## 4 Discussion  
### Variability of the SAR Signal with the Spatial Scale  
The variability of the SAR signal with the size of the considered area of interest is analyzed by focusing on the comparison between the values of the backscattering coefficients extracted with different buffer sizes. For each studied satellite configuration, Figure 8 shows the dispersion as well as two statistical parameters (determination coefficients and RMSE), taking as a reference the signals extracted with the best performances (with a 30 m radius), as demonstrated in Section 3. The signal variability decreases with the increasing size of the area of interest, regardless of the SAR signal, with a rate specific to the configuration of the considered image. In the X-band, the significant difference observed between the signals extracted with buffers of 5 and 30 m of radius is rapidly fading, as shown by the values of the determination coefficient and error obtained from the next spatial scale (R\({}^{2}\) of 0.92 and RMSE of 0.60 dB for a 10 m radius). This variability is higher in the C-band, where the thresholds of 0.9 for the determination coefficient and 1 dB for the RMSE are reached earlier, for areas of interest with a buffer of 20 m radius. The difference in performance observed between the images acquired in the X- and C-bands is explained by the characteristics of the sensors onboard the TerraSAR-X and Radarsat-2 satellites. A first criterion for analyzing the quality of the SAR images is the noise equivalent sigma zero (NESZ), which measures the thermal noise of the instrument. In the X-band, the NESZ is equal to \(-19\) dB regardless of the considered beam mode [34], while the C-band images acquired with the full quad-polarization mode present a best NESZ of \(-36.5\pm 3\) dB [35]. Whatever the considered beam mode, the value of NESZ was always lower than the recorded backscattering coefficients. In these conditions, the median signal noise ratios (SNRs) are equal to 9.78 and 9.93 dB in the X-band, for a buffer with a radius of 5 and 30 m, respectively. In the C-band, higher values of SNR are observed, with minimal median values equal to 16.36 and 17.66 dB for a 5 m and 30 m buffer radius (for signals acquired with cross-polarized states), respectively. Even if some points are getting closer to the NESZ threshold at the finer spatial scale (especially in the C-band), the values of SNRs are important and acceptable in most cases. The second criterion is the radiometric resolution (RRAD). It determines the ability of a SAR system to distinguish different uniform regions by assuming negligibly the radar noise from the  
Figure 7: Comparison between observed and estimated backscattering coefficients in C-band for a buffer with a radius of 30 m in three polarization states: (**a**) HH, (**b**) VV, and (**c**) VH. The gray and black dots represent the estimations performed considering the training or validation subsets of samples, respectively. distributed target. The RRAD is derived from several parameters of the SAR images (i.e., the number of azimuthal and range pixels, the number of azimuthal and range looks, the azimuth and ground range spatial resolutions, and the azimuth and ground range pixel spacing). Figure 9 presents the evolution of the RRAD with the size of the buffer for the three beam modes used in the present study. A comparable exponential decrease in the value of RRAD is observed, and more than 80% of the RRAD decrease is reached from the buffer of a 20 m radius. The beam modes are distinguished by their absolute value levels, closely related to image resolution. The RRAD values are thus maximum for the 5 m radius buffer, varying between 2.3 and 0.71 dB, and minimum for the 30 m radius buffer, where they are then between 0.49 and 0.13 dB, for modes FQP and SL, respectively. The decrease in the radiometric resolution partly explains the increase in the correlation coefficients obtained in Figures 4 and 6.