## 5 Discussion  
Three inversion configurations using VV alone, VH alone, and both VV and VH were developed. Each inversion configuration was built with and without the consideration of a priori information on the soil moisture condition. The consideration of a priori information (dry to slightly wet and very wet) was realized by limiting the range of soil moisture values in the training database to _mv_ between 2 and 30 vol % for dry to slightly wet soil conditions and between 20 and 40 vol % for very wet soil conditions. These two soil moisture conditions will be selected in an operational procedure of soil moisture estimation according to meteorological information (rainfall events for example). The developed neural networks were trained using the synthetic database and validated using both real and synthetic databases. Using the synthetic database, the results showed that the consideration of a priori information improves the precision on the soil moisture estimates. In addition, the results showed that the use of VV alone gives a better precision on the soil moisture estimates than using VH alone. Similar precisions were obtained with VV alone and in using VV and VH together. Thus, for soil moisture estimation, it is better to use either VV polarization alone or both VV and VH polarizations with a priori information that could be easily defined from in situ precipitation stations. For all neural networks, the errors (bias and RMSE) on the _mv_ estimates are found to depend on the _Hrms_ values. For an _mv_ between 2 and 25 vol % (with or without a priori information on the  
Figure 9: Retrieved soil moisture versus in situ measurements. Inversion was performed using real SAR data and NDVI derived from optical images. (**a**) VV alone with no a priori information (NN1); (**b**) VH alone with no a priori information (NN2); (**c**) Both VV and VH with no a priori information (NN3); (**d**) VV alone with a priori information (NN1_dry and NN2_wet); (**e**) VH alone with a priori information (NN2_dry and NN2_wet); (**f**) Both VV and VH with a priori information (NN3_dry and NN3_wet). Red dashed ellipses indicate rough plots. Blue ellipses indicate very smooth plots. _mv_), underestimation and overestimation of estimated _mv_ were observed respectively for an _Hrms_ lower and higher than a given threshold of the _Hrms_. With the consideration of a priori information on the _mv_ in the case of dry to slightly wet soils, this _Hrms_ threshold is equal to 1.5 cm when used the VV alone (NN1_dry) or the VV and VH together (NN3_dry). It is approximately 1 cm when VH is used alone (NN2_dry). In addition, the results show that the RMSE on the _mv_ is the lowest for _Hrms_ between 1 and 2 cm for all SAR inversion configurations (VV alone, VH alone, VV and VH together) used in this study, considering a priori information on the _mv_ in the case of dry to slightly wet soils. In the case of very wet soil conditions (_mv_ between 25 and 40 vol %), an underestimation of _mv_ is observed for all _Hrms_ between 0.5 and 3.8 cm. This underestimation decreased with the increase of soil roughness. In addition, the RMSE on the _mv_ decreases with the _Hrms_. The lowest RMSE values correspond to _Hrms_ values that are higher than 2.5 cm. The above conclusions on the dependence between the error on the _mv_ estimates and the _Hrms_ is related to the fact that a smooth surface (_Hrms_ lower than 1 cm) leads to a specular reflection of the emitted radar signal and therefore a low backscatter coefficient, providing an underestimation of the _mv_ with a high RMSE (for all _mv_ values). On the other hand, increasing surface roughness (_Hrms_ higher than 2 cm) results in an increase of the radar backscattering signal that leads to an overestimation of the _mv_ values associated with a high RMSE for dry to slightly wet soils, and provides a slight underestimation with a low RMSE for very wet soils (between 25 and 40 vol %).