Balance</td>
</tr>
<tr>
<td align="center">Pacific</td>
<td align="center">Subtropical</td>
<td align="center">Fasham<sup>48</sup>
</td>
<td align="center">ROMS</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#2F5496"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">2</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Pacific</td>
<td align="center">Tropical</td>
<td align="center">Fasham<sup>49</sup>
</td>
<td align="center">ROMS</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#2F5496"/>
<td align="left"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">4</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Pacific</td>
<td align="center">Tropical</td>
<td align="center">PISCES<sup>50</sup>
</td>
<td align="center">ROMS</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#2F5496"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">3</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Pacific</td>
<td align="center">Tropical</td>
<td align="center">TOPAZ<sup>51</sup>
</td>
<td align="center">GOTM</td>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left"/>
<td align="center" style="background-color:#FFF2CC">&#x2b;</td>
<td align="center" style="background-color:#FFF2CC">&#x2b;</td>
<td align="center" style="background-color:#FFF2CC">&#x2b;</td>
<td align="center" style="background-color:#FFF2CC">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center">3</td>
<td align="left"/>
<td align="center">1</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">Sed-Box</td>
</tr>
<tr>
<td align="center">Pacific</td>
<td align="center">Tropical</td>
<td align="center">Chai<sup>52</sup>
</td>
<td align="center">ROMS</td>
<td align="left" style="background-color:#2F5496"/>
<td align="left" style="background-color:#D9E2F3"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">3</td>
<td align="left"/>
<td align="left"/>
<td align="center">&#x2b;</td>
<td align="center">Meta-Mod</td>
</tr>
<tr>
<td align="center">Pacific</td>
<td align="center">Tropical</td>
<td align="center">Fasham<sup>53</sup>
</td>
<td align="center">ROMS</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#2F5496"/>
<td align="left"/>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">2</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
<tr>
<td align="center">Pacific</td>
<td align="center">Tropical</td>
<td align="center">Kearney<sup>54</sup>
</td>
<td align="center">Bering 10K ROMS</td>
<td align="left" style="background-color:#8EAADB"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">2</td>
<td align="center">5</td>
<td align="center">2</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">Model-layer</td>
</tr>
<tr>
<td align="center">Pacific</td>
<td align="center">HNLC</td>
<td align="center">Chai<sup>55</sup>
</td>
<td align="center">ROMS</td>
<td align="left" style="background-color:#2F5496"/>
<td align="left" style="background-color:#8EAADB"/>
<td align="center" style="background-color:#FFCC00">&#x2b;</td>
<td align="center" style="background-color:#FF9900">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="center">&#x2b;</td>
<td align="left"/>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">4</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">No</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>
<sup>1) (</sup>
<xref ref-type="bibr" rid="B96">Gregg et al., 2003</xref>), <sup>2) (</sup>
<xref ref-type="bibr" rid="B9">Aumont et al., 2003</xref>), <sup>3) (</sup>
<xref ref-type="bibr" rid="B19">Blackford et al., 2004</xref>), <sup>4) (</sup>
<xref ref-type="bibr" rid="B178">Moore et al., 2004</xref>), <sup>5) (</sup>
<xref ref-type="bibr" rid="B178">Moore et al., 2004</xref>), <sup>6) (</sup>
<xref ref-type="bibr" rid="B282">Buitenhuis et al., 2013</xref>), <sup>7) (</sup>
<xref ref-type="bibr" rid="B8">Aumont et al., 2015</xref>), <sup>8) (</sup>
<xref ref-type="bibr" rid="B58">Dutkiewicz et al., 2015</xref>), <sup>9) (</sup>
<xref ref-type="bibr" rid="B281">Andrews et al., 2017</xref>), <sup>10) (</sup>
<xref ref-type="bibr" rid="B8">Aumont et al., 2015</xref>), <sup>11) (</sup>
<xref ref-type="bibr" rid="B291">Pant et al., 2018</xref>), <sup>12) (</sup>
<xref ref-type="bibr" rid="B116">Jung et al., 2019a</xref>)<sup>, 13) (</sup>
<xref ref-type="bibr" rid="B290">Oschlies and Gar&#xe7;on, 1999</xref>), <sup>14) (</sup>
<xref ref-type="bibr" rid="B74">Fennel et al., 2008</xref>),<sup>15) (</sup>
<xref ref-type="bibr" rid="B52">Druon et al., 2010</xref>), <sup>16) (</sup>
<xref ref-type="bibr" rid="B271">Xue et al., 2013</xref>)<sup>, 17) (</sup>
<xref ref-type="bibr" rid="B138">Lazzari et al., 2016</xref>)<sup>, 18) (</sup>
<xref ref-type="bibr" rid="B119">Kalaroni et al., 2019</xref>)<sup>, 19) (</sup>
<xref ref-type="bibr" rid="B120">Kalaroni et al., 2020</xref>)<sup>, 20) (</sup>
<xref ref-type="bibr" rid="B292">Ryabchenko et al., 1998</xref>)<sup>, 21) (</sup>
<xref ref-type="bibr" rid="B20">Blackford and Burkill, 2002</xref>)<sup>, 22</sup> (<xref ref-type="bibr" rid="B107">Hood et al., 2006</xref>), <sup>23) (</sup>
<xref ref-type="bibr" rid="B123">Kawamiya and Oschlies, 2003</xref>)<sup>, 24) (</sup>
<xref ref-type="bibr" rid="B126">Kon&#xe9; et al., 2009</xref>)<sup>, 25) (</sup>
<xref ref-type="bibr" rid="B203">Resplandy et al., 2011</xref>)<sup>, 26) (</sup>
<xref ref-type="bibr" rid="B289">McCreary et al., 2013</xref>)<sup>, 27) (</sup>
<xref ref-type="bibr" rid="B131">Lachkar et al., 2017</xref>)<sup>, 28) (</sup>
<xref ref-type="bibr" rid="B209">Sankar et al., 2018</xref>)<sup>, 29) (</sup>
<xref ref-type="bibr" rid="B130">Lachkar et al., 2019</xref>)<sup>, 30) (</sup>
<xref ref-type="bibr" rid="B287">Guieu et al., 2019</xref>)<sup>, 31) (</sup>
<xref ref-type="bibr" rid="B43">Das et al., 2019</xref>)<sup>, 32) (</sup>
<xref ref-type="bibr" rid="B217">Sharada et al., 2020</xref>)<sup>, 33) (</sup>
<xref ref-type="bibr" rid="B132">Lachkar et al., 2020</xref>)<sup>, 34) (</sup>
<xref ref-type="bibr" rid="B139">Le Qu&#xe9;r&#xe9; et al., 2016</xref>)<sup>, 35) (</sup>
<xref ref-type="bibr" rid="B294">Trull et al., 2018</xref>)<sup>, 36) (</sup>
<xref ref-type="bibr" rid="B249">Uchida et al., 2019</xref>)<sup>, 37) (</sup>
<xref ref-type="bibr" rid="B188">Person et al., 2019</xref>)<sup>, 38) (</sup>
<xref ref-type="bibr" rid="B150">Lo et al., 2019</xref>)<sup>, 39) (</sup>
<xref ref-type="bibr" rid="B288">Jiang et al., 2019</xref>)<sup>, 40) (</sup>
<xref ref-type="bibr" rid="B24">Bronselaer et al., 2020</xref>)<sup>, 41) (</sup>
<xref ref-type="bibr" rid="B162">Manizza et al., 2011</xref>)<sup>, 42) (</sup>
<xref ref-type="bibr" rid="B13">Babin et al., 2016</xref>)<sup>, 43) (</sup>
<xref ref-type="bibr" rid="B214">Schourup-Kristensen et al., 2018</xref>)<sup>, 44) (</sup>
<xref ref-type="bibr" rid="B30">Castro de la Guardia et al., 2019</xref>)<sup>, 45) (</sup>
<xref ref-type="bibr" rid="B163">Manizza et al., 2012</xref>)<sup>, 46) (</sup>
<xref ref-type="bibr" rid="B283">Christian et al., 2001</xref>)<sup>, 47) (</sup>
<xref ref-type="bibr" rid="B270">Xiu and Chai, 2011</xref>)<sup>, 48) (</sup>
<xref ref-type="bibr" rid="B286">Gan et al., 2014</xref>)<sup>, 49) (</sup>
<xref ref-type="bibr" rid="B111">Ji et al., 2017</xref>)<sup>, 50) (</sup>
<xref ref-type="bibr" rid="B295">Vergara et al., 2017</xref>)<sup>, 51) (</sup>
<xref ref-type="bibr" rid="B115">Jung et al., 2019b</xref>)<sup>, 52) (</sup>
<xref ref-type="bibr" rid="B156">Ma et al., 2019</xref>)<sup>, 53) (</sup>
<xref ref-type="bibr" rid="B153">Lu et al., 2020</xref>)<sup>, 54) (</sup>
<xref ref-type="bibr" rid="B124">Kearney et al., 2020</xref>), <sup>55) (</sup>
<xref ref-type="bibr" rid="B277">Zhang et al., 2021</xref>). &#x2a;For the surface nutrients: dark orange: 0.8&#x2264;r &#x3c; 1; Bias: &#x3c; 0.5; RMSD &#x3c;0.2, Medium orange: 0.5 &#x2264;r &#x3c; 0.8; 0.5&#x2264;Bias&#x3c; 1; 0.5&#x3c; RMSD &#x3c;0.2 and Light orange: r &#x3c; 0.5; Bias &#x2265; 1; RMSD &#x2265;0.5. &#x2a;For the vertical resolution: dark blue: &#x3e; 50 layers, medium blue: 20&#x3c;layers&#x3c; 50, light blue: &#x3c; 20 layers. &#x2a;For the horizontal resolution: dark blue: &#x3c; 0.1degrees, medium blue: 0.1&#x3c;degrees&#x3c;0.5 and light blue: &#x3e;0.5 degrees. For the chlorophyll (Chl): dark green. DOM, dissolved organic matter. POM, particulate organic matter.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>The common statistical metrics for model assessment used in the analysed studies.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Method</th>
<th align="left">Description</th>
<th align="left">Equation</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">RMSE</td>
<td align="left">Calculate the model&#x2019;s error between the predicted data (<inline-formula id="inf1">
