Introduction

The variations of the topographic parameters (slope, aspect and altitude) affect the variation in the vividness of the satellite images in rugged mountainous terrain due to which object lying in shadow gets less solar irradiance than one on a sunny side. South aspect (Sun facing illuminated slopes) shows more reflectance whereas the effect is opposite in north aspect (Riano et al., 2003; Ghasemi et al., 2013). These differential illumination effects in satellite imagery will restrain the maximum information on the north facing slopes, thus negatively affecting the results of various quantitative methods of snow cover mapping specifically classification, change analysis and other information (Mishra et al. 2010). Various algorithms have been proposed to correct this problem among these are cosine correction (Teillet et al., 1982), C-correction (Teillet et al., 1982), two-stage normalization (Civco, 1989), sun–canopy–sensor (SCS) correction (Gu and Gillespie, 1998), SCS + C correction (Soenen et al., 2005) and Minnaert correction (Smith et al., 1980) using specific sensors. Systematic comparisons of the performance of these algorithms were reported by Riano et al. (2003); Ghasemi et al. (2013) and Mishra et al. (2010). Riano et al. (2003) and Ghasemi et al. (2013) concluded that cosine correction and the SCS correction overcorrect the shaded areas in an image whereas the correction methods such as the C, SCS + C and Minnaert correction perform better. On the other hand Mishra et al. (2010) concluded especially for snow applications that C-correction and Minnaert methods are not very successful and produce poor results, Minnaert method shows completely non-Lambertian behaviour of the Himalayan terrain and slope-matching method has advantages in quantitative retrieval of spectral reflectance, especially in shady area. However, in practice it was found that these glowing algorithms are sticky in operation and some of them are not adequate in some situations. Literature review (Riano et al., 2003; Nichol et al., 2006) suggests, mostly the research is focused on vegetation analysis at low altitudes.

In the present work an attempt has been made to overcome the above mentioned shortcomings for the removal of the topographic effect from AWiFS and MODIS data based on empirical-statistical relationship between image radiance value and cosine of the solar illumination angle for snow cover applications at varying altitude from 1100 m to 6700 m. In situ, visual and graphical analysis was used for the effective evaluation of the topographic correction algorithm for reflectance modeling and practical performance of the approach was evaluated on comparision with cosine correction, C-correction, Minnaert correction, sun–canopy–sensor with c-correction (SCS + C) and slope matching.

Study Area

The study area (Fig. 1) is divided in three different zones of Himalaya. The first study area is located in Pir-Panjal range of lower Himalayan zone (Sharma and Ganju, 2000) lies between 31°45″00 N-32°26′24″N latitude to 76°33”00“E-78°41′24″E longitude. The area is thickly forested covered maximum with coniferous trees in lower altitude along the valley. The average slope of this area is about 30 degree. The altitude varies from 1100 m to 5100 m. The lower Himalayan zone is adjacent to second study area, that lies between 32°26′24"N-33°45'36"N latitude to 75°46′19″E-78°24′36″E longitude in middle (greater) Himalayan zone which is characterized by fairly cold temperature, heavy snowfall and higher elevations (Singh et al., 2013). The altitude varies from 2700 m to 5700 m and the slope area varies from 10–69 degree. Whereas third study area is located in Karakoram range of upper Himalayan zone lies between 33°56′24″N-36°05′25″N latitude to 74°56′24″E-77°40′12″E longitude. The majority of slopes inclination in this area lies in the range of 55–60 degree and its altitude lies between 3300 m to 6700 m. SASE (Snow and Avalanche Study Establishment) has permanent field observatories located in study areas at Dhundi (Lat/Log: 32°21′22″N/77°07′38″E) at an altitude of about 2851 m and Patseo (Lat/Log: 32°45′18″N/77°15′43″E) at an altitude of about 3800 m.

Figure 1
figure 1

AWiFS aerial view of study area in (a) Lower Himalayan zone (b) Middle Himalayan zone and (c) Upper Himalayan zone

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Methodology

Satellite Data

The multi-temporal Advance Wide Field Sensor (AWiFS) sensor, on board IRS-P6 RESOURCESAT-I dated 10-Nov-2010, 25-Mar-2011 and 26-Jan-2012 with spatial resolution of 56 m, and Moderate Resolution Imaging Spectroradiometer (MODIS) sensor, on board the Terra satellite, dated 12-Feb-2008 and 13-Apr-2009 in spectral bands 1–2 at 250 m and 3–7 at 500 m spatial resolution are used in the present work. The purpose of selection these images are to examine the topographic correction for diverse solar illumination, zenith, and azimuth angles.

