Interannual variability of summertime eddy-induced heat transport in the Western South China Sea and its formation mechanism

Abstract

The interannual variability of summertime eddy-induced heat transport (EHT) in the western South China Sea (WSCS) is investigated based on the downgradient eddy diffusivity method and explored its formation mechanism. Estimations of long-term mean EHT and its monthly evolution reveal that the largest EHT in the SCS occurs in the WSCS region during the summer. In the WSCS, enhanced EHT and eddy kinetic energy (EKE) levels are simultaneously observed in 1994, 1999, 2002, 2006, 2008, 2009, 2012, 2014 whereas the lower EHT and EKE levels are observed in 1995, 2000, 2001, 2003, 2004, 2007, 2010, 2015, 2017 during JAS (July, August and September) months. Analysis of the Simple Ocean Data Assimilation, version 3.3.1 (SODAv3) data along 110.75° E reveals a strong surface intensification of the summertime eastward jet (SEJ) in the EHT-strong years than the EHT-weak years. Linear stability analysis conducted by adopting a 2 ½-layer reduced gravity model shows that the increased EHT in EHT-strong years is due to the enhanced baroclinic instability caused by the strong vertical shear developed through the surface-intensification of SEJ. The cause for the interannually varying vertical shear can be sought in the interannually varying meridional temperature gradient which is influenced by the combined forcing of the meridional Ekman flux convergence, meridional geostrophic flux convergence, and convergence of the latitudinally dependent surface heat flux forcing. It is also found that the interannual variations of EHT in the SCS are partially influenced by the local wind stress curl and remote forcing from the eastern boundary.

Appendix

According to Chen et al. (2012), the quasi-geostrophic equations governing the perturbation potential vorticity ${q}_{n}$ are

$$\left(\frac{\partial }{\partial t}+{U}_{n}\frac{\partial }{\partial x}\right){q}_{n}+\frac{\partial {\Pi }_{n}}{\partial y}\frac{\partial {\phi }_{n}}{\partial x}=0$$

(8)

in which ${\phi }_{n}$ is the perturbation stream function, ${U}_{n}$ is the zonal mean velocity, and ${\Pi }_{n}$ is the mean potential vorticity in each layer ($n=1$ and $n=2$ refer to the surface and lower layers, respectively). Assuming ${U}_{n}$ is meridionally uniform, ${q}_{n}$ and the meridional gradient of ${\Pi }_{n}$ can be expressed as

$${q}_{n}={\nabla }^{2}{\phi }_{n}+\frac{{\left(-1\right)}^{n}}{{\gamma }_{2}{\delta }_{n}{\lambda }^{2}}\left({\phi }_{1}-{\phi }_{2}-{\gamma }_{n}{\phi }_{2}\right)$$

(9)

and

$${\Pi }_{ny}=\beta -\frac{{\left(-1\right)}^{n}}{{\gamma }_{2}{\delta }_{n}{\lambda }^{2}}\left({U}_{1}-{U}_{2}-{\gamma }_{n}{U}_{2}\right)$$

(10)

Here,

$${\delta }_{n}=\frac{{H}_{n}}{{H}_{2}}, {\gamma }_{n}=\frac{{\rho }_{n}-{\rho }_{1}}{{\rho }_{3}-{\rho }_{2}}\mathrm{ and }\lambda =\frac{1}{{f}_{0}}\sqrt{\frac{{\rho }_{3}-{\rho }_{2}}{{\rho }_{0}}g{H}_{2}}$$

(11)

where ${H}_{n}$ is the mean thickness of layer $n$, ${\rho }_{n}$ is the density of layer $n$, ${f}_{0}$ is the Coriolis parameter at the reference latitude, $\beta$ is the meridional gradient of the Coriolis parameter, ${\rho }_{0}$ is the reference density, and ${\rho }_{3}$ is the density of the motionless layer. The stability of the system can be analyzed by substituting the normal mode solution ${\phi }_{n}=\mathrm{Re}\left[{A}_{n}\mathrm{exp}i\left(kx+ly-kct\right)\right]$ into Eq. (8). Requiring nontrivial solutions for ${A}_{n}$ leads to the dispersion relationship

$${c}^{2}-\left({U}_{1}+{U}_{2}-\frac{P+Q}{R}\right)c+\left({U}_{1}{U}_{2}+\frac{{\Pi }_{1y}{\Pi }_{2y}}{R}-\frac{{U}_{1}P}{R} -\frac{{U}_{2}Q}{R}\right)=0$$

(12)

where

$$P=\left({K}^{2 }+\frac{1}{{\gamma }_{2}{\delta }_{1}{\lambda }^{2}}\right) {\Pi }_{2y}, Q=\left({K}^{2 }+\frac{1+{\gamma }_{2}}{{\gamma }_{2}{\lambda }^{2}}\right){\Pi }_{1y}, R=\left(\frac{PQ}{{\Pi }_{1y}{\Pi }_{2y}}-\frac{1}{{\gamma }_{2}^{2}{\delta }_{1}{\lambda }^{4}}\right)$$

(13)

and ${K}^{2 }={k}^{2}+ {l}^{2}$ is the total wavenumber. For a system with ${U}_{1}-{U}_{2}>0$, it can be shown that the necessary and sufficient condition for instability is ${\left({U}_{1}-{U}_{2}\right)}_{min}>{\gamma }_{2}{\lambda }^{2}\beta +{\gamma }_{2}{U}_{2}$ (Qiu 1999).