An Analysis of Angle-Based With Ratio-Based ... - Semantic Scholar
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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 44, NO. 9, SEPTEMBER 2006
An Analysis of Angle-Based With Ratio-Based Vegetation Indices Zhangyan Jiang, Alfredo R. Huete, Member, IEEE, Jing Li, and Yunhao Chen
Abstract—Remotely sensed, angle-based vegetation indices that measure vegetation amounts by the angle between an approximated soil line and a simulated vegetation isoline in the red– near-infrared reflectance space were developed and evaluated in this paper. Ünsalan and Boyer previously proposed an angle-based vegetation index, θ (denoted as θNDVI in this paper), based on the normalized difference vegetation index (NDVI) with the objective of overcoming the saturation problem in the NDVI. However, θNDVI did not consider strong soil background influences present in the NDVI. To reduce soil background noise, an angle-based vegetation index, θSAVI , based on the soil-adjusted vegetation index (SAVI), was derived using trigonometric analysis. The performance of θNDVI and θSAVI was evaluated and compared with their corresponding vegetation indices, NDVI and SAVI. The soil background influence on θNDVI was found to be as significant as that on the NDVI. θNDVI was found to be more sensitive to vegetation amount than the NDVI at low vegetation density levels, but less sensitive to vegetation fraction at high vegetation density levels. Thus, the saturation effect at high vegetation density levels encountered in the NDVI was not mitigated by θNDVI . By contrast, θSAVI exhibited insignificant soil background effects and weaker saturation, as in SAVI, but also improved upon the dynamic range of SAVI. Analyses and evaluation suggest that θSAVI is an optimal vegetation index to assess and monitor vegetation cover across the entire range of vegetation fraction density levels and over a wide variety of soil backgrounds. Index Terms—θSAVI , angle-based vegetation indices, saturation effect, soil background effects.
I. I NTRODUCTION
M
ANY strategies have evolved over the last two decades to extract land surface biophysical information from remotely sensed data (e.g., [1]–[4]). The interpretation of the radiometric information gathered on vegetation is mainly based on spectral variations observed among a small number of broad wavelength bands such as SPOT Haute Résolution Visible (HRV), the Landsat Thematic Mapper (TM), or the NOAA Advanced Very High Resolution Radiometer (AVHRR). Although some sensors such as the Earth Observing System Moderate Resolution Imaging Spectroradiometer (MODIS) have addi-
Manuscript received September 28, 2005; revised January 30, 2006. This work was supported in part by the Project of the Ministry of Education on Doctorial Discipline of China (20030027014) and in part by the Natural Science Foundation of China (40201036). Z. Jiang, J. Li, and Y. Chen are with the College of Resources Science and Technology, Beijing Normal University, Key Laboratory of Environmental Change and Natural Disaster Research of the Education Ministry of China, Beijing 100875, China (e-mail: [email protected]). A. R. Huete is with the Department of Soil, Water, and Environmental Science, University of Arizona, Tucson, AZ 85721 USA. Digital Object Identifier 10.1109/TGRS.2006.873205
tional spectral bands than the red and near-infrared (NIR), a large proportion of studies evaluating vegetation amount remain focused on the use of these two bands because red and NIR bands provide a high contrast between soil and vegetation optical properties [5]–[10]. One important method of extracting canopy biophysical characteristics from radiometric measurements involves the use of vegetation indices. The normalized difference vegetation index (NDVI), which is the difference of the NIR and red bands divided by their sum, has been the most widely used index in global vegetation studies [11]–[15], crop management [16]–[18], land cover studies [19]–[21], and climate studies [22], [23]. Nevertheless, and apart from atmospheric and bidirectional effects, NDVI has been limited by two prominent constraints, namely: 1) soil background contamination associated with variations in soil brightness, which may produce large variations in the NDVI for constant vegetation amounts [24]–[26], and 2) the saturation problem in high biomass areas [27], [28]. The sensitivity of the NDVI to biophysical quantities such as leaf area index (LAI) or vegetation fraction becomes increasingly weak with increasing vegetation densities beyond a threshold value (e.g., [29] and [30]). Significant progress has been made in improving the vegetation index equations themselves, primarily in reducing canopy background, atmospheric contamination, and saturation problems in the NDVI [7], [8], [31]–[33]. Huete [7] found that vegetation biophysical isolines in NIR–red reflectance space, i.e., lines of constant vegetation amount but varying pixel brightness, are neither parallel to a soil line nor converge at the origin, but instead approximately converge at a point on the soil line shifting from the origin in the negative direction. For various crop canopies, the convergence point was approximately at (−0.25, −0.25). The soil-adjusted vegetation index (SAVI) was subsequently developed based on this general vegetation biophysical isoline behavior SAVI =
N −R (1 + L) N +R+L
(1)
where N and R are NIR and red reflectances, respectively. With the soil adjustment factor L (usually L = 0.5), SAVI minimizes soil brightness influences, which are prominent in ratio-based vegetation indices such as NDVI [24], [25]. SAVI minimizes first-order soil–vegetation interactions by simple modeling of differential red and NIR flux extinction through vegetated canopies [7], which are neither considered in rationor orthogonal-based indices, such as NDVI, the difference
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vegetation index (DVI), defined as the difference between NIR and red reflectances [6], and the perpendicular vegetation index (PVI) [5]. PVI is defined as PVI =
N − aR − b √ 1 + a2
(2)
where a and b are the slope and intercept of a soil line, respectively. Using a radiative transfer model, Baret et al. [34] introduced soil line parameters into SAVI formulation to reduce soil background influences for plant canopies with very low LAI or low vegetation coverage and found vegetation biophysical isolines to converge at another point (S) along the soil line with abscissa—X, resulting in the transformed SAVI (TSAVI). Baret and Guyot [30] gave an improved version of the initial definition TSAVI =
a(N − aR − b) aN + R − ab + X(1 + a2 )
(3)
where the value of X was adjusted to minimize soil background effects (X = 0.08). With the goal of overcoming the saturation problem of NDVI, Ünsalan and Boyer [28] developed a new vegetation index, θ, based on NDVI and principal components analysis (PCA) in red–NIR reflectance space, defined as θ=
4 arctan(NDVI). π
(4)
Inasmuch as θ is a nonlinear transformation of NDVI, the isolines of equal θ values are the same as those of NDVI, which are lines convergent to the origin, but with the values of θ transformed from the NDVI values by the inverse tangent function. Graphically, the value of a θ isoline in red–NIR space is the ratio of the angle between the isoline and the approximated soil line Y = X to the maximal angle π/4. In this sense, θ is an angle-based vegetation index. By applying this nonlinear transformation, Ünsalan and Boyer [28] found that the nonlinearity and saturation problems of NDVI were offset by θ based on the comparison of entropies of θ with those of the NDVI in several images. However, the linearity of θ has not been theoretically analyzed nor explained, and the soil background contamination contained in NDVI may not be reduced by θ because it is specifically designed to overcome the saturation problem of NDVI. Inasmuch as SAVI is designed to minimize the soil background influence, an angle-based vegetation index derived from SAVI instead of NDVI may be helpful to reduce the soil background influence on θ. The purpose of this paper is to derive an angle-based vegetation index with minimal soil background contamination and enhanced sensitivity to vegetation biophysical parameters, such as vegetation fraction. The performances of the two angle-based vegetation indices are then evaluated and compared with their corresponding NDVI and SAVI.
Fig. 1. Vegetation index isolines and their angles in red–NIR reflectance space. (a) Isolines convergent to the origin as in NDVI isolines. (b) Isolines convergent to a shifted origin as in the case of SAVI isolines. (c) Isolines convergent to a shifted origin as in the case of TSAVI isolines.
II. D ERIVATION OF A NGLE -B ASED V EGETATION I NDICES If the vegetation amount of a pixel in red–NIR reflectance space [Fig. 1(a)], with red reflectance R and NIR reflectance N , is measured by the angle α between an approximated soil line (baseline) Y = X and the line formed by the spectral point of the pixel, (R, N ) to the origin, the tangent function of α can be calculated by tan α = tan(γ − β)
(5a)
γ = arctan(N/R)
(5b)
β = π/4.
