2.1

Study Area

This study was conducted in a subset of a 23x23 km area in South Sulawesi, further referred to as the area of interest (AOI). The AOI is laid on an old volcanic region, specifically on Baturappe – Cindakko volcanic rock formation (Tpbv). The landscape is dominated by forest and agriculture landcover, with undulating relief forming a circular pattern. The relatively flat area is also visible in southwest region, near the left bottom of the rectangular shown in figure 1. The combination of slopped and flat area is essential to evaluate the performance of topographic correction since it can give a more comprehensive variation on the pixel values.

Figure 1.

Overview of the Area of Interest (marked by the red rectangle) over South Sulawesi.

2.2

Digital Elevation Model (DEM)

DEM represents the 3D information on the ground and is a paramount variable needed for semi-empirical Topographic correction. Shuttle Radar Topographic Mission (SRTM) has been around since 2000 and been widely used for various applications. Among these studies, ^{1,2,4,6,8,9,14,24–27} were all used SRTM data for correcting the topographic effect on EO Satellite data.

ALOS World 3D-30m (AW3D30) is the Japan Aerospace Exploration Agency (JAXA) project to provide a global digital 3D map. This project utilized PRISM panchromatic stereo mapping sensors aboard the Advanced Land Observing Satellite (ALOS), which is operated from 2006 to 2011. AW3D30 is a global Digital Surface Model (DSM) with 30 meters spatial resolution and first released on March 2017^25,28–30.

^9,10,31,32 Previously explained that it is appropriate to use a DEM with a similar grid size as the spatial resolution of the analyzed imagery. In this initial study, three types of DEM with different spatial resolution were analyzed based on their original resolution without prior resampling. Table 1 summarizes the DEMs used in this study.

Table 1.

Digital Elevation Model Specification used in this study.

2.3

LAPAN-A3/LAPAN-IPB

For convenience, LAPAN-A3/LAPAN-IPB will be addressed as LA3 in the further section of this paper. The LA3 data used in this study was acquired on 28^th August 2018 at 09.34 AM local time. The sun azimuth was at 69.4437, with the elevation of 50.7594.

2.4

Preprocessing

The first step of our study started with geometric correction. Fifty 50 ground control points (GCP) were manually selected and used in the geometric correction. Landsat-8 Tier-1 data were used as the reference using image-to-image correction ³³ methods. Due to the undulating nature of the scene, the geometric correction was performed using the second degree of polynomial³⁴. The root means the square error was kept under 1 pixel (15 meters). After the image was geometrically corrected, the next step was to subset all the data using the same AOI boundary, described before. Noticed that, no prior radiometric and atmospheric correction were performed to the LA3 data. The main reason was that at the time of the writing of this paper, the necessary parameters for atmospheric correction was not available yet²⁰.

2.5

Topographic Correction

The Minnaert algorithm is based on the non-Lambertian reflectance assumption. What makes it different from the Lambertian model is the use of k constant. This particular k constant was based on the bidirectional reflectance distribution function. The k values range from 0 to 1.0 indicates non-Lambertian surface, and 1 indicates a Lambertian surface¹⁵. The Minnaert algorithm can be expressed with the following formula:

Where,

L_m = radiance after correction

L = radiance before correction

L_min = minimum radiance before the correction

i = solar incident angle

e = angle of incidence the sensor received

k = the Minnaert constant

the equation (1) can be rewritten as,

Using both sides of the variable, the equation (1) can be translated as:

If we consider ln L_m as m, ln(L * cos e) as y, and ln(cos i * cos e) as x, then the equation (3) can be formulated as a linear function of,

The linear regression function was plotted from the point samples and must be extracted from the same landuse/landcover type³⁵. All samples used in this study were taken from the forest region. As the middle ground, k values were set at 0.5 for all bands since the AOI is a combination of the flat and sloped area as shown in figure 1.

2.6

Performance Evaluation

To evaluate the performance of different DEMs used for topographic correction, visual inspection used to see the difference before and after correction⁷. The next step was to perform quantitative analysis on both before and after topographic correction. The decreased variation coefficient (CV) is a widely used method for validating topographic correction^1,9. It is also referred to as a test of homogeneity^{3,4,6,9,36,37}. To assess the effectiveness of each DEM, the means and standard deviation (SD) were calculated and compared for both before and after correction. Next, the variation coefficient was calculated as well, also referred as Dispersion Indices⁸. For the statistical analysis, 85 sample points were selected on slopped region.

