# Flood Inundation Mapping by Combining GNSS-R Signals with Topographical Information
## 3 Methodology  
The proposed model workflow for the conceptual near-global flood inundation mapping technique is shown in Figure 1. The multi-temporal SNR data available from CYGNSS as point information, although useful in providing information regarding the underlying surface, has considerable spatial gaps in their daily ground footprint, which prevents mapping floods consistently across inland areas. Therefore, in order to obtain spatially contiguous flood inundation maps, the daily SNR point data was accumulated across a temporally moving window of 30 days length, traversing a two-month period before and during the flood event for the given region; i.e., SNR values from the (1 July to 1 August) window are used cumulatively to obtain an SNR spatial map by following the inverse distance weighted (IDW) interpolation technique, before proceeding to the next window iteration (2 July to 2 August), until the (30 July to 30 August) iteration. Extreme rainfall was observed from 1 August in both the case studies; hence the study period was considered for a total of two months, i.e., one month prior to and one month after the start of the rainfall event. The temporally moving window of a duration of roughly 30 days was taken as a baseline for mapping observed flood events of about 2-week duration. Since there existed no meaningful relationship between the semi-variance of SNR data as a function of the search radius, the value at a particular pixel was interpolated from the values of the three nearest neighboring SNR data points using IDW at 30 m spatial resolution to produce continuous surface values. The maximum value among the SNR spatial maps generated for each pixel was recorded and combined with the topographical information in the form of the HAND-SND terrain index to enhance the spatial extent of maximum inundation that can be mapped. Calculation of the HAND value for a given pixel was performed as follows (Figure 2):  
1. ASTER DEM was filled, to avoid sinks and to make it hydrologically consistent. 2. The D8 flow direction algorithm (Figure 2c) was applied to the filled DEM. 3. Flow accumulation raster was obtained from flow direction, to find how many pixels drain to neighboring downstream pixels. 4. Stream raster was delineated by choosing the appropriate cumulative area (CA) threshold. In this case, the CA value of 1.000 was chosen. Figure 1: Workflow of the conceptual flood inundation mapping technique undertaken in this study. Based on the flow direction raster and the stream raster delineated in the earlier step, the nearest drainage pixel for every pixel in the study area was found. 6. Finally, the HAND value of a pixel at 30 m spatial resolution was calculated as the height of pixel relative to its nearest drainage pixel. The effect of critical parameters that affect the flood extent is determined for the integration of CYGNSS and HAND-SND datasets. A flooded pixel is associated with higher SNR value, and hence the maximum SNR value mapped in the window period, w, can be assumed to have a directly proportional relationship with the likelihood of flooding P(F), where F represents the flood variable, i.e.,  
\[\text{P(F)}\propto\text{Max (SNR)}|_{\text{w}} \tag{1}\]  
Furthermore, based on the HAND flood terrain model, it can be concluded that the higher the HAND value of a pixel, the less likely it is to be flooded than a pixel with a relatively lower HAND value, and hence,  
\[\text{P(F)}\propto\frac{1}{\text{HAND}} \tag{2}\]  
Similarly, once we have the nearest drainage map derived from step 5 mentioned above, the slope of the nearest drainage (SND) is then assigned to its corresponding floodplain pixel (Figure 2h). This step was performed because drainage pixels with the same HAND value and nearest channel pixels with higher slope values are less likely to inundate than those drainage pixels with lower slope values. Also, [PERSON]'s Equation shows that a given discharge amount (\(Q\)) in the channel is proportional to hydraulic radius (\(R\)) and channel slope (\(S\)), where \(Q\propto R^{5/3}S^{1/2}\).