slope values accuracy vs resolution of the digital

PROCEEDINGS OF ICC&GIS 2014 |1

SLOPE VALUES ACCURACY VS RESOLUTION OF THE DIGITAL ELEVATION MODELS (EXAMPLE OF THE REPUBLIC OF MACEDONIA) IVICA MILEVSKI PhD, Institute for geography, Ss. Cyril and Methodius University, Skopje Abstract In this study, analysis of slope angle accuracy measured from the available digital elevation models (DEM) covering the area of the Republic of Macedonia is made. Aside of global coarse to fine scale DEM’s (30"SRTM, 3"SRTM, 1"ASTER GDEM), two of the national 20 m and 5 m DEM’s are processed. Several test areas with different topography (plains, hilly-mountains and mountains) are selected for detailed analysis. Final data are compared with 5 m DEM which is used as a referent and most accurate model previously validated with traditional cartographic measurements from 25K topographic maps. Results show significant differences and degree of inaccuracy which grown from fine-scale to coarse scale DEM’s, and from flat areas to areas with high vertical relief. For minimize of these DEM’s-resolution related errors, several simple equations are realized. Key words: DEM, comparison accuracy assessment, Republic of Macedonia. SRTM (30 m) and 20 m DEM of the Agency of Real Estate and Cadastre of the Republic of Macedonia (ARECRM).

Dr. Ivica Milevski, Faculty for Natural Sciences and Mathematics, Ss. “Cyril and Methodius” University in Skopje. Gazi Baba n.n., 1000-Skopje, Republic of Macedonia e-mail: [email protected] INTRODUCTION In last decade several good quality DEM’s with global or almost global coverage and coarse to fine scale resolution were released for public usage. That is very significant because of increased needs for applications based on digital terrain modeling versus insufficient free or inexpensive high quality national DEM’s. These include free semi-fine scale 3"SRTM DEM (90 m) released to the public in 2004, and also free 1"ASTER GDEM (30 m) released in 2009 (v1) and revised in 2011 (v2). There are many discussions and studies which of both models is superior, because 1"ASTER GDEM has better resolution, but lower overall quality (Hengl & Reuter, 2011; Rexer & Hirt, 2014). Hence 3"SRTM DEM (which is downscaled version from the original 1"SRTM DEM) today is most used worldwide because of the quality as well as tolerable vertical and horizontal accuracy. Because of international coverage of this model, there are possibilities for topography comparison of different areas, regions and entire countries. After the initial release of the model in 2004, its quality was gradually improved by software algorithm corrections (Jarvis et al., 2008). According to our tests, 3"SRTM model has average horizontal and vertical accuracy of ±5 m, with maximum errors up to ±15 m (Milevski, 2005). Such height inaccuracies are generally due to the resolution of the model and the location of DEM points around the prominent peaks (Milevski et al., 2013). Aside of these two original models, there were many its derivatives like global 30"SRTM DEM (900 m) used for topography of large areas, ETOPO1 with resolution of 1 arc minute (about 1800 m) etc. The latest global DEM released this (2014) year is 12 m WorldDEM produced from image stereo pairs of TerraSAR-X and TanDEM-X mission. By many indications and preliminary analyses, this is the highest quality global DEM available yet (Huber et al., 2012). However, for now this product is commercial at relatively high price per km2. Except free SRTM and ASTER international DEM’s, another two models are available for the area of the Republic of Macedonia. That is 20 m DEM provided by the State Agency of Cadastre (SAC) in 2006, and the second is 5 m DEM provided by the Ministry of Agriculture, Forestry and Water Economy of the Republic of Macedonia

