Grazer Schriften der Geographie und Raumforsc Raumforschung hung
Band 45/ 45/2010 2010
pp. 187 - 194 194
Topographic correction of satellite images for improved LULC classification in alpine areas P. Füreder Z_GIS Centre for Geoinformatics, Salzburg, Austria
Abstractt Abstrac Automated land use / land cover (LULC) classification is hampered in areas of high relief due to shadowing effects, which results in different values for one and the same land cover class. The purpose of this study was to reduce the topographic effect of Landsat TM images in a mountainous study area in Tibet. Different methods of topographic normalization (cosine correction, Minnaert correction, C-correction and statistic-empirical correction) were evaluated and compared visually and statistically concerning concerning quality and usability in order to improve the following LULC classification. KEY WORDS: topographic correction, land use / land cover (LULC) classification, Landsat Thematic Mapper (TM)
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1. Introduction The operational use of remote sensing data is often limited due to sensor variation, atmospheric effects as well as topographically induced illumination effects (Ekstrand 1996, Twele and Erasmi 2005). Topographic normalization is therefore, especially in rough terrain, important for improving analysis of remote sensing data (e. g. image classification). Although numerous topographic normalization methods have been proposed in the past, none of them has been found to be universally applicable, and therefore topographic normalization is still a pre-processing issue rarely used. The intensity of illumination on the surface depends on the orientation of the surface in respect to the sun. Different slope and aspect angles are inducing variable illumination angles and thus diverse reflection values. Areas of high relief therefore show high radiometric variation. Depending on topography reflection values within one land cover type can vary a lot. The illumination variations result in lower reflection values in the shadow and higher values in the sun for the same land cover class. Hence, reflection values of different land cover types in equal conditions of illumination can be more similar than within one land cover type in shadow and sun, leading to problems in image segmentation and possible misclassifications (Twele and Erasmi 2005, Civco 1989). Topographic normalization methods try to compensate for the topographically induced illumination variations in advance.
2. Study area
area is characterised by steep slopes and rugged terrain with elevations ranging from 3.500 to more than 7.000 meters. These conditions create significant shadowing effects in the data. The vegetation in the study area is mainly alpine grassland, minor parts are covered by shrubland, pasture, bushland, arable land and a very small part by forest. A relatively high portion of the land cover can be attributed to non-vegetated areas, mainly bare ground, ice and snow.
3. Topographic correction methods The simplest method for compensating the topographic induced variable illumination is building of band ratios wherefore no additional data is required. It is based on the assumption that the relative topographic effect is similar in all bands and the quotient of two bands can compensate for this. This method does not account for the diffuse irradiance, which depends on each band, and therefore can only partly compensate the topographic effect, provided that the atmospheric path radiance is eliminated in advance (Ekstrand 1996). A further disadvantage in terms of multispectral classification is the loss of spectral resolution when using band ratios (Riaño et al. 2003). Real topographic correction methods try to model the illumination characteristics of a horizontal surface by means of a DEM. For this purpose it is required to calculate the local solar incident angle (i), the angle between the current position of the sun (depending on solar zenith angle and solar azimuth) and the local surface (terrain slope and aspect) (see Fig. 2).
The study area, which was defined within the project BrahmaTWinn, is located as part of the Brahmaputra (in Tibet called Yarlung Tsangpo) catchment in Tibet (China) and represents the catchment of the Lhasa River. The ma jor part of the area is situated in the prefecture-level city Lhasa and a minor part in the pr efecture Naqu (Fig. 1). The total area is about 33.000 km 2. The mountainous study
Figure 2: Angles necessary for computing the incident angle
(based on Teillet et al. 1982).
Figure 1: study area “catchment of the Lhasa River” in Tibet (Chi-
na).
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The illumination (cos i) can be computed as follows: cos i cos e cos z sin e sin z cos (a a' ) where
local solar incident angle slope angle z solar zenith angle a solar azimuth angle a' aspect angle
incident angles and is therefore problematical for steep and sun-averted slopes, which appear brighter than sunfacing slopes (Civco 1989, Twele and Erasmi 2005, Teillet et al. 1982, see chapter 6).
i
e
The value of cos i varies from -1 to +1, whereas a value < 0 indicates shadowed slopes, which do not receive direct irradiance (Ekstrand 1996).
