The Red-Edge Inflection Point Index algorithm was developed for applications in biomass and nitrogen (N) uptake measurement/management in heterogeneous fields.- Guyot et al. (1988). Red edge as the inflection point of the strong red absorption to near infrared reflectance includes the information of both crop N and growth status. The reflectance around red edge is sensitive to wide range of crop chlorophyll content N content LAI and biomass (Hatfield et al. 2008 Mutanga and Skidmore 2007 Steele et al. 2008b). The REIP general formula is based on linear four-point interpolation technique and it uses four wavebands (670 700 740 and 780 nm) - Guyot and Baret (1988). The REIP results from the following (Sensor-dependent) equation: REIP = 700 + 40 * ((r670 + r780)/2 - r700) / (r740 - r700) - as general formula or: REIP = 700 + 40 * ( (red1_factor * red1 + IR_factor * near_IR)/2) - red2_factor * red2 ) / (red3_factor * red3 - red2_factor * red2) )

The Normalized Burn Ratio Index (NBR) uses the NIR and SWIR bands to emphasize burned areas while mitigating illumination and atmospheric effects. NBR = (NIR - SWIR) / (NIR+ SWIR)

The Green Normalized Difference Vegetation Index algorithm was developed by Gitelson et al. (1996). The authors verified that GNDVI was more sensible than NDVI to identify different concentration rates of chlorophyll which is highly correlated at nitrogen. The use of green spectral band was more efficient than the red spectral band to discriminate nitrogen. The GNDVI results from the following equation: GNDVI = (IR_factor * near_IR - green_factor * green) / (IR_factor * near_IR + green_factor * green)

MCARI gives a measure of the depth of chlorophyll absorption and is very sensitive to variations in chlorophyll concentrations as well as variations in Leaf Area Index (LAI). MCARI values are not affected by illumination conditions the background reflectance from soil and other non-photosynthetic materials observed.

Inverted Red-Edge Chlorophyll Index: The Inverted Red-Edge Chlorophyll Index algorithm incorporates the reflectance in four bands to estimate canopy chlorophyll content (Guyot and Baret 1988 Clevers et al. 2000). The 'red edge' is the name given to the abrupt reflectance change in the 680-740 nm region of vegetation spectra that is caused by the combined effects of strong chlorophyll absorption and leaf internal scattering. Increases in the amount of chlorophyll visible to the sensor either through an increase in leaf chlorophyll content or Leaf Area Index (LAI) result in a broadening of a major chlorophyll absorption feature centred around 680 nm. The effect is to cause a movement of the point of maximum slope termed the red edge position (REP). The position of the red edge has been used as an indicator of stress and senescence of vegetation (Collins1978 Horler et al. 1983 Rock et al. 1988 Boochs et al. 1990 Jago and Curran 1995). The IRECI results from the following (Sensor-dependent) equation: IRECI = (IR_factor * near_IR - red1_factor * red1) / (red2_factor * red2 / red3_factor * red3). For Sentinel-2 the formula is: (B7 - B4) / (B5 / B6) where (Central wavelength/Bandwidth): B7 = 783 nm (15 nm) B6 = 740 nm (15 nm) B5 = 705 nm (15 nm) B4 = 665 nm (30 nm)

Atmospherically Resistant Vegetation Index: This index takes advantage of the different scattering responses from the blue and red band to retrieve information regarding the atmosphere opacity. The Atmospherically Resistant Vegetation Index algorithm was introduced by Kaufman and Tanre (1992). The resistance of the ARVI to atmospheric effects (in comparison to the NDVI) is accomplished by a self-correction process for the atmospheric effect on the red channel. This is done using the difference in the radiance between the blue and the red channels to correct the radiance in the red channel. Compared to the red band the blue band is much more easily scattered by the atmosphere particles. This explains why the sky is usually perceived as being blue. Thus the ARVI index takes advantage of the different scattering responses from the blue and red band to retrieve information regarding the atmosphere opacity. Simulations using radiative transfer computations on arithmetic and natural surface spectra for various atmospheric conditions show that ARVI has a similar dynamic range to the NDVI but is on average four times less sensitive to atmospheric effects than the NDVI. The ARVI results from the following equation:ARVI = (IR_factor * near_IR - rb) / (IR_factor * near_IR + rb) where: rb = (red_factor * red) - gamma * (blue_factor * blue - red_factor * red) with gamma = 1. The main reason why the blue band is more susceptible to atmospheric scattering than the red band is because its wavelength is shorter. Generally the shorter wavelength has stronger scattering. It's very similar to the way sea waves behave over oceans. When a large wave strikes an object such as a ferryboat it is more capable of continuing on its path by going around the object. On the other hand it is dispersed more easily when the waves are smaller in size. Consequently by obtaining the difference between the reflectance of the highly sensitive blue band and the less sensitive red band (blue - red) it serves like an indicator of what the atmospheric conditions were like. Here gamma serves as a weighting function for the difference reflectance of the two bands. Various values can be chosen for it which mainly depends on the type of aerosol size. According to Kaufaman and Tanre's statement in 1992 it is best to select a gamma value of 1 when information on the aerosol type is not available. Consequently the main purpose of the above rb equation is to decrease the influence brought forth from the atmosphere where a more accurate assessment of the value of the red reflectance can be obtained.

