Specific features of interest, like for example vegetation, water or burnt areas, react differently to various wavelenghts of light.
Spectral Indices use these special properties to derive this specific information from applying mathematical operations to at least two different wavelenghts the feature is especially sensitive to.
Most commonly, those mathematical operations are based on the Normalized Difference: (a-b)/(a+b).
Spectral Indices can be essentially useful for discovering, analysing and monitoring those specific features of interest.

There are spectral indices for almost any application imaginable, ranging from Vegetation Indices over Burnt Area Indices to Geological or (Human) Built Up Indices. This Site for example features a whole lot of different spectral indices, along with instructions on how to calculate them for different sensors.

Spectral Indices are an essential tool for geoscientists, as they allow to rather easily derive important information from satellite bands. In the following chapters, we are going to look at two of the most important spectral indices for geoscientists: the Normalized Difference Vegetation Index (NDVI) and the Normalized Burn Ratio (NBR).

Normalized Difference Vegetation Index (NDVI):
The NDVI is a vegetation index that uses the reflectance properties of healthy vegetation to distinguish vegetated areas from non-vegetated areas, as well as estimate how healthy the present vegetation is.
This is done by calculating the normalized difference of the Near Infrared and the Red band, as healthy vegetation highly reflects Near Infrared light, but barely reflects Red light.

NDVI = (NIR-Red)/(NIR+Red)
The result is a range of values from -1 to 1, with high positive values indicating an abundance of healthy vegetation, values around zero low to none vegetation and high negative values most likely water.

The NDVI, however, is prone to errors when the density of biomass is either very high, as in tropical forests, or when there is a high influence of very bright soils.
To cope with this, there are many different versions of Vegetation indices available, like the Enhanced Vegetation Index (EVI) that can deal with high biomass densities or the Soil Adjusted Vegetation Index (SAVI) that corrects for very bright soils.
 
 
 
Normalized Burn Ratio (NBR):
The NBR is a spectral index that is capable of detecting and highlighting burnt areas. It works in the same manner as the NDVI, however it uses the normalized difference of the Near Infrared and the Short Wave Infrared bands.

NBR = (NIR-SWIR)/(NIR+SWIR)
The result is again a range of values from -1 to 1, with high positive values indicating healthy vegetation, values around zero non-burnt areas and high negative values either bare ground or recently burned areas.

The NBR can also be used to estimate the burn severity of an event. This can be achieved by calculating a Difference Image, that means subtracting a NBR-Image after a fire-event from a NBR-Image before a fire-event. The result is an Image with pixel values showing the difference in NBR, hence allowing to estimate the severity of the fire for specific areas.