OPEM-MOM6 incorporates coupled model components using MOM6 for ocean physics and SIS2 for sea ice dynamics. The Arakawa-C grid system (Arakawa and Lamb, 1977) with 1704 × 1392 tracer points was used to solve the primitive equations under the Boussinesq and hydrostatic approximations. The model domain encompassed the NWP region, spanning from 5 to 63° N to 99 to 170° E. The model had a horizontal resolution of 1/24° in both longitude and latitude, equivalent to approximately 4 km. The bathymetry data were constructed by integrating the General Bathymetric Chart of the Oceans (GEBCO) 2024 and the KorBathy30s dataset, a regional bathymetry dataset for the Korean Peninsula (Seo, 2008). The minimum bathymetric depth was set to 10 m to account for tidal variations, as wetting and drying were not employed, while the maximum depth was limited to 5000 m to enhance efficiency of vertical grid utilization.

To integrate the ocean model forward in time, a split explicit method (Hallberg, 1997; Hallberg and Adcroft, 2009) was employed, efficiently separating the handling of fast and slow processes. The baroclinic time step was set to 300 s, while the barotropic time step varied and was determined as the largest integer fraction of the baroclinic time step required for stability. A longer time step of 900 s was applied for thermodynamic calculations.

In this study, two vertical coordinate systems, HYBRID and ZSTAR, were configured with 75 layers. Both configurations featured the finest vertical resolution near the surface. In ZSTAR, the layer thickness gradually increased with depth, reaching a maximum of 349.43 m just above the deepest model depth of 5000 m, and the bottom topography was represented using partial-step layers to better capture sloping bathymetry and improve pressure-gradient consistency.

In the HYBRID configuration, ZSTAR was used to effectively resolve the mixed layer in unstratified regions, providing high resolution where vertical mixing and surface interactions were most significant. Below the mixed layer, isopycnal coordinates were employed to minimize spurious diapycnal mixing and accurately represent the stratified conditions found in deeper waters. The HYBRID in MOM6 is implemented through a column-wise algorithm that combines the strengths of both approaches. In each water column, a stable, monotonic density profile is first derived from temperature, salinity, and pressure and mapped onto a prescribed set of target densities to obtain isopycnal candidate interface depths. Independently, a nominal ZSTAR grid is defined and used as a one-sided lower-bound constraint for each layer. At every vertical level, the model selects the deeper of the two, either the isopycnal candidate or the ZSTAR floor, and then applies bottom and optional thickness/depth limits. As a result, there is no discrete switch between coordinate systems: the transition depth naturally occurs where an isopycnal surface would otherwise lie above the ZSTAR floor. Because mixed layers are deeper and stratification weaker at higher latitudes, the crossing with the ZSTAR floor occurs at greater depths, leading to a poleward deepening of the transition layer. Over continental shelves, the strength of the ZSTAR constraint scales with the local depth. In shallow regions this scaling makes the ZSTAR floor very shallow, so when residual stratification exists, the interfaces tend to follow the target isopycnals through most of the water column. The overall structure of the model interfaces and their interaction with topography are illustrated in Fig. , which schematically shows how the HYBRID coordinate transitions from ZSTAR near the surface to isopycnal layers in the ocean interior.

In MOM6, HYBRID assigned a target density referenced to 2000 dbar for each interface. The choice of a 2000 dbar reference pressure is widely accepted, as it balances monotonicity in near-surface waters with stability in the deep ocean (Megann, 2018) and maximizes the neutrality of isopycnal surfaces (McDougall and Jackett, 2005). However, variations in the vertical density distribution across global and regional scales led to inefficient resolution use, particularly in weakly stratified regions. To address this, 1 % of the compressibility was artificially retained but centered at 2000 dbar when generating the vertical grid at each time step (Adcroft et al., 2019). In this study, the target density ranged from 1010 to 1037.2479 kgm-3 referenced 2000 dbar, specifically constructed for the Northwest Pacific rather than using the global target density adopted in OM4.0 (Adcroft et al., 2019).

The physical subgrid-scale parameterization settings followed those of Adcroft et al. (2019) and Ross et al. (2023). The ePBL scheme developed by Reichl and Hallberg (2018), with updates accounting for Langmuir turbulence (Reichl and Li, 2019), was employed to parameterize the planetary boundary layer. To parameterize mixed-layer restratification by sub-mesoscale eddies, the scheme proposed by Fox-Kemper et al. (2011) was used, with a frontal-length scale of 1500 m applied for the upscaling of buoyancy gradients. A biharmonic form of horizontal viscosity was used in these simulations. The viscosity was calculated as the maximum value between a biharmonic Smagorinsky viscosity (Griffies and Hallberg, 2000) and a predefined fixed viscosity expressed as u4Δx3, where u4 represents a velocity scale and Δx denotes the local grid spacing. The velocity scale was set to 0.01 ms-1, with a Smagorinsky coefficient of 0.015. Shear-driven turbulence mixing was parameterized by Jackson et al. (2008). The bottom friction was represented using a quadratic drag formulation with a coefficient CD = 0.003. Lateral solid boundaries employed free-slip conditions, allowing tangential flow along the wall while preventing normal flow. Table  provides a summary of the model configurations and parameters.