<mml:math id="m5">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:math>
</inline-formula> and the observational data (<inline-formula id="inf2">
<mml:math id="m6">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>).</td>
<td align="center">
<inline-formula id="inf3">
<mml:math id="m7">
<mml:mrow>
<mml:msqrt>
<mml:mrow>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:mfrac>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:msqrt>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
<tr>
<td align="left">R</td>
<td align="left">Correlation coefficient which determines how linearly connected the observations are to their model equivalents. r &#x3d; 1 means a perfect correlation or relationship. r &#x3d; 0 means there is no relationship, and r &#x3c; 0 indicates that the two data are negatively correlated.</td>
<td align="center">
<inline-formula id="inf4">
<mml:math id="m8">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mover accent="true">
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xaf;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mover accent="true">
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xaf;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:msqrt>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mover accent="true">
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xaf;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2211;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mover accent="true">
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xaf;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:msqrt>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
<tr>
<td align="left">R<sup>2</sup>
</td>
<td align="left">Coefficient of determination (between 0 and 1) which measures how well the model predicts the observed data. As it is closer to 1 means strong correlation while closer to 0 means weak correlation between the predicted and observed data. It is defined</td>
<td align="center">
<inline-formula id="inf5">
<mml:math id="m9">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
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<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:mi>y</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:msqrt>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:msubsup>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2212;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msqrt>
<mml:mi>n</mml:mi>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="" close="]" separators="|">
<mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2212;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
<tr>
<td align="left">Bias</td>
<td align="left">Bias is to what degree the model overestimates (bias&#x3e;0) or underestimates (bias&#x3c;0) the observed data.</td>
<td align="center">
<inline-formula id="inf6">
<mml:math id="m10">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Biogeochemical variables performance for some of the models applied in the tropical ecosystems along with their temporal scale and type of observational data used to validate the model components.</p>
</caption>
<graphic xlink:href="fenvs-11-1198856-g003.tif"/>
</fig>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Biogeochemical variables performance for some of the models applied in the tropical Pacific ecosystems along with their temporal scale and type of observational data used to validate the model components.</p>
</caption>
<graphic xlink:href="fenvs-11-1198856-g004.tif"/>
</fig>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Biogeochemical variables performance for some of the models applied in the temperate, and tropical to subtropical ecosystems along with their temporal scale and type of observational data used to validate the model components.</p>
</caption>
<graphic xlink:href="fenvs-11-1198856-g005.tif"/>
</fig>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Biogeochemical variables performance for some of the models applied in the polar/subpolar ecosystems along with their temporal scale and type of observational data used to validate the model components.</p>
</caption>
<graphic xlink:href="fenvs-11-1198856-g006.tif"/>
</fig>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Biogeochemical variables performance for some of the models applied in the HNLC zone along with their temporal scale and type of observational data used to validate the model components.</p>
</caption>
<graphic xlink:href="fenvs-11-1198856-g007.tif"/>
</fig>
<sec id="s3-1">
<title>3.1 Tropical zones</title>
<p>The aforementioned biogeochemical models have been applied in various tropical seas due to their high dynamism and significant biogeochemical activity, making them among the most active zones in the ocean (<xref ref-type="bibr" rid="B151">L&#xf8;nborg et al., 2021</xref>). This section encompasses multiple regions, including the tropical Indian Ocean (specifically the Arabian Sea), the South China Sea, the tropical Pacific Ocean, and the oxygen minimum zone in the Arabian Sea. One prime example of a tropical ecosystem is the Indian Ocean, which experiences the world&#x2019;s most significant monsoon system caused by the seasonal warming and cooling of massive air masses (<xref ref-type="bibr" rid="B262">Wiggert et al., 2005</xref>). In winter and summer, the wind patterns near the ocean change, with the southwest monsoon (SWM) providing half of the year&#x2019;s wind and the northeast monsoon (NEM) providing the other half (<xref ref-type="bibr" rid="B262">Wiggert et al., 2005</xref>). The dynamics of the Arabian Sea&#x2019;s (the most extensively studied ecosystem in the Indian Ocean) phytoplankton bloom clearly show a temporal alignment with the southwest monsoon and northeast monsoon (<xref ref-type="bibr" rid="B158">Madhupratap et al., 1996</xref>; <xref ref-type="bibr" rid="B262">Wiggert et al., 2005</xref>). Strong south-westerly winds during the summer propel coastal upwelling and offshore movement of entrained nutrients, which promote the Arabian Sea&#x2019;s observed phytoplankton blooms (<xref ref-type="bibr" rid="B23">Brock and Mcclain, 1992</xref>; <xref ref-type="bibr" rid="B104">Hitchcock et al., 2000</xref>; <xref ref-type="bibr" rid="B148">Lierheimer and Banse, 2002</xref>). Modest north-easterly winds during the winter carry cool, dry air from the Tibetan Plateau over the northern Arabian Sea (<xref ref-type="bibr" rid="B109">Huang, 2010</xref>). Additionally, convective mixing during NEM entrains nutrients and promotes biological activity north of 15&#xb0;N (<xref ref-type="bibr" rid="B158">Madhupratap et al., 1996</xref>). Thus, primary productivity and nutrients budgets in the Arabian Sea, spanning a temporal scale of seasonal variations and a spatial scale ranging from 5&#xb0;S to 27&#xb0;N are highly impacted by the seasonal cycle and mesoscale impacts (<xref ref-type="bibr" rid="B203">Resplandy et al., 2011</xref>). The primary production in terms of surface Chl-<italic>a</italic> production in the Arabian Sea is widely studied using several types of ocean biogeochemical models. For example, the estimated surface Chl-<italic>a</italic> by PISCES coupled to the Nucleus for European Modelling of the Ocean (NEMO) is compared with the weekly climatology of SeaWiFS (Sea-viewingWide Field-of-view Sensor Data). The PISCES-NEMO reproduced surface Chl-<italic>a</italic> levels of more than 0.2&#xa0;mg&#xa0;m<sup>-3</sup> during the NEM. It also predicted the maximum intensity of surface Chl-<italic>a</italic>, which exceeds 0.5&#xa0;mg&#xa0;m<sup>-3</sup>, but underpredicted surface Chl-<italic>a</italic> by 30%&#x2013;50% north of 20&#xb0;N. This bias was found in other studies and may be attributed to the lack of diurnal layer mixing (<xref ref-type="bibr" rid="B123">Kawamiya and Oschlies, 2003</xref>; <xref ref-type="bibr" rid="B263">Wiggert et al., 2006</xref>; <xref ref-type="bibr" rid="B126">Kon&#xe9; et al., 2009</xref>). The bias in the bloom dynamics is explained by the lack of deepening of the mixed layer and nutrient feed (<xref ref-type="bibr" rid="B263">Wiggert et al., 2006</xref>), and light limitation (<xref ref-type="bibr" rid="B126">Kon&#xe9; et al., 2009</xref>). Another cause of inconsistencies in the PISCES model (<xref ref-type="bibr" rid="B203">Resplandy et al., 2011</xref>) is partially linked to the underprediction of silicate input from the Sea of Oman. PISCES captured the observed high surface Chl-<italic>a</italic> along the coasts of Somalia and southwestern India, reaching values higher than 0.4&#xa0;mg&#xa0;m<sup>-3</sup> during the SWM. On the other hand, it underestimated Chl-<italic>a</italic> in Oman. These inconsistencies can be