## 5 Conclusions  
This study aimed at modeling the backscattering coefficients observed at the plot spatial scale with different viewing configurations (regarding the frequency, polarization and incidence angle) over bare agricultural surfaces. The two statistical algorithms developed in this study (i.e., multiple linear regression and random forest) present a higher magnitude of performance than those in previous studies (based on different modeling assumptions, that is, semi-empirical or physical), with higher accuracy in the X-band (correlation of 0.86 and RMSE of 1.03 dB) compared to that obtained with the different polarizations in  
Figure 10: Comparison of the importance (expressed in percent) of the input parameters (incidence angle and soil descriptors) considering the RF algorithms in the X-band and C-band in the 3 polarizations states (HH, VV and VH). the C-band (correlations greater than 0.58 and RMSE less than 2.22 dB). These two models are not influenced in the same way by surface descriptors. In the linear approach, the information is mainly carried by the surface moisture and the angle of incidence (especially in the case of co-polarized signals, regardless of the frequency), while the influence of roughness or texture becomes significant for cross-polarized signals in the C-band. On the contrary, all the surface descriptors contribute information in the approach based on RF, with the algorithm giving access to more complex relations. Overall, the RF algorithm is the most robust and reliable for simulating all radar configurations (from the band and polarization perspectives). Both surpass the performance presented in previous studies based on either empirical, semi-empirical or physical models. The analyses carried out in this study highlight the importance of toposoil moisture in the dynamics of backscattering coefficients, opening the way to a new perspective on its estimation from SAR images. Random Forest modeling was performed using R software. For each of the tested configurations, the trained models are available on request from the authors. They can also be downloaded at [[https://www.mdpi.com/article/10.3390/app1308493/s1](https://www.mdpi.com/article/10.3390/app1308493/s1)]([https://www.mdpi.com/article/10.3390/app1308493/s1](https://www.mdpi.com/article/10.3390/app1308493/s1)), where a sample formatted data matrix of the input file and an RDS file per configuration are available. [PERSON] and [PERSON] contributed to the data collection, conceptualization, analysis of the results, and writing of the manuscript. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The data presented in this study are available on request from the corresponding author. The authors wish to thank the DLR (German Space Agency), SOAR Project, and CNES (Centre National des Etudes Spatiales) for their support, funding, and satellite images (proposals HYD0611 and SOAR-EU and Categorie-1 ESA project no. 6843). In addition, the authors wish to thank the farmers ([PERSON], [PERSON], [PERSON], [PERSON], and [PERSON]) for their time and valuable discussions and the people who helped to collect the ground data. The authors declare no conflict of interest. The values of the multiple linear regression parameters are listed in Table 11 for the analyzed satellite configurations. The backscattering coefficients can be estimated using Equation (A1) and the parameters corresponding to the chosen satellite configuration. \[\sigma^{\circ}Freq_{Pol}=X_{1}\times P_{Inc.Ang.}+X_{2}\times P_{TSM}+Cte,\] (A1)  
where \(Freq\) is the considered band, \(Pol\) is the polarization state, \(X_{1}\) is the incidence angle, \(X_{2}\) is \(TSM\), and \(P\) is the corresponding parameter. The backscattering coefficients can be estimated using Equation (A2) and the parameters corresponding to the chosen satellite configuration.