Introduction

The unprecedented warming of oceans has evidently impacted climate change1,2,3,4. As anthropogenic activities release greenhouse gases into the atmosphere, a considerable portion of the excess heat is absorbed by the oceans, leading to persistent warming, especially in recent decades5,6. This warming can dramatically affect marine ecosystems, change the hydrodynamic environment, and alter interactions between the ocean and atmosphere7,8,9,10. As a result, appreciable attention has been given to understanding the behavior and prolonged effect of ocean warming4,11,12. One of the evident efforts is on the responses of large-scale circulations, including the deep ocean circulation13,14. The deep circulation plays a crucial role in transporting heat, nutrients, and dissolved gases. Thus, understanding how deep circulation responds to ocean warming is important for comprehensively understanding changes in the deep ocean environment. The South China Sea (SCS) is one region where ongoing warming processes have been observed15,16. However, the exact influences of warming on circulation in the deep SCS remain largely unclear.

In recent decades, rising sea surface temperatures have been observed, changing the pattern and pathway of surface circulation and affecting ocean‒atmosphere interactions, which further impact the global climate2. Below the surface, heat propagates deep into the ocean17. Observations indicate that the globally integrated decadal heat content trends can reach 34.5 (±8.3) TW in the deep ocean, thus inducing widespread deep warming18. Multiple factors can contribute to deep ocean warming. Such as reductions in the formation rate and density of Antarctic Bottom Water18, increased melting rates of ice19,20, and decreased sea-ice export21. In addition, dynamic processes such as internal tides (ITs) can also convey the surface and upper ocean warming effects down to the deep ocean22,23. ITs are internal waves with tidal frequencies24,25. ITs play essential roles in conveying the kinetic energy (KE) of surface waves into the deep ocean. ITs propagate into the interior of the ocean and can enhance vertical mixing when they dissipate, thereby transporting heat from the upper layers to the deep ocean. The breaking of ITs serves as the primary energy source, maintaining deep ocean mixing, evidently impacting meridional overturning circulation by providing approximately half of the energy needed through turbulent mixing26,27,28. Ocean warming has been shown to increase stratification29 and will inevitably change the behavior of ITs. Yang et al. pointed out that warming increases ITs conversion globally30. It may affect deep ocean circulation through variations in mixing. The SCS is a region with extremely active ITs and has experienced warming16,31,32. However, the role of ITs in modulating deep SCS circulation under global warming remains unclear and needs to be quantified. Although Wang et al. pointed out a reduction in global deep ocean circulation and attributed it to weakened mesoscale eddies14. In comparison with the open ocean, marginal seas such as the SCS may experience more multifaceted warming processes. Circulations had a cyclonic–anticyclonic–cyclonic structure in the upper (above 750 m), middle (750–1500 m), and deep (under 1500 m) layers in the SCS33. Cai and Gan advanced the understanding of the intrinsic-extrinsic dynamic coupling that forms, develops, and sustains this circulation structure34. Cai and Gan further provided a new interpretation from energy prospect to the sustaining of this circulation pattern35. Owing to the complicated structure of circulation in the SCS, multiple factors may participate in governing the variation in deep circulation. Since deep ocean circulation is largely driven by geostrophic currents, the warming may have an irrefutable effect on changing the density field, thereby evidently modulating deep circulation. Thus, we explore this process from aspects distinct from those of Wang et al.14 to further improve the understanding of warming effects on deep SCS circulations. We present an analysis of the evolution of deep SCS circulation under ocean warming using the Global Ocean Reanalysis and Simulation (GLORYS) and Simple Ocean Data Assimilation (SODA) datasets. Then we carried out numerical experiments to quantify the effects of warming on deep circulation in the SCS.

To emphasize the main idea, the contents of the paper are organized as follows. In the section “Results,” the effects of warming on deep SCS circulation, the possible dominating mechanisms are presented. A discussion and summary are presented in the section “Conclusions and discussion.” In the section “Methods,” the data, model configuration method, the diapycnal diffusivity, and energy calculation methods are introduced.

