## 4 Results and Discussion
### Overall Performance of the Statistical Approaches
#### 4.1.2 Multi-Incidence and Multi-Polarization Estimates of C-Band Backscattering Coefficients
The studies used in the comparison of performance with the models developed in this work did not all use the same performance evaluation statistics. Indeed, some of them used only the correlation coefficient, while others used only the RMSE. Figure 9 summarizes the statistical performance obtained for each model used for the comparison (r and/or RMSE) for the four satellite configurations analyzed in the present study. It is important to note that these performance measures were obtained from the original datasets used to build the models, unlike the previous parts, where the models were evaluated on the dataset used in this study. Semi-empirical models tested on different study sites present error levels ranging from 2.3 to 4.7 dB in the X-band (and correlations close to 0.58) and from 2.3 to 4.4 dB in the C-band (and correlations between 0.31 and 0.44). The results of the signal estimations acquired with HH polarization show similarities, namely, lower error levels for the models proposed by [PERSON] [11; 12] compared to the performance associated with the [PERSON] model [10]. Concerning the other polarization states (i.e., VV or VH), fewer studies show error levels ranging from 2.4 to 2.8 dB. Physical approaches do not offer any improvement in the estimation of radar signals. Their performance appears limited, as evidenced by the error  
Figure 9: Statistical performance: RMSE (dots) and correlations (bars) obtained in previous studies by comparing the modeled and satellite-derived backscattering coefficients in the X-band in the HH polarization state (**a**) and in the C-band in HH, VV and VH polarizations states (**b–d**, respectively). In each figure, the vertical dotted line distinguishes the original models (on the left) from the modified versions of the models (on the right) [24; 29; 30; 60; 61; 62; 63]. levels in the X- and C-bands, with values from 3.5 to 11.7 dB and 3.3 to 26.7 dB, respectively, and correlations less than 0.35. Given these results, in order to overcome the limitations displayed by these models, different approaches have been proposed, such as the semi-empirical calibration of the IEM model [25; 26; 27; 28], the recalibration of the initial equations of the models or the reduction in different biases of semi-empirical models [24; 29; 30]. These changes are accompanied by a decrease in estimate dispersion, which is accompanied by a higher level of performance. The IEM model corrected for roughness bias has, for example, lower error levels in the X- or C-band (with values between 1.8 and 3.2 dB and between 1.9 and 3.1 dB, respectively). The same applies to approaches that aim at modifying semi-empirical models, with error levels in X- or C-band between 1.4 and 1.9 dB and between 1.7 and 2.2, respectively. Nevertheless, these approaches remain limited, and the levels of precision of the statistical approaches (presented in this study) exceed those obtained with semi-empirical (i.e., [PERSON]'s [11; 12] and Dubois' [10] models, results presented in [30]) or physical (i.e., IEM [13], results presented in [24]) models implemented at the same study site (results presented in the two previous sections). This raises the question of the initial formalism of the models and the question of the representativeness/quality of the ground measurements. Indeed, models adjusted for different biases should have a performance at least equivalent to that of statistical approaches. At this stage, the modified models are in a deadlock, having extracted as much information as possible from the biases toward the input variables.