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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Mar. Sci.</journal-id>
<journal-title>Frontiers in Marine Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Mar. Sci.</abbrev-journal-title>
<issn pub-type="epub">2296-7745</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fmars.2023.1223772</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Marine Science</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Assessment of sea ice thickness simulations in the CMIP6 models with CICE components</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Xu</surname>
<given-names>Mengliu</given-names>
</name>
<uri xlink:href="https://loop.frontiersin.org/people/2221792"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Li</surname>
<given-names>Junde</given-names>
</name>
<xref ref-type="author-notes" rid="fn001">
<sup>*</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1390656"/>
</contrib>
</contrib-group>
<aff id="aff1">
<institution>College of Oceanography, Hohai University</institution>, <addr-line>Nanjing</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>Edited by: Junhong Liang, Louisiana State University, United States</p>
</fn>
<fn fn-type="edited-by">
<p>Reviewed by: Haijin Dai, National University of Defense Technology, China; Valentin Ludwig, Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research (AWI), Germany</p>
</fn>
<fn fn-type="corresp" id="fn001">
<p>*Correspondence: Junde Li, <email xlink:href="mailto:junde.li@hhu.edu.cn">junde.li@hhu.edu.cn</email>
</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>18</day>
<month>10</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>10</volume>
<elocation-id>1223772</elocation-id>
<history>
<date date-type="received">
<day>16</day>
<month>05</month>
<year>2023</year>
</date>
<date date-type="accepted">
<day>27</day>
<month>09</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 Xu and Li</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Xu and Li</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>Arctic sea ice plays a critical role in modulating our global climate system and the exchange of heat fluxes in the polar region, but its impact on climate varies across different sea ice thickness (SIT) categories. Compared to sea ice cover, the performance of ice models in simulating SIT has been less evaluated, particularly in the sixth Coupled Model Intercomparison Project Phase (CMIP6). Here, we chose 12 CMIP6 models with the Community Ice Code model (CICE) components and compared their SIT simulations with the satellite observations and the Pan-Arctic Ice Ocean Modeling and Assimilation System (PIOMAS) model between 1980 and 2014. Our results show that the seasonal cycle of the PIOMAS SIT is consistent with satellite observations. Compared to the PIOMAS reanalysis, the multi-model ensemble mean (MME) well represents the sea ice extent in both the thin ice (&lt;0.6 m) and thick ice (&gt; 3.6 m). However, the MME SIT has larger biases in the Chukchi Sea, the Beaufort Sea, the central Arctic, and the Greenland Sea during winter and mainly in the central Arctic during summer. Both the MME and PIOMAS show decreasing trends in SIT over the entire Arctic Ocean in all seasons, but the interannual variability of SIT in MME is smaller than that in PIOMAS. Among the 12 CMIP6 models, the FIO-ESM-2.0 model shows the best simulation of the annual mean SIT, but the SAM0-UNICON and NESM3 models have the largest biases in the climatological mean SIT over the Arctic Ocean. We also demonstrate that the FIO-ESM-2.0 performs the best in the seasonal cycles of SIT. Our study suggests that more attention should be paid to the coupling of the CICE model with ocean and atmosphere models, which is vital to improving the SIT simulation in CMIP6 models and to better understanding the impact of Arctic sea ice on our climate system.</p>
</abstract>
<kwd-group>
<kwd>sea ice thickness</kwd>
<kwd>PIOMAS</kwd>
<kwd>CICE MME</kwd>
<kwd>CMIP6</kwd>
<kwd>Arctic Ocean</kwd>
</kwd-group>
<counts>
<fig-count count="9"/>
<table-count count="0"/>
<equation-count count="3"/>
<ref-count count="53"/>
<page-count count="11"/>
<word-count count="4343"/>
</counts>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-in-acceptance</meta-name>
<meta-value>Physical Oceanography</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1" sec-type="intro">
<label>1</label>
<title>Introduction</title>