Results

Response of deep circulation in the SCS to warming

Time series of horizontally and vertically averaged KEs in the deep ocean (below 2400 m) in the SCS were calculated via GLORYS (from years 1993 to 2020) and SODA (SODA 3.7.2 from years 1980 to 2016) datasets and are shown in Fig. 1 (the region of the SCS is outlined by the red box in Fig. 2). The KEs calculated from both GLORYS and SODA indicate a weakening of motion in the deep SCS. The error information related to KE computation is shown in Supplementary Table S1. Given the large standard deviation of the data, the KE exhibits a high degree of dispersion, leading to relatively evident fitting errors when applying a linear regression. However, the aim here is not to achieve a precise temporal fit of KE, but to capture its long-term variability. The present results suggest that the reanalysis datasets are adequate for identifying the underlying trend in KE. The time series of horizontally and vertically averaged temperatures tend to increase in the deep ocean of the simulation domain for decades (Supplementary Fig. S1a). These findings suggest that the SCS has experienced sustained warming. However, similar variations in salinity are not observed; instead, there is a weak decreasing trend, with a much smaller magnitude than that in temperate areas (Supplementary Fig. S1b). The noticeable warming in the deep SCS may have an irrefutable effect on changing the density fields, which will further affect mixing through ITs. Since deep ocean circulation is largely driven by geostrophic currents, changes in density fields will thereby evidently modify deep circulation. Thus, we carried out numerical experiments to quantify the effects of warming-induced density changes and variations in ITs in the reconstruction of deep circulation in the SCS.

Fig. 1: Evolution of KEs in the deep SCS revealed by reanalysis datesets.
Fig. 1: Evolution of KEs in the deep SCS revealed by reanalysis datesets.
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Time series of horizontally and vertically averaged KE in the deep SCS (below 2400 m depth) calculated via the a GLORYS product (the black solid line represents the variation in KE, the red dashed line represents the varying tendency of KE, and the gray shading indicates the 95% confidence interval) and the b SODA product (the blue solid line represents the variation in KE, the yellow dashed line represents the varying tendency of KE, and the gray shading indicates the 95% confidence interval).

Fig. 2
Fig. 2
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The simulation domain (the red box indicates the SCS domain; the orange arrows indicate the circulation path in the deep SCS).

Validation based on numerical experiments

Numerical experiment one (EX1) and experiment two (EX2) are conducted based on the average SODA temperature and salinity fields from 1980 to 1986 and from 2010 to 2016, which represent the cold and warm conditions, respectively (details of numerical experiment settings can be found in the section “Methods”). Supplementary Table S2 shows the KE in the deep ocean in the cold experiment (EX1) and warm experiment (EX2). The KE in EX2 is ~13.66% smaller than that in EX1, indicating the weakening of deep horizontal circulation, which is also revealed by reanalysis products by previous studies36. Figure 3a, b shows EX1 and EX2 horizontal currents, respectively, in the deep SCS, which are vertically averaged at depths greater than 2400 m. The simulation reveals a basin-scale cyclonic circulation pattern in the SCS basin. The current first flows north-eastward along the SCS continental slope, then it turns south-westward along the northern slope and western boundary, and then the current flows eastward along the southern boundary and northward along the eastern boundary. The diagram of deep SCS circulation is also labeled in Fig. 2 by orange arrows. This pattern is similar to that identified by previous studies37,38,39. The strong western boundary current, which has been proven by observations and simulations36,40, is also simulated by our model. In other words, the most identical features of the deep SCS circulation of the basin-scale cyclonic gyre and western intensification are successfully captured by our model. Figure 3c indicates that EX1 and EX2 are different in current intensity. Circulation is generally weakened, except for that in the northeast corner of the SCS, where the enhancement is observed. In regions near the western boundary, where currents were previously stronger, the circulation was evidently weakened. Supplementary Fig. S2 indicates that the propagation of the current is even reversed, especially in layers near the ocean bottom. Current variations were calculated according to \({{\mathrm{Current}}}\,{{\mathrm{variations}}}=({{{{\boldsymbol{u}}}}}_{2}-{{{{\boldsymbol{u}}}}}_{1})/{{{{\boldsymbol{u}}}}}_{1}\), where \({{{{\boldsymbol{u}}}}}_{2}\) and \({{{{\boldsymbol{u}}}}}_{1}\) are the simulated horizontal velocities in EX2 and EX1, respectively. Supplementary Fig. S2c, f displays the current variations, which also exhibit a bottom-intensified tendency, especially in terms of the zonal velocity. Stronger current variations appear in layers near the ocean bottom, implying that proximity to the ocean bottom enhances the capacity of warming to modulate circulation.

