TOPOGRAPHIC EFFECT ON SPECTRAL VEGETATION INDICES FROM LANDSAT TM DATA: IS TOPOGRAPHIC CORRECTION NECESSARY?

: The full potentiality of spectral vegetation indices (VIs) can only be evaluated after removing topographic, atmospheric and soil background effects from radiometric data. Concerning the former effect, the topographic effect was barely investigated in the context of VIs, despite the current availability correction methods and Digital elevation Model (DEM). In this study, we performed topographic correction on Landsat 5 TM spectral bands and evaluated the topographic effect on four VIs: NDVI, RVI, EVI and SAVI. The evaluation was based on analyses of mean and standard deviation of VIs and TM band 4 (near-infrared), and on linear regression analyses between these variables and the cosine of the solar incidence angle on terrain surface ( cos i ). The results indicated that VIs are less sensitive to topographic effect than the uncorrected spectral band. Among VIs, NDVI and RVI were less sensitive to topographic effect than EVI and SAVI. All VIs showed to be fully independent of topographic effect only after correction. It can be concluded that the topographic correction is required for a consistent reduction of the topographic effect on the VIs from rugged terrain.


Introduction
Remote sensing data have become an important source of information for studying vegetation on regional, continental and global scale.Vegetation indices (VIs) calculated from remote sensing data are widely used to either estimate biophysical attributes such as biomass, leaf area index (LAI) and the photosynthetic activity (Lehmann et al., 2012;Dube and Mutanga, 2015) or for monitoring and mapping land cover and land cover change (Kolios and Stylios, 2013;Sexton et al., 2013).Most VIs are based on the red and near infrared spectral information, since green vegetation usually decreases the spectral response in the red due to chlorophyll absorption and increases the spectral response in the near infrared.However, in rugged mountainous areas the use of remote sensing data can be limited by the topographic effect (Horn, 1981).The topographic (or illumination) effect consists in variations of radiance levels of spectral data caused by differences in surface slope angle and aspect of the terrain, in combination with solar zenith and azimuth angles (Holben and Justice, 1980).Consequently, a certain land cover/use type may not have the same spectral response at different topographic positions (Figure 1).The topographic effect is responsible for a large part of the spectral variation of the land cover in rugged terrain (Civco, 1989;Hantson and Chuvieco, 2011).It is assumed that topographic effect is considerably reduced in band ratio compared to single spectral bands (Holben and Justice, 1981).Based on this rationale, most studies consider that band ratio VIs (for example, the Normalized Difference Vegetation Index -NDVI) can overcome topographic effects on radiometric levels (Lee and Kaufman, 1986;Ekstrand, 1996;Huete at al., 1999).However, some studies showed that topography significantly affects VIs in rugged mountainous area (Verbyla et al., 2008;Veraverbeke et al., 2010;Wang et al., 2012).For example, Deng et al. (2007) observed that the NDVI and the Normalized Difference Infrared Index (NDII) showed a significant correlation (r 2 ) (p = 0.001) with topography variables such as slope and the cosine of the aspect.In order to correct topographic effect, a range of methods have been developed (Smith et al., 1980;Teillet et al., 1982;Shepherd and Dymond, 2003;Kobayashi and Sanga-Ngoie, 2009).The methods are based on the cosine of the solar incidence angle on the surface (cos i) (Sellers, 1965).The cos i is a factor related the the solar illumination at each pixel of the scene.Low values of cos i indicate pixels under low illumination and high cos i are well-illuminated pixels (Dubayah and Rich, 1995).The influence of topographic effect on VIs and the correction performance varies according to the applied vegetation index, spectral and topographic data, study area, methodology of correction, among other factors (Teillet et al., 1997;Vanonckelen et al., 2013).Despite the broad availability of Digital Elevation Models (DEM) data and the development of correction methods, there are still few studies about topographic effects on VIs addressing topographic correction (Matsushita et al., 2007).Thus, the objective of this study was to assess the topographic effect on four widely used VIs, through the examination of uncorrected and topography-corrected Landsat 5 TM data: the NDVI (Rouse et al., 1974), the Ratio Vegetation Index (RVI) (Pearson and Miller, 1972), the Enhanced Vegetation Index (EVI) (Liu and Huete, 1995) and the Soil Adjusted Vegetation Index (SAVI) (Huete, 1988).

