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spectral indices. Remote sensing

The Normalized Difference Vegetation Index (NDVI) is a numerical indicator that uses the red and near-infrared spectral bands. NDVI is highly associated with vegetation content. High NDVI values correspond to areas that reflect more in the near-infrared spectrum. Higher reflectance in the near-infrared correspond to denser and healthier vegetation.
Formula
NDVI = (NIR – Red) / (NIR + Red)
NDVI (Landsat 8) = (B5 – B4) / (B5 + B4)

Green Normalized Difference Vegetation Index (GNDVI):
Green Normalized Difference Vegetation Index (GNDVI) is modified version of NDVI to be more sensitive to the variation of chlorophyll content in the crop. " The highest correlation values with leaf N content and DM were obtained with the GNDVI index in all data acquisition periods and both experimental phases. … GNDVI was more sensible than NDVI to identify different concentration rates of chlorophyll, which is highly correlated at nitrogen, in two species of plants." (Gitelson et al. 1996)

Formula of GNDVI = (NIR-GREEN) /(NIR+GREEN)
GNDVI (Landsat 8) = (B5 – B3) / (B5 + B3)

Enhanced Vegetation Index (EVI):
EVI is similar to Normalized Difference Vegetation Index (NDVI) and can be used to quantify vegetation greenness. However, EVI corrects for some atmospheric conditions and canopy background noise and is more sensitive in areas with dense vegetation. It incorporates an "L" value to adjust for canopy background, "C" values as coefficients for atmospheric resistance, and values from the blue band (B).  These enhancements allow for index calculation as a ratio between the R and NIR values, while reducing the background noise, atmospheric noise, and saturation in most cases (USGS, 2019).

Formula of EVI = G * ((NIR – R) / (NIR + C1 * R – C2 * B + L))
EVI (Landsat 8) = 2.5 * ((B5 – B4) / (B5 + 6 * B4 – 7.5 * B2 + 1))

Advanced Vegetation Index (AVI):
Advanced Vegetation Index (AVI) is a numerical indicator, similar to NDVI, that uses the red and near-infrared spectral bands. Like NDVI, AVI is used in vegetation studies to monitor crop and forest variations over time. Through the multi-temporal combination of the AVI and the NDVI, users can discriminate different types of vegetation and extract phenology characteristics/parameters (GU, 2019).

Formula of AVI = [NIR * (1-Red) * (NIR-Red)] 1/3
AVI (Landsat 8) = [B5 * (1 – B4)*(B5 – B4)]1/3

Soil Adjusted Vegetation Index (SAVI):
SAVI is used to correct Normalized Difference Vegetation Index (NDVI) for the influence of soil brightness in areas where vegetative cover is low. Landsat Surface Reflectance-derived SAVI is calculated as a ratio between the R and NIR values with a soil brightness correction factor (L) defined as 0.5 to accommodate most land cover types (USGS, 2019).

Formula of SAVI = ((NIR – R) / (NIR + R + L)) * (1 + L)
SAVI (Landsat 8) = ((B5 – B4) / (B5+ B4 + 0.5)) * (1.5)

Normalized Difference Moisture Index (NDMI):
NDMI is used to determine vegetation water content. It is calculated as a ratio between the NIR and SWIR values in traditional fashion (USGS, 2019).

Formula of NDMI = (NIR – SWIR) / (NIR + SWIR)
NDMI (Landsat 8) = (B5 – B6) / (B5 + B6)

Moisture Stress Index (MSI):
Moisture Stress Index is used for canopy stress analysis, productivity prediction and biophysical modeling. Interpretation of the MSI is inverted relative to other water vegetation indices; thus, higher values of the index indicate greater plant water stress and in inference, less soil moisture content. The values of this index range from 0 to more than 3 with the common range for green vegetation being 0.2 to 2 (Welikhe et al., 2017).
Formula of MSI = MidIR / NIR
MSI (Landsat 8) = B6 / B5