Fig. 3: Effects of warming on current, MKE and EKE.
Fig. 3: Effects of warming on current, MKE and EKE.
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Vertically averaged horizontal current in the deep SCS in a EX1 (the cold experiment) and b EX2 (the warm experiment), the color indicates the current intensity, and the arrows indicate the direction; c the difference in the deep horizontal current between EX2 and EX1; d–f corresponding results for the MKE; g–i corresponding results for the EKE.

The KE, which balances the time-mean flow (MKE) and the eddies (EKE). Figure 3d–i shows the influence of warming on the MKE and EKE. The magnitude of the MKE (Fig. 3d, e) is comparable to that of the EKE (Fig. 3g, h); however, the spatial distributions are distinct. Generally, strong MKEs are predominantly found in the northeastern SCS. In this region, the MKE is much stronger than the EKE. Intensive EKE can be observed in the western boundary regions. The circulation is evidently weakened at the western boundary (Fig. 3c). The differences in MKE (DMKE) and EKE (DEKE) between EX2 and EX1 are shown in Fig. 3f and i, respectively. The variation in current can largely be explained by that of the MKE (Fig. 3f), especially in regions north of 16°N. In regions south of 16°N, the EKE also slightly contributes to the reduction in deep circulation (Fig. 3i). In other words, ocean warming weakens deep circulation in the SCS generally through the modulation of the MKE.

Potential energy (PE) is also balanced by the time-mean flow (MPE) and the eddies (EPE). The MPE first weakens and then enhances with water depth increasing under ocean warming (Fig. 4a). And the warming process generally weakens the EPE in the deep SCS (Fig. 4b). The energy transfers that affect the KE field can be expressed by T1, T2, and T3. T1 and T2 describe the transmissions of energy, respectively, from the MKE and EPE to EKE. T3 qualifies energy transfers from MKE to MPE. The magnitudes of T1 and T2 are much smaller than those of the EKE. Variation in T1 is small (Fig. 4c). T2 generally has a positive variation. (Fig. 4d). Changes in T3 are also relatively small (Fig. 4e).

Fig. 4: Variatins in MPE, EPE and the transfers of energy.
Fig. 4: Variatins in MPE, EPE and the transfers of energy.
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Horizontally averaged a MPE, b EPE, c T1, d T2, and e T3 in the deep SCS in EX1 (blue lines) and EX2 (orange lines).

Underlying mechanisms

Maps of vertically averaged density, temperature and salinity in oceans beneath 2400 m in EX1 are shown in Fig. 5a–c, with corresponding results for EX2 shown in Fig. 5d–f. The density field exhibits a pattern of intensification toward the south, with greater density in the southwestern basin and lower values in the northeastern SCS. In the cold experiment (EX1), the spatial variations in temperature and salinity are relatively pronounced. The temperature and salinity also have evident southward intensified distributions. However, with continuous ocean warming, the ocean temperature not only increases but also becomes more uniformly spatially distributed (Fig. 5e). With respect to salinity, despite a reduction in intensity, the spatial distribution continues to exhibit an uneven pattern. Accordingly, the horizontal density generally becomes more uniform owing to the change in temperature under a warming climate. The horizontal gradient of density is calculated according to

$${{{\mathrm{density}}}}\,{{{\mathrm{gradient}}}}={\left[{\left(\frac{\partial \rho }{\partial x}\right)}^{2}+{\left(\frac{\partial \rho }{\partial y}\right)}^{2}\right]}^{\frac{1}{2}},$$
(1)
Fig. 5: Evolution of density, temperature, salinity and density gradient.
Fig. 5: Evolution of density, temperature, salinity and density gradient.
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Maps of vertically averaged a density, b temperature, and c salinity in the deep SCS in EX1; d–f corresponding results for EX2; maps of vertically averaged density gradient in g EX1 and h EX2 in the deep SCS; i the difference in density gradient between EX2 and EX1.