Geometric Corrections

First of all a master image was prepared by rectifying IRS-Linear Imaging Self-Scanning (LISS-III) sensor (spatial resolution 23.5 m) with the Survey of India (SoI) maps of different study areas. Thereafter, AWiFS images were georeferenced with LISS-III images. Similarly, MODIS data were rectified using medium resolution (56 m) AWiFS images to the Everest datum in ERDAS/ Imagine 9.2 (Leica Geosystems GIS & Mapping LLC) with sub-pixel accuracy using nearest neighborhood re-sampling technique.

Digita Elevation Model (DEM)

A DEM of the study area was generated using 1:50,000 SoI toposheet at 40 m contour level. The Shuttle Radar Topography Mission (SRTM) data of the DEM at 90 m spatial resolution were also used for certain regions of the study area on MODIS images. The non-linear interpolation function was used for 3-D surface generation. The grid resolution of the DEM is 6 m and 90 m which were further resampled at 56 m and 500 m to make it equal to the grid resolution of AWiFS and MODIS satellite images respectively. Thereafter, the DEM was used to generate terrain parameters such as slope and aspect for topographic models using ERDAS Imagine 9.2. The flow chart of the detailed methodology is given in Fig. 2.

Figure 2
figure 2

Flow chart summarizing the methodology followed in the study

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Field Measurement

In the study areas, SASE has two permanent field observatories located at Dhundi (Lat/Log: 32°21′22″N/ 77°07′38″E) at an altitude of about 2851 m and Patseo (Lat/Log: 32°45′18″N/77°15′43″E) at an altitude of about 3800 m where the study was conducted with spectroradiometer (Field Spec Pro FR (Analytical Spectral Devices 1999) in the wavelength range 350–2500 nm on snow spectral reflectance at the time of satellite passes. The reflectance is calculated as the ratio of incident solar radiation reflected from the target and the incident radiation reflected from a white reference Spectralon (approximately a Lambertian surface). Numerous instruments are used to collect the reflectance and ancillary parameters in the field as shown in Fig. 3. These field results are used for validation with satellite estimated spectral reflectance in AWiFS and MODIS spectral bands after atmospheric and topographic corrections.

Figure 3
figure 3

(a-b) Instruments used during field experiment (c) Field site at Dhundi Lat/Log: 32°21′22″N/ 77°07′38″E (d) Field Investigation to record Hyper Spectral Characteristics by author

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Classification by Support Vector Machine (SVM)

To perform supervised classification on images, support vector machine (SVM) is used to identify the class associated with each pixel. It separates the classes with a decision surface that maximizes the margin between the classes. SVM is radial basis function (RBF) kernel. This kernel nonlinearly maps samples into a higher dimensional space so it can handle the case when the relation between class labels and attributes is nonlinear. Mathematical representation of radial basis function (RBF) kernel (Hsu et al., 2007) is listed as

$$ \mathrm{K}\left({\mathrm{x}}_{\mathrm{i}},{\mathrm{x}}_{\mathrm{j}}\right) = \exp \left(-\gamma {\left|\left|{\mathrm{x}}_{\mathrm{i}} - {\mathrm{x}}_{\mathrm{j}}\right|\right|}^2\right),\ \gamma > 0 $$

Where γ is the gamma term in the kernel function for all kernel types except linear.

To evaluate all above selected methodology and classification results, the selection of endmembers based on “Spectral Hourglass” processing scheme (Kruse et al., 2003) were implemented. This Procedure includes the generation of Minimum Noise Fraction-Images (MNF) for data dimensionality estimation and reduction by decorrelating the useful information and separating noise (Green et al., 1988), Pixel Purity Index-Mapping (PPI) for the determination of the purest pixels in an image (as potential endmembers) utilizing the (uncorrelated) MNF-images and finally the extraction of endmembers utilizing the n-Dimensional-Visualizer tool. The extracted endmembers spectra are then compared with the in-situ measured spectral reflectance using optical spectroradiometer.