3.1. Lambertian and non-Lambertian methods The topographic correction methods can be classified in two categories according to their assumption of reflection characteristics of surfaces: Lambertian and non-Lambertian methods. Lambertian methods like the cosine correction are assuming a surface, which reflects the incident radiation in all directions equally, neglecting the atmospherical influences. Non-Lambertian methods are actually not physically based but try to model the diffuse irradiance by means of constants of the bidirectional reflectance distribution function (BRDF), which describes reflection characteristics of surfaces. The amount of the correction depends on the wavelength. So the assessment of the constants for each band separately is required. The topographic effect is thereby most dominant in the near infrared band (Civco 1989). As reflection characteristics are related to the land cover, the constants should also be calculated for each land cover individually (Twele and Erasmi 2005, Teillet et al. 1982, Bishop et al. 2003), resulting in a respectable effort.
3.2. Cosine correction The cosine correction, which neglects the diffuse irradiance, only considers the solar zenith angle and the local solar incident angle for computation of the local illumina LT
L H
cos z cos i
where L H LT z i
reflectanc e of a horizontal surface reflectanc e of an inclined surface
solar zenith angle local solar incident angle
3.3. Minnaert correction The most common non-Lambertian topographic correction method is the Minnaert correction, which is based on the ideas of Minnaert (1941), who initially proposed a semi-empirical equation for describing the roughness of the moon’s surface. The Minnaert correction extends the cosine correction as follows: cos z L H LT cos i
k
where L H LT z i k
reflectanc e of a horizontal surface reflectanc e of an inclined surface solar zenith angle local solar incident angle Minnaert constant
The constant k models the extent, to which a surface is Lambertian. It is determined by linear regression between reflection values of the input image (LH) and the angles (i and e). The value of k lies between 0 and 1, whereas 1 characterises a Lambertian surface.
3.4. C-correction This semi-empirical approach, developed by Teillet et al. (1982), is similar to the Minnaert correction. The factor c should model the diffuse irradiance and compensate the overcorrection effects of the cosine correction (Twele et al. 2006). The factor c can be derived from the quotient of the gradient and intercept from the regression line: LT
L H
cos z c cos i c
where
reflectanc e of a horizontal surfac e reflectanc e of an inclined surface LT z solar zenith angle i local solar incident angle L H
c m b
b m
for LT m cos i b
gradient of regression line : LT cos i intercept of regression line : LT cos i
tion:
3.5. Statistic-empirical correction
This method is frequently used because of its implementation in many software programs but it strongly over-estimates the influence of direct irradiance in areas of high
The statistic-empirical correction is a regression-based approach which assumes a linear correlation between the reflection of each band (LT) and the illumination (cos i)
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L H
geo
LT cos i mk b LT
where L H LT
reflectanc e of a horizontal surface reflectanc e of an inclined surface
local solar incident angle mk gradient of regression line for band k
i
b
intercept of regression line
LT
average reflectanc e of the land cover type under investigat ion
(Twele and Erasmi 2005, Meyer et al. 1993). The equation also contains the gradient and intercept of t he regression line: A disadvantage of this method is the inclusion of a class average since the topographic correction has to be applied to each land cover type separately, resulting in a time-consuming effort.
4. Data and methods 4.1. Satellite data The study area is covered by 5 Landsat TM scenes (with 30 m spatial resolution). The Landsat images acquired from GLCF (http://glcf.umiacs.umd.edu) have been corrected geometrically and transformed into the coordinate system UTM WGS 84, Zone 46 North within the project BrahmaTWinn. All Landsat TM scenes are cloud free. The acquisition dates vary in years and seasons (see Table 1). The images taken in September have good illumination conditions, whereas in the winter images (November) steep areas are fully shady due to the low sun elevation angle. But these images cover only a minor part of the study area (see Fig. 3).
4.2. Digital elevation model (DEM) For the topographic normalization and the following ob ject-based LULC classification, a SRTM (Shuttle Radar Topography Mission) with 90 m spatial resolution has been available already corrected and calibrated within the pro ject BrahmaTWinn. As the quality of the topographic normalization is highly depending on the spatial resolution of the DEM the resolution should be at least as fine as the satellite image (Civco 1989). The SRTM is therefore suboptimal for topographic correction of Landsat TM data, but the availability of high resolution DEMs is - especially in remote areas - often limited. In this study the result could be improved by resampling the SRTM to the resolution of the satellite image by a bilinear interpolation algorithm. The nearest neighbor algorithm is not adequate for resampling to a smaller cell size, because it results in a “ stair stepped effect around diagonal lines and curves” (Leica Geosystems 2003).
