Drivers of Sea Level Variability in the Yellow Sea and East Sea (1993–2021): A 29-Year Decomposition Using Satellite Altimetry and Reanalysis Data

Abstract

Understanding and monitoring regional sea level (SL) variability in semi-enclosed marginal seas such as the Yellow Sea (YS) and East Sea (ES) are essential for climate impact assessment, coastal risk management, and regional model validation. This study presents a 29-year (1993–2021) observational analysis of SL and sea level differences (SLDs) around the Korean Peninsula, primarily based on gridded satellite altimetry and complemented by atmospheric and ocean reanalysis datasets. We implemented a reproducible decomposition framework that partitions satellite-derived monthly SL variations into two primary components: a local steric term driven by surface net heat flux, and a residual term representing lateral oceanic transport and other dynamic effects. Results derived from absolute dynamic topography (ADT) climatology revealed pronounced seasonal variability in SLDs between the YS and ES, with peaks in September and a minimum in December. In September, lateral transport contributed to SL increases of approximately 2.1 cm in the YS and 2.8 cm in the ES, whereas in December, atmospheric cooling and enhanced eastward wind stress dominated SL decline in the ES, accompanied by transport-related SL reduction observed in the YS. Furthermore, the relationship between monthly mean SL and inferred volume transport through the Korea, Tsugaru, and Soya Straits revealed region-specific correlations that highlight the spatial complexity of marginal sea dynamics. By integrating multiple freely available datasets and emphasizing seasonal-to-interannual climatology, this study provides a transparent and transferable framework for decomposing sea level variability in the Northwest Pacific.

1. Introduction

Temporal variations in global mean sea level (SL) (MSL) have long been recognized as one of the most robust indicators of climate change, as they reflect interconnected shifts among various components of the climate system [1]. However, regional and coastal MSL changes can differ substantially from the global trend, and in some cases, even oppose it [2]. These regional deviations arise from a combination of oceanic and atmospheric dynamics, topographic constraints, and land–sea interactions [3].

Accurately identifying these influences is essential for predicting regional sea level changes (SLCs), particularly in areas where observational data are sparse. At the global scale, SL rise is primarily attributed to two components: steric changes (due to ocean temperature and salinity variations) and nonsteric changes (related to ocean mass changes from melting land ice) [4,5,6]. Steric effects are largely controlled by thermal expansion from global warming and salinity-driven density changes, while nonsteric effects are linked to mass contributions from glacial and ice sheet melt.

In contrast, regional SL variability is governed by a broader suite of dynamical processes, including wind forcing and buoyancy exchanges. Wind stress alters ocean circulation and redistributes heat (steric) and water mass (nonsteric), while surface fluxes such as evaporation, precipitation, and runoff modulate local density and buoyancy budgets [1,7]. These air–sea exchanges, along with wind-driven Ekman transport and thermocline adjustments, generate diverse and spatially heterogeneous SL signals at regional scales [8,9]. For example, steric changes from surface warming and halosteric effects from salinity variations often combine with nonsteric influences like river discharge and precipitation divergence, producing highly localized SL responses. At even smaller coastal scales, vertical land motions (e.g., tectonic uplift, earthquakes, and anthropogenic subsidence) further modify the relative SL [2].

Steric SL studies have employed both historical temperature-salinity datasets (e.g., [10]) and satellite observations (e.g., Gravity Recovery and Climate Experiment (GRACE) and altimetry) [11]. Theoretical [12,13] and numerical [14,15] approaches have been used to derive thermosteric and halosteric components. Nonsteric (mass-related) SL contributions have been quantified using GRACE gravimetric data [16,17], ocean models [18,19], and in situ sensors such as pressure-equipped inverted echo sounders (PIES) and tide gauges [20,21].

The East Sea (ES; Japan Sea) is a semi-enclosed marginal sea bordered by the Korean Peninsula, China, Japan, and Russia, with an average depth of ~1700 m [22]. In contrast, the Yellow Sea (YS) is a shallow shelf sea (mean depth of ~44 m) enclosed by Korea and China [23,24] (Figure 1a). In the ES, the MSL variability has been examined using observations, satellite altimetry, reanalysis, and numerical simulations, demonstrating the influence of both local and remote drivers [9,25,26,27]. The YS has similarly been studied using diverse datasets, highlighting its sensitivity to conditions in the adjacent East China Sea (ECS) and broader climate indices [24,28,29,30]. The MSLs of both the ES and YS have been studied collectively as part of the SLs in the northeast Asian marginal seas using tide gauges and satellite altimeter data [31,32]. Most studies treat the YS and ECS as a connected system due to their shallow bathymetry and direct exchange, while the deeper, stratified ES is often investigated separately because of its distinct internal circulation and restricted outflows through narrow straits.

Although previous work has explored SL variability within each basin individually, direct comparative studies between the ES and YS remain limited, particularly with respect to their spatial and temporal SL differences and respective responses to seasonally varying forcing mechanisms such as wind stress and surface heat fluxes. Given their geographic proximity and semi-enclosed nature, a comparative analysis of SL variability in the ES and YS offers valuable insight into coupled marginal-sea dynamics and supports improved regional SL forecasting. These two seas play critical roles in cross-basin water exchange, ecosystem productivity, and coastal hazard exposure around the Korean Peninsula. A better understanding of their dynamics will aid in forecasting seasonal and interannual SL variations and inform coastal adaptation strategies. Accurate predictions support climate-resilient infrastructure planning (e.g., seawalls, drainage systems) and help protect vulnerable coastal populations.

Therefore, the primary objective of this study was to quantify and interpret SL variability and the mean SLD between the YS and ES over the period 1993–2021, with a particular focus on the underlying physical mechanisms. To achieve this, we:

1.

Characterized and compared the spatial and temporal patterns of SL variability in the YS and ES, identifying both shared and contrasting seasonal features;

2.

Decomposed satellite-derived SL variability into dominant components, including the local response to surface air–sea heat fluxes and remote processes associated with lateral heat and mass advection; and

3.

Evaluated the inter-basin SLD to assess whether the YS MSL is persistently higher than that of the ES and examined its relationship with volume transport through the Korea, Tsugaru, and Soya Straits.

