The input data for the AI model consist of gridded sea surface data derived from satellite observations. For this study, we focus on variables that directly describe the ocean's physical state. These variables, with daily temporal resolution from 1993 to 2023, include sea surface temperature (SST), sea surface salinity (SSS), and absolute dynamic topography (ADT). This approach intentionally excludes variables related to external atmospheric forcing (e.g., surface wind) or biogeochemical processes (e.g., ocean color). We used three daily products from the Copernicus Marine Service (CMEMS): Multi-mission ADT product at 1/8° spatial resolution (ID: SEALEVEL_GLO_PHY_L4_MY_008_047), OSTIA SST at 1/20° spatial resolution (ID: SST_GLO_SST_L4_NRT_OBSERVATIONS_010_001), and the SSS at 1/8° spatial resolution (ID: MULTIOBS_GLO_PHY_S_SURFACE_MYNRT_015_013). These products include error variables that represent the formal mapping error calculated via an optimal interpolation process. The variables indicate the uncertainty of the gridded field relative to the raw data along satellite tracks; however, they do not represent a complete error budget or include errors arising from physical processes . To unify the spatial resolution of the input data, all variables were regridded to a 1/8° grid resolution using linear interpolation. To encode geographic information and preserve the periodicity of the spherical domain, we transformed the coordinates into X, Y, and Z features : 1XYZ=sin⁡(ϕ×π180)sin⁡(λ×π180)⋅cos⁡(ϕ×π180)-cos⁡(λ×π180)⋅cos⁡(ϕ×π180) where ϕ is latitude and λ is longitude. These X, Y and Z features were used as the model input.

For the training dataset, thermohaline profiles from CTD and Argo floats were sourced from the Coriolis Ocean dataset for Reanalysis version 5.2 (CORA5) Easy CORA product provided by CMEMS (ID: INSITU_GLO_PHY_TS_DISCRETE_MY_013_001). This is a delayed-mode dataset with preprocessed and quality-controlled profiles from CTD, Argo floats, and other platforms. The profiles are separated into training set (1993–2020) and test set (2021–2023). We selected profiles that reached a maximum pressure greater than 700 dbar for the training process. This resulted in a training set of 155 030 profiles distributed across the study area (Fig. ). For monthly climatological thermohaline profiles, we used the World Ocean Atlas 2023 (WOA23) dataset, which has a 1/4° spatial resolution and it was linearly interpolated into 1/8° resolution. All in-situ and climatological profiles were linearly interpolated onto 128 evenly spaced vertical layers between 10 and 700 dbar. In-situ profiles from regions where WOA23 climatological profiles extended to at least 700 dbar were included in both training and test datasets. Only profiles containing more than 50 valid observation points within the sampled depth range (typically 10–1500 dbar) were used. For these profiles, linear interpolation was applied as a vertical resampling step to align the data onto the 128 vertical levels. Profiles with gaps were excluded from training. For the test dataset, profiles with gaps were retained by applying masks to use only valid-level observations for error estimation.

Our validation involved a two-step procedure: basin-scale and core validation.

The first step, basin-scale validation, assessed the overall performance throughout the study area by a 10° meridional interval. For this, we used the number of 23 631 profiles from the test set (2021–2023).

The second step, core validation, focused on evaluating the model's long-term temporal consistency using continuous time series data from mooring observations. For this purpose, we used data from the Kuroshio Extension Observatory (KEO), the East/Japan Sea (EJS) Current Measurements (EC1) mooring, and two Pressure-Inverted Echo Sounder (PIES) arrays. The KEO buoy was deployed in the Kuroshio Extension recirculation gyre (32.3° N, 144.6° E) and has measured TS at 32 depths down to 525 m since June 2004. The EC1 mooring is located in the Ulleung Interplain Gap (UIG) of the EJS and is equipped with sensors at multiple depths (e.g., 400, 1400, 2200 m). For the EC1 mooring data, only temperature data are compared due to the lack of salinity observations. The analysis focused on the 2006–2012 period, as the observations were concentrated in the thermocline. Both KEO and EC1 moorings are part of the OceanSITES network. Since OceanSITES data are routinely assimilated into ocean reanalysis models, these moorings do not provide independent observations for validation. On the other hand, data from the PIES array are not assimilated into ocean reanalysis products, providing independent observations for validation. We used two PIES arrays. One, an array of 46 instruments was deployed during the KESS project (2004–2006), and the other, an array of 25 PIES deployed in the EJS, covering the Ulleung Basin from 1999–2001. As a broader performance benchmark, we also compared our results with temperature and salinity outputs from the HYCOM, GLORYS, and ARMOR3D reanalysis products for the period from 1994 to 2015 (Table ). This period corresponds to the available period of the HYCOM reanalysis outputs. While all three are data-assimilative products, HYCOM and GLORYS are based on numerical ocean models, whereas ARMOR3D is a statistically-based product. To ensure temporal consistency, all mooring and model outputs used in the validation step were averaged to daily resolution.

