*4.1. Effectiveness Validation*

In this study, the proposed DBNN model is compared with conventional SR and PR methods, which are frequently employed for flood monitoring. The SR can be calculated following the equations in the literature [20]. Most studies on flood monitoring by SR methods use simple threshold judgments [18,19], where the average value of the surface reflectivity of permanent water bodies throughout the study area is used as the classification threshold [18–20]. In this study, 15 dB is used as the threshold of the SR method to delineate the flood inundation areas. In addition, the PR is computable according to the literature [23] and uses the constant value of 2 as the threshold to distinguish between flood or land. In this study, the CYGNSS data ranging from 1 to 15 October 2020 are used as an example to investigate the inundation extent of the study area. In Figure 7, the inversion and classification results are presented for the flood monitoring in the study area, where the inversion results refer to the continuous values output by the methods, such as the surface reflectivity output of the SR method, and the classification results refer to the extent of flooding and land divided by the thresholds in various methods. In this study, the reference for judging the flood inundation range is obtained by the SMAP soil moisture threshold method due to the lack of measured data of the surface flood extent. Areas with soil moisture greater than 0.4 cm3/cm3 are classified as the inundated areas, and areas less than 0.4 cm3/cm3 are regarded as non-inundated areas [43]. Figure 7a shows the continuous spatial distribution of soil moisture, and Figure 7b shows flood inundation extent extracted by the soil moisture threshold method.

In this study, type I error, type II error, and overall accuracy are used to evaluate the classification results, which can be calculated as follows:

$$\begin{array}{l} E\_1 = \frac{a}{\frac{a+b+c}{a+b+c}}\\ E\_2 = \frac{b}{\frac{a+b+c}{a+b+c}}\\ C = \frac{c}{a+b+c} \end{array} \tag{7}$$

where *E*<sup>1</sup> and *E*<sup>2</sup> denote the type I error and type II error, respectively. *C* represents the overall accuracy, *a* indicates the number of samples that misclassify water bodies as land, *b* is the number of samples that misclassify land as water bodies, and *c* is the number of correctly classified samples.

**Figure 7.** The inversion and classification results for the flood monitoring in the study area. (**a**) Soil moisture values provided by SMAP mission and (**b**) flood inundation extent classified by threshold method, respectively. The inversion results of (**c**) DBNN method, (**e**) PR method, and (**g**) SR method. The classification result of (**d**) DBNN method, (**f**) PR method, and (**h**) SR method.

According to flood inundation extent delineated by the SMAP soil moisture threshold method, the overall accuracy, type I error, and type II error of the classification result of SR, PR, and DBNN methods are shown in Figure 8 and Table 4, where the DBNN method has the highest inversion accuracy of 85.4%, and the SR and PR methods have inversion accuracies of 80.17% and 81.34%, respectively. In addition, the DBNN method is additionally superior to SR and PR methods in terms of both type I error and type II error, which can be mainly attributed to the following aspects. Firstly, the DBNN model can fully exploit the underlying abstract features from DDMs, while combining the representative features as inputs of the model, which greatly enhances the utilization of GNSS-R data. Secondly, the DBNN model considers the influence of the vegetation factor on GNSS direct signals and reflected signals. However, it is worth noting that the DBNN model is fed with vegetation information from SMAP, whereas the previous SR and PR methods operate based on the CYGNSS data only.

**Table 4.** Classification error and accuracy of PR and DBNN.


**Figure 8.** (**a**) The difference image between SR classification result and SMAP classification result. (**b**) The difference image between PR classification result and SMAP classification result. (**c**) The difference image between DBNN classification result and SMAP classification result.