Topographically Uncorrected Surface Reflectance

Image-based atmospherically corrected spectral reflectance (RλT) on the tilted surface from sensor radiance (Lλ) is obtained by using the following model (Song et al., 2001; Pandya et al., 2002)

$$ {\mathrm{R}}_{\lambda \mathrm{T}}=\frac{\pi \left({\mathrm{L}}_{\lambda }-{\mathrm{L}}_{\mathrm{p}}\right){\mathrm{d}}^2}{\mathrm{t}\mathrm{v}\left({E}_0\ \cos {\theta}_{\mathrm{z}}{\mathrm{t}}_{\mathrm{z}}+{E}_{\mathrm{d}}\right)} $$
(1)

Where Lp is the path radiance in mW/cm2/sr/μm and estimated according to Chavez (1989), d is the Earth–Sun distance in astronomical units and calculated using the approach of Van (1996). E0 is an exoatmospheric spectral irradiance (Mishra et al., 2010), Ed is the downwelling spectral irradiance at the surface due to diffused radiation and assumed to be equal to zero according to Chavez (1989), θ z is the solar zenith angle and calculated (Kasten, 1962) for each pixel of the study area, tv is the atmospheric transmittance along the path from ground surface to sensor and tz is the atmospheric transmittance along the path from Sun to ground. Further this model was modified by Shepherd and Dymond (2003) as

$$ {\mathrm{R}}_{\lambda \mathrm{T}}=\frac{\pi \left({\mathrm{L}}_{\lambda }-{\mathrm{L}}_{\mathrm{p}}\right){\mathrm{d}}^2}{\mathrm{t}\mathrm{v}\left({E}_0\ \cos {\theta}_{\mathrm{z}}{\mathrm{t}}_{\mathrm{z}}+{E}_{\mathrm{d}}+{E}_{\mathrm{t}}\right)} $$
(2)

Where the parameter Et is the terrain irradiance contributed due to reflected radiation from the adjacent terrain. The effect needs to be included in topographic correction for satellite data with fine spatial resolution (Liu et al., 2009). In case of coarse spatial resolution, it is negligible (Richter, 1998).

Topographic Models: A Brief Review

The removal of topographic effects based on DEM as an (a) empirical approache (b) Lambertian method (c) non-Lambertian methods can be found in many research papers (Smith et al., 1980; Teillet et al., 1982; Civco, 1989; Gu and Gillespie, 1998; Soenen et al., 2005; Hantson and Chuvieco, 2011; Ghasemi et al., 2013 and Sola et al. 2014) and few correction methods are experienced here in detail.

Cosine Correction

This method assumes the surface to be Lambertian and compute spectral reflectance of the land cover based on Teillet et al., (1982) as

$$ {\mathrm{R}}_{\lambda H}={\mathrm{R}}_{\lambda T}\left(\frac{ \cos\ \theta \mathrm{z}}{ \cos\ i}\right) $$
(3)

Where RλH is the spectral reflectance for horizontal surface, RλT is spectral reflectance observed over the inclined terrain; cos i is illumination (IL) and calculated using equation proposed by (Civco, 1989; Kawata and Ueno, 1995; Riano et al., 2003):

$$ \mathrm{I}\mathrm{L} = \cos i = \cos \left({\theta}_p\right)\ \cos \left({\theta}_z\right) + \sin \left({\theta}_p\right)\ \sin \left({\theta}_z\right)\ \cos \left({\phi}_a-{\phi}_0\right) $$
(4)

The local incidence angle, ‘i’ is defined as the angle between the direct solar rays and normal to the surface. θ z is solar zenith angle, θ p is the slope of the surface, ф a and ф 0 are the aspects of the surface and solar azimuth angle respectively.

C-Correction

The modified version of cosine correction algorithm has been introduced by Teillet et al., (1982) by assuming a non-Lambertian surface with the introduction of a quantity, C as

$$ {\mathrm{R}}_{\lambda H}={\mathrm{R}}_{\lambda T}\left(\frac{ \cos\ \theta C}{ \cos +i\ \mathrm{C}}\right) $$
(5)

In C-correction algorithm (equation 5), ‘C’ is a wavelength dependent correction parameter used to counterbalance and prevent the overcorrection of image. It is a quotient between intercept (bλ) and slope (mλ) in different spectral bands i.e. C = (bλ/mλ). This is estimated by using a regression equation assuming the linear relationship between original uncorrected reflectance and cos i as:

$$ {\mathrm{R}}_{\lambda \mathrm{T}} = {\mathrm{m}}_{\lambda }\ \cos\ i + {\mathrm{b}}_{\lambda } $$
(5a)

