Wind‐Driven Seasonal Variability of Deep‐Water Overflow From the Pacific Ocean to the South China Sea

The South China Sea (SCS) is a semi‐enclosed marginal sea linked to the broader oceans via various geographically constrained channels. Beneath the main thermocline depth, Luzon Strait is the only conduit for water‐mass exchanges. Observations indicate a substantial seasonal variability in the inflow transport of deep water from the Pacific Ocean. This study aims to identify and examine key drivers for such seasonal changes. It is found that seasonal variability of the deep‐water transport into the SCS is primarily driven by surface wind stress. An imbalance in wind‐driven exchanges of surface water between the SCS and external seas demands compensational transports in subsurface layers so that the net volume transport into the SCS is conserved, resulting in seasonal variations in deep‐water overflow. Changes in Karimata Strait exert a particularly influential impact on deep‐water inflow, likely due to its unique position as the sole connecting channel across the Equator.


Introduction
The South China Sea (SCS) is a large marginal sea in the Pacific Ocean.It is connected to the Philippine Sea through Luzon Strait and to several other neighboring marginal seas via Taiwan, Mindoro, Balabac, Karimata and Malacca Straits (Figure 1a).Through these passages, the SCS serves as a transport and exchange hub for various water masses from Indo-Pacific Oceans.While most of the straits connecting to the SCS are shallow (<400 m), the Luzon Strait stands out as a sole deep passage with a sill depth of approximately 2,400 m.Therefore, the deep SCS beneath the 2,400 m is topographically restricted from direct exchanges with external seas.However, hydrographic analyses have revealed that the deep-water mass in the SCS beneath 2,400 m can be traced to the deep Philippine Sea on the eastern side of Luzon Strait (Broecker et al., 1986), pointing to a deep-water transport overflowing the sill through Luzon Strait (Qu et al., 2000).
The deep-water inflow through Luzon Strait plays a crucial role in setting the hydrographic and biogeochemical structures in the SCS and directly drives the abyssal circulation.Studies by Lan et al. (2013Lan et al. ( , 2015) ) and Gan et al. (2016) showed that the abyssal circulation in the SCS is predominantly cyclonic so that the torque of the bottom friction balances the lateral potential vorticity (PV) flux associated with the deep-water inflow through Luzon Strait-a mechanism based on a PV integral constraint (J.Yang, 2005;Yang & Price, 2000, 2007).
Topographically restricted flows between two deep basins, such as the deep-water overflow through Luzon Strait, are studied often in the context of rotational hydraulics (Gill, 1977;Pratt & Whitehead, 2007;Whitehead et al., 1974).A flow becomes critically controlled when its Froude Number (Fr), which is the ratio between the velocity magnitude and internal Kelvin wave speed, reaches or exceeds 1.If the Luzon Strait deep-water overflow is critically controlled, as assumed in some previous studies (e.g., Qu et al., 2006;Zhu et al., 2017), its transport would be determined by processes in the upstream Pacific Ocean only because those Kelvin waves that carry information from the downstream SCS would be prevented by the overflow from reaching the sill.
Using observations, Zhou et al. (2018) estimated that Fr is only about 0.01 at the Luzon Strait sill, far smaller than 1.In addition, the observed mean transport was about 0.84 Sv (Zhou et al., 2023)-much weaker than 2.5 Sv from a hydraulics model (Qu et al., 2006).Together they indicate strongly that the overflow is subcritical in terms of rotational hydraulics.Therefore, the overflow transport and its variability can be influenced by processes in either the Pacific or SCS.This study focuses the seasonal variability of the overflow transport with a hypothesis that it is primarily driven by wind stress, consistent with previous studies of seasonal changes in Pacific marginal seas (e.g., Kida et al., 2016).To examine the hypothesis, the Estimating the Circulation and Climate of the Ocean version 4 (ECCO4) (Forget et al., 2015;Fukumori et al., 2017) is analyzed and several model simulations are conducted.
This study aims to explore the mechanisms and processes driving the seasonal variability of deep-water transport through Luzon Strait, contributing to a more comprehensive understanding of the intricate dynamics in this critical region.This paper is organized as follows: The analysis method and 3-layer model setup will be introduced in Section 2, which will be followed by analyses of a data-assimilated ocean estimate product and 3-layer model simulations, and the discussion of mechanisms is in Section 3. The main results will be summarized in Section 4.