To evaluate the spectral dependence of the model's performance, we computed the magnitude squared coherence between the observed and estimated time series. The coherence estimates were obtained using Welch's method with a Hanning window of 128 d and 50 % overlap. The 95 % significance level for the coherence estimates was determined based on the degrees of freedom .

Our proposed model, the thermohaline profile estimating network (TS-Cast), is designed to estimate vertical thermohaline profiles by dynamically adjusting monthly climatological profiles using satellite-measured sea surface data (Fig. 2). TS-Cast's key innovation lies in its hybrid approach. Rather than generating profiles solely from instantaneous satellite data, it treats the monthly climatological profile as a physically-grounded prior and learns its dynamic adjustments from real-time satellite observations. This conditioning is performed within a U-Net architecture by leveraging Feature-wise Linear Modulation (FiLM) layers . The architecture consists of four components: (i) a satellite feature encoder, (ii) a U-Net backbone operating on the climatological prior, (iii) FiLM conditioning layers that inject satellite information into the U-Net, and (iv) parallel output heads for the temperature/salinity prediction and the error variance. Each component is described below.

To ensure physical consistency in the model's estimations, we incorporated two key strategies into our loss function: a density-based physical constraint and an uncertainty-aware weighting scheme. TS-Cast network directly estimates temperature (T^) and salinity (S^) profiles, but also their associated depth-dependent uncertainty via the predicted error variance (σ2). Instead of predicting the variance directly, the network outputs the logarithmic error variance (log⁡σ2) to ensure numerical stability. This approach, based on the work of multi-task learning using uncertainty , allows the model to learn spatiotemporal and depthwise varying error variances, effectively giving less weight to predictions in regions or depths with naturally high variability. The loss for temperature and salinity is formulated to minimize the negative Gaussian log-likelihood, which results in the following expression for each vertical level (i): 3LT=1N∑i=1N12σ^T,i2(Ti-T^i)2+12log⁡σ^T,i24LS=1N∑i=1N12σ^S,i2(Si-S^i)2+12log⁡σ^S,i2

Here, (Ti,Si) are the ground-truth values, (Ti^,S^i) are the model predictions, and (σ^T2,σ^S2) are the predicted error variances for temperature and salinity, respectively. This formulation encourages the model to produce smaller errors where its estimated error variance (σ^2) is low and allows for larger deviations where the error variance is high. The 12log⁡σ^2 term prevents the network from trivially inflating the variance to evade the consistency penalty. Notably, this uncertainty-weighted loss acts as an adaptive normalization mechanism, allowing the model to handle the different scales of temperature, salinity, and density without requiring explicit pre-standardization of the target variables. The model learns to predict this error variance by using the local monthly climatology profile as input, which provides essential information about regional variability and seasonal water mass characteristics.

In addition to the prediction accuracy of TS profiles, we enforce a physical constraint based on the equation of state for seawater , adopting the physics-informed approach . While the network does not directly output density, we compute the density profile (ρ^) from the predicted TS profiles (T^,S^) and compare it to the ground-truth density (ρ) derived from the label profiles (T,S). This term penalizes the model for generating physically implausible combinations of temperature and salinity. 5Lρ=1N∑i=1N12σ^ρ,i2(ρi-ρ^i)2+12log⁡σ^ρ,i2 where σ^ρ2 is the predicted error variance for density. The final composite loss function for training is a sum of these individual components: 6Ltotal=LT+LS+Lρ

This formulation addresses the weighting among the different error terms. Instead of using fixed hyperparameters, the model learns the optimal, data-dependent weight for each observation through the predicted variance σ2. This multi-objective loss function guides the model to produce results that are not only accurate but also physically consistent.