Minnaert Methods

Minnaert methods are non-Lambertian and implemented for topographic corrections by introducing Minnaert constant k (λ) that depends on the type of surface and spectral wavelength bands. It varies from 0 (ideally non-Lambertian surface) to 1 (perfect Lambertian surface). Minnaert method was further modified by Colby (1991) to include terrain slope, θ p , as follows:

$$ {\mathrm{R}}_{\lambda \mathrm{H}}={\mathrm{R}}_{\lambda \mathrm{T}}\ \cos\ \theta p{\left(\frac{ \cos\ \theta z}{ \cos\ i\ \cos\ \theta p}\right)}^{k\left[\lambda \right]} $$
(6)

The value of k (λ) can be determined by linearizing equation (6).

Slope-Matching Method

The slope-matching method was proposed by Nichol et al. (2006) a modification of Civco’s (1989) model and considered the topographic corrections in two stages. The final reflectance for topographic correction by Nichol et al. (2006) is estimated using:

$$ {\mathrm{R}}_{\mathrm{n}\lambda \mathrm{i}\mathrm{j}}={\mathrm{R}}_{\lambda \mathrm{i}\mathrm{j}}+\left({\mathrm{R}}_{\max } - {\mathrm{R}}_{\min}\right)\frac{\left[\left(\left\langle \mathrm{cosi}\right\rangle \mathrm{s}-\mathrm{cosij}\kern0.24em \mathrm{i}\right)\right]\mathrm{C}\lambda }{\left\langle \mathrm{cosi}\right\rangle \mathrm{s}} $$
(7)

Where Rnλij is the normalized reflectance values for image pixel ij in waveband λ, Rλij = RλT is the uncorrected original reflectance on the tilted surface for image pixel ij in waveband λ, Rmax and Rminare the maximum and minimum reflectance values, \( \left\langle \cos i\right\rangle s \) is the scaled (0–255) mean IL on the south aspect and Cλ is the coefficient estimated by equation proposed by Nichol et al. (2006).

Sun–Canopy–Sensor with C-Correction (SCS + C) Method

According to sun-terrain-sensor correction which is the combination of cosine correction and C-correction involves the terrain rotation to the horizontal surface does not correctly deal with canopy concept (Gu and Gillespie, 1998). Hence a concept of sun-canopy-sensor (SCS) correction was introduced by (Soenen et al., 2005) with C-correction as

$$ {\mathrm{R}}_{\mathrm{n}}=\mathrm{R}*\left(\frac{ \cos\ \theta p\ .\ \cos\ \theta z+C}{ \cos i+C}\right) $$
(8)

Where Rn is the normalized reflectance, R is the uncorrected reflectance, θ z is solar zenith angle, θ p is the terrain slope and the parameter C was chosen due to its past success in moderating the cosine correction.

Proposed Model (ESbTC) Description

A DEM based topographic correction model is proposed in the study to decrease the divergence caused by solar illumination on the same land cover but located on different (north and south) aspect of mountain so that the land cover class with the same reflectance in a different solar azimuth shows the same spectral response in optical remote sensing image. For this an improved dark object subtraction (DOS) technique (Chavez, 1996) was implemented and atmospheric transmittance from ground surface to sensor (tv) as well as atmospheric transmittance along the path from Sun to ground (tz) is calculated for AWiFS and MODIS sensor (Table 1) using the model (Pandya et al., 2002) as tv = exp (−τr/cosθ v ) and tz = exp (−τr/cosθ z ); where θ v is sensor zenith angle and τr is the optical thickness for Rayleigh scattering estimated by Kaufman (1989) as

Table 1 Atmospheric transmissivity in different spectral bands of AWiFS and MODIS dated
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$$ {\tau}_{\mathrm{r}} = 0.008569{\lambda}^{-4}\left(110.0113{\lambda}^{-2} + 0.00013{\lambda}^{-4}\right) $$

