Wintertime Cross-Correlational Structures Between Sea Surface Temperature Anomaly and Atmospheric-and-Oceanic Fields in the East/Japan Sea Under Arctic Oscillation

Abstract

The winter Arctic Oscillation (AO) modulates the East Asian climate and the East/Japan Sea (EJS) thermodynamics, yet the local, scale-dependent air–sea couplings remain unclear. Using 30 years of daily fields (1993–2022), we map at each grid point, the cross-persistence and scale-dependent cross-correlations between sea surface temperature anomalies (SSTA) and (i) atmospheric anomalies, (ii) turbulent heat-flux anomalies (sensible and latent), and (iii) oceanic anomalies. Detrended Fluctuation/Cross-Correlation Analyses (DFA/DCCA, 5–50 days) yield the Hurst exponent ($H, h_{XY}$) and the DCCA coefficient (${\rho }_{dcca}$). Significance is assessed with iterative-AAFT surrogates and Benjamini–Hochberg false discovery rate (FDR). Three robust features emerge: (1) during AO+, the East Korean Bay–Subpolar Front corridor shows large SSTA variance and high long-term memory ($H\ge$ 1.5); (2) turbulent heat-flux anomalies are anti-phased with SSTA and show little cross-persistence; (3) among oceanic fields, SSHA and meridional geostrophic velocity provide the most AO-robust positive coupling. Within a fractal frame, DFA slopes ($1<H<2$) quantify local self-similarity; interpreting winter anomalies as fBm implies a fractal-dimension proxy $D=3-H$, so AO+ hot spots exhibit $D\le 1.5$. These fractal maps, together with ${\rho }_{dcca}$, offer a compact way to pre-locate marine-heatwave-prone regions. The grid-point, FDR-controlled DFA/DCCA approach is transferable to other marginal seas.

1. Introduction

The Arctic Oscillation (AO) is a leading mode of Northern Hemisphere variability that reorganizes the extratropical circulation and exerts a first-order control on the East Asian winter climate. In its positive (negative) phase, a strengthened (weakened) polar vortex accompanies a pressure seesaw that generally weakens (strengthens) the East Asian winter monsoon, favoring warmer (colder) winters across Northeast Asia through adjustments in the Siberian High, Aleutian Low, and the East Asian jet stream [1,2,3]. These AO-forced circulation anomalies project onto near-surface winds and surface fluxes, providing a canonical pathway for AO influence on regional ocean–atmosphere exchanges over the marginal seas of East Asia [3].

The East/Japan Sea (EJS) is a semi-enclosed marginal sea bounded by Korea, Japan, and Russia. Its wintertime environment features a pronounced meridional sea surface temperature (SST) gradient with a climatological Subpolar Front (SPF) near ~40° N, persistent cold and dry north-westerlies under the monsoon flow, and vigorous turbulent heat exchange [4]. Observational syntheses over the East Asian marginal seas show large wintertime sensible and latent heat losses and strong event-scale variability, underscoring the need for high-frequency analysis of air–sea coupling [5]. In the EJS, SST variability is further organized by the Tsushima Warm Current (TWC)/East Korea Warm Current (EKWC) system and associated eddy activity, which modulate advective heat transport along the Subpolar Front and into the East Korea Bay (EKB) [4,6,7].

Recent work has linked AO variability to EJS winter extremes, including marine heatwaves (MHWs). Using daily satellite SST and reanalysis, Song et al. [4] documented that during positive AO winters, anticyclonic eddy-like anomalies and Ekman downwelling develop around the EKB, coincident with anomalously warm SST and a marked increase in MHW days; notably, the anomalies could not be primarily explained by local net surface heat flux, pointing instead to oceanic dynamical adjustments as the proximal driver [4]. These results motivate a grid-point assessment of which specific atmospheric, oceanic, and coupled-flux fields co-vary with winter SSTA locally, and how such co-variability depends on AO phase.

From a process perspective, atmospheric fields can influence SST anomalies (SSTA) through both mechanical and thermodynamic pathways—momentum input (wind stress), wind-stress curl and Ekman pumping, and turbulent heat fluxes (sensible and latent) [4,8]—while oceanic fields such as sea surface height anomalies (SSHA) and geostrophic currents (geo-U and geo-V) directly impose advective and mesoscale controls on SST [8,9]. Model-based studies over East Asia emphasize that realistic air–sea coupling at daily time scales requires representing wind-driven mixed-layer responses, surface roughness, and skin-temperature physics, especially when diagnosing feedback between SST and the lower troposphere [10]. These considerations suggest that different drivers may exhibit distinct scale-dependent couplings with SSTA—some resembling slow “integration” of synoptic atmospheric forcing by the mixed layer, others reflecting direct, advective ocean dynamics.

