2.1. Vegetation Isolines Simulations Using the 6S Radiative Transfer Code
Huete
et al. (1985) and Huete and Jackson (1987) found that observed vegetation isolines (constant vegetation amount) at various canopy densities for cotton and grass with different soil backgrounds in red-NIR wavelength space converge at one point located at the third quadrant rather than at the origin [
29,
30]. They added a constant,
l, to the red and NIR reflectance values and proposed a new VI called the soil-adjusted vegetation index (SAVI). Soil backgrounds influence the NDVI by keeping canopies of the same NDVI but with different soil moisture backgrounds away from the NDVI isoline. Assuming that the fraction of vegetation cover does not change over a short period of time but is disturbed by the soil background, the observed NDVI changes. Similarly, aerosols in the atmosphere cause the observed NDVI to deviate from the surface true NDVI by affecting the observed reflectance in the red and NIR bands that compose NDVI. Thus, it is necessary to determine how aerosols affect the apparent reflectance values.
A simulation of aerosol effects on apparent reflectance in the red (0.662 μm) and NIR (0.835 μm) bands was performed using the Second Simulation of the Satellite Signal in the Solar Spectrum (6S) radiative transfer model. 6S has been extensively validated, and the accuracy of simulated top-of-atmosphere (TOA) reflectance falls within 0.5% that has met the standard RT code accuracy requirement [
31,
32]. The zenith and azimuth angles for the satellite were both set to be 0°, and the zenith and azimuth angles for the sun were 21° and 142°, respectively. The mid-latitude summer model was selected. The simulation was performed across the band with a constant filter function of 1.0. The surface was assumed to be Lambertian. Studies on uncertainties of the atmospheric correction by 6S show that errors due to uncertainties in aerosol model assumptions dominate other sources such as atmospheric parameters and calibration uncertainties [
33]. Aerosol model selection has strong effects on atmospheric correction results [
34,
35,
36]. In 6S, pre-defined standard aerosol models include continental, maritime, urban, user’s model and three new models (biomass burning smoke, background desert and stratospheric models) [
37]. In this paper, continental, urban, biomass burning and maritime models were used for simulation, as these aerosol types are typical in continents characterized by large areas of vegetation.
Simulations were performed on apparent reflectance in the red and NIR bands for various coverage fractions of four vegetation types with different AOD conditions at 550 nm. The four vegetation types (grass, shrub, arbor and forest) naturally represent almost all vegetation types. The following six vegetation fractions were used: 0.25, 1/3, 0.5, 2/3, 0.75 and 1. The AOD values at 550 nm are the same for the red and NIR band and are dependent on aerosol types. For continental, urban and maritime aerosol models, AOD variations were defined as 0.0001, 0.25, 0.5, 1.0, 1.5 and 1.95. In areas characterized by biomass burning, large quantities of smoke aerosols at high optical depths are produced and AOD at 550 nm can extend up to a value of 2 [
38]. Thus, AOD variations were defined as 2, 2.1, 2.2, 2.3, 2.4, 2.5 and 2.6 for the simulation. The surface reflectance values for soil and vegetation are reported in
Table 1. The hybrid reflectance value is treated as the coverage weighted linear combination of the reflectance of soil and vegetation.
Simulated apparent reflectance for the red (0.662 μm)
vs. NIR (0.835 μm) channel as a function of AOD and vegetation coverage fraction of four vegetation types are shown in
Figure 1. The values of AOD range from 0.0001 to 1.95 under the continental aerosol type defined in 6S model. Points denoted by the same label in each panel (vegetation spectral isoline) share the same surface reflectance but are fluctuated by different aerosol optical depths. Apparent reflectance in the red band increases as AOD increases while apparent reflectance in the NIR band decreases as AOD increases for hybrid surface reflectivity values in this case. For low surface reflectance in the red band (
p < 0.17 as simulation results), net aerosol effects on reflectance are typically characterized by an increase in the detected signal strength. For higher surface reflectance (
p > 0.12) in the NIR band, aerosols weaken the signal. For all green vegetation and many soil types, the scattering of signal is more than absorption in the red band while the opposite trend is found in the NIR band. The aerosol degrades NDVI value by reducing the contrast between the red and NIR reflected energies [
5]. These findings are almost consistent with the research by Kaufman [
20,
40].