This is further implemented in topographic correction method based on empirical statistical analysis of the radiance values of remotely sensed data acquired for rugged terrain and the cosine of the solar illumination angle (cos i) as

$$ \begin{array}{c}\hfill {P}_{\lambda \mathrm{T}}={P}_{\mathrm{a}}\left(\mathrm{x},\mathrm{y}\right) + K\left(\lambda \right)*{P}_b\left(\mathrm{x},\mathrm{y}\right)\hfill \\ {}\hfill {P}_a\left(\mathrm{x},\mathrm{y}\right)=\left[\frac{\pi \left({\mathrm{L}}_{\lambda }-{\mathrm{L}}_{\mathrm{p}}\right){\mathrm{d}}^2}{\mathrm{t}\mathrm{v}\ \left({E}_{0\;}\; \cos {\theta}_{\mathrm{z}}{\mathrm{t}}_{\mathrm{z}}+{E}_{\mathrm{d}}+\mathrm{p}\left(1- \cos \theta {p}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right.\right)\ }\right]\hfill \end{array}\mathrm{And}\;{P}_b\left(\mathrm{x},\mathrm{y}\right)=\left[\frac{\left(\left\langle \cos i\right\rangle \mathrm{south}- \cos {}_{\mathrm{xy}}\;i\right)}{\left\langle \cos \mathrm{i}\right\rangle \mathrm{south}}\right] $$
(9)

Where (x,y) are the horizontal coordinates corresponding to the georeferenced pixel position,P λT Image-based atmospherically as well as topographic corrected spectral reflectance on the tilted surface, P a is the at-sensor radiance reflected for the pixel and a surrounding region, Ed is the diffuse solar radiation based on solar constant (S0 = 1353 W/m2), slope of the surface θ p and elevation angle of the sun, a i.e. Ed = S0 τd cos2 θ p /2sina. Gates (1980) explained as scattering increasing, the radiation diffusion coefficient τd increases represented as τd = (0.271-0.294τm), τ is atmospheric transmittance and m is the air mass ratio defined as the ratio of the path length in the direction of the sun (the zenith angle of the sun with respect to the surface) and the path length in the vertical direction. ρ is the initial value of the average terrain reflectance. Whereas in the second part of the equation 9, K (λ) is the correction coefficient for different spectral wave band λ represented as

$$ K\left(\lambda \right)=\frac{\left(\varDelta \lambda -\eta \lambda \right)}{\left(\varDelta \lambda -\eta \lambda \right)-\left(\varDelta \lambda -\eta^{\prime}\lambda \right)}+\frac{\left(\varDelta \lambda -\lambda \right)}{\left(\varDelta \lambda -\omega \lambda \right)-\left(\varDelta \lambda -\omega^{\prime}\lambda \right)} $$
(10)

In uncorrected image for different spectral waveband λ; ηλ and ωλ are the mean reflectance value on north and south aspect of the image respectively with ∆λ is the mean original reflectance of the entire image and after normalization η’λ and ω’λ are considered as the mean reflectance values on north and south aspect respectively. Whereas cosxy i is the illumination image for each pixel (x,y) of the study area and 〈 cos i〉 south, is the scaled (0–255) mean illumination on the south aspect of the image.

In this paper several parameters defined above are repeated and their parameter definitions are the same throughout this document.

Results and Discussion

Terrain and Solar Parameters Generation

Terrain parameters viz., slope, aspect, illumination and solar parameters like solar zenith angle, solar azimuth angle and sun elevation angles are computed for each pixel of AWiFS–10-Nov-2010, 25-Mar-2011, 26-Jan-2012 and MODIS- 12-Feb-2008, 13-Apr-2009 by using equations given in the literature (Kasten, 1962; Teillet et al., 1982). Slope varies from 0°–89° and Terrain aspect varies from 0°–360°. These inputs are required in topographic correction models for Himalayan terrain. These images are selected in such a way to test the suitability of the models for different varying sun elevation angle approx from 33° (low sun elevation) to 55° (high sun elevation). Other parameters values are given in Table 2.

Table 2 Terrain and Solar Parameters
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Terrain slope, aspect and illumination image of the study area in AWiFS-26 Jan 2012 and MODIS-13 Apr 2009 are shown in Fig. 4 (a-f). Illumination images are computed by using equation 4 (Civco, 1989; Kawata and Ueno, 1995; Riano et al., 2003). The Illumination vary from − 1 (low illumination) to +1 (high illumination) which is rescaled to a range of 0–255 for the topographic models.

Fig 4
figure 4

Images (a-b) Slope (c-d) Aspect (e-f) Illumination of study area for AWiFS-26 January 2012 and MODIS – 13 April 2009 respectively.