attributed to the overprediction of the offshore advection by the Great Whirl and the Socotra Passage, resulting in an excessive outflow of warmer and oligotrophic waters from the Aden Gulf. Therefore, PISCES-NEMO showed better agreement with observations (seasonal SeaWiFS data) for the surface Chl-<italic>a</italic> distribution than in (<xref ref-type="bibr" rid="B126">Kon&#xe9; et al., 2009</xref>) with a correlation coefficient (r) around 0.6. These comparisons encompass a spatial scale ranging from 30&#xb0;S to 30&#xb0;N and from 30&#xb0;E to 120&#xb0;E, with a focus on seasonal variations. In addition to PISCES, the PFT model NOBM coupled with the oceanic general circulation and radiative forcing model was able to capture the intra-seasonal variability of the Indian summer monsoon, specifically focusing on the spatial scale of the Bay of Bengal (BOB) (6&#xb0;&#x2013;22&#xb0; N; 80&#xb0;&#x2013;100&#xb0; E) and Arabian Sea (AS) (3&#xb0;&#x2013;17&#xb0; N; 55&#xb0;&#x2013;73.5&#xb0; E) in the North Indian Ocean. The study showed important differences between the two regions indicating that the Arabian Sea is richer in nutrients than the Bay of Bengal with a coefficient of determination (R<sup>2</sup>) around 0.78 for the monthly mean surface Chl-<italic>a</italic> (<xref ref-type="bibr" rid="B43">Das et al., 2019</xref>). Furthermore, surface Chl-<italic>a</italic> is reproduced by Fasham-ROMS (Regional Ocean Modeling System), in the study region, which extends in latitude from 5&#xb0;S to 30&#xb0;N and in longitude from 34&#xb0;E to 78&#xb0;E. The performance of the model is evaluated by comparing its outputs with seasonal SeaWiFs observations, resulting in correlation coefficient ranging from 0.69 in summer to 0.74 in winter (<xref ref-type="bibr" rid="B131">Lachkar et al., 2017</xref>).</p>
<p>In addition to surface Chl-<italic>a</italic> estimation, surface nitrogen content in the Arabian Sea is estimated by the European Regional Seas Ecosystem Model (ERSEM) coupled with a 1D Princeton/Mellor&#x2013;Yamada (<xref ref-type="bibr" rid="B20">Blackford and Burkill (2002)</xref>. The model performance was assessed at three stations located at 19&#xb0;N 59&#xb0;E, 16&#xb0;N 62&#xb0;E, and 8&#xb0;N 67&#xb0;E, covering a seasonal timescale. The coupled model has a bias for surface nitrate concentration (3&#xa0;mmol&#xa0;m<sup>-3</sup>) and lacks horizontal advective processes, which might be enhanced by including diurnal physical processes (horizontal advection, vertical mixing, or tidal currents). Another study by using Fasham-ROMS indicated a correlation coefficient (r) of 0.88 with observation for surface nitrate in summer. Nitrogen is not the only limiting nutrient affecting phytoplankton growth in the Arabian Sea and the ignorance of other components such as iron may underestimate nitrogen budget in the region. Iron, as an important limiting nutrient in the Arabian Sea, plays a significant role in facilitating nitrogen fixation, which is a crucial process driving biological productivity. However, nitrogen fixation is not taken into account in the NPZD, which may amplify the impact of denitrification on the nitrogen budgets in the Arabian Sea (<xref ref-type="bibr" rid="B131">Lachkar et al., 2017</xref>). A few studies have been conducted to examine the effect of iron limitation on global biogeochemical processes, including those in the Indian Ocean. For instance, studies using PFT approach, such as PISCES-ROMS and TOPAZ-MOM (<xref ref-type="bibr" rid="B115">Jung et al., 2019b</xref>) have explored the implications of iron limitation on various aspects, including macronutrient availability and ecosystem dynamics. Unlike the previous version of PISCES in (<xref ref-type="bibr" rid="B7">Aumont and Bopp, 2006</xref>), this version incorporated new parametrizations for iron chemistry and nitrogen fixation. PISCES exhibited a better iron estimate than TOPAZ, whereas TOPAZ showed larger bias with observation (SeaWiFS) (1.5 nMol m<sup>-3</sup>) (<xref ref-type="bibr" rid="B115">Jung et al., 2019b</xref>).</p>
<p>Another prominent feature of the Arabian Sea is its oxygen minimum zone which is noted for its low oxygen concentrations (&#x3c;4 mmol/m<sup>-3</sup>) at depths of 150&#x2013;1,250&#xa0;m in the central part of the Arabian Sea. Thus, the dynamics of the oxygen minimum zone (OMZ) at spatial coordinates (65&#xb0;E, 13&#xb0;N) is studied by applying ERSEM coupled with General Ocean Turbulence Model (GOTM). The model incorporates most of the biogeochemical processes driving the dynamics of OMZ with the inclusion of denitrification process which was not considered in <xref ref-type="bibr" rid="B27">Butensch&#xf6;n et al. (2016)</xref>. ERSEM-GOTM ignores the episodic intrusion of oxygen within the OMZ which may play a role in maintaining aerobic microorganisms. Therefore, the aerobic biomass within the OMZ is maintained by the residual initial conditions (<xref ref-type="bibr" rid="B209">Sankar et al., 2018</xref>). In addition, the model is unable to reproduce meso-zooplankton at depth, and the discrepancy between the estimates and the climatological seasonal cycles of nutrients and oxygen at depth might be due to the absence of lateral circulation in the model. Further studies on the OMZs in the Arabian Sea were investigated by Lachkar using a simple NPZD approach with the addition of the oxygen cycle (Fasham- ROMS) (<xref ref-type="bibr" rid="B131">Lachkar et al., 2017</xref>; <xref ref-type="bibr" rid="B130">Lachkar et al., 2019</xref>; <xref ref-type="bibr" rid="B132">Lachkar et al., 2020</xref>). Fasham-ROMS indicated that the primary productivity and OMZ are highly impacted by monsoon wind intensification, with an overall high correlation coefficient (r) 0.93 for oxygen (both seasons) in the upper layer. While the model&#x2019;s horizontal grid resolution of 1/12&#xb0; and vertical grid consisting of 32 sigma layers allow for some representation of eddy dynamics, the resolution may still be too coarse to fully capture all eddy processes.The OMZ intensity (oxygen concentration) has also been overestimated because of the underestimation of the northern Arabian Sea ventilation. Studies on OMZ in the Arabian Gulf are still limited.</p>
<p>In addition to the Indian Ocean, some parts of the Pacific Ocean are also located in the tropical zone, and south China Sea, which is the largest marginal seas of the West Pacific Ocean (<xref ref-type="bibr" rid="B192">Qi-zhou et al., 1994</xref>), is an example of an ecosystem that belongs to this region. Similar to the Arabian Sea, this region is largely controlled by seasonal monsoon circulation. Strong northeast (NE) winter monsoon and weaker southeast (SE) summer monsoon predominate at the sea surface of the South China Sea (SCS) (<xref ref-type="bibr" rid="B192">Qi-zhou et al., 1994</xref>; <xref ref-type="bibr" rid="B146">Li et al., 2021</xref>). Studies have shown a clear response of Chl-<italic>a</italic> and temperature of the upper oceanic conditions to atmospheric forcing in the SCS (<xref ref-type="bibr" rid="B232">Sun et al., 2009</xref>; <xref ref-type="bibr" rid="B233">Sun et al., 2010</xref>; <xref ref-type="bibr" rid="B274">Yang et al., 2010</xref>; <xref ref-type="bibr" rid="B278">Zhao et al., 2014</xref>). Estimates of the mean surface Chl-<italic>a</italic> has been reported with varying performances. A correlation coefficient (r) of 0.85 for the annual mean surface Chl-<italic>a</italic> is obtained by (<xref ref-type="bibr" rid="B115">Jung et al., 2019b</xref>) using both global PISCES and TOPAZ coupled to NEMO representing surface Chl-<italic>a</italic> concentration conditions (i.e., phytoplankton blooms) in the tropical Pacific. Furthermore, the monthly mean surface Chl-<italic>a</italic> was determined by PISCES-NEMO and TOPAZ-NEMO (<xref ref-type="bibr" rid="B115">Jung et al., 2019b</xref>) with r equal to 0.6 and 0.75, respectively. However, both models overpredicted the zonal averaged Chl-<italic>a</italic> in the Pacific Ocean east of Japan by 67%, primarily because of errors in the Kuroshio current path, as seen in low-resolution models (<xref ref-type="bibr" rid="B92">Gnanadesikan et al., 2002</xref>; <xref ref-type="bibr" rid="B57">Dutkiewicz et al., 2005</xref>; <xref ref-type="bibr" rid="B7">Aumont and Bopp, 2006</xref>). Nevertheless, the regional Chai&#x2019;s NPZD model (<xref ref-type="bibr" rid="B32">Chai et al., 1996</xref>) configured for the central South China Sea was modified by adding phosphate, silicate, dissolved oxygen, DIC, two phytoplankton groups (diatoms, small phytoplankton) and their chlorophyll components (Chl1 and Chl2) has shown a correlation coefficient of approximately 0.62 for the monthly mean surface Chl-<italic>a</italic> in the SCS compared to SeaWiFS data (<xref ref-type="bibr" rid="B156">Ma et al., 2019</xref>). Other NPZD models were also applied in the tropical Pacific seas (SCS) to study the physical processes of mesoscale eddies&#x2019; impacts on biology such as in (<xref ref-type="bibr" rid="B270">Xiu and Chai, 2011</xref>). The study covered the entire Pacific Ocean, spanning from 45&#xb0;S to 65&#xb0;N and from 99&#xb0;E to 70&#xb0;W. The model exhibited a bias of approximately 0.05&#xa0;mg&#xa0;m<sup>-3</sup> (April) and &#x223c;0.1&#xa0;mg&#xa0;m<sup>-3</sup> (September) for mean surface Chl-<italic>a</italic> concentrations when compared to SeaWiFS data for the respective months.</p>
