## 4 Results
### CYGNSS SMC Validation Using SMAP Data  
Due to the above-mentioned lack of spatial coverage with the ICESat-2 BSR data, CYGNSS SMC has been definitely derived using BSR and VOD estimates from SMAP products. In this scheme, we first compute soil surface reflectivity values according to the suggested methodology. Concerning the incidence angle (\(\theta\)), we employ the model of [67], which allows computing soil permittivity by means of the linear \(R_{hh}\) reflectivity, with best results within the limit of \(\theta_{1}<35^{\circ}\), which verifies the observations made by [31]. In order to substantiate that the number of CYGNSS observations under these circumstances provides a sufficient number of SPs, Figure 10 shows the histogram for CYGNSS incidence angles on April 2019 limited to the study area. Assuming the combined geometry of the CYGNSS with the GNSS satellites, this estimate is assumed to be similar even on a daily basis. In this figure, the number of SPs with \(\theta_{1}<35^{\circ}\) represents about 60% of the monthly population of observables. This percentage of SPs is significantly high in order to prove the suitability of the suggested SMC inversion process. Once SMC is retrieved for the selected SPs, the final estimates are validated with SMAP SMC products, which are considered as reliable SMC reference [71]. For the CYGNSS data, the need for a bias value has already been pointed out in [42; 43], and the authors in [37] provided an estimate for specific BSR and VOD values. Following these indications, we employ a reflectivity constant bias value of 0.15. With the finality to avoid unwanted biases in the validation process, since SMAP SMC products are derived using their own BSR and VOD (equivalent to VWC) products, we also employ these estimates to derive CYGNSS SMC. Moreover, we reduce the errors in the validation process by limiting VOD to \(\sim\)0.5 for the southern regions (\(\phi<\sim\)32\({}^{\circ}\)N). This limit is reduced to about 0.3-0.4 depending on the rainfall probability. For the northern regions (\(\phi>\sim\)32\({}^{\circ}\)N), VOD is limited to about 0.3. Concerning the incidence angle (\(\theta\)), the model of [67] has provided the best results with a limit of \(\theta<35^{\circ}\). Figure 10: The empirical probability density for CYGNSS incidence angles during the whole month of April 2019 over the study area. In few cases of high VOD, or under elevated rainfall probability, better results have been shown by limiting the incidence angle to lower values (\(\theta<15^{\circ}\)). These constraints agree with the above sensitivity analysis (Figure 7). Finally, the last filter involves looking for coincident locations between CYGNSS SP, SMAP, and/or ICESat-2 estimates in a range inferior of 500 m. Figure 11 shows the resulting set of 4568 validation SPs (CYGNSS \(\cap\) SMAP) for April 2019 and the corresponding statistics in the linear regression model, showing strong linear evidence (Figure 11b) with zero p-value, small Root Mean Squared Error (RMSE = 0.05), and an R-squared = 0.6. Parameters of the regression model are shown in Table 1. The sparse distribution over the area of study is shown in Figure 11a. Finally, Figure 12a shows an example of CYGNSS GNSS-R SMC estimates for 1 April 2019. We limit the data to SPs whose incidence angle is \(\theta<40^{\circ}\) and employ SMAP VOD \(<0.5\) estimates from 1-12 April 2019. In Figure 12b the same day is shown for SMAP SMC estimates at 500-sample intervals. In this figure, the reader can see the higher temporal resolution and the capability of GNSS-R to estimate SMC, which, in contrast to SMAP SMC estimates, that need about a half a month to register the exact same area, these cover globally and at a continuous rate. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of observations & 4568 \\ RMSE & 0.05 \\ R-squared & 0.6 \\ p-value & 0 \\ \(\beta_{0}\) & \(0.0669\pm 0.0290\) \\ \(\beta_{1}\) & \(0.4916\pm 0.0135\) \\ \hline \hline \end{tabular}
\end{table}