Study area and processing resources
The study site is an agricultural region of Brazil in the south of Minas Gerais State, with undulating relief type, with varied conditions of illumination and land cover types (Figure 2).It is an area of 11,5 per 11,5 km located in the municipalities of Alfenas and Machado and it is covered predominantly by agriculture, and sparse patches of forest fragments from the Atlantic Forest biome.The main crops in the region are coffee, corn and beans (IBGE, 2013).According to the used topographic data, the slope average is 7.5° with a maximum of 35° and altitude ranges from 765 to 1030 meters.The spectral bands 1 (450-520 nm), 3 (630-690 nm) e 4 (760-900 nm) of Landsat 5 TM, scene 219/75 (path/row), obtained from INPE's image catalog (http://www.dgi.inpe.br/CDSR)were used in this study.The date of the Landsat image was June 8, 2011, acquired with solar zenith angle of 54.32° and solar azimuth angle of 37.01° (NE).Aspect and slope layers (Figure 3 a and b) corresponding to study site were downloaded from Topodata Project, available on the website www.dsr.inpe.br/topodata(Valeriano and Rossetti, 2012).High-resolution image from Google Earth, acquired in 2011, were consulted for verification of land cover in the control sample positions.All processing steps were performed using the R programming language, version 3.0 (R, 2013).

Methodology
Figure 4 shows the data flow and the processes of this research.As an initial phase of processing, we performed the registration and preparation of the data in the geographic coordinate system (non-projected), with WGS 1984 as geodetic datum.The original data were already georeferenced and, to maximize co-registration, a simple displacement of the spectral data based on distinctive corner points with sharp contrast to their surroundings observed on all datasets was necessary to match spectral and topographic data.The notable features in both sources were drainage junctions, which were promptly contrasting in optical images.For topographic data, the sharp positioning of the drainage features required the use of second-derivative thalweg delineation (based on plan curvature), also available among Topodata products (Valeriano et al., 2006).In order to align pixels between data, the pixel positions were structured with the nearest neighbour resampling method.According to the methodology described by Chander et al. (2009) the digital numbers of the image were converted to radiance and then to top of atmosphere (TOA) reflectance.Atmospheric correction was performed using the DOS (Dark Object Subtraction) technique proposed by Chavez (1988) based on the analysis of histogram frequency of the spectral bands.Subsequently, we calculated the cosine of the solar incidence angle on surface (cos i), which was used for the correction of topographic effect.
Based on a previous study (Moreira and Valeriano, 2014) the c-correction method proposed by Teillet et al. (1982) was chosen to be applied in this study: Where, ρ c λij is the corrected reflectance of band λ and pixel ij, ρ λij is the uncorrected reflectance, bλ and m λ are parameters from the linear regression represented by the equation: The estimation of c λ parameter was based on samples and calculated for each land cover class.
The classes used in this study were the predominant in the study area, which were coffee, corn, forest and soil.Figure 5 shows the distribution of slope values, aspect and cos i for the samples.Land cover samples were distributed in a wide range of slope, aspect and cos i, what is important for the estimation of cλ parameter (Reese and Olsson, 2011) and for the correction evaluation.Samples of land cover were classified by illumination (cos i) classes, where cos i higher than 0.58 (median of cos i) are well-illuminated samples and cos i equal or lower than 0.58 are weakly illuminated.The criterion to define weakly or well-illuminated pixels is illustrated in Figure 3 (c).This classification was carried out only to evaluate the differences in the VIs between these two illumination classes.The four different VI formulations tested in this study were chosen regarding mostly the wideness of their use in different applications, but simple ratio was included because of the fundamental simplicity, which would theoretically result in variations free from cos i effects.The VIs were calculated according to the equations shown in Table 1.To determine the influence of topography on the VIs, some statistics were computed.Firstly, the coefficient of determination (r 2 ) of the linear regression between VIs and cos i was calculated and evaluated.The radiometric levels of the spectral bands tend to vary together with the incident flux density, resulting in a correlation with cos i, which is the fundamental mechanism of topographic effect.Topographic correction techniques are developed to remove this effect, thus topography-corrected VIs should have lower correlation (r 2 ) to cos i than uncorrected VIs (Meyer et al., 1993;Mcdonald et al., 2000).Standard deviation (SD) was also used in this study to evaluate the topographic effect on VIs, before and after correction.SD of radiometric levels theoretically decreases after correction, since the topographic effect, which increases radiometric variations, is removed or minimized (Hantson and Chuvieco, 2011).Finally, the means of VIs of pixels located in weakly illuminated areas and well-illuminated areas were compared.These means are expected to exhibit a statistical difference when calculated from original images, which should be significantly reduced or removed after topographic correction.The t-test was performed to verify whether the two means (from weakly illuminated versus well-illuminated pixels) are statistically different.All evaluations were performed for each vegetation index calculated for each land cover classes.
In order to compare single band reflectance with VIs, band 4 also was included in all analyses.It is expected that VIs levels are less sensitive to topographic effect than single band reflectance.
Table 1: Vegetation index analyzed in this study