To quantify such scale-dependent persistence and cross-dependence between SSTA and atmospheric/oceanic/air–sea-coupled fields, we employ Detrended Fluctuation Analysis (DFA) [11] and Detrended Cross-Correlation Analysis (DCCA) [9,12,13], which characterize, respectively, the memory of a single timeseries (Hurst exponent, $H$) and the cross-persistence between two non-stationary timeseries (cross-Hurst exponent, $H_{XY}$) together with a scale-resolved DCCA coefficient, ${\rho }_{dcca}$ [14]. In the context of winter AO forcing, these methods are particularly attractive: (i) they accommodate non-stationarity and wideband variability inherent in daily anomaly fields; (ii) they can reveal integration-like responses expected for several atmospheric variables [15]; and (iii) they also diagnose direct oceanic controls that may couple to SSTA without a slow atmospheric integration pathway [9]. Relative to our prior basin-scale study of wintertime EJS air–sea thermal interactions [16], which emphasized large-scale patterns and integration-time-based air–sea coupling, we move here to grid-point diagnostics to resolve spatial heterogeneity and local couplings under opposite AO phases.

The EJS, in this study, using 30 winters (1993–2022) of daily fields, we investigate, at each grid point of the EJS, the cross-persistence and scale-dependent cross-correlations between SSTA and (i) atmospheric anomalies (2m air temperature, sea-level pressure, wind-stress curl, and 10m zonal/meridional winds), (ii) coupled-flux anomalies (surface sensible and latent heat flux), and oceanic anomalies (sea surface height and geostrophic currents/curl). Surrogate-based significance testing [17,18] and false discovery rate control [19] are applied to identify robust local couplings quantified by $H_{XY}$ and ${\rho }_{dcca}$. The remainder of this paper is organized as follows: Section 2 describes the data and methods (DFA/DCCA workflow, surrogate generation, and multiple-testing controls). Section 3 presents the grid-point results for $H_{XY}$ and ${\rho }_{dcca}$ across atmospheric, oceanic, and coupled fields under positive vs. negative AO. Section 4 discusses the physical interpretations—persistence vs. direct dynamical control—and consequences for winter MHW risk and prediction over the EJS.

2. Materials and Methods

2.1. Data

2.1.1. Sea Surface Temperature (SST)

Daily Optimum Interpolation SST, version2.1 (OISST v2.1), from the National Oceanic and Atmospheric Administration (NOAA) was used on a 0.25° × 0.25° grid [20,21]. OISST blends AVHRR satellite retrievals with in situ ship, buoy, and Argo observations, applies bias correction to drifting/buoy records, and includes sea-ice adjustments in high-latitude grid cells [20]. We analyzed the EJS (34°–45° N, 127°–144° E) for 1 January 1993–31 December 2022. SSTA were formed by removing a day-of-year climatology computed over 1993–2022 from the daily fields at each grid point.

2.1.2. Atmospheric and Air–Sea-Coupled Variables (ERA5)

Atmospheric and surface-flux fields were taken from the ERA5 reanalysis produced by ECMWF [22]. We used single-level variables on the native 0.25° grid, retrieved six-hourly (00, 06, 12, and 18 UTC), then averaged to daily means and bilinearly mapped onto the OISST grid. The atmospheric set are as follows: 2 m air temperature (ATMP), sea-level pressure (SLP), 10 m zonal and meridional winds (U10, V10), and turbulent surface stresses (${\tau }_x$, ${\tau }_y$). Wind-stress curl (CurlTau) was computed from the ERA5 stress components, not from U10/V10 directly, using second-order centered differences as follows:

$$\mathrm{Curl} \tau ={\displaystyle \frac{\partial {\tau }_y}{\partial x}}-{\displaystyle \frac{\partial {\tau }_x}{\partial y}}.$$

(1)

Daily anomalies (ATMPA, SLPA, UA10, VA10, CurlTauA) were obtained by subtracting day-of-year climatology (1993–2022), respectively. Because our target scales are 5–50 days, a day-of-year (DOY) climatology suppresses leakage of the evolving seasonal cycle into the synoptic band.

For the air–sea-coupled variables, we used ERA5 surface sensible heat flux (SSHF) and surface latent heat flux (SLHF), which are archived as time-integrated accumulations ($\mathrm{J}{\mathrm{m}}^{-2}$). Following ECMWF guidance, we de-accumulated each six-hourly step to flux units ($\mathrm{W}{\mathrm{m}}^{-2}$) and then formed daily means. Let $A\left(t_i\right)$ be the accumulated value at valid times and $t_i\in \left\{\mathrm{06,12,18,24} \mathrm{UTC}\right\}$. The six-hourly mean flux is

$$F_{6h}\left(t_i\right)={\displaystyle \frac{A\left(t_i\right)-A\left(t_{i-1}\right)}{∆t}}, ∆t=6\times 3600 \mathrm{s},$$

(2)

and the daily mean is

$${\overline{F}}_{day}={\displaystyle \frac{1}{4}}\sum _{k=1}^4{F}_{6h,k} .$$

(3)

We retain the ECMWF sign convention (positive downward into the surface). Thus, over the ocean, upward turbulent heat loss from the sea to the atmosphere appears as negative flux; anomalies in our maps preserve this sign.