PROCEEDINGS OF ICC&GIS 2014 |2 (MAFWE) in 2010. Both have high overall quality, much better than 3"SRTM DEM and 1"ASTER GDEM (Milevski et al., 2013). However, because of some shifts and artifacts, with our work 20 m DEM of SAC is recently improved to 15 m resolution, while 5 m TIN-like DEM of MAFWE is interpolated to "soft-surface" 10 m and 15 m DEM resolutions. Thus, for the area of the Republic of Macedonia, several "original" models are available now: 5 m DEM (MAFWE), 12 m WorldDEM, 20 m DEM of SAC, 30 m ASTER GDEM, 90 m SRTM DEM, 900 m SRTM DEM etc., as well as improved and interpolated derivatives like 10 m and 15 m DEM. Because of such many available models with different resolution, quality and accessibility, the problem of selection and use of most suitable DEM for topographic modelling and other applications appear. That is especially important considering that DEM’s with highest quality are commercial and even highly priced for wider use. An comparison of resolution, data and modelling shifts and downgrades between 5 m, 10 m, 20 m, 30 m, 90 m DEM’s will bring good indications for right choice. One of the most representative indicators is differences between modelled and calculated slope values for the same area and this is actually intention of this work. A number of studies have attempted to establish direct, simplified linkages between DEM resolution, data quality, and modelling uncertainty (Chang and Tsai, 1991; Zhang and Montgomery, 1994; Chaplot et al., 2000; Wilson et al., 2000; Thompson et al., 2001; Milevski, 2005; Deng et al., 2007; Milevski et al., 2013). Chang and Tsai (1991) used DEM of different resolutions (20 m, 40 m, 60 m and 80 m) in order to examine the effect of resolution on slope gradient and slope aspect characteristics. The authors concluded that the accuracy of slope gradient and slope aspect computations decreased with larger cell sizes. Zhang and Montgomery (1994) found that the choice of resolution greatly affected the computation of slope gradient, specific catchment area and wetness index. Wilson et al. (2000) demonstrated that steep slopes were shown to disappear as the cell size was increased from 30 m to 200 m. Chaplot et al. (2000) show that 10 m and 30 m DEM were able to predict terrain characteristics (elevation above stream bank, downslope gradient and upslope contributing areas) in similar ways, however, the amount of error produced by these characteristics dramatically increased when using a 50-m DEM. Thompson et al. (2001) examined how the vertical and horizontal accuracy of DEM affects terrain attributes founding that using larger cell sizes produces lower slope gradients on steeper slopes and steeper slope gradients on flatter slopes. According to Deng et al. (2007), terrain attributes respond to resolution change in characteristically different ways, especially when the resolution is coarsened in the range of 5-50 m. Plan and profile curvatures are the most sensitive among the tested attributes, whereas slope is the least sensitive. Most of these authors have generally concluded that as cell size increases, slope gradients tend to decrease, ranges in curvatures decrease, flow-path lengths tend to decrease and the accuracy of terrain attributes at particular locations tends to decrease. The results of these studies also suggest that recently emergent fine-resolution 1 m - 5 m DEM’s, may have reached beyond certain threshold resolutions for environmental analysis (e.g. Zhang and Montgomery 1994). However, when comparing different DEM's several things must be taken into considerations. First, the exact locations of grid points that are to be compared may not coincide at different spatial resolutions. In this situation, spatially aggregated comparisons of data resolutions are inappropriate, especially in rugged mountainous landscapes where terrain characteristics often display enormous variation over short horizontal distances. Second, the population of grid points is small at a coarse resolution, implying unstable statistics. Third, spatial autocorrelation between neighboring sample points may be stronger at fine resolutions because of close sample distances (Wilson et al. 2000).

STUDY AREA For the purpose of this study, square test area with sides of 20 x 20 km or 400 km2 is selected. This area cover the west part of Skopje city region and it is characterized by very heterogeneous topography: from flat plains to deep canyon and steep mountain slopes. For that reason, it is divided into 4 more homogenous quadrants each of 10 x 10 km or 100 km2. These quadrants are named according to its dominant topographic feature as: Skopje (city plain), Vodno (mountain), Matka (canyon) and Zeden (mountain). Minimal elevation of the test area is in the Vardar riverbed (233 m) in the Skopje quadrant, while maximal elevation is on the Suva Gora mountain (1378 m) in the Matka quadrant (Fig. 1).


Figure 1, Location of study area.

METHODOLOGY AND DATA In our methodological approach, seven DEM’s covering this area was selected for the comparisons: 5 m DEM of MAFWE as a reference, derived 15 m DEM's of MAFWE (from 5 m) and SAC (from 20 m), original 20 m DEM of SAC, 30 m ASTER GDEM (v2), 90 m 3”SRTM DEM (v4) and 900 m SRTM DEM (Fig. 2).

Figure 2, Some of DEM's of whole test area used in the study.

PROCEEDINGS OF ICC&GIS 2014 |4 All of the models are cropped to the test area, checked and converted in the same projection (UTM, WGS84, Z34). After validation of horizontal position and overlapping, slope angle calculations are performed for each type of DEM and each of 4 quadrants. In the same time, 5 m reference DEM is interpolated to corresponding resolutions of other DEM's i.e. 30 m, 90 m and 900 m allowing direct comparisons with SRTM DEM and ASTER GDEM. For slope calculation, SAGA GIS v2.1 software is used and related modules for morphometry analysis. The main slope parameters used into considerations were: minimal slope, maximum slope, slope range, mean slope and standard deviations. Finally, based on the results DEM's-correlation and evaluation is made.