Both configurations were forced using lateral open boundary conditions from the GLORYS12 reanalysis (Lellouche et al., 2021). The variables used for lateral boundary conditions included daily mean temperature, salinity, sea surface height (SSH), and ocean velocity. The model was forced by astronomical tidal potential forcing, with explicit tidal forcing from boundary conditions rather than parameterized tidal mixing. Tidal harmonics, including four semidiurnal (M2, S2, N2, and K2), four diurnal (K1, O1, P1, and Q1), and two long-period (Mm and Mf) constituents from the TPXO9 v1 dataset (Egbert and Erofeeva, 2002), were applied to impose tidal variations in sea level and velocity on the subtidal boundary data. These 10 constituents were also applied as body forces in the momentum equations to simulate astronomical tidal forcing across the domain. Combined tidal and subtidal sea levels, along with barotropic velocities, were prescribed using the radiation boundary conditions described by Flather (1976). For baroclinic flow, a radiation scheme based on Orlanski (1976) was applied, incorporating nudging toward external data following the approach outlined by Marchesiello et al. (2001).

Inflow boundary velocities were strongly constrained with a 3 d nudging timescale, while outflow velocities were weakly adjusted using a 360 d timescale. Temperature and salinity at the boundaries were managed using a reservoir scheme, which adapted boundary conditions based on the internal model state for outflow and external forcing for inflow. The reservoir length scale was set to 9 km.

Surface fluxes between the ocean and atmosphere were derived from hourly ERA5 reanalysis data (Hersbach et al., 2020), including variables such as 2 m air temperature, specific humidity, surface net solar and thermal radiation, mean sea level pressure, total cloud cover, 10 m wind velocity, and precipitation, using the bulk formula from Large and Yeager (2004). River discharge was prescribed using the GloFAS reanalysis version 3.1 (Alfieri et al., 2020). Following the approach of Ross et al. (2023), river discharge was mapped onto the MOM6 grid by identifying coastal outlet points and assigning streamflow to the nearest ocean grid cell using a local drain direction map. A comparison with observations from Datong station revealed that the GloFAS dataset overestimated the Yangtze River discharge. To correct this bias, GloFAS discharge data were adjusted using a bias correction based on the monthly climatological runoff ratio. Freshwater, with zero salinity and a temperature equal to the surface temperature of the discharge grid cell, was added at the surface. Additionally, turbulent kinetic energy was introduced to mix the water column up to a depth of 5 m at discharge points.

Both configurations were initialized using temperature and salinity fields from GLORYS12, which were interpolated to the model grid from 1 January 1993. The spin-up simulation was run for 10 years (1993–2002) using time-varying open boundary and surface atmospheric forcing data. Following the spin-up period, hindcast simulations were performed for 2003–2012 to capture and analyze oceanographic conditions and dynamics. This approach ensured that the models were sufficiently spun up and provided a reliable representation of ocean conditions during the specified period.

The performance of each configuration was evaluated using observational data and physical reanalysis datasets that assimilated observations. For statistical evaluation, Iris v3.1.0 (Hattersley et al., 2023), a Python package for analyzing and visualizing multi-dimensional meteorological and oceanographic datasets, was used to compare both configurations with the reference dataset. For visualization, Cartopy (Met Office, 2022) was employed to represent geographic features, while Iris was utilized to display the computed variable distributions.

Since reference datasets generally had a lower spatial resolution than the model outputs, model outputs from both configurations were conservatively re-gridded onto the coarser-resolution reference dataset grid using Iris before conducting statistical analysis. The statistical evaluation included spatial mean bias (Bias), root mean squared error (RMSE), median absolute error (MedAE), and the Pearson correlation coefficient (Corr). Bias indicated whether the model systematically overestimated or underestimated values. RMSE quantified the overall discrepancy between the model and reference datasets by measuring squared differences, making it sensitive to large errors. In contrast, MedAE provided a robust measure of error by calculating the median of absolute differences, reducing the influence of outliers compared to RMSE. Corr measured similarity in spatial or temporal patterns, ranging from -1 (inverse correlation) to 1 (perfect correlation), independent of magnitude differences.