3.1

Visual Evaluation

Figure 2 shows the confirmed effect of the topographic correction on LA3 using all three DEMs. The topographic correction has visibly taken effect on the west and southwest facing slopes. The visual appearance on SRTM gives better results (figure 2a, while DEMNAS and AW3D30 give similar appearances (figure 2b and 2c). Looking closer, some overcorrection was found on DEMNAS and AW3D30, specifically on high slopes and shadowed slopes (greater than 40° as shown in figure 2b and 2c).

Figure 2.

Hillshade of Digital Elevation Model used in this study, (a) SRTM, (b) AW3D, (c) DEMNAS, and (d) False-color composite of LAPAN-A3 data of the same area. Hillshade at the sun azimuth of 315° and the sun altitude of 45°.

Figure 3.

Visual comparison of topographically corrected LAPAN-A3 using Minnaert Correction using different DEM, (a) SRTM, (b) AW3D, (c) DEMNAS, and (d) Original LA3 image. All images are shown in the RGB composite of NIR-R-G.

3.2

Quantitative Evaluation

Table 2 shows the coefficient of variation for each band and each DEM source, including the original and corrected image. Looking at how much CV change after correction, each DEM gives different change in the CV. The best performance, however, is not dominated by a single DEM source. AW3D performed best on both B and R band, while SRTM and DEMNAS performed best for G and NIR bands, respectively. Figure 4a to figure 4d shows how all these DEM performed for each band, while 4e shows the different magnitude of CV changes. A good topographic correction should decrease CV values⁶. This case only happens for NIR bands. All three DEMs were able to decrease CV value. For the R band, AW3D and SRTM were able to reduce the CV. DEMNAS, however, saw an increase in the CV. The G and B bands were all saw increased CV values after corrected. The initial assessment presented here shows how the topographic correction method produces an increase in CV value. The increase in CV values is more common than the reduction of CV. On average, AW3D30 performed the best as it offers an even result between the numbers of bands with CV value was decreased and vice versa. Looking at the number of bands with decreased CV in table 2, it would be easy to point out that DEMNAS performed the worst of all three DEMs, as it was only able to reduce the CV for 1 band (NIR). However, looking at figure 2E, SRTM gave the biggest increase in CV value after corrected. Looking at the graph in figure 2E, SRTM eclipsed other DEM in terms of CV value change. For the B band, SRTM increased the CV up to 196.40, compared to both AW3D and DEMNAS.

Figure 4.

Coefficient correlation for three different DEM compared to the original value. (a) Coefficient variation for Blue band, (b) Coefficient variation for green band, (c) coefficient variation of red band, (d) coefficient variation of Near-Infrared Band, (e) coefficient variation for all bands to show the different magnitude of CV across four different DEMs.

Table 2.

Coefficient variation and standard deviation for each band before and after topographic correction. A negative value indicates an increase in coefficient variation after correction. Bold CV value marked the best performer.

Table 3 shows the comparison parameters for all three DEMs used. The overall better performer is the AW3D, with the most number of bands reduced, and the only DEM source to give positive value on total CV reduced for all bands. While SRTM gave the same amount of bands with reduced CV and a better visual appearance, its total CV changed after correction with the magnitude of more than 400 times the best performer is just too much. The AW3D performance has also been a nod to how earlier findings of ^6,9 explained that for topographic correction based on modeling of illumination, the same spatial resolution between DEM and the investigated image is required. Thus, the next plan of this study is to see how these DEMs performed when its spatial resolution is at the same size.

Table 3.

Comparison overview for all three DEMs used with the topographic correction performance parameters used in this study. A negative value on the total CV value indicates an increase in coefficient variation after correction.

The success in CV reduction for the NIR band found in this study is consistent with what ⁶ previously found, who found the reduction on CV for the vegetation-sensitive band (NIR and SWIR of Landsat TM-5). Since no prior radiometric/atmospheric correction was performed to LA3 data, the fact that NIR band is the least affected by atmospheric conditions compared to B, G, and R band¹⁶ is also a factor to how the topographic correction could be performed well. Therefore, it is vital to investigate further how the topographic correction performed when prior radiometric/atmospheric correction was conducted.