2.1.3. Oceanic Variables

Sea surface height anomaly (SSHA) and the associated geostrophic currents were taken from the DUACS (Data Unification and Altimeter Combination System) delayed-time, multi-mission gridded products, distributed by the Copernicus Marine Environment Monitoring Service (CMEMS) at 0.25° resolution, daily, from 1 January 1993 onward [23,24]. Horizontal geostrophic velocities (geo-U, geo-V) are provided with the product and derive from the mapped sea-level fields via the standard geostrophic relation. The geostrophic-current curl (geo-Curl) was computed with second-order centered differences,

$$\mathrm{geo}\text{-}\mathrm{Curl}={\displaystyle \frac{\partial \mathrm{geo}\text{-}V}{\partial x}}-{\displaystyle \frac{\partial \mathrm{geo}\text{-}U}{\partial y}},$$

(4)

on the CMEMS grid; to avoid numerical edge effects, we masked one grid ring adjacent to land before differencing. Daily anomalies (SSHA, geo-UA, geo-VA, geo-CurlA) were formed by removing a 1993–2022 day-of-year climatology at each grid point.

2.1.4. Arctic Oscillation (AO) and Phase Selection

The AO index was obtained from the NOAA Climate Prediction Center (CPC) [25], which projects 1000 hPa height anomalies onto the leading empirical mode of Northern Hemisphere variability (cf. the AO framework of Thompson & Wallace [26]). For each year, we computed the JMF (January–February–March) mean AO. Winters with JMF AO $>+0.8\mathsf{\sigma }$ ($\sigma$ computed from the 1993–2022 JFM series) were tagged AO+, and those with AO $>-0.8\sigma$ were tagged AO−; remaining winters were not used for the phase-contrasted compositing. For all fields, we first extracted JMF segments, concatenated them (“cut-and-stitch”), and then applied the anomaly definitions above before the DFA/DCCA analyses.

2.2. Methodology

We diagnose scale-dependent persistence and cross-dependence between SSTA and candidate drivers using DFA and DCCA. DFA estimates a (univariate) Hurst exponent $H$ that summarizes long-range memory in non-stationary series [11,27]. DCCA extends DFA to pairs of series, yielding a cross-Hurst exponent $H_{XY}$ that characterizes the persistence of their detrended covariance and a normalized, scale-resolved cross-correlation coefficient ${\rho }_{dcca}\left(s\right)\in \left[-1,1\right]$ [12,14,18]. In the context of winter air–sea interactions, these tools are appropriate because (i) daily anomalies are broadband and weakly non-stationary, (ii) several atmospheric influences on SST (e.g., pressure and winds acting through mixed-layer integration) can yield persistent responses even when instantaneous Pearson correlations are small [15,28], and (iii) oceanic fields (SSH, currents, vorticity) can imprint direct, advective controls that act at synoptic and mesoscale time scales. All analyses are performed grid-point-wise and separately for the AO+ and AO− winter subsets.

2.2.1. Detrended Cross-Correlation Analysis (DCCA)

Let ${\left\{x_i,y_i\right\}}_{i=1}^N$ be a pair of daily anomaly series at a grid cell. We form the cumulative profiles

$$X\left(k\right)=\sum _{i=1}^k\left[x_i-〈x〉\right],\hspace{1em}\hspace{1em}Y\left(k\right)=\sum _{i=1}^k\left[y_i-〈y〉\right]$$

(5)

where $〈·〉$ denotes the temporal mean. For each window size $s\in S$ (winter band 5–50 days), the profiles are partitioned into 2$N_s$ segments ($N_s=⌊N/s⌋$) by scanning from the front and back. In each segment, we remove a local linear trend ($m=1$) separately from $X$ and $Y$, and compute the detrended variances and covariance. Averaging over segments yields the fluctuation functions $F_X\left(s\right)$, $F_Y\left(s\right)$, and a sign-preserving detrended covariance $F_{XY}\left(s\right)$; detailed descriptions are given in Appendix B.