Data and Methods
The ECCO4 (1992-2017) is dynamically and kinematically consistent with assimilations of various data types including sea level height and ocean bottom pressure (OBP, p B hereafter) from satellite observations and hydrography from Argo floats.The assimilation of p B from GRACE gravimeters is particularly desirable because deep flows at Luzon Strait are largely geostrophic (Chen, 2020).Our analyses showed that the monthly overflow transport variability from ECCO, including the seasonal cycle, is highly consistent with observations from Zhou et al. (2023) in overlap period from October 2009 to December 2017.The correlation coefficient for monthly variability is about 0.6 with p-value less than 0.01.
The 3-layer wind-driven model used in this study is constructed based on the 2-layer model that was used by J. Yang (2015) and Yang and Chen (2021) for studies of seasonal variability of ocean circulations in the Atlantic Ocean, and Chen et al. (2023) for seasonal variability of OBP in the North Pacific Ocean.A 3-layer model is chosen because the exchange flow at the Luzon Strait exhibits a 3-layer structure (Figure 1b) (e.g., Gan et al., 2016).For simplicity, we use the linear version of the model, which is governed by the following equations: (1) where u n ,v n ,and h n are anomalies of velocity components and layer thickness, and H n the mean layer thickness of the nth layer.The wind stress is applied to the upper layer through F → 1 and the bottom drag is applied to the layer that is in contact with seafloor.For example, in shallow shelves the whole water column is included in the upper layer and thus bottom drag is applied to the layer 1.In the vast deep ocean areas, all three layers are active and so the bottom friction is applied to layer 3. The model uses a linear bottom drag, that is, H n , where λ = 2 × 10 4 .For lateral friction, we use both Laplacian and biharmonic mixing of momentum with A = 10 2 m 2 s 1 and B = 5 × 10 10 m 4 s 1 .The widths of Munk-like frictional boundary layer associated with these two lateral frictions are (A/β) 1 3 ≈ 17 km and (B/β) 1/5 ≈ 14 km at 25°N.The biharmonic mixing suppresses gridscale numerical instabilities that tend to develop near sharp and narrow topographic features.
All three layers are active so that the model includes the barotropic and the first two baroclinic modes.The initial layer interfaces are set at 750 and 1,500 m based on a previous analysis of the three-layer exchange structure at Luzon Strait (Gan et al., 2016).The pressure gradients are related to anomalies in interface height η n : where ∆ρ 1 = 1 kg m 3 and ∆ρ 2 = 0.2 kg m 3 .The domain extends from 20°S to 65°N, 30°E to 90°W, including both the Indian and Pacific Oceans.The model resolution is 1/8°on staggered C-grid.The wind stress is from the ECMWF's ERA5 (Hersbach et al., 2019).Realistic topography (General Bathymetric Chart of Oceans, GEBCO, 2019) is used with a minimum water depth of 5 m.