<p>Arctic sea ice plays a critical role in the global climate system (<xref ref-type="bibr" rid="B39">Stjern et&#xa0;al., 2019</xref>). Since the beginning of the 21st century, the decline in Arctic sea ice extent (SIE) has been accelerating dramatically (<xref ref-type="bibr" rid="B21">Kwok and Rothrock, 2009</xref>; <xref ref-type="bibr" rid="B40">Stroeve et&#xa0;al., 2012</xref>; <xref ref-type="bibr" rid="B8">Comiso et&#xa0;al., 2017</xref>), accompanied by the emergence of a dark open ocean with a lower albedo, leading to increased heat absorption in the surface ocean (<xref ref-type="bibr" rid="B32">Previdi et&#xa0;al., 2020</xref>). At the same time, sea ice volume (SIV) and sea ice thickness (SIT) in the Arctic Ocean are also declining rapidly (<xref ref-type="bibr" rid="B25">Mallett et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B17">Kacimi and Kwok, 2022</xref>). SIV has a loss rate of 2870 km<sup>3</sup>/decade in winter (February&#x2013;March) and 5130 km<sup>3</sup>/decade in the fall (October&#x2013;November) (<xref ref-type="bibr" rid="B20">Kwok, 2018</xref>). The decreasing rate of SIT is 0.13 &#xb1; 0.02 cm/year from 2002 to 2021 (<xref ref-type="bibr" rid="B51">Zhang et&#xa0;al., 2023</xref>). As a result, the sea surface temperatures in the ice-free region of the Arctic Ocean are increasing two times faster than the global average (<xref ref-type="bibr" rid="B35">Screen et&#xa0;al., 2012</xref>; <xref ref-type="bibr" rid="B10">D&#xf6;scher et&#xa0;al., 2014</xref>). In the Arctic Ocean, the reduction of SIE in the fall, which is associated with the sea ice albedo feedback (<xref ref-type="bibr" rid="B11">Feldl and Merlis, 2021</xref>), may also affect the mid-latitude atmospheric circulation (<xref ref-type="bibr" rid="B6">Chatterjee et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B4">Cai et&#xa0;al., 2023</xref>). Therefore, evaluating sea ice simulation in the Arctic Ocean will be beneficial for us to understand the impact of sea ice on the climate.</p>
<p>In contrast to sea ice concentration (SIC) and SIE, few studies have focused on the SIT variability in the Arctic Ocean due to limited observations. Changes in SIE and SIC can affect atmospheric circulation by altering the surface albedo and absorption of short-wave radiation (<xref ref-type="bibr" rid="B13">Frey et&#xa0;al., 2011</xref>; <xref ref-type="bibr" rid="B11">Feldl and Merlis, 2021</xref>). The decrease in SIT significantly influences the atmospheric circulation and heat transfer to the ocean through the insulation effect (<xref ref-type="bibr" rid="B37">Serreze and Barry, 2011</xref>). In a warming climate, changes in SIT significantly influence sea ice area and atmospheric circulation in the Northern Hemisphere (<xref ref-type="bibr" rid="B18">Koenigk et&#xa0;al., 2014</xref>; <xref ref-type="bibr" rid="B12">Francis and Wu, 2020</xref>). Examining the spatial and temporal variation of SIT in different seasons can also help us predict the trends of Arctic sea ice (<xref ref-type="bibr" rid="B2">Balan-Sarojini et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B53">Zhou et&#xa0;al., 2022</xref>). Moreover, SIT significantly affects surface heat fluxes. Sea ice thinning results in the enhancement of near-surface warming of about 1&#x2da;C per decade in winter, especially in the marginal sea ice areas, which further leads to a 37% increase in the Arctic amplification factor (<xref ref-type="bibr" rid="B23">Lang et&#xa0;al., 2016</xref>). Thus, assessing SIT simulations in the CMIP6 models is important for us to understand the sea ice evolution in climate models and to further improve the performance of sea ice models.</p>
<p>Previous climate model simulations underestimated SIT in the northern Canadian Arctic Islands, northern Greenland, and the Floran Channel but overestimated SIT on the Eurasian shelf (<xref ref-type="bibr" rid="B50">Zachary et&#xa0;al., 2018</xref>). Compared to satellite observations, the Arctic Ocean Model Intercomparison Project model simulations overestimated the thickness of observed ice thinner than 2 m but underestimated the thickness of observed ice thicker than approximately 2 m (<xref ref-type="bibr" rid="B16">Johnson et&#xa0;al., 2012</xref>). The Polar Ocean and Sea Ice Reanalysis Products Mutual Comparison Project showed large differences in SIT simulations within 10 ocean and sea ice reanalysis products (<xref ref-type="bibr" rid="B45">Uotila et&#xa0;al., 2019</xref>). Although the differences between models in the sixth Coupled Model Intercomparison Project Phase (CMIP6) are smaller than those in CMIP5 and CMIP3 (<xref ref-type="bibr" rid="B29">Notz and Community, 2020</xref>), there are still large uncertainties in model simulations and vast discrepancies between models and observations (<xref ref-type="bibr" rid="B38">Shu et&#xa0;al., 2015</xref>; <xref ref-type="bibr" rid="B44">Tsujino et&#xa0;al., 2020</xref>). However, the evaluation of the Arctic SIT simulation in the CMIP6 models via the multi-model ensemble mean (MME) with Community Ice Code model (CICE) components has not yet been studied. Therefore, there is a pressing need to investigate the performance of CMIP6 models with CICE components in simulating the SIT.</p>
