Course 2C - Calculating Spectral Indices (Equations) from Satellite Imagery for Free
* A VAST AMOUNT OF SPECTRAL INDICES EXIST FOR A WIDE ARRAY OF PURPOSES; A SMALL PORTION OF INDICES ARE DESCRIBED BELOW IN ORDER TO GET YOU STARTED. *
In order to calculate spectral indices (see below), imagery needs to first be converted to surface reflectance. You can use the free GIS Ag Maps Landsat & Sentinel-2 Surface Reflectance Tutorials (available above) - the tutorials will take you step-by-step through the process of converting free imagery with free QGIS software (or other software, such as ArcGIS). A small amount of well-documented indices are included below so you can get some experience calculating index values in GIS software. It is important to understand that for vegetation in particular (crops and others), a large amount of indices have been developed that are used for different purposes and different stages of the growing season.
After imagery is converted to surface reflectance, it is a simple task to convert imagery to indices by using the Raster Calculator. Below, we have included index information for crops/vegetation, wildfire, and snow. If you need help getting started with free QGIS, see the Free Courses page.
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CALCULATING SPECTRAL INDICES
VEGETATION INDICES
A spectral vegetation index (SVI), is a value based on an equation that includes different spectral bands and is meant to better reveal vegetation condition. It is important to understand that there are numerous different SVIs that have been developed, some of which can be viewed through the next link:
List of 71 Spectral Vegetation Indices for Broad or Narrow Band Sensors (PDF)
Surface reflectance is necessary to calculate indices. After imagery has been converted to surfaces reflectance, calculating indices is a simple task using the Raster Calculator.
VEGETATION CONDITION
The most known (and one of the earliest) SVIs is Normalized Difference Vegetation Index (NDVI; see equation below) (Rouse et al., 1973). NDVI is useful only after soil has been covered enough by vegetation and before the canopy is too dense - after that, NDVI is overall too insensitive to change (due to lack of variability of the red band) and a non-normalized index (such as Difference Vegetation Index or Simple Ratio) should be used (NDVI can still distinguish significantly lower condition areas in a dense canopy, but cannot effectively distinguish moderate to minor differences well enough). The graphic below shows a comparison late in year when NDVI should not be used; the comparison shows that solely using NIR reflectance is superior not only because it has about 5 times more variability, but it also produces a much more coherent and realistic crop condition (as well as yield prediction) map. Click here to view a publication that describes in more details when NDVI should and should not be used (PDF; opens in new tab).
WHEN TO USE AND NOT USE NDVI
Comparison Showing that NIR Solely is Superior to NDVI Later in Season
NIR surface reflectance (SR) solely can be effectively used later in the season for types of crops with high SR (>55 percent), such as soybeans, and is much more effective than NDVI. Simple Ratio (NIR/Red) or Difference Vegetation Index (NIR-Red) maps would both look similar to the NIR solely map, and also be more effective than NDVI. It is important to note that corn NIR SR is too low (due to the structure of the plant) and that it is difficult to map corn well later in season with any index.
If applied at the proper time, NDVI is able to take advantage of the fact that healthier green vegetation has higher near infrared surface reflectance and lower red surface reflectance (NDVI has a value between -1.0 and 1.0). Different indices have been designed for different situations and purposes, including assessing dense canopies.
NDVI is written as follows: (all values are in surface reflectance): (NIR - Red) / (NIR + Red)
(When vegetation becomes too dense, red reflectance is virtually the same throughout even if condition varies and, as a result, the NDVI value is virtually 1.0 throughout because the equation essentially equals NIR/NIR; a different index should be used at that point).
(For Sentinel-2, use Band 8a NIR [as opposed to band 8], which is more similar to Landsat 8 band 5 NIR).
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Earlier in the season when it is appropriate to use a normalized index (after the canopy is full enough, yet not too dense), NIR surface reflectance (SR) is much higher than red SR, which reduces the impact of red SR variability (which is very important at that time of the season). A VSI that corrects for this is Wide Dynamic Randge Index (WDRI) (Gitelson, 2004). WDRI more equally weights red and NIR surface reflectance. For healthy green vegetation at this time of the season, NIR surface reflectance is roughly 10 times greater than red surface reflectance (multiplying NIR by a 0.1 factor helps produce more equal NIR and red values; a 0.2 factor can also be used).