By separating these contributions, we aimed to clarify the relative importance of local versus remote processes in shaping seasonal and interannual SL variability in each basin. This study advances the understanding of inter-basin linkages in Northwest Pacific marginal seas, supports sustained observational SL monitoring, and contributes to the development of improved forecasting frameworks for the region. The remainder of this paper is organized as follows. Section 2 describes the data and methodology; Section 3 presents the results; Section 4 provides the discussion; and Section 5 summarizes the main findings. To clarify the structure of the analysis, a schematic diagram (Figure 1b) summarizes the overall workflow. It consists of five main steps: (i) acquisition of freely available satellite and reanalysis datasets; (ii) basin-scale preprocessing for the YS and ES; (iii) decomposition of monthly sea-level change into atmospheric-heat and oceanic/residual components; (iv) comparison with strait-specific volume transports and other diagnostic variables; and (v) interpretation of the seasonal lag and SLD between the two marginal seas.

2. Data and Methodology

2.1. Data

To calculate the monthly MSL and SLC, we utilized daily gridded absolute dynamic topography (ADT) fields from satellite altimetry, spanning a 29-year period (1993–2021). These data were obtained from the Archiving, Validation, and Interpretation of Satellite Oceanographic Data/Copernicus Marine Service (AVISO/CMS) [33]. To compare satellite-derived SL with reanalysis-based values and decompose the total SEL into steric and mass components, we used sea surface height (SSH), temperature, salinity, and mixed layer depth data from the Ocean Reanalysis System 5 [34]. Although SSH from ORAS5 is not fully independent, due to assimilation of satellite altimetry, it differs from ADT in its model physics, assimilation methods, and resolution, allowing for a meaningful cross-dataset comparison. Sea level heights in this study were referenced to the mean sea surface relative to the geoid, an equipotential gravitational surface that approximates MSL in the absence of tides, pressure gradients, and ocean currents [35]. For sea surface temperature (SST), we used the Optimum Interpolation SST [36]. Monthly mean air temperature (AT) (2 m above surface), net surface heat flux components, and wind stress (momentum flux) data were obtained from the European Center for Medium-Range Weather Forecasts Reanalysis v5 [37]. To estimate the mass-related nonsteric component of MSL, we used liquid water equivalent (LWE) anomalies from the GRACE mission (2002–2021) [38]. A concise summary of all satellite, reanalysis, and ancillary datasets used in this study is provided in

Table 1. Summary of satellite and reanalysis datasets used in this study.

Dataset/Product	Variables Used	Temporal Coverage	Spatial Resolution
AVISO/CMS	Absolute Dynamic Topography (ADT)	1993–2021 (daily → monthly)	0.25° × 0.25°
ORAS5	Sea Surface Height (SSH), Temperature, Salinity, Mixed Layer Depth	1993–2021 (monthly)	0.25° × 0.25°
ERA5	Air Temperature (2 m), Surface Net Heat Flux Components (SWR, LWR, LHF, SHF), Wind Stress	1993–2021 (monthly)	0.25° × 0.25°
OISST	Sea Surface Temperature (SST)	1993–2021 (monthly)	0.25° × 0.25°
GRACE/GRACE-FO	Liquid Water Equivalent (LWE) Mass Anomalies	2002–2021 (monthly)	3.0° × 3.0°

.

All datasets (CMS/AVISO ADT, ERA5 fluxes, ORAS5 ocean reanalysis, OISST, and GRACE) were first converted to a common monthly time axis, spanning January 1993 to December 2021 (with the exception of GRACE, which spans 2002–2021). We then applied (1) spatial masking to the YS (117.50–126.75° E, 34.25–41.00° N) and ES (127.50–142.25° E, 35.00–52.00° N); (2) averaging over each basin to obtain basin-mean sea level derived from satellite altimetry; and (3) detrending where stated to better highlight the seasonal and interannual signals. These steps provide a reproducible preprocessing option before applying the AH/OE decomposition. All datasets used in this study are publicly available from international data portals. No classified, bilateral, or restricted national datasets were employed; therefore, no separate authorization from neighboring countries was required. Tide-gauge records from the Permanent Service for Mean Sea Level (PSMSL) were initially examined for comparison because of the clear relationship between SL and land in some regions [39]; however, their characteristics differ substantially from those of gridded satellite altimetry and reanalysis products in terms of spatial representativeness, reference datum, seasonal behavior, sensitivity to atmospheric pressure, uneven geographical distribution of tide stations, and temporal coverage within the study region. Because this study focused on basin-scale and inter-basin variability using spatially continuous datasets, tide-gauge data were excluded from the main analysis to avoid confusion between local (point-based) and basin-mean signals. The PSMSL database [40] is nevertheless cited here as a valuable reference for future validation and comparison efforts. In this study, MSL denotes the basin-mean sea surface height relative to the geoid, represented by the monthly mean of ADT from satellite altimeter data and by the monthly mean SSH from reanalysis data, which together approximate the mean sea surface in the absence of tides, pressure gradients, and transient currents.

2.2. Methodology

We focused on two regions:

-

ES: 127.50–142.25° E, 35.00–52.00° N;

-

YS: 117.50–126.75° E, 34.25–41.00° N.

These areas are shown in Figure 2, with dashed (ES) and dotted (YS) boundaries.

To calculate the monthly MSL from satellite altimetry (${\mathrm{MSL}}_{\mathrm{ADT}}$: (average of the arithmetic mean), we averaged the daily ADT values for each month. The monthly SLC (denoted as ${\mathrm{SLC}}_{\mathrm{ADT}}$) was calculated using the difference between the first data of the next month and the first day of the current month as follows [9]:

$${\mathrm{SLC}}_{\mathrm{ADT}} = {\mathrm{ADT}}_{\mathrm{FN}} - {\mathrm{ADT}}_{\mathrm{FT}} = {\mathrm{SLC}}_{\mathrm{AH}} + {\mathrm{SLC}}_{\mathrm{OE}}$$

(1)

where:

${\mathrm{SLC}}_{\mathrm{ADT}}$ (m): Monthly SLC as reflected in the ADT within a month;

${\mathrm{ADT}}_{\mathrm{FT}}$and ${\mathrm{A}\mathrm{D}\mathrm{T}}_{\mathrm{F}\mathrm{N}}$ (m): ADT at 00:00 UTC on the first day of this month and the next month;

${\mathrm{SLC}}_{\mathrm{AH}}$ (m): Component due to surface net heat flux;

${\mathrm{SLC}}_{\mathrm{O}\mathrm{E}}$ (m): Component due to oceanic lateral heat and mass transport (including residual terms).