<p>In this study, we evaluate the performance of CMIP6 models with CICE components in simulating the SIT using the PIOMAS reanalysis product, which has been validated with satellite observations. In Section 2, we introduce the SIT dataset and the methodology. In Section 3, we first validate the SIT simulation in PIOMAS with CS2SMOS satellite observations, then compare the mean state, seasonal cycle, and spatial distributions of SIT between PIOMAS and MME, and finally show the intercomparison of 12 CMIP6 models. Section 4 presents the discussion and conclusion.</p>
</sec>
<sec id="s2" sec-type="materials|methods">
<label>2</label>
<title>Materials and methods</title>
<sec id="s2_1">
<label>2.1</label>
<title>Satellite observations</title>
<p>In this study, we used the weekly averaged SIT from CS2SMOS, product version v205, which spans from January 2011 to December 2022. The CS2SMOS SIT (<xref ref-type="bibr" rid="B1">AWI, 2023</xref>) was derived by merging the CryoSat-2 (CS2) altimeter and the Soil Moisture and Ocean Salinity (SMOS) radiometer ice thickness using an optimal interpolated scheme with a horizontal resolution of 25 km&#xd7;25 km. Compared to the product of CS2 and SMOS ice thicknesses, the relative uncertainties of the ice thickness retrieval methods for thin ice (&lt;1 m) from the CS2 altimeter measurements and thick ice (&gt;1 m) from the SMOS radiometer observations were significantly reduced in CS2SMOS (<xref ref-type="bibr" rid="B33">Ricker et&#xa0;al., 2017</xref>). The SIV was estimated by the product of the CS2SMOS SIT and &#xfeff;the Ocean and Sea Ice Satellite Application Facility (OSI SAF) SIC. The SIE data were obtained from the NOAA/NSIDC Climate Data Record of Passive Microwave Sea Ice Concentration, version 3, with a horizontal resolution of 25 km &#xd7; 25 km (<xref ref-type="bibr" rid="B26">Meier et&#xa0;al., 2017</xref>). For comparison, the CS2SMOS dataset was remapped to an NSIDC grid.</p>
</sec>
<sec id="s2_2">
<label>2.2</label>
<title>CMIP6 model simulations and PIOMAS reanalysis</title>
<p>There are several different sea ice model components in the CMIP6 models, such as CICE, FESOM, SIS, LIM3, GFDL-SIM, GISS SI, NEMO-LIM, COCO, and MPIOM. Among all sea ice models, the CICE model is a dynamic-thermodynamic model that includes a subgrid-SIT distribution and multiple layers in each thickness category (<xref ref-type="bibr" rid="B15">Hunke and Elizabeth, 2014</xref>), which has been widely used in previous sea ice simulations and has shown good performance (<xref ref-type="bibr" rid="B15">Hunke and Elizabeth, 2014</xref>; <xref ref-type="bibr" rid="B19">Kumar et&#xa0;al., 2021</xref>). In this study, a total of 12 different models were chosen from the CMIP6 models with a CICE component. The SIT in the CMIP6 models was interpolated into a grid with a horizontal resolution of 25 km&#xd7;25 km. The monthly historical SIT used in this study spans from January 1980 to December 2014. Here, we evaluated not only the performance of each CMIP6 model but also its MME.</p>
<p>The Pan-Arctic Ice Ocean Modeling and Assimilation System (PIOMAS) was used to evaluate the sea ice simulation in the CMIP6 models, which include the SIT and SIE. The PIOMAS reanalysis has a horizontal resolution of 1&#xb0;&#xd7;1&#xb0;. Monthly PIOMAS SIT data from 1980 to 2022 were used in this study. The PIOMAS assimilates the sea surface temperature and SIC observations (<xref ref-type="bibr" rid="B52">Zhang and Rothrock, 2003</xref>), and has shown good agreement in sea ice simulations with satellite observations (<xref ref-type="bibr" rid="B48">Wang et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B33">Ricker et&#xa0;al., 2017</xref>). It is an excellent sea ice reanalysis product in the Arctic Ocean for long-term studies of sea ice evolution (<xref ref-type="bibr" rid="B52">Zhang and Rothrock, 2003</xref>; <xref ref-type="bibr" rid="B7">Collow et&#xa0;al., 2015</xref>). Therefore, we compared the sea ice simulations in the CMIP6 models with the PIOMAS reanalysis in the Arctic Ocean (<xref ref-type="fig" rid="f1">
<bold>Figure&#xa0;1</bold>
</xref>).</p>
<fig id="f1" position="float">
<label>Figure&#xa0;1</label>
<caption>
<p>Subregions of the Arctic Ocean with the same definition in <xref ref-type="bibr" rid="B24">Li et&#xa0;al. (2021)</xref> and <xref ref-type="bibr" rid="B19">Kumar et&#xa0;al. (2021)</xref>, which are shaded with 11 different colors.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1223772-g001.tif"/>
</fig>
</sec>
<sec id="s2_3">
<label>2.3</label>
<title>Taylor diagram</title>