The distributions of the vertically averaged density gradients at depths greater than 2400 m are shown in Fig. 5g, h. A large gradient is primarily observed in the northeastern SCS and along the western boundary regions, which is highly consistent with the pattern of deep circulation (Fig. 3a, b). Deep ocean circulation is largely driven by the geostrophic current. A large horizontal density gradient generates a stronger horizontal pressure gradient force, which drives intensive ocean currents. Under ocean warming conditions, the density gradient in the northeastern SCS increases; however, that in the western boundary regions decreases (Fig. 5i). The spatial evolution of the density gradient is generally consistent with that of the deep circulation (Fig. 3c). These results suggest that the weakening of deep circulation may be highly connected to the modulation of the horizontal density gradient. However, we also find that the variation in the density gradient in the area between 18°N and 20°N is not exactly aligned with the current change, where the circulation experiences an evident decrease, but a evident reduction in the density gradient is not observed. It is possible that other factors also modulate the variation in deep circulation. For example, based on the Community Earth System Model Wang et al. examined the variation of deep ocean circulation from the years 1920 to 210014. They noted that enhanced vertical stratification under global warming reduces the available potential energy stored in large-scale ocean circulations, diminishing its conversion into KE, then weakens deep circulation. The important role of density gradient in governing circulation was reported by previous studies. Herbaut et al. pointed out that forcings due to density gradients through the strait contribute to generating a realistic cyclonic surface circulation in the Western Mediterranean Sea41. Wang and Meredith emphasized the importance of density gradients in driving the deep Ross Sea circulation42. Arthun et al. attributed future strengthening between 2040 and 2100 of the Nordic Seas overturning circulation to a strengthened horizontal circulation and zonal density gradient43. In the SCS, the importance of density gradient was also revealed by previous studies. Using the U.S Navy Generalized Digital Environment Model monthly climatology of dataset, Wang et al. revealed the importance of density gradient in modulating the deep SCS circulation37. They pointed out that the strong density gradient along the northwestern margin induced the strong boundary current. Our study further reveals that the weakening of density gradient in the deep SCS, especially near the western boundary, to a large extent may slow the deep SCS circulation.

As the ocean warms, diapycnal diffusivity clearly increases (Supplementary Fig. S3). The largest enhancement occurs in the Luzon Strait, where ITs are primarily generated. When ITs radiate south-westward from the Luzon Strait to the SCS, they bring an intensive increase in diapycnal diffusivity to the SCS and can reach as long as the central SCS (Supplementary Fig. S3c). In the Luzon Strait, diapycnal diffusivity as strong as O(10−1) m2 s−1 can be observed in layers near the ocean bottom (Supplementary Fig. S4a, b). The warming process further increases diapycnal diffusivity in the deep ocean (depths greater than 2400 m). However, oceans above these layers may experience a slight decrease in diapycnal diffusivity (Supplementary Fig. S4c). In the SCS, diapycnal diffusivity is approximately one order of magnitude lower than that in the Luzon Strait (Supplementary Fig. S5). The warming climate still effectively increases it in both the northern and central deep SCS. Thus, diapycnal diffusivity in the deep ocean is generally enhanced under a sustained warming climate.

These results indicate that warming can effectively increase mixing, it may play essential roles in altering deep SCS circulation. Thus, we carried out groups of experiments to quantify the roles of variations in the density field and diapycnal diffusivity in the modulation of the deep circulation in the SCS. Numerical experiment 3 (EX3) and numerical experiment 4 (EX4) were conducted to explore the effects of mixing. Moreover, numerical experiments 5 (EX5) and 6 (EX6) were designed to analyze the influence of the density field. Details of settings in EX3 to EX6 can be found in the section “Methods.”

