## 4 Results and Discussion
### Optimization of the Emission Models for ECS Waters  
#### 4.2.1 The Choice of \(\mathrm{k_{c}}\)  
The choice of \(k_{c}\) is rather arbitrary in previous studies; for example, \(k_{c}=k_{0}/4\), \(k_{c}=k_{0}/5\) and \(k_{c}=k_{0}/10\) according to [32], [45] and [24], respectively. The \(\mathrm{k_{c}}\) values were given in the range of \(k_{0}/10\) to \(k_{0}/3\). The reason is that, as shown in [32], for the range of \(k_{0}/10\) to \(k_{0}/3\), the effect of \(k_{c}\) on the predicted brightness temperature is small or even negligible. In addition, when using the DV2 spectrum, the difference caused by the cutoff wavenumber is less than 0.4 K with the incidence angle at \(30^{\circ}\) and \(40^{\circ}\). Thus, \(k_{c}=k_{0}/3\), \(k_{c}=k_{0}/5\) and \(k_{c}=k_{0}/10\) were tested in this study. As shown in Figure 6, the horizontally polarized brightness temperatures had higher correlations with a0 and cutoff wavenumbers than the vertically polarized brightness temperatures. Moreover, the brightness temperature was underestimated when a0 was set as 0.004, especially for horizontal polarization, and when a0 was 0.006, or a0 = 0.008 together with \(k_{c}=k_{0}/3\), the errors were relatively small compared to other combinations of a0 and \(\mathrm{k_{c}}\) values. The performances of the TSM model with different a0 and \(\mathrm{k_{c}}\) values are shown in Table 4, by comparison between the predicted and in situ brightness temperatures. The results show that a0 = 0.006 with \(k_{c}=k_{0}/10\) fit the in situ values best with the rms values of 0.39 K and 0.37 K for horizontally polarized and vertically polarized brightness temperatures, respectively. In addition, the biases and standard deviations were also small when a0 = 0.006 and \(k_{c}=k_{0}/10\). Although the rms values were similar for different a0 and \(k_{c}\) values, the biases for horizontally and vertically polarized brightness temperatures had a significant influence on the \(SSS\) retrieval using these models. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**rms Difference (K)**} & \multicolumn{2}{c}{\(\Delta\)\(\boldsymbol{T_{B}}\) Std (K)} & \multicolumn{2}{c}{**Biases (K)**} \\ \cline{2-7}  & **H-pol** & **V-pol** & **H-pol** & **V-pol** & **H-pol** & **V-pol** \\ \hline a0 = 0.006, \(k_{c}=k_{0}/10\) & 0.39 & 0.37 & 0.39 & 0.37 & 0.07 & 0.02 \\ a0 = 0.006, \(k_{c}=k_{0}/5\) & 0.45 & 0.40 & 0.41 & 0.37 & \(-0.20\) & \(-0.17\) \\ a0 = 0.006, \(k_{c}=k_{0}/3\) & 0.59 & 0.49 & 0.46 & 0.39 & \(-0.39\) & \(-0.31\) \\ a0 = 0.008, \(k_{c}=k_{0}/3\) & 0.47 & 0.57 & 0.42 & 0.52 & 0.20 & \(-0.25\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the model predicted and in-situ measured brightness temperatures. V-pol: vertical polarization; H-pol: horizontal polarization. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**rms Difference (K)**} & \multicolumn{2}{c}{\(\Delta\)\(\boldsymbol{T_{B}}\) Std (K)**} & \multicolumn{2}{c}{**Biases (K)**} \\ \cline{2-7}  & **H-pol** & **V-pol** & **H-pol** & **V-pol** & **H-pol** & **V-pol** \\ \hline M1 & 1.35 & 0.93 & 1.03 & 0.89 & \(-0.88\) & \(-0.28\) \\ M2 & 0.60 & 0.50 & 0.46 & 0.39 & \(-0.39\) & \(-0.31\) \\ M3 & 0.47 & 0.57 & 0.42 & 0.52 & 0.20 & \(-0.25\) \\ M4 & 2.99 & 1.69 & 1.49 & 1.70 & 2.60 & 0.08 \\ SPM/SSA & 1.13 & 0.71 & 0.73 & 0.71 & \(-0.86\) & 0.08 \\ EMP1 & 1.06 & 0.73 & 1.01 & 0.71 & \(-0.34\) & \(-0.19\) \\ EMP2 & 1.05 & 0.78 & 0.97 & 0.73 & \(-0.41\) & \(-0.27\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the model predicted and in-situ measured brightness temperature. V-pol: vertical polarization; H-pol: horizontal polarization. Figure 6: The errors in the predicted brightness temperatures from the TSM model using different a0 and cutoff wavenumbers, solid lines represent for mean value at different wind speed. (**a**,**b**) results with a0 = 0.004. (**c**,**d**) results with a0 = 0.006. (**e**,**f**) results with a0 = 0.008.