# Detection of Surface Water and Floods with Multispectral Satellites
## 3 Multispectral Indices for Water Segmentation  
Spectral indices are a combination of two or more spectral bands through which the water class is detected and separated from other features by exploiting the reflectance characteristics of different bands. Since 1974, several spectral indices have been proposed in the literature, each formed by a different band composition to enhance water features from other objects. The NDVI was introduced by [PERSON] et al. [33] to detect the vegetation greenness using Landsat 1-MSS images. This index exploits the contrast between the reflectance in the infrared and red bands, where negative values indicate the presence of water. To enhance water features, [PERSON] [34] proposed the NDWI, which uses the green and NIR bands. In this case, the index assumes positive values in water regions. Using the same name, [PERSON] [104] introduced an index that uses the NIR and SWIR1 bands. To avoid confusion, [PERSON]'s NDWI was later renamed as Normalized Difference Moisture Index (NDMI) by [PERSON] [26]. The same author, using Landsat TM images, developed a modified version of the NDWI, the so-called MNDWI, which exploits reflectance differences between the green and SWIR1 bands. This index was successfully introduced to better discriminate water surfaces in regions where built-up land areas dominate the background [26]. Other features can lead to the misclassification of water pixels, including dark surfaces and the presence of shadow, which can be predominant especially in mountainous areas. To reduce such environmental noises and improve surface water mapping, [PERSON] et al. [105] proposed an Automated Water Extraction Index (AWEI). Two indices were formulated by the authors to distinguish situations in which shadow does not represent a major problem (AWEInsh) from those in which shadows and dark surfaces predominate (AWEInsh). A modification of the MNDWI was introduced by [PERSON] et al. [106] for Landsat 7-ETM+ and MODIS sensors. The author proposed to substitute the Landsat 7-ETM+ SWIR1 band with the SWIR2 band to form an index named NDWI\({}_{\text{L2,7}}\). The same substitution was proposed for the MODIS SWIR1 band, replaced by the SWIR2 band to form the NDWI\({}_{\text{M4,7}}\). Hereinafter, the index formed by the green and SWIR2 bands, regardless of the sensor, is referred to as MNDWI\({}_{7}\), as proposed by [PERSON] et al. [59]. A further investigation of the literature was carried out to identify the most employed spectral indices derived from Landsat, Sentinel-2, and MODIS data. In particular, the NDVI, NDWI, NDMI, MNDWI, AWEIsh, AWEInsh, and MNDWI\({}^{\prime}\) were found to be applied to both flooded area detection and water body mapping, while the Water Ratio Index (WRI) introduced by [PERSON] and [PERSON] [107] for Landsat ETM+ imagery, was also found to be used in surface water delineation studies. Among these indices, the most frequently used are the NDWI (around 65.2% of applications with Landsat, 21.4% with Sentinel-2, and 16.1% with MODIS) and the MNDWI (66.7% of use with Landsat and 16.7% with both Sentinel-2 and MODIS). In Figure 2, the percentages of use of the MNDWI (left panel) and NDWI (right panel) from 2002 to 2021 for each satellite are shown. Similar trend patterns on their applications with Landsat, Sentinel-2, and MODIS were found both for the MNDWI and