# Automated Rain Detection by Dual-Polarization Sentinel-1 Data
## 3 Co-Analysis of Rain Rate and C-Band SAR Backscattering
### Statistical Analysis  
To further document the effective rain impact, we follow methodology from [PERSON] and [PERSON] [18] and rely on the NRCS\({}_{\text{ratio}}\) quantity, defined as the ratio of NRCS from rainy area over the NRCS from the sea surface in the surrounding area without rain as indicated by the rain radar:  
\[\text{NRCS}_{\text{ratio}}=10\log_{10}\frac{\text{NRCS}_{\text{rain}}}{\text{ NRCS}_{\text{rain-free}}}\text{ with } \begin{cases}\text{rain}&\text{if }Z\ \geq Z_{0}\\ \text{rain-free}&\text{if }Z\ <Z_{0}\end{cases}  \tag{1}\]  
where \(Z\) is the base reflectivity (in dBZ) measured by NEXRAD and \(Z_{0}\) the threshold to define rain-free area. \(Z_{0}=20\) dBZ hereinafter. The threshold of 20 dBZ usually indicates the falling precipitation according to the National Oceanic and Atmospheric Administration (NOAA). The NRCS\({}_{\text{ratio}}\) value indicates how much NRCS increases or decreases with rainfall in comparison to rain-free sea surface area, assuming a multiplicative effect on the backscattering intensities in linear scale. To account for the joint effect of local incidence angle and sea state, this variable is computed locally as illustrated in Figure 6.  
We have split the entire S-1/NEXRAD database into four ranges of incidence angles angle bins to analyze the NRCS\({}_{\text{ratio}}\). The incidence angle intervals are 29\({}^{\circ}\)-33\({}^{\circ}\), 33\({}^{\circ}\)-37\({}^{\circ}\), 37\({}^{\circ}\)-41\({}^{\circ}\) and 41\({}^{\circ}\)-46\({}^{\circ}\). Figure 7 displays the statistics of NRCS\({}_{\text{ratio}}\) as a function of base reflectivity with 5 dBZ bins. For convenience, we have also converted the NEXRAD base reflectivity into rain rate using the conversion Z\({}_{\text{lin}}=300\)R\({}^{1.4}\)[35], where Z\({}_{\text{lin}}\) is not in dBZ, but in linear scale. First and second rows show the results for VV and VH polarizations, respectively. In addition, for each range of base reflectivity, the NRCS\({}_{\text{ratio}}\) is analyzed for different ranges of NRCS\({}_{\text{rain-free}}\) as a proxy of the wind speed condition. As expected from our ratio computation method, the ratio tends toward 0 when the rain rate tends toward the threshold used for rain-free areas (\(Z_{0}=20\) dBZ). Figure 5: Hydrometeor classification at elevation of 0.5\({}^{\circ}\) provided by NEXRAD for the three cases in Figure 2.  
For VV polarization, at low to moderate winds (\(<\)16 m/s), the NRCSratio shows an increasing trend with rain rate at all incidence angles except as wind speed exceeds 8 m/s with incidence angle lower than 33\({}^{\circ}\). Overall, these results conform with results obtained by [PERSON] et al. [29] and [PERSON] et al. [22]. The mean NRCSratio values are found to be positive excepted for low winds (black lines corresponding to lowest values of NRCS without rain) and light rain (base reflectivity lower than 25 dBZ) for which the ratio is found to be around zero. This is different from statistical analysis carried out by [PERSON] et al. [22] scatterometer data from ASCAT, which shows a significant increase of the NRCS even for very light rain. Figure 6: Illustration of NRCSratio calculation based on a VV-polarized SAR image. **(a)** a VV-polarized SAR image acquired on 12 Feb 2017 at 04:29 UTC. The red star marks a single pixel for calculation of NRCSratio. The red rectangle covers the calculation area for the pixel, with a width of 0.5\({}^{\circ}\) incidence angle range and the length of 50 km in the azimuth direction. The blue area in the most left panel denotes the calculation area without rain (\(Z~{}<Z_{0}=20\) dBZ). **(b)** co-located base reflectivity measured by NEXRAD at the same time and **(c)** the result of NRCSratio for all the pixels under rain. Figure 7: Statistics of NRCSratio with respect to base reflectivity for VV polarization (**a-Top**) and VH polarization (**b-Bottom**). The value of rain rate is computed from base reflectivity, according to conversion \(Z_{\text{lin}}=300\)R\({}^{1.4}\) from NEXRAD manual [35].