WDRI (using a 0.1 factor) can be written as follows (all bands are in surface reflectance): ([NIR * 0.1] - Red) / ([NIR * 0.1] + Red)
For Sentinel-2, use Band 8a NIR.
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Once familiar with the above indices, you can try to calculate a soil adjusted vegetation index from the link near the top of the page (such as MSAVI).
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For times later in season, apply a ratio index (such as the Simple Ratio [NIR/Red]) or the Difference Vegetation Index [NIR - Red]). (For corn, use the Simple Ratio rather than the Difference Vegetation Ratio.)
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RED EDGE (available with Sentinel-2 imagery)
The red edge is the spectral region where vegetation reflectance abruptly increases from red to NIR. Clevers and Gitelson (2013) found there would be a high correlation between total crop and grass chlorophyll and nitrogen content based on the Sentinel-2 red edge Band 6:Band 5 ratio (research was completed prior to Sentinel-2 acquiring imagery by deriving information based on another satellite platform).
Use an equation from the publication accessed through the previous link or get started by simply dividing (in surface reflectance) Sentinel-2 Band 6 by Band 5 with the Raster Calculator; also try Band 7 divided by Band 5. The value of red edge applied to vegetation is quite well-documented.
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VEGETATION WATER CONTENT
Normalized Difference Water Index (NDWI) (Gao, 1996) represents plant water content and is written as follows (all bands are in surface reflectance):
(SWIR - NIR) / (SWIR + NIR)
For Landsat 8, use Band 6 SWIR; for Landsat 7, 5, and 4, use Band 5 SWIR; for Sentinel-2, use Band 8a NIR and Band 11 SWIR.
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WILDFIRE
The extent of a wildfire is mapped with the Differenced Normalized Burn Ratio (dNBR) which is as follows (in surface reflectance):
dNBR = NBRprefire - NBRpostfire
where, NBR = (NIR - SWIR) / (NIR + SWIR)
(For Landsat 5, 7, and 8 use Band 7 SWIR; for Sentinel-2, use Band 8a NIR and Band 12 SWIR)
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SNOW
The extent of snow can be mapped with the Normalized Difference Snow Index (NDSI) (Dozier, 1989). NDSI is as follows (in surface reflectance):
(Green - SWIR) / (Green + SWIR)
(For Landsat 4, 5, and 7; and 5 use Band 5 SWIR. For Landsat 8, use Band 6 SWIR; For Sentinel-2, use Band 11 SWIR)
Though NDSI has been used to map snow, for small scale-areas we recommend using Sentinel-2 green band solely (though the blue and red band also work well) because of the fine 10-meter resolution. See the snow mapping page on this website for an example.
References
Chavez, P.S., Jr. 1996. Image-based atmospheric corrections–revisited and improved. Photogrammetric Engineering and Remote Sensing 62(9): pp.1025-1036.
Chavez, P.S., Jr. 1988. An improved dark-object subtraction technique for atmospheric scattering correction of multispectral data. Remote Sensing of Environment 24: pp.459-479.
Clevers, J.G.P.W. and A.A. Gitelson. 2013. Remote estimation of crop and grass chlorophyll and nitrogen content using red-edge bands on Sentinel-2 and -3. International Journal of Applied Earth Observation and Geoinformation 23: pp. 344–351.
Dozier, J. 1989. Spectral signature of alpine snow cover from the Landsat Thematic Mapper. Remote Sensing of Environment 28: pp. 9-22.
Gao, B.C. 1996. NDWI - A normalized difference water index for remote sensing of vegetation liquid water from space. Remote Sensing of Environment 58: pp. 257-266.
Gitelson, A.A. 2004. Wide dynamic range vegetation index for remote quantification of biophysical characteristics of vegetation. Journal of Plant Physiology 161; pp. 165–173.
Rouse, J. W., R. H. Haas, J. A. Schell, and D. W. Deering (1973). Monitoring vegetation systems in the Great Plains with ERTS, Third ERTS Symposium, NASA SP-351 I, 309-317.