We assumed that the net heat flux modifies the water column down to the mixed layer depth (MLD), defined as the depth where the temperature decreased by 0.03 °C below the SST [38,41]. The thermal expansion resulting from the atmospheric net surface heat flux was estimated using the following integral [9]:

$${\mathrm{SLC}}_{\mathrm{AH}} ={\int }_{{\mathrm{y}}_{\mathrm{S}}}^{{\mathrm{y}}_{\mathrm{N}}}{\int }_{{\mathrm{x}}_{\mathrm{W}}}^{{\mathrm{x}}_{\mathrm{E}}}{\displaystyle \frac{\mathrm{\alpha }\left({\mathrm{Q}}_{\mathrm{SWR}}+{\mathrm{Q}}_{\mathrm{LWR}}+{\mathrm{Q}}_{\mathrm{LHF}}+{\mathrm{Q}}_{\mathrm{SHF}}\right)}{\mathrm{\rho }{\mathrm{C}}_{\mathrm{P}}}}\mathrm{dx}\mathrm{dy}·{\displaystyle \frac{∆\mathrm{t}}{\mathrm{A}}}$$

(2)

where:

$\mathrm{\alpha }$: thermal expansion coefficient for seawater (°C⁻¹);

$\mathrm{\rho }$: potential density of seawater (kg m⁻³) at the mid-depth of the MLD;

${\mathrm{C}}_{\mathrm{P}}$: specific heat capacity of seawater (approximately 4000 J kg⁻¹ °C⁻¹);

$∆\mathrm{t}$: one-month interval (s);

$\mathrm{A}$: sea surface horizontal area (m²).

${\mathrm{Q}}_{\mathrm{SWR}}$, ${\mathrm{Q}}_{\mathrm{LWR}}$, ${\mathrm{Q}}_{\mathrm{LHF}}$, and ${\mathrm{Q}}_{\mathrm{SHF}}$: shortwave, longwave, latent, and sensible heat fluxes (W m⁻²), respectively.

$\mathrm{x}$, ${\mathrm{x}}_{\mathrm{W}}$, ${\mathrm{x}}_{\mathrm{E}}$, $\mathrm{y}$, ${\mathrm{y}}_{\mathrm{S}}$, and ${\mathrm{y}}_{\mathrm{N}}$: longitude, westernmost and easternmost points, latitude, and southernmost and northernmost points (°), respectively. The ${\mathrm{SLC}}_{\mathrm{AH}}$ in Equation (2) captures the vertically integrated thermal expansion effect of atmospheric forcing on sea level within each basin.

We further assumed that the net mass exchange with the atmosphere (precipitation—evaporation, ${\mathrm{SLC}}_{\mathrm{AM}}$) propagates rapidly from these semi-enclosed seas to the open ocean within a few days; thus, its contribution to the monthly mean ${\mathrm{SLC}}_{\mathrm{ADT}}$ is negligible:

$${\mathrm{SLC}}_{\mathrm{AM}} \approx 0$$

(3)

The oceanic (and residual) component was estimated by subtracting the atmospheric heat flux effect from the observed SLC using Equation (4) as follows [9]:

$${\mathrm{SLC}}_{\mathrm{OR}} = {\mathrm{SLC}}_{\mathrm{ADT}} - {\mathrm{SLC}}_{\mathrm{AH}}$$

(4)

This term incorporates lateral heat and mass transport divergence as well as any remaining unexplained variability.

To separate long-term MSL into steric and mass-related components, we applied the relation that the steric contribution of MSL (${\mathrm{MSL}}_{\mathrm{Steric}}$) as the difference between the total sea level derived from satellite altimetry (${\mathrm{MSL}}_{\mathrm{ADT}}$) and the nonsteric (mass-related) component (${\mathrm{MSL}}_{\mathrm{Nonsteric}}$) obtained from GRACE-based mass anomalies, as expressed in Equation (5) [11,42]:

$${\mathrm{MSL}}_{\mathrm{Steric}} = {\mathrm{MSL}}_{\mathrm{ADT}} - {\mathrm{MSL}}_{\mathrm{Nonsteric}}$$

(5)

3. Results

3.1. Seasonal and Spatial Variability of MSL

Satellite altimetry showed that the maximum, minimum, and mean of climatological ${\mathrm{M}\mathrm{S}\mathrm{L}}_{\mathrm{A}\mathrm{D}\mathrm{T}}$ from 1993 to 2021 were 74.90 (September), 52.39 (February), and 62.08 cm in the YS, and 60.81 (October), 44.69 (March), and 51.89 cm in the ES (filled and open red circles in Figure 2a), respectively. A one-month phase lag of the maximum and minimum ${\mathrm{MSLs}}_{\mathrm{ADT}}$ values were evident between the YS and ES; thus, the maximum, minimum, and mean of the SLD between the YS and ES were 16.11 (September), 2.36 (December), and 10.19 cm (bars in Figure 2a), respectively. Consistent with this seasonality, the monthly ${\mathrm{MSL}}_{\mathrm{ADT}}$ was higher in September than in December in both the YS and ES (Figure 3a–c).

Reanalysis-based ${\mathrm{MSL}}_{\mathrm{ORAS}5}$ exhibited consistent seasonal timing with satellite data (Figure 3d–f), but with lower absolute values: 26.06 cm (September), 7.84 cm (March), and 15.78 cm in the YS, and 13.36 (October), 1.96 (April), and 7.54 cm in the ES (filled and open red circles in Figure 2b), respectively. A similar one-month phase lag between basins was present, with the maximum, minimum, and mean of the SLD of 19.29 (September), 1.24 (December), and 9.71 cm (bars in Figure 2b), respectively.

