**3. Method**

In this study, a DBNN model for flood monitoring is proposed, which is mainly composed of two parallel subnetworks: the CNN and BP neural network. In this model, two-dimensional DDMs are input into the CNN, which automatically extracts the abstract features from images, while the BP neural network is fed with seven typical GNSS-R features, including surface reflectivity [18], power ratio [23], and the leading edge of slope [37], etc., as well as vegetation information from SMAP data [28]. The output results of the model are the probability values that DDMs belong to the submerged region. The proposed method consists of three steps, as follows: (1) data pre-processing and features extraction; (2) construction and training of DBNN model; and (3) prediction of DBNN model. The process of this method is shown in Figure 3.

**Figure 3.** Flow chart of the inversion method.

#### *3.1. Data Pre-Processing and Features Extraction*

In order to obtain good inversion results, only CYGNSS data meeting the following conditions are employed in this study:


The power values of some pixels in DDMs, which cannot be mapped to the real Earth's surface, are mainly generated by thermal noise (as shown in the white area in Figure 4). Fortunately, the thermal noise pixels in DDMs can be eliminated by using the method provided by Al-Khaldi [23] after screening CYGNSS data. The DDMs before and after removing the thermal noise pixels are displayed in Figure 5.

The dielectric constant and roughness of the land surface obviously vary when floods occur, so they can be regarded as very useful physical parameters for judging whether floods have occurred or not. Therefore, seven features related to the above two parameters are extracted from DDMs in this study as the inputs of the BP neural network, which include surface reflectivity [18], power ratio [32], leading edge of slope [37], trailing edge of slope [25], peak point power, DDM average [39], and signal-to-noise ratio [12] (as shown in Table 3).

**Figure 4.** Mapping relationship between the spatial coordinate system and delay-Doppler coordinate system. The subfigure on the left depicts the spatial coordinate system. The ellipse and the curve represent a delay isoline and a Doppler shift isoline, respectively. The subfigure on the right represents the delay-Doppler coordinate system, where the blue and yellow delay Doppler pixels in DDMs correspond to one and two spatial points in the left subfigure, respectively, while white pixels represent the thermal noise pixels without corresponding spatial point. SP: the specular point.

**Figure 5.** (**a**) DDM before removing the thermal noise pixels; (**b**) DDM after removing the thermal noise pixels.