(5c)
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Thus, tan(α) can be written in terms of R and N , which is equivalent to the NDVI tan α =
N −R = NDVI. N +R
(6)
Ünsalan and Boyer [28] found this formulation by way of PCA in red–NIR reflectance space, then calculated α from the NDVI and normalized this angle by π/4 (4). However, Huete [7] found that vegetation biophysical isolines in NIR–red reflectance space are not convergent at the origin, and the increase of soil background brightness would result in the decrease of the NDVI with constant vegetation density. Vegetation index isoline behavior may be graphically modeled by shifting the red–NIR space origin toward an approximate isoline convergence point E (−0.25, −0.25) [Fig. 1(b)] [7]. Similar to α, the angle α between the soil line and a simulated vegetation index isoline can be used as a measure of vegetation amount of a pixel [Fig. 1(b)]. Similarly, α can be calculated by
tan α = tan(γ − β ) N + 0.25 γ = arctan R + 0.25 β = π/4.
(7a) (7b) (7c)
Thus, tan(α ) can be expressed in terms of R and N , which is different from the SAVI only by a scaling factor of 1.5 tan α =
N −R = SAVI/1.5. N + R + 0.5
(8)
According to experimental measurements [24], [35], the red and NIR reflectances of infinitely dense vegetation are approximately 0.03 and 0.7, respectively. Thus, the maximal α corresponding to infinite LAI can be estimated as 0.5 rad. Normalizing α , we can define a new angle-based vegetation index, θSAVI N −R θSAVI = 2 arctan = 2 arctan(SAVI/1.5). N + R + 0.5 (9) Baret et al. [34] used a locally measured soil line Y = aX + b as the baseline and assumed that the convergence point of vegetation index isolines was located at point S (−X, −aX + b) [Fig. 1(c)]. In this case, the angle α between the soil line and a vegetation index isoline can be calculated by tan α = tan(γ − β ) N + aX − b γ = arctan R+X β = arctan(a).
(10a) (10b) (10c)
Similarly, tan(α ) can be expressed in terms of R and N , which is different from TSAVI only by a scaling factor a tan α =
N − aR − b = TSAVI/a. aN + R − ab + X(1 + a2 )
TABLE I DYNAMIC RANGE OF THE FOUR VEGETATION INDICES
(11)
If the vertices of α and α (points E and S) are located at the same point, α and α are equivalent in concept, and their relationship is α = α + αsoil
(12)
where αsoil is the angle between the soil line Y = aX + b and the line Y = X. For this reason, TSAVI will not be used in the comparison of the different indices. III. E VALUATION OF θSAVI AND I TS C OMPARISON W ITH O THER V EGETATION I NDICES To facilitate comparisons, we denote θ in (4) as θNDVI . The baseline values of the four vegetation indices (NDVI, θNDVI , SAVI, and θSAVI ) are 0, but their maximum values are different according to the reflectances of infinitely dense vegetation mentioned above. The dynamic ranges of the four vegetation indices (maximum values minus values of the baseline) are listed in Table I. The dynamic range of θNDVI is slightly larger than that of NDVI, whereas the dynamic range of θSAVI is significantly larger than that of SAVI. Although the SAVI was formulated from the NDVI equation, there was a loss in the amplitude of the vegetation index signal between NDVI and SAVI [7]. The NDVI and θNDVI are normalized to 1 when red reflectance is 0 and NIR reflectance is larger than 0, and the SAVI is normalized to 1 when red and NIR reflectances are 0 and 1, respectively. To obtain the same dynamic range as θSAVI , the SAVI can be renormalized using the reflectances of infinitely dense vegetation (denoted as SAVIN ), which results in SAVI being multiplied by 1.22. A. Sensitivity to Angles The two angle-based vegetation indices, θNDVI and θSAVI , were evaluated and compared with their corresponding vegetation indices, NDVI and SAVIN . We first compared the sensitivities of the four vegetation indices to the angles between the baseline and their vegetation index isolines, α or α [Fig. 1(a)–(c)]. The derivatives of the four vegetation indices on their corresponding angles are dNDVI dα dθNDVI dα dSAVIN dα dθSAVI dα
= sec2 α =
4 π
(13a) (13b)
= 1.84 sec2 α
(13c)
= 2.
(13d)
The derivatives of the two angle-based vegetation indices on angles are constant. However, the derivatives of the nonangular
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Fig. 2. Sensitivities of the four vegetation indices to the angles between the soil line and their vegetation index isolines.
Fig. 3. Vegetation index values for different vegetation fractions over various soil backgrounds.
vegetation indices, NDVI and SAVIN , are determined by their angle values. According to the reflectances of infinitely dense vegetation, the maximal α and α are 42.5◦ and 28.6◦ , respectively. The value of α and α of the baseline is obviously 0. The derivatives of the four vegetation indices are presented in Fig. 2. The derivative of θNDVI on α is larger than that of NDVI when α is less than 27.6◦ and smaller than that of NDVI when α is larger than 27.6◦ . Thus, θNDVI is more sensitive to α than NDVI at low vegetation density levels and less sensitive to α at high vegetation density levels. If α can indicate vegetation amounts, the saturation effect of the NDVI at high vegetation density levels was not mitigated by θNDVI . Analogously, the derivative of θSAVI on α is larger than that of SAVIN when α is less than 16.6◦ and smaller than that of SAVIN when α is larger than 16.6◦ .
TABLE II STANDARD DEVIATIONS OF VEGETATION INDICES CAUSED BY S OIL B ACKGROUND I NFLUENCES
B. Soil Background Influence Ground-based spectral measurements of cotton canopies for a full season (0%–100% green cover) under varying soil background conditions [24] were used for the evaluation of the performance of θSAVI and subsequent comparisons with the other vegetation indices. At each cotton density level, soil backgrounds were varied by inserting different soils with a wide range of soil brightness underneath the cotton canopies. This data set enables us to study soil background effects on vegetation indices and the sensitivities of vegetation indices to vegetation amount. The values of the three vegetation indices, θNDVI , θSAVI , and SAVIN , for different vegetation density levels over various soil backgrounds are presented in Fig. 3. For the various constant vegetation density levels, soil background influences on θNDVI were evident when vegetation fractions were less than 75% and insignificant when vegetation fractions exceeded 75% and θNDVI became saturated. In contrast, the soil background influence was greatly reduced by SAVIN and θSAVI over the full range of vegetation density levels. The standard deviations of the four vegetation indices caused by soil background influences are summarized in Table II. The soil background influence on θNDVI was slightly larger than that of the NDVI when vegetation fraction was less than 25% and
slightly smaller than that of the NDVI at higher vegetation fractions. The soil background influence on θSAVI was almost equal to that of SAVIN at each vegetation density level. The total standard deviations of the angle-based vegetation indices were almost equal to the nonangular vegetation indices, indicating that the soil background influence contained in the ratio-based vegetation indices is not reduced by their corresponding anglebased vegetation indices. Therefore, in general, the strong soil background contamination contained in the NDVI was not reduced by θNDVI , and the soil background influence on θSAVI almost remained as small as that of SAVIN . The overall soil background influences on NDVI and θNDVI were about five times those on SAVIN and θSAVI , respectively. C. Sensitivities to Vegetation Fraction The sensitivities of vegetation indices to vegetation amount may be presented by the slopes of the vegetation index versus vegetation fraction (VI−f ) curves at a specific vegetation fraction f . The average slopes, dVI/df , were estimated by the average difference in vegetation index values at two adjacent vegetation fraction levels divided by the corresponding vegetation fraction interval over eight vegetation intervals
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TABLE III VEGETATION INDEX SENSITIVITIES AS REPRESENTED BY THE MEAN SLOPES OF VEGETATION INDEX–VEGETATION FRACTION CURVES
(Table III). NDVI was sensitive to vegetation fraction at green levels below 40% and became less sensitive to vegetation fraction with increases in vegetation and began to saturate at vegetation fractions above 75%. A small negative slope at the highest green level demonstrated that the NDVI no longer responds to increases of vegetation amount. The negative slope may be explained by a slight increase of red reflectance at 100% vegetation fraction relative to that at 95% vegetation fraction [24]. The sensitivity of θNDVI to the vegetation fraction was slightly larger than that of the NDVI at green levels below 40% and slightly smaller than that of the NDVI at the higher vegetation fraction levels. The NDVI and θNDVI sensitivities decreased with increases of vegetation fraction, but the decrease rate of the θNDVI sensitivity was much stronger than that of NDVI sensitivity, demonstrating that the saturation problem of the NDVI remains in θNDVI , with the linearity of θNDVI slightly worse than that of the NDVI according to our data set. The overall sensitivities of NDVI and θNDVI were equal, suggesting that the sensitivity of θNDVI to vegetation fraction is not improved compared with the NDVI as a whole. The sensitivity of SAVIN was relatively constant, although it also decreased with increases in vegetation fraction similar to the NDVI. The sensitivity of SAVIN at the higher green density levels remained about half of the larger sensitivity values at the lower green density levels, indicating that the linearity of SAVI is improved over that of NDVI. There was a steep increase in the slope of SAVIN and θSAVI at the 90%–95% interval, which is attributed to rapidly accumulating green biomass with only gradual lateral percent cover increases at this stage [24]. The sensitivity of θSAVI behaved similar to that of SAVIN , and their overall sensitivities were equal (Table III). The sensitivity of PVI normalized with the reflectances of infinite dense vegetation (PVIN ) was also calculated to compare the sensitivity of orthogonal vegetation indices with those of other types of vegetation indices. The PVIN sensitivities were consistent at all vegetation fraction intervals except for at 90%–95% interval. No saturation effects could be found for PVIN in our data. As an orthogonal vegetation index, PVI is a linear function of red and NIR reflectances with constant sensitivity to red and NIR reflectances, independent of red
Fig. 4. Vegetation index sensitivities to the NIR reflectance as a function of NIR and red reflectances. (a) NDVI sensitivity. (b) SAVI sensitivity.