3.2. Correlation with Volume Transport in Major Straits

We calculated the cross-correlation coefficients between MSLs from satellite altimetry and VTs from ORAS5 in the YS and ES. In the Korea Strait, the cross-correlation coefficients between ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the YS and VT in the Korea Strait, between ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the ES and VT in the Korea Strait, and between the SLD between the YS and ES and VT in the Korea Strait were all significant, at 0.81, 0.64, and 0.60 (p-value < 0.01,

Table 2. Cross correlation coefficients between ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the YS, ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the ES, SLD between the YS and ES, and VTs in the Korea Strait, Tsugaru Strait, and Soya Strait with the monthly mean from 1993 to 2021. Coefficients with p-values of less than 0.05 are underlined.

	${\mathbf{VT}}_{\mathbf{KS}}$	${\mathbf{VT}}_{\mathbf{TS}}$	${\mathbf{VT}}_{\mathbf{SS}}$
${\mathrm{MSL}}_{\mathrm{ADT}}$ (YS)	0.81	0.75	0.55
${\mathrm{MSL}}_{\mathrm{ADT}}$ (ES)	0.64	0.82	0.07
SLD (YS−ES)	0.60	0.30	0.81

), respectively, which means that the VT in the Korea Strait was more correlated with ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the YS than with SLD between the YS and ES. This is likely because the SLD between the YS and ES includes a steric component, which reflects density-driven changes due to temperature and salinity but does not directly contribute to VT through the Korea Strait. In contrast, VT was primarily influenced by barotropic pressure gradients associated with mass redistribution. In the Tsugaru Strait, the cross-correlation coefficients between ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the YS and VT in the Tsugaru Strait, between ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the ES and VT in the Tsugaru Strait, and between SLD between the YS and ES and VT in the Tsugaru Strait were all significant, such as 0.75, 0.82, and 0.30 (p-value < 0.01, Table 2), respectively, which means that the VT in the Tsugaru Strait was more correlated with ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the YS and ES rather than with SLD between the YS and ES. In the Soya Strait, the cross-correlation coefficients between ${\mathrm{M}\mathrm{S}\mathrm{L}}_{\mathrm{A}\mathrm{D}\mathrm{T}}$ in the YS and VT in the Soya Strait, between ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the ES and VT in the Soya Strait, and between the SLD between the YS and ES and VT in the Soya Strait were all significant at 0.55, 0.07, and 0.81 (Table 2), respectively, which means that the VT in the Soya Strait was more correlated with the SLD between the YS and ES than with ${\mathrm{MSLs}}_{\mathrm{ADT}}$ in the YS and ES.

Hereafter, we focus on the values in September and December, when the SLD between the YS and ES reached its maximum and minimum, respectively. From satellite altimetry, the mean ± standard deviation of the monthly ${\mathrm{MSLs}}_{\mathrm{ADT}}$ values from 1993 to 2021 were 74.90 ± 4.88 (YS) and 58.85 ± 4.39 cm (ES) in September (filled red circle and blue square in Figure 4a), and 55.25 ± 5.44 (YS) and 53.41 ± 4.47 cm (ES) in December (filled red circle and blue square in Figure 4b). From the reanalysis data (ORAS5), the mean ± standard deviation of the monthly ${\mathrm{MSLs}}_{\mathrm{ORAS}5}$ values from 1993 to 2021 were 26.06 ± 4.65 (YS) and 12.16 ± 3.02 cm (ES) in September (open red circle and blue square in Figure 4a), and 12.90 ± 4.39 (YS) and 10.25 ± 3.36 cm (ES) in December (open red circle and blue square in Figure 4b). In terms of MSL patterns, there was little difference between the MSLs from the satellite altimeter and reanalysis data; hereafter, we concentrated on the satellite altimeter data.

3.3. Subregional Variation Within the East/Japan Sea

The area of the ES was approximately 10¹² m² and approximately three times larger than that of the YS. For comparison with the YS in Figure 2, the ES was divided into three areas: southern (<39.00° N), middle (between 39.00° and 42.25° N), and northern (>42.25° N) ES. The mean ± standard deviations of monthly ${\mathrm{MSLs}}_{\mathrm{ADT}}$ values of the three areas in the ES for the 29 years were 72.92 ± 4.95 (southern), 55.49 ± 4.61 (middle), and 48.29 ± 4.04 cm (northern) in September, and 66.92 ± 4.73 (southern), 50.59 ± 4.77 (middle), and 42.80 ± 4.18 cm (northern) in December (

Table 3. Monthly mean, standard deviation, and trends of ADT in the southern (<39.00° N), middle (between 39.00° and 42.25° N), and northern (>42.25° N) ES in September and December from 1993 to 2021. Trends were rounded to one decimal place to avoid overstating precision. ±1σ denotes the estimated standard error of the slope.

	September			December
	Mean (cm)	Standard Deviation (cm)	Trend (±1σ, mm yr−1)	Mean (cm)	Standard Deviation (cm)	Trend (±1σ, mm yr−1)
Northern ES (>42.25° N)	48.29	4.04	3.8 ± 0.6	42.80	4.18	3.7 ± 0.5
Middle ES (between 39.00° and 42.25° N)	55.49	4.61	3.9 ± 0.7	50.59	4.77	3.8 ± 0.6
Southern ES (<39.00° N)	72.92	4.95	4.1 ± 0.6	66.92	4.73	4.1 ± 0.5

). The mean value of monthly ${\mathrm{MSLs}}_{\mathrm{ADT}}$ in the YS (74.90 cm) was the highest in September, and that in the southern ES (66.92 cm) was the highest in December among the YS and southern, middle, and northern ES. The corresponding trends in the ES were 4.07 (southern), 3.89 (middle), and 3.81 mm yr⁻¹ (northern) in September, and 4.06 (southern), 3.79 (middle), and 3.70 mm yr⁻¹ (northern) in December (Table 3).

3.4. Seasonal Atmospheric and Oceanic Forcing

Figure 5 shows the air temperatures at 2 m above the sea surface from ERA5 data (green) and the SSTs from OISST data (red) in the YS (open) and ES (filled) in (a) September and (b) December from 1993 to 2021. The mean values of air temperature and SST were 22.25 (YS) and 19.99 °C (ES), and 23.33 (YS) and 21.19 °C (ES), respectively, in September (Figure 5a); thus, the SST was higher than the air temperature in September. The mean values of air temperature and SST in December were 4.00 (YS) and 1.81 °C (ES), and 9.86 (YS) and 9.75 °C (ES), respectively (Figure 5b); thus, the SST was considerably higher than the air temperature in December.