The DCCA coefficient is then

$${\rho }_{dcca}\left(s\right)={\displaystyle \frac{F_{XY}\left(s\right)}{F_X\left(s\right)F_Y\left(s\right)}}\in [-1, 1]$$

(6)

which quantifies scale-dependent cross-correlation [14]. The cross-Hurst exponent $H_{XY}$ is estimated as the ordinary-least-squares slope of $\log F_{XY}$ on $\log s$ over $s\in S$. We adopt a goodness-of-fit requirement $R^2\ge R_0$ (here $R_0=0.90$); cells failing this test are labeled “no reliable cross-scaling” and are excluded from $H_{XY}$ inference [12]. For heterogeneous series (persistent vs. anti-persistent) driven by a common white-noise forcing, $H_{XY}$ tends toward 0.5 [29,30]. Significance testing for ${\rho }_{dcca}(s)$ and $H_{XY}$ uses iAAFT surrogates (Monte Carlo $p$-values) and BH-FDR control across the relevant families (see Section 2.2.2 and Section 2.2.3). The algorithmic details and derivations of DCCA (segmentation/indexing, end-effects, detrending order, absolute-value variances, and finite-sample slope notes) are compiled in Appendix B, which mirrors the implementation used here. The detailed description of DFA algorithm is also given in Appendix C.

DFA/DCCA exponents used here are fractal descriptors of self-similarity. Over 5–50 days, the winter anomalies behave as fractional Brownian motion-like signals (non-stationary scaling, $1<H<2$). Under the standard convention, the graph’s fractal dimension for fBm is $D=2-H_{\mathrm{fBm}}$ with $H_{\mathrm{fBm}}=H-1$; hence, a convenient fractal-dimension proxy for our DFA slopes is $D=3-H$ [11,31,32,33]. We use this link in Section 4 to interpret spatial patterns of persistence as maps of geometric roughness and to propose a simple fractal indicator for hot-spot diagnosis.

2.2.2. Monte Carlo Significance and Quality Control for $H_{XY}$ and ${\rho }_{dcca}$

There are no closed-form null distributions for $H_{XY}$ or ${\rho }_{dcca}(s)$. We therefore adopt a surrogate-based Monte Carlo framework following Podobnik et al. [18]. For each cell $i$ and variable pair ($x, y$), we generate $N_{sur}=1000$ iterative amplitude-adjusted Fourier transform (iAAFT) surrogate pairs ${\left\{x_{i,sur}^{\left(k\right)}, y_{i,sur}^{\left(k\right)}\right\}}_{k=1}^{N_{sur}}$ that preserve the empirical amplitude distributions and approximately match the power spectra (hence the linear auto-correlations) of the originals [17]. Two-sided Monte Carlo p-values are

$$\begin{gathered} p_{\rho }\left(i,s\right)={\displaystyle \frac{\#\left\{k: \left|{\rho }_{sur}^{\left(k\right)}\left(i,s\right)\right|\ge \left|{\rho }_{obs}\left(i,s\right)\right|\right\} }{N_{sur}}} \\ {p}_H(i)={\displaystyle \frac{\#\left\{k:\left|H_{sur}^{\left(k\right)}\left(i\right)-1\right|\ge \left|H_{obs}\left(i\right)-1\right|\right\}}{N_{sur}}} \end{gathered}$$

(7)

For $H_{XY}$, the log–log linearity is verified by the coefficient of determination $R^2$ of the fit over $S$. We pre-declare a quality threshold $R^2\ge R_0$ (here, $R_0=0.90$). Cells not meeting this criterion are labeled “no reliable cross-persistence” and masked in $H_{XY}$ figures rather than being assigned $H_{XY}=1$. The same check is applied to each surrogate. Let $K_i=\left\{k:R_{sur}^{2,\left(k\right)}(i)\ge R_0\right\}$ and $N_{\mathrm{eff}}\left(i\right)=\#K_i$. We then compute

$$p_H\left(i\right)={\displaystyle \frac{\#\left\{k\in K_i:\left|H_{sur}^{\left(k\right)}\left(i\right)-1\right|\ge \left|H_{obs}\left(i\right)-1\right|\right\}}{N_{\mathrm{eff}}\left(i\right)}}.$$

(8)

If $N_{\mathrm{eff}}\left(i\right)<200$ (20% of $N_{\mathrm{sur}}$), the cell is deemed not testable for $H_{XY}$ and is masked. This treatment avoids anticonservative p-values that would arise from coercing poorly fit surrogates to $\mathrm{H}=1$.

2.2.3. False Discovery Rate (FDR) Control Across Space and Scale

Because we test thousands of hypotheses in parallel (across grid cells and also across scales for ${\rho }_{dcca}$), we control multiplicity using the Benjamini–Hochberg (BH) procedure at a target FDR $q=0.05$ [19]. Families are defined as follows:

(1)

For ${\rho }_{dcca}(s)$, for each fixed scale $s$, the family comprises all cells’ p-values $\left\{p_{\rho }\left(i,s\right)\right\}$.

(2)

For $H_{XY}$, there is one statistic per cell, so the family is $\left\{p_H\left(i\right)\right\}$ over all cells.

