## 4 Results and Discussion
### Optimization of the Emission Models for ECS Waters
#### 4.2.3 Comparison of the Retrieved Sea Surface Salinity using Different Models  
For \(SSS\) retrieval, the iterative Levenberg and Marquard method was used, which is fully described in the literature [47; 48]. The L-M method was performed by minimizing the cost function defined as:  
\[\chi^{2}=\sum_{i}\frac{\left(T_{Bi}^{max}-T_{Bi}^{\mathrm{mod}}\right)^{2}}{ \sigma_{T_{Bi}}^{2}}+\frac{\left(SSS-SSS^{prior}\right)^{2}}{\sigma_{SSS}^{2}}, \tag{23}\]  
where \(T_{Bi}^{max}\) and \(T_{Bi}^{\mathrm{mod}}\) are the measured and model-predicted brightness temperatures, respectively; \(\sigma_{T_{Bi}}^{2}\) is the expected error variance of the measurements; \(SSS^{prior}\) represents the priori value of \(SSS\) and \(\sigma_{SSS}^{2}\) is the expected error variances of the priori \(SSS\). The horizontally polarized brightness temperature, vertically polarized brightness temperature and the first Stokes parameter (i.e., (\(T_{BH}+T_{BV}\))/2) can all be used to retrieve \(SSS\) (Equation. (23)). It is known that using the first Stokes parameter can achieve a higher sensitivity to \(SSS\), however, when the forward model overestimates or underestimates the sea surface emission, the error of retrieved \(SSS\) would be larger. In this paper, three models were used to retrieve \(SSS\): (1) TSM with a0 = 0.006 and \(k_{c}=k_{0}/10\), (2) modified EMP1 and (3) modified EMP2 (the results are reported in Table 5). It can be seen that the RMS of the retrieved \(SSS\) was about 0.4 psu for all three models, but the modified TSM model had the highest accuracy. The lower performance of the EMP models compared to the TSM model might be due to the fewer in-situ measurements used to improve the empirical model. As mentioned in Section 4.2, the \(\Delta T_{B,rough}\) needs to be calculated separately at low and high incidence angles in order to achieve the higher accuracy.  
The spatial distributions of retrieval errors are shown in Figure 8. Clearly, the accuracy of retrieved \(SSS\) using the modified TSM model was higher than the two empirical models, especially at stations in the vicinity of the coast. For these stations, the shallow water was one of the factors that affected the sea surface roughness contributions, since shallow water waves were significantly affected by  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **RMS \(\Delta SSS\) (psu)** & **Std\(\Delta SSS\) (psu)** & **Biases \(\Delta SSS\) (psu)** \\ \hline TSM & 0.38 & 0.37 & 0.04 \\ EMP1 & 0.44 & 0.43 & 0.08 \\ EMP2 & 0.48 & 0.48 & \(-\)0.01 \\ \hline \hline \end{tabular}
\end{table}
Table 5: A comparison of errors obtained between the retrieved and in-situ measured sea surface salinity (\(SSS\)) from shipborne radiometric measurements (\(N\) = 41).  
Figure 7: Linear relationships between brightness temperatures and rough sea surface/wind speed sensitivities for horizontal polarization (**left panel**) and vertical polarization (**right panel**).  
the seab topography in these coastal areas. Moreover, the error of the _SWH_ was another source, which hampered the accuracy of model prediction and _SSS_ retrieval. In this study, the spatial resolution of the _SWH_ data obtained from the ECMWF ERA-5 reanalysis dataset was \(0.5\lx@math@degree\times 0.5\lx@math@degree\), which was too coarse to match the field of view of radiometer. Thus, in order to derive an empirical model with high accuracy, the _SWH_ should be measured simultaneously with the radiometer measurement.