<p>Other biogeochemical components such as nutrients including nitrate, phosphate, silicate, and iron have been estimated using global ocean biogeochemical models in the Pacific region. Higher positive bias for nutrients is obtained using the global TOPAZ-NEMO model compared to PISCES-NEMO in the Southern Pacific Ocean using the same physical model setup. With bias of 4.5&#xa0;&#x3bc;mol&#xa0;kg<sup>&#x2212;1</sup>,0.32&#xa0;&#x3bc;mol&#xa0;kg<sup>&#x2212;1</sup>, and 16&#xa0;&#x3bc;mol&#xa0;kg<sup>&#x2212;1</sup> for nitrate, phosphate, and silicate respectively, with a higher positive bias in the central and southern Pacific for silicate (8&#xa0;&#x3bc;mol&#xa0;kg<sup>&#x2212;1</sup>). With regards to a NPZD based approach, Fasham-ROMS exhibited the impact of physical processes, such as lateral and vertical fluxes, as well as vertical diffusion in the shelf water, on nutrient distribution in the SCS (<xref ref-type="bibr" rid="B111">Ji et al., 2017</xref>; <xref ref-type="bibr" rid="B153">Lu et al., 2020</xref>) showing a reasonable linearity between the model estimates and field observations (JGOFS: a global, multidisciplinary program with participants from over 20 countries) for surface nitrate with R<sup>2</sup>: 0.95 (<xref ref-type="bibr" rid="B111">Ji et al., 2017</xref>). In (<xref ref-type="bibr" rid="B111">Ji et al., 2017</xref>), the model domain focused on the northwestern Pacific (NWP) region (3&#xb0;&#x2013;52&#xb0;N, 98&#xb0;&#x2013;158&#xb0;E), while in (<xref ref-type="bibr" rid="B153">Lu et al., 2020</xref>), the model domain extended from approximately 0.95&#xb0;N, 99&#xb0;E in the southwest corner to around 50&#xb0;N, 147&#xb0;E in the northeast corner.</p>
<p>With regards to iron, low surface concentrations of iron were predicted in the North and North Central Pacific, while high concentrations were predicted in the North and Equatorial Indian Ocean using global NOBM (<xref ref-type="bibr" rid="B96">Gregg et al., 2003</xref>). The model domain considered spans from approximately &#x2212;84&#xb0;S to 72&#xb0;N latitude in increments of 1.25&#xb0; longitude by 2/3&#xb0; latitude. The overall correlation coefficient for the annual mean iron with <italic>in situ</italic> data is 0.86 and the reason for the iron overprediction is attributed to the lack of scavenging, excessive remineralization, and slow detritus sinking rate.</p>
</sec>
<sec id="s3-2">
<title>3.2 Temperate, and tropical to subtropical zones</title>
<p>Compared to the tropical zones, the temperate zone is characterized by moderate climate with mean annual temperatures. Average monthly air temperatures in the temperate zone typically exceed 10&#xb0;C during the warmest months while water temperatures generally remain above &#x2212;3&#xb0;C, with a minimum around &#x223c;-2&#xb0;C. (<xref ref-type="bibr" rid="B293">Trewartha and Horn, 1980</xref>). In contrast, the subtropical zones, located between the tropical and temperate zones, are characterized by hot summers and moderate winters. Some parts of the North Atlantic Ocean comprises both temperate and varying tropical to subtropical zones. Biogeochemical studies in this region have focused on understanding primary productivity in continental shelves and coastal areas, which are highly productive ecosystems and are significantly influenced by human activities (<xref ref-type="bibr" rid="B59">Economidou, 1982</xref>; <xref ref-type="bibr" rid="B72">Fennel, 2010</xref>). Additionally, air-sea CO<sub>2</sub> fluxes in coastal waters exhibit greater variability and larger amplitudes compared to fluxes in the open ocean (<xref ref-type="bibr" rid="B246">Tsunogai et al., 1999</xref>; <xref ref-type="bibr" rid="B28">Cai et al., 2003</xref>; <xref ref-type="bibr" rid="B243">Thomas et al., 2004</xref>). For instance, in the Mid Atlantic Bight, located in the central region of the eastern U.S. continental shelf, high primary productivity rates, sediment denitrification, and strong residual circulation contribute to the region&#x2019;s significance as a potential source of organic carbon export to the open ocean (<xref ref-type="bibr" rid="B52">Druon et al., 2010</xref>). In the Northwest North Atlantic and other ecosystems within the region, many studies have utilized simple NPZD models to investigate the influence of physical processes on biological dynamics, rather than aiming to capture the full complexity of ecological interactions. Therefore, this section covers both coastal areas and open sea regions of the Mid Atlantic Bight, northeastern US continental shelves, Georges Bank, Gulf of Mexico, and Mediterranean waters. An example of such modeling approach is demonstrated in (<xref ref-type="bibr" rid="B74">Fennel et al., 2008</xref>), where the distribution of Chl-<italic>a</italic>, an indicator of productivity in the Atlantic regions, is predicted using a NPZD model. The model is coupled with a high-resolution physical model ROMS, which incorporates accurate descriptions of physical processes and an explicit representation of inorganic carbon chemistry and air-sea gas exchange of CO<sub>2</sub> (<xref ref-type="bibr" rid="B74">Fennel et al., 2008</xref>). The model&#x2019;s inclusion of tides in ROMS improves the seasonal mean surface Chl-<italic>a</italic> representations, showing good agreement with SeaWiFS climatology in Georges Bank (correlation coefficients: 0.75 in winter, 0.72 in spring, 0.85 in summer, and 0.83 in fall) (<xref ref-type="bibr" rid="B74">Fennel et al., 2008</xref>). In another study by <xref ref-type="bibr" rid="B52">Druon et al., 2010</xref>, Fennel&#x2019;s model (<xref ref-type="bibr" rid="B74">Fennel et al., 2008</xref>) was further enhanced by incorporating a dissolved organic matter (DOM) module to investigate organic carbon dynamics in the North-eastern U.S. continental shelves. The model demonstrated good agreement with monthly satellite data, particularly in the inner shelf and on Georges Bank, attributing this agreement to tidal mixing and continuous nutrient suppl (Bias: Chl-<italic>a</italic> (with DOM) &#x3d; 4&#xa0;mg&#xa0;m<sup>-3</sup>, Chl-<italic>a</italic> (without DOM) &#x3d; 6&#xa0;mg&#xa0;m<sup>-3</sup>). The inclusion of the DOM module improved the model by capturing the role of dissolved organic matter in nutrient cycling and its influence on primary production in the North-eastern U.S. continental shelf. In a separate study by (<xref ref-type="bibr" rid="B271">Xue et al., 2013</xref>), phosphate cycling was omitted from Fennel&#x2019;s model (<xref ref-type="bibr" rid="B70">Fennel et al., 2011</xref>) because previous studies (<xref ref-type="bibr" rid="B195">Rabalais et al., 2002</xref>) showed that the primary production is generally nitrogen limited in the Louisiana-Texas shelf in the Gulf of Mexico. Therefore, the correlation coefficient of the seasonal mean of simulated and observed (MODIS: Moderate Resolution Imaging Spectroradiometer) surface Chl-<italic>a</italic> for the spring, summer, fall and winter were 0.6, 0.65, 0.53, 0.45 respectively. The simulated data successfully captured the high concentration of surface Chl-<italic>a</italic> in coastal areas close to main rivers, such as the Bay of Campeche, Campeche Bank, and the Louisiana-Texas shelf, whereas Chl-<italic>a</italic> concentrations were very low in the deep ocean. It is important to note that while Louisiana/Texas shelf in the Gulf of Mexico, as discussed in <xref ref-type="bibr" rid="B271">Xue et al. (2013)</xref>, falls outside the tropics, the Gulf of Mexico circulation does include tropical latitudes. This reference to the Gulf of Mexico was mentioned to highlight the omission of phosphate cycling in Fennel&#x2019;s model due to nitrogen limitation in the primary production observed in the Louisiana-Texas shelf (<xref ref-type="bibr" rid="B195">Rabalais et al., 2002</xref>). In contrast to continental shelves and coastal areas of the Mid Atlantic Bight, some areas of the Atlantic Ocean and the Mediterranean