## 4 Results
### Using the Synthetic Database
#### 4.1.2. Neural Networks Using the VH Alone (NN2, NN2_dry, and NN2_wet)  
Figure 5 shows the performance of the VH polarization (inputs: noisy \(\sigma^{\circ}\)VH, \(\theta\), and noisy NDVI) for estimating soil moisture. The neural network built with no a priori information on the \(mv\) (NN2) shows a non-biased estimation of \(mv\) and an RMSE of 8.5 vol % (Figure 5a). Moreover, for a reference \(mv\) lower than 25 vol %, the results show that NN2 provides an overestimation of the reference \(mv\) of 4.6 vol % with an RMSE of 7.6 vol %. For a reference \(mv\) higher than 25 vol %, the \(mv\) estimated from NN2 underestimates the reference \(mv\) by 6.9 vol % with an RMSE equal to 9.7 vol %. Moreover, the results show that the use of both a priori information for dry to slightly wet (NN2_dry) and very wet soil conditions (NN2_wet) allows more precise soil moisture estimates. For a reference \(mv\) between 2 and 25 vol %, the RMSE on the \(mv\) estimates decreases from 7.6 vol % with NN2 to 5.8 vol % with NN2_dry (bias decreases from 4.6 vol % with NN2 to 1.9 vol % with NN2_dry) (Figure 5a,b). In very wet soil conditions, the use of a priori information improves the RMSE on the \(mv\) estimates from 9.7 vol % with NN2 to 5.3 vol % with NN2_wet (bias decreases from \(-6.9\) vol % with NN2 to \(-2.6\) vol % with NN2_wet) (Figure 5a,c). In the case of no a priori information, the errors on the \(mv\) estimated from the VH (NN2) are higher than those from the VV (NN1) for both soil conditions, dry to slightly wet soils and very wet soils (Figures 3a and 5a). For an \(mv\) between 2 and 25 vol %, the RMSE on the \(mv\) estimates are 7.6 vol % with NN2 (bias = 4.6 vol %) and 5.5 vol % with NN1 (bias = 2.7 vol %). For an \(mv\) between 25 and 40 vol %, the RMSE on the \(mv\) estimates are 9.7 vol % with NN2 (bias = \(-6.9\) vol %) and of 6.9 vol % with NN1 (bias = \(-4.1\) vol %). Similarly, the use of a priori information in the case of dry to slightly wet soils (reference \(mv\) between 2 and 25 vol %), the errors are higher with the VH (bias = 1.9 vol %, RMSE = 5.8 vol %) than with the VV (bias = 1.2 vol %, RMSE = 4.04 vol %) (Figures 3b and 5b). Finally, in the case of a priori information on the \(mv\) with very wet soils (reference \(mv\) between 25 and 40 vol %), the errors on the \(mv\) estimated from the VH alone (bias = \(-2.6\) vol % and RMSE = 5.3 vol %) and the VV alone (bias = \(-2.3\) vol %, RMSE = 5.1 vol %) are similar (Figures 3c and 5c). The behavior of errors (bias and RMSE) on the \(mv\) estimates with the VH polarization (NN2, NN2_dry, and NN2_wet) according to the \(Hrms\), NDVI, and \(\theta\) is similar to that on the \(mv\) estimates with the VV polarization (NN1, NN1_dry, and NN_wet) (Figures 4 and 6). For an \(mv\) between 2 and 25 vol % (with or without a priori information on the \(mv\)), the RMSE on the \(mv\) estimates increases more strongly with the NDVI for the VH alone (NN2, and NN2_dry) than for the VV alone (NN1, and NN1_dry). Indeed, the RMSE increases from 4.1 to 7.3 vol % with NN2_dry and from 3.6 vol % to 4.9 vol % as the NDVI increases from 0 to 0.75 (Figures 4e and 6e). Similarly, in the case of very  
Figure 4: Bias (estimated \(mv\)—reference \(mv\)) and the RMSE on the \(mv\) estimates when the VV is used alone as a function of the \(Hrms\) (**a**,**d**), NDVI (**b**,**e**), and \(\theta\) (**c**,**f**) for each of NN1, NN1_dry, and NN1_wet. wet soils without the use of a priori information on the \(mv\), the increase of the RMSE according to the NDVI is more rapid when the VH is used alone instead of the VV alone (Figures 4e and 6e). Finally, with the consideration of a priori information on the \(mv\) in the case of very wet soils, the RMSE on the \(mv\) estimated from the VV alone and the VH alone do not depend on the NDVI (RMSE approximately 5.1 vol %) (Figures 4e and 6e). Figure 5: The estimated \(mv\) as a function of the reference \(mv\) when the VH is used alone.