<p>Taylor diagrams provide a way to graphically summarize how well model simulations match observations (<xref ref-type="bibr" rid="B41">Taylor and Karl, 2001</xref>), and have been widely used in model evaluations (<xref ref-type="bibr" rid="B28">Mu et&#xa0;al., 2018</xref>; <xref ref-type="bibr" rid="B19">Kumar et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B24">Li et&#xa0;al., 2021</xref>). To compare the performance of different CMIP6 models on the same plot, here we have used the correlation coefficient (R), the normalized centered root mean square error (CRMSE), and the standard deviation (STD) in the Taylor diagrams, which are defined as follows:</p>
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<mml:mo stretchy="true">&#xaf;</mml:mo>
</mml:mover>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mstyle>
</mml:mrow>
</mml:msqrt>
</mml:mrow>
<mml:mrow>
<mml:msqrt>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mo>=</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>N</mml:mi>
</mml:munderover>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mi>n</mml:mi>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mover accent="true">
<mml:mi>r</mml:mi>
<mml:mo stretchy="true">&#xaf;</mml:mo>
</mml:mover>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mstyle>
</mml:mrow>
</mml:msqrt>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</disp-formula>
<p>Where <inline-formula>
<mml:math display="inline" id="im2">
<mml:mi>f</mml:mi>
</mml:math>
</inline-formula> and <inline-formula>
<mml:math display="inline" id="im1">
<mml:mi>r</mml:mi>
</mml:math>
</inline-formula> represent the SIT in the CMIP6 and PIOMAS models with a sample size of N, and their means are indicated by their overbars <inline-formula>
<mml:math display="inline" id="im3">
<mml:mrow>
<mml:mover accent="true">
<mml:mi>f</mml:mi>
<mml:mo>&#xaf;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula>
<mml:math display="inline" id="im4">
<mml:mrow>
<mml:mover accent="true">
<mml:mi>r</mml:mi>
<mml:mo>&#xaf;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:math>
</inline-formula> , respectively.</p>
</sec>
</sec>
<sec id="s3" sec-type="results">
<label>3</label>
<title>Results</title>
<sec id="s3_1">
<label>3.1</label>
<title>Mean state and seasonal cycle of SIT</title>
<p>Because of the lack of suitable satellite observations during the sea ice melt season, SIT observations are not continuous during the summer season. PIOMAS (version 2.1) provides an estimate of SIV from simulations with the assimilation of SIC and sea surface temperature observations (<xref ref-type="bibr" rid="B52">Zhang and Rothrock, 2003</xref>), which fill the SIT gaps in the summer. This product has been extensively validated against a wide range of observations, such as satellite and <italic>in situ</italic> mooring observations (<xref ref-type="bibr" rid="B34">Schweiger et&#xa0;al., 2011</xref>). <xref ref-type="fig" rid="f2">
<bold>Figure&#xa0;2</bold>
</xref> shows the evolution of the monthly mean SIE and SIT in the Arctic Ocean from satellite observations, CMIP6 models, and the PIOMAS reanalysis. The biases of SIE between NSIDC observations, PIOMAS reanalysis, and MME of CMIP6 models are very small during the sea ice melt season (July-September) but the biases grow during the sea ice growth season (<xref ref-type="fig" rid="f2">
<bold>Figure&#xa0;2A</bold>
</xref>). The SIT of the PIOMAS reanalysis averaged for 2011-2022 agrees well with the CS2SMOS observations in winter, with biases of less than 0.3 m (<xref ref-type="fig" rid="f2">
<bold>Figure&#xa0;2B</bold>
</xref>). Although the CMIP6 models have a large ensemble spread, the MME from 1980 to 2014 shows good agreement with PIOMAS (<xref ref-type="fig" rid="f2">
<bold>Figure&#xa0;2B</bold>
</xref>). This gave us the confidence to use PIOMAS to evaluate the mean state and seasonal cycle of SIT from the selected 12 CMIP6 models based on the PIOMAS reanalysis.</p>
<fig id="f2" position="float">
<label>Figure&#xa0;2</label>
<caption>
<p>
<bold>(A)</bold> Monthly climatological mean sea ice extent in the Arctic Ocean from NSIDC (black line), MME (red line), and PIOMAS reanalysis (blue line) from 1980 to 2014. <bold>(B)</bold> Monthly climatological mean sea ice thickness in the Arctic Ocean from PIOMAS reanalysis (red line), and CS2SMOS observations (black line) from 2011 to 2022. The orange and green lines indicate the sea ice thickness from PIOMAS and MME, averaged from 1980 to 2014. The green shading denotes the ensemble spread in the CMIP6 models.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1223772-g002.tif"/>
</fig>
<p>To further investigate the performance of CMIP6 models in simulating different SIT categories, we show the seasonal evolution of SIE covered by different SIT from MME and PIOMAS (<xref ref-type="fig" rid="f3">
<bold>Figure&#xa0;3</bold>