To compare SST from both configurations, the NOAA 1/4° daily Optimum Interpolation Sea Surface Temperature (OISST) dataset, which interpolates and extrapolates observations from satellites, Argo floats, ships, and buoys, was used to evaluate SST performance in the experiments. Sea surface salinity (SSS) validation was conducted using the GLORYS12 reanalysis dataset. Although observational data for SSS are limited, alternative datasets, such as the CMEMS Multi-Observation Global Ocean Sea Surface Salinity product, have been used in previous studies (e.g., Seijo-Ellis et al., 2024). However, the CMEMS product relies on climatological data for coastal areas, where observational coverage is sparse and uncertainty is high. Specifically, the coastal dataset incorporates pseudo-observations derived from climatological backgrounds within 200 km of the coast, as described in CMEMS documentation. In contrast, GLORYS12 has been shown to exhibit relatively low bias around the Korean Peninsula when compared with in-situ observations (Chang et al., 2023), and also demonstrated reasonable temporal variability when compared with SSS time series from the IEODO Ocean Research Station, located in East China Sea (not shown here). Based on these findings, GLORYS12 was deemed a suitable reference for SSS validation in this study.

The marginal seas of the NWP are heavily influenced by significant freshwater discharge from the Yangtze and Yellow Rivers, which creates extensive low-salinity areas that play a critical role in regional salinity distribution and stratification. Therefore, validating SSS in coastal regions is essential for accurately assessing model performance. Given its consistency in representing salinity distributions across both coastal and open-ocean areas, the GLORYS12 reanalysis dataset was selected as the reference.

The boreal winter and summer mixed layer depth (MLD) was compared to the long-term MLD climatology constructed from World Ocean Database and Argo profiles (de Boyer Montégut, 2024). In this dataset, MLD is calculated using the Δ 0.03 kgm-3 density criterion relative to surface density. The MOM6 diagnostic MLD_003 was used for validation, defining MLD as the depth where potential density exceeds the density at 10 m by 0.03 kgm-3.

To evaluate sea surface height (SSH) variability, monthly absolute dynamic topography (ADT) data from CMEMS were used. These data, produced by merging SSH observations from various satellite altimetry sources, have a horizontal resolution of 0.25°. Additionally, GLORYS12 was used to validate surface current speed and eddy kinetic energy (EKE) in the model simulations. The EKE for each experiment was calculated by interpolating velocity data onto the AVISO geostrophic current data grid and applying the following equation: EKE=12u′2+v′2 where u′2 and v′2 represent deviations of the zonal and meridional velocity components from their respective means over the evaluation period (2003–2012).

To assess the model's ability to reproduce tides, the tidal amplitudes and phases of the M2 (semidiurnal) and K1 (diurnal) constituents were calculated using hourly SSH output with the UTide Python package (Codiga, 2011). The results were then compared with TPXO9, which served as the tidal boundary condition.

Additionally, two reanalysis datasets, GLORYS12 and KOOS-OPEM ReAnalysis 2022 (K-ORA22; Chang et al., 2024), were used to evaluate the performance of each experiment in reproducing vertical temperature and salinity structures. A comparative evaluation by Chang et al. (2023) assessed multiple NWP reanalysis datasets, finding that GLORYS12 exhibited the best performance in reproducing temperature, salinity, and large-scale/mesoscale variability. Meanwhile, K-ORA22 demonstrated superior performance in representing marginal seas, particularly excelling in the Yellow Sea. Given these complementary strengths, GLORYS12 and K-ORA22 were selected as reference datasets for evaluating vertical temperature and salinity structures.

To compare regional variations in temperature and salinity between the two configurations, the analysis was divided into five distinct regions, as shown in Fig. c:

Open ocean area of the NWP,

The Kuroshio and its Extension regions were defined not only based on areas where the climatological surface current speed in GLORYS12 exceeds 0.3 ms-1 but also by including adjacent regions dynamically affected by the K-KE. A summary of the parameters and datasets used in the evaluation is provided in Table .

Figure  compares the SST distributions for boreal winter (DJF) between the OISST observational dataset and simulations from the HYBRID and ZSTAR configurations. The winter mean SST distributions from OISST and both model configurations exhibited strong agreement in both spatial structure and magnitude across the NWP. Biases relative to OISST were low, with HYBRID showing a bias of -0.02 °C and ZSTAR showing a bias of 0.15 °C, indicating overall consistency with observations. Despite this broad agreement, regional biases were evident. In higher latitudes north of 45° N, both configurations exhibited a moderate cold bias of approximately -0.8 °C, with ZSTAR displaying a more pronounced cold bias compared to HYBRID. Warm biases were observed in the Kuroshio and the Kuroshio–Oyashio transition zone, reaching up to 2.0 °C in both configurations. However, this warm bias was more prominent in the HYBRID configuration, particularly in the Kuroshio–Oyashio transition zone. Additionally, the HYBRID configuration exhibited a warm bias in the South China Sea, whereas the ZSTAR configuration demonstrated a more substantial warm bias exceeding 3.0 °C in the East/Japan Sea, which was notably larger than in HYBRID. Statistical metrics further supported the agreement between the models and OISST. Both configurations achieved high spatial correlations of 0.98, with RMSE values of 0.75 °C for HYBRID and 0.74 °C for ZSTAR. MedAE were 0.31 °C for HYBRID and 0.31 °C for ZSTAR, reflecting similar levels of accuracy in representing SST variability across the region.