Therefore, the AH values, mainly LHF and SHF, were negative (from the ocean to the atmosphere), namely, –11.0 (YS) and –20.4 W m⁻² (ES) in September (Figure 6a), and –212.2 (YS) and –319.9 W m⁻² (ES) in December (Figure 6c). The correlation coefficient between ${\mathrm{MSL}}_{\mathrm{ADT}}$and AH was only significant in the YS in December (0.40, p-value = 0.03, Figure 6b), whereas those between ${\mathrm{MSL}}_{\mathrm{ADT}}$ and AH and between ${\mathrm{SLC}}_{\mathrm{ADT}}$ and AH were insignificant (p-value > 0.23) (Figure 5a,b). Although AH can lower the ${\mathrm{MSL}}_{\mathrm{ADT}}$ and ${\mathrm{SLC}}_{\mathrm{ADT}}$ in September and December, it was not a major factor controlling them, except for AH to ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the YS in December (Figure 6c).

3.5. Sea Level Change and Forcing Attribution

The values of ${\mathrm{SLC}}_{\mathrm{ADT}}$, ${\mathrm{SLC}}_{\mathrm{A}\mathrm{H}}$, and ${\mathrm{SLC}}_{\mathrm{OE}}$, as defined in Equations (1)–(3), are presented in Figure 6 and

Table 4. Mean values and trends of ${\mathrm{SLC}}_{\mathrm{ADT}}$, ${\mathrm{SLC}}_{\mathrm{A}\mathrm{H}}$, and ${\mathrm{SLC}}_{\mathrm{OE}}$ in the YS and ES in September and December from 1993 to 2021 using the CMS, ERA5, and ORAS 5 data. Trends were rounded to one decimal place to avoid overstating precision. ±1σ denotes the estimated standard error of the slope.

		September		December
		YS	ES	YS	ES
Mean (cm)	${\mathrm{S}\mathrm{L}\mathrm{C}}_{\mathrm{A}\mathrm{D}\mathrm{T}}$	1.93	2.49	−4.88	−3.65
	${\mathrm{S}\mathrm{L}\mathrm{C}}_{\mathrm{A}\mathrm{H}}$	−0.19	−0.34	−2.06	−3.19
	${\mathrm{S}\mathrm{L}\mathrm{C}}_{\mathrm{O}\mathrm{E}}$	2.12	2.83	−2.83	−0.45
Trend (±1σ, mm yr−1)	${\mathrm{S}\mathrm{L}\mathrm{C}}_{\mathrm{A}\mathrm{D}\mathrm{T}}$	0.4 ± 0.6	−0.8 ± 0.6	0.4 ± 0.6	0.0 ± 0.6
	${\mathrm{S}\mathrm{L}\mathrm{C}}_{\mathrm{A}\mathrm{H}}$	0.1 ± 0.6	0.0 ± 0.6	−0.1 ± 0.6	−0.3 ± 0.6
	${\mathrm{S}\mathrm{L}\mathrm{C}}_{\mathrm{O}\mathrm{E}}$	0.4 ± 0.6	−0.8 ± 0.6	0.4 ± 0.6	0.4 ± 0.6

for the YS and the ES during September and December. The YS data are represented by red open circles and blue open squares, while the ES data are shown as red filled circles and blue filled squares. These values were derived from the CMS (${\mathrm{SLC}}_{\mathrm{ADT}}$), ERA5 (${\mathrm{SLC}}_{\mathrm{A}\mathrm{H}}$), and ORAS5 (${\mathrm{SLC}}_{\mathrm{OE}}$) datasets. The results highlight the spatial and temporal variability of sea level components between the two regions, with notable differences observed between September and December. The mean ${\mathrm{S}\mathrm{L}\mathrm{C}}_{\mathrm{A}\mathrm{D}\mathrm{T}}$ values were 1.93 (YS) and 2.49 (ES) cm in September, and −4.88 (YS) and −3.65 (ES) cm in December (Figure 7a). The mean ${\mathrm{S}\mathrm{L}\mathrm{C}}_{\mathrm{A}\mathrm{H}}$ values for the 29 years were −0.19 (YS) and −0.34 (ES) cm in September, and −2.06 (YS) and −3.19 (ES) cm in December, assuming that the AH is only transferred from the sea surface to a mixed layer depth to calculate the effect of heat (Figure 7b). The mean ${\mathrm{S}\mathrm{L}\mathrm{C}}_{\mathrm{A}\mathrm{H}}$ showed that the AH lowered the SL more in December than in September in the YS and ES. The mean ${\mathrm{S}\mathrm{L}\mathrm{C}}_{\mathrm{O}\mathrm{E}}$ values, which are the sum of SLCs by lateral ocean heat and mass transport divergences including other errors (${\mathrm{SLC}}_{\mathrm{ADT}}-{\mathrm{SLC}}_{\mathrm{A}\mathrm{H}}$), for the 29 years were 2.12 (YS) and 2.83 (ES) cm in September, and −2.83 (YS) and −0.45 (ES) cm in December (Figure 7c). The mean ${\mathrm{SLC}}_{\mathrm{OE}}$ showed that ocean transport raises the SL in September and lowers the SL in December in the YS and ES. The corresponding trends were as follows: 0.41 (YS) and −0.82 (ES) cm yr⁻¹ in September, and 0.35 (YS) and 0.04 (ES) mm yr⁻¹ in December for ${\mathrm{SLC}}_{\mathrm{ADT}}$; 0.05 (YS) and −0.02 (ES) cm yr⁻¹ in September, and −0.08 (YS) and −0.32 (ES) mm yr⁻¹ in December for ${\mathrm{SLC}}_{\mathrm{A}\mathrm{H}}$; and 0.36 (YS) and −0.79 (ES) cm yr⁻¹ in September, and 0.43 (YS) and 0.36 (ES) mm yr⁻¹ in December for ${\mathrm{SLC}}_{\mathrm{OE}}$ (Table 4).