Sea shows limitation of phosphate rather than nitrogen. The Mediterranean Sea encompasses the most oligotrophic ecosystems in the global ocean, with low nutrient and low chlorophyll content (<xref ref-type="bibr" rid="B128">Krom et al., 1991</xref>; <xref ref-type="bibr" rid="B54">Durrieu et al., 2011</xref>; <xref ref-type="bibr" rid="B242">Thingstad et al., 2014</xref>), being characterised by strong seasonality as well as highly dynamic system in terms of physics and biology (<xref ref-type="bibr" rid="B185">Ortenzio et al., 2009</xref>; <xref ref-type="bibr" rid="B35">Christaki et al., 2011</xref>). This limitation of phosphate was modelled using ERSEM which accounts for variable stoichiometric formulation in phytoplankton cells allowing the adaptation of internal N:P quota to different limiting environments (<xref ref-type="bibr" rid="B138">Lazzari et al., 2016</xref>). ERSEM reproduced the seasonal cycle and the observed patterns of surface Chl-<italic>a</italic> and inorganic nutrients in the Mediterranean Sea (MS). The interannual variability of Chl-<italic>a</italic> showed an agreement of r: 0.75 with SeaWiFS observation for the MS. However, the model underestimates phytoplankton blooms in the western basin of the MS while overestimates the blooms in the eastern basin during spring chlorophyll peaks. This discrepancy is attributed to the overestimation/underestimation of the winter mixing intensity by the physical model (<xref ref-type="bibr" rid="B119">Kalaroni et al., 2019</xref>). The spatial variability of the simulated surface Chl-<italic>a</italic> was assessed by calculating the correlation coefficient (r) between the model outputs and SeaWiFS observations. The correlation coefficient (r) was found to be 0.64, indicating a moderate positive linear association between the two datasets. The standard deviation of the spatial model variability was computed to be lower than 1 (normalised), suggesting relatively low dispersion of Chl-<italic>a</italic> values across the Mediterranean Sea. The temporal variability, on the other hand, was evaluated using unbiased root mean square differences (RMSDs) for the annual mean surface spatial and temporal variability. The RMSD value for the annual mean surface spatial variability was 0.78, indicating the average magnitude of differences between the model simulations and the observed data. Likewise, the RMSD value for the annual mean surface temporal variability was 0.68, suggesting the average magnitude of differences between the model simulations and the observed data over time. Lower RMSD values indicate better agreement in terms of both spatial and temporal variations.</p>
</sec>
<sec id="s3-3">
<title>3.3 Polar/subpolar and seasonally stratified zones</title>
<p>The effects of climate change, such as a considerable decrease in ice extent and rising sea levels, can exacerbate stratification in polar and subpolar regions (<xref ref-type="bibr" rid="B64">Farmer et al., 2021</xref>). In addition, changes to the global climate system are anticipated to have a significant impact on polar and subpolar marine ecosystems through their effects on water temperature and sea ice cover hence affecting marine production and carbon cycle (<xref ref-type="bibr" rid="B91">Gibson et al., 2020</xref>). This section covers the Arctic Ocean, Antarctic Peninsula, Drake Passage, Scotia Sea, northern Weddell Sea, South Georgia, Barents Sea, Hudson Bay, Beaufort Gyre, Labrador Sea, Baffin Bay, Canadian Arctic Archipelago, Russian shelves (East Siberian Sea), and the Dotson Ice Shelf in West Antarctica, along with the adjacent Amundsen Sea Polynya. Several ocean biogeochemical studies in the polar region focused on the effect of climate change on the carbon cycle (<xref ref-type="bibr" rid="B169">MCGUIRE et al., 2009</xref>; <xref ref-type="bibr" rid="B241">Terhaar et al., 2021</xref>; <xref ref-type="bibr" rid="B240">2019</xref>; <xref ref-type="bibr" rid="B239">2020</xref>; <xref ref-type="bibr" rid="B182">Negrete-garc&#xed;a et al., 2019</xref>; <xref ref-type="bibr" rid="B25">Bruhwiler et al., 2021</xref>) and nutrients dynamics (<xref ref-type="bibr" rid="B101">H&#xe1;t&#xfa;n et al., 2017</xref>; <xref ref-type="bibr" rid="B198">Randelhoff et al., 2018</xref>; <xref ref-type="bibr" rid="B197">2019</xref>; <xref ref-type="bibr" rid="B247">Tuerena et al., 2021</xref>). Therefore, carbon is estimated using biogeochemical models with the inclusion of an explicit representation of the DIC component, such as PISCES-MIT general circulation model (MITgcm), which have been used to qualitatively examine the carbon cycle in the Arctic Ocean and have demonstrated their capacity to capture observed seasonal and regional changes in dissolved pCO<sub>2</sub> (<xref ref-type="bibr" rid="B162">Manizza et al., 2011</xref>). PISCES-MITgcm represented summer levels of surface pCO<sub>2</sub> in the Canadian Archipelago (200&#x2013;250&#xa0;&#xb5;atm) correctly, but underestimated pCO<sub>2</sub> spring values (&#x223c;300&#xa0;&#xb5;atm) relative to observations (Carbon Dioxide in the Atlantic (CARINA) data set (<xref ref-type="bibr" rid="B117">Jutterstrom et al., 2010</xref>)) (400&#x2013;450&#xa0;&#xb5;atm). The lack of riverine POC and the impact of terrestrial carbon resulting from coastal erosion in the model resulted in the underprediction of the observed carbon levels. Additionally, sedimentation and resuspension processes, which may be important to enrich the water column with carbon hence impacting air-sea gas exchange, were neglected in the model. When comparing PISCES-NEMO and TOPAZ-NEMO (<xref ref-type="bibr" rid="B115">Jung et al., 2019b</xref>) for annual mean (averaged over all depths) DIC, TOPAZ-NEMO&#x2019;s results agreed with observation (r &#x3e; 0.95), and the zonally averaged surface content was better represented by TOPAZ-NEMO in the Northern Hemisphere (bias &#x3c; 10&#xa0;&#x3bc;mol&#xa0;kg<sup>&#x2212;1</sup>). However, surface mean DIC reproduced by TOPAZ and PISCES showed a bias of &#x2212;90 and 90 respectively with GLobal Ocean Data Analysis Project version 2 (GLODAPv2 (<xref ref-type="bibr" rid="B137">Lauvset et al., 2016</xref>)).</p>
<p>In addition, a modified version of Chai&#x2019;s model (<xref ref-type="bibr" rid="B32">Chai et al., 1996</xref>) coupled to ROMS is applied over a model domain that spans the Antarctic Peninsula, Drake Passage, Scotia Sea, northern Weddell Sea, and South Georgia, indicating that dominant iron sources in the Scotia Sea are derived from sediments in the Antarctic Peninsula shelf along with the South Orkney Plateau (<xref ref-type="bibr" rid="B288">Jiang et al., 2019</xref>). In addition to these sources, the Antarctic Circumpolar Current, the northern side of the Weddell Gyre, upwelling, atmospheric dust deposition, and icebergs are the common sources of iron in the Southern Ocean (<xref ref-type="bibr" rid="B288">Jiang et al., 2019</xref>). However, the monthly means of iron levels estimated by the modified Chai&#x2019;s model have shown an average overestimation by 0.26 nM, deviating from the observed average value of 0.35 nM, resulting in r: 0.76.</p>
<p>On the other hand, the representation of the monthly observed nitrate, mixed layer depth, as well as euphotic layer depth is reproduced in the Arctic region using a skill assessment of 21 regional and global coupled biogeochemical models based on a phytoplankton functional types, including PISCES, PlankTOM, COBALT, TOPAZ, HAMOCC, BIOMASS, MEDUSA, ERSEM, PELAGOS, PISCES and NOBM (<xref ref-type="bibr" rid="B13">Babin et al., 2016</xref>). Most of these models have shown a positive bias for depth-averaged nitrates, explaining the overestimation of nitrates in the upper layer (r &#x2264; 0.68), and none of these models were able to represent accurately the variability in field measurements (NOAA/NODC ArcNut database (<xref ref-type="bibr" rid="B39">Codispoti et al., 2013</xref>)). However, REcoM with its variable stoichiometry for phytoplankton&#x2019;s growth and nutrient cycling (<xref ref-type="bibr" rid="B86">Geider et al., 1998</xref>), coupled with a high-resolution physical model: Finite Element Sea Ice-Ocean Model (FESOM), exhibited a correlation coefficient of (r &#x3d; 0.75) for spatial seasonal surface values of both dissolved inorganic nitrogen (DIN) and silicate (<xref ref-type="bibr" rid="B214">Schourup-Kristensen et al., 2018</xref>). The simulated DIN concentration indicated low levels in the Russian shelves (East Siberian Sea) with the exception of the Lena Delta in which the nutrients are added to the water by the riverine supply.</p>