RESULTS AND DISCUSSION
For the topography-uncorrected data, band 4 reflectance showed the highest correlation with cos i (Figure 6), wherein 58%, 54%, 45% and 35% of the band variations are expressed by the topographic effect (cos i) for the land cover classes corn, coffee, forest and soil, respectively.These correlations for Landsat TM band 4 are larger than those obtained by Veraverbeke et al. (2010), which were 2 and 14% for burned areas of two dates, but comparable to the 41% in forested area observed by Meyer et al. (1993).The comparison of r 2 coefficients between VIs and band 4 indicates that VIs is less sensitive to topographic effect than band 4. SAVI and EVI showed larger r 2 than NDVI and RVI for the studied land covers.Considering the forest cover, r 2 between cos i and band 4, RVI, NDVI, SAVI and EVI were 45, 22, 22, 41 and 40%, respectively.In this case, SAVI and EVI respond to topographic effect similarly to band 4, what was not very different from other vegetation classes.A noticeable contrast occurred in results from soil areas, where the topographic effect was not apparent in VIs (Figure 6).The NDVI is highly correlated with the RVI (high r2) and moderately correlated to band 4, thus we assume that NDVI behave as band ratios, which would be the less sensitive formulation to topographic effect (Holben and Justice, 1981).As opposed, SAVI and EVI are moderately correlated to RVI and highly correlated to band 4, that is more sensitivity to topographic effect.According to Matsushita et al. (2007) EVI does not behave like the RVI because of soil adjustment factor "L".The authors concluded that it is the soil adjustment factor in the EVI that makes it much more sensitive to the topographic effect than NDVI.
After applying the topographic correction on the spectral data, the band 4 and all the VIs showed no topographic effect, according to the values of r 2 between corrected data and cos i, which is zero for all land cover classes (Figure 6).A comparison of the standard deviation of band 4 and VIs between the results of data analyzed before and after the topographic correction (Figure 7) leads to similar conclusions of those obtained from the r 2 evaluation.In general, the standard deviation decreased after correction.Minor differences between the standard deviation before and after topographic correction were observed for the NDVI and RVI, what was expected due to their lower sensitivity to the topographic effect, as previously discussed.The average levels of band 4 and VIs were similar when comparing values before and after correction (Figure 7).This was already expected because the VI values from well-illuminated areas (high cos i) decrease after correction as those of weakly illuminated areas increase.Therefore, the overall mean of the samples should maintain similar after correction.However, this may not happen for a single land cover class which is predominantly located in one illumination condition (for example, weakly illuminated areas).This can explain the greater mean of forest samples after correction, which is the less extent class and predominantly distributed on weakly illuminated areas (Figure 5).The results of r 2 and standard deviation for the uncorrected band 4 indicate that data of "corn" and of "soil" classes showed the largest and the smallest presence of topographic effect in the studied area, respectively.This can be explained by the spectral variability of both classes.In the study area, corn is a quite homogeneous class, with little phenological variation and little appearance of self-shadowing, which would increase the spectral variability in and between patches in addition to the topographic effect, as observed on other cover types, like forest and coffee.In the other hand, soil class presents quite a spectral variation among its patches, due to the variety of conditions comprised in this class, including plowed soil, soil with crop residues and degraded pasture, each of these varying in relation to other factors, such as moisture and roughness (Moreira, 2014).Because of this greater spectral variability, the topographic effect is less apparent in the soil class.Comparing well-illuminated pixels with pixels under weak illumination, the averages of band 4 and VIs showed to be statistically different (significance level of 0.01) (Table 2).After correction of the topographic effect, band 4 and also the VIs were statistically equal in the two illumination classes.This indicates that the illumination, or the topographic effect, has relevant influence on the band 4 reflectance and on the values of VIs.The topographic correction contributed significantly to reduce this influence (Table 2).
Table 2: Mean values of band 4 and of vegetation index (NDVI, RVI, SAVI, EVI) of the corn land cover class in well-illuminated pixels (cos i > 0,58class I) and weakly illumination pixels (cos i ≤ 0,58class II), before and after applying topographic correction In summary, topography can affect the approached vegetation indices.In addition, it was shown that the applied correction method could fully remove their statistics characteristics related to topographic effect.It is expect that topographic effect reduce the ability of vegetation indices to estimate biophysical parameters of the vegetation or to be used in automatic process of land cover classification, as supported by other studies (Verbyla et al., 2008;Cuo et al., 2010;Vanonckelen et al., 2013;Moreira and Valeriano, 2014).We suggest for further studies that authors address different types of relief, latitude, date of image acquisition and sensors.In addition, it is recommended to evaluate other topographic correction methods, including nonempirical based methods (Shepherd and Dymond, 2003;Zhang and Gao, 2011).

