## 4 Results and Discussion
### Optimization of the Emission Models for ECS Waters
#### 4.2.2 Adjustment of the Empirical Model for the ECS  
Following Equations (17)-(19), for every incidence angle, the sensitivity of \(\Delta T_{B,rough}\) to \(WS\) (or \(SWH\)) is represented by the slope of linear regression of \(\Delta T_{B,rough}\) to \(WS\) (or \(SWH\)). Generally, \(\Delta T_{B,rough}\) can be expressed as:  
\[\Delta T_{B,rough}=a\ \cdot S_{WS}(\theta_{i})\cdot U_{10}+c, \tag{20}\]  
\[\Delta T_{B,rough}=a\ \cdot S_{WS}(\theta_{i})\cdot U_{10}+b\cdot S_{SWH}( \theta_{i})\cdot SWH+c, \tag{21}\]  
where \(S_{i}(\theta_{i})\) is the sensitivity of \(\Delta T_{B,rough}\) to \(WS\) (or \(SWH\)), \(i=1\), \(2\) and \(3\) and \(c\) is the offset. In this study, although all the in situ data were used, the number of measured brightness temperature was still small for different incidence angles. Thus, the wind speed sensitivity was obtained based on the previous studies. It should be noted that the fitted sensitivity of vertically polarized brightness temperature to wind speed from different campaigns was quite different. For example, at \(20^{\circ}\) and \(30^{\circ}\) incidence angles, the vertical polarization sensitivity to wind speed, as derived by the WISE, was half as it was obtained from the PALS and [PERSON]'s data. It decreased to \(-0.03\) with the incidence angle at \(50^{\circ}\), whereas it was \(0.22\) from the PALS dataset. This could be attributed to the discrepancies in the dielectric constant model used to compute the flat sea surface brightness temperature (Equation (16)). The dielectric constant model used in this study was from [PERSON] and swift (2007), which is the same used in ([PERSON] et al., 2017). Thus, the wind speed sensitivity at different incidence angles was exactly the same as ([PERSON] et al., 2017). A linear regression method was used to obtain the coefficients in Equations (20) and (21). The relationships of \(\Delta T_{B,rough}\) with wind speeds and incidence angles are shown in Figure 7. Overall, the \(\Delta T_{h,rough}\) shows a good correlation with sensitivity and wind speed, and the vertical polarization variations show a lower sensitivity to wind speed compared to the horizontal polarization, which were consistent with the previous studies ([PERSON] et al., 2017). This might be attributed to the fact that the vertically polarized brightness temperature was less influenced by the \(WS\) and roughness. It should be noted that, for both polarizations, the brightness temperature variations did not fit well with incidence angle at \(60^{\circ}\) (green points), this was particularly more evident for horizontal polarization. When the data at a \(60^{\circ}\) incidence angle were excluded, the correlation coefficients between \(\Delta T_{h,rough}\) and wind speed (multiplying sensitivity) increased from \(0.78\) to \(0.88\). Although the brightness temperature measured at high incidence angles were less used for \(SSS\) retrieval, further study is still needed to examine the variation of sea surface roughness induced brightness temperature at low incidence angles and high incidence angles separately. From this analysis, the optimized \(\Delta T_{h,rough}\) and \(\Delta T_{v,rough}\) models for the ECS are given by:  
\[ \begin{array}{l}\Delta T_{h,rough}=0.57692S_{h,WS}(\theta_{i})U_{10}+1.583 S_{h,SWH}(\theta_{i})SWH+0.30231\\ \Delta T_{v,rough}=0.36248S_{v,WS}(\theta_{i})U_{10}+0.77851S_{v,SWH}(\theta_{i })SWH-0.311863\end{array} , \tag{22}\]  
where \(S\) is the sensitivity of different parameters (i.e., \(WS\) and \(SWH\)), subscripts \"\(h\)\" and \"\(v\)\" represent horizontal and vertical polarizations, respectively. It should be noted that the sensitivity of horizontally polarized brightness temperature to \(SWH\) obtained from ([PERSON] et al., 2017) is notably different from that of ([PERSON] et al., 2017) (\(\theta\)/142 comparing to \(1-\theta\)/50). For example, when the incidence angle at \(60^{\circ}\), the sensitivity was \(0.4225\) and \(-0.2\) from these two models.