Figure  presents a comparison of SST distributions for boreal summer (JJA) between OISST observations and simulations from the HYBRID and ZSTAR configurations. Both configurations exhibited similar performance, with RMSE values of 0.67 °C for HYBRID and 0.66 °C for ZSTAR, and both maintained high correlations with OISST (Corr = 0.98), consistent with their performance in winter. However, unlike in winter, both models exhibited warm biases, particularly in the Yellow Sea and high-latitude regions, where biases of approximately 1.0 °C were observed. In contrast, biases in the open ocean of the NWP remained relatively low, typically below -0.3 °C.

The simulated mean SSS values for both HYBRID and ZSTAR configurations (33.97 psu) aligned closely with the GLORYS12 reference mean (33.92 psu), demonstrating good agreement in the large-scale salinity distribution across the NWP (Fig. ). However, the standard deviations (STD) revealed slightly higher variability in the models, with values of 1.54 psu for HYBRID and 1.61 psu for ZSTAR, compared to 1.32 psu in GLORYS12. This indicated that while both models captured regional salinity gradients reasonably well, they tended to overestimate variability.

Regional biases were evident in specific areas. In the Yellow Sea, both configurations exhibited a pronounced negative bias exceeding -1.0 psu, suggesting that excessive freshwater discharge from nearby rivers led to an overestimation of low-salinity water in this region. Conversely, positive biases dominated in the South China Sea, the southeastern Chinese coast, the northern East/Japan Sea, and Sea of Okhotsk, with values exceeding 1.0 psu in some locations. ZSTAR exhibited larger biases than HYBRID in the Yellow Sea, and HYBRID exhibited larger biases than ZSTAR in the South China Sea, the Sea of Okhotsk, and the Kuroshio–Oyashio transition zone. A quantitative comparison with GLORYS12 highlighted differences in model performance. HYBRID achieved a lower RMSE of 0.72 psu compared to 0.80 psu for ZSTAR, suggesting better overall agreement with the reference dataset. Additionally, HYBRID showed a marginally higher spatial correlation with GLORYS12 (0.82) compared to ZSTAR (0.81).

During summer (JJA), the SSS distribution remained similar to winter, with both configurations aligning well with GLORYS12 but showing slightly higher variability (Fig. S1 in the Supplement). The negative bias in the Yellow Sea intensified, exceeding -1.0 psu, while regional bias patterns persisted, with HYBRID showing stronger positive biases in the open ocean and HYBRID exhibiting more negative biases in the Kuroshio–Oyashio transition zone and Sea of Okhotsk. The pronounced fresh bias in the Yellow Sea that, despite applying bias corrections for Yangtze River discharge, river discharge forcing in both configurations may have still been overestimated for other rivers, such as the Yellow River. Therefore, further investigation into discharge from other major rivers is necessary, comparing them with observational datasets for potential corrections.

Figure  compares the MLD distributions for boreal winter (DJF) between the estimates of de Boyer Montégut et al. (2024) and simulations from the HYBRID and ZSTAR configurations. ZSTAR generally simulated a deeper MLD, particularly in regions influenced by western boundary currents, such as the Kuroshio and EKWC, where it overestimated MLD by approximately 20 m relative to the reference, with a mean bias of 1.57 m and an RMSE of 18.27 m. HYBRID exhibited a larger negative bias of about 15 m compared to ZSTAR in the southern open ocean. In addition, HYBRID showed a significant negative bias exceeding 30 m in Sea of Okhotsk. The RMSE for HYBRID was 19.48 m, higher than that for ZSTAR (18.27 m), primarily due to the substantial bias in the Sea of Okhotsk. This indicated that while both configurations showed high spatial correlations with the reference data, they exhibited tendencies to either overestimate or underestimate MLD depths depending on the region, with ZSTAR particularly overestimating MLD in dynamic boundary current areas and HYBRID showing larger biases in high-latitude regions.

Figure S2 in the Supplement also presents the MLD distribution for boreal summer (JJA), when the mixed layer is generally shallower due to enhanced stratification. The estimated summer MLD was shallow across most of the domain (mean: 19.15 m), deepening in western boundary current regions. HYBRID underestimated the MLD (mean: 17.21 m), while ZSTAR slightly overestimated it. ZSTAR showed a higher spatial correlation with the observation and along with lower RMSE.