3.6. Wind Stress Influence on MSL

To investigate the effects on the ${\mathrm{SLC}}_{\mathrm{ADT}}$, excluding ${\mathrm{SLC}}_{\mathrm{A}\mathrm{H}}$ and ${\mathrm{SLC}}_{\mathrm{OE}}$, wind stresses, which can carry seawater into and out of the seas and change the SL in September and December around the Korean Peninsula, are plotted in Figure 8. In September, southwestward wind stresses were observed in the YS and ES (Figure 8a), whereas southeastward wind stresses occurred in December in both regions (Figure 8b). The correlation coefficients between ${\mathrm{MSL}}_{\mathrm{ADT}}$ and wind stress are shown in Figure 9 and presented in

Table 5. Correlation coefficients between ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the YS and ES (first column from the left) and monthly mean wind stress values in the YS, ES, and ECS (second column from the left) in September (upper) and December (lower) from 1993 to 2021 using CMS and ERA5 data. Coefficients with p-values < 0.05 are shown in bold and underlined.

${\mathrm{MSL}}_{\mathrm{ADT}}$ (Sep.)	Mean Wind Stress	Eastward	Northward	Northwestward	Northeastward
YS	YS	−0.54	−0.10	0.38	−0.40
	ES	−0.59	−0.36	0.35	−0.61
	ECS	−0.06	0.02	0.05	−0.02
ES	YS	−0.22	0.00	0.19	−0.14
	ES	−0.25	−0.09	0.19	−0.23
	ECS	−0.01	0.14	0.13	0.11
${\mathrm{MSL}}_{\mathrm{ADT}}$ (Dec.)	Mean Wind Stress	Eastward	Northward	Northwestward	Northeastward
YS	YS	−0.82	0.31	0.70	−0.45
	ES	−0.61	0.35	0.57	−0.21
	ECS	−0.67	0.48	0.75	−0.26
ES	YS	−0.53	0.06	0.37	−0.40
	ES	−0.44	0.14	0.34	−0.26
	ECS	−0.39	0.19	0.39	−0.21

. In September, significant (p < 0.05) correlations were observed between ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the YS and eastward wind stress in the YS (−0.54) and ES (−0.59) (Table 5). In December, significant correlations were observed between ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the YS and eastward wind stress in the YS (−0.82), ES (−0.61), and ECS (−0.67), and between ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the ES and eastward wind stress in the YS (−0.53), ES (−0.44), and ECS (−0.39) (Table 5). These relationships are consistent with wind-driven Ekman dynamics in winter: westward winds induce onshore Ekman transport, raising coastal SL, while eastward winds cause offshore transport and SL drop. While correlation analysis alone cannot establish causality, the physical consistency between wind forcing and sea level response in winter lends support to the robustness of these findings.

3.7. Steric and Nonsteric Components of MSL

We calculated the nonsteric (${\mathrm{MSL}}_{\mathrm{Nonsteric}}$) and steric (${\mathrm{MSL}}_{\mathrm{Steric}}$) MSL in Figure 10 with GRACE data from 2002 to 2021, which is insufficient compared to the total (${\mathrm{MSL}}_{\mathrm{ADT}}$) MSL of ADT satellite altimeter data from 1993 to 2021. There were no data before 2002 and data gaps from 2002 to 2021 in Figure 10a. Although there were not enough data to compare the ADT satellite altimeter, we decomposed ${\mathrm{MSL}}_{\mathrm{ADT}}$ into nonsteric and steric components. The maximum, minimum, and mean of climatological ${\mathrm{MSL}}_{\mathrm{Nonsteric}}$ were 9.70 (September), −1.26 (March), and 2.93 cm in the YS, and 0.15 (August), −2.67 (June), and −1.26 cm in the ES (filled and open red circles in Figure 10c), respectively. The maximum, minimum, and mean of the ${\mathrm{MSL}}_{\mathrm{Nonsteric}}$ difference between the YS and ES were 10.59 (September), −0.69 (March), and 4.18 cm (bars in Figure 10c), respectively. The maximum, minimum, and mean of climatological ${\mathrm{MSL}}_{\mathrm{Steric}}$ were 65.29 (September), 53.33 (February), and 59.16 cm in the YS, and 60.81 (October), 45.26 (March), and 53.15 cm in the ES (filled and open red circles in Figure 10d), respectively. The maximum, minimum, and mean of the ${\mathrm{MSL}}_{\mathrm{Steric}}$ difference between the YS and ES were 9.84 (April), −0.45 (December), and 6.01 cm (bars in Figure 10d), respectively. The ranges of total (${\mathrm{MSL}}_{\mathrm{ADT}}$), nonsteric (${\mathrm{MSL}}_{\mathrm{Nonsteric}}$) and steric (${\mathrm{MSL}}_{\mathrm{Steric}}$) MSLs were 22.60, 10.96, and 11.96 cm in the YS, and 16.12, 2.81, and 15.55 cm in the ES (circles in Figure 10b–d), respectively. The ranges of total (${\mathrm{MSL}}_{\mathrm{ADT}}$), nonsteric (${\mathrm{MSL}}_{\mathrm{Nonsteric}}$), and steric (${\mathrm{MSL}}_{\mathrm{Steric}}$) MSL differences between the YS and ES were 13.75, 11.28, and 10.28 cm (bars in Figure 10b–d), respectively.

4. Discussions

4.1. Seasonal Lag and Heat Flux Effects

We systematically investigated several factors that may have contributed to variations in SL and the SLD between the YS and ES from 1993 to 2021, including basin-scale circulation, heat content, and atmospheric forcing. These analyses were based on CMS satellite altimetry and ERA5 and ORAS5 reanalysis data. The climatological differences in ${\mathrm{MSLs}}_{\mathrm{ADT}}$ between the YS and ES, defined as the ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the YS minus that in the ES, reached their peak and trough in September and December, respectively. These extremes could be attributed to a combination of ocean heat content, atmospheric heat flux, net lateral heat transport, and net mass transport [9].

Additionally, interannual fluctuations in these differences may be associated with broader climate variability and change, including global warming, regional sea level rise, El Niño–Southern Oscillation events, and other low-frequency phenomena. These results confirm that although the YS and ES are geographically adjacent, their seasonal SL cycles exhibit distinct amplitudes and timing, driven by different regional heat budgets, advection timescales, and wind patterns. This highlights the presence of both local and remote forcing mechanisms operating within each marginal sea.

