A clustering-based approach to ocean model-data comparison 1 around Antarctica 2

10 The Antarctic Continental Shelf Seas (ACSS) are a critical, rapidly-changing element of the Earth system. 11 Analyses of global-scale general circulation model (GCM) simulations, including those available through the 12 Coupled Model Intercomparison Project, Phase 6 (CMIP6), can help reveal the origins of observed changes and 13 predict the future evolution of the ACSS. However, an evaluation of ACSS hydrography in GCMs is vital: previous 14 CMIP ensembles exhibit substantial mean-state biases (reflecting, for example, misplaced water masses) with a wide 15 inter-model spread. Because the ACSS is also a sparely sampled region, grid-point based model assessments are of 16 limited value. Our goal is to demonstrate the utility of clustering tools for identifying hydrographic regimes that are 17 common to different source fields (model or data), while allowing for biases in other metrics (e.g., water mass core 18 properties) and shifts in region boundaries. We apply K-means clustering to hydrographic metrics based on the 19 stratification from one GCM (Community Earth System Model version 2; CESM2) and one observation-based 20 product (World Ocean Atlas 2018; WOA), focusing on the Amundsen, Bellingshausen, and Ross Seas. When 21 applied to WOA temperature and salinity profiles, clustering identifies “primary” and “mixed” regimes that have 22 physically interpretable bases. For example, meltwater-freshened coastal currents in the Amundsen Sea, and a region 23 of high salinity shelf water formation in the southwestern Ross Sea emerge naturally from the algorithm. Both 24 regions also exhibit clearly differentiated inner-and outer-shelf regimes. The same analysis applied to CESM2 25 demonstrates that, although mean-state model biases in water mass T-S characteristics can be substantial, using a 26 clustering approach highlights that the relative differences between regimes, and the locations where each regime 27 dominates, are well represented in the model. CESM2 is generally fresher and warmer than WOA and has a limited 28 fresh-water-enriched coastal regimes. Given the sparsity of observations on the ACSS, this technique is a promising 29 tool for the evaluation of a larger model ensemble (e.g., CMIP6) on a circum-Antarctic


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The Antarctic Continental Shelf Seas (ACSS, defined here as the ocean regions adjacent to Antarctica with 4 evident in the Amundsen, Bellingshausen, and Ross Seas (ABRS) sector of the ACSS. There, the time-mean ocean state of the objectively analyzed temperature and salinity field, as represented in the 0.25-degree World Ocean Atlas version 2018 (WOA hereafter), suggests that the ABRS can be roughly separated into two geographical regions, the locally, through brine rejection from winter sea ice formation in coastal polynyas, resulting in regionally averaged water well below 0°C at water depths of 100 m to 700 m (Figure 1c). At the same depth range in the Amundsen-

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Bellingshausen Seas, water temperatures can reach +1.2°C due to the presence of Circumpolar Deep Water (CDW).

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In addition to these stark contrasts in regional mean temperature (and salinity), there is also significant 68 spatial variability within each region of the ABRS, and across the continental shelf break. For example, Figure 1  to calculate seawater properties. The absolute salinity (S A ) has unit of g/kg, and conservative temperature (Θ) is in 7 recalculating the distances, and redistributing data points among the groups. The K-means algorithm will have multiple solutions because it is initialized with randomly selected data. We apply the K-means 1,000 times and The K-means algorithm requires specification of the number of groups (K). We use Silhouette scores s i (n) In Eqn. 2, n represents the number of data points in group k i , a(ξ) is the mean dist from a data point ξ to all other 148 data points within the group k i , and b(ξ) is mean dist from ξ to all other data points outside the group k i . Silhouette 149 scores are evaluated for each data point ξ in the group k i and range between -1 and 1. If ξ lays perfectly at the 150 centroid of group k i , then s i (n)=1.

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A rigid interpretation of the Silhouette algorithm would choose the value of K that corresponds to the 152 highest mean value of s i (n). However, the optimal K value can vary with different clustering evaluation methods (e.g., Elbow method: Thorndike, 1953) and different domains. The selection of K is thus based not only on the 154 results of Silhouette assessment but also on the ability to interpret the groups as representative of different 155 underlying physical processes (see section 3).

