# Ocean Wind Retrieval Models for RADARSAT Constellation Mission Compact Polarimetry SAR
## 2 Materials and Methods
### CoVe-Pol Model for Right Circular-Vertical (RV) Polarization
#### 2.2.1 Sensitivity Analysis  
As there are 28 CMOD coefficients (\(c_{1}\)\(\sim\)\(c_{28}\)) in the empirical model formulation, the sensitivity analysis is used to reduce the computations and to allow a determination of the coefficients. We define the sensitivity analysis factor (\(SAF\)) of the CMOD coefficients to make the adjustment process more efficient:  
\[SAF=\left|(\delta\sigma^{0}/\sigma^{0})/(\delta c_{i}/c_{i})\right| \tag{2}\]  
where \(\sigma^{0}\) represents the RV-polarized backscatter value (NRCS), the independent variable, and the \(c_{i}\) coefficients (\(c_{1}\)\(\sim\)\(c_{28}\)) are dependent variables. In this approach, \(SAF\)s indicate the degree of influence of each coefficient on the CMOD parameterization. From equation (2), we know that for any particular coefficient \(c_{i}\), the corresponding NRCS (\(\sigma^{0}\)) can have multiple values, and in each case the ratio is  
Figure 4: Flowchart for building the CoVe-Pol model through adjustment of the C-band geophysical model function (GMF) model series (CMOD) coefficients obtained by application of a sensitivity analysis. indicative of the degree of influence, \(SAF\). If \(SAF\) cannot provide the required computational accuracy, the corresponding coefficients \(c_{i}\) can be ignored. For any particular coefficient, the basis for this decision is the magnitude of the degree of influence, \(SAF\). Average values of the \(SAF\)s under various wind speeds range from 1 m/s to 25 m/s as shown in Figure 5, assuming typical conditions for radar incidence angles and wind directions. Thus, it is shown that \(SAF\) values range widely from 0 to \(10^{1}\), which means the influence of different coefficients, \(c_{i}\), vary greatly. As shown in Figure 5, very close to 0, most \(SAF\) values are less than 1 and only a few have values exceeding 1, for three typical radar incidence angles (25\({}^{\circ}\), 35\({}^{\circ}\) and 45\({}^{\circ}\)). Thus, we only focus on coefficients \(c_{i}\), where \(SAF\) values indicate greater influence (>0.1) so that the parameterization is simplified and a huge calculation can be avoided. In this study, we can classify the coefficients by the orders of magnitude of the corresponding \(SAF\)s, namely \(10^{0}\), \(10^{-1}\) and less than \(10^{-1}\). Thus, when we attempt to get the accuracy of computed NRCS values to \(10^{0}\) order of magnitude, we don't need to consider the coefficients with \(SAF\) values less than \(10^{0}\), because their influence is negligible. Likewise, when we focus on the \(10^{-1}\) order of magnitude, the coefficients with \(SAF\) values lower than \(10^{-1}\) can be ignored. Therefore, based on the \(SAF\)s of each coefficient, \(c_{i}\), we firstly tune the coefficients whose \(SAF\) values have orders of magnitude higher than \(10^{0}\), without considering other coefficients. Secondly, we tune the coefficients whose \(SAF\) values have orders of magnitude higher than \(10^{-1}\), without considering other coefficients. Then, we tune the coefficients whose SAF values have progressively higher orders of magnitude than \(10^{-1}\). The reason for this approach is that coefficients whose \(SAF\) values have orders of magnitude lower than \(10^{-1}\) have essentially no effect on computed NRCSs derived from coefficients whose SAF values have higher orders of magnitude. We note that although the radar incidence angles can vary as shown in Figure 5, their influence on the coefficients \(c_{i}\), and on the resultant NRCSs is quite minor. Thus, we combine the average \(SAF\)s under different radar incidence angles, as shown in Figure 6. The extent of influence for incidence angles on the coefficients \(c_{i}\) for the \(SAF\) orders of magnitude \(10^{0}\) and \(10^{-1}\) are shown in Figure 6a,b, respectively.