Coherent Interannual–Decadal Potential Temperature Variability in the Tropical–North Pacific Ocean and Deep South China Sea

Climate variability over the Tropical and North Pacific Ocean (TPO and NPO, respectively) modulates marginal sea variability. The South China Sea (SCS), the largest marginal sea in the western NPO, is an outstanding example of a region that responds quickly to climate change. However, there is considerable uncertainty regarding the response of the deep SCS to large‐scale climate variability. Multivariate empirical orthogonal function analysis revealed three prominent modes of interconnected temperature anomaly fluctuations within the TPO and NPO. These coherent modes highlight the interactive dynamics among climate variations and reveal their modulation mechanisms for previously less explored potential temperature variabilities in the deep SCS. On the atmospheric bridge, external forces modify the upper‐layer Luzon Strait Transport (LST) by adjusting the Ekman transport and Kuroshio intrusion. For the oceanic pathway, climate variations disturb the deep‐layer LST by adjusting the barotropic flows in the upper layer.

example, the NPMM may trigger a Central Pacific (CP) El Niño (Amaya et al., 2019;Di Lorenzo et al., 2023;Power et al., 2021).The VM tends to force an initial warming in the central TPO for the East Pacific (EP) El Niño and CP El Niño, and ENSO diversity is derived depending on the background features in the TPO (Shi et al., 2022).
These climate variabilities over the TPO and NPO have global impacts through both oceanic pathways and atmospheric bridges, such as altering the atmospheric heat fluxes and the Walker and Hadley circulations (C.Wang, 2019).Oceanic pathways are significant for connecting these climate variabilities to marginal seas, which serve as receivers and modulators of climate signals.For example, the ENSO and PDO alter the water exchange between the Pacific Ocean and adjacent marginal seas, including the South China Sea (SCS), which is the largest marginal sea in the NPO (C.Wang, 2019).Through the accommodated unique alternatively rotating three-layer circulation and meridional overturning circulation (SCS-MOC) originating from Luzon Strait exchange flows, or Luzon Strait Transport (LST) (Gan et al., 2016;Qu et al., 2006;Shu et al., 2014), the SCS, as the keystone of climate variability telecommunications between the TPO and NPO and the Tropical Indian Ocean, plays a dominant role in regional and global climate variability modulation (Yu et al., 2019).Thus, the SCS is an ideal location for assessing the importance of the TPO and NPO in the oceanic and climatic processes of marginal seas.
Several studies have focused on the climate variability of the upper-layer temperature in the SCS.For example, during EP El Niño events involving an anomalous atmospheric anticyclone (AAC) over the NPO, water intrusions through the Luzon Strait associated with surface warming in the SCS are strengthened (C.Wang et al., 2006), whereas a warm semi-basin mode exists during CP El Niño events associated with insignificant northward North Equatorial Current Bifurcation (NECB) migration (Liu et al., 2014;X. Wang et al., 2020).Positive wind stress curl anomalies in the North Pacific shift the NECB further northward during positive PDO years, thereby resulting in an enhanced upper-layer LST (Yu & Qu, 2013).Seasonal variations in the upper layer can influence those in the deep layer through mesoscale ocean eddies and topographic Rossby waves (Chen et al., 2015;Li & Lan, 2022;Shu et al., 2016;D. X. Wang et al., 2019).However, the climate variability of potential temperature in the deep SCS (θ d ) remains largely unclear.Given the integrated climate variabilities in the TPO and NPO, the aforementioned diverse findings indicate how the climatic variabilities in the TPO and NPO telecommunicate, and their impacts on θ d variations warrant further investigations.
The conventional indices of the climate variabilities in the TPO and NPO, such as the Nino3.4,El Niño Modoki (EMI), NPMM, and VM indices, are based on processed sea surface temperature (SST) data from their respective regions.However, previous studies have suggested that decadal SST anomalies (SSTAs) in the TPO drive a portion of the PDO-related variability (Alexander et al., 2002(Alexander et al., , 2010)), and those SSTAs over the NPO also greatly impact the ENSO (Di Lorenzo et al., 2010;Vimont, 2005;S.-Y. Wang et al., 2012).Consequently, separating the variability of SSTAs over the TPO and NPO into interannual and decadal components is a rather complex process, as these signals are integrated.

