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The long-term variation in intermediate water salinity in the NSCS was tracked using two oceanic dataset products. The first dataset was obtained from the Institute of Atmospheric Physics (IAP) ocean gridded products supplied by the Chinese Academy of Sciences. The reconstructive monthly IAP dataset is from 1940 to the present, with a resolution of 1° × 1° horizontally and 41 vertical levels ranging from 1–2000 m. The data were primarily input using all of the available measurements (such as Argo, CTD, XBT, bottle, glider) from the World Ocean Database (WOD) (Cheng et al. [20]). The IAP product was designed to minimize the sampling errors and is thus particularly suitable for long-term change studies (Cheng et al. [21]). The second dataset was obtained from the Ishii products from the Japan Meteorological Agency (JMA), which provided data from 1960 to 2014. This dataset had a horizontal resolution of 1° × 1° and 28 vertical levels ranging from 1–2000 m (Ishii and Kimoto [22]).
Data on oceanic currents were used to assess the impacts of horizontal salt transport and vertical entrainment in salinity budget analysis. Horizontal and vertical velocities were obtained from the Simple Ocean Data Assimilation (SODA, version 2.2.4) reanalysis dataset (Carton and Giese [23]). Monthly velocity data from SODA has a time coverage from 1960 to 2010, a horizontal resolution of 1/4° × 1/4°, and 40 vertical levels ranging from 1–5000 m.
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Salinity budget analysis has been widely used to identify the dynamics processes that mainly contribute to salinity changes. The equation for box-averaged intermediate water salinity budget (Gao et al. [24]; Yu [25]; Liu et al. [26]) is as follows:
$$ \frac{\partial[S]}{\partial t}=-\left[\nabla_H \cdot(u S, v S)\right]_{\text {int }}-\frac{1}{h} \Delta S \frac{\partial h}{\partial t}-\left[\nabla_H \cdot(u S, v S)\right]_{\text {lat }}-\left[\partial_z \cdot w S\right]+\varepsilon $$ (1) where the square brackets denote the depth average within the given layer with potential density between 26–27 kg m–3 and [S] represents the mean salinity of the intermediate water, $\frac{\partial[S]}{\partial t}$ depicts salinity tendency, h is the intermediate layer depth, defined as the depth at which the potential density is between 26–27 kg m–3. ∆S is the salinity difference between the intermediate water and upper subsurface water, and the lower top layer in deep water. The variables u, v, and w represent the zonal (x), meridional (y), and vertical (z) velocities, respectively. The subscripts H and Z denote the horizontal and vertical components of the variables, respectively. The first four terms on the right-hand side of Eq. (1) represent horizontal advection, the sum of salt fluxes across the isopycnal due to intermediate layer deepening/shoaling, lateral induction, and vertical advection, respectively. ε represents the residual of the salinity budget, including turbulent diffusion and cross-isopycnal mixing in both the horizontal and vertical directions.
In this study, we consider the intermediate layer in the NSCS (15°–22°N, 108°–120°E) as a box and only consider the salinity exchange through the Luzon Strait (AdvLZ) and the southern boundary of the NSCS (AdvSSCS) at 15°N in the horizon. The lateral induction can be ignored because of the few horizontal advections across the gentle-slope top and bottom boundaries of the intermediate layer. The intermediate water salinity budget equation can be simplified as (Zeng et al. [6, 11]):
$$ \frac{\partial S}{\partial t}=\frac{T_{\text {in }} \cdot \Delta S_{\mathrm{WP}}-T_{\text {out }} \cdot \Delta S_{\text {sscs }}}{V_S}+\frac{T_{\text {up }} \cdot \Delta S_{\text {sub }}-T_{\text {bot }} \cdot \Delta S_{\text {deep }}}{V_S}-\frac{\partial h_{\text {up }}}{\partial t} \frac{\Delta S_{\text {sub }}}{H}-\frac{\partial h_{\text {bot }}}{\partial t} \frac{\Delta S_{\text {deep }}}{H}+\varepsilon $$ (2) where Tin and Tout represent the transports flowing in and out of the NSCS, respectively, Tup and Tbot are the transports across the upper and bottom boundaries of the intermediate layer, respectively. ∆SWP and ∆Ssscs are the salinity differences between the intermediate water NSCS and the northwest Pacific and southern SCS, respectively, ∆Ssub represents the salinity difference between the intermediate and subsurface layers, and ∆Sdeep represents the salinity difference between intermediate and deep layers in the NSCS. Vs is the volume of the NSCS intermediate water. hup and hbot are the depth of 26σθ and 27σθ isohalines where the upper and bottom boundaries of the intermediate layer locate, respectively. H is the thickness of the intermediate layer. The simplified intermediate salinity budget equation contains horizontal advection term (the first term of Eq. (2)), vertical advection term (the second term), deepening/shoaling terms (the third and fourth terms) and ε represents the residual.