Green Coverage Index (GCI):
In remote sensing, the Green Chlorophyll Index is used to estimate the content of leaf chlorophyll in various species of plants. The chlorophyll content reflects the physiological state of vegetation; it decreases in stressed plants and can therefore be used as a measurement of plant health (EOS, 2019).
Formula of GCI = (NIR) / (Green) – 1
GCI (Landsat 8) = (B5 / B3) -1
..
Normalized Burned Ratio Index (NBRI):
Forest fires are a severe manmade or natural phenomena that destroy natural recourses, live stock, unbalances the local environments, release huge amount of Green House Gases etc. NBRI takes advantage of the near infrared and short wave infrared spectral bands, which are sensitive in vegetation changes, to detect burned areas and monitor the recovery of the ecosystem (GU, 2019).
Formula of NBR = (NIR – SWIR) / (NIR+ SWIR)
NBRI (Landsat 8) = (B5 – B7) / (B5 + B7)
..
Bare Soil Index (BSI):
Bare Soil Index (BSI) is a numerical indicator that combines blue, red, near infrared and short wave infrared spectral bands to capture soil variations. These spectral bands are used in a normalized manner. The short wave infrared and the red spectral bands are used to quantify the soil mineral composition, while the blue and the near infrared spectral bands are used to enhance the presence of vegetation (GU, 2019).

Formula of BSI = ((Red+SWIR) – (NIR+Blue)) / ((Red+SWIR) + (NIR+Blue))
BSI (Landsta 8) = (B6 + B4) – (B5 + B2) / (B6 + B4) + (B5 + B2)
BSI (Landsta 4 – 7) = (B5 + B3) – (B4 + B1) / (B5 + B3) + (B4 + B1)
BSI (Sentinel 2) = (B11 + B4) – (B8 + B2) / (B11 + B4) + (B8 + B2)
..
Normalized Difference Water Index (NDWI):
Normalize Difference Water Index (NDWI) is use for the water bodies analysis. The index uses Green and Near infra-red bands of remote sensing images. The NDWI can enhance water information efficiently in most cases. It is sensitive to build-up land and result in over-estimated water bodies. The NDWI products can be used in conjunction with NDVI change products to assess context of apparent change areas (Bahadur, 2018).
Formula of NDWI = (NIR – SWIR) / (NIR + SWIR)
NDWI (Landsat 8) = (B3 – B5) / (B3 + B5)
NDWI (Landsat 4 – 7) = (B2 – B4) / (B2 + B4)
NDWI (Sentinel 2) = (B3 – B8) / (B3 + B8)
..
Normalized Difference Snow Index (NDSI):
The Normalized Difference Snow Index (NDSI) is a numerical indicator that shows snow cover over land areas. The green and short wave infrared (SWIR) spectral bands are used within this formula to map the snow cover. Since snow absorbs most of the incident radiation in the SWIR while clouds do not, this enables NDSI to distinguish snow from clouds. This formula is commonly used in snow/ice cover mapping application as well as glacier monitoring (Bluemarblegeo, 2019).
Formula of NDSI = (Green-SWIR) / (Green+SWIR)
NDSI (Landsat 8) = (B3 – B6) / (B3 + B6)
NDSI (Landsat 4 – 7) = (B2 – B5) / (B2 + B5)
NDSI (Sentinel 2) = (B3 – B11) / (B3 + B11)
...
Normalized Difference Glacier Index (NDGI):
Normalized Difference Glacier Index (NDGI) is used to help detect and monitor glaciers by using the green and red spectral bands. This equation is commonly used in glacier detection and glacier monitoring applications (Bluemarblegeo, 2019).
Formula of NDGI = (NIR-Green)/(NIR+Green)
NDGI (Landsat 8) = (B3 – B4) / (B3 + B4)
NDGI (Landsat 4 – 7) = (B2 – B3) / (B2 + B3)
NDGI (Sentinel 2) = (B3 – B4) / (B3 + B4)

Atmospherically Resistant Vegetation Index (ARVI)
As the name suggests, the Atmospherically Resistant Vegetation Index is the first vegetation index, which is relatively prone to atmospheric factors (such as aerosol). The formula of ARVI index invented by Kaufman and Tanré is basically NDVI corrected for atmospheric scattering effects in the red reflectance spectrum by using the measurements in blue wavelengths.
Formula of ARVI = (NIR – (2 * Red) + Blue) / (NIR + (2 * Red) + Blue)
..
Structure Insensitive Pigment Index (SIPI)
The Structure Insensitive Pigment Index is good for analysis of vegetation with the variable canopy structure. It estimates the ratio of carotenoids to chlorophyll: the increased value signals of stressed vegetation
Formula of SIPI = (NIR – Blue) / (NIR – Red)




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