and NIR reflectances (i.e., for any vegetation density level) and, thus, sensitive to vegetation fraction unless both red and NIR reflectances become insensitive to vegetation fraction. However, the NDVI becomes decreasingly sensitive to the NIR reflectance at high NIR and low red reflectances [Fig. 4(a)]. For N/R 1, both the numerator and denominator of the NDVI equation approach equivalence, and thus, the sensitivity of the NDVI to the NIR reflectance becomes negligible [33]. The SAVI is less sensitive to NIR reflectance at low NIR values and more sensitive to NIR reflectance than the NDVI at high NIR values, and this sensitivity is almost independent of the value of red reflectance [Fig. 4(b)]. The θNDVI and θSAVI sensitivities on NIR reflectance are similar to those of NDVI and SAVI, respectively. When vegetation fractions are larger than 60%–80%, red reflectance approached asymptotic values and exhibited little additional change, whereas NIR reflectances continued to increase with the increase of vegetation fraction [24], [33]. Thus, the saturation effects of NDVI and θNDVI are more prominent than those of SAVI and θSAVI , which, in turn, are more prominent than those of PVI. D. Differences Between NDVI and SAVIN With Their Angle-Based Counterparts The relationships of the differences between angle-based vegetation indices and their corresponding nonangular vegetation index counterparts with vegetation fraction over various soil backgrounds are presented in Fig. 5. The difference
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TABLE IV ENTROPIES OF THE FOUR VEGETATION INDICES SAMPLED AT T HREE I NTERVALS (NATS)
Fig. 5. Difference between angle-based vegetation indices and their nonangular vegetation index counterparts for different vegetation fractions over various soil backgrounds.
between θNDVI and NDVI (θNDVI − NDVI) was positively related to vegetation fraction at green density levels below 25%, but negatively related to vegetation fraction at higher green density levels, resulting in the slightly larger sensitivity of θNDVI at low green density levels and smaller sensitivity at green levels above 40% compared with the NDVI. The differences between θNDVI and NDVI at intermediate vegetation fraction levels were larger than those at high vegetation fraction levels, aggravating the saturation effect of θNDVI compared with NDVI. The difference between θSAVI and SAVIN was much smaller than the difference between θNDVI and NDVI and approached 0 at very low and very high vegetation density levels. E. Entropies The entropy measures the amount of information obtained, on average, in drawing samples from a given distribution by quantifying the uncertainty or randomness in the experiment [28]. Therefore, the entropy increases as the distribution becomes more uniform, and relates to sample intervals, with the smaller sample intervals resulting in less information loss and larger entropy. The entropy E is defined as E=−
N
p(i) log (p(i))
(14)
i=1
where p(i) is the probability of a stochastic variable within an interval i, and N is the total number of quantization levels, related to the length of intervals. Here, vegetation indices were regarded as stochastic variables, and p(i) was calculated by the frequency of vegetation index values within an interval. Entropies of the four vegetation index experimental data sets were calculated for three sample intervals, 0.05, 0.1, and 0.2 (Table IV). For interval 0.05, the θNDVI entropy was the same as the NDVI entropy, but the θSAVI entropy was larger than the SAVIN entropy. For interval 0.1, the entropies of the anglebased vegetation indices were larger than those of the NDVI and SAVI counterparts, indicating more uniform distributions of values in the angle-based vegetation indices at this interval. The low NDVI entropy was partly caused by nonlinearity
and saturation effects, as 41.8% of NDVI values were within the 0.8–0.9 interval. With a small difference between θNDVI and the NDVI (about 0.04), the densest vegetation fraction group of θNDVI values was split into two intervals, 0.8–0.9 and 0.9–1.0 (Fig. 3), resulting in a more uniform distribution of θNDVI values, but not necessarily mitigating the saturation effect. At interval 0.2, the θNDVI entropy was less than that of the NDVI, but the entropy of θSAVI was equal to that of SAVIN . The entropies of θSAVI and SAVIN were larger than those of θNDVI and NDVI at intervals 0.1 and 0.2, indicating a weaker saturation effect and better linearity of θSAVI and SAVIN compared with the NDVI counterparts. IV. C ONCLUSION AND D ISCUSSION In this study, we first introduced an angle-based vegetation index, θNDVI , which has been derived from NDVI through PCA by Ünsalan and Boyer [28]. Inspired by their ideas, we graphically studied θNDVI in the red–NIR reflectance space. Because of the strong soil background influences on NDVI, we also derived another angle-based vegetation index, θSAVI , from SAVI through trigonometric analysis to minimize soil background influences. The performance of the two anglebased vegetation indices was then evaluated and compared with the corresponding NDVI and SAVI. The soil background influence on θNDVI was found to be as prominent as that of NDVI. θNDVI is more sensitive to vegetation amount than NDVI at low vegetation density levels and less sensitive to vegetation amount than the NDVI at high vegetation density levels. Unlike the findings of Ünsalan and Boyer [28], we found that the saturation problem at high vegetation density levels encountered by the NDVI was not mitigated by θNDVI . The dynamic range of θSAVI was found to be larger than that of the SAVI. θSAVI was evaluated and compared with the normalized SAVI (SAVIN ). The difference between them was very small, and they had similar soil background influence and sensitivities to vegetation fraction. The saturation effect of SAVI and θSAVI was also much weaker compared with NDVI and θNDVI . The entropies of vegetation index values measured the uniformities of distributions of vegetation index values. Saturation effects in vegetation indices result in a concentration of vegetation index values within a particular range of values and hence small values of entropies. The larger entropy of θSAVI indicates a weaker saturation effect, better linearity, larger dynamic range, and enhanced sensitivity of θSAVI compared with the other vegetation indices.