4.2. One-Month Lag and Horizontal Advection

A consistent one-month lag was observed between the seasonal maxima and minima of ${\mathrm{MSLs}}_{\mathrm{ADT}}$ over the 29-year period, with seasonal peaks occurring in September for the YS and October in the ES, and troughs in February (YS) and March (ES). Consequently, the climatological SLD reached a maximum of 16.11 cm in September, a minimum of 2.36 cm in December, and an average of 10.19 cm over the full timeseries (bars in Figure 3). Although Figure 2a,b illustrates basin-averaged seasonal sea level variations in the YS and ES, it is important to note that these patterns are not spatially uniform across the entire basins. In the YS, the amplitude and phase of seasonal sea level fluctuations vary significantly between the southern entrance and northern coasts due to differences in bathymetry, wind forcing, and river discharge [24]. Similarly, in the ES, regional features such as the Tsushima Warm Current and mesoscale eddies introduce spatial variability in sea level seasonality [43]. Therefore, these averaged seasonal signals should be interpreted as large-scale tendencies and may not capture localized features. To support the seasonal signals detected in satellite altimetry and reanalysis data, we also examined the monthly sea level anomalies from tide gauge stations around the YS and ES (Figure 2c). These records reveal consistent seasonal cycles, with peak sea level typically occurring in summer (July–September) and minimum values in winter to early spring, broadly consistent with our reanalysis-based findings. Tide gauge observations are particularly valuable in coastal regions, where satellite altimetry becomes less reliable due to land contamination and coarse spatial resolution, even though the distribution of tide stations is uneven.

This seasonal pattern reflects the role of nonlinear thermosteric expansion, where thermal expansion is more efficient at higher temperatures. Therefore, even if net surface heat flux is similar in summer and winter, summer heating results in greater SL rise due to a larger thermal expansion coefficient. The mean advection times from the ECS to the YS and ES were approximately 1.5 and 2.5 months, respectively, based on upper-layer current velocities (~0.2 m s⁻¹) in the Korea Strait. This implies that horizontal advection of heat contributes to the observed lag in seasonal SL peaks between the YS and ES. Hence, both atmospheric heat fluxes and lateral heat transport from the ECS modulate ${\mathrm{MSL}}_{\mathrm{ADT}}$ and explain the observed one-month seasonal lag, supporting a mechanism driven by the advection-controlled redistribution of heat content and its influence on steric height.

4.3. Strait-Specific Volume Transport Effects

The VT in the Korea Strait was found to correlate more strongly with ${\mathrm{MSL}}_{\mathrm{ADT}}$ in the YS rather than with SLD between the YS and ES, whereas the VT in the Soya Strait was correlated more with SLD between the YS and ES rather than with ${\mathrm{MSLs}}_{\mathrm{ADT}}$ in either sea. These contrasting patterns suggest that strait-specific transport processes influence SL differently depending on basin geometry, flow direction, and connectivity. In particular, local dynamics dominate the YS–Korea Strait system, while downstream conditions and back-pressure effects may be more relevant for the Soya Strait–ES system. Seasonal sea level changes associated with volume transport through the Korea Strait predominantly affect the southern ES, including areas along the eastern coast of Korea and Tsushima Island, where the Tsushima Warm Current enters the basin. These regions exhibit coherent seasonal signals that correspond to variations in transport intensity and wind stress across the strait [44,45]. Thus, southern ES coastal areas are more directly influenced by Korea Strait dynamics than the northern or central basin.

4.4. Spatial Patterns of MSL and Influence of Warm Currents

The horizontal area of the ES is approximately three times that of the YS, and much of the ES lies at higher latitudes, resulting in generally cooler water temperature and lower ${\mathrm{MSL}}_{\mathrm{ADT}}$, especially in the northern part of the ES. Observed ${\mathrm{MSL}}_{\mathrm{ADT}}$ was higher in the YS and southern ES compared to the northern ES, likely due to the influence of the Tsushima Warm Current, which transports relatively warm waters northward from the ECS. This warm water influx leads to spatial heterogeneity in SL through differential steric expansion, enhancing sea level in the southern portion of the ES and contributing to the latitudinal gradient in ${\mathrm{MSL}}_{\mathrm{ADT}}$.

4.5. Regional Differences in Strait Correlations

Our analysis showed that volume transport in the Korea Strait plays a dominant role in controlling SL variability in the YS, while SLD is more closely linked to VT in the Soya Strait. In contrast, VT in the Tsugaru Strait showed no significant correlation with either SL or SLD, possibly due to its narrower geometry, shallower depth, or distinct local forcing mechanisms. These results imply that SLD between the YS and ES is a complex response to both upstream and downstream transport processes, which are modulated by regional topography and strait-specific hydrodynamics.

4.6. Thermosteric Effects and Horizontal Transport Timescales

The climatological differences in ${\mathrm{MSL}}_{\mathrm{ADT}}$, ${\mathrm{MSL}}_{\mathrm{ORAS}5}$, and ${\mathrm{MSL}}_{\mathrm{TIDE}}$ between the YS and ES were found to be highest and lowest in September and December (bars in Figure 3), respectively, consistent with the nonlinear dependence of thermal expansion on temperature [46], and the thermosteric expansion caused by oceanic and atmospheric heat was larger in September than in December (Figure 2 and Figure 3). To estimate advection timescales, we adopted a mean current velocity of 0.2 m s⁻¹ for the KS. This value is consistent with long-term observational studies that report a typical inflow transport of 2.5–3.0 Sv through the strait, corresponding to depth-averaged velocities of ~0.2 m s⁻¹ over a cross-sectional area of ~1.5 × 10⁷ m² [22,45,47]. Using this velocity, we estimate that surface waters originating in the ECS (126.0° E and 30.0° N) would take approximately 2.5 months to reach the ES (135.0° E and 39.0° N; ~1300 km), and 1.5 months to reach the YS (124.0° E and 37.0° N; ~800 km). The selected locations for the ECS, YS, and ES represent open-ocean areas away from coastal boundaries, chosen to characterize broad-scale steric and mass-related variability near the main path of inflow through the Korea Strait. These advection timescales help explain the observed seasonal lag in sea level peaks, with the ES showing a delayed maximum relative to the YS. This supports the interpretation that large-scale ocean circulation and transit time influence the timing of regional sea level variability.