</xref>), using the same SIT category boundaries from <xref ref-type="bibr" rid="B15">Hunke and Elizabeth (2014)</xref> and <xref ref-type="bibr" rid="B19">Kumar et&#xa0;al. (2021)</xref>: 0-0.6 m, 0.6-1.4 m, 1.4-2.4 m, 2.4-3.6 m, and &gt; 3.6 m. Overall, the SIE difference between MME and PIOMAS was very small, with biases of less than 1.0&#xd7;10<sup>6</sup> km<sup>2</sup> throughout the year. The ice thickness category with a range of 1.4-2.4 m (purple bars) had the largest bias in the first three months of the year (<xref ref-type="fig" rid="f3">
<bold>Figure&#xa0;3B</bold>
</xref>). In both the MME and PIOMAS, we can also see that the fraction of sea ice coverage was dominated by ice with a thickness ranging from 1.4 m to 2.4 m in most months except April, May, and June, which were characterized by thicker ice, between 2.4 m and 3.6 m (<xref ref-type="fig" rid="f3">
<bold>Figure&#xa0;3A</bold>
</xref>). The percentage of ice thickness greater than 3.6 m was the smallest among the five SIT categories (<xref ref-type="fig" rid="f3">
<bold>Figure&#xa0;3A</bold>
</xref>), and the bias between MME and PIOMAS was also the smallest (<xref ref-type="fig" rid="f3">
<bold>Figure&#xa0;3B</bold>
</xref>) implying that the MME model represents the SIE of thick ice well. For thin ice of less than 0.6 m, we can see that the biases between MME and PIOMAS were also very small in all months (<xref ref-type="fig" rid="f3">
<bold>Figure&#xa0;3B</bold>
</xref>). This suggests that the MME can also represent the SIE of thin ice well.</p>
<fig id="f3" position="float">
<label>Figure&#xa0;3</label>
<caption>
<p>
<bold>(A)</bold> Monthly mean SIE covered by different SIT categories from MME (solid line) and PIOMAS (dashed line) from 1980 to 2014. <bold>(B)</bold> Absolute values (bars) of SIE differences between MME and PIOMAS and the bias in percent of SIE differences relative to PIOMAS SIE.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1223772-g003.tif"/>
</fig>
</sec>
<sec id="s3_2">
<label>3.2</label>
<title>Spatial distributions of SIT</title>
<p>To investigate the spatial distribution of SIT in March and September in the Arctic Ocean, we plotted the SIT averaged from 1980 to 2014 from the PIOMAS and CMIP6 models. As shown in <xref ref-type="fig" rid="f4">
<bold>Figures&#xa0;4A, B</bold>
</xref>, most regions of the Arctic Ocean are covered by sea ice during the winter. The ice-covered area in the MME is larger than that in the PIOMAS (purple lines), particularly in the Bering Sea, Baffin Sea, Greenland Sea, and Barents Sea, where the ocean is covered by thin new ice with SIT less than 0.5 m. This result is consistent with a previous study by <xref ref-type="bibr" rid="B24">Li et&#xa0;al. (2021)</xref>. Compared to SIT in PIOMAS, the MME SIT is much larger in the Chukchi Sea, the Beaufort Sea, and the central Arctic, but smaller in the Greenland Sea (<xref ref-type="fig" rid="f4">
<bold>Figure&#xa0;4C</bold>
</xref>), with differences greater than 1 m in some regions. The thin new ice melts during the summer season (<xref ref-type="fig" rid="f4">
<bold>Figures&#xa0;4D, E</bold>
</xref>), so we can see the sea ice retreat in the Bering Sea, Chukchi Sea, Barents Sea, Greenland Sea, and Baffin Sea. As a result, most regions in the Arctic Ocean are covered by thick ice with a SIT greater than 0.5 m. The sea ice areas between PIOMAS and MME are very similar, but there is more sea ice in the Kara Sea in PIOMAS than in the MME. The SIT in the central Arctic is much larger in PIOMAS than in MME, but it is smaller in the other ice-covered regions (<xref ref-type="fig" rid="f4">
<bold>Figure&#xa0;4F</bold>
</xref>).</p>
<fig id="f4" position="float">
<label>Figure&#xa0;4</label>
<caption>
<p>Spatial distributions of SIT averaged between 1980 and 2014 from <bold>(A)</bold> PIOMAS and <bold>(B)</bold> MME in March, and <bold>(C)</bold> the differences between PIOMAS and MME. The purple lines in <bold>(A)</bold> and <bold>(B)</bold> indicate the ice edge (SIC of 15%) from PIOMAS and MME, respectively, while the yellow lines indicate the ice thickness of 0.5 m. <bold>(D-F)</bold> Same as <bold>(A-C)</bold>, but for September.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1223772-g004.tif"/>
</fig>
<p>Due to the sea ice melting and refreezing in the Arctic Ocean, the interannual variability of SIT varies in different regions. To examine the difference in the interannual variability of SIT between PIOMAS and MME, we present the spatial distributions of the variance of the annual mean SIT (<xref ref-type="fig" rid="f5">
<bold>Figure&#xa0;5</bold>
</xref>). The variances of the annual mean SIT in PIOMAS are very small in most of the Arctic Ocean, except for the Canadian Archipelago and East Siberia (<xref ref-type="fig" rid="f5">
<bold>Figure&#xa0;5A</bold>
</xref>). The variances of the annual mean SIT in MME have a similar pattern to PIOMAS (<xref ref-type="fig" rid="f5">
<bold>Figure&#xa0;5B</bold>