Density-based clustering technique
8 algorithm continues until all data points are either clustered into pools of data or labeled as outliers. In the current study, we choose MinPts = 10 and = √ 2 + 2 . The value of ε is then selected (Table 1) so that the largest pool of 169 data contains at least 97% of non-outlier points (Table 2). This pool of data constitutes the core of each group.

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Our goal in this analysis is to utilize key features of local water columns to identify regions with similar 173 hydrographic properties. Such metrics must be able to capture stratification, and the changes in T and S in both along-and cross-shelf directions. For the ACSS, the metrics must include salinity because it is the dominant factor influencing water column stability and reflects critical processes such as brine input during sea ice formation, and freshwater inputs from melting sea ice and ice shelves. By itself, however, salinity poorly represents the vertical composition of water masses since it increases monotonically with water depth over most of the ACSS (   above 200 m, where salinity is often less than 34.2 g/kg. In contrast, in the southwestern Ross Sea, the minimum 186 temperature is usually located below 350 m and coincides with much higher salinity (>34.8 g/kg). The northwestern its salinity (between 34.2 to 34.6 g/kg) is higher than near-surface water in the Amundsen-Bellingshausen Seas.

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The salinity at the vertical temperature maximum shows pronounced variations in the cross-shelf direction shelf direction, with lower salinity (<34.7 g/kg) near the coast and ice shelves and higher salinity (>34.8 g/kg) on the continental shelves and near the shelf break.
for WOA and CESM2, testing 2≤K≤13 ( Figure 3). For WOA, the highest value of s i occurs when K=3; for CESM2,

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K=6 has the highest Silhouette score (Figure 3a

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Vertical profiles of temperature and salinity are shown for each WOA group in Figure 5. The mean vertical 232 structure of each group is clearly different; furthermore, the standard deviations at each depth within groups are 233 much smaller than those of regional mean profiles (Table 3). With these vertical structures as context, we examine lying between the properties of surface waters in groups 1 and 5. In the subsurface, group 2 has a temperature above -0.5°C and salinity above 34.5 g/kg, which represents modified CDW on the shelf (Carmack, 1970; Orsi and Group 3, which is found on the outer continental shelf and the continental slope of the Ross Sea (Figure 3e),

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shows high standard deviations in temperature above 700 m (Figure 5c), similar to group 2. However, the water in 253 this regime is generally denser than group 2. The surface water in group 3 is fresher than that of group 5 (Figure5c, 5d). In this region, Winter Water (WW) with salinity 33.8-34.5 g/kg, temperature -2 to -0.5°C and density 27 to 27.5 g/m 3 , overlays CDW (salinity 34.6 to 36.8 g/kg, temperature 0 to +2°C and density 27.8 to 27.9 g/m 3 ), with a mean group 4 has a pronounced thermocline and halocline at shallow depth. These three groups (1, 4 and 5) represent the complex vertical structures, more spatial variability in thermocline at depths above about 600 m (roughly the shelf break) and can be considered as "mixed" regimes.

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To identify hydrographic regimes in CESM2, we conduct the same analyses as described for WOA in the    In this study, WOA has been employed to assess CESM2 results. However, the hydrographic regimes

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The success of this technique at identifying locations and properties of HSSW regimes at other locations 368 on the Antarctic continental shelf suggests that it might be used to evaluate other global and/or regional models on a 369 circum-Antarctic basis. Other metrics might be employed depending on specific research goals. For example, the 370 pycnocline depth, or the mean or maximum temperature below a fixed depth, may be better metrics of subsurface 371 water masses. It will also be interesting to track water masses and their pathways with metrics based on their 372 characteristic properties. However, we note that comparisons of the locations of groups could become complex if the 373 approach is applied to multiple models with substantial biases between their representations of specific water masses.     583   584  585  586  587  588  589  590  591  592  593  594  595  596  597  598  599  600  601  602  603  604  605  606  607