In
Figure 1, it also shows that the slope between reflectance in red and NIR band becomes smaller as vegetation coverage fraction increases. The apparent NDVI begins to be more sensitive to changes in aerosol optical depth for higher vegetation coverage fractions. Thus, the effects of aerosol optical depth on apparent reflectance NDVI values at the pixel scale are related to the surface reflectance which are determined by vegetation coverage fractions in the same panel and different vegetation types represented by four panels in
Figure 1. After fitting each vegetation isoline, it could be deduced that these isolines approximately converge at one point.
To find reasons for this phenomenon, relationships between surface reflectance in the red (0.662 μm) and NIR (0.835 μm) band and sensitivity of their apparent reflectance to AOD variations were explored from 6S model calculation. Simulation results are shown in
Table 2. It reveals that for different surface reflectivity values in red and NIR band (
R0,
N0), the sensitivity of apparent reflectance (
R*,
N*) to aerosol optical depth (Δ
R*/ΔAOD, Δ
N*/ΔAOD) is different. As AOD increases, aerosols can scatter more photons into the sensor but at the same time increase the signal absorbed by aerosol particles [
41]. This combined effect on the detected signal is a result of compensation between path radiance that increases the observed signal and transmittance that decreases the signal [
20]. The reflectivity in the red channel is low and the scattering components weigh more. As surface reflectance increases in the red channel, apparent reflectance tends to lose sensitivity to AOD variations. This is attributable to the fact that, in brighter surfaces (high reflectance), high surface reflectivity contributes considerably to apparent reflectance causing apparent reflectance to lose sensitivity to the variation of AOD. In contrast, for the NIR channel, as surface reflectance increases, apparent reflectance becomes more sensitive to AOD variations. Optical effects on the NIR band are more significant for brighter surfaces. This is because, for the NIR band, atmospheric transmission plays a more important role in apparent reflectance. Thus, although the aerosol free reflectances from densely vegetated surfaces to sparsely vegetated areas are different, their responses to aerosol effects are different as well causing apparent reflectance to gradually become similar.
The relationship between surface reflectance and sensitivity of its apparent reflectance to AOD variations was quantitatively investigated based on the data in
Table 2. When AOD variation is the same for the red and NIR band, ratio of the apparent reflectance variation in the red band to that in the NIR band can be expressed as Equation (1). Value of Δ
N*/Δ
R* is equal to the slope of vegetation spectral isoline (k) shown in
Figure 1. This formula indicates that for an arbitrary level of partial vegetation cover, its vegetation spectral isoline in relation to AOD is likely to pass through point (
r,
n). Point (
r,
n) is the convergence point of extended vegetation spectral isolines for different vegetation cover fractions and different vegetation species. In this case, the convergence point is approximate to point (0.2, 0.1). The location of this convergence point in red-NIR reflectance space is related to parameter
r and
n, which is dependent on aerosol types and wavelengths for simulation.
where
k is the slope of vegetation spectral isoline in
Figure 1. Δ
R* and Δ
N* are variations of apparent reflectance in the red and NIR band, respectively.
N0 and
R0 are surface reflectance in the red and NIR band, respectively.
n and
r are constants.
2.2. Derivation of Aerosol Corrected NDVI That Incorporates Neighborhood Information
In
Figure 1, variations of simulated apparent NDVI in densely vegetated areas (high vegetation coverage fraction) caused by AOD variation are more significant than those found in sparsely vegetated areas. Results are consistent with previous researches [
20,
42,
43]. For dark target and bright target of the same NDVI, Goward
et al. [
44] found that NDVI variation for dark targets is larger than that for bright targets caused by the same reflectance errors. It indicates that NDVI of dark target is more sensitive to reflectance variation. The atmosphere-induced NDVI degradation for a specific canopy is greater for increasing atmospheric turbidities [
3]. Under the same aerosol concentrations, differences between NDVI degradation of different vegetation covered pixels depend on aerosol free NDVI (represented by different vegetation cover fractions and different vegetation species) and canopy brightness (determined by its surface reflectance in red and NIR band (
R0,
N0)). NDVI free of aerosol effects can be surface reflectance NDVI or NDVI that is only contaminated by atmospheric molecular scattering and water absorption. In this section, aerosol free NDVI was used uniformly unless particularly specified.
