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Calculating the vegetation index faster
REMOTE SENS. ENVIRON. 34:71-73 (1990)
Short Communication
Calculating the Vegetation Index Faster Robert E. Crippen Jet Propulsion Laboratory, California Institute of Technology, Pasadena
T h e near-infrared (NIR) versus red "'infrared percentage vegetation index," NIR /(NIR + Red), is functionally and linearly equivalent to the normalized difference vegetation index, (NIR-Red) / (NIR + Red). Advantageously, it is both computationally faster and never negative. INTRODUCTION This short communication describes a vegetation index that is functionally and linearly equivalent to, but computationally faster than, the normalized difference vegetation index. Unlike the normalized difference, the new index has a fully non-negative range. Computational savings of 15-30% are possible, which is especially significant in the monitoring of global biomass and in other vegetation studies that require the processing of vast amounts of remotely sensed data. BACKGROUND
The ratio of radiances in the near-infrared (NIR) and red bands has long been recognized as a useful measure of vegetation amount (Jordan, 1969; Address correspondence to Robert E. Crippen, Jet Propulsion Laboratory 300-233, California Institute of Technology, Pasadena, California 91109. Received 9 July 1990; revised 6 September 1990.
ISSN / 90 /$O.O0 Published 1990 by Elsevier Science Publishing Company, Inc.
Pearson and Miller, 1972). The "simple" band ratio (NIR/Red) has been used, but other algebraic forms of ratios have also been proposed and implemented. These include log ratios (Goetz et al., 1975), arctangent ratios (Wecksung and Breedlove, 1977), and normalized differences (Kriegler et al., 1969), among others. All of these ratio types are functionally equivalent but differ from each other nonlinearly (Perry and Lautenschlager, 1984; Crippen, 1989). The normalized difference, N I R - Red NIR + Red ' has become a standard form of band ratio for vegetation studies and is now widely used (e.g., Tarpley et al., 1984; Townshend et al., 1985; Tucker et al., 1986). The normalized difference (one subtraction, one addition, and one division) is computationally more cumbersome than the simple ratio (just one division). Possible reasons why it has often been favored over the simple ratio (and other forms of ratios) for vegetation studies include the following: 1. A closer functional linearity with measures of vegetation amount, such as leaf area index (although this has not been documented clearly and consistently). 2. Its finite range of - 1 to 1, compared to the more awkward 0 to ~ range of simple ratios.
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Crippen
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3. The self-perpetuating benefits of using an index that is increasingly accepted as an established standard. This short communication does not address the merits of the normalized difference versus the simple ratio or other ratios in terms of the linearity of its relationship to vegetation amount, nor versus indices that are not functionally related to the simple ratio but which may more adequately suppress the effects of variable soil backgrounds (e.g., Richardson and Wiegand, 1977; Huete, 1988). It also does not address other important considerations, such as data adjustments for atmospheric effects and sensor calibration (e.g., Crippen, 1987; Price, 1987; Singh and Saull, 1988). Instead, the following discussion simply shows that a faster, more direct formula can be used to produce resuits that are functionally and linearly identical to normalized differences.
T H E FASTER I N D E X
Computationally, the proposed index differs from the normalized difference vegetation index (NDVI) only in that the subtraction of the red radiance in the ratio numerator is eliminated. Thus, the formula becomes NIR NIR + Red " This index ranges from 0 to 1, thus avoiding negative values (unlike the NDVI). It measures the percentage of near-infrared radiance in relation to the combined radiance in both the nearinfrared and red bands and can therefore be termed the "infrared percentage vegetation index." The linear relationship between this index and the NDVI is shown algebraically below: NIR I(NIR-Red ) NIR+Red=2 NIR+Red +1 . Thus, the proposed index differs from the NDVI only by a gain of 0.5 after an offset of 1. Figure 1 graphically shows this relationship.