<p>As for the representation of Chl-<italic>a</italic> in polar ecosystems, the original version of BLING coupled with NEMO was used to study monthly high surface Chl-<italic>a</italic> levels (i.e., blooms) in the high-latitude eastern North Atlantic and the central Arctic (<xref ref-type="bibr" rid="B30">Castro de la Guardia et al., 2019</xref>). This model is compared with MODIS observations and showed R<sup>2</sup>: 0.76, 0.42, 0.81, 0.9, 0.1, and 0.93 in the Barents Sea (BB), Hudson Bay (HB), Beaufort Gyre (BG), Labrador Sea (LS), Baffin Bay (BB), and Canadian Arctic Archipelago (CAA) respectively. However, it underestimated the spring bloom by 1.7&#xa0;mg&#xa0;m<sup>-3</sup> and the fall bloom by 0.7&#xa0;mg&#xa0;m<sup>-3</sup> in the BB, likely because it did not take into account nutrients from riverine input. Furthermore, the model exhibited a tendency to overpredict the spring blooms in Hudson Bay (HB) and Baffin Bay (BB) by approximately 0.5&#xa0;mg&#xa0;m<sup>-3</sup> and 0.3&#xa0;mg&#xa0;m<sup>-3</sup> respectively, occurring about a month earlier than expected (March instead of April). This discrepancy might be attributed to the underprediction of sea ice concentration. Additionally, the REcoM model exhibited a bias of 1.1&#xa0;mg&#xa0;m<sup>-3</sup> in predicting widespread subsurface chlorophyll maxima in the central Arctic Ocean, as compared to the mean summer surface Chl-<italic>a</italic> data obtained from Globcolor observations (<xref ref-type="bibr" rid="B214">Schourup-Kristensen et al., 2018</xref>).</p>
<p>Moreover, the MITgcm-REcoM model is used to investigate the impact of sea ice on phytoplankton blooms and surface dissolved inorganic carbon (DIC) in the ocean coastal-shelf-slope ecosystem west of the Antarctic Peninsula (<xref ref-type="bibr" rid="B215">Schultz et al., 2019</xref>). The study area encompasses a vast region ranging from 74.7&#xb0;S, 95&#xb0;W in the southwest to 55&#xb0;S, 55.6&#xb0;W in the northeast. Simulation results were compared with ocean color observations, and research ship surveys from the Palmer Long-Term Ecological Research (LTER) program. The Palmer LTER data and MODIS/SeaWifs data showed significant discrepancies in the study of the interannual variability of the phytoplankton bloom, with correlations for surface Chl-<italic>a</italic> in different sub-regions ranging from 0.52 to 0.73. While late summer retreat years displayed positive or low negative anomalies, early sea-ice retreat years primarily displayed negative or neutral anomalies in Chl-<italic>a</italic>. The model demonstrated the influence of sea-ice dynamics on phytoplankton dynamics by indicating an earlier bloom and lower Chl-<italic>a</italic> concentrations (relative to climatology) in years with early retreat of sea ice, resulting in lower chlorophyll concentrations at the end of the summer. Conversely, in years with late retreat of sea ice, the model showed greater Chl-<italic>a</italic> concentrations later in the season. Despite discrepancies between the model and observations, the model captured the temporal shifts in bloom timing during years characterized by high or low ice extent. Additionally, the model reproduced overall seasonal anomalies in dissolved inorganic carbon (DIC), which are related to seasonal net community production (NCP).</p>
<p>DARWIN is another model that has been used to study regional phytoplankton distribution in the Southern Ocean (<xref ref-type="bibr" rid="B150">Lo et al., 2019</xref>). The model was customized to improve its accuracy by increasing the affinity of phytoplankton for nutrients, adding two distinct size classes of diatoms, and considering two different life stages for Phaeocystis (single-cell vs. colonial). These improvements increased the agreement between the simulated coccolithophore and diatom levels with the <italic>in-situ</italic> observations. However, the model inaccurately simulated monthly diatoms and haptophytes, including small non-silicified phytoplankton, in the Ross Sea. Additionally, the model overestimated small non-silicified phytoplankton in this region, resulting in a general mean absolute error for diatoms and haptophytes of 0.74&#xa0;mg&#xa0;m<sup>&#x2212;3</sup> and 0.22&#xa0;mg&#xa0;m<sup>&#x2212;3</sup>, respectively. This inconsistency can be partially attributed to inaccuracies in representing PFT phenology and distribution, and the potential impact of iron limitation should also be considered. The representation of co-existing coccolithophores and Phaeocystis remains a challenge, and any small changes in DARWIN physiological parameters can lead to either Phaeocystis or coccolithophores loss. Furthermore, the explicit representation of sea-ice algae, which is important for accurately modeling ice-covered regions, has not been adequately incorporated.</p>
<p>In addition to studying Arctic and Antarctic phytoplankton dynamics, researchers have also been investigating the role of polynyas in polar ecosystems. Polynyas, which refer to expansive openings in the sea ice cover, play a crucial role in facilitating the exchange of heat, moisture, and gases between the atmosphere and the ocean (<xref ref-type="bibr" rid="B164">Maqueda et al., 2004</xref>; <xref ref-type="bibr" rid="B46">Dieckmann and Hellmer, 2009</xref>). Moreover, they drive patterns of ocean circulation, contribute to nutrient cycling, and influence ecosystem dynamics in polar regions (<xref ref-type="bibr" rid="B164">Maqueda et al., 2004</xref>). The rapid melting beneath the Dotson Ice Shelf (DIS) in West Antarctica, caused by warm, saline Circumpolar Deep Water (CDW) intrusions, has a significant impact on the adjacent Amundsen Sea Polynya (ASP) and its biology. Further, studies focusing on polynyas has garnered significant attention due to their substantial impact (<xref ref-type="bibr" rid="B75">Fichefet and Goosse, 1999</xref>; <xref ref-type="bibr" rid="B110">Hunke and Ackley, 2001</xref>; <xref ref-type="bibr" rid="B268">Wu et al., 2003</xref>). A recent study by (<xref ref-type="bibr" rid="B248">Twelves et al., 2020</xref>) using a coupled MITgcm-BLING model examined the effect of ice shelf melting on net primary production (NPP). The results show that melting ice shelves enhances upper ocean iron concentrations, which increases NPP. The study highlights how phytoplankton self-shading delays the bloom and reduces peak NPP while simultaneously emphasizing that changes in CDW intrusion regulate the horizontal dispersion of iron-rich meltwater, thereby impacting NPP levels.</p>
</sec>
<sec id="s3-4">
<title>3.4 High nutrient low chlorophyll (HNLC) zones</title>
<p>Biogeochemical models applied in this zone are mostly based on PFT approach which account for at least two plankton species. The section covers the Subarctic northeast Pacific at Ocean Station Papa (OSP), HNLC areas of the Southern Ocean, and the Southern Ocean (Antarctic Circumpolar Current region). Surface Chl-<italic>a</italic> concentrations are low in this region caused by iron limitation (<xref ref-type="bibr" rid="B60">Edwards et al., 2004</xref>). More recently (<xref ref-type="bibr" rid="B277">Zhang et al., 2021</xref>), used an extended version of the Chai&#x2019;s model (CoSiNE-Fe) that incorporated iron cycling to investigate phytoplankton dynamics at the Ocean Station Papa (OSP) in the subarctic northeast Pacific (50&#xb0;N, 145&#xb0;W). The model was able to demonstrate a strong correlation between nitrate and the averaged depth-integrated Chl-<italic>a</italic> in the upper 200&#xa0;m of the water column, with correlation coefficients of 0.8 and 0.69, respectively, compared to observations from a Biogeochemical-Argo float (BGC-Argo). The model&#x2019;s performance was also evaluated using root-mean-square differences (RMSDs), which were 0.65 and 0.98 for nitrate and averaged depth-integrated Chl-<italic>a</italic> (in the upper 200&#xa0;m), respectively.</p>
<p>However, the global PFT-based model PlankTOM10 coupled to NEMO was used to evaluate the role of grazing versus iron limitation in HNLC areas of the Southern Ocean (<xref ref-type="bibr" rid="B139">Le Qu&#xe9;r&#xe9; et al., 2016</xref>). PlankTOM10 was able to reproduce annual mean surface Chl-<italic>a</italic> estimates with a correlation coefficient (r) around 0.8 in the summer season when macro-zooplankton grazing is more intense. While this suggests that microzooplankton grazing may be a significant factor contributing to the low Chl-<italic>a</italic> concentrations observed in HNLC areas, it is important to note that high growth of phytoplankton can coexist with grazing (<xref ref-type="bibr" rid="B155">Lu&#xa8;rling, 2021</xref>). While both PlankTOM10 and PlankTOM6 share similar formulations, the former encompasses a greater number of plankton groups. These models yielded comparable outcomes for the annual mean surface Chl-<italic>a</italic> concentrations, demonstrating a correlation coefficient (r) of approximately 0.8 when compared with SeaWiFS satellite data. PlankTOM10, in particular, displayed slightly better performance to PlankTOM6 in terms of seasonal surface Chl-<italic>a</italic> distribution, with a bias of only 1.2%.</p>
