# Ocean Wind Retrieval Models for RADARSAT Constellation Mission Compact Polarimetry SAR
## 2 Materials and Methods
### CoVe-Pol Model for Right Circular-Vertical (RV) Polarization
#### 2.2.2 Determination of the Coefficients for CoVe-Pol Model  
We divide the coefficients into three groups according to the magnitude of corresponding \(SAF\)s, which represent the degree of influence of every coefficient \(c_{i}\) on the computed NRCSs. Thus, we adjust the coefficients, proceeding from higher magnitudes of their degree of influence, to lower orders of magnitude. Through this method, the computational accuracy of the CoVe model reaches \(10^{-2}\) \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \(SAF\) of \(c_{1}\) & 1.8081 & \(SAF\) of \(c_{8}\) & 0.0630 & \(SAF\) of \(c_{15}\) & 0.0200 & \(SAF\) of \(c_{22}\) & 0.0171 \\ \(SAF\) of \(c_{2}\) & 0.6366 & \(SAF\) of \(c_{9}\) & 3.7931 & \(SAF\) of \(c_{16}\) & 0.0276 & \(SAF\) of \(c_{23}\) & 0.0024 \\ \(SAF\) of \(c_{3}\) & 0.1145 & \(SAF\) of \(c_{10}\) & 0.2767 & \(SAF\) of \(c_{17}\) & 0.0158 & \(SAF\) of \(c_{24}\) & 0.6617 \\ \(SAF\) of \(c_{4}\) & 0.0308 & \(SAF\) of \(c_{11}\) & 0.1012 & \(SAF\) of \(c_{18}\) & 0.0332 & \(SAF\) of \(c_{25}\) & 0.0895 \\ \(SAF\) of \(c_{5}\) & 0 & \(SAF\) of \(c_{12}\) & 0.0724 & \(SAF\) of \(c_{19}\) & 0.1381 & \(SAF\) of \(c_{26}\) & 0.0056 \\ \(SAF\) of \(c_{6}\) & 0.0399 & \(SAF\) of \(c_{13}\) & 0.0335 & \(SAF\) of \(c_{20}\) & 0.0774 & \(SAF\) of \(c_{27}\) & 0.9411 \\ \(SAF\) of \(c_{7}\) & 1.3219 & \(SAF\) of \(c_{14}\) & 0.0262 & \(SAF\) of \(c_{21}\) & 0.1697 & \(SAF\) of \(c_{28}\) & 0.1344 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Average \(SAF\) values of the \(c_{i}\) coefficients. Figure 6: The sensitivity analysis factor (\(SAF\)) values for different orders of magnitude for computed NRCSs: (**a**) \(SAF\) over 1; (**b**) \(SAF\) over 0.1. The colors represent different wind directions (\(15^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\), \(75^{\circ}\), \(90^{\circ}\)). and calculation of the required adjustments in the coefficients \(c_{i}\) can be achieved using a common computer cluster because the computation has been significantly reduced. As a first step, we change the values of coefficients \(c_{1}\), \(c_{7}\), \(c_{9}\), which determine the accuracy of computed NRCSs at _SAF_ order of magnitude \(10^{0}\). Thus, the NRCSs are computed by using the conventional GMF formulation with input of the wind speed, incidence angles and wind direction observed by buoys. Comparing the root mean square errors (RMSEs) between the resulting CMOD parameterization and the simulated RCM data (computed and simulated values for NRCSs), there is an optimal set of computed NRCSs with corresponding \(c_{1}\), \(c_{7}\), \(c_{9}\) values that minimize the RMSE, as defined in (3) below. Secondly, in order to achieve the CMOD adjustment at \(10^{-1}\) order of magnitude coefficients, we change the values of coefficients \(c_{2}\), \(c_{3}\), \(c_{10}\), \(c_{11}\), \(c_{19}\), \(c_{21}\), \(c_{27}\), \(c_{28}\) and \(c_{1}\), \(c_{7}\), \(c_{9}\) based on the new CMOD obtained in the first step above. The optimal values of the coefficients are obtained in the same way as previously. For the \(10^{-2}\) order of magnitude, there are 25 sensitive coefficients which must be adjusted, making the calculation too huge to be practical. Thus, we tune the \(c_{i}\) coefficients empirically. Thus, a GMF with new coefficients for compact RV-polarization SAR is proposed following this adjustment procedure, as displayed in Table 1 in the Appendix A. The RV-polarized NRCSs computed by the new GMF are in good agreement with simulated RCM data, shown in Figure 7a. Additional details are given in Appendix A. The definitions of bias, RMSE, and correlation coefficient (\(R\)) are,  
\[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(G_{i}-D_{i}\right)} \tag{3}\]  
\[bias=\frac{\left(G-D\right)}{n} \tag{4}\]  
\[R=\frac{Cov(G,D)}{\sqrt{Cov(G,D)Cov(G,D)}} \tag{5}\]  
where \(G\) represents the computed results from the GMF, \(D\) is the wind speed from the data sets, \(n\) is the number of measurements.