The deep circulations in EX3 and EX4 share similar spatial patterns with those in EX1 and EX2; however, they vary in current intensity (Fig. 6a, b). EX3 and EX4 have identical initial density fields but are distinct in diapycnal diffusivity settings. Changes in diapycnal diffusivity generally intensify the deep current (Fig. 6c). The density gradient also generally increases in the deep SCS (Fig. 6d). Changes in diapycnal diffusivity may cause horizontal variations in density fields, thus enhancing the deep SCS circulation. This finding indicates that diapycnal diffusivity change cannot weak deep circulation, instead, it will accelerate the deep ocean currents.

Fig. 6: Evolution of circulation and density gradient in EX3 and EX4.
Fig. 6: Evolution of circulation and density gradient in EX3 and EX4.
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Vertically averaged horizontal current in the deep SCS in a EX3 and b EX4 (the color indicates the current intensity, and the arrows indicate the direction); differences in c deep horizontal current and d density gradient between EX4 and EX3.

EX5 and EX1 adopt the same diapycnal diffusivity (calculated on the basis of simulations under cold ocean conditions), but the density fields in these two experiments are distinct. By comparing the model outputs of EX5 and EX1, the effects of density evolution on deep ocean circulation can be obtained. The influence of the density field can also be explored by comparing the results of EX2 and EX6. In EX5, the deep SCS circulation becomes extremely weak, especially at the western boundary, where the intensification of circulation nearly disappears (Fig. 7a). The evolution of the density field effectively weakens the circulation in the deep SCS (Fig. 7b). The density gradient in the deep SCS also clearly decreases (Supplementary Fig. S6a). It is plausible that the density change weakens the deep circulation largely through decreasing the density gradient. The deep current in EX6 is the strongest among all these experiments (Fig. 7c). EX6 has a cold density field and enhanced diapycnal diffusivity structure. These factors both contribute to the enhancement of deep circulation. Thus, EX6 has the strongest current. Moreover, a more evident change in density gradient is observed (Supplementary Fig. S6b). This decrease can induce evident changes in deep circulation.

Fig. 7: Evolution of circulation in EX5 and EX6.
Fig. 7: Evolution of circulation in EX5 and EX6.
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Vertically averaged horizontal current in the deep SCS in a EX5 and c EX6 (the color indicates the current intensity, and the arrows indicate the direction); differences in deep horizontal current b between EX5 and EX1 and d between EX2 and EX6.

Conclusions and discussion

In this study, we analyzed the evolution of deep SCS circulation under ocean warming via the GLORYS and SODA datasets and numerical simulations. By using the GLORYS and SODA datasets, we found that the deep SCS circulation has weakened under ocean warming in recent decades. The weakening of deep circulation, which revealed by reanalysis products, is validated by numerical simulations. The results of the numerical simulations suggest that evident weakening can generally be expected in the western boundary region, in which circulations are largely dominated by the EKE. However, a reduction in deep circulation is generally expressed by a decrease in the MKE.

The underlying mechanism that decreases deep circulation is explored. By using idealized experiments, we found that the weakening of deep circulation is likely to be attributed to a decrease in the horizontal density gradient. With continuous ocean warming, the temperature in the deep ocean not only increases but also has a more uniform spatial distribution. Thus, the density gradient in the deep SCS, especially near the western boundary, has weakened and eventually slowed the deep SCS circulation. Direct heating from the atmosphere causes the upper layers of the ocean to increase in temperature, and the warming signal propagates down to the deep ocean via multiscale motions, such as ITs which can have a warming effect on the deep ocean through the modulation of diapycnal diffusivity. Ocean warming increases diapycnal diffusivity in the northern and central SCS. An increase in diapycnal diffusivity facilitates deep circulation. In other words, ocean warming, on the one hand, directly reduces the density gradient, and on the other hand, increases diapycnal diffusivity. However, those two factors have diametrically opposite effects. A reduction in the density gradient causes a decrease in circulation, whereas an increase in diapycnal diffusivity accelerates the deep current. Owing to the lack of in situ observations, the varying of deep SCS circulations are usually analogized based on reanalysis data including the seasonality and long-term effects36,44. Zhu et al. pointed out that trends in the Circulation and Climate of the Ocean bottom pressure gradients dataset indicate a decadal weakening of deep SCS circulation36. Our study is consistent with their findings, and we further found that ocean warming is the essential driver which induces that change. However, there is also a discrepancy against some recent studies, such as Zhou et al.45. Based on two mooring observations, they estimated 12-year (from 2009 to 2021) mean volume transport of the deep water overflow and pointed out a 9% increasing trend. However, our simulation results indicate no evident changes in deep overflow between warm and cold conditions (Supplementary Fig. S7). The discrepancy can most possibly be attributed to the differences in study time span. Our study has a longer time span. Enlarging the study period can cover extended variation, which may show different changing trends. Thus, differences in temporal durations may partially cause this discrepancy. Wang et al. also found out that the strength of deep SCS circulation is not corresponded to that of overflow transport46. The largest transport in the deep layer in their experiment does not correspond to the strongest circulation. They also attributed relatively smaller velocities of current to the relatively weaker density gradient. The long-term impact of deep overflow on deep SCS circulation needs to be further explored when long-time observations are available.