The fraction of absorbed photosynthetically active radiation (FAPAR sometimes also noted fAPAR or fPAR) is the fraction of the incoming solar radiation in the photosynthetically active radiation spectral region that is absorbed by a photosynthetic organism typically describing the light absorption across an integrated plant canopy. This biophysical variable is directly related to the primary productivity of photosynthesis and some models use it to estimate the assimilation of carbon dioxide in vegetation in conjunction with the leaf area index. FAPAR can also be used as an indicator of the state and evolution of the vegetation cover with this function it advantageously replaces the Normalized Difference Vegetation Index (NDVI) provided it is itself properly estimated.

Atmospherically Resistant Vegetation Index: This index takes advantage of the different scattering responses from the blue and red band to retrieve information regarding the atmosphere opacity. The Atmospherically Resistant Vegetation Index algorithm was introduced by Kaufman and Tanre (1992). The resistance of the ARVI to atmospheric effects (in comparison to the NDVI) is accomplished by a self-correction process for the atmospheric effect on the red channel. This is done using the difference in the radiance between the blue and the red channels to correct the radiance in the red channel. Compared to the red band the blue band is much more easily scattered by the atmosphere particles. This explains why the sky is usually perceived as being blue. Thus the ARVI index takes advantage of the different scattering responses from the blue and red band to retrieve information regarding the atmosphere opacity. Simulations using radiative transfer computations on arithmetic and natural surface spectra for various atmospheric conditions show that ARVI has a similar dynamic range to the NDVI but is on average four times less sensitive to atmospheric effects than the NDVI. The ARVI results from the following equation:ARVI = (IR_factor * near_IR - rb) / (IR_factor * near_IR + rb) where: rb = (red_factor * red) - gamma * (blue_factor * blue - red_factor * red) with gamma = 1. The main reason why the blue band is more susceptible to atmospheric scattering than the red band is because its wavelength is shorter. Generally the shorter wavelength has stronger scattering. It's very similar to the way sea waves behave over oceans. When a large wave strikes an object such as a ferryboat it is more capable of continuing on its path by going around the object. On the other hand it is dispersed more easily when the waves are smaller in size. Consequently by obtaining the difference between the reflectance of the highly sensitive blue band and the less sensitive red band (blue - red) it serves like an indicator of what the atmospheric conditions were like. Here gamma serves as a weighting function for the difference reflectance of the two bands. Various values can be chosen for it which mainly depends on the type of aerosol size. According to Kaufaman and Tanre's statement in 1992 it is best to select a gamma value of 1 when information on the aerosol type is not available. Consequently the main purpose of the above rb equation is to decrease the influence brought forth from the atmosphere where a more accurate assessment of the value of the red reflectance can be obtained.

The Modified Normalized Difference Water Index algorithm was developed by Xu 2006 and can enhance open water features while efficiently suppressing and even removing built-up land noise as well as vegetation and soil noise. The greater enhancement of water in the MNDWI-image will result in more accurate extraction of open water features as the built-up land soil and vegetation all negative values and thus are notably suppressed and even removed. The MNDWI results from the following equation: MNDWI = (green_factor * green - mir_factor * middle_IR) / (green_factor * green + mir_factor * middle_IR)

The Transformed Normalized Difference Vegetation Index algorithm indicates a relation between the amount of green biomass that is found in a pixel. (Senseman et.al. 1996). Transformed Normalised Difference Vegetation index (TNDVI) is the square root of the NDVI. It has higher coefficient of determination for the same variable and this is the difference between TNDVI and NDVI. The formula of TNDVI has always positive values and the variances of the ratio are proportional to mean values. The TNDVI results from the following equation: TNDVI = sqrt( (IR_factor * near_IR - red_factor * red) / (IR_factor * near_IR + red_factor * red) + 0.5)