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Overall, the performance of NDVI was not improved by its corresponding angle-based vegetation index, θNDVI . However, θSAVI not only maintained the merits of SAVI, such as negligible soil background influences, weak saturation, and better linearity, but also resulted in a larger dynamic range than SAVI. Our results and analyses suggest that θSAVI is an optimal vegetation index to evaluate and monitor vegetation cover across all density levels and over a wide variety of soil backgrounds. Our study also provided geometrical interpretations for NDVI, SAVI, and TSAVI and revealed that they are tangent functions of the angles between an approximated soil line and their vegetation index isolines in red–NIR reflectance space. Angle-based vegetation indices use spectral angles as measurements of vegetation amount, whereas their NDVI and SAVI counterparts use the tangent functions of angles as measurements of vegetation amount, although they share the same vegetation isolines. Some of the main limitations of ratio-based vegetation indices, such as NDVI, are the high saturation and nonlinearity effects. The orthogonal vegetation indices, such as PVI, are linear functions of red and NIR reflectances and thus have little saturation effect with respect to vegetation fraction unless red and NIR reflectances become saturated simultaneously, but they measure vegetation amount by the perpendicular distance of a vegetated spectral point to a soil line in red–NIR space. The perpendicular distance, however, is influenced by variations in soil brightness because the actual observed biophysical or greenness lines are not parallel to the bare soil line [24]. The SAVI equation (1) reduces to the NDVI equation when L is 0 and reduces to the DVI equation when L goes to infinity [7]. We may conclude that the linearity of the SAVI will be improved with an increase of L. However, increases in L greater than 0.5 would also introduce increasing soil background influences in the SAVI [7]. It would be highly desirable to improve both the linearity and sensitivity of the SAVI and θSAVI across all vegetation density levels without introducing soil background influences. The performance of θSAVI should be evaluated further using other data sets and satellite images. Including an atmospheric resistance term in the formulation of θSAVI may also be helpful to improve this index. R EFERENCES [1] W. Verhoef, “Light scattering by leaf layers with application to canopy reflectance modeling: The SAIL model,” Remote Sens. Environ., vol. 16, no. 2, pp. 125–141, Oct. 1984. [2] P. J. Sellers, J. A. Berry, G. J. Collatz, C. B. Field, and F. G. Hall, “Canopy reflectance, photosynthesis, and transpiration. III. A reanalysis using improved leaf models and a new canopy integration scheme,” Remote Sens. Environ., vol. 42, no. 3, pp. 187–216, Dec. 1992. [3] R. B. Myneni and G. Asrar, “Simulation of space measurements of vegetation canopy bidirectional reflectance factors,” Remote Sens. Rev., vol. 7, no. 1–2, pp. 19–41, 1993. [4] R. H. Fraser, T. A. Abuelgasim, and R. Latifovic, “A method for detecting large-scale forest cover change using coarse spatial resolution imagery,” Remote Sens. Environ., vol. 95, no. 4, pp. 414–427, Apr. 2005. [5] A. J. Richardson and C. L. Wiegand, “Distinguishing vegetation from soil background information,” Photogramm. Eng. Remote Sens., vol. 43, no. 12, pp. 1541–1552, 1977. [6] C. J. Tucker, “Red and photographic infrared linear combinations for monitoring vegetation,” Remote Sens. Environ., vol. 8, no. 2, pp. 127–150, May 1979.
[7] A. R. Huete, “A soil-adjusted vegetation index (SAVI),” Remote Sens. Environ., vol. 25, no. 3, pp. 295–309, Aug. 1988. [8] J. G. P. W. Clevers, “The application of a weighted infrared-red vegetation index for estimating leaf area index by correction for soil moisture,” Remote Sens. Environ., vol. 29, no. 1, pp. 25–37, Jul. 1989. [9] F. Baret, J. G. P. W. Clevers, and M. D. Steven, “The robustness of canopy gap fraction estimations from red and near-infrared reflectances: A comparison of approaches,” Remote Sens. Environ., vol. 54, no. 2, pp. 141–151, Nov. 1995. [10] M. Raffy and K. Soudani, “On the LAI of mixed soils-forests regions,” Int. J. Remote Sens., vol. 25, no. 15, pp. 3073–3090, Aug. 2004. [11] S. N. Goward, C. J. Tucker, and D. G. Dye, “North American vegetation patterns observed with the NOAA-7 Advanced Very High Resolution Radiometer,” Vegetatio, vol. 6, pp. 3–14, 1985. [12] J. R. G. Townshend, C. O. Justice, D. Skole, J. P. Malingreau, J. Cihlar, P. Teillet, F. Sadowski, and S. Ruttenberg, “The 1 km resolution global data set: Needs of the international geosphere biosphere programme,” Int. J. Remote Sens., vol. 15, no. 17, pp. 3417–3441, 1994. [13] C. J. Tucker and P. J. Sellers, “Satellite remote sensing of primary productivity,” Int. J. Remote Sens., vol. 7, no. 11, pp. 1395–1416, 1986. [14] J. P. Malingreau, C. J. Tucker, and N. Laporte, “AVHRR for monitoring global tropical deforestation,” Int. J. Remote Sens., vol. 10, no. 4, pp. 855–867, 1989. [15] Q. Wang, S. Adiku, J. Tenhunen, and A. Granier, “On the relationship of NDVI with leaf area index in a deciduous forest site,” Remote Sens. Environ., vol. 94, no. 2, pp. 244–255, Jan. 2005. [16] R. D. Jackson, P. N. Slater, and P. J. Pinter, “Discrimination of growth and water stress in wheat by various vegetation indices through clear and turbid atmospheres,” Remote Sens. Environ., vol. 13, no. 3, pp. 187–208, Jul. 1983. [17] M. S. Moran, Y. Inoue, and E. M. Barnes, “Opportunities and limitations for image-based remote sensing in precision crop management,” Remote Sens. Environ., vol. 61, no. 3, pp. 319–346, Sep. 1997. [18] P. S. Thenkabail, R. B. Smith, and E. D. Pauw, “Hyperspectral vegetation indices and their relationships with agricultural crop characteristics,” Remote Sens. Environ., vol. 71, no. 2, pp. 158–182, Feb. 2000. [19] J. R. G. Townshend, C. Justice, W. Li, C. Gurney, and J. McMaus, “Global land cover classification by remote sensing: Present capabilities and future possibilities,” Remote Sens. Environ., vol. 35, no. 2/3, pp. 243–256, Feb./Mar. 1991. [20] V. Caselles and E. Valor, “Mapping land surface emmisivity from NDVI: Application to European, African and American areas,” Remote Sens. Environ., vol. 57, no. 3, pp. 167–184, Sep. 1996. [21] J. M. C. Pereira, “A comparative evaluation of NOAA/AVHRR vegetation indexes for burned surface detection and mapping,” IEEE Trans. Geosci. Remote Sens., vol. 37, no. 1, pp. 217–226, Jan. 1999. [22] P. J. Sellers, C. J. Tucker, G. J. Collatz, S. O. Los, C. O. Justice, D. A. Dazlich, and D. A. Randali, “A global 1◦ by 1◦ NDVI data set for climate studies. Part 2—The adjustment of the NDVI and generation of global fields of terrestrial biophysical parameters,” Int. J. Remote Sens., vol. 15, no. 1717, pp. 3519–3545, 1994. [23] G. Gutman and A. Ignatov, “The derivation of the green vegetation fraction from NOAA/AVHRR data for use in numerical weather prediction models,” Int. J. Remote Sens., vol. 19, no. 8, pp. 1533–1543, May 1998. [24] A. R. Huete, R. D. Jackson, and D. F. Post, “Spectral response of a plant canopy with different soil backgrounds,” Remote Sens. Environ., vol. 17, no. 1, pp. 37–53, Feb. 1985. [25] C. D. Elvidge and R. J. P. Lyon, “Influence of rock-soil spectral variation on the assessment of green biomass,” Remote Sens. Environ., vol. 17, no. 3, pp. 265–279, Jun. 1985. [26] W. C. Bausch, “Soil background effects on reflectance-based crop coefficients for corn,” Remote Sens. Environ., vol. 46, no. 2, pp. 213–222, Nov. 1993. [27] J. Qi, A. Chehbouni, A. R. Huete, H. Y. Kerr, and S. Sorooshian, “A modified soil adjusted vegetation index,” Remote Sens. Environ., vol. 48, no. 2, pp. 119–126, May 1994. [28] C. Ünsalan and K. L. Boyer, “Linearized vegetation indices based on a formal statistical framework,” IEEE Trans. Geosci. Remote Sens., vol. 42, no. 7, pp. 1575–1585, Jul. 2004. [29] T. N. Carlson and D. A. Ripley, “On the relation between NDVI, fractional vegetation cover, and leaf area index,” Remote Sens. Environ., vol. 62, no. 3, pp. 241–252, Dec. 1997. [30] F. Baret and G. Guyot, “Potentials and limits of vegetation indices for LAI and APAR assessment,” Remote Sens. Environ., vol. 35, no. 2/3, pp. 161– 173, Feb./Mar. 1991. [31] Y. J. Kaufman and D. Tanré, “Atmospherically resistant vegetation index (ARVI) for EOS-MODIS,” IEEE Trans. Geosci. Remote Sens., vol. 30, no. 2, pp. 261–270, Mar. 1992.
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[32] H. Liu and A. R. Huete, “A feedback based modification of the NDVI to minimize canopy background and atmospheric noise,” IEEE Trans. Geosci. Remote Sens., vol. 33, no. 2, pp. 457–465, Mar. 1995. [33] A. A. Gitelson, “Wide dynamic range vegetation index for remote quantification of biophysical characteristics of vegetation,” J. Plant Physiol., vol. 161, no. 2, pp. 165–173, Feb. 2004. [34] F. Baret, G. Guyot, and D. Major, “TSAVI: A vegetation index which minimizes soil brightness effects on LAI and APAR estimation,” in Proc. 12th Can. Symp. Remote Sens. and IGARSS, Vancouver, BC, Canada, Jul. 10–14, 1989, pp. 1355–1358. [35] O. Lillesaeter, “Spectral reflectance of partly transmitting leaves: Laboratory measurements and mathematical modeling,” Remote Sens. Environ., vol. 12, no. 3, pp. 247–254, Jul. 1982.