Methods and Data
Four observational data sets were used to characterize deep-water temperature variability.These data sets were monthly objective analyses of in situ observations (e.g., expendable bathythermographs (XBTs), conductivitytemperature-depth (CTD) measurements from research vessels, and Argo floats) with a 1° × 1° horizontal resolution (Boyer et al., 2013).The synoptic monthly gridded World Ocean Database (SMG-WOD) data set was established from observational hydrographic profiles from the NOAA National Centers for Environmental Information (NCEI) WOD (1945WOD ( -2014)), using the optimal spectral decomposition method (Chu et al., 2003a(Chu et al., , 2003b(Chu et al., , 2004(Chu et al., , 2015(Chu et al., , 2016)); it provides three-dimensional gridded world ocean temperature with 28 standard vertical levels from the ocean surface to 3,000 m depth (Zhu, Sun, Wang, et al., 2017).Data in this study covered the 1970-2014 period, as the number of high-resolution observations and spatial coverage increased significantly after 1970 (Figure S1 in Supporting Information S1).The other three observational data sets used to validate the θ d variability from SMG-WOD are from the ARGO project (2005ARGO project ( -2020)), the EN4 reanalyses by Met Office Hadley Centre (Good et al., 2013) since 1900, and the reanalysis data sets from Cheng (Cheng et al., 2017) produced by the Institute of Atmospheric Physics, Chinese Academy of Sciences (IAP) (1940 to present).
The SST over the Pacific Ocean was derived from the Hadley Centre Sea Ice and Sea Surface Temperature (HadISST), which is a combination of complete monthly global SST fields from 1871 to present.The wind vector was derived from the NOAA-CIRES-DOE Twentieth Century Reanalysis (V3), spanning from 1836 to 2015.Monthly heat flux data from the NCEP reanalysis was used in this study.The ¼° sea level anomaly (SLA) was obtained from satellite observations (1993-2022) from the Copernicus Marine Environment Monitoring Service (CMEMS) portal, and the sea surface height (SSH) anomaly over the longer, 1871-2010 period was obtained from SODA2.2.In this study, we calculated the deep-layer LST according to the ocean bottom pressure (OBP), which was based on the Estimating the Circulation and Climate of the Ocean (ECCO) project, version 4 revision 4b (V4r4b), between 1992 and 2017 (Fukumori, 2002;Kim et al., 2007;Tapley et al., 2004).
To obtain the coherent spatiotemporal characteristics of SSTAs in the TPO and NPO, multivariate empirical orthogonal function (MVEOF) analysis was applied.MVEOF is an extension of the conventional EOF method that builds a combined matrix for multiple variables, which can extract coupled patterns of variability among these variables (B.Wang, 1992).Contrary to the traditional indices mentioned above, MVEOF analysis considers the interplay among TPO and NPO signals.

Results
The MVEOF method provided the synergies between the climate variabilities of the detrended SSTAs from HadISST in the TPO (20.5°S-20.5°N)and NPO (20.5°N-62.5°N).The first three leading modes, namely M1, M2, and M3, explaining 46.23%, 12.92%, and 9.15%, respectively, of the coherently varying components of SSTAs, were subsequently retrieved (Figure 1).The first three leading spatial MVEOF modes exhibited great similarity to those derived from singular value decomposition (SVD; Figure S2 in Supporting Information S1), with temporal correlation coefficients of 0.99, 0.76, and 0.70, respectively.The variations of SSTAs explained by these three modes (M1-M3) contributed 78.59% and 65.80% of the total variance of the original variations of SSTAs in the TPO and NPO, respectively.This suggests that these three coherent modes describe the dominant variations of SSTAs in the TPO and NPO.
The fluctuations of SSTAs (M1; Figure 1a) indicate that the ENSO and PDO are in-phase combinations (EP El Niño and warm PDO-like pattern or La Niña and cold PDO-like pattern).The time series of the corresponding principal component (PC1) is strongly correlated with the ENSO (correlation coefficient at the 90% confidence interval: r = 0.93) and PDO (r = 0.71) indices (Figure 1d).The pattern of SSTAs (M2; Figure 1b) forms a spatially coherent structure resembling the NPMM, which is associated with extratropical-tropical interactions that favor CP El Niño events (Amaya et al., 2019;Di Lorenzo et al., 2023;Power et al., 2021).Accordingly, the time series of the second principal component (PC2) is highly correlated with the NPMM (r = 0.82) and EMI (r = 0.50) indices (Figure 1e).The spatial distribution of SSTAs (M3; Figure 1c) is similar to that of the VM, indicating a positive SST band over the eastern NPO and a negative SST band over the western NPO.NPO-forced VM events are likely to trigger positive SSTAs in the central TPO (Ren et al., 2023).Furthermore, the time series of the third principal component (PC3) is moderately correlated with the VM (r = 0.64) and EMI (r = 0.54) indices (Figure 1f).Therefore, these synergistic modes demonstrate that ENSO diversity is evident in separate TPO SSTAs based on their teleconnections with the NPO.
We used observation-based SMG-WOD data from 1970 to 2014 to explore the potential temperature variability in the deep SCS.The deepest sill of the Luzon Strait is ∼2,500 m deep, below which the basin is enclosed.Since the SMG-WOD provides temperature data only from the ocean surface to 2,500 m depth in the SCS, we refer the deep SCS to the 1,000-2,500 m depth range and define the waters below 2,500 m depth as abyssal waters (Wyrtki, 1961).Annually averaged θ d is applied to better highlight the interannual and decadal variabilities.The observed θ d variability also exhibits great similarity with those from other observation-oriented data sets (r = 0.54 for Argo profiling, r = 0.64 for EN4 reanalyses (Good et al., 2013), and r = 0.65 for Institute of Atmospheric Physics (IAP) data (Cheng et al., 2017)) (Figure 2c).A power-spectrum analysis of the 45-year volume-averaged θ d (Figure 2b) indicates two dominant peaks at 3-4 years (interannual timescale) and 10 years (decadal timescale) that pass the 90% significance test.This study addresses the potential atmospheric and oceanic processes that the TPO and NPO impose on the climatic regulations of θ d variations.

