## 3 Soil Moisture Mapping Methodology
### Artificial Neural Networks (ANN)  
In this study, the neural network technique was used to invert the SAR data for estimating the soil moisture because the direct inversion of the IEM model is not possible. Three SAR configurations for estimating the soil moisture are considered:  
* Configuration 1: incidence angle, noisy radar signal at VV polarization, and noisy NDVI are the inputs of the network;
* Configuration 2: incidence angle, noisy radar signal at VH polarization, and noisy NDVI are the inputs of the network; and
* Configuration 3: incidence angle, both noisy radar signal at VV and VH polarizations and noisy NDVI are the inputs of the network. Neural networks (NNs) were trained in using the noisy synthetic training database generated from the parameterized WCM and the modified IEM. The _Hrms_ was not used as an input parameter for the neural networks training and validation. Although, synthetic database was simulated using _Hrms_ values between 0.5 and 3.8 cm. All neural networks were trained in using the Levenberg-Marquardt algorithm [55] with two hidden layers [20]. The number of neurons for each hidden layer is 20 [20; 56]. Linear and tangent-sigmoid transfer functions were associated with the first and second hidden layers, respectively. To improve the soil moisture estimates, a priori knowledge about the soil moisture state is introduced. Indeed, it is easily to define from the weather forecasts (precipitation and temperature) if the soil is either dry to slightly wet (no precipitation for many days before SAR acquisition) or very wet (heavy rainfall preceding SAR acquisition) [20]. The integration of a priori information constrains the range of possible soil moisture parameter values estimated by the neural networks and thus leads to a better estimation of the soil moisture. The requirement for rainfall information is not an obstacle for our operational approach to soil moisture mapping at a high spatial resolution because the information about rainfall (date and amount) are easily available from the in situ sensors. In the case of soil moisture mapping at a low spatial resolution, rainfall remote sensing satellite products (such as the Tropical Rainfall Measuring Mission: TRMM) could be used to define a priori knowledge about the soil moisture. Accordingly, neural networks are built either using or neglecting a priori information on the soil moisture conditions:  
* Case 1: No a priori information is available for the soil moisture state. In this case, the _mv_ will be estimated between 2 and 40 vol %. * Case 2: A priori information is available for \(mv\). The soil is supposed to be dry to slightly wet according to expertise based mainly on meteorological data (precipitation, temperature). Soil moisture values are assumed to range from 2 to 25 vol %. * Case 3: A priori information is available for \(mv\). The soil is supposed to be very wet according to the expertise of the meteorological data. The \(mv\) values are assumed to vary between 25 and 40 vol %. For the case with no a priori information (case 1), the three neural networks (configurations 1, 2, and 3) were developed using the entire training database (\(mv\) between 2 and 40 vol %). For the two cases with a priori information on the \(mv\) (cases 2 and 3), an overlap of 10 vol % on the \(mv\) is considered between the databases used for the training of the networks. For a priori information that soil is dry to slightly wet (case 2), the three neural networks (configurations 1, 2, and 3) were developed using the training database elements with the \(mv\) between 2 and 30 vol %. For a priori information that soil is very wet (case 3), the three neural networks (configurations 1, 2, and 3) were developed using the training database elements with the \(mv\) between 20 and 40 vol %. To summarize, 9 neural networks are developed for the estimation of soil moisture. Table 2 shows the mains properties for each neural network.