Zhangyan Jiang received the B.S. degree from Jiangxi Normal University, Nanchang, China, in 1998, and the M.S. and Ph.D. degrees from Beijing Normal University, Beijing, China, in 2002 and 2006, respectively, all in geography. His research interests include optimization of remotely sensed vegetation indices, remote sensing of vegetation biophysical parameters, and retrieving land surface temperature by thermal infrared remote sensing.
Alfredo R. Huete (M’92) received the M.S. degree from the University of California at Berkeley and the Ph.D. degree from the University of Arizona, Tucson, in 1984, under the guidance of Ray D. Jackson. He is currently a Professor in the Department of Soil, Water, and Environmental Science, University of Arizona, where he serves as the Chair of the Interdisciplinary Academic Program, Committee on Remote Sensing and Spatial Analysis. He is a MODIS Science Team Member and is responsible for the development, implementation, and validation of the vegetation index products. He is part of the NPOESS Preparatory Project Science Team to evaluate vegetation indices as environmental data records. He is also an active Member of the Large-Scale Biosphere Atmosphere in the Amazon interdisciplinary experiment and serves on the editorial review board for Remote Sensing of the Environment.
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Jing Li received the B.S. degree in geography and the M.S. degree in graphics and remote sensing from Peking University, Beijing, China, in 1982 and 1985, respectively. He is currently the Director of the Institute of Resource Technology and Engineering, College of Resource Science and Technology, Beijing Normal University, Beijing. From 1990 to 1991, he was a Visiting Scholar at the University of Hawaii. From 1993 to 2003, he was with the Institute of Remote Sensing and Geographical Information Systems, Peking University. From 2003 up to the present, he has been a Professor with Beijing Normal University and Chief Engineer of the National Disaster Reduction Committee, Ministry of Civil Affairs of China. His research interests include remote sensing of natural resources, remote sensing applications in natural disaster reduction, and monitoring of oceanic and coastal ecology by remote sensing.
Yunhao Chen received the B.S. and M.S. degrees in resource management from the University of Science and Technology of China, Hefei, in 1994 and 1997, respectively, and the Ph.D. degree in geodesic engineering from the China University of Mining and Technology, Beijing, in 1999. He is currently an Assistant Professor at Beijing Normal University, Beijing, and a Special Research Scholar of the National Disaster Reduction Committee, Ministry of Civil Affairs of China. From 2000 to 2001, he did postdoctoral research in Beijing Normal University. From 2001 up to the present, he has been with the College of Resource Science and Technology, Beijing Normal University. His research interests include thermal remote sensing applications in urban heat island phenomena, evapotranspiration, and natural disaster reduction.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 44, NO. 9, SEPTEMBER 2006
An Analysis of Angle-Based With Ratio-Based Vegetation Indices Zhangyan Jiang, Alfredo R. Huete, Member, IEEE, Jing Li, and Yunhao Chen
Abstract—Remotely sensed, angle-based vegetation indices that measure vegetation amounts by the angle between an approximated soil line and a simulated vegetation isoline in the red– near-infrared reflectance space were developed and evaluated in this paper. Ünsalan and Boyer previously proposed an angle-based vegetation index, θ (denoted as θNDVI in this paper), based on the normalized difference vegetation index (NDVI) with the objective of overcoming the saturation problem in the NDVI. However, θNDVI did not consider strong soil background influences present in the NDVI. To reduce soil background noise, an angle-based vegetation index, θSAVI , based on the soil-adjusted vegetation index (SAVI), was derived using trigonometric analysis. The performance of θNDVI and θSAVI was evaluated and compared with their corresponding vegetation indices, NDVI and SAVI. The soil background influence on θNDVI was found to be as significant as that on the NDVI. θNDVI was found to be more sensitive to vegetation amount than the NDVI at low vegetation density levels, but less sensitive to vegetation fraction at high vegetation density levels. Thus, the saturation effect at high vegetation density levels encountered in the NDVI was not mitigated by θNDVI . By contrast, θSAVI exhibited insignificant soil background effects and weaker saturation, as in SAVI, but also improved upon the dynamic range of SAVI. Analyses and evaluation suggest that θSAVI is an optimal vegetation index to assess and monitor vegetation cover across the entire range of vegetation fraction density levels and over a wide variety of soil backgrounds. Index Terms—θSAVI , angle-based vegetation indices, saturation effect, soil background effects.
I. I NTRODUCTION
M
ANY strategies have evolved over the last two decades to extract land surface biophysical information from remotely sensed data (e.g., [1]–[4]). The interpretation of the radiometric information gathered on vegetation is mainly based on spectral variations observed among a small number of broad wavelength bands such as SPOT Haute Résolution Visible (HRV), the Landsat Thematic Mapper (TM), or the NOAA Advanced Very High Resolution Radiometer (AVHRR). Although some sensors such as the Earth Observing System Moderate Resolution Imaging Spectroradiometer (MODIS) have addi-
Manuscript received September 28, 2005; revised January 30, 2006. This work was supported in part by the Project of the Ministry of Education on Doctorial Discipline of China (20030027014) and in part by the Natural Science Foundation of China (40201036). Z. Jiang, J. Li, and Y. Chen are with the College of Resources Science and Technology, Beijing Normal University, Key Laboratory of Environmental Change and Natural Disaster Research of the Education Ministry of China, Beijing 100875, China (e-mail: [email protected]). A. R. Huete is with the Department of Soil, Water, and Environmental Science, University of Arizona, Tucson, AZ 85721 USA. Digital Object Identifier 10.1109/TGRS.2006.873205
tional spectral bands than the red and near-infrared (NIR), a large proportion of studies evaluating vegetation amount remain focused on the use of these two bands because red and NIR bands provide a high contrast between soil and vegetation optical properties [5]–[10]. One important method of extracting canopy biophysical characteristics from radiometric measurements involves the use of vegetation indices. The normalized difference vegetation index (NDVI), which is the difference of the NIR and red bands divided by their sum, has been the most widely used index in global vegetation studies [11]–[15], crop management [16]–[18], land cover studies [19]–[21], and climate studies [22], [23]. Nevertheless, and apart from atmospheric and bidirectional effects, NDVI has been limited by two prominent constraints, namely: 1) soil background contamination associated with variations in soil brightness, which may produce large variations in the NDVI for constant vegetation amounts [24]–[26], and 2) the saturation problem in high biomass areas [27], [28]. The sensitivity of the NDVI to biophysical quantities such as leaf area index (LAI) or vegetation fraction becomes increasingly weak with increasing vegetation densities beyond a threshold value (e.g., [29] and [30]). Significant progress has been made in improving the vegetation index equations themselves, primarily in reducing canopy background, atmospheric contamination, and saturation problems in the NDVI [7], [8], [31]–[33]. Huete [7] found that vegetation biophysical isolines in NIR–red reflectance space, i.e., lines of constant vegetation amount but varying pixel brightness, are neither parallel to a soil line nor converge at the origin, but instead approximately converge at a point on the soil line shifting from the origin in the negative direction. For various crop canopies, the convergence point was approximately at (−0.25, −0.25). The soil-adjusted vegetation index (SAVI) was subsequently developed based on this general vegetation biophysical isoline behavior SAVI =
N −R (1 + L) N +R+L
(1)
where N and R are NIR and red reflectances, respectively. With the soil adjustment factor L (usually L = 0.5), SAVI minimizes soil brightness influences, which are prominent in ratio-based vegetation indices such as NDVI [24], [25]. SAVI minimizes first-order soil–vegetation interactions by simple modeling of differential red and NIR flux extinction through vegetated canopies [7], which are neither considered in rationor orthogonal-based indices, such as NDVI, the difference
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vegetation index (DVI), defined as the difference between NIR and red reflectances [6], and the perpendicular vegetation index (PVI) [5]. PVI is defined as PVI =
N − aR − b √ 1 + a2
(2)
where a and b are the slope and intercept of a soil line, respectively. Using a radiative transfer model, Baret et al. [34] introduced soil line parameters into SAVI formulation to reduce soil background influences for plant canopies with very low LAI or low vegetation coverage and found vegetation biophysical isolines to converge at another point (S) along the soil line with abscissa—X, resulting in the transformed SAVI (TSAVI). Baret and Guyot [30] gave an improved version of the initial definition TSAVI =
a(N − aR − b) aN + R − ab + X(1 + a2 )
(3)
where the value of X was adjusted to minimize soil background effects (X = 0.08). With the goal of overcoming the saturation problem of NDVI, Ünsalan and Boyer [28] developed a new vegetation index, θ, based on NDVI and principal components analysis (PCA) in red–NIR reflectance space, defined as θ=
4 arctan(NDVI). π
(4)
Inasmuch as θ is a nonlinear transformation of NDVI, the isolines of equal θ values are the same as those of NDVI, which are lines convergent to the origin, but with the values of θ transformed from the NDVI values by the inverse tangent function. Graphically, the value of a θ isoline in red–NIR space is the ratio of the angle between the isoline and the approximated soil line Y = X to the maximal angle π/4. In this sense, θ is an angle-based vegetation index. By applying this nonlinear transformation, Ünsalan and Boyer [28] found that the nonlinearity and saturation problems of NDVI were offset by θ based on the comparison of entropies of θ with those of the NDVI in several images. However, the linearity of θ has not been theoretically analyzed nor explained, and the soil background contamination contained in NDVI may not be reduced by θ because it is specifically designed to overcome the saturation problem of NDVI. Inasmuch as SAVI is designed to minimize the soil background influence, an angle-based vegetation index derived from SAVI instead of NDVI may be helpful to reduce the soil background influence on θ. The purpose of this paper is to derive an angle-based vegetation index with minimal soil background contamination and enhanced sensitivity to vegetation biophysical parameters, such as vegetation fraction. The performances of the two angle-based vegetation indices are then evaluated and compared with their corresponding NDVI and SAVI.