Within each family (and for each predictor–SSTA pair), sort p-values $p_{\left(1\right)}\le \dots \le p_{\left(m\right)}$ and find $k^{\ast }=\max \left\{k:p_{\left(k\right)}\le \left(k/m\right)q\right\}$. Declare the first $k^{\ast }$ tests significant at FDR $q$; if no such $k$ exists, no cell is significant. For visualization, we optionally convert p-values to BH $q$-values (the minimal FDR level at which each test would be called significant) and mask cells that are not significant. When scale-mean ${\overline{\rho }}_{dcca}$ maps are shown, blank cells indicate locations where ${\rho }_{dcca}\left(s\right)$ failed BH at all scales in $S$ (or where fewer than a minimal fraction of scales passed, as noted in captions). BH-FDR controls the expected proportion of false positives across the entire map (and, for ${\rho }_{dcca}$, across scales), so colored features represent discoveries that remain significant after multiplicity control.

2.2.4. Implementation Details and Robustness

All variables are bilinearly regridded to the OISST 0.25° grid before analysis. We use detrending ($m=1$) for DFA/DCCA, integer scales $s=5,\dots , 50$ days, and ordinary least-squares regression on $\log s$ to estimate slopes. Results are qualitatively insensitive to using a slightly narrower scale band (e.g., 7–45 days) or to exclude the smallest two scales; these checks alter magnitude modestly but not the spatial patterns emphasized here. For ${\rho }_{dcca}$, we report both per-scale maps and (for compactness) scale-means ${\overline{\rho }}_{dcca}$ over $S$; significance is always assessed at the per-scale level as described above.

3. Analysis Results

This section examines how the wintertime AO phase modulates local air–sea coupling in the EJS by mapping (i) DCCA-based cross-persistence ($H_{XY}$) and (ii) scale-dependent detrended cross-correlations ${\rho }_{dcca}\left(s\right)$ between SSTA and three classes of drivers: atmospheric anomalies (ATMPA, SLPA, UA10, VA10, CurlTauA), coupled turbulent heat-flux anomalies (SSHFA, SLHFA), and oceanic anomalies (SSHA, geo-CurlA, geo-UA, geo-VA). Synoptic atmospheric “weather” typically forces SST via mixed-layer integration, so air-to-sea impacts build over multi-day to multi-week windows; by contrast, turbulent heat fluxes act as fast, largely damping feedbacks, while ocean currents imprint advective tendencies on intermediate time scales. The DCCA framework separates persistence (via $H_{XY}$) from phase-coherent co-variability across scales (via ${\rho }_{dcca}(s)$).

3.1. SSTA Variability and Persistence: AO–Phase Contrasts

Wintertime SSTA variance (Figure 1A–C) is maximized in the East Korean Bay (EKB) and along the Subpolar Front (SPF). The AO-positive composite shows markedly higher standard deviation along the SPF and in the western basin relative to AO−, yielding a positive “AO+ minus AO−” difference in those corridors (Figure 1C). DFA-based persistence (Figure 1D–F) co-locates with these variance hot spots: during AO+, Hurst exponents are broadly elevated ($H\approx$ 1.2–1.5), indicating strong long-range memory in daily SSTA. This co-occurrence of large variance and high $H$ under AO+ is consistent with a heightened propensity for winter marine heatwaves (MHWs) in the EKB/SPF sector, even though the full causal chain is beyond the present scope. These baseline contrasts identify the regions where subsequent DCCA diagnostics merit the closest attention.

3.2. Local Coupling with Atmospheric Fields

In all atmospheric-coupling figures, panels (A,B) show the cross-persistence $H_{XY}$ for AO+ and AO−, respectively; panels (C,D) show the scale-averaged ${\overline{\rho }}_{dcca}$ over $s\in \left[5,50\right] \mathrm{days}$ for AO+ and AO−. Cells are blank where $H_{XY}$ is not reliably defined (log–log fit $R^2<R_0$) or fails BH-FDR at $q=0.05$ (Section 2.2.3). For ${\rho }_{dcca}$, a cell is blank if no scale within $s\in \left[5,50\right]$ survives BH-FDR.

SSTA vs. ATMPA (Figure 2): Basin-wide positive ${\overline{\rho }}_{dcca}$ dominates in both AO phases, with greater spatial extent and amplitude during AO−. Thus, over 5–50-day windows, warmer air tends to co-vary locally with warmer SST (and vice versa), consistent with mixed-layer integration [15,16,28]. Significant $H_{XY}$ appears in elongated patches along the SPF/EKB and coastal bands—more continuous in AO—indicating that persistent, scale-invariant co-evolution emerges where mixed-layer memory is strong and air–sea coupling is sustained.

SSTA vs. CurlTauA (Figure 3): Scale-averaged ${\overline{\rho }}_{dcca}$ forms a red/blue mosaic that rearranges between AO phases, with limited areal coherence and only sparse significant $H_{XY}$ pixels. Because horizontal vorticity influences SSTA mainly through stirring and deformation rather than direct, sign-consistent advection, its imprint on local grid cell SST is intermittent and geometry-dependent; small spatial displacements of fronts or eddies can flip the sign of the local tendency. AO phase reorganizes these patches without producing a consistent basin-scale tendency.