The overall performance of the TS-Cast model was first evaluated against a test set of scattered CTD/ARGO profiles across the Northwestern Pacific. Figure shows the vertical profiles of the root mean square error (RMSE) for both temperature and salinity, binned into six distinct latitudinal bands between 20° N and 50° N. The evaluation also includes a specific regional validation for the EJS, shown as blue and green lines for latitudes north of 35° N.

For temperature, the RMSE across the wider Northwestern Pacific (black line) is generally below 1.0° C but shows a clear latitudinal trend. In the southern bands (20° N–35° N), the RMSE is consistently low (≤1° C), while performance degrades in the northern bands (40° N–45° N), with the RMSE peaking at nearly 2° C. This subsurface maximum corresponds to the main thermocline. In sharp contrast, below 300 dbar, the model shows high accuracy for the EJS (blue line). The RMSE in the EJS remains close to 1° C or lower than 2° C, comparable to the basin-scale results. This suggests the model effectively captures the unique and relatively uniform thermal structure of the EJS.

For salinity, the basin-scale RMSE (black line) also increases with latitude, rising from 0.1 psu in the south to nearly 0.2 psu in the north. The largest errors are in the upper 200 dbar. Again, the model's performance in the EJS (blue line) shows a different pattern. The salinity RMSE for the EJS is consistently lower than in the open Pacific, generally staying below 0.1 psu. This highlights the model's capability in handling the distinct water mass properties of this semi-enclosed marginal sea.

To assess the contribution of the climatological information to TS-Cast, we conducted an ablation experiment in which the climatological profile prior and the ADT anomaly vector were replaced with zeros, hereafter referred to as TS-Cast (no clim.). The results (Fig. ) show that removing the climatological inputs has minimal impact on the basin-scale RMSE, with the climatological prior providing only modest gains in final prediction accuracy. However, the training dynamics reveal a clear difference. The TS-Cast model exhibits substantially more stable validation loss compared with TS-Cast (no clim.), which shows large fluctuations throughout training. We therefore retain the climatological input as a physically meaningful architectural component that stabilizes learning, while being transparent about its limited contribution to prediction accuracy.

To address concerns regarding the independence of our validation, we benchmarked TS-Cast against GLORYS12v1, ARMOR3D, and the WOA23 monthly climatology on the test set. HYCOM is excluded from the basin-scale comparison because its reanalysis output does not extend to the 2021–2023 test period. We note that this comparison inherently favors the reanalysis products, as both GLORYS12v1 and ARMOR3D assimilate in-situ profiles from the CORA dataset, which includes the Argo and CTD profiles used for evaluation. Despite this disadvantage, TS-Cast achieves performance comparable to GLORYS12v1 across all latitude bands for both temperature and salinity, and substantially outperforms the WOA23 climatological baseline (Fig. ). ARMOR3D exhibits the lowest RMSE overall, consistent with its direct assimilation of the evaluation data.

These results demonstrate that the TS-Cast model can produce physically realistic and accurate TS profiles. The comparative analysis reveals a nuanced picture of its performance: while the model provides a strong baseline for the entire basin, its accuracy is highest in the subtropical regions and within the geographically distinct EJS. The model's performance is somewhat lower in the highly variable subarctic frontal zones of the open Pacific, highlighting the challenge of modeling these complex regions.

TS-Cast performance was validated against long-term mooring observations from two contrasting regions: the KEO station (Kuroshio Extension) and EC1 station (EJS). Validation context differs by product type. The reanalysis products (GLORYS, HYCOM, and ARMOR3D) assimilate OceanSITES mooring data . Their agreement with these moorings reflects self-consistency of the data assimilation rather than independent skill. TS-Cast was trained exclusively on satellite surface data and sparse ARGO/CTD profiles, so it was not exposed to any subsurface mooring observations. Therefore, this comparison tests its genuine generalization capability to infer vertical structure from surface patterns.

The KEO mooring has provided continuous multi-year observations since 2004 in the energetic Kuroshio Extension, a region characterized by intense mesoscale eddy activity. The reconstructed TS-Cast temperature field (Fig. b) demonstrates high fidelity to observations (Fig. a), successfully infilling significant temporal gaps while robustly capturing both the pronounced seasonal cycle in the upper ocean and the deeper, irregular isotherm displacements driven by eddy or meandering processes.