Results
We first examine the annual-mean and depth-integrated circulations in and around the SCS using 26-year data from ECCO4 (Figure 1a).The mean circulation is predominantly cyclonic within the SCS.A net inflow transport into the SCS through Luzon Strait is balanced by outflows through Taiwan, Karimata and Mindoro Straits.These flows form the SCS Throughflow (SCSTF).The mean transport through Luzon Strait is about 5.2 Sv.Previous estimates have given a wide range of Luzon Strait transport estimates ranging from as low as 1.5 Sv to as high as over 10 Sv (Hsin et al., 2012 for a review).Most studies, however, agree that the transport is weak in the summer and strong in winter.This seasonal pattern is captured in ECCO4 (Figure 1b).
The exchange flow at Luzon Strait exhibits a 3-layer and sandwich-like structure, with an eastward outflow in the intermediate layer being sandwiched by westward inflows in both top and bottom layers (Fang et al., 2009;Gan et al., 2016;Qu et al., 2006;Tian et al., 2006;Wei et al., 2016;Yuan, 2002;Zhu et al., 2019).The exchange flow at 120.75°E across Luzon Strait indeed exhibits a 3-layer structure in ECCO4 as shown in Figures 1d and 1e  The mean overflow transport of 1.2 Sv is well within the range from previous studies (Chang et al., 2010;Lan et al., 2015;Liu & Liu, 1988;Qu et al., 2006;Tian et al., 2006;J. Wang, 1986;Yang et al., 2010;Zhao et al., 2014Zhao et al., , 2016;;Zhou et al., 2014).In a more recent study, Zhou et al. (2023) analyzed observations from two deep mooring sites within Luzon Strait and estimated that the mean transport between 2009 and 2021 is about 0.84 Sv.
Figure 1b shows the seasonal variations of the outward transports from the SCS in the surface layer through six connecting straits (the annual mean is removed in each transport).Large seasonal variations occur in Luzon, Karimata and Mindoro Straits.The sum of all transports (bold black line) is nontrivial and varies seasonally, indicating a considerable transport convergences or divergences into the SCS in the upper layer.For instance, there is a net inward transport to SCS in the upper layer between January and May and an outward one in June-September.The combined transports in all layers must be zero so that the conservation of volume transport can be satisfied.Indeed, the net inward transports into the SCS in layer 2 and 3 (Figure 1c) balance exactly the outward transport in the upper layer.
Chen et al. ( 2023) demonstrated that seasonal p B variability in the North Pacific Ocean is primarily driven by wind stress.The overflow transport through Luzon Strait is intimately tied to p B through the geostrophy (Chen, 2020;Zhu et al., 2022).Therefore, we hypothesize that the seasonal variability of the deep overflow transport through Luzon Strait is primarily driven by wind stress as well.Chen (2020) demonstrated that wind-stress forcings both locally within the SCS and remotely from the broader Pacific Ocean make considerable contributions to the seasonal variability of flows through the SCS.In this study, we are mainly interested in the role of wind stress forcing and will not try to partition contributions from local and remote forcings.
We decided to test the hypothesis that the seasonal variability of the overflow is primarily driven by wind stress using the 3-layer model described by Equations 1-3.The model is adiabatic, meaning that there are no diapycnal fluxes of water masses.The Luzon Strait is the sole conduit for surrounding ocean deep-water exchange with the SCS, therefore, the annual mean transports in both the intermediate and bottom layers are zero in this wind-driven model.This is analogous to wind-driven variability of the Atlantic Meridional Overturning Circulation (AMOC) in which the mean AMOC transport is forced by the deep-water formation while seasonal variability is winddriven (J.Yang, 2015).
The model is integrated for 50 years to an equilibrium seasonal cycle.The mean transport through Luzon Strait in the upper layer is 4.2 Sv, close to ECCO4's 4.5 Sv.The annual mean circulation inside the SCS (not shown) is dominated by a cyclonic wind-driven gyre akin to the one illustrated in Figure 1a from ECCO4.Figures 2a and 2b display the seasonal anomalies of depth-integrated velocity in winter (February) and summer (July).
The volume transports through connecting straits, displayed in Figure 2c, show that seasonal changes are most profound in Luzon, Karimata and Taiwan Straits.The amplitude of the seasonal cycle in Taiwan Strait is about 3.3 Sv (red line, Figure 2b), considerably larger than 1.3 Sv in ECCO4 (red line, Figure 1b).Previous analyses give a wide spread of estimated seasonal changes, ranging from as low as 1 Sv to as high as more than 3.5 Sv (e.g., Jan et al., 2006;Liu et al., 2021;Wu & Hsin, 2005).Apparently, the ECCO4 and 3-layer model appear near the two ends of this range.
Observations indicate that a major portion of transport through Taiwan Strait occurs along the deep Penghu Channel (Wu & Hsin, 2005).This relatively narrow channel, however, is absent in ECCO4 bathymetry.The maximum water depth across Taiwan Strait in ECCO4 is 50 m at 23.75°N as compared with about 100 m in GEBCO.Those f/H contours with H > 50 m along Penghu Channel would be blocked in ECCO4.Therefore, we speculate that some geostrophic transport that is expected to pass through Taiwan Strait would have to be diverted to Luzon Strait.Indeed, the combined transport through Taiwan and Luzon Straits (upper layer) is similar in both magnitude and phase between ECCO4 and 3-layer model simulation.
For seasonal changes in transport through Karimata Strait, previous studies provided a wide range of amplitude from as low as 2.5-8 Sv (e.g., Nie et al., 2023;Wang et al., 2019;Xu et al., 2021;Xue et al., 2004).The amplitude of seasonal changes is about 6 Sv in 3-layer model and 3.85 Sv in ECCO4, both are within the range of previous estimates.Like that in Taiwan Strait, some deeper passages in Karimata Strait are not adequately resolved in ECCO4 and this may have contributed to a smaller transport and weaker variability than that from 3-layer model and most previous studies.
The transport through Mindoro Strait varies in a similar phase to that along Karimata Strait (Figures 1 and 2).Notably, the amplitude of the transport is more pronounced in ECCO4 compared to the 3-layer model.Nevertheless, the combined transport through these two straits exhibits similar seasonal amplitude changes between ECCO4 and the 3-layer model.
Transports are small through both Malacca and Balabac Straits.Therefore, the seasonal variability of the net transport in the upper layer is mainly determined by that through Luzon-Taiwan Straits and Karimata-Mindoro Straits.The seasonal anomaly of the net outward transport from the SCS in the upper layer is shown in Figure 3a.It varies from a minimum in late winter (March) to a maximum in the summer (June-July) with an annual amplitude of about 2.5 Sv.The modeled seasonal variability of the transport (red line) agrees reasonably well with that from ECCO4 (black line) both in the phase of seasonal changes and in amplitude.The good model-ECCO4 agreement is also seen for the seasonal variability for the bottom-layer overflow transport through Luzon Strait (Figure 3c).The overflow transport from ECCO4 (black line) varies annually and semi-annually with maximum transport occurring in late fall/early winter and in summer, and minimum in late winter and fall seasons.This seasonal cycle is well captured by the model (red line).Interestingly, the transport in the intermediate layer shows a similar pattern of seasonal changes as that in the bottom layer (Figure 3b).Since the model is forced by the wind stress alone, transport variations in the lower two layers must be induced by changes in the wind-driven upper layer.The SCS is connected to surrounding seas through many straits of which only the Luzon Strait is deeper than 750 m-the depth of interface between the upper and intermediate layers in the model.Wind stress forces convergence or divergence of the upper layer water mass into the SCS.In response, the thermocline depth and the water volume beneath it would have to change.In an adiabatic model, there must be a change in deep-water inflow to accommodate changes in deep-water volume inside the SCS.Through this mechanism, the upper ocean's response to wind forcing leads to changes in Luzon Strait inflow of deep water.Figures 3d and 3e schematize this mechanism, which was also used by J. Yang (2015) to explain the seasonal variation in AMOC.
We postulate that the seasonal changes of volume transports through Luzon Strait in the intermediate and low layers are determined by the net transport into the SCS through all straits.Through this connection, changes in any straits, even the very shallow ones, could potentially affect the deep-water overflow transport through Luzon Strait.To test this hypothesis, we conduct 5 additional experiments in each of them of the following straits, Taiwan, Karimata, Mindoro, Balabac and Malacca, is closed by inserting a solid boundary across the channel.All other components in the model setup, including the forcing field, remain unchanged as the control run shown in Figure 2.
Blocking a single strait has the potential to trigger transportation shifts through other straits.Consequently, the alteration in net transport into the SCS via all straits may not necessarily match the original transport that is being obstructed.Figure 4a shows the difference in the depth-integrated velocity between the closed Taiwan Strait simulation and control run in the month of July when the northward transport through Taiwan Strait is maximum.Karimata Strait, however, stands out as an exception in terms of its impacts on the net transport into the SCS.
Blocking transport there would result in considerable changes in the net transport into the SCS in the upper layer and thus in the subsurface layers (red lines in Figures 4c and 4d).Closing Karimata Strait does influence transports through other straits as revealed in Figure 4b, but transport changes elsewhere do not compensate sufficiently for transport closure at Karimata Strait.It remains to be further studied regarding why Karimata Strait has different impact on the net transport into the SCS.It is noted that Karimata Strait extends across the Equator.Adjustments to cross-equatorial flows involve different dynamical processes than those without involving equatorial dynamics.

