## 3 Data and Methods
### Sea Surface Emissivity Models
\right](1-S_{x}\tan\theta)h(S_{x})P\Big{(}S_{x },S_{y}\Big{)}, \tag{11}\]  
where \(\mathbf{R}\) is the rotation matrix, which rotates the coordinate from every local patch to the global coordinate, and the explicit expression of \(\mathbf{R}\) is given in [23]; h is the hydrodynamic modulation (HM), which induces upwind/downwind asymmetry, and is also given in [23] and P is the probability density function of large-scale waves, which can be expressed as the Gaussian function as [42]:  
\[P\Big{(}S_{x},S_{y}\Big{)}=\frac{1}{2\pi\sigma_{u}\sigma_{c}}\exp\!\left(- \frac{S_{x}^{2}}{2\sigma_{u}^{2}}-\frac{S_{y}^{2}}{2\sigma_{c}^{2}}\right), \tag{12}\]  
where \(\sigma_{u}\) and \(\sigma_{c}\) are variances of wave slope for upwind and crosswind directions, respectively. The variances can be calculated by a double integral over the wave and azimuth angle as:  
\[S_{u}^{2}=\int_{0}^{\infty}dk\int_{0}^{2\pi}d\phi k^{3}\cos^{2}\phi W_{l}(k, \phi). \tag{13}\]  
\[S_{c}^{2}=\int_{0}^{\infty}dk\int_{0}^{2\pi}d\phi k^{3}\sin^{2}\phi W_{l}(k, \phi). \tag{14}\]  
(3) Empirical model:  
Unlike the TSM and SPM/SSA models, the empirical model decouples the effects of \(SST\), \(SSS\) and sea surface roughness by expanding the sea surface emission with the Taylor series function and only the first order term of the series is used to describe the sea surface roughness effect. In that case,the observed brightness temperatures at the sea surface were firstly divided into two parts due to the perfectly flat sea surface and roughness sea surface conditions as:  
\[T_{B}^{mean}=T_{B,flat}+\Delta T_{B,rough}, \tag{15}\]  
where  
\[T_{B,flat}=\left[1-\left|R_{p}(SSS,SST,\theta_{i})\right|^{2}\right]\cdot SST, \tag{16}\]  
where \(R_{p}\) is the Fresnel reflection coefficient, subscript \"\(p\)\" stands for the polarization. It is widely accepted that \(\Delta T_{B,rough}\) is a function of _WS_. Camps [13] also showed that the \(\Delta T_{B,rough}\) is determined by both _WS_ and _SWH_. In addition, the incidence angle is another parameter that is to be considered. Thus, the emission vector is expressed as:  
\[\left[ \begin{array}{c}T_{Bh}\\ T_{Bv}\end{array} \right]=SST\left[ \begin{array}{c}1-\left|R_{hh}^{(0)} \right|^{2}\\ 1-\left|R_{vv}^{(0)}\right|^{2}\end{array} \right]+\left[ \begin{array}{c} \Delta T_{h}(\theta_{i},U_{10},SWH)\\ \Delta T_{v}(\theta_{i},U_{10},SWH)\end{array} \right], \tag{17}\]  
where \(\Delta T_{h}(\theta_{i},U_{10},SWH)\) and \(\Delta T_{v}(\theta_{i},U_{10},SWH)\) represent the emitted brightness temperature variations due to the sea surface roughness, and subscripts \"\(h\)\" and \"\(v\)\" denote horizontal and vertical polarizations, respectively. There are two similar methods to estimate sea surface roughness terms [25; 43], and the only difference between these two methods is that the significant wave height (_SWH_) is introduced rather than using wind speeds (_WS_) directly to obtain \(\Delta T(\theta_{i},U_{10})\)[44]. The sea surface roughness terms developed by [PERSON] (hereafter Emp1) are given by:  
\[\left\{ \begin{array}{c}\Delta T_{H}\approx 0.25\big{(}1+\frac{\theta_{i}}{ 44}\big{)}U_{10}\\ \Delta T_{V}\approx 0.24\big{(}1-\frac{\theta_{i}}{48}\big{)}U_{10}\end{array} \right., \tag{18}\]  
where \(\theta_{i}\) is the incidence angle and \(U_{10}\) is the wind speed at 10 m above the sea surface. The other one (hereafter Emp2) is:  
\[\left\{ \begin{array}{c}\Delta T_{H}\approx 0.12\big{(}1+\frac{\theta_{i}}{ 24}\big{)}U_{10}+0.59\big{(}1-\frac{\theta_{i}}{50}\big{)}SWH\\ \Delta T_{V}\approx 0.12\big{(}1-\frac{\theta_{i}}{40}\big{)}U_{10}+0.59\big{(}1- \frac{\theta_{i}}{50}\big{)}SWH\end{array} \right.. \tag{19}\]  
These two empirical models are both based on the wind and salinity experiment (WISE), which were performed around the Casablanca oil rig platform, and the validity of these models in East China Sea waters remains to be explored.