To ensure a consistent reference level when comparing SSH between the models and the Altimetry dataset, the mean absolute difference between each model and Altimetry SSH was subtracted from the respective model outputs. Overall, both the HYBRID and ZSTAR configurations exhibited SSH distributions that closely aligned with Altimetry, effectively capturing the large-scale features of the region (Fig. ). The standard deviation values of SSH variability, representing spatial gradients, were 43.50 cm for HYBRID and 42.13 cm for ZSTAR, compared to 41.78 cm for Altimetry. These values indicate that both configurations reproduced SSH gradients well, with HYBRID exhibiting slightly larger spatial variability than ZSTAR. Both configurations showed similar SSH biases, with an overall underestimation south of Japan, where Kuroshio recirculation occurs. The spatial correlation coefficients for both HYBRID and ZSTAR indicate strong agreement with the reference dataset.

As described by Qiu (2023) and Chang et al. (2024), SSH variability can be divided into large-scale and mesoscale components. This classification was based on a frequency spectrum analysis of Altimetry data, which revealed prominent peaks at both high and low frequencies, with a sharp decline to near zero at approximately two years. Accordingly, applying low-pass and high-pass filters allows for the separation of these components, effectively distinguishing large-scale ocean circulation, which evolves over interannual to decadal timescales, from high-frequency mesoscale eddy variability, which is characterized by shorter-lived fluctuations such as eddies and meanders.

Figure  compares the large-scale SSH variability of the HYBRID and ZSTAR configurations with Altimetry after applying a 2 year low-pass filter. The root-mean-square (RMS) SSH variability was 2.73 cm for HYBRID and 2.69 cm for ZSTAR, both lower than the Altimetry reference value of 4.92 cm. The standard deviations for HYBRID and ZSTAR similarly indicated reduced variability compared to Altimetry, which had a standard deviation of 3.48 cm. Both models underestimated large-scale variability in key dynamic regions, including the North Equatorial Current, Kuroshio Current, and Kuroshio Extension. In particular, HYBRID exhibited a pronounced underestimation in the Kuroshio Extension region while overestimating variability in the Kuroshio Recirculation area and the East/Japan Sea. In terms of spatial correlation, ZSTAR achieved a higher correlation coefficient (0.66) with Altimetry than HYBRID (0.60), indicating better spatial agreement in large-scale variability patterns.

Figure  illustrates the mesoscale variability of SSH after applying a high-pass filter, which extracts the high-frequency components associated with mesoscale eddies and smaller-scale oceanographic features. The mean RMS SSH variability was 4.78 cm for HYBRID and 4.41 cm for ZSTAR, both significantly lower than the Altimetry reference value of 8.54 cm. Similarly, the standard deviations for HYBRID (4.68 cm) and ZSTAR (4.42 cm) were lower than those of Altimetry (4.76 cm). The discrepancies between both configurations and Altimetry were further reflected in the bias and RMSE values. HYBRID exhibited a bias of -3.76 cm and an RMSE of 2.43 cm, while ZSTAR had a bias of -4.05 cm and an RMSE of 2.64 cm. ZSTAR underestimated mesoscale variability in the open ocean of the NWP, whereas HYBRID showed a more pronounced underestimation in the Kuroshio and its Extension compared to ZSTAR. Additionally, both configurations had low spatial correlations with Altimetry, with HYBRID achieving a correlation of 0.57 and ZSTAR a slightly higher correlation of 0.59. These results suggest that while both configurations captured some aspects of mesoscale variability, they tended to underestimate its intensity and struggled to fully resolve the finer-scale structures observed in the Altimetry data.

Figure  compares the surface current speeds of the HYBRID and ZSTAR configurations with the GLORYS12 reanalysis. Both models effectively captured the complex ocean current systems in the NWP, including key currents such as the Kuroshio, Oyashio, and North Equatorial Current. However, both configurations tended to underestimate current speeds in regions influenced by these currents. Specifically, in areas such as the Kuroshio and its extension, the Subtropical Counter Current, the North Equatorial Current, and the South China Sea, both models underestimated current speeds compared to GLORYS12. In contrast, both configurations overestimated current speeds in the East/Japan Sea. Both HYBRID and ZSTAR underestimated current speeds, as reflected in their bias and RMSE values. HYBRID exhibited a bias of -2.18 cms-1 and an RMSE of 6.64 cms-1, while ZSTAR showed a slightly larger bias of -3.54 cms-1 and an RMSE of 7.16 cms-1. The correlation with respect to GLORYS12 was high for both configurations, indicating good overall agreement in capturing large-scale current patterns.