Ocean warming in the upper ocean is observed globally. This trend has increased in recent decades, increasing stratification, inducing frequent marine heat waves, and causing extreme sea level rises47,48. These responses of ocean physical processes further have ecological and economic consequences, such as impacting upper ocean primary productivity and increasing the risk of frequent marine disasters. As a result, upper ocean warming has attracted considerable attention. Images that depict the characteristics and impacts of deeper ocean warming are limited at present. Studies on warming in the deep ocean and its associated influences are rare compared with those in the upper ocean. However, a recent study successfully noted a decrease in deep circulation in the global ocean14. Thus, the role and effect of deep ocean warming still need to be further studied. The impact of deep circulation changes on the climate also requires a comprehensive approach. In particular, it is necessary to carry out new measurements, especially in the deep ocean, to acquire a clear understanding of prolonged impacts.

Methods

Ocean reanalysis datasets

The GLORYS dataset is used to identify varying trends in deep circulation in the SCS. The monthly GLORYS product, which has a resolution of 1/12° × 1/12° and covers the period of 1993–2020, is used in this study. It is based on the NEMO model driven by ECMWF ERA-Interim and ERA5 reanalysis. Observations, including altimeter data, satellite sea surface temperature, sea ice concentration, and in situ temperature and salinity profiles, are assimilated using a reduced-order Kalman filter. GLORYS has been proven to be appropriate for investigating ocean warming12,49,50. GLORYS products are also widely used to investigate global or regional sea circulation, such as those in the SCS51,52,53,54. In addition, to ensure the accuracy of the analysis, additional data sources, such as the SODA dataset, are employed55. The monthly SODA dataset, which has a resolution of 1/2° × 1/2°, covering the period of 1980–2016, is also used to extract deep circulation in the SCS. The SODA dataset has successfully been used to explore ocean warming and SCS circulation27,56,57. The SODA reconstructs the historical ocean physical conditions back to the early twentieth century. The SODA emphasizes agreement with direct measurements within observational error margins and unbiased statistics, providing reliable seasonal-to-decadal ocean reanalysis to complement atmospheric reanalysis. It enhances horizontal and vertical resolution, provides better meteorological forcing, and improves tidal mixing. By using datasets from GLORYS and SODA, the KE in the deep SCS (beneath 2400 m depth) can be estimated according to

$${{{\rm{KE}}}} = \frac{1}{2}{\rho }_{0}({u}^{2}+{v}^{2}),$$
(2)

where \({\rho }_{0}\) is the reference density and u and v are the zonal and meridional velocities, respectively. Then, the responses of deep SCS circulation to ocean warming can be explored.