CONCLUSIONS
In this study, we evaluated the topographic effect on four vegetation indices from uncorrected and topography-corrected Landsat 5 TM data.The studied vegetation indices partially contributed to reduce the topographic effect on the spectral data.NDVI and RVI were less sensitive to the topographic effect than EVI and SAVI.Band 4 reflectance and the four vegetation indices proved to be fully independent of the topographic effect only after topographic correction, evidencing the conceptual fragility of the use of vegetation indices to overcome topographic effects in satellite images, in contrast to techniques specifically developed for topographic correction.This study reinforces that prior to vegetation indices estimation, proper pre-processing steps of satellite imageries need to be conducted.The topographic correction is important for data from rugged terrain.The prospects supported by this research indicate the importance of similar studies to be conducted under different relief, latitude and acquisition situations, as well as tests with other methods of topographic correction.On the other hand, given the availability of DEM used in this work, the gains from the topographic correction are potentially available to all those who deal with radiometric variables obtained by satellite sensors of medium spatial resolution, like Landsat 5 TM.

Figure 1 :
Figure 1: A schematic diagram illustrating the variation of reflectance on Landsat spectral data as function of topography and illumination effects.A: Slope facing away from the sun (weakly illuminated area); B: Slope facing to the sun (well-illuminated area).Source: Modified from Moreira (2014).

Figure 2 :
Figure 2: Location of the test site in south of Minas Gerais State, Brazil.Landsat 5 TM 453 (RGB) composition with the identification of the land cover types.
Figure 3 presents the momentary variation among pixel values of cos i at the time of the optical image acquisition and the occurring values of slope and aspect within the test site.These plots show a continuous and relatively homogeneous distribution of the variables, without significant gaps that could disturb result analysis due to poly-modal effects.Slope values were concentrated below 15°, in an indication of a relatively gentle terrain (Figure 3-b).Indeed, there was no negative value of cos i in the area, what would indicate pixels with no direct solar illumination due to extreme shadowing (Figure 3-c).

Figure 3 :
Figure 3: Aspect (a), slope (b) and cos i (c) distributions for the test site.The cos i was calculated considering parameters of the solar geometry at the local and time of the Landsat image acquisition: solar zenith angle equal to 54.32°; and solar azimuth angle equal to 37.01°(NE).

Figure 4 :
Figure 4: Data flow and processes performed in this research.

Figure 5 :
Figure 5: Sample distribution (dark grey points) of the land cover types in relation to slope, aspect and cos i (isoline).The points in light grey represent values of the whole test site.

Figure 6 :
Figure 6: Coefficient of determination (r 2 ) of the linear regression between the studied variables for each land cover class.Where, cos i is the cosine of solar incident angle, B4 is the uncorrected band 4, c (subscript) indicates that data has topographic correction.

Figure 7 :
Figure 7: Mean and standard deviation of the corrected and uncorrected band 4 (B4) and vegetation index.Land cover: A -Corn; B -Soil; C -Coffee; e D -Forest.