## 4 Results and Discussion
### Importance of the Soil Descriptors and Incidence Angle in Backscattering Estimates  
In the case of MLR, the models rely on a limited number of explanatory variables, especially in the case of signals acquired with co-polarization. For the X-band, incidence angles and TSM account for 59.2 and 40.8% of the explained variance, respectively. Regarding the C-band, the variance explained by TSM is more important, with 77.1 and 79.7% for HH and VV polarizations, respectively (the variance explained by the incidence angle is 22.9 and 20.3%, depending on the considered polarization). Finally, for the C-band in the cross-polarization state, the proportion of variance explained by TSM reaches 86.3%; the clay fraction, the standard deviation of roughness heights and the autocorrelation length collected in the direction parallel to the tillage orientation regarding the surface roughness account for 3.6, 8.5 and 1.6%, respectively. The relative importance of the descriptors used as input variables of RF algorithms for the estimation of backscattering coefficients is presented in Figure 10. The general trends in the level of importance of the variables for the tested satellite configurations are relatively close (absolute levels are, however, specific to the considered frequency and polarization) and appear consistent with previous studies dealing with the analysis of microwave signals observed over bare agricultural soils. Regardless of the microwave wavelength considered, the topsoil moisture is the most significant surface descriptor. The importance of this variable in the estimation of backscatter coefficients is the highest in the case of the C-band, with values ranging from 44.0 to 46.7% for the various polarizations (Figure 10). For the X-band, the importance level associated with surface moisture is 38.8%. For the other variables, the order and level of importance vary with the considered satellite configuration. The effect of the incidence angle is the highest in the case of the X-band (importance of 39.9%, Figure 10), with a level close to that of the surface humidity (38.8%). This importance of the incidence angle is lower in the case of the C-band, with an average level close to 20% for co-polarizations. In the case of cross-polarization, the importance of the incidence angle is the lowest, exceeded by topsoil moisture, roughness and texture, whose levels reach 44.0, 27.7 and 18.0%, respectively. This difference between polarization states is consistent with various studies that show a low angular sensitivity in the case of signals acquired with cross-polarization [2; 64; 65; 66]. Conversely, the large difference between signals acquired in the same polarization state (i.e., HH) in the X- and C-bands regarding the effect of the incidence angle should be interpreted with caution. Indeed, images acquired in the X-band are mainly acquired at 27.3 and 53.3\({}^{\circ}\), therefore displaying a maximum angular difference of \(\sim\)26\({}^{\circ}\). In the C-band, this difference is smaller (close to 16\({}^{\circ}\)), limiting the comparison of the importance of the incidence angle between signals acquired at different frequencies. The four components of roughness considered in the approach have a higher importance in the C-band, with levels of 23.5% for HH, 19.9% for VV and 27.7% for VH polarization, compared to 15.1% for the X-band (Figure 10, topmost values). This lower importance of roughness in signals acquired in the X-band is also highlighted in various other studies; the sensitivity to surface roughness thus increases with the considered wavelength [9, 67]. Among the four components considered in this study, the levels of importance of h\({}_{\text{rms}}\) are slightly higher than those associated with l\({}_{\text{c}}\) (averages of 6.5 and 4.8%, respectively).