</xref>), but with larger variances along the east coast of Greenland, implying that the SIT in CMIP6 models has larger interannual variability around this region. Additionally, we also show the variances of the mean SIT during the sea ice growth and melting seasons. Regions with strong interannual variability of SIT in March (<xref ref-type="fig" rid="f5">
<bold>Figures&#xa0;5C, D</bold>
</xref>) and September (<xref ref-type="fig" rid="f5">
<bold>Figures&#xa0;5E, F</bold>
</xref>) are similar to those in <xref ref-type="fig" rid="f5">
<bold>Figures&#xa0;5A, B</bold>
</xref> but with much larger amplitudes. The interannual variability of SIT in PIOMAS is stronger than that in the MME during these two seasons.</p>
<fig id="f5" position="float">
<label>Figure&#xa0;5</label>
<caption>
<p>Spatial distributions of the variance of the annual mean SIT between 1980 and 2014 from <bold>(A)</bold> PIOMAS and <bold>(B)</bold> MME. <bold>(C, D)</bold> and <bold>(E, F)</bold> same as <bold>(A, B)</bold>, but for March and September, respectively.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1223772-g005.tif"/>
</fig>
<p>We further show the linear trends in SIT between 1980 and 2014 in the winter (<xref ref-type="fig" rid="f6">
<bold>Figures&#xa0;6A, B</bold>
</xref>) and summer (<xref ref-type="fig" rid="f6">
<bold>Figures&#xa0;6C, D</bold>
</xref>) seasons. We observe decreasing trends in SIT over the whole Arctic Ocean in all seasons, which is consistent with previous studies (<xref ref-type="bibr" rid="B22">Kwok et&#xa0;al., 2013</xref>; <xref ref-type="bibr" rid="B43">Tilling et&#xa0;al., 2019</xref>). Compared to the March SIT trends in PIOMAS (<xref ref-type="fig" rid="f6">
<bold>Figure&#xa0;6A</bold>
</xref>), we can also see negative trends along the eastern coast of Greenland and the Baffin Sea in the MME (<xref ref-type="fig" rid="f6">
<bold>Figure&#xa0;6B</bold>
</xref>). The areas with negative trends retreat in September, but the decreasing trends are much larger (<xref ref-type="fig" rid="f6">
<bold>Figures&#xa0;6C, D</bold>
</xref>), particularly in PIOMAS. As there is some thin sea ice from the MME along the eastern coast of Greenland in September (<xref ref-type="fig" rid="f4">
<bold>Figure&#xa0;4E</bold>
</xref>), we can still see negative trends of SIT in the MME (<xref ref-type="fig" rid="f6">
<bold>Figure&#xa0;6D</bold>
</xref>).</p>
<fig id="f6" position="float">
<label>Figure&#xa0;6</label>
<caption>
<p>Spatial distributions of <bold>(A)</bold> PIOMAS and <bold>(B)</bold> MME SIT trends between 1980 and 2014 in March. <bold>(C, D)</bold> same as <bold>(A, B)</bold>, but for September.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1223772-g006.tif"/>
</fig>
<p>As shown in <xref ref-type="fig" rid="f7">
<bold>Figure&#xa0;7</bold>
</xref>, the climatological mean SIT in PIOMAS between 1980 and 2014 was 1.61 m, with an STD of 0.22 m. The largest SIT could be found in the SAM0-UNICON model, which reached 3.13 m. NESM3 had the smallest SIT, with a value of 1.03 m. This indicates that SAM0-UNICON and NESM 3 had the largest model biases in the climatological mean SIT over the Arctic Ocean compared to PIOMAS (blue bars). The same model biases could also be found in the mean SIT for March (orange bars) and September (gray bars). However, the model biases between PIOMAS and the 12 CMIP6 models were smaller in September than in March, suggesting that the CMIP6 models performed better in the sea ice melt season than in the sea ice growth season.</p>
<fig id="f7" position="float">
<label>Figure&#xa0;7</label>
<caption>
<p>Sea ice thickness averaged between 1980 and 2014 from CMIP6 models and PIOMAS reanalysis. The blue, orange, and gray bars indicate the climatological mean SIT over the entire period, in March and September, respectively. The horizontal dashed lines denote the corresponding MME mean SIT. Error bars indicate significance at the 95% confidence level.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1223772-g007.tif"/>
</fig>
<p>We then compared the monthly mean SIT between the PIOMAS and CMIP6 models. The monthly mean SIT of MME and PIOMAS peaked in May, and they decreased during the sea ice melt season, with a minimum MME SIT in August and a minimum PIOMAS SIT in October (<xref ref-type="fig" rid="f8">
<bold>Figure&#xa0;8A</bold>
</xref>). The monthly mean SIT differences between MME and PIOMAS were within 0.10 m, which occurred in summer (June-September). Compared to PIOMAS, the SAM0-UNICON model had the largest SIT difference, which was 1.41 m in October and 1.06 m for the entire 12 months. The SIT difference between the FIO-ESM-2.0 model and PIOMAS averaged over 12 months was only 0.004 m, suggesting that this model performed the best in seasonal cycles among the 12 CMIP6 models.</p>
<fig id="f8" position="float">
<label>Figure&#xa0;8</label>
<caption>