DISCUSSION
Tests using task-specific software were run to demonstrate computational savings of 15-30% in
-
0.0 -1.0
-0.5
~ 0.0
0.5
1.0 NIR - Red NIR + Red
Figure 1. Linear relationshipbetween the normalizeddif-
ferencevegetationindex(abscissa)and the faster, never-negative "infraredpercentagevegetationindex"(ordinate). overall computer time in using the proposed index versus the normalized difference. Actual computational savings on various processing systems using various implementations will range from very substantial to very minor as data-calibration, indexscaling, and any other "overhead" calculations reduce the fraction of computer time devoted to the fundamental index calculation. However, the proposed index is always faster to some degree because it requires at least one fewer computational step. CONCLUSION Calculation of the normalized difference is not computationally demanding. A simplification that results in an equivalent vegetation index will therefore not be significant to many users. Nonetheless, it is interesting to realize that this widely used index is both unnecessarily "complex" (utilizing a useless step) and unnecessarily awkward (allowing negative-value results). More importantly, however, as data volumes grow with the increasing availability and use of multitemporal continental and global data sets, the advantages of the proposed index will become increasingly valuable. It has a nonnegative, finite range, and it is functionally and linearly identical with normalized differences, yet it provides increased computational speed. This work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.
Calculating the Vegetation Index Faster
REFERENCES Crippen, R. E. (1987), The regression intersection method of adjusting image data for band ratioing, Int. J. Remote Sens. 8:137-155. Crippen, R. E. (1989), Development of remote sensing techniques for the investigation of neotectonic activity in the eastern Transverse Ranges and vicinity, southern California, Ph.D. dissertation, University of California, Santa Barbara. Goetz, A. F. H., Billingsley, F. C., Gillespie, A. R., Abrams, M. J., Squires, R. L., Shoemaker, E. M., Lucchitta, I., and Elston, D. P. (1975), Application of ERTS images and image processing to regional geologic problems and geologic mapping in northern Arizona, JPL Technical Report 32-1597, Jet Propulsion Laboratory, Pasadena, CA. Huete, A. R. (1988), A soil-adjusted vegetation index, Remote Sens. Environ. 25:295-309. Jordan, C. F. (1969), Derivation of leaf area index from quality of light on the forest floor, Ecology 50:663-666. Kriegler, F. J., Malila, W. A., Nalepka, R. F., and Richardson, W. (1969), Preprocessing transformations and their effects on multispectral recognition, in Proceedings of the Sixth International Symposium on Remote Sensing of Environment, University of Michigan, Ann Arbor, MI, pp. 97-131. Pearson, R. L., and Miller, L. D. (1972), Remote mapping of standing crop biomass for estimation of the productivity of the shortgrass prairie, in Proceedings of the Eighth International Symposium on Remote Sensing of Environment, Environmental Research Institute of Michigan, Ann Arbor, MI, pp. 1357-1381.
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Perry, C. R., Jr., and Lautenschlager, L. F. (1984), Functional equivalence of spectral vegetation indices, Remote Sens. Environ. 14:169-182. Price, J. C. (1987), Calibration of satellite radiometers and the comparison of vegetation indices, Remote Sens. Environ. 21:15-27. Richardson, A. J., and Wiegand, C. L. (1977), Distinguishing vegetation from soil background information, Photogramm. Eng. Remote Sens. 43:1541-1552. Singh, S. M., and Saull, R. J. (1988), The effect of atmospheric correction on the interpretation of multitemporal AVHRRderived vegetation index dynamics, Remote Sens. Environ. 25:37-51. Tarpley, J. D., Schneider, S. R., and Money, R. L. (1984), Global vegetation indices from the NOAA-7 meteorological satellite, J. Climate Appl. Meteorol. 23:491-494. Townshend, J. R. G., Goff, T. E., and Tucker, C. J. (1985), Multitemporal dimensionality of images of normalized difference vegetation index at continental scales, IEEE Trans. Geosci. Remote Sens. 23:888-895. Tucker, C. J., Fung, I. Y., Keeling, C. D., and Gammon, R. H. (1986), Relationship between atmospheric CO 2 variations and a satellite-derived vegetation index, Nature 319: 195-199. Wecksung, G. W., and Breedlove, J. R., Jr. (1977), Some techniques for digital processing, display, and interpretation of ratio images in multispectral remote sensing, in Applications of Digital Image Processing, Proceedings of Society of Photo-Optical Instrumentation Engineers, Bellingham, Washington, Vol. 119, pp. 47-54.