Model configuration method

The ocean model used in this study is the Massachusetts Institute of Technology general circulation model (MITgcm). Figure 2 shows the simulation area (2°–24°N, 105°–125°E), which covers the Luzon Strait, the SCS (indicated by the box with red dashed lines), and part of the western Pacific Ocean. The model topography is derived from the General Bathymetric Chart of the Oceans (GEBCO_08) bathymetry data46. The simulation is conducted at a horizontal resolution of 1/12° × 1/12°. In the vertical direction, there are 60 uneven vertical layers varying from 0 m at the top to 5700 m at the bottom. The initial temperature and salinity profiles are derived from the SODA dataset58. The circulation is simulated in two steps. In step one, the focus is on modeling ITs to establish initial diapycnal diffusivity fields for the circulation simulations (details can be found in the following descriptions in this section) in step two. In addition, in step one, the initial temperature and salinity fields are horizontally homogenized via the horizontally average and temporal mean values of years 1980 to 1986 and 2010 to 2016 in SODA, which represent cold and warm states of the ocean, respectively. Barotropic tidal currents for M2 and K1, which represent semidiurnal and diurnal ITs, respectively, are added at the open boundaries. The amplitudes and phases of these constituents are extracted from the Oregon State University Tidal Inversion Software (OTIS)59. In the open boundaries, sponge layers are applied. In this stage, the ITs are simulated for 30 days, and the outputs of 2 days in the spring-tide period are used to calculate the diapycnal diffusivity. The diapycnal diffusivity is used as the initial field in circulation simulation (simulation stage two, which is presented in following descriptions in this subsection). The horizontal eddy viscosity in the IT simulation is calculated with the Smagorinsky scheme60. According to Thakur et al.61, the K-profile parameterization (KPP) scheme62 was redundant in internal wave simulations. Therefore, a vertical mixing scheme is not employed at this stage. The vertical eddy viscosity is set to 10−4 m2 s−1.

In step two, which involves simulating circulation, the initial fields for EX1 are based on the mean SODA temperature and salinity fields of years 1980 to 1986, which represents the cold ocean condition. Initial temperature and salinity fields of EX2 are set to the temporal mean values of years 2010 to 2016 of SODA. EX2 represents the warm ocean condition. The tidal effect is represented by diapycnal diffusivities which are estimated according to the results from step one (IT simulations). Then, the effects of warming on deep circulation can be explored. The models are forced by the climatological monthly mean wind stress calculated from cross-calibrated multiplatform datasets63, with relaxation of the sea surface temperature and salinity to the SODA monthly climatology. The heat fluxes, which include the monthly mean latent heat and sensible heat exchanges, as well as longwave and shortwave radiation at the sea surface, are derived from National Centers for Environmental Prediction reanalysis data. In the open boundaries, sponge layers are also applied, and the thermodynamic variables of the model are relaxed to the SODA monthly climatology. At this stage of the simulation, the horizontal eddy viscosity is calculated with the Smagorinsky scheme, and the vertical counterpart is estimated via the KPP scheme. Both EX1 and EX2 are initiated from a state of rest and run for 20 years.

Groups of experiments are carried out to quantify the roles of variations in the density field and diapycnal diffusivity in the modulation of the deep circulation in the SCS. EX3 and numerical EX4 were conducted to explore the effects of diapycnal diffusivity. EX5 and EX6 were designed to analyze the influence of the density field. In EX3 and EX4, the initial temperature and salinity fields were set to the mean values of 1980–2016 in SODA. The diapycnal diffusivities in EX3 and EX4 were set respectively to be the same as those in EX1 and EX2. In EX5, the initial temperature and salinity fields were the same as those in EX2 (the warm run, initial fields of temperature and salinity use mean SODA data from 2010 to 2016), but the diapycnal diffusivity was the same as that in EX1 (the cold experiment). The settings of EX6 are opposite those of EX5. The initial temperature and salinity fields were the same as those in EX1, and EX2 diapycnal diffusivity was employed in this experiment. Details of numerical experiment settings can be found in Supplementary Table S2.

Diapycnal diffusivity

Diapycnal diffusivity is estimated on the basis of baroclinic energy dissipation64,65,66:

$$K = -\frac{\alpha D}{\rho {N}^{2}}F+{K}_{0},\\ F = \frac{\exp [-(H+\eta +z)/\beta ]}{\beta \{1-\exp [-(H+\eta )/\beta ]\}},$$
(3)

where α = 0.2 is the mixing efficiency, D is the dissipation of baroclinic energy, \(\rho\) is the density, N is the buoyancy frequency, K0 = 10−5 m2 s−1 is the background diffusivity, F is the vertical structure function and β is the vertical decay scale.