Fig. 1. Vegetation index isolines and their angles in red–NIR reflectance space. (a) Isolines convergent to the origin as in NDVI isolines. (b) Isolines convergent to a shifted origin as in the case of SAVI isolines. (c) Isolines convergent to a shifted origin as in the case of TSAVI isolines.
II. D ERIVATION OF A NGLE -B ASED V EGETATION I NDICES If the vegetation amount of a pixel in red–NIR reflectance space [Fig. 1(a)], with red reflectance R and NIR reflectance N , is measured by the angle α between an approximated soil line (baseline) Y = X and the line formed by the spectral point of the pixel, (R, N ) to the origin, the tangent function of α can be calculated by tan α = tan(γ − β)
(5a)
γ = arctan(N/R)
(5b)
β = π/4.
(5c)
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Thus, tan(α) can be written in terms of R and N , which is equivalent to the NDVI tan α =
N −R = NDVI. N +R
(6)
Ünsalan and Boyer [28] found this formulation by way of PCA in red–NIR reflectance space, then calculated α from the NDVI and normalized this angle by π/4 (4). However, Huete [7] found that vegetation biophysical isolines in NIR–red reflectance space are not convergent at the origin, and the increase of soil background brightness would result in the decrease of the NDVI with constant vegetation density. Vegetation index isoline behavior may be graphically modeled by shifting the red–NIR space origin toward an approximate isoline convergence point E (−0.25, −0.25) [Fig. 1(b)] [7]. Similar to α, the angle α between the soil line and a simulated vegetation index isoline can be used as a measure of vegetation amount of a pixel [Fig. 1(b)]. Similarly, α can be calculated by
tan α = tan(γ − β ) N + 0.25 γ = arctan R + 0.25 β = π/4.
(7a) (7b) (7c)
Thus, tan(α ) can be expressed in terms of R and N , which is different from the SAVI only by a scaling factor of 1.5 tan α =
N −R = SAVI/1.5. N + R + 0.5
(8)
According to experimental measurements [24], [35], the red and NIR reflectances of infinitely dense vegetation are approximately 0.03 and 0.7, respectively. Thus, the maximal α corresponding to infinite LAI can be estimated as 0.5 rad. Normalizing α , we can define a new angle-based vegetation index, θSAVI N −R θSAVI = 2 arctan = 2 arctan(SAVI/1.5). N + R + 0.5 (9) Baret et al. [34] used a locally measured soil line Y = aX + b as the baseline and assumed that the convergence point of vegetation index isolines was located at point S (−X, −aX + b) [Fig. 1(c)]. In this case, the angle α between the soil line and a vegetation index isoline can be calculated by tan α = tan(γ − β ) N + aX − b γ = arctan R+X β = arctan(a).
(10a) (10b) (10c)
Similarly, tan(α ) can be expressed in terms of R and N , which is different from TSAVI only by a scaling factor a tan α =
N − aR − b = TSAVI/a. aN + R − ab + X(1 + a2 )
TABLE I DYNAMIC RANGE OF THE FOUR VEGETATION INDICES
(11)
If the vertices of α and α (points E and S) are located at the same point, α and α are equivalent in concept, and their relationship is α = α + αsoil
(12)
where αsoil is the angle between the soil line Y = aX + b and the line Y = X. For this reason, TSAVI will not be used in the comparison of the different indices. III. E VALUATION OF θSAVI AND I TS C OMPARISON W ITH O THER V EGETATION I NDICES To facilitate comparisons, we denote θ in (4) as θNDVI . The baseline values of the four vegetation indices (NDVI, θNDVI , SAVI, and θSAVI ) are 0, but their maximum values are different according to the reflectances of infinitely dense vegetation mentioned above. The dynamic ranges of the four vegetation indices (maximum values minus values of the baseline) are listed in Table I. The dynamic range of θNDVI is slightly larger than that of NDVI, whereas the dynamic range of θSAVI is significantly larger than that of SAVI. Although the SAVI was formulated from the NDVI equation, there was a loss in the amplitude of the vegetation index signal between NDVI and SAVI [7]. The NDVI and θNDVI are normalized to 1 when red reflectance is 0 and NIR reflectance is larger than 0, and the SAVI is normalized to 1 when red and NIR reflectances are 0 and 1, respectively. To obtain the same dynamic range as θSAVI , the SAVI can be renormalized using the reflectances of infinitely dense vegetation (denoted as SAVIN ), which results in SAVI being multiplied by 1.22. A. Sensitivity to Angles The two angle-based vegetation indices, θNDVI and θSAVI , were evaluated and compared with their corresponding vegetation indices, NDVI and SAVIN . We first compared the sensitivities of the four vegetation indices to the angles between the baseline and their vegetation index isolines, α or α [Fig. 1(a)–(c)]. The derivatives of the four vegetation indices on their corresponding angles are dNDVI dα dθNDVI dα dSAVIN dα dθSAVI dα
= sec2 α =
4 π
(13a) (13b)
= 1.84 sec2 α
(13c)
= 2.
(13d)
The derivatives of the two angle-based vegetation indices on angles are constant. However, the derivatives of the nonangular
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Fig. 2. Sensitivities of the four vegetation indices to the angles between the soil line and their vegetation index isolines.
Fig. 3. Vegetation index values for different vegetation fractions over various soil backgrounds.
vegetation indices, NDVI and SAVIN , are determined by their angle values. According to the reflectances of infinitely dense vegetation, the maximal α and α are 42.5◦ and 28.6◦ , respectively. The value of α and α of the baseline is obviously 0. The derivatives of the four vegetation indices are presented in Fig. 2. The derivative of θNDVI on α is larger than that of NDVI when α is less than 27.6◦ and smaller than that of NDVI when α is larger than 27.6◦ . Thus, θNDVI is more sensitive to α than NDVI at low vegetation density levels and less sensitive to α at high vegetation density levels. If α can indicate vegetation amounts, the saturation effect of the NDVI at high vegetation density levels was not mitigated by θNDVI . Analogously, the derivative of θSAVI on α is larger than that of SAVIN when α is less than 16.6◦ and smaller than that of SAVIN when α is larger than 16.6◦ .