SSTA vs. SLPA (Figure 4): Cross-persistence is largely absent, and ${\overline{\rho }}_{dcca}$ is regionally selective (e.g., positive belts near the northern margin in AO+ with mixed patterns in AO−). As SLP organizes synoptic systems rather than acting as a local flux, it modulates the placement and sign of weather forcing without yielding a persistent, scale-invariant local coupling with SSTA.

SSTA vs. UA10 (Figure 5): Scale-averaged ${\overline{\rho }}_{dcca}$ is predominantly negative in both AO phases, stronger and more extensive under AO−. This sign is physically reasonable: westerly anomalies enhance surface cooling and offshore Ekman transport in the EJS winter, favoring colder SST; the converse holds for easterlies. Notably, $H_{XY}$ is largely undefined—the coupling is strong in sign but not persistent, consistent with rapidly varying synoptic winds that project onto SST tendencies without establishing a scale-invariant cross-memory.

SSTA vs. VA10 (Figure 6): Scale-averaged ${\overline{\rho }}_{dcca}$ is mostly positive, with particularly strong AO− signals across the southern–central basin. Patches of significant $H_{XY}$ are more frequent under AO−, especially along the EKB/SPF corridor, suggesting that southerly anomalies (warm-advection-like patterns) are more phase-coherent with SSTA during cold AO winters. In contrast, AO+ shows weaker persistence despite positive ${\overline{\rho }}_{dcca}$, implying shorter, event-like coupling.

Summarizing, across 5–50 days, the sign of local coupling is robust (positive for ATMPA and VA10, negative for UA10), whereas cross-persistence is selective—emerging mainly where mixed-layer memory is large (EKB/SPF) and under AO-configurations that reinforce advection/integration. Wind-stress curl and SLP imprint patchy ${\rho }_{dcca}$ with little persistence, consistent with their intermittent, geometry-dependent impacts.

3.3. Local Coupling with Coupled Heat-Flux Anomalies

For both SSHFA (Figure 7) and SLHFA (Figure 8), the scale-averaged ${\overline{\rho }}_{dcca}$ over s ∈ [5, 50] days are predominantly negative across the basin in both AO phases, with broader coverage during AO−. This sign is expected from turbulent-flux physics and the ERA5 sign convention (positive downward): a positive SSTA increases the air–sea temperature and humidity gradients and, together with wind speed, enhances upward sensible and latent heat loss from the ocean. In downward-flux units, this appears as a negative anomaly, hence the anti-correlation between SSTA and SSHFA/SLHFA at these scales. The near-absence of cross-persistence $H_{XY}$ indicates that, although the sign is robust, the flux coupling is a fast, dissipative feedback with little joint long-memory: flux anomalies respond quasi-instantaneously to SSTA and synoptic wind bursts but do not create scale-invariant co-evolution. The AO− maps show a larger area of significant negative ${\overline{\rho }}_{dcca}$, consistent with colder/drier outbreaks intensifying the air–sea gradients and wind dependence in the bulk formulas and thus strengthening the damping. All patterns reported here remain after iAAFT surrogate testing and BH-FDR control across space (and scale for ${\overline{\rho }}_{dcca}$).

3.4. Local Coupling with Oceanic Fields

Mesoscale sea-level and geostrophic-current anomalies provide the oceanic pathways through which temperature is advected and retained in winter. Because SSHA integrates steric and dynamical signals, a positive association with SSTA is expected (warm/thick anomalies raise sea level), whereas velocity anomalies influence SSTA via along-front advection and eddy stirring. The DCCA maps confirm these expectations but also reveal clear AO modulations.

SSTA vs. SSHA (Figure 9): Scale-averaged ${\overline{\rho }}_{dcca}$ is basin-wide positive in both AO phases, with especially coherent coverage in AO− across the western and central basin. Patches of significant $H_{XY}$ occur along/near the SPF/EKB corridor and in the northern interior, indicating shared, scale-invariant co-memory where mesoscale features repeatedly affect the same locations. Among all drivers, SSHA exhibits the most extensive and AO-robust positive coupling, underscoring the central role of mesoscale structure in organizing SSTA variability.

SSTA vs. Geo-Curla (Figure 10): A fine-scale red/blue mosaic appears in both phases with little $H_{XY}$. Horizontal vorticity primarily affects SSTA via stirring and deformation, producing intermittent, sign-changing local tendencies that are highly sensitive to frontal geometry; small spatial shifts in eddies/fronts can flip the local sign.