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Figure 3: Landsat TM scenes and proportion of the study area on
the scenes. path / row
acquisition date
cloud cover (%)
solar azimuth
solar zenith
137/038
14-Sep-88
0
132
52
137/039
14-Sep-88
0
130
53
137/040
1-Nov-90
0
148
41
138/039
14-Sep-91
0
128
52
138/040
14-Nov-90
0
147
36
Table 1: Details on Landsat scenes.
4.3. Topographic corrections tested For reducing the topographic effect cosine-correction, Minnaert correction, statistic-empirical correction and Ccorrection were tested. Two different software programs - ERDAS Imagine and PG-Steamer - were used for the computation. In ERDAS Imagine the cosine correction and Minnaert correction are incorporated, whereas the value of constant k has to be specified by the user. The software program PG-Steamer provides the cosine correction, the Minnaert correction, the C-correction and the statisticempirical correction. The factor c for the C-correction is calculated automatically, the Minnaert correction, however, also requires the input of constant k. According to Mäkelä et al. (2004) the constant k can also be determined by visual interpretation. The constants were estimated as shown in Tab. 2. The statistic-empirical correction implemented in PGSteamer requires the input of the average reflectance from each land cover type in each band. As previous clasband Minnaert constant
1
2
3
4
5
7
0.22
0.3
0.3
0.3
0.25
0.3
Table 2: Estimated Minnaert constants.
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sification was not intended, the average reflectance value of each band was used to test this method.
5. Results The results of the different topographic methods were analysed visually and statistically. The visual analysis clearly indicates that the cosine correction strongly overcorrects weakly illuminated areas like slopes facing away from the sun whereas they appear brighter than sun-facing slopes. Instead of reducing spectral variances, the normalized image appears more distorted. As already observed in other studies (Meyer et al. 1993, Twele et al. 2006) the C-correction, the Minnaert correction and the statistic-empirical correction visually do not show major differences and could successfully reduce the topographic effect (see Fig. 4), which implicates the loss of the three-dimensional impression. Overcorrection of mountain ridges, where illumination is very low, is also here evident. A higher resolution of the DEM could compensate the topographic effect better, whereby also smaller illumination variations could be corrected.
tion should reduce spectral variances and standard deviation and retain the mean (Law and Nichol 2004). The cosine correction also shows in the statistical comparison the worst result. Instead of reducing the standard deviation, there are even more spectral variances produced (Tab. 3). The C-correction could reduce standard deviation more effectively than the Minnaert correction, whereas the Minnaert correction could better retain the mean. The statistic-empirical correction provides the best statistical result with lowest deviation of the mean value and highest reduction of standard deviation in all bands although only the mean of each band instead of the mean for each land cover class was used for computation. In order to approve the results, the topographic correction methods have also been calculated on another subset. The statistic-empirical correction again revealed the best statistical result for vegetated areas. The reason for this could be that there are only minor differences of vegetation in the study area.
6. Constraints
5.1. Statistical Analyses
6.1. Overcorrection
Spectral differences between original and topographic normalized image should be low, otherwise it would be a sign of over- or undercorrection. Slopes facing away from the sun should get higher values, sun-facing slopes respectively lower values. An effective topographic correc-
The overcorrection of the cosine correction is a well-known phenomenon. In many cases, however, an overcorrection of low illuminated pixels with low value of cos i can be detected in non-Lambertian methods too (cf. Riaño et al. 2003, Meyer et al. 1993, Twele et al. 2006, Teillet et al. 1982,
Figure 4: Visual results of topographic correction methods (subset of Landsat TM 1 38/039, band combination 4-3-2).
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cosine correction
statististic-empirical correction
geo
C-correction
Minnaert-correction
band
μ
σ
μ
1
32.76
13.63
-0.59
-0.61
1.34
-0.03
0.36
0.87
2
16.39
7.79
-0.55
-0,6
0.96
0.2
0.56
0.65
3
19.4
7.53
-0.58
-1.07
1.75
0.11
1.5
0.58
4
28.09
11.02
-0.58
-1.54
2.2
-0.58
2.08
-0.14
5
37.22
9.74
-0.61
-3.48
4.72
-1.91
0.85
-1.12
7
17.8
5.32
-0.57
-1.85
2.49
-0.74
1.06
-0.15
total change
151.66
55.03
-3.48
-8.55
13.46
-2.95
6.41
0.69
μ
σ
σ
μ
σ
Table 3: Change of mean (μ) and standard deviation (σ ) of the reflection values from different topographic correction methods respecting
the original satellite image (Landsat TM 1 38/039).
