## 3 Methodology
### Computation of Monthly Land-Water Masks with Data Gaps
#### 3.2.2 Calculation of Water Indexes  
Over the last few decades, many water indexes used for classifying water bodies have been developed. However, no optimal water index exists working in all areas. Especially near shores water indexes react with a different sensitivity. Each water index is developed to separate land and water pixels as good as possible. The resulting histograms of the water indexes have bimodal-like shapes, wherein land and water must be separated. Therefore, we combine five indexes to use their individual strengths for the identification of water bodies. In detail, we use the  
* Modified Normalized Difference Water Index (MNDWI) [10],
* New Water Index (NWI) [11],  
Figure 5: Combined Landsat and Sentinel-2 bands (_RED_, _green_, _blue_, _NIR_, _SWIR_, _SWIR_) and _QUALITY_ mask (voids, clouds, cloud shadows, snow) used for the computation of indexes for Lake Ray Roberts in April 2016. Data gaps in the Figure 5a–f are highlighted in yellow. * Automated Water Extraction Index for Non-Shadow Areas (AWEI\({}_{\text{nsh}}\)) [12],
* Automated Water Extraction Index for Shadow Areas (AWEI\({}_{\text{sh}}\)) [12] and
* Tasseled Cap for Wetness (TC\({}_{\text{wet}}\)) [13]. For calculating the indexes, different combinations of visible bands (\(RED\), \(GREEN\), \(BLUE\)) and infrared bands (\(NIR\), \(SWIR_{1}\), \(SWIR_{2}\)) are used. All five water indexes used in this study are now presented in detail. Figure 6 shows as an example the results of all five indexes for the Lake Ray Roberts in January 2017. Figure 6: The used water indexes, Modified Normalized Difference Water Index (MNDWI), New Water Index (NWI), Automated Water Extraction Index for Non-Shadow Areas (AWEI\({}_{\text{nsh}}\)), Automated Water Extraction Index for Shadow Areas (AWEI\({}_{\text{sh}}\)) and Tasseled Cap for Wetness (TC\({}_{\text{wet}}\)) are shown for Lake Ray Roberts in January 2017. Modified Normalized Difference Water Index (MNDWI)  
The MNDWI [10] is a modified version of the well-known Normalized Difference Water Index (NDWI) [32] shown in Equation (1). Here, the \(NIR\) band has been replaced by the \(SWIR_{1}\) band. The value range of the MNDWI is always scaled between \(-1.0\) and \(1.0\). A threshold of \(0.0\) can be selected to get a good but not the best separation of land and water pixels. \[MNDWI=\frac{GREEN-SWIR_{1}}{GREEN+SWIR_{1}} \tag{1}\]  
New Water Index (NWI)  
The NWI, shown in Equation (2), is a water index using spectral rationing, considering more bands in the infrared spectrum and the blue instead of the \(GREEN\) band [11]. Additionally, the result is multiplied by a constant value \(C\) (e.g., 100) to scale the index, to avoid low decimal numbers. NWI has already been used in different studies such as [33]. The NWI is expressed as:  
\[NWI=\frac{BLUE-(NIR+SWIR_{1}+SWIR_{2})}{BLUE+(NIR+SWIR_{1}+SWIR_{2})}\times C \tag{2}\]  
The Automated Water Extraction Index for Non-Shadow Areas (AWEI\({}_{\text{nsh}}\)) has been developed to maximize separability of water and other dark areas [12] which is shown in Equation (3). In contrast to the previous methods no ratio is used, but weighted indicators are subtracted from each other. The AWEI\({}_{\text{nsh}}\) is specifically formulated to separate water from dark surfaces such as buildup areas, disregarding shadows. It is expressed as:  
\[AWEI_{nsh}=4.0\times(GREEN-SWIR_{1})-(0.25\times NIR+2.75\times SWIR_{2}) \tag{3}\]  
The Automated Water Extraction Index for Shadow Areas (AWEI\({}_{\text{sh}}\)) (Equation (4)) works similar to the AWEI\({}_{\text{nsh}}\) but is more suited for regions where shadows are a major problem such as valleys in alpine regions [12]. The index additionally includes the \(BLUE\) band and uses a different weighting of the bands.