<p>In contrast, DARWIN-MITgcm (<xref ref-type="bibr" rid="B58">Dutkiewicz et al., 2015</xref>) captured significant spatial variability in the annual mean surface Chl-a across the global oceans. Despite this, the model exhibited a relatively lower correlation coefficient of around 0.55 and tended to overestimate surface Chl-a concentration, particularly in the Southern Ocean.</p>
<p>Surface nitrate concentration, on the other hand, is high relative to surface Chl-<italic>a</italic> production in the HNLC zone (<xref ref-type="bibr" rid="B60">Edwards et al., 2004</xref>) and the global PlankTOM10 model predicted slightly lower (by 5%) of annual mean surface nitrate concentrations than observations World Ocean Atlas 2009 (<xref ref-type="bibr" rid="B85">Garcia et al., 2006</xref>; <xref ref-type="bibr" rid="B139">Le Qu&#xe9;r&#xe9; et al., 2016</xref>). Biases in the PlankTOM10 model can indeed be attributed to various limitations, including simplified overwintering strategies for zooplankton, coarse representation of iron (Fe) dynamics, the absence of certain organic matter types such as semi-refractory organic matter, and the exclusion of ecosystem pathways like viral lysis. Additionally, the model&#x2019;s omission of specific zooplankton groups like salps, pteropods, and auto- and mixotrophic dinoflagellates can also contribute to biases in its predictions.</p>
<p>Although iron is required at low concentrations for phytoplankton growth, the lack of its sources in the HNLC zone particularly the Southern Ocean highly impact the primary productivity and phytoplankton composition. For example, in the simplified version of DARWIN biogeochemical model (<xref ref-type="bibr" rid="B56">Dutkiewicz et al., 2009</xref>), which consists of two species (diatoms and small phytoplankton), coupled with MITgcm model, suggested that iron supply to the surface layer of the open Southern Ocean (Antarctic Circumpolar Current region) is highly driven by eddies (<xref ref-type="bibr" rid="B249">Uchida et al., 2019</xref>). Eddies can improve vertical mixing, influencing the upwelling of iron from deeper waters. This transport of iron from subsurface reservoirs to the sunlit layer where phytoplankton thrive can stimulate their growth and productivity. Therefore, to improve the accuracy of iron fluxes in the Southern Ocean, it is important to consider the role of eddies in addition to the atmospheric source. In particular, the inverse energy cascade caused by meso- and sub-mesoscale baroclinic instabilities plays a crucial role in determining iron distributions (<xref ref-type="bibr" rid="B188">Person et al., 2019</xref>).</p>
<p>Additionally, a recent study by <xref ref-type="bibr" rid="B285">Fu (2022)</xref> which used an inverse biogeochemical model with phosphorus, carbon, and oxygen Modules (<xref ref-type="bibr" rid="B258">Wang et al., 2019</xref>) to investigate the effects of ocean iron fertilization (OIF) in high nutrient low chlorophyll (HNLC) regions, specifically the Southern Ocean, North Pacific, and eastern equatorial Pacific. The findings revealed that OIF led to increased productivity, causing a downward transfer of nutrients and carbon to deeper waters. This process was accompanied by improved efficiency of the soft tissue pump and an increased in the CO<sub>2</sub> uptake. However, these positive effects were counterbalanced by a decrease in global mean oxygen levels and an expansion of oxygen minimum zones, suggesting potential consequences for ocean oxygenation and the development of hypoxic conditions. Notably, the study used (<xref ref-type="bibr" rid="B258">Wang et al., 2019</xref>) biogeochemical model and exhibited strong agreement with observations (GLODAPv2), showing correlation coefficients of 0.92 for dissolved inorganic phosphorus (DIP), 0.93 for dissolved inorganic carbon (DIC), and 0.85 for oxygen (O<sub>2</sub>). Interestingly, a comprehensive investigation conducted by (<xref ref-type="bibr" rid="B17">Bianchi et al., 2022</xref>) revealed the specific role of nitrogen cycling within the oxygen minimum zone (OMZ) of the HNLC Pacific Ocean, highlighting its implications for ecosystem dynamics. A new nitrogen cycling model was developed and specifically designed for integration into an ocean biogeochemical model, aiming to explore the impact of different nitrogen transformation processes on the biogeochemistry of the Eastern Tropical South Pacific OMZ. The model successfully captured typical OMZ conditions, providing valuable insights into the sensitivity of nitrogen transformations to environmental factors. However, it should be noted that while the model explicitly resolved N chemical tracers and their transformations, it did not directly incorporate the microbial communities responsible for these reactions, potentially limiting the understanding of the crucial role of microbes. Additionally, the model did not explicitly account for the conversion of dissolved CO<sub>2</sub> to organic matter through chemolithotrophy due to the relatively small rates compared to organic matter remineralization in the upper ocean, posing challenges in achieving a more comprehensive integration between chemolithotrophy and the carbon cycle.</p>
</sec>
</sec>
<sec id="s4">
<title>4 Limitations and future developments</title>
<p>Although the aforementioned biogeochemical models performed well in several ecosystems, they have been modified and improved over the years by incorporating more components and processes to improve their reliability and predictability. Even in the most recent and advanced biogeochemical research, however, some limits remain. This section discusses the limitations of the existing biogeochemical models applied in several oceans, as well as recommendations for future modeling studies.</p>
<p>The absence of viruses in current biogeochemical models is a noteworthy drawback that demands more attention. Viruses play an important role in marine ecosystems by controlling microbial population numbers and altering the dynamics of nutrient and carbon cycling (<xref ref-type="bibr" rid="B261">Weitz and Wilhelm, 2012</xref>; <xref ref-type="bibr" rid="B166">Mateus, 2017</xref>). Their ability to infect and lyse bacteria and other microbes leads to the release of intracellular organic materials, which other species can then uptake (<xref ref-type="bibr" rid="B279">Zhao et al., 2019</xref>). Incorporating viruses into biogeochemical models may help us gaining a deeper understanding of how ecosystems work and the complex connections that exist between the different components of the microbial community (<xref ref-type="bibr" rid="B260">Weitz et al., 2015</xref>). These models may more accurately represent the intricate feedback systems that control nutrient availability, primary productivity, and carbon sequestration in the oceans by taking the viral impact into account. Furthermore, viruses can alter the variety and dominance of species by profoundly altering the structure and makeup of microbial communities (<xref ref-type="bibr" rid="B245">Tran and Anantharaman, 2021</xref>). Their impact on community dynamics and adaptability to environmental changes emphasizes how crucial they are in determining the stability and resiliency of the ecosystem.</p>
<p>In addition to not properly representing viruses, biogeochemical models often neglect the inclusion of archaea, despite their important role in ammonia oxidation processes. Archaea are important in ammonia oxidation and have the ability to affect nitrogen cycling, according to studies by (<xref ref-type="bibr" rid="B250">Urakawa et al., 2010</xref>; <xref ref-type="bibr" rid="B272">Yakimov et al., 2011</xref>). Similarly, mixotrophs, organisms capable of both photosynthetic and heterotrophic feeding, are often overlooked in biogeochemical models. Studies by (<xref ref-type="bibr" rid="B228">Stoecker et al., 2017</xref>; <xref ref-type="bibr" rid="B61">Edwards, 2019</xref>; <xref ref-type="bibr" rid="B67">Faure et al., 2019</xref>; <xref ref-type="bibr" rid="B264">Wilken et al., 2019</xref>) have revealed mixotrophs&#x2019; ecological importance and possible impact on nutrient dynamics and ecosystem functioning. Unfortunately, most models do not treat mixotrophs as distinct Plankton Functional Types (PFTs), limiting our understanding of their contributions.</p>