Short Communication
Calculating the Vegetation Index Faster Robert E. Crippen Jet Propulsion Laboratory, California Institute of Technology, Pasadena
T h e near-infrared (NIR) versus red "'infrared percentage vegetation index," NIR /(NIR + Red), is functionally and linearly equivalent to the normalized difference vegetation index, (NIR-Red) / (NIR + Red). Advantageously, it is both computationally faster and never negative. INTRODUCTION This short communication describes a vegetation index that is functionally and linearly equivalent to, but computationally faster than, the normalized difference vegetation index. Unlike the normalized difference, the new index has a fully non-negative range. Computational savings of 15-30% are possible, which is especially significant in the monitoring of global biomass and in other vegetation studies that require the processing of vast amounts of remotely sensed data. BACKGROUND
The ratio of radiances in the near-infrared (NIR) and red bands has long been recognized as a useful measure of vegetation amount (Jordan, 1969; Address correspondence to Robert E. Crippen, Jet Propulsion Laboratory 300-233, California Institute of Technology, Pasadena, California 91109. Received 9 July 1990; revised 6 September 1990.
ISSN / 90 /$O.O0 Published 1990 by Elsevier Science Publishing Company, Inc.
Pearson and Miller, 1972). The "simple" band ratio (NIR/Red) has been used, but other algebraic forms of ratios have also been proposed and implemented. These include log ratios (Goetz et al., 1975), arctangent ratios (Wecksung and Breedlove, 1977), and normalized differences (Kriegler et al., 1969), among others. All of these ratio types are functionally equivalent but differ from each other nonlinearly (Perry and Lautenschlager, 1984; Crippen, 1989). The normalized difference, N I R - Red NIR + Red ' has become a standard form of band ratio for vegetation studies and is now widely used (e.g., Tarpley et al., 1984; Townshend et al., 1985; Tucker et al., 1986). The normalized difference (one subtraction, one addition, and one division) is computationally more cumbersome than the simple ratio (just one division). Possible reasons why it has often been favored over the simple ratio (and other forms of ratios) for vegetation studies include the following: 1. A closer functional linearity with measures of vegetation amount, such as leaf area index (although this has not been documented clearly and consistently). 2. Its finite range of - 1 to 1, compared to the more awkward 0 to ~ range of simple ratios.
71
72
Crippen
10]
3. The self-perpetuating benefits of using an index that is increasingly accepted as an established standard. This short communication does not address the merits of the normalized difference versus the simple ratio or other ratios in terms of the linearity of its relationship to vegetation amount, nor versus indices that are not functionally related to the simple ratio but which may more adequately suppress the effects of variable soil backgrounds (e.g., Richardson and Wiegand, 1977; Huete, 1988). It also does not address other important considerations, such as data adjustments for atmospheric effects and sensor calibration (e.g., Crippen, 1987; Price, 1987; Singh and Saull, 1988). Instead, the following discussion simply shows that a faster, more direct formula can be used to produce resuits that are functionally and linearly identical to normalized differences.
T H E FASTER I N D E X
Computationally, the proposed index differs from the normalized difference vegetation index (NDVI) only in that the subtraction of the red radiance in the ratio numerator is eliminated. Thus, the formula becomes NIR NIR + Red " This index ranges from 0 to 1, thus avoiding negative values (unlike the NDVI). It measures the percentage of near-infrared radiance in relation to the combined radiance in both the nearinfrared and red bands and can therefore be termed the "infrared percentage vegetation index." The linear relationship between this index and the NDVI is shown algebraically below: NIR I(NIR-Red ) NIR+Red=2 NIR+Red +1 . Thus, the proposed index differs from the NDVI only by a gain of 0.5 after an offset of 1. Figure 1 graphically shows this relationship.