SSTA vs. Geo-UA (Figure 11): Scale-averaged ${\overline{\rho }}_{dcca}$ shows mixed-sign dipoles aligned with the SPF and western boundary. This is expected: East–West flow anomalies project onto SSTA through cross-front advection, and the sign depends on the local meridional SST gradient. Cross-persistence $H_{XY}$ is sporadic, appearing where climatological fronts are quasi-stationary and eddy passages recur. The AO phase changes the spatial reach of significant ${\overline{\rho }}_{dcca}$ (AO− tends to broaden the coherent belts) but does not alter the overall dipolar character.

SSTA vs. Geo-VA (Figure 12): In contrast, geostrophic meridional anomalies present widespread positive ${\overline{\rho }}_{dcca}$, particularly during AO+. Significant $H_{XY}$ pixels are comparatively numerous and concentrated along the EKWC/SPF pathways, indicating that recurrent along-front advection can generate scale-invariant cross-memory at grid points embedded in persistent current routes.

Summarizing, SSHA provides the most cohesive and AO-robust positive coupling with SSTA, while geo-VA yields the clearest advective signature and the most frequent $H_{XY}$ detections along EKWC/SPF pathways. By contrast, vorticity (geo-CurlA) and zonal flow (geo-UA) yield patchy, sign-changing patterns with little cross-persistence, highlighting their sensitivity to local frontal geometry.

Taken together with Section 3.1, Section 3.2 and Section 3.3, the maps support a two-tier view of winter SSTA variability in the EJS: (i) mesoscale structure and along-front advection (SSHA, geo-VA) organize the persistent component and yield detectable $H_{XY}$, while (ii) synoptic winds and turbulent heat exchanges supply strong but largely non-persistent tendencies whose net impact depends on AO-phase-dependent storm tracks and their interaction with the pre-existing oceanic state.

4. Discussion

4.1. Synthesis of the Main Findings

A grid-point DFA/DCCA diagnostic over the EJS reveals a consistent, AO-phase-dependent hierarchy of wintertime couplings between SSTA and atmospheric, coupled-flux, and oceanic fields. The key findings are as follows:

• SSTA variance and persistence ($H$) concentrate along the EKB and the SPF during AO+, with $H\approx$ 1.4–1.5 (Figure 1), indicating strong long-memory behavior in the daily anomaly field and, by implication, elevated susceptibility to persistent warm events in those corridors.
• Among atmospheric drivers, near-surface air temperature (ATMPA) exhibits basin-wide positive, scale-averaged ${\overline{\rho }}_{dcca}$ (5–50 days) and localized cross-persistence $H_{XY}$, whereas sea-level pressure and wind-stress curl produce patchy ${\overline{\rho }}_{dcca}$ and rarely yield robust $H_{XY}$ (Figure 2, Figure 3 and Figure 4). Zonal (UA10) and meridional (VA10) winds display physically consistent signs—mostly negative and positive ${\overline{\rho }}_{dcca}$, respectively—with $H_{XY}$ that is sparse or confined to advective corridors.
• SSHF and SLHF act as fast, negative feedbacks: ${\overline{\rho }}_{dcca}<0$ is widespread and $H_{XY}$ is virtually absent.
• Oceanic fields show the most cohesive coupling with SSTA: SSHA yields basin-wide positive ${\overline{\rho }}_{dcca}$ with $H_{XY}$ along the SPF/EKB and in the northern interior, while geostrophic V anomalies imprint the clearest advective signature and the most frequent $H_{XY}$ detections (Figure 9, Figure 10, Figure 11 and Figure 12).

All maps were screened with iAAFT-based Monte Carlo p-values and BH-FDR control across space and scale.

4.2. Physical Interpretation and AO Modulation

This hierarchy aligns with known winter processes that connect AO to the East Asian circulation and air–sea exchanges. During AO+, a weakened East Asian winter monsoon favors warmer, less stormy conditions over the EJS, enhancing mixed-layer memory and along-front poleward advection along the EKWC/SPF. These conditions co-locate large SSTA variance and high $H$ (Section 3.1) and promote persistent SSTA–SSHA/geo-V co-variability (Section 3.4). During AO−, stronger outbreaks and enhanced winds reorganize wind–SST covariances, yielding sign-changing ${\overline{\rho }}_{dcca}$ mosaics for dynamical wind metrics (CurlTau, U10) and a broader spatial reach of positive coupling for ATMPA and V10, where advection integrates forcing into SST (Section 3.2 and Section 3.3).

ATMPA stands out among atmospheric variables because it projects directly onto the ocean mixed layer through bulk heat exchange and stability control; hence ${\overline{\rho }}_{dcca}$ and episodic $H_{XY}$ are in regions with strong mixed-layer memory. In contrast, SSHF/SLHF are quintessential negative feedbacks: they damp SSTA tendencies quickly, explaining the widespread ${\overline{\rho }}_{dcca}<0$ and the lack of cross-scaling. Among oceanic drivers, SSHA provides a basin-coherent, AO-robust “dynamic height” control on SSTA that naturally yields positive coupling; meridional geostrophic flow (V10) maps the advective corridors where repeated along-front transport produces scale-invariant cross-memory.