A comparison of the EKE between the HYBRID and ZSTAR configurations and GLORYS12 showed that both configurations exhibited high spatial correlation with GLORYS12, successfully capturing the general EKE distribution (Fig. ). However, both models tended to underestimate EKE across most regions, with mean biases of -46.73 cm2s-2 for HYBRID and -60.12 cm2s-2 for ZSTAR. Specifically, both configurations underestimated EKE in the southern boundary regions, the Subtropical Counter Current region, and the Kuroshio and its extension, while overestimating EKE in the Kuroshio recirculation region and the East/Japan Sea. ZSTAR underestimated EKE in the open ocean of the NWP but overestimated it in the Kuroshio recirculation region and the East/Japan Sea, consistent with its higher bias in these areas. In contrast, HYBRID exhibited a more significant underestimation of EKE in the Kuroshio and its extension region compared to ZSTAR. Additionally, the MedAE was 29.56 cm2s-2 for HYBRID and 39.71 cm2s-2 for ZSTAR, suggesting that HYBRID performed slightly better in capturing the magnitude of EKE variability across the domain.

The vertical profiles of temperature and salinity biases for the HYBRID and ZSTAR configurations were compared against GLORYS12 and K-ORA22 across different regions in the NWP (Fig. ). In the open ocean of the NWP (Fig. a), both configurations exhibited low biases and closely followed the vertical structures of temperature and salinity observed in GLORYS12. However, in the Kuroshio and its extension (Fig. b), the bias patterns differed between the two configurations. ZSTAR showed lower temperature and salinity biases up to 200 m compared to HYBRID, whereas HYBRID better maintained the vertical structure of GLORYS12 below 200 m, with temperature biases remaining below 0.3 °C and salinity biases under 0.05 psu.

In the Sea of Okhotsk (Fig. c), HYBRID exhibited larger negative biases than ZSTAR between 100 and 600 m, with a temperature bias of approximately -1 °C at 400 m. The salinity bias for HYBRID was also more pronounced, reaching around -0.3 psu at 400 m, whereas ZSTAR showed relatively lower biases. In the East/Japan Sea (Fig. d), both models simulated salinity patterns similar to K-ORA22, but ZSTAR exhibited a greater temperature bias of approximately 1 °C below 200 m than HYBRID. In the Yellow Sea (Fig. e), both models displayed similar temperature and salinity profiles. The Yellow Sea is characterized by the Yellow Sea Bottom Cold Water Mass (YBCWM), a cold and dense water mass that forms near the bottom. However, both configurations showed positive temperature biases exceeding 2 °C near the bottom, suggesting limitations in accurately representing YBCWM. For salinity, both models exhibited large negative biases at the surface, with HYBRID and ZSTAR showing deviations of approximately -4 psu. This suggests that the river discharge forcing applied in both models overestimated freshwater input from major rivers in the region, such as the Yangtze and Yellow Rivers.

The NWP is characterized by two distinct water masses: Subtropical Mode Water (STMW) and North Pacific Intermediate Water (NPIW), both of which play crucial roles in the region's physical and biogeochemical processes. STMW is typically found within the upper thermocline at depths of 100–300 m, while NPIW occupies the intermediate layer, extending from approximately 300 to 800 m.

Figure  presents a comparison of the vertical temperature section along 148° E for HYBRID and ZSTAR against GLORYS12. Both configurations reproduced an overall temperature structure similar to that of GLORYS12, effectively capturing the vertical thermal structure. However, ZSTAR exhibited a positive temperature bias exceeding 1 °C in high-latitude regions.

Figure  compares the vertical salinity section along 148° E between HYBRID, ZSTAR, and GLORYS12. HYBRID closely reproduced the NPIW salinity structure, while ZSTAR exhibited a salinity bias of approximately 0.3 psu, indicating challenges in accurately representing NPIW. When examining σ2 (density referenced to 2000 dbar) within the range of 35.0 to 36.6, HYBRID accurately captured the thickness of the σ2 layer associated with NPIW, whereas ZSTAR tended to overestimate its thickness. However, both configurations showed a positive salinity bias of approximately 0.3 psu in STMW, suggesting a slight overestimation of salinity in this region.

The σ2 value of 35.8 is defined as the salinity minimum layer of NPIW, and the depth at which this minimum layer is located was extracted from each dataset. The temperature and salinity values at this depth from both configurations were then compared with those obtained from GLORYS12.

Figure  compares the temperature at the depth of the salinity minimum layer for both configurations against GLORYS12. HYBRID generally exhibited a spatial temperature distribution similar to GLORYS12, except for a positive temperature bias exceeding 1 °C in the OKH region. In contrast, ZSTAR tended to exhibit a positive bias across most regions, except for areas influenced by open boundaries. Notably, ZSTAR exhibited a temperature bias of approximately 1 °C in the transition zone where the Kuroshio and Oyashio currents converge, a critical region for NPIW formation.

