# Sentinel-1 and -2 Based near Real Time Inland Excess Water Mapping for Optimized Water Management
## 2 Materials and Methods
### Methodology
#### 2.3.3 Processing  
Radar-Based Processing  
The preprocessed Sentinel-1 images were filtered using a Refined Lee speckle filter to reduce noise. Then, the backscatter values were converted to decibel (db) units for easier handling in the processing workflow. The radar processing workflow was based on the assumption that the radar response of water was considerably lower than the response of other pixels. The challenge is to find the maximum backscatter value of water [33; 46]. To determine this value, training data were collected for both the VV and VH bands of an image. The training data consists of the statistics of the known water bodies as described in 2.2.3. For each band, the minimum, average and standard deviation were determined. Based on these values, the upper and lower thresholds are calculated using an empirically determined method:  
\[uthr_{b}=\overline{x}+k*\sigma \tag{1}\]  
\[lthr_{b}=x_{min}+(3*(\overline{x}-x_{min})/5) \tag{2}\]  
where  
\(b\) is, respectively, band VV or band VH;  
\(uthr_{b}\) is the upper threshold in db;  
\(lthr_{b}\) is the lower threshold in db;  
\(\overline{x}\) is the mean of the training samples in db;  
\(\sigma\) is the standard deviation of the training samples in db;  
\(x_{min}\) is the minimum of the training samples in db;  
\(k\) is a user defined constant that can be adapted to specify the sensitivity of the algorithms to water, where a higher value results in more pixels to be identified as water. The value for k is empirically determined based on the inland excess water events in 2016 and 2018 described in the research. In the future, when more data are available for new IEW periods, the value for this constant can be fine-tuned.  
Sometimes, due to speckle or artifacts, pixels with very low backscatter values occur in the images. These pixels are excluded as water using the lower threshold. All pixels that are between the upper and lower thresholds in both bands are stored as water pixels:  
\[water\;pixel=lthr_{b}<x_{b}<uthr_{b} \tag{3}\]  
where \(x_{b}\) is the value of an individual pixel.  
In the rare case that the statistics of the training samples are beyond the normal range, the predetermined standard values are used for the lower and upper thresholds. These are band-specific (\(lthr_{VV}=-40\), \(uthr_{VV}=-17\), \(lthr_{VH}=-50\) and \(uthr_{VH}=-23\)) because backscatter values for water are normally lower in the VH band. The predetermined standard values are a requirement for full automation of the algorithm. Their values are based on examining the values of water in the radar images and literature [27; 30]. Ascending and descending orbits are processed using the same methods because each image is processed individually, meaning that every image has its own set of training statistics that is used for the extraction on the water pixels.  
It was observed that in areas with sandy soils, the backscatter values were lower, resulting in overestimation of the number of water pixels. Therefore, an adaptation of the radar processing was applied to each sandy pixel in the image, and the upper threshold was reduced by 25%. This value was empirically calibrated. So far, its value could not be better determined from other research. The value can be adapted when more data become available from other IEW periods or other areas. Pixels defined as water in both bands are considered water pixels and are stored in the final map.  
The final map is a binary map showing all water in the area, whether it is an inland excess water inundation or a permanent water body like a lake or a river.