4.7. Attribution of Sea Level Change Components

We decomposed SLC into components driven by surface net heat flux (${\mathrm{SLC}}_{\mathrm{AH}}$) and lateral ocean transport flux (${\mathrm{SLC}}_{\mathrm{OE}}$), as derived from reanalysis products. Atmospheric heat flux (${\mathrm{SLC}}_{\mathrm{AH}}$) caused a stronger SL drop in December than in September due to greater ocean cooling. In contrast, ocean transport processes (${\mathrm{SLC}}_{\mathrm{OE}}$) raised the SL in September, likely from inflows of warm water, and lowered it in December, especially in the YS.

In the ES, ${\mathrm{SLC}}_{\mathrm{AH}}$ was more pronounced in December than ${\mathrm{SLC}}_{\mathrm{AH}}$, highlighting the seasonal dominance of local atmospheric forcing. However, uncertainties in reanalysis products limit the precise quantification of these contributions. Oceanic processes such as baroclinic adjustment, mass divergence at straits, and buoyancy-driven inflow from the ECS are likely contributors to ${\mathrm{SLC}}_{\mathrm{OE}}$, but their magnitudes remain difficult to resolve due to the broad and open boundaries of the YS and ES.

For the YS, our 29-year analysis shows that (i) wintertime atmospheric cooling (negative AH) and (ii) seasonally reversing wind stress associated with the East Asian monsoon act to reduce the sea level in December, whereas (iii) lateral oceanic transport from the ECS to the YS raises the sea level in late summer–early autumn. In addition, (iv) volume transport through the Korea Strait is highly correlated with YS ${\mathrm{MSL}}_{\mathrm{ADT}}$ (r = 0.81; Table 2), confirming that strait exchange is an effective dynamical control on YS sea level.

Although the present application targets the YS and EJS, the decomposition in Equation (1) based on satellite altimetry and global reanalysis products is fully transferable to other marginal seas where (i) basin boundaries can be objectively defined and (ii) standard surface flux and ocean reanalysis fields are available. Only the basin masks, mixed-layer depth, and validation straits require regional adjustments.

4.8. Role of Wind Stress and Monsoon Influence

Wind stress, as a proxy for momentum forcing, exhibited clear seasonal patterns. Southwestward wind stresses prevailed in September, while southeastward (or eastward) monsoonal winds dominated in December (Figure 8). Correlation analysis showed that eastward wind stress significantly reduced ${\mathrm{MSL}}_{\mathrm{ADT}}$ in both YS and ES in December, likely via Ekman-induced coastal divergence. In particular, the eastward or southeastward winter monsoon winds likely drove surface waters southward (to the right of the wind vector in the Northern Hemisphere), creating coastal divergence and subsequent sea level depression near the coasts. This mechanism leads to a net flow of 90° to the right of the wind direction in the Northern Hemisphere, resulting in southward flow. The wind stress in December was stronger than that in September, suggesting that the eastward or southeastward wind stress around the Korean Peninsula may have played a more significant role in the reduction in ${\mathrm{MSL}}_{\mathrm{ADT}}$ during December.

4.9. Steric and Nonsteric Contributions to Sea Level Variability

We compared the total (${\mathrm{MSL}}_{\mathrm{ADT}}$), nonsteric (${\mathrm{MSL}}_{\mathrm{Nonsteric}}$), and steric (${\mathrm{MSL}}_{\mathrm{Steric}}$) MSLs in Figure 10, although ${\mathrm{MSL}}_{\mathrm{Nonsteric}}$ data from 2002 to 2021 were less extensive than the ${\mathrm{MSL}}_{\mathrm{ADT}}$ data from 1993 to 2021. The ranges of total, mass, and steric MSLs were 22.60, 10.96, and 11.96 cm, respectively, in the YS, and 16.12, 2.81, and 15.55 cm, respectively, in the ES. Thus, the ranges of mass and steric components of MSL in the YS were similar, and the steric component was much larger than the mass component in the ES. This suggests that thermal expansion is the dominant mechanism for sea level variability in the ES, whereas the YS is influenced by both steric and mass effects (e.g., from inflows/outflows or precipitation/evaporation).

4.10. Summary of Key Findings

This study addressed three primary questions concerning sea level variability in the YS and ES. First, we found distinct seasonal patterns and a one-month lag between SL peaks in the YS and ES, driven by differential heat flux, wind forcing, and advection timescales. Second, we confirmed that the YS generally exhibits higher MSL than the ES, though the magnitude of the SLD varies seasonally. Third, we showed that volume transport in the Korea Strait and Soya Strait is variably associated with MSL and SLD, with Korea Strait transport influencing YS SL more strongly, and Soya Strait transport correlating with SLD.

5. Summary

This study developed a reproducible framework to decompose and interpret sea level (SL) variability and sea level differences (SLDs) between the Yellow Sea (YS) and East Sea (ES) from 1993 to 2021. Using satellite altimetry and ocean–atmosphere reanalysis data, we identified key physical drivers of regional SL change. The two basins exhibited distinct seasonal cycles, with a one-month lag in SL peaks caused by horizontal advection from the East China Sea and differential thermosteric expansion. The maximum and minimum SLDs occurred in September and December, respectively, primarily reflecting the combined effects of surface heat flux and lateral ocean transport. Volume transport through the Korea and Soya Straits exerted contrasting influences on regional SL, while monsoonal wind stress modulated coastal SL through Ekman dynamics. Decomposition into steric and nonsteric components confirmed that thermal expansion dominates SL variability in the ES, whereas the YS is jointly influenced by mass and steric effects. Overall, our findings demonstrate that SL variability and SLD between the YS and ES are governed by interconnected atmospheric, oceanic, and dynamic processes, including seasonal heat fluxes, lateral advection, monsoonal wind stress, and strait-specific transports. The complex coupling of these mechanisms distinguishes marginal-sea behavior from that of the open ocean. This framework provides a transparent and transferable approach for decomposing regional sea level variability, offering insights for climate impact assessment, model validation, and coastal adaptation strategies in the Northwest Pacific.