<p>Monthly <bold>(A)</bold> and annual <bold>(B)</bold> climatological mean SIT in the Arctic Ocean between 1980 and 2014. <bold>(C)</bold> Monthly evolution of the difference between MME and PIOMAS from 1980 to 2014 in March (black line), September (red line), and the annual mean (blue line). The dashed lines indicate the corresponding linear trends.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1223772-g008.tif"/>
</fig>
<p>At interannual time scales, we found decreasing SIT trends and interannual variability in PIOMAS and all CMIP6 models from 1980 to 2014 (<xref ref-type="fig" rid="f8">
<bold>Figure&#xa0;8B</bold>
</xref>), consistent with previous studies (<xref ref-type="bibr" rid="B5">Cavalieri and Parkinson, 2012</xref>; <xref ref-type="bibr" rid="B3">Bindoff et&#xa0;al., 2019</xref>). The annual mean MME showed consistent variability with PIOMAS, with differences of less than 0.28 m. Among the 12 CMIP6 models, the SAM0-UNICON had the largest positive bias compared to PIOMAS, with a value of 1.28 m in 1985, and the NESM 3 model had the largest negative bias, -0.65 m, in 1997. Overall, the FIO-ESM-2.0 model had the smallest difference of 0.11 m over the whole period between 1980 and 2014, which was the best simulation of the annual mean SIT. The differences between MME and PIOMAS in March and September and the annual mean from 1980 to 2014 were within 0.4 m (<xref ref-type="fig" rid="f8">
<bold>Figure&#xa0;8C</bold>
</xref>). The smallest differences occurred between 1990 and 2010, which were less than 0.15 m. We could also find decreasing trends in the differences between MME and PIOMAS, which indicates that the performance of CMIP6 models has improved over the past decades.</p>
<p>
<xref ref-type="fig" rid="f9">
<bold>Figure&#xa0;9</bold>
</xref> shows the simulation skills of the CMIP6 models. We found that most models have correlation coefficients of 0.8-0.9 and CRMSEs of 0.3-0.9 m. The correlation coefficients in almost all CMIP6 models were larger than 0.8, except the SAM0-UNICON model, which had a correlation coefficient of 0.7. The MME showed the highest correlation with PIOMAS, with a correlation coefficient of 0.93 (above the 95% significance level). Additionally, the CRMSE of the MME was the smallest among all CMIP6 models, with a value of 0.37. The SAM0-UNICON and CESM2-WACCM had CRMSE greater than 0.75, implying large biases in these two models. It was also shown that the NorESM2-MM model had the smallest variability, but the SIT variability in CESM2-WACCM was the highest. These results further demonstrate that the SAM0-UNICON model performs worse than the other CMIP6 models shown in <xref ref-type="fig" rid="f7">
<bold>Figures&#xa0;7</bold>
</xref>, <xref ref-type="fig" rid="f8">
<bold>8</bold>
</xref>, suggesting that it is necessary to use the MME results to better represent the sea ice evolution in the CMIP6 models.</p>
<fig id="f9" position="float">
<label>Figure&#xa0;9</label>
<caption>
<p>Taylor diagrams displaying statistical comparisons of monthly mean SIT over the Arctic Ocean from January 1980 to December 2014 between different models and PIOMAS. The blue, green, and gray lines represent the correlation coefficient, normalized centered root mean square errors, and standard deviations, respectively. PIOMAS is indicated with the red dot.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-10-1223772-g009.tif"/>
</fig>
</sec>
</sec>
<sec id="s4" sec-type="discussion">
<label>4</label>
<title>Discussion and conclusion</title>
<p>In this study, we evaluated the SIT simulation in 12 CMIP6 models using satellite observations and PIOMAS reanalysis. We assessed not only the mean state, seasonal cycle, and spatial distributions of SIT but also the intercomparison of SIT simulations in 12 CMIP6 models. We found that the CMIP6 MME can well represent the mean state and monthly cycle of SIT in the Arctic Ocean. The variances of the annual mean SIT in PIOMAS are very small in most of the Arctic Ocean. We also found decreasing trends in SIT over the entire Arctic Ocean in all seasons. The CMIP6 models performed better in the sea ice melt season than in the sea ice growth season. The FIO-ESM-2.0 model performed the best among 12 CMIP6 models in seasonal cycles, but the SAM0-UNICON model had the largest bias and performed worse than the other CMIP6 models.</p>