The salinity distribution at depths, where the salinity minimum layer is located was also compared between HYBRID and ZSTAR relative to the GLORYS12 (Fig. S3 in the Supplement). In most regions, HYBRID showed minimal salinity biases relative to GLORYS12, except for the OKH region, where it exhibited a positive salinity bias. In contrast, ZSTAR showed a salinity bias of approximately 0.2 psu, except for areas influenced by open boundaries.

These results indicate that ZSTAR exhibited more significant positive temperature and salinity biases at depths where the minimum salinity layer is present compared to HYBRID. The larger biases observed in ZSTAR at intermediate depths are likely attributable to spurious diapycnal mixing, a well-known issue in ZSTAR configurations (Griffies et al., 2000). This excessive mixing can lead to artificial erosion of water mass properties, reducing the sharpness of the salinity minimum layer and contributing to the observed biases.

To further investigate the differences in vertical structure and water mass representation between the HYBRID and ZSTAR configurations, an idealized age tracer experiment was conducted following the spin-up simulation. This experiment was performed over a 10 year integration period to assess ventilation and subduction processes in both configurations. To facilitate comparison, the age tracer values were normalized following the approach of Adcroft et al. (2019). A value of 0 represents older water that has remained in the interior for an extended period, while a value of 1 indicates younger water that has been more recently ventilated from the surface.

In high-latitude regions where ZSTAR exhibited positive temperature and salinity biases, the normalized age values were lower in ZSTAR compared to HYBRID, indicating the presence of older water. At depths associated with NPIW formation, ZSTAR showed higher normalized age values than HYBRID, meaning it simulated younger water in this critical layer. These patterns suggest that spurious diapycnal mixing – a known issue in traditional Eulerian geopotential coordinate models – plays a significant role in ZSTAR. In high-latitude regions, stronger diapycnal mixing in ZSTAR allows older water from deeper layers to diffuse upward, leading to the observed positive temperature and salinity biases (Figs. f and f). Conversely, at NPIW depths, enhanced diapycnal mixing in ZSTAR facilitates the downward diffusion of young surface water, disrupting the natural vertical separation of water masses and eroding the salinity minimum layer. While HYBRID preserved vertical water mass properties more effectively, spurious diapycnal mixing in ZSTAR reduced its ability to accurately simulate intermediate water properties, particularly in regions critical for NPIW formation (Figs.  and S3).

In the Yellow Sea, the YBCWM is a distinct water mass that plays a crucial role in shaping regional hydrography and seasonal dynamics. It primarily forms in winter, when surface cooling induces vertical convection, allowing cold, dense water to accumulate in the deeper regions of the Yellow Sea. As spring and summer progress, surface warming enhances stratification, effectively trapping the YBCWM at the subsurface. Accurate representation of the YBCWM is critical, as it influences regional circulation, water mass transformation, and broader atmospheric and biogeochemical processes. The presence of the YBCWM modulates ocean-atmosphere interactions, potentially impacting typhoon intensification over the Yellow Sea basin (Moon and Kwon, 2012). Additionally, it plays a key role in regulating nutrient availability, oxygen dynamics, and primary production, thereby shaping regional biogeochemical cycling and ecosystem productivity (Huo et al., 2012; Su et al., 2013).

Figure  presents the bottom temperature distribution during summer and its bias relative to the K-ORA22 reanalysis. Since GLORYS12 fails to represent the YBCWM entirely (Chang et al., 2024), K-ORA22 was used as the reference dataset for comparison. The YBCWM in summer is generally characterized by a circular water mass enclosed by the 10 °C isotherm near the bottom (Zhang et al., 2008; Li et al., 2021). This structure was well captured in K-ORA22, and both the HYBRID and ZSTAR configurations successfully reproduced its overall pattern.

However, as shown in Fig. e, both configurations exhibited a warm bias of approximately 2 °C at the bottom compared to K-ORA22, with the bias being more pronounced in ZSTAR. Additionally, the YBCWM was shifted westward, resulting in a cold bias on the western side. Despite these biases, it is notable that both configurations successfully simulated the YBCWM without data assimilation – a significant improvement, as previous models have often failed to reproduce this feature due to the absence of explicit tidal forcing and reliance on parameterized tidal mixing.

The volume transport through key straits in the Northwest Pacific (NWP) was analysed to evaluate the performance of the HYBRID and ZSTAR configurations (Fig. ). The Tokara Strait serves as a crucial passage for the Kuroshio Current, making it a key indicator of the current's transport dynamics. Meanwhile, the Korea/Tsushima Strait, Tsugaru Strait, and Soya Strait play significant roles in regulating the inflow and outflow of heat and salt from lower latitudes into the East/Japan Sea and their subsequent exchange with the open ocean. Given the limited availability of direct observational data for these straits, observed climatology or long-term mean values from previous studies were used for comparison.