4.3. Role of Single-Field Memory

The appendix DFA-based $H$ maps (Figure A1, Figure A2 and Figure A3) clarify why some pairs develop cross-persistence while others do not. Atmospheric anomalies generally display weak persistence ($H\approx$ 0.6–1.0) with gentle spatial gradients (Figure A1), consistent with synoptic “weather” forcing that co-varies with SST without forming strong joint scaling at grid-point level. Coupled heat-flux anomalies are anti-persistent to near-white over most of the basin (Figure A2), matching their role as fast, dissipative feedbacks and explaining the absence of $H_{XY}$ with SSTA. Oceanic fields, by contrast, show high persistence ($H\approx$ 1.3–2.0) organized along the SPF, EKWC, and the northern boundary (Figure A3), mirroring the corridors of significant $H_{XY}$ and positive ${\overline{\rho }}_{dcca}$ in the main figures. This memory hierarchy—fluxes < atmosphere < ocean—maps directly onto the bivariate outcomes in Section 3.2, Section 3.3 and Section 3.4.

4.4. Implication for MHW Susceptibility and Predictability

The co-occurrence of large SSTA variance, high $H$, positive ${\overline{\rho }}_{dcca}$, and significant $h_{XY}$ along the EKB–SPF, especially during AO+, points to enhanced susceptibility to winter MHWs under positive AO forcing. Because the oceanic corridors that support cross-persistence are spatially stable (fronts, boundary currents), they offer subseasonal predictability windows, provided the preconditioning by mesoscale structure (SSHA, geo-VA) is monitored. By contrast, the strongly negative, memory–light coupling with turbulent fluxes limits stand-alone predictability from SSHF/SLHF anomalies.

4.5. Methodological Considerations and Limitations

DFA/DCCA are well suited to diagnose integration-like responses (for atmosphere$\to$SST) and direct advective controls (for ocean$\to$SST) in non-stationary daily anomalies, provided the scaling range is declared a priori and goodness-of-fit is screened. Here, we set a winter-appropriate 5–50-day band and enforced an $R^2$ threshold on the log–log fits; cells failing this condition were masked rather than force-tested. For statistical control, we used iAAFT surrogates (to preserve marginals and auto-correlation) and BH-FDR across space/scale, which is appropriate under the positive spatial dependence typical of geophysical fields. Observationally, DUACS geostrophic fields derive from altimetric SLA; along-track sampling and mapping can imprint anisotropy and small-scale noise. While the surrogate/FDR framework mitigates spurious detections, some fine-patch features in $H$ and ${\rho }_{dcca}$ may still reflect sampling and gridding choices. Finally, blanks in $H_{XY}$ maps indicate no reliable power-law joint scaling; in such cases, scale-specific ${\rho }_{dcca}$ becomes the appropriate metric of local co-variability.

4.6. Fractal and Multifractal View—A Practical Application

DFA/DCCA quantify long-range memory and cross-memory that arise from self-similar dynamics. Interpreting our wintertime scaling as fBm over 5–50 days implies that the DFA slope $H\in [1, 2]$ directly yields a fractal-dimensional proxy $D=3-H$ [31,32,33]. Thus, the AO+ corridors where we observe $H\approx$ 1.3–2.0 (Figure 1) correspond to $D\approx$ 1.0–1.7, i.e., smoother (less jagged) SSTA trajectories indicative of strong persistence. Conversely, areas with lower $H$ approach $D\to 2$, reflecting rougher, memory-poor fluctuations. This fractal recasting is not merely semantic: maps of $D\left(x\right)=3-H\left(x\right)$ provide a compact diagnostic of spatially coherent self-similarity that complements ${\rho }_{dcca}$. In practice, pre-locating winter marine heatwave susceptibility can exploit a simple mask combining (i) low fractal dimension $D\lesssim 1.6$ (high $H$), and (ii) significant positive ${\rho }_{dcca}$ with SSHA or meridional geostrophic velocity. Over AO+, this mask selects the EKB-SPF corridor; over AO−, it shifts with the advective pathways—consistent with our physical interpretation.

While our results are monofractal in the analyzed band, the framework naturally extends to multifractal diagnostics [13]. Multifractal DFA (MFDFA) and multifractal DCCA (MF-DCCA) return q-dependent exponents and singularity spectra that separate amplitude intermittency from linear memory [13,27,34]. Applying MFDFA/MF-DCCA to the same grid-point fields would test whether oceanic couplings (SSHA, geo-VA) display broader spectra than atmospheric drivers and whether AO phase modulates intermittency as well as persistence—an avenue we leave for future work.