## 1 Introduction  
Several studies have established performance levels and discussed the limitations and main biases of the most commonly used backscatter models for estimating microwave signals over bare soils [1, 2, 3, 4, 5, 6, 7]. Initially, the studies carried out on study sites with a wide range of surface conditions were used to qualify the performance levels of various electromagnetic models. Semi-empirical approaches, as proposed by [PERSON] et al. and [PERSON] et al. [8, 9, 10], as well as physically based models, such as the IEM [11, 12, 13], were implemented, and estimates of backscattering coefficients were compared with the values derived from satellite images. In those works, the best performance levels were associated with semi-empirical models, with error levels varying between 2.3 and 4.7 dB, and higher correlations in the X-band (with values close to 0.60) compared with those observed in the C-band (values below 0.50). Those previous studies have highlighted the limitations of existing models, and identified which variables were poorly taken into account in the original approaches. Correcting these biases then became a major focus of work on electromagnetic modeling. Various modalities were then proposed, with an emphasis on roughness descriptors (each of the studies presenting a modification of the formalism with respect to this variable), resulting in new versions of the models. In the end, this work made it possible to extend the validity of backscatter models, notably to the wide range of roughness levels observable in agricultural conditions. However, there is no consensus on any of the proposed models, whatever the considered assumption regarding formalism, as they still have important limitations (with an explained variance level close to 50%, in the best cases [5]). The difficulty in obtaining higher levels of performance is partly explained by the spatial scale at which these studies were conducted. In those studies, satellite signals and ground measurements were aggregated/averaged at the scale of the agricultural plot, an entity that can show strong contrasts in soil conditions. This variability within the plot may be highlighted by a difference in backscatter levels closely related to moisture [14], texture [15], or roughness [16], and delimiting intra-plot spatial patterns with comparable values. With access to high spatial resolution SAR images which are becoming more systematic with current and future satellite missions (Sentinel-1, Radarsat constellation, TerraSAR-X, Tandem-X...), one challenge is to use these images at a resolution close to the pixel, while limiting speckle effects [17]. Deriving metrics of interest on an intra-plot scale is a major challenge, particularly in the context of precision agriculture, where modulation approaches based on satellite images mainly use optical data [18; 19]. Integrating SAR signals into these methods would provide information that could replace optical data (in the case of unfavorable atmospheric conditions) or complement it (when the signals provide differentiated information), as shown by work carried out in vegetative periods [20; 21]. Moreover, the definition of this spatial scale would be particularly useful for studies aimed at estimating surface humidity at very high resolution, as the statistical performances associated with current approaches are limited and contrasted [22]. In this context, this study aims at evaluating the possibilities of estimating backscattering coefficients in X- and C-bands, on bare soils at the intra-plot spatial scale, using the random forest (RF) algorithm [23]. Such a statistical approach has already been implemented at the spatial scale of the plot [24], showing a significant increase in accuracy compared to semi-empirical (proposed by [PERSON] et al. and [PERSON] et al. [8; 9; 10]) or physical models (IEM [11; 12; 13]) as well as to modified models involving a change in the formalism to correct observed biases [5; 6].