Summary
In this paper, we analyze ECCO4 data to quantify and examine the mean and seasonal variability of deep-water transport to the SCS through Luzon Strait.ECCO4 confirms a previously identified 3-layer structure of exchange flows in Luzon Strait (Gan et al., 2016).The seasonal variations of transports through major connecting straits are quantified.It was hypothesized that the seasonal variability of the deep-water overflow is driven by wind stress and caused by changes in the net transport into the SCS in the wind-driven upper layer.
A 3-layer wind-driven model is used to test this hypothesis.The modeled seasonal variations of the net transports into the SCS in three layers agree reasonably well with that from ECCO4 (Figures 3a-3c), indicating that the seasonal variability of the deep-water overflow transport is indeed driven primarily by wind stress.Our analyses indicate that changes in transport in both intermediate and bottom layers through Luzon Strait are mandated by the conservation of volume transport into the SCS.In winter months (e.g., February-March), for instance, the inward transport into the SCS is larger than the outward transport in the upper layer (Figures 1b and 2c).The conservation of the volume transport into the SCS requires that there must be an anomalous outward transport in deeper layers so that the net transport is zero (schematized in Figures 3d and 3e).This results in a seasonally weak transports into the SCS in the lower two layers.The opposite occurs in the summer months.Through this layer-compensation mechanism, the wind stress forcing regulates the seasonal variability of the Luzon Strait overflow transport.
The upper layer water in the SCS is connected to external oceans through multiple straits.Our further analyses indicate that the overflow transport is rather insensitive to changes in most straits except the Karimata Strait.
Closing transport through Taiwan Strait, for instance, would lead to changes in Luzon Strait and the net transport into the SCS is little affected.Blocking transport through Karimata Strait, however, has more significant effects on the overflow.We speculate that the higher sensitivity is related to the fact that Karimata Strait is the one that extends across the Equator, and thus transport adjustments between straits would involve different dynamical processes.This topic will be pursued in future studies.