In the Tokara Strait, the observed annual mean volume transport from 1987 to 2010 was 21.39 Sv (Wei et al., 2013). Both configurations overestimated this transport, with HYBRID simulating an annual mean of 28.39 Sv (overestimating by 7.01 Sv) and ZSTAR simulating 27.15 Sv (overestimating by 5.76 Sv). The transport magnitude was consistently higher in HYBRID than in ZSTAR.

For the Korea/Tsushima Strait, the observed annual mean transport, derived from sea-level differences (Shin et al., 2022), was 2.61 Sv. HYBRID simulated a higher transport of 2.72 Sv, exceeding the observed value by 0.11 Sv, while ZSTAR underestimated it with an annual mean of 2.48 Sv, showing a negative bias of 0.13 Sv.

According to acoustic Doppler current profiler measurements from 2003 to 2007, the mean volume transport through the Tsugaru Strait was 1.47 Sv (Han et al., 2016), consistent with previous estimates of approximately 1.50 Sv (Na et al., 2009; Ohshima and Kuga, 2023). Both configurations overestimated this value, with HYBRID predicting an annual mean transport of 2.38 Sv and ZSTAR predicting 2.04 Sv.

In the Soya Strait, the observed annual mean transport, estimated from high-frequency radar observations between 2003 and 2015 (Ohshima and Kuga, 2023), was 0.90 Sv. Both configurations underestimated the transport, with HYBRID simulating 0.47 Sv and ZSTAR showing 0.56 Sv.

Overall, the HYBRID configuration tended to overestimate transport, particularly through the Tokara and Tsugaru Straits, while underestimating it in the Soya Strait. In contrast, ZSTAR generally underestimated transport, as observed in the Korea/Tsushima Strait and Soya Straits.

Tides play a crucial role in shaping ocean dynamics in the NWP, where tidal forces strongly influence circulation, mixing, and water mass distribution. This is particularly evident in the Yellow Sea, which is characterized by exceptionally large tidal amplitudes, with a tidal range exceeding 8 m. Given the significant impact of tides on the physical and biogeochemical characteristics of this region, it is essential to assess the performance of tidal representations in these configurations.

Figure  compares the tidal amplitude and phase of the semidiurnal M2 component between the HYBRID and ZSTAR configurations using TPXO, which served as the tidal boundary forcing dataset. Both configurations accurately simulated the tidal amplitude and phase, with HYBRID achieving a spatial correlation of 0.90 and ZSTAR showing 0.88, indicating a strong representation of tidal characteristics in the region. However, both models underestimated the M2 amplitude along the southeastern coast of China and in the Yellow Sea, while overestimating it in the Korea/Tsushima Strait. Notably, ZSTAR exhibited a more pronounced underestimation of the M2 amplitude than HYBRID in these regions.

Both configurations effectively simulated the K1 tidal amplitude and phase, with a high spatial correlation of 0.94 against TPXO data (Fig. S3). However, both models underestimated the K1 amplitude in the Yellow Sea, with a stronger bias in ZSTAR. In the Sea of Okhotsk coastal region, HYBRID overestimated the amplitude, whereas ZSTAR showed a mixed bias, overestimating in the west and underestimating in the east, reflecting regional differences in tidal representation.

Overall, both configurations performed well in reproducing the amplitude and phase of the semidiurnal and diurnal tidal components. Nevertheless, the consistent underestimation of the Yellow Sea tidal amplitude across both configurations highlighted a common limitation. Importantly, the results suggested that tidal representation was influenced by the vertical coordinate system, with HYBRID showing better agreement with TPXO tidal amplitudes than ZSTAR. This suggests that HYBRID may offer advantages in improving tidal simulations, particularly in regions with complex bathymetry and strong tidal forcing.

Compared with the previous MOM5-based regional model described in Jin et al. (2024), MOM6 demonstrated noticeably higher computational efficiency, primarily due to improvements in numerical stability that allow longer stable timesteps. Specifically, the maximum baroclinic timestep increased from 150 s in MOM5 to 300 s in MOM6, and the tracer timestep increased from 300 s in MOM5 to 900 s in MOM6, substantially reducing the total number of integration steps required for a given simulation period. This enhancement in numerical stability directly translates into greater computational efficiency under the same model resolution.

To further assess how the choice of vertical coordinate system influences computational cost within MOM6, we compared the HYBRID and ZSTAR configurations using the same supercomputer node and identical processor layouts (42 × 40 PE decomposition, with 536 PEs masked through land processor masking). The ZSTAR configuration required an average of 23 h per simulated year, whereas HYBRID completed the same simulation in 20.2 h, indicating that ZSTAR consumed approximately 2 h more. This difference primarily reflects the number of active vertical layers in each configuration: ZSTAR maintained a consistently high number of layers across most of the domain, while HYBRID adaptively reduced active layers in weakly stratified and shallow regions (Fig. S5 in the Supplement), leading to fewer computations