Telecommunications on the Atmospheric Bridge
Figure 3 shows the composites of the regressions of wind stress and wind stress curl anomalies onto the principal components (positive phase; Figures 1d-1f) of M1, M2, and M3.During the warm PDO and EP El Niño-like phase (Figure 1d; hereafter, P1), the Aleutian Low deepens, accompanied by changes in the Ekman transport, wind-driven mixing, and heat fluxes (Figure S3a in Supporting Information S1), which facilitate the production of warm PDO SSTAs, strengthen the Hadley circulation, and weaken the Walker circulation (Figure 3a) (Alexander et al., 2002;Strong & Magnusdottir, 2009;C. Wang, 2019).During the NPMM and CP El Niño-like phase (Figure 1e; hereafter, P2), the NPMM is characterized by weaker winds and evaporative heat loss over the central subtropical NPO (Vimont et al., 2001(Vimont et al., , 2009)), where the positive footprint of SSTAs extends southwestward through the wind-evaporation-SST (WES) feedback (Stuecker, 2018;Xie & Philander, 1994), favoring anomalous cyclone (AC) formation over the western TPO (Figure 3b).During the VM and CP El Niño-like phase (Figure 1f; hereafter, P3), the anomalous warming in the central TPO and negative SSTAs in the eastern TPO and NPO generate positive and negative Walker circulation anomalies over the western and eastern TPO, respectively, resulting in the suppression of the eastward propagation of warm SSTAs and AC enhancement over the western TPO (Shi et al., 2022) (Figure 3c).
To illustrate the oceanic pathways that connect the climate variabilities with marginal seas, the current over the upper-layer Luzon Strait was inverted using the P-vector inverse method (Chu, 1995(Chu, , 2006;;Stommel & Schott, 1977;Wunsch, 1978).The three coherent modes of the TPO and NPO SSTAs explain 30% of the total variance of the upper-layer LST, confirming their modulation of the upper-layer processes in the SCS.Previous research has demonstrated that the upper-layer LST is a key process conveying the impact of the Pacific climate variability to the upper-layer heat content of the SCS (Qu et al., 2004).Moreover, the strengthened information flow (IF)-based causality (Figure 4d) (Liang, 2014(Liang, , 2016) ) and partial correlation coefficients (PCC, Figure S4 in Supporting Information S1) between the time series of the upper-layer LST and θ d indicate that, in the northern deep SCS, the upper-layer LST contributes to the θ d change.
Given the atmospheric forcings that could also affect the LST, particularly in the upper layer (Qu et al., 2004;D. Wang et al., 2006;Yu & Qu, 2013;Zhu, Sun, Wang, et al., 2017), we explored the atmospheric bridge by synthesizing its regional (Figure 4) and remote functions (Figure 3).During the warm PDO and EP El Niñolike phase (P1), the cooling SSTAs over the western TPO develop Rossby waves, thereby contributing to AAC formation over the SCS (Figure 4a) (Tim et al., 2017).The resulting southwesterly wind anomaly over the Luzon Strait locally weakens the westward surface Ekman transport.By contrast, the time series of PC1 is negatively correlated (Figure 4e; r = −0.71)with the SSH anomalies in the region of 12°N-14°N and 127°E-130°E which serves as a proxy for the NECB (Qiu & Chen, 2010).Along the band of 12°N-14°N, the strengthened wind stress curls at 140°E-170°E (blue box in Figure 3a) induce baroclinic Rossby waves to reach the SSH box (black box in Figure 3a), leading to a northerly NECB (Qiu & Chen, 2010).This remote impact offsets the local Ekman transport reduction in the Luzon Strait (Figure 4f), thereby promoting upper-layer (i.e., upper 200 m) LST (Figure 4a), which, in turn, directly influences surface temperature variability.The negative wind stress curl anomalies associated with increased upper-layer LST leave a warming surface in the southern SCS (Figure 4a).The upward net heat flux anomalies over the northern SCS surface (Figure S3a in Supporting Information S1) offset the warming induced by the AAC.During the NPMM and CP El Niño-like phase (P2), negative SSTAs predominate in the northern SCS (Figure 4b) owing to positive wind stress curl anomalies and upward net heat flux anomalies (Figure S3b in Supporting Information S1).Remarkable northeasterly wind stress anomalies are established in the Luzon Strait.Nevertheless, the regressed positive wind stress curl anomalies east of the Philippines are smaller in amplitude; therefore, the NECB latitude shifts insignificantly (X.Wang et al., 2020) (Figure 3e).The enhanced upper-layer LST is dominated by a westward Ekman transport anomaly (Figures 4e  and 4f).Given that the causality from the upper-layer LST to θ d is significant over the northern SCS (Figure 4d), where a significant positive PCC with a lag of 1 year between these two variabilities is detected (Figure S4b in Supporting Information S1), the strengthened upper-layer LST during P1 and P2 partially modulates the θ d variability.However, these two modes explain only the negligible variance in the total upper-layer LST variability.
During the VM and CP El Niño-like phase (P3), the enhanced wind stress curl to the east of the Philippines further lowers the SSH (Figure 4f) through westward-propagating Rossby waves, causing the NECB to move northward.This remote forcing and westward local wind stress over the Luzon Strait (Figure 4c) results in enhanced upper-layer LST (Figure 3c), which contributes to 28% of the total variance of the upper-layer LST.Therefore, P3 generates greater upper-layer LST change compared to the other two coherent modes owing to the combined atmospheric effects.The surface SCS cools (Figure 4c) in accordance with the positive wind stress anomalies and negative net heat flux anomalies (Figure S3c in Supporting Information S1), thereby offsetting the impact of the strengthened Kuroshio intrusion.The negative anomalies of SSTAs in the southern SCS weaken relative to those in the northern SCS as the downward net heat flux anomalies increase.In terms of θ d , with the significant causality over the continental slope (Figure S5a in Supporting Information S1), the upper-layer LST modulates θ d through altering the convergence/divergence of horizontal flows inside the basin.