Figure 1 .
Figure 1.(a) The annual-mean and depth-integrated velocity field in the South China Sea (SCS) regions (vectors, truncated at 10 m 2 /s) and bathymetry (color) from ECCO4 (1992-2017); and (b) seasonal anomalies of outward transport from SCS in the upper layer through Luzon Strait (marked by A in the upper left panel), Taiwan Strait (B), Malacca Strait (C), Karimata Strait (D), Balabac Strait (E) and Mindoro Strait (F); (c) seasonal changes of inward transports in the middle and deep layers; (d) and (e) zonal velocity across Luzon Strait at 120.75°E (color) in March and November.The interfaces for the three layers are defined by potential densities of σ θ = 27.375 kg/m 3 (between upper and middle layers) and σ θ = 27.675kg/m 3 .These values are selected based on the averaged velocity and potential density profiles at 120.75°E across Luzon Strait.
. The flow is westward in surface layer with σ θ < 27.375 kg m 3 , and eastward in the middle layer with 27.375 ≤ σ θ ≤ 27.675 kg m 3 .The deep water with σ θ > 27.675 kg m 3 moves westward into the SCS.These two values of potential density, that is, σ θ = 27.375 and 27.675 kg m 3 , are used to define the 3-layer exchange flows.The annual mean transports for these three layers are 4.5 Sv westward in the upper layer, 0.45 Sv eastward in the intermediate layer, and 1.2 Sv westward in the bottom layer.All transports vary considerably with seasons as shown in Figures1d and 1e .

Figure 2 .
Figure 2. Simulations from the 3-layer wind-driven model, (a)-(b) seasonal anomalies of the vertically integrated velocity field in February and July (vectors truncated at 15 m 2 /s); (c) seasonal anomalies of the outward transports through 6 straits and the sum of them (bold black line); and (d) anomalies of the inward transports through Luzon Strait in the intermediate and bottom layers and their sum.The annual mean fields are removed in all plots.The annual mean transport through Luzon Strait is about 4.2 Sv in the upper layer.

Figure 3 .
Figure 3. Seasonal anomalies of (a) net outward transport from South China Sea (SCS) in the upper layer, (b)-(c) transports into the SCS through Luzon Strait in the intermediate and bottom layers (black lines from ECCO4 and red lines from 3-layer model), (d)-(e) schematics of how changes in the upper-layer transport affect the exchange flows in the lower layers, which include the intermediate and bottom layers in this study.

Figure 4 .
Figure 4. (a) The difference of depth-integrated velocity in the upper layer in July between the closed Taiwan Strait simulation and the control run; (b) same as (a) except for the closed Karimata Strait simulation; (c) the seasonal variability of westward transport in the intermediate layer through Luzon Strait for the control run (black) and 5 addition simulations in which one connecting strait to the South China Sea is closed; and (d) same as (c) except for the bottom layer.