<p>Furthermore, autotrophic bacteria such as nitrifying bacteria which carry out two-step nitrification processes are oversimplified in many biogeochemical models. These types of bacteria compete with the photosynthesizers for inorganic carbon and their current representation may underestimate or overestimate the primary productivity in the ocean. In addition, the detritus component is not well classified in many marine biogeochemical models and the representation of organic matter is not fully considered, leading to a possible under/overestimation of organic matter. Although the most intricate models include more components, they omit some important processes, including day-night cycles, zooplankton&#x2019;s diurnal migration (<xref ref-type="bibr" rid="B80">Ford et al., 2018</xref>). The omission of fish from biogeochemical models represent another significant area that needs exploration. Fish play an important part in the recycling and regeneration of nutrients within marine environments (<xref ref-type="bibr" rid="B170">Mcintyre et al., 2007</xref>). Thus, incorporating their interactions with other ecosystem components, such as feeding patterns and nutrient excretion, would provide valuable insights into nutrient dynamics and enhance our understanding of ecosystem functioning. Furthermore, the omission or simplification of benthic (e.g., <xref ref-type="bibr" rid="B138">Lazzari et al., 2016</xref>; <xref ref-type="bibr" rid="B120">Kalaroni et al., 2020</xref>) and sea ice components in biogeochemical models can hinder accurate predictions of ecosystem responses to environmental changes, thereby affecting the carbon and nutrient cycling assessment.</p>
<p>Biogeochemical models commonly simplify the representation of nitrogen (N) transformations, failing to capture the complexity of the underlying network of N reactions and their controlling factors. In the case of N<sub>2</sub>O cycling, many models rely on oversimplified parameterizations that consider N<sub>2</sub>O production solely from nitrification or aerobic respiration, while neglecting the important N<sub>2</sub>O sources and sinks associated with denitrification (<xref ref-type="bibr" rid="B234">Suntharalingam and Sarmiento, 2000</xref>; <xref ref-type="bibr" rid="B112">Jin and Gruber, 2003</xref>; <xref ref-type="bibr" rid="B183">Nevison et al., 2003</xref>; <xref ref-type="bibr" rid="B163">Manizza et al., 2012</xref>). The comprehensive consideration of nitrite cycling in the presence of low oxygen conditions, encompassing the concurrent processes of nitrite production from nitrate dissimilatory reactions, reduction to N<sub>2</sub>O and N<sub>2</sub> via denitrification and anammox, and subsequent reoxidation to nitrate, is insufficiently addressed (<xref ref-type="bibr" rid="B134">Lam and Kuypers, 2011</xref>; <xref ref-type="bibr" rid="B121">Kalvelage et al., 2013</xref>; <xref ref-type="bibr" rid="B11">Babbin et al., 2014</xref>; <xref ref-type="bibr" rid="B10">Babbin et al., 2015</xref>; <xref ref-type="bibr" rid="B26">Buchwald et al., 2015</xref>; <xref ref-type="bibr" rid="B12">Babbin et al., 2017</xref>).</p>
<p>In summary, although many biogeochemical models are able to simulate certain phenomenon/conditions, in certain regions of the global oceans they may underpredict/overpredict concentrations of some components that can be largely dependent on other missing elements mentioned above. Therefore, biogeochemical models could be improved through the inclusion of dissolved organic carbon (labile, semi-labile, refractory), mixotrophic functional groups, viruses which in turn improve the representation of plankton functional groups, heterotrophic and microbial food web. While assessing biogeochemical models for current conditions reveals model biases, it does not always explain how they behave outside of the observed conditions (<xref ref-type="bibr" rid="B71">Fennel et al., 2022</xref>). Nevertheless, adding complexity does not always guarantee improved model performance or changes in rates. For example, <xref ref-type="bibr" rid="B154">Luo et al. (2022)</xref> found that while the drivers of export rate can change with the addition of an extra zooplankton component like tunicates, the total export amount may not vary significantly.</p>
<p>Obtaining comprehensive and high-quality data for model initialization and parameterization continues to be a challenge, with limited accessible sources available. Moreover, the challenges associated with data acquisition in polar regions make it difficult to effectively compare models with the available data. These challenges are primarily related to factors such as sea ice and cloud cover, which often result in substantial gaps in the coverage of remote sensing data.</p>
<p>Improvement in the zooplankton component may help further in constraining processes that regulate Chl-<italic>a</italic> distribution in the models (<xref ref-type="bibr" rid="B37">Clerc et al., 2021</xref>; <xref ref-type="bibr" rid="B200">Ratnarajah et al., 2023</xref>). Moreover, re-considering simulations of under-ice and near-ice phytoplankton blooms in the cold ecosystems by defining the photosynthesis irradiance curve for each phytoplankton group and allowing seasonal plasticity in the model parameters may increase the reliability of models applied in Arctic regions (<xref ref-type="bibr" rid="B124">Kearney et al., 2020</xref>). Most of the current models use a simplified, single-size detritus component, but in fact, detritus consists of different sizes and sinking rates, which may result in significant limitations in some regions (<xref ref-type="bibr" rid="B80">Ford et al., 2018</xref>). Considering different types of detrital matter with various timescales in the remineralization process would produce a more realistic model output for the organic matter.</p>
</sec>
<sec sec-type="conclusion" id="s5">
<title>5 Conclusion</title>
<p>This review presents different biogeochemical models applied to various ecosystems of the world&#x2019;s ocean. Most of these widely used ocean biogeochemical models are an extension of NPZD models and have undergone several modifications and developments which increased their complexity in terms of number of PFTs, organic matter, physics, and sediments interactions. We divided the oceans into four zones, tropical, temperate and varying from tropical to subtropical, polar/subpolar, and HNLC zones to review the biogeochemical modelling studies been done on the biogeochemical components in these regions separately. Estimation of biogeochemical model variables, such as Chl-<italic>a</italic>, nutrients, carbon and oxygen in various ecosystems have shown varying performances. The varying performances for these biogeochemical model variables are dependent on the features of the ecosystems and the resolution of the physical environment. In the tropical and subtropical ecosystems, seasonal variations are highly strong and have a great impact on the biogeochemical cycles in these regions. These regions are known to be the most productive ecosystems in the ocean and nutrients can be supplied to the open ocean from the coastal enriched nutrients. Due to considerable decrease in ice extent and rising sea levels caused by climate change, the Arctic/Antarctic region experiences rapid changes in the physical and biological ecosystems. This is observed in the changes of the Arctic carbon and nutrients cycles. Ocean biogeochemical models play a critical role in climate studies, particularly in regions that are prone to experiencing high variations in extreme climates. The increase in carbon and nitrogen concentrations in the biosphere, resulting from anthropogenic activities, has the potential to disrupt biogeochemical cycles. This alteration of biogeochemical cycles can have wide-ranging impacts, making biodiversity, food security, and water quality more susceptible to the impacts of climate change.</p>
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<sec id="s6">
<title>Author contributions</title>
<p>KI and MA-S defined the content of the manuscript. KI prepared the manuscript and MA-S contributed in conceptualization, revisions and improvements. All authors contributed to the article and approved the submitted version.</p>
</sec>
<ack>
<p>The authors would like to thank Khalifa University for the financial support. This paper is under the project of modelling the biogeochemistry of the Arabian Gulf waters.</p>
</ack>
<sec sec-type="COI-statement" id="s7">
<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 sec-type="disclaimer" id="s8">
<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>
<ref-list>
<title>References</title>
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