Telecommunications on the Oceanic Pathway
Since the variabilities of deep-water exchange between marginal sea and open ocean have often been linked to upper-layer processes through vertical coupling (Cai et al., 2023;Hamilton et al., 2019;Quan et al., 2021; ∆OBP contains barotropic components associated with sea level differences in the upper layer and baroclinic components related to cross-strait density differences in the lower layer.Previous studies have confirmed that both the barotropic and baroclinic components of pressure contribute to the variability of the deep-layer LST (Cai et al., 2023;Song, 2006;Zhou et al., 2023;Zhu, Sun, Wei, et al., 2017;Zhu, Yao, et al., 2022).The detrending ∆SLA between the two sides of the Luzon Strait moderately correlates (r = 0.48) with the ∆OBP, implying remote modulation from upper-layer processes.Thus, though modulating the ∆SLA crossing the Luzon Strait, the TPO and NPO influence the deep-layer LST and θ d indirectly.During the warm PDO and EP El Niño-like phase (P1), ∆SLA increases due to the influence of southwesterly wind stress anomaly (Figure 4a), and its time series moderately correlates with that of PC1 (Figure 4e; r = 0.55).However, it cannot be concluded that the three coherent modes change the ∆SLA and then dominate the ∆OBP variability.How these processes in the TPO and NPO affect the changes in deep density variability should be further investigated in future studies.

Summary
In this study, we first reconstructed the variability of SSTAs in the TPO and NPO into three coherent modes.The results indicate that the teleconnection of the TPO and NPO greatly contributes to the formation of different climate variabilities, especially the ENSO diversity.Second, we showed how these variabilities are impacting the θ d variability of the deep SCS.Our results, which differ from previous studies, attribute θ d variability to a joint imposition of climatic distortions, rather than the upper layer.These results have important implications for depicting the variability in marginal seas in response to the global climate variability.However, causality and PCC cannot represent the dynamic aspects of how LST modulates θ d variability.How the interior of the upper SCS contributes to θ d variability is a topic to be addressed in the future.