TABLE II STANDARD DEVIATIONS OF VEGETATION INDICES CAUSED BY S OIL B ACKGROUND I NFLUENCES
B. Soil Background Influence Ground-based spectral measurements of cotton canopies for a full season (0%–100% green cover) under varying soil background conditions [24] were used for the evaluation of the performance of θSAVI and subsequent comparisons with the other vegetation indices. At each cotton density level, soil backgrounds were varied by inserting different soils with a wide range of soil brightness underneath the cotton canopies. This data set enables us to study soil background effects on vegetation indices and the sensitivities of vegetation indices to vegetation amount. The values of the three vegetation indices, θNDVI , θSAVI , and SAVIN , for different vegetation density levels over various soil backgrounds are presented in Fig. 3. For the various constant vegetation density levels, soil background influences on θNDVI were evident when vegetation fractions were less than 75% and insignificant when vegetation fractions exceeded 75% and θNDVI became saturated. In contrast, the soil background influence was greatly reduced by SAVIN and θSAVI over the full range of vegetation density levels. The standard deviations of the four vegetation indices caused by soil background influences are summarized in Table II. The soil background influence on θNDVI was slightly larger than that of the NDVI when vegetation fraction was less than 25% and
slightly smaller than that of the NDVI at higher vegetation fractions. The soil background influence on θSAVI was almost equal to that of SAVIN at each vegetation density level. The total standard deviations of the angle-based vegetation indices were almost equal to the nonangular vegetation indices, indicating that the soil background influence contained in the ratio-based vegetation indices is not reduced by their corresponding anglebased vegetation indices. Therefore, in general, the strong soil background contamination contained in the NDVI was not reduced by θNDVI , and the soil background influence on θSAVI almost remained as small as that of SAVIN . The overall soil background influences on NDVI and θNDVI were about five times those on SAVIN and θSAVI , respectively. C. Sensitivities to Vegetation Fraction The sensitivities of vegetation indices to vegetation amount may be presented by the slopes of the vegetation index versus vegetation fraction (VI−f ) curves at a specific vegetation fraction f . The average slopes, dVI/df , were estimated by the average difference in vegetation index values at two adjacent vegetation fraction levels divided by the corresponding vegetation fraction interval over eight vegetation intervals
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TABLE III VEGETATION INDEX SENSITIVITIES AS REPRESENTED BY THE MEAN SLOPES OF VEGETATION INDEX–VEGETATION FRACTION CURVES
(Table III). NDVI was sensitive to vegetation fraction at green levels below 40% and became less sensitive to vegetation fraction with increases in vegetation and began to saturate at vegetation fractions above 75%. A small negative slope at the highest green level demonstrated that the NDVI no longer responds to increases of vegetation amount. The negative slope may be explained by a slight increase of red reflectance at 100% vegetation fraction relative to that at 95% vegetation fraction [24]. The sensitivity of θNDVI to the vegetation fraction was slightly larger than that of the NDVI at green levels below 40% and slightly smaller than that of the NDVI at the higher vegetation fraction levels. The NDVI and θNDVI sensitivities decreased with increases of vegetation fraction, but the decrease rate of the θNDVI sensitivity was much stronger than that of NDVI sensitivity, demonstrating that the saturation problem of the NDVI remains in θNDVI , with the linearity of θNDVI slightly worse than that of the NDVI according to our data set. The overall sensitivities of NDVI and θNDVI were equal, suggesting that the sensitivity of θNDVI to vegetation fraction is not improved compared with the NDVI as a whole. The sensitivity of SAVIN was relatively constant, although it also decreased with increases in vegetation fraction similar to the NDVI. The sensitivity of SAVIN at the higher green density levels remained about half of the larger sensitivity values at the lower green density levels, indicating that the linearity of SAVI is improved over that of NDVI. There was a steep increase in the slope of SAVIN and θSAVI at the 90%–95% interval, which is attributed to rapidly accumulating green biomass with only gradual lateral percent cover increases at this stage [24]. The sensitivity of θSAVI behaved similar to that of SAVIN , and their overall sensitivities were equal (Table III). The sensitivity of PVI normalized with the reflectances of infinite dense vegetation (PVIN ) was also calculated to compare the sensitivity of orthogonal vegetation indices with those of other types of vegetation indices. The PVIN sensitivities were consistent at all vegetation fraction intervals except for at 90%–95% interval. No saturation effects could be found for PVIN in our data. As an orthogonal vegetation index, PVI is a linear function of red and NIR reflectances with constant sensitivity to red and NIR reflectances, independent of red
Fig. 4. Vegetation index sensitivities to the NIR reflectance as a function of NIR and red reflectances. (a) NDVI sensitivity. (b) SAVI sensitivity.
and NIR reflectances (i.e., for any vegetation density level) and, thus, sensitive to vegetation fraction unless both red and NIR reflectances become insensitive to vegetation fraction. However, the NDVI becomes decreasingly sensitive to the NIR reflectance at high NIR and low red reflectances [Fig. 4(a)]. For N/R 1, both the numerator and denominator of the NDVI equation approach equivalence, and thus, the sensitivity of the NDVI to the NIR reflectance becomes negligible [33]. The SAVI is less sensitive to NIR reflectance at low NIR values and more sensitive to NIR reflectance than the NDVI at high NIR values, and this sensitivity is almost independent of the value of red reflectance [Fig. 4(b)]. The θNDVI and θSAVI sensitivities on NIR reflectance are similar to those of NDVI and SAVI, respectively. When vegetation fractions are larger than 60%–80%, red reflectance approached asymptotic values and exhibited little additional change, whereas NIR reflectances continued to increase with the increase of vegetation fraction [24], [33]. Thus, the saturation effects of NDVI and θNDVI are more prominent than those of SAVI and θSAVI , which, in turn, are more prominent than those of PVI. D. Differences Between NDVI and SAVIN With Their Angle-Based Counterparts The relationships of the differences between angle-based vegetation indices and their corresponding nonangular vegetation index counterparts with vegetation fraction over various soil backgrounds are presented in Fig. 5. The difference
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TABLE IV ENTROPIES OF THE FOUR VEGETATION INDICES SAMPLED AT T HREE I NTERVALS (NATS)
Fig. 5. Difference between angle-based vegetation indices and their nonangular vegetation index counterparts for different vegetation fractions over various soil backgrounds.
between θNDVI and NDVI (θNDVI − NDVI) was positively related to vegetation fraction at green density levels below 25%, but negatively related to vegetation fraction at higher green density levels, resulting in the slightly larger sensitivity of θNDVI at low green density levels and smaller sensitivity at green levels above 40% compared with the NDVI. The differences between θNDVI and NDVI at intermediate vegetation fraction levels were larger than those at high vegetation fraction levels, aggravating the saturation effect of θNDVI compared with NDVI. The difference between θSAVI and SAVIN was much smaller than the difference between θNDVI and NDVI and approached 0 at very low and very high vegetation density levels. E. Entropies The entropy measures the amount of information obtained, on average, in drawing samples from a given distribution by quantifying the uncertainty or randomness in the experiment [28]. Therefore, the entropy increases as the distribution becomes more uniform, and relates to sample intervals, with the smaller sample intervals resulting in less information loss and larger entropy. The entropy E is defined as E=−
N
p(i) log (p(i))
(14)
i=1
where p(i) is the probability of a stochastic variable within an interval i, and N is the total number of quantization levels, related to the length of intervals. Here, vegetation indices were regarded as stochastic variables, and p(i) was calculated by the frequency of vegetation index values within an interval. Entropies of the four vegetation index experimental data sets were calculated for three sample intervals, 0.05, 0.1, and 0.2 (Table IV). For interval 0.05, the θNDVI entropy was the same as the NDVI entropy, but the θSAVI entropy was larger than the SAVIN entropy. For interval 0.1, the entropies of the anglebased vegetation indices were larger than those of the NDVI and SAVI counterparts, indicating more uniform distributions of values in the angle-based vegetation indices at this interval. The low NDVI entropy was partly caused by nonlinearity
and saturation effects, as 41.8% of NDVI values were within the 0.8–0.9 interval. With a small difference between θNDVI and the NDVI (about 0.04), the densest vegetation fraction group of θNDVI values was split into two intervals, 0.8–0.9 and 0.9–1.0 (Fig. 3), resulting in a more uniform distribution of θNDVI values, but not necessarily mitigating the saturation effect. At interval 0.2, the θNDVI entropy was less than that of the NDVI, but the entropy of θSAVI was equal to that of SAVIN . The entropies of θSAVI and SAVIN were larger than those of θNDVI and NDVI at intervals 0.1 and 0.2, indicating a weaker saturation effect and better linearity of θSAVI and SAVIN compared with the NDVI counterparts. IV. C ONCLUSION AND D ISCUSSION In this study, we first introduced an angle-based vegetation index, θNDVI , which has been derived from NDVI through PCA by Ünsalan and Boyer [28]. Inspired by their ideas, we graphically studied θNDVI in the red–NIR reflectance space. Because of the strong soil background influences on NDVI, we also derived another angle-based vegetation index, θSAVI , from SAVI through trigonometric analysis to minimize soil background influences. The performance of the two anglebased vegetation indices was then evaluated and compared with the corresponding NDVI and SAVI. The soil background influence on θNDVI was found to be as prominent as that of NDVI. θNDVI is more sensitive to vegetation amount than NDVI at low vegetation density levels and less sensitive to vegetation amount than the NDVI at high vegetation density levels. Unlike the findings of Ünsalan and Boyer [28], we found that the saturation problem at high vegetation density levels encountered by the NDVI was not mitigated by θNDVI . The dynamic range of θSAVI was found to be larger than that of the SAVI. θSAVI was evaluated and compared with the normalized SAVI (SAVIN ). The difference between them was very small, and they had similar soil background influence and sensitivities to vegetation fraction. The saturation effect of SAVI and θSAVI was also much weaker compared with NDVI and θNDVI . The entropies of vegetation index values measured the uniformities of distributions of vegetation index values. Saturation effects in vegetation indices result in a concentration of vegetation index values within a particular range of values and hence small values of entropies. The larger entropy of θSAVI indicates a weaker saturation effect, better linearity, larger dynamic range, and enhanced sensitivity of θSAVI compared with the other vegetation indices.
