# Ka-Band Doppler Scatterometry: A Strong Wind Case Study
## 3 Sea Surface Cross-Section
### NRCS Decomposition
To explain possible origins of the minimum in PR wind dependence, the NRCS is decomposed as a sum of polarized (Bragg) and NP components following [55; 58],  
\[\sigma_{0}^{\text{PP}}=\sigma_{\text{br}}^{\text{PP}}+\sigma_{\text{np}}, \tag{2}\]  
where \(\sigma_{\text{br}}^{\text{PP}}\) is the resonant Bragg backscattering component described by a two-scale composite NRCS model. Given that both polarization NRCS, \(\sigma_{0}^{\text{vv}}\) and \(\sigma_{0}^{\text{hh}}\), and theoretical Bragg polarization ratio, \(P_{\text{br}}=\sigma_{0}^{\text{hh}}/\sigma_{0}^{\text{vv}}\), are all known, the NP backscattering component can be estimated as,  
\[\sigma_{\text{np}}=\sigma_{0}^{\text{vv}}-\frac{\Delta\sigma_{0}}{1-P_{\text{ br}}}, \tag{3}\]  
where \(\Delta\sigma_{0}=\sigma_{0}^{\text{vv}}-\sigma_{0}^{\text{hh}}=\sigma_{\text{ br}}^{\text{vv}}-\sigma_{\text{br}}^{\text{hh}}\) is the measured polarization difference (PD) and \(P_{\text{br}}\) is estimated using the simplified RM (see Appendix A of [50] for details). Equation (3) provides estimates of the non-polarized (NP) backscattering component from the \(\sigma_{0}^{\text{vv}}\), \(\sigma_{0}^{\text{hh}}\), and Bragg polarization ratio, \(P_{\text{br}}=\sigma_{\text{br}}^{\text{hh}}/\sigma_{\text{br}}^{\text{vv}}\). If applied to the known empirical GMFs and the present Ka-band radar measurements, the results display different wind dependencies in different radar bands (Figure 7). In the L-band, the polarized (PP = VV, HH) contribution grows monotonically with wind for both polarizations. In the Ka-band, a tendency for PP saturation and further decrease at \(U>10\)-12 m s\({}^{-1}\) is detected. To a lesser extent, the tendency for PP saturation is also present in the C- and Ku-bands. Figure 6: Measured (**a**) NRCS, \(\sigma_{0}\), and (**b**) polarization ratio, \(P=\sigma_{0}^{\text{hh}}/\sigma_{0}^{\text{vv}}\), for Record #7 at \(\theta=45^{\circ}\). Each point in data clouds corresponds to 0.2-s average. Open circles are 2 m s\({}^{-1}\) wind speed bin averages. No-mark solid and dashed lines show model predictions. In the Ku- and Ka-band, the NP shows a weaker tendency for saturation in contrast to the PP and, thus, can retain some wind sensitivity at strong winds. At moderate winds, \(U<10\) m s\({}^{-1}\), the NP is comparable in magnitude with the HH in the L-band, but its relative contribution increases systematically with decreasing radar wavelength and reaches the level of VV component in the Ku- and Ka-band at \(U\geq 15\)-20 m s\({}^{-1}\) (Figure 7). These changes are better seen when the relative NP contribution, \(\sigma_{0}^{\text{np}}/\sigma_{0}^{\text{PP}}\), is explicitly shown (Figure 8). For instance, at \(U\approx 15\) m s\({}^{-1}\), our Ka-band data, as well as Ku-NSCAT4 GMF have the relative NP contribution of \(\approx\)50% (80%) for VV (HH) polarization, respectively. At \(U\approx 30\) m s\({}^{-1}\), this proportion increases to \(\approx\)70% (90%). Equation (3) can also be seen as an explicit relationship between the relative NP contribution, \(\sigma_{0}^{\text{np}}/\sigma_{0}^{\text{PP}}\), and the polarization ratio, \(P=\sigma_{0}^{\text{hh}}/\sigma_{0}^{\text{vv}}\). As the Bragg TSM PR, \(P_{\text{br}}=\sigma_{\text{br}}^{\text{hh}}/\sigma_{\text{br}}^{\text{vv}}\), in (3) only weakly varies with wind speed (through the wind speed dependence of mean-square slope of long modulating waves, see black line in Figure 6b), the relative NP contribution should have the wind dependence very similar to that of PR, including the local minimum at \(U\approx 10\) m s\({}^{-1}\). Thus the observed PR behavior (Figure 6b) can be attributed to specific balances between polarized and NP backscattering components. At light winds \(\approx\)4-5 m s\({}^{-1}\), the Bragg contribution is not strong enough to dominate the NP. Speculatively, this NP component might arise due to micro-scale wave breaking and steep features with very rare but strong quasi-specular reflections.