Figure 1 .
Figure 1.Coherent variations between sea surface temperature anomalies (SSTAs) in the Tropical Pacific Ocean (TPO; 20.5°S-20.5°N) and SSTAs in the North Pacific Ocean (NPO; 20.5°S-62.5°N).(a, d) First, (b, e) second, and (c, f) third multivariate empirical orthogonal function (MVEOF) modes and principal components (PC, black solid line) of the NPO and TPO SSTAs during the 1970-2014 period.The orange and blue lines in panel (d) represent the Nino3.4 and Pacific Decadal Oscillation (PDO) indices, respectively.(e) Similar to panel (d), but for the El Niño Modoki (EMI) and North Pacific Meridional Mode (NPMM) indices.(f) Similar to panel (d), but for the EMI and Victoria Mode (VM) indices.

Figure 2 .
Figure 2. (a) Shaded areas in the Pacific Ocean represent the correlation coefficients between Pacific SSTAs (north of 25°S) and domain-averaged South China Sea (SCS) SSTAs (5.5°N-23.5°N,100.5°E-122.5°E).Shaded areas in the SCS represent the depth-averaged climatological potential temperature in the deep (1,000-2,500 m depth) SCS.Arrows indicate the deep-layer LST and the cyclonic circulation (Gan et al., 2016) in the deep SCS.(b) Power spectrum (orange dashed line indicates the 90% confidence levels) of the depth-averaged (1,000-2,500 m depth) observed θ d anomaly in the SCS (5.5°N-23.5°N,100.5°E-122.5°E)from the SMG-WOD data set.(c) Time series of the detrended and normalized θ d anomaly (red, SMG-WOD; blue, EN4; green, ARGO; purple, IAP) at the depth of 2,000 m after applying a 9-year running mean, except for data from the ARGO profiler.Shaded area following the red line indicates one standard deviation of the monthly data from the averaged θ d in the specific year from SMG-WOD observation.

Figure 3 .
Figure 3. Composites of regression maps of wind stress anomaly (arrows) and wind stress curl anomaly (shading) over the Pacific Ocean onto the PC1, PC2, and PC3 time series during their respective positive phases are shown in panels (a)-(c).The colored (white) shading areas and black (gray) arrows are significant (insignificant) at the 90% confidence interval.The small black box (12°N-14°N, 127°E-130°E) in panel (a) indicates the area serving as an index of the North Equatorial Current Bifurcation (NECB) latitude to the east coast of the Philippines (Qiu & Chen, 2010).The blue box (12°N-14°N, 140°E-170°E) indicates the region where the wind stress curl is important for NECB migration.

Figure 4 .
Figure 4. Composites of regression maps of wind stress anomaly (arrows) and SSTA (shading) over the SCS onto the PC1, PC2, and PC3 time series during their respective positive phases are shown in panels (a)-(c).The colored (white) shading areas are significant (insignificant) at the 90% confidence interval.Orange arrows indicate the direction of the upper-layer LST anomaly; numbers beside the arrows indicate the anomaly intensity.Absolute information flow from the time series of (d) upper-layered anomaly to those of the SCS θ d anomaly during 1970-2014.Here, information flow means the transfer of predictability from one series to another.The colored (white) shading areas are significant (insignificant) at the 90% confidence interval.(e) Time series of the normalized PC1 (black line) and sea level anomaly (black box in Figure 3a) from satellite product (orange line, CMEMS) and from model product (red line, SODA2.2.4).Light (dark) blue line shows the normalized ∆OBP (∆SLA) between eastern (21°N-23°N, 122°E-123°E) and western (19°N-21°N, 120°E-121°E) sides of the Luzon Strait.The SLA (purple bar) averaged in the area to the east of the Philippines and the u-component of local wind stress (LWS; blue bar, westward direction is positive) averaged in the area of 12°N-15°N and 119°E-123°E for P1-P3 are presented in panel (f).A black cross indicates that the value is significant at the 90% confidence interval.
42376013, 42006007), the Science and Technology Development Fund, Macau SAR (File/Project no.0093/2020/ A2 and SKL-IOTSC-2021-2023), Science, Technology and Innovation Commission of Shenzhen Municipality (JCYJ20210324105401004 and 20220815093611001), and the Natural Science Foundation of Shanghai (23ZR1419100).The work described in this paper is also substantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project Reference Number: AoE/P-601/23-N).