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Overall, the performance of NDVI was not improved by its corresponding angle-based vegetation index, θNDVI . However, θSAVI not only maintained the merits of SAVI, such as negligible soil background influences, weak saturation, and better linearity, but also resulted in a larger dynamic range than SAVI. Our results and analyses suggest that θSAVI is an optimal vegetation index to evaluate and monitor vegetation cover across all density levels and over a wide variety of soil backgrounds. Our study also provided geometrical interpretations for NDVI, SAVI, and TSAVI and revealed that they are tangent functions of the angles between an approximated soil line and their vegetation index isolines in red–NIR reflectance space. Angle-based vegetation indices use spectral angles as measurements of vegetation amount, whereas their NDVI and SAVI counterparts use the tangent functions of angles as measurements of vegetation amount, although they share the same vegetation isolines. Some of the main limitations of ratio-based vegetation indices, such as NDVI, are the high saturation and nonlinearity effects. The orthogonal vegetation indices, such as PVI, are linear functions of red and NIR reflectances and thus have little saturation effect with respect to vegetation fraction unless red and NIR reflectances become saturated simultaneously, but they measure vegetation amount by the perpendicular distance of a vegetated spectral point to a soil line in red–NIR space. The perpendicular distance, however, is influenced by variations in soil brightness because the actual observed biophysical or greenness lines are not parallel to the bare soil line [24]. The SAVI equation (1) reduces to the NDVI equation when L is 0 and reduces to the DVI equation when L goes to infinity [7]. We may conclude that the linearity of the SAVI will be improved with an increase of L. However, increases in L greater than 0.5 would also introduce increasing soil background influences in the SAVI [7]. It would be highly desirable to improve both the linearity and sensitivity of the SAVI and θSAVI across all vegetation density levels without introducing soil background influences. The performance of θSAVI should be evaluated further using other data sets and satellite images. Including an atmospheric resistance term in the formulation of θSAVI may also be helpful to improve this index. R EFERENCES [1] W. Verhoef, “Light scattering by leaf layers with application to canopy reflectance modeling: The SAIL model,” Remote Sens. Environ., vol. 16, no. 2, pp. 125–141, Oct. 1984. [2] P. J. Sellers, J. A. Berry, G. J. Collatz, C. B. Field, and F. G. Hall, “Canopy reflectance, photosynthesis, and transpiration. III. A reanalysis using improved leaf models and a new canopy integration scheme,” Remote Sens. Environ., vol. 42, no. 3, pp. 187–216, Dec. 1992. [3] R. B. Myneni and G. Asrar, “Simulation of space measurements of vegetation canopy bidirectional reflectance factors,” Remote Sens. Rev., vol. 7, no. 1–2, pp. 19–41, 1993. [4] R. H. Fraser, T. A. Abuelgasim, and R. Latifovic, “A method for detecting large-scale forest cover change using coarse spatial resolution imagery,” Remote Sens. Environ., vol. 95, no. 4, pp. 414–427, Apr. 2005. [5] A. J. Richardson and C. L. Wiegand, “Distinguishing vegetation from soil background information,” Photogramm. Eng. Remote Sens., vol. 43, no. 12, pp. 1541–1552, 1977. [6] C. J. Tucker, “Red and photographic infrared linear combinations for monitoring vegetation,” Remote Sens. Environ., vol. 8, no. 2, pp. 127–150, May 1979.
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[32] H. Liu and A. R. Huete, “A feedback based modification of the NDVI to minimize canopy background and atmospheric noise,” IEEE Trans. Geosci. Remote Sens., vol. 33, no. 2, pp. 457–465, Mar. 1995. [33] A. A. Gitelson, “Wide dynamic range vegetation index for remote quantification of biophysical characteristics of vegetation,” J. Plant Physiol., vol. 161, no. 2, pp. 165–173, Feb. 2004. [34] F. Baret, G. Guyot, and D. Major, “TSAVI: A vegetation index which minimizes soil brightness effects on LAI and APAR estimation,” in Proc. 12th Can. Symp. Remote Sens. and IGARSS, Vancouver, BC, Canada, Jul. 10–14, 1989, pp. 1355–1358. [35] O. Lillesaeter, “Spectral reflectance of partly transmitting leaves: Laboratory measurements and mathematical modeling,” Remote Sens. Environ., vol. 12, no. 3, pp. 247–254, Jul. 1982.
Zhangyan Jiang received the B.S. degree from Jiangxi Normal University, Nanchang, China, in 1998, and the M.S. and Ph.D. degrees from Beijing Normal University, Beijing, China, in 2002 and 2006, respectively, all in geography. His research interests include optimization of remotely sensed vegetation indices, remote sensing of vegetation biophysical parameters, and retrieving land surface temperature by thermal infrared remote sensing.
Alfredo R. Huete (M’92) received the M.S. degree from the University of California at Berkeley and the Ph.D. degree from the University of Arizona, Tucson, in 1984, under the guidance of Ray D. Jackson. He is currently a Professor in the Department of Soil, Water, and Environmental Science, University of Arizona, where he serves as the Chair of the Interdisciplinary Academic Program, Committee on Remote Sensing and Spatial Analysis. He is a MODIS Science Team Member and is responsible for the development, implementation, and validation of the vegetation index products. He is part of the NPOESS Preparatory Project Science Team to evaluate vegetation indices as environmental data records. He is also an active Member of the Large-Scale Biosphere Atmosphere in the Amazon interdisciplinary experiment and serves on the editorial review board for Remote Sensing of the Environment.
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Jing Li received the B.S. degree in geography and the M.S. degree in graphics and remote sensing from Peking University, Beijing, China, in 1982 and 1985, respectively. He is currently the Director of the Institute of Resource Technology and Engineering, College of Resource Science and Technology, Beijing Normal University, Beijing. From 1990 to 1991, he was a Visiting Scholar at the University of Hawaii. From 1993 to 2003, he was with the Institute of Remote Sensing and Geographical Information Systems, Peking University. From 2003 up to the present, he has been a Professor with Beijing Normal University and Chief Engineer of the National Disaster Reduction Committee, Ministry of Civil Affairs of China. His research interests include remote sensing of natural resources, remote sensing applications in natural disaster reduction, and monitoring of oceanic and coastal ecology by remote sensing.
Yunhao Chen received the B.S. and M.S. degrees in resource management from the University of Science and Technology of China, Hefei, in 1994 and 1997, respectively, and the Ph.D. degree in geodesic engineering from the China University of Mining and Technology, Beijing, in 1999. He is currently an Assistant Professor at Beijing Normal University, Beijing, and a Special Research Scholar of the National Disaster Reduction Committee, Ministry of Civil Affairs of China. From 2000 to 2001, he did postdoctoral research in Beijing Normal University. From 2001 up to the present, he has been with the College of Resource Science and Technology, Beijing Normal University. His research interests include thermal remote sensing applications in urban heat island phenomena, evapotranspiration, and natural disaster reduction.