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Estimation of Coefficients

For different date images of AWiFS and MODIS, the results of different coefficients values in C-correction method is estimated by using a regression (equation 5a) assuming the linear relationship between original uncorrected reflectance and cos i. The value of coefficient in Minnaert method is determined by linearizing the equation 6. In slope matching methods coefficient is estimated by equation proposed by Nichol et al. (2006) and in SCS + C method coefficient is estimated by moderating the cosine correction (equation 8). On the other hand the value of coefficient for ESbTC model is estimated by using equation 10. An estimated coefficient of different models is shown in Table 3. It is noticed that the differences among the coefficients are accredited to different solar zenith, azimuth angle, illumination condition and temporal changes in snow surface physical properties. The results of correction coefficient K (λ) form equation 10 are attributed to non-Lambertian surface. It can be inferred that Himalayan snow is non-Lambertian although most of the authors have assumed snow surface to be Lambertian in their reflectance model (Xin et al., 2002; Srinivasulu and Kulkarni, 2004).

Table 3 Coefficient for different topographic models
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Qualitative (Visual) Analysis

The comparative visual analysis of topographic uncorrected image with one of the results of AWiFS (26 January 2012) and MODIS (13 April 2009) in false colour composite images using different topographic methods (cosine, C-orrection, Minnaert, slope match, SCS + C and ESbTC) are shown in Figs. 5, 6 and 7 respectively reveals that occlusion due to terrain illumination effects in the original image (Topographic uncorrected) are still prominent except slope matching and ESbTC model.

Fig 5
figure 5

Topographic uncorrected FCC reflectance image (a) in band 3, 2 and 1 of AWiFS-26 January 2012 (b) in band 3, 4 and 3 of MODIS −13 April 2009.

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Fig 6
figure 6

Topographic corrected image of AWiFS (26-Jan-2012): (a) Cosine Correction (b) C-Correction (c) Minnaert Correction (d) SCS + C (d) Slope Match (f) ESbTC

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Fig 7
figure 7

Topographic corrected image of MODIS (13-April-2009): (a) Cosine Correction (b) C-Correction (c) Minnaert Correction (d) SCS + C (d) Slope Match (f) ESbTC

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Area of slopes in north aspect are still darker and 3-D relief is not suppressed completely (Figs. 6 (a-d) and 7 (a-d). Whereas corrected image using slope match (Fig. 6e and 7e) and ESbTC (Fig. 6f and Fig. 7f) shows flat view of the terrain and minimize 3-D relief that shows very high brightness on the sunny (south aspect) and shady slopes (north aspect). Fig. 8 (a-e) shows topographic corrected images by using ESbTC algorithm all AWiFS and MODIS images.

Fig 8
figure 8

Topographic corrected images using proposed ESbTC algorithm for AWiFS (a) 26-Jan-2012 (b) 10-Nov-2010 (c) 25-Mar-2011 and MODIS (d) 12-Feb-2008 (e) 13-Apr-2009.

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Quantitative Analysis

In order to evaluate the model efficiency quantitatively, a snow spectral reflectance on North (shady slopes) and South (Sun-facing) aspect of entire image of the study area in radiometrically corrected and uncorrected images of AWiFS and MODIS bands are computed as shown in Table 4. Fig. 9 (in-situ observation) indicate the snow reflectance is very high in visible bands which suggests that the value of apparent reflectance of snow in north aspect of uncorrected images cannot be low otherwise it can be attributed to shadowing effects on shady slopes. But it has been noticed from Table 4 corrected values of snow reflectance on north aspect using cosine correction, C-correction, Minnaert correction and SCS + C are not comparable in fact both aspects has same snow cover whereas in slope matching it is slightly comparable to the true values of south aspect. After radiometric correction (atmospheric and topographic) with ESbTC model, the snow reflectance on north aspect (shady slopes) shows true situation (Table 4).

Table 4 Comparative analysis of snow spectral reflectance on North and South aspect of entire image of the study area in AWiFS and MODIS using different topographic models
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Fig 9
figure 9

In-situ observations of spectral reflectance characteristics of pure snow (a) 26 January 2012 and (b) 13 February 2009.

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Graphical Analysis

To check the authenticity of the models a graphical analysis of spectral response with illumination, before and after correction by using different models for AWiFS and MODIS images has been analyzed. The results suggest that reflectance changes with illumination for the uncorrected image (Fig. 10 (a)). It suggests that topographic correction is required for satellite imagery. The results after topographic correction using Cosine Correction, C-Correction, Minnaert Correction and SCS + C model still shows the variation in reflectance value with illumination (Fig. 10 (b-e)). While reflectance is constant with different values of illumination for slope match and ESbTC model (Fig. 10 (f) and Fig. 10 (g)). Table 5 shows the value of slope of the linear regression with better sun angle independency for slope match and ESbTC than other above discussed model.