Quantitative validation metrics (Fig. f, g) confirm this visual assessment. In the upper 300 m, where seasonal variability dominates, TS-Cast achieves lower RMSE and higher correlation outperforming both GLORYS and HYCOM reanalyses. ARMOR3D exhibits the highest overall performance (r>0.85 at all depths), consistent with its direct assimilation of KEO mooring data. Notably, TS-Cast performance converges with ARMOR3D below 300 m depth (both r≈0.9), demonstrating that satellite surface observations alone can achieve subsurface reconstruction skill comparable to in-situ assimilative products in the main thermocline.

TS-Cast demonstrates similarly strong performance for salinity (Fig. ). Correlation coefficients (Fig. g) remain significantly higher than GLORYS and HYCOM reanalyses down to 500 m layer, indicating accurate capture of subsurface salinity variability in both phase and amplitude, properties that challenge numerical ocean models. The consistently lower RMSE between 300 and 500 m (Fig. f) further demonstrates enhanced skill in representing the complex vertical haline structure of the Kuroshio Extension. Below 300 m depth, TS-Cast achieves correlation (r≈0.9) outperforming ARMOR3D, demonstrating that satellite surface observations can effectively constrain main halocline properties. Additionally, qualitative differences are reflected in reconstruction characteristics by exhibiting vertical discontinuities, particularly evident between 100–300 m depth, which appear to be artifacts in ARMOR3D fields (Fig. e).

Validation at the EC1 mooring (Fig. ) serves as a strict test of the model's generalization ability in a different physical environment under conditions of data sparsity. TS-Cast successfully reconstructs the dominant oceanographic features of the EJS, including the deep vertical mixing in winter that forms thick mixed layers and the strong, shallow stratification in summer (Fig. b). The discrete performance metrics (Fig. f, g), plotted as scatter points due to the data gaps, reveal a consistent trend. TS-Cast (red triangles) exhibits generally lower RMSE and higher correlation values across the water column than the reanalysis products. There was no significant difference between RMSE (depth-mean RMSE ∼1.6° C), but the HYCOM and GLORYS show lower correlation (∼0.2) than TS-Cast and ARMOR3D (∼0.6). This reconstruction from limited data demonstrates the model's robustness and its capability to infer realistic subsurface structures, confirming its applicability across diverse circulation regimes.

To evaluate the model's ability to represent key vertically integrated properties of the water column and its variability, we validated its outputs against data from two arrays of PIES located in the EJS and the Kuroshio Extension (Fig. ). These PIES arrays provide observations independent of ocean reanalysis data assimilation systems. PIES measures the round-trip acoustic travel time (τ), a proxy for the depth-integrated heat and salt content, thus providing a robust test of the model's baroclinic structure. In this study, the τ anomaly is used to isolate the baroclinic variability from the time-mean state. Since τ is dominated by water depth, using its anomaly facilitates a direct comparison of baroclinic signals across instruments deployed at different depths. We compared the observed τ anomaly against the τ anomaly calculated from the temperature and salinity profiles of TS-Cast, GLORYS, HYCOM, and ARMOR3D.

The spatial distribution of temporal correlation coefficients (Fig. ) reveals the performance of TS-Cast. Across both arrays, TS-Cast (Fig. a, e) demonstrates spatially coherent and remarkably high correlations with the PIES observations, with coefficients consistently exceeding 0.5 in the EJS and ranging from 0.8 to nearly 1.0 in the Kuroshio Extension. Similarly, ARMOR3D (Fig. d, h) also demonstrates high, spatially coherent correlations comparable to TS-Cast. In contrast, both GLORYS and HYCOM exhibit significantly lower and more spatially heterogeneous correlations. In many locations, particularly in the EJS, the correlation coefficients for GLORYS and HYCOM are close to 0.5 or even less, indicating a failure to capture the observed variability.

These statistics are further supported by direct time series comparisons at individual sites (Fig. ). Visually, the τ anomaly from TS-Cast (red lines) closely tracks the observed variability (black lines), while the other reanalysis products show more incoherent high-frequency variability. For instance, at site P32 in the EJS, TS-Cast achieves a correlation of 0.81, whereas other reanalysis products score below 0.55. Similarly, at site A2 in the KESS array, TS-Cast's correlation of 0.95 is higher than that of GLORYS (0.75), HYCOM (0.78), and slightly higher than ARMOR3D (0.92). This comprehensive comparison confirms that TS-Cast more accurately captures the baroclinic variability integrated over the entire water column, a critical aspect of understanding ocean dynamics and heat content.