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Band Arithmetic function

The Band Arithmetic function performs an arithmetic operation on the bands of a raster dataset. There are predefined algorithms you can pick or you can enter your own single-line formula. The operators supported are -,+,/,*, and unary -.

The inputs for this function are the following:

  • Input Raster
  • Method—Either a predefined expression or user defined.
  • Band Indices or Expression
    • For Band Indices, enter a space-delimited list indicating the band numbers to be used in the predefined formulas.
    • For Expression, enter the single-line expression.

User defined method

You can enter a single-line algebraic formula to create a single-band output. The supported operators are -,+,/,*, and unary -. To identify the bands, prepend the band number with a B or b. For example:

B1 + B2
b1 + (-b2)
(B1 + B2) / 2(B3 * B5)

Predefined methods

For these predefined methods, you can enter a space-delimited list indicating the band numbers to be used.

GEMI method

The Global Environmental Monitoring Index (GEMI) is a nonlinear vegetation index for global environmental monitoring from satellite imagery. It's similar to NDVI, but it's less sensitive to atmospheric affects. It is affected by bare soil; therefore, it's not recommended for use in areas of sparse or moderately dense vegetation.

GEMI=eta*(1-0.25*eta)-((Red-0.125)/(1-Red))

where,

eta=(2*(NIR2-Red2)+1.5*NIR+0.5*Red)/(NIR+Red+0.5)
  • NIR = pixel values from the near infrared band
  • Red = pixel values from the red band

Using a space-delimited list, you will identify the near infrared and red bands in the following order: NIR Red. For example, 4 3.

This index outputs values between 0 and 1.

Reference: Pinty, B. and Verstraete, M. M. 1992, "GEMI: a non-linear index to monitor global vegetation from satellites," Plant Ecology, Vol. 101, 15–20,

GVI (Landsat TM) method

The Green Vegetation Index (GVI) was originally designed from Landsat MSS imagery and has been modified for Landsat TM imagery. It's also known as the Landsat TM Tasseled Cap green vegetation index. It could be used with imagery whose bands share the same spectral characteristics.

GVI=-0.2848*Band1-0.2435*Band2-0.5436*Band3+0.7243*Band4+0.0840*Band5-1.1800*Band7

Using a space-delimited list, you will identify the six Landsat TM bands, ordered one through five and six. For example, 1 2 3 4 5 7. If your input contains 6 bands, in the order expected, then you do not need to enter a value in the Band Indexes text box.

This index outputs values between -1 and 1.

Reference: Todd, S. W., R. M. Hoffer, and D. G. Milchunas, 1998, "Biomass estimation on grazed and ungrazed rangelands using spectral indices," International Journal of Remote Sensing, Vol. 19, No. 3, 427–438.

Modified SAVI method

The Modified Soil Adjusted Vegetation Index (MSAVI2) tries to minimize the effect of bare soil on the SAVI.

MSAVI2 = (1/2)*(2(NIR+1)-sqrt((2*NIR+1)2-8(NIR-Red)))
  • NIR = pixel values from the near infrared band
  • Red = pixel values from the red band

Using a space-delimited list, you will identify the near infrared and red bands in the following order: NIR Red. For example, 4 3.

Reference: Qi, J. et al., 1994, "A modified soil vegetation adjusted index, " Remote Sensing of Environment, Vol. 48, No. 2, 119–126.

NDVI method

The Normalized Difference Vegetation Index (NDVI) is a standardized index allowing you to generate an image displaying greenness (relative biomass). This index takes advantage of the contrast of the characteristics of two bands from a multispectral raster dataset—the chlorophyll pigment absorptions in the red band and the high reflectivity of plant materials in the near-infrared (NIR) band.

The documented and default NDVI equation is as follows: 

NDVI = ((NIR - Red)/(NIR + Red))
  • NIR = pixel values from the near infrared band
  • Red = pixel values from the red band

Using a space-delimited list, you will identify the near infrared and red bands in the following order: NIR Red. For example, 4 3.

This index outputs values between -1.0 and 1.0.

Learn more about NDVI

PVI method

The Perpendicular Vegetation Index (PVI) is similar to a difference vegetation index; however, it is sensitive to atmospheric variations. When using this method to compare different images, it should only be used on images that have been atmospherically corrected.

PVI=(NIR-a*Red-b)/(sqrt(1+a2))
  • NIR = pixel values from the near infrared band
  • Red = pixel values from the red band
  • a = slope of the soil line
  • b = gradient of the soil line

Using a space-delimited list, you will identify the near infrared and red bands and enter the a and b values in the following order: NIR Red a b. For example, 4 3 0.3 0.5.

This index outputs values between -1.0 and 1.0.

SAVI method

The Soil-Adjusted Vegetation Index (SAVI) is a vegetation index that attempts to minimize soil brightness influences using a soil-brightness correction factor. This is often used in arid regions where vegetative cover is low.

SAVI = ((NIR - Red) / (NIR + Red + L)) x (1 + L)

NIR and Red refer to the bands associated with those wavelengths. The L value varies depending on the amount of green vegetative cover. Generally, in areas with no green vegetation cover L=1; in areas of moderate green vegetative cover, L=0.5; and in areas with very high vegetation cover, L=0 (which is equivalent to the NDVI method). This index outputs values between -1.0 and 1.0.

Using a space-delimited list, you will identify the near infrared and red bands and enter the L value in the following order: NIR Red L. For example, 4 3 0.5.

Reference: Huete, A. R., 1988, "A soil-adjusted vegetation index (SAVI)," Remote Sensing of Environment, Vol 25, 295–309.

Sultan's Formula method

The Sultans process takes a six-band 8-bit image and uses the Sultan's formula to produce a three-band 8-bit image. The resulting image highlights rock formations called ophiolites on coastlines. This formula was designed based on the TM or ETM bands of a Landsat 5 or 7 scene. The equations applied to create each output band is as follows:

Band 1 = (Band5 / Band6) x 100
Band 2 = (Band5 / Band1) x 100
Band 3 = (Band3 / Band4) x (Band5 / Band4) x 100

Using a space-delimited list, you will identify the six bands, ordered one through six. For example, 1 2 3 4 5 6. If your input contains 6 bands, in the order expected, then you do not need to enter a value in the Band Indexes text box.

Transformed SAVI method

The Transformed Soil Adjusted Vegetation Index (TSAVI) is a vegetation index that attempts to minimize soil brightness influences by assuming the soil line has an arbitrary slope and intercept.

TSAVI=(s(NIR-s*Red-a))/(a*NIR+Red-a*s+X*(1+s2))
  • NIR = pixel values from the near infrared band
  • R = pixel values from the red band
  • s = the soil line slope
  • a = the soil line intercept
  • X = an adjustment factor which is set to minimize soil noise

Using a space-delimited list, you will identify the near infrared and red bands and enter the s, a, and X values in the following order: NIR Red s a X. For example, 3 1 0.33 0.50 1.50.

Reference: Baret, F. and G. Guyot, 1991, "Potentials and limits of vegetation indices for LAI and APAR assessment," Remote Sensing of Environment, Vol. 35, 161–173.

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