Fig 10
figure 10

Graphical analysis of reflectance in visible band with illumination for AWiFS 26 January 2012 (a) before topographic correction and after topographic corrections using (b) Cosine Correction (c) C-Correction (d) Minnaert Correction (e) SCS + C (f) Slope Match (g) ESbTC Model

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Table 5 Regression relationship and correlation coefficients (R2) between visible band reflectance (AWiFS-B2 and MODIS-B3) and illumination cos i
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Model Validation with Field Results

Topographic results of AWiFS (26 Jan 2012) and MODIS (13April 2009) images are validated with in situ observations collected at number of points for pure snow spectral reflectance samples recorded at Dhundi (Lat/Log: 32°21′22″N/ 77°07′38″E) at an altitude of about 2851 m and Patseo (Lat/Log: 32°45′18″N/77°15′43″E) at an altitude of about 3800 m respectively (a SASE’s permanent field observatory) using optical spectroradiometer at the time of satellite pass in the wavelength range 350–2500 nm. Snow reflectance value of field observation for both dates is shown in Fig. 9. The comparison of field results with satellite-estimated reflectance values before and after the topographic corrections in Table 6 shows that all the methods except ESbTC underestimate the reflectance values whereas slope match is slightly matched. Snow reflectance values on north and south aspect from Table 4 and reflectance values at test site from Table 6 designate a better response of the ESbTC model as it retrieve information under shadow area.

Table 6 Validation of topographic models with field results of spectral reflectance using spectroradiometer
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Snow Cover Estimation and Validation

After topographic corrections, in order to confirm the actual land cover especially in shady areas the results are compared with the normalized difference snow index (NDSI) for AWiFS and MODIS images (Hall et al., 1995). Its values vary from −1 to +1. The positive value for snow and negative for non-snow. This classification further validated with support vector machine (SVM), a supervised classification technique (Table 7). A classified map of snow and non-snow area with NDSI and SVM for AWiFS (25 Mar 2011) and MODIS (13 April 2009) shown in Fig. 11. The visual comparative analysis of topographically corrected results by ESbTC (Fig. 8) with NDSI and SVM (Table 7) shows that only this method gives most acceptable results and retrieves the actual land cover information for low illumination and other methods not succeed for Himalayan terrain especially with varying altitude from 1100 m to 6700 m.

Table 7 Percentage SCA with NDSI for different topographic models and its validation with supervised classification technique (SVM).
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Fig 11
figure 11

A Classified snow and non-snow area with (a-b) NDSI and (c-d) SVM; For AWiFS (25 Mar 2011) and MODIS (13 April 2009) respectively.

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Conclusion

In the present paper the qualitative (visual) and quantitative analysis of different topographic correction methods for AWiFS and MODIS images has been discussed. Results (i) Visual analysis: suggests that ESbTC method is most suitable than slope matching methods where as other methods are not suitable for Himalayan terrain especially with varying altitude from 1100 m to 6700 m. (ii) Results from Table 4 i.e. on comparing snow spectral reflectance on north and south aspect of entire image display the weightage of ESbTC algorithm than other topographic algorithms as mentioned above. (iii) Graphical analysis also satisfies the topographic correction condition for the method and validates suitability for Himalayan region. (iv) Model validation with field results except ESbTC and slope matching fails for all the other methods. The cosine correction, C-correction, Minnaert correction, SCS + C correction not very successful and produce poor results. These methods show completely non-Lambertian behaviour of the Himalayan terrain. Further (v) the classification of land cover (snow and non-snow) area with NDSI and supervised classification (SVM) also indicates the suitability of ESbTC algorithm for Himalayan region. Hence it is concluded that the above discussed models satisfies only one or two criteria of their performance whereas slope matching methods satisfies all the five criteria successfully but ESbTC model satisfies the same criteria with better efficiency than slope matching. Thus ESbTC model is found to be a unique and most suitable algorithm for Himalayan terrain with varying solar geometry, altitude from 1100 m to 6700 m for qualitative and quantitative analysis of snow cover.

Further research can be focus on the entire Himalaya with higher altitude (>7000 m) for different periods of satellite images to check the suitability of ESbTC model.