<p>We chose 12 CMIP6 models with CICE components and compared their performance in simulating the SIT in the Arctic Ocean. Our results showed that the model performances vary in different CMIP6 models, although with the same sea ice component. Various factors can cause the SIT biases in CMIP6 models. On the one hand, the bias can originate from the CICE model, e.g., the version of the CICE model, the uncertainty of the subgrid-scale ice thickness distributions and ice thickness categorization, etc. (<xref ref-type="bibr" rid="B46">Urrego-Blanco et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B47">Wang et&#xa0;al., 2020</xref>). On the other hand, the CICE model is coupled with ocean and atmosphere models that transfer heat, salt, and momentum fluxes to the ice model (<xref ref-type="bibr" rid="B19">Kumar et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B49">Yu et&#xa0;al., 2022</xref>). Biases from unrealistically simulated surface air and ocean temperature, 10 m winds, snowfall/depth, and surface albedo or coarse spatial resolution can also affect the SIT simulation in the CICE model (<xref ref-type="bibr" rid="B9">Crawford et&#xa0;al., 2023</xref>). Our study shows which combination of CICE, ocean, and atmosphere models in CMIP6 is the best, which will be beneficial for the development of the next generation of CMIP models with a CICE component. </p>
<p>In addition to the CICE components, there are also other sea ice model components in CMIP6, such as FESOM, SIS2, LIM3, GFDL, GISS SI, NEMO-LIM3, COCO 4.9, and MPIOM 1.63. Although previous studies have evaluated the SIT simulations in FESOM, LIM3, and NEMO-LIM3 (<xref ref-type="bibr" rid="B31">Pemberton et&#xa0;al., 2017</xref>; <xref ref-type="bibr" rid="B36">Semmler et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B42">Tian et&#xa0;al., 2021</xref>), our understanding of the SIT simulations in the other sea ice models is limited. Therefore, further investigations are needed to assess the SIT simulations in the CMIP6 models with the other sea ice model components.</p>
<p>As shown in <xref ref-type="fig" rid="f4">
<bold>Figures&#xa0;4</bold>
</xref>&#x2013;<xref ref-type="fig" rid="f6">
<bold>6</bold>
</xref>, the biases, variability, and trends of SIT vary in different subregions. Previous studies have shown different changes in SIT and SIE in the Arctic Ocean. For example, the edge of the seasonal Arctic sea ice is constantly retreating toward the central Arctic under global warming, resulting in a decrease in SIE (<xref ref-type="bibr" rid="B27">Meier et&#xa0;al., 2007</xref>). SIT also decreased by 36% in the western and central Arctic from the 1980s to the early 2000s (<xref ref-type="bibr" rid="B21">Kwok and Rothrock, 2009</xref>). The decrease in SIT will further reduce sea ice cover and increase the area of the open ocean (<xref ref-type="bibr" rid="B30">Park et&#xa0;al., 2015</xref>). The decreasing rate of SIE is the largest in the Beaufort and Chukchi Seas, with values of 0.36&#xd7;10<sup>5</sup> km<sup>2</sup>/year (<xref ref-type="bibr" rid="B14">Hu et&#xa0;al., 2022</xref>). Our results show that the decreasing trends of SIT vary in different subregions of the Arctic Ocean. However, our understanding of SIT simulations in CMIP6 models with CICE components in these subregions is limited and needs further evaluation.</p>
</sec>
<sec id="s6" sec-type="data-availability">
<title>Data availability statement</title>
<p>The CS2SMOS product version v205 can be downloaded from <uri xlink:href="https://data.seaiceportal.de/data/cs2smos_awi/">https://data.seaiceportal.de/data/cs2smos_awi/</uri>. The PIOMAS reanalysis (version 2.1) is available at <uri xlink:href="http://psc.apl.uw.edu/research/projects/arctic-sea-ice-volume-anomaly/">http://psc.apl.uw.edu/research/projects/arctic-sea-ice-volume-anomaly/</uri>. The CMIP6 model simulations can be accessed from <uri xlink:href="https://esgf-node.llnl.gov/projects/cmip6/">https://esgf-node.llnl.gov/projects/cmip6/</uri>. The NOAA/NSIDC Climate Data Record of Passive Microwave Sea Ice Concentration, Version 3 datasets, are obtainable from <uri xlink:href="https://nsidc.org/data/G02202/versions/3">https://nsidc.org/data/G02202/versions/3</uri>.</p>
</sec>
<sec id="s7" sec-type="author-contributions">
<title>Author contributions</title>
<p>JL conceived the study and developed the conceptual framework. MX analyzed the results and plotted the figures. All authors contributed to the interpretation of the results and the writing and editing of the manuscript. All authors contributed to the article and approved the submitted version.</p>
</sec>
</body>
<back>
<sec id="s8" sec-type="funding-information">
<title>Funding</title>
<p>This study was funded by the National Science Foundation Funds of China (41706008, 42130409), the Fundamental Research Funds for the Central Universities, China (1074-423102), Hohai University (522020512), and the Jiangsu Provincial Innovation and Entrepreneurship Program (JSSCRC2021492).</p>
</sec>
<sec id="s9" sec-type="COI-statement">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec id="s10" sec-type="disclaimer">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<ref-list>
<title>References</title>
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<citation citation-type="book">
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