Ekstrand 1996). These areas have a high proportion of diffuse irradiance, the direct irradiance approximates zero. Due to an insufficient estimation of the diffuse irradiance the value is highly adjusted upwards. Areas where cos i is zero, get “no data” values, as a division by zero is impossible (see Equation 1). In areas of low sun elevation angles or very steep slopes a huge amount of pixels can be affected by this problem. In this case it has to be appreciated if the topographic normalization still provides more advantages than disadvantages. Within the study area this problem occurred in the winter images (Fig. 5). As they have only a very small part on the study area (Fig. 3), these areas were classified as shadow. Mäkelä et al. (2004) avoid this problem by marginally changing the sun zenith angle. Other methods for solving this problem could be the smoothing of the slope, as suggested by Riaño et al. (2003) or the substitution of the nodata values with the original values.
6.2. Cast shadow Areas of sun-facing slopes, which are lying in the cast shadow of surrounding topographic features, are handled within the topographic correction methods as non-shadowed slopes (Leica Geosystems 2003, Meyer et al. 1993, Twele et al. 2006). The reflection values are adjusted downwards as cos i is high although these areas do not receive any direct solar irradiance (Fig. 6). The topographic effect can therefore not be corrected from steep areas - like deep valleys - and cast shadowed slopes. By means of a shaded relief areas of low irradiance (cos i <= 0°) can be detected and a line-of-sight algorithm
Figure 6: Exemplary situation of cast shadow.
Figure 5: Falsely corrected areas in terms of “no data” values.
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can identify pixels lying in cast shadow (Leica Geosystems 2003).
7. Conclusion The visual as well as statistical analysis clearly indicated that the cosine correction is not suitable for normalizing the topographic effect in the study area. Minnaert correction, C-correction and statistic-empirical correction proved to successfully reduce topographically induced illumination variations. Overcorrection, however, also occurs in areas of low illumination due to the inadequate estimation of the diffuse irradiance as well as the insufficient resolution of the DEM. Visual estimation of the Minnaert constant is not a very robust method, not transferable and furthermore timeconsuming. The statistic-empirical correction revealed surprisingly the best statistical result although the mean of each band instead of each land cover type was included. As already mentioned, topographic normalization should be applied to single land cover types due to their specific reflection characteristics. This, however, requires the identification of the land cover types in advance, which is rather the aim of the subsequent classification. Hence, this method turns out to be a vicious circle and results in a time-consuming application. Some authors (Twele and Erasmi 2005, Bishop et al. 2003, Herold et al. 2000) suggest dividing the image according to the NDVI. Further research is required for testing this recommendation and comparing the topographic normalization with land cover dependent constants and with global constants. Topographically normalized satellite images can, in general, obtain better classification results (Meyer et al. 1993, Colby 1991, Riaño et al. 2003, Twele et al. 2006). The lack of standardized methods, however, makes the application difficult. There are several software programs offering topographic normalization methods, however, most without automatically computation of constants, requiring previous knowledge about topographic normalization and therefore hampering the widespread use of topographic normalization.
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mination in Mountainous Areas of Central Sulawesi. -In: Erasmi S., B. Cyffka und M. Kappas (Ed.) (2005): Remote Sensing & GIS for Environmental Studies (= Göttinger Geographische Abhandlungen), Vol. 113, S. 287-295. - Göttingen. TWELE, A. et al., 2006: The effect of stratified topographic correction on land cover classification in tropical mountainous regions. - In: ISPRS 2006. VINCINI, M. and E. FRAZZI, 2003: Multitemporal Evaluation of Topographic Normalization Methods on Deciduous Forest TM Data. - In: IEEE Transactions on Geoscience and Remote Sensing, Vol. 41, No. 11, S. 2.586 - 2.590.
Correspondence to:
PETRA FÜREDER Z_GIS Centre for Geoinformatics University of Salzburg
Schillerstraße 30, A-5020 Salzburg, Austria e-mail:
[email protected]
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