The dissipation of baroclinic energy is estimated via the following direct computation method:

$$D = - \left\langle \int _{-H}^{\eta }{\varepsilon }_{vis}dz+{\varepsilon }_{bd}\right\rangle ,\\ {\varepsilon }_{vis} = {\rho }_{0}{A}_{h}{\nabla }_{h}{{{{\boldsymbol{u}}}}}_{bc}\cdot {\nabla }_{h}{{{{\boldsymbol{u}}}}}_{bc}+{\rho }_{0}{A}_{r}\frac{\partial {{{{\boldsymbol{u}}}}}_{bc}}{\partial z}\cdot \frac{\partial {{{{\boldsymbol{u}}}}}_{bc}}{\partial z},\\ {\varepsilon }_{bd} = {\rho }_{0}{C}_{d}|{{{\boldsymbol{u}}}}|(u{u}_{bc}+v{v}_{bc}) \quad \quad z=-H,$$
(4)

where \(\eta\) and H are the time-mean sea level and water depth, respectively. \({\varepsilon }_{vis}\) and \({\varepsilon }_{bd}\) are the dissipations caused by eddy viscosity and bottom drag, respectively. \({A}_{h}\) is the model output of horizontal eddy viscosity, and \({A}_{{{{\rm{r}}}}}\) is the vertical eddy viscosity, which equals 10−4 m2 s−1 and is set at simulation step one. Cd = 0.0025 is the bottom friction coefficient. \({{{\boldsymbol{u}}}}=(u,v)\) and \({{{{\boldsymbol{u}}}}}_{bc}=({u}_{bc},{v}_{bc})\) are the simulated horizontal velocity and horizontal baroclinic velocity, respectively. \({{{{\boldsymbol{u}}}}}_{bc}\) can be estimated according to Wang et al.64. The symbol \(\langle \rangle\) indicates the temporal average over tidal periods.

Energy budgets

The KE, which balances the time-mean flow (MKE) and the eddies (EKE), is obtained according to Boning and Budich67:

$${{{\rm{MKE}}}} = \frac{1}{2}({\bar{u}}^{2}+{\bar{v}}^{2}), \\ {{{\rm{EKE}}}} = \frac{1}{2}({u}^{{\prime} 2}+{v}^{{\prime} 2}),$$
(5)

Velocities can be separated into time mean and transient parts, where (\(\bar{u}\), \(\bar{v}\)) are simulated temporally averaged zonal and meridional velocities, respectively. \(({u}^{\prime} ,{v}^{\prime} )\) are the transient parts of velocities. Potential energy (PE), which is balanced by the time-mean flow (MPE) and the eddies (EPE), is also estimated.

$${{{\rm{MPE}}}} = \frac{g{(\bar{\rho }-{\rho }_{z})}^{2}}{2{\bar{\rho }}^{2}(d{\rho }_{z}/dz)},\\ {{{\rm{EPE}}}} = \frac{g{\rho }^{{\prime} 2}}{2\rho (d{\rho }_{z}/dz)},$$
(6)

Density can also be separated into the time mean part (\(\bar{{\rho }}\)) and transient part (\({\rho}^{\prime}\)). The transient parts of velocities and density can be obtained by subtracting the time mean part from the original velocities or density. \({\rho }_{z}\) is the horizontally and temporally averaged background potential density profile. The MKE can transfer to the EKE at a rate of T1. T2 describes the transmission of energy from EPE to EKE. T3 qualifies energy transfers from MKE to MPE.

$$T1 = - \left[{u}^{\prime} {u}^{\prime} \frac{\partial \bar{u}}{\partial x}+{u}^{\prime} {v}^{\prime} \left(\frac{\partial \bar{v}}{\partial x}+\frac{\partial \bar{u}}{\partial y}\right)+{v}^{\prime} {v}^{\prime} \frac{\partial \bar{v}}{\partial y}\right],\\ T2 = - \frac{g{\rho}^{\prime} {w}^{\prime} }{\rho },\\ T3 = \frac{g \bar{\rho }\bar{w}}{\rho }.$$
(7)