DISCUSSION
Tests using task-specific software were run to demonstrate computational savings of 15-30% in
-
0.0 -1.0
-0.5
~ 0.0
0.5
1.0 NIR - Red NIR + Red
Figure 1. Linear relationshipbetween the normalizeddif-
ferencevegetationindex(abscissa)and the faster, never-negative "infraredpercentagevegetationindex"(ordinate). overall computer time in using the proposed index versus the normalized difference. Actual computational savings on various processing systems using various implementations will range from very substantial to very minor as data-calibration, indexscaling, and any other "overhead" calculations reduce the fraction of computer time devoted to the fundamental index calculation. However, the proposed index is always faster to some degree because it requires at least one fewer computational step. CONCLUSION Calculation of the normalized difference is not computationally demanding. A simplification that results in an equivalent vegetation index will therefore not be significant to many users. Nonetheless, it is interesting to realize that this widely used index is both unnecessarily "complex" (utilizing a useless step) and unnecessarily awkward (allowing negative-value results). More importantly, however, as data volumes grow with the increasing availability and use of multitemporal continental and global data sets, the advantages of the proposed index will become increasingly valuable. It has a nonnegative, finite range, and it is functionally and linearly identical with normalized differences, yet it provides increased computational speed. This work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.
Calculating the Vegetation Index Faster
REFERENCES Crippen, R. E. (1987), The regression intersection method of adjusting image data for band ratioing, Int. J. Remote Sens. 8:137-155. Crippen, R. E. (1989), Development of remote sensing techniques for the investigation of neotectonic activity in the eastern Transverse Ranges and vicinity, southern California, Ph.D. dissertation, University of California, Santa Barbara. Goetz, A. F. H., Billingsley, F. C., Gillespie, A. R., Abrams, M. J., Squires, R. L., Shoemaker, E. M., Lucchitta, I., and Elston, D. P. (1975), Application of ERTS images and image processing to regional geologic problems and geologic mapping in northern Arizona, JPL Technical Report 32-1597, Jet Propulsion Laboratory, Pasadena, CA. Huete, A. R. (1988), A soil-adjusted vegetation index, Remote Sens. Environ. 25:295-309. Jordan, C. F. (1969), Derivation of leaf area index from quality of light on the forest floor, Ecology 50:663-666. Kriegler, F. J., Malila, W. A., Nalepka, R. F., and Richardson, W. (1969), Preprocessing transformations and their effects on multispectral recognition, in Proceedings of the Sixth International Symposium on Remote Sensing of Environment, University of Michigan, Ann Arbor, MI, pp. 97-131. Pearson, R. L., and Miller, L. D. (1972), Remote mapping of standing crop biomass for estimation of the productivity of the shortgrass prairie, in Proceedings of the Eighth International Symposium on Remote Sensing of Environment, Environmental Research Institute of Michigan, Ann Arbor, MI, pp. 1357-1381.
73
Perry, C. R., Jr., and Lautenschlager, L. F. (1984), Functional equivalence of spectral vegetation indices, Remote Sens. Environ. 14:169-182. Price, J. C. (1987), Calibration of satellite radiometers and the comparison of vegetation indices, Remote Sens. Environ. 21:15-27. Richardson, A. J., and Wiegand, C. L. (1977), Distinguishing vegetation from soil background information, Photogramm. Eng. Remote Sens. 43:1541-1552. Singh, S. M., and Saull, R. J. (1988), The effect of atmospheric correction on the interpretation of multitemporal AVHRRderived vegetation index dynamics, Remote Sens. Environ. 25:37-51. Tarpley, J. D., Schneider, S. R., and Money, R. L. (1984), Global vegetation indices from the NOAA-7 meteorological satellite, J. Climate Appl. Meteorol. 23:491-494. Townshend, J. R. G., Goff, T. E., and Tucker, C. J. (1985), Multitemporal dimensionality of images of normalized difference vegetation index at continental scales, IEEE Trans. Geosci. Remote Sens. 23:888-895. Tucker, C. J., Fung, I. Y., Keeling, C. D., and Gammon, R. H. (1986), Relationship between atmospheric CO 2 variations and a satellite-derived vegetation index, Nature 319: 195-199. Wecksung, G. W., and Breedlove, J. R., Jr. (1977), Some techniques for digital processing, display, and interpretation of ratio images in multispectral remote sensing, in Applications of Digital Image Processing, Proceedings of Society of Photo-Optical Instrumentation Engineers, Bellingham, Washington, Vol. 119, pp. 47-54.