Thus, NDVI variations are related to
AOD, brightness of targets
f (
R0,
N0) and aerosol free NDVI (
NDVI0). This relationship could be described in Equation (2). For objects with higher aerosol free NDVI and lower brightness values, aerosol-induced NDVI degradations are larger. Thus, even though the spatial distribution of AOD is homogeneous, NDVI variations for different pixels are still different. Due to spatial heterogeneities of aerosols, the surface reflectance NDVI value cannot be determined without access to aerosol content data. Other solutions need to be found to solve this ill-posed problem.
Two partial canopies with an equal aerosol free NDVI value were assumed. Aerosol free reflectance in red and NIR band of these two canopies are denoted by (
R10,
N10) and (
R20,
N20), respectively. Since the aerosol free NDVI was assumed to be the same for these two canopies, the slope of the line connecting them equals the slope of the aerosol free NDVI isoline (as shown in Equation (3)) in red-NIR reflectance space. If the sky were to become hazier and AOD variations for the two canopies were to remain similar, the slope of the line connecting their apparent reflectance was expressed as Equation (4). Based on the continental aerosol model simulation results,
a1 is approximately equal to
a2. Thus,
k′ is equal to
k. This means that the slope of line connecting two canopies’ reflectance is invariant to AOD variations (
k′ =
k) which could help us develop an algorithm to reduce the aerosol effects on NDVI values. The apparent reflectance of at least two pixels with a similar aerosol free NDVI can be used to derive the slope value of
k′. Then, the estimated value of the aerosol corrected NDVI (
NDVI′) could be derived from
k′ based on Equation (5). The same conclusion can be applied to other surface types such as urban impervious surfaces or water.
where
R10,
N10,
R20 and
N20 denote aerosol free reflectance in the red and NIR band for the two pixels covered by partial canopies, respectively.
R1*,
N1*,
R2* and
N2* denote apparent reflectance in the red and NIR bands for the two pixels covered by partial canopies, respectively. Regression coefficients
a1 and
a2 represent the rate of change of apparent reflectance in the red and NIR band as a function of changes in AOD.
k indicates the slope of line connecting two canopies’ aerosol free reflectance and
k′ indicates the slope of line connecting two canopies’ apparent reflectance.
The spectral dependence of aerosol scattering and absorption are determined by the aerosol type, size and chemical composition features examined [
20]. In this study, four 6S standard aerosol models (the continental, urban, biomass burning and maritime models) were used to study how values of parameter
a1 and
a2 vary across these aerosol types. The simulation results are presented in
Table 3. The values of
a1 and
a2 are approximately equal in each aerosol model. Thus, the new aerosol correction method can be satisfactorily applied to any one of these four models. The difference between values of
a1 and
a2 is one of the reasons for uncertainties in aerosol correction.
To illustrate what is mentioned above, six partial canopies (A–F) in clear sky conditions are assumed in
Figure 2. These six canopies have the same aerosol free NDVI (surface true NDVI or NDVI corrected for molecular scattering and water vapor absorption). In this experiment, AOD varies (0.0001, 0.25, 0.5, 1.0, 1.5 and 1.95) and is assumed to remain the same in all canopies during each phase. Influenced by AOD variations, the apparent reflectance of each canopy changes its value in red-NIR space, and the best fitting straight lines through them in each process could in turn be determined. Value of k0 is the slope of the aerosol free NDVI isoline. The fitted lines with the slope from k1′ to k6′ represent variations of AOD from 0.0001 to 0.25, 0.5, 1.0, 1.5 and 1.95 from the upper-left to the lower-right corner in
Figure 2. Lines that connect six canopies’ apparent reflectance are roughly parallel to each other under different AOD conditions. These slope values do not vary considerably and their effects on final NDVI values are minor. In this case, a variation in the AOD of 0.1 results in an error of
δ (NDVI) ≈ 0.00156 in NDVI.