RESULTS In Table 1, basic elevation parameters of analyzed DEM's compared with 5 m DEM of MAFWE as a reference are presented. It is evident that largest differences are for maximal elevation, thus coarser resolution tending to have lower peak elevations. However, mean elevation of the test area is almost the same, while minimal elevations are irregular in tendency, except for 30"SRTM DEM. Peak elevations slowly decrease from 5 m to 15 m DEM, and after that the size of downgrade is significant, even for 30 m ASTER GDEM. Thus, for 30"SRTM DEM, the peak elevation is only 0,68 from 5 m reference value. It is interesting that even comparing mean elevation of entire country, the differences between 5 m MAFWE and 900 m SRTM DEM is almost insignificant i.e. 830 m versus 828 m. Thus, 30"SRTM DEM can be used for mean elevations calculation and comparison of larger areas (more than 100 km2) without significant uncertainty. Table 1, Elevation differences and deviations from referent 5 m DEM. Type of DEM 5 m MAFWE 15 m MAFWE 15 m SAC 20 m SAC 30 m ASTER v2 90 m SRTM v4 900 m SRTM

Min. elev. m 233 234 232 233 232 229 235

Dev. 1.00 1.00 1.00 1.00 1.00 0.98 1.01

Max. elev. m 1378 1373 1372 1368 1357 1347 932

Dev. 1.00 1.00 1.00 0.99 0.98 0.98 0.68

Mean elev. m 457 456 457 457 457 454 457

Dev. 1.00 1.00 1.00 1.00 1.00 0.99 1.00

However, as shown bellow, slopes are much more sensitive to different resolution of DEM's than elevation. Calculated slope values depends on the quality of the DEM, cell spacing and type of topography (morphology of landscape), while minor significance has used slope algorithm. In general, as cell spacing increase, the DEM captures less of the fine scale changes of slope, including the extreme values and the slope distribution becomes less steep (Guth, 2010). These shifts and rising inaccuracies highly reflect on landscape modelling and result of analyses. In our work as mentioned before, three main slope parameters were analyzed for each of the 4 quadrants: minimal slope, maximal slope, average slope and standard deviation of slope values. Results of calculations are presented in Table 2 and as graph in Fig. 3. Here, again maximal slope values show highest differences, compared to mean and minimal slope. Actually, in minimal slope almost no change is evident. In correlation with spatial resolution, the highest slope differences of analyzed DEM's show SRTM30, where mean slope value for the entire test area is only 1/3 compared to 5 m reference DEM. Results for quadrant areas shows that on flats and gentle slopes, deviation is much smaller than on steep slope areas arising to more than 70% in regard to the reference DEM. In all quadrants (i.e. 4 different types of terrain), freely available 1"ASTER GDEM and 3"SRTM DEM shows tolerable deviations from reference DEM in regard to mean slope (10-20% lower values), but much higher inaccuracies for maximal slopes (30-53%). Exactly the maximal slope value deviations indicate fine-scale slope refinement which is necessary for precise landscape modelling. SRTM30 is out of order because of extreme inaccuracy for peak slopes. Thus, 1"ASTER and 3"SRTM DEM can be used with good confidence for mean slope calculation when keep in mind 10-20% underestimated values. As shown further, these shifts for mean slope can be improved empirically with simple mathematical equations in form: a*1+(a/125) for 3"SRTM DEM and a*1+(a/150) for 1"ASTER GDEM, where a is slope angle (Milevski, 2005). In that way, slope values will increase gradually with higher steepness. However, for precise improvement, much detailed regression is needed depending of local terrain (landscape) type and DEM features.

PROCEEDINGS OF ICC&GIS 2014 |5 Table 2, Slope values of the tested DEM's compared to the 5 m DEM of MAFWE. Quad. Skopje 5m 10 m 15 m 15 m 20 m 30 m 90 m 900 m Matka 5m 10 m 15 m 15 m 20 m 30 m 90 m 900 m Vodno 5m 10 m 15 m 15 m 20 m 30 m 90 m 900 m Zeden 5m 10 m 15 m 15 m 20 m 30 m 90 m 900 m

Type Type MAFW1 MAFW2 MAFW3 SAC2 SAC1 ASTER SRTM SRTM MAFW1 MAFW2 MAFW3 SAC2 SAC1 ASTER SRTM SRTM MAFW1 MAFW2 MAFW3 SAC2 SAC1 ASTER SRTM SRTM MAFW1 MAFW2 MAFW3 SAC2 SAC1 ASTER SRTM SRTM

min 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,1 min 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,2 min 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,2 min 0,0 0,0 0,0 0,0 0,0 0,0 0,0 0,2

Slope values max mean 54,7 4,7 45,6 4,6 41,8 4,5 36,7 4,6 29,6 4,3 28,9 4,4 25,7 3,8 5,4 1,6 max mean 78,8 17,2 72,1 17,0 69,4 16,7 62,0 16,3 57,6 15,7 63,1 15,5 58,3 14,4 13,2 4,9 max mean 57,2 10,0 46,2 9,8 39,3 9,6 41,2 9,0 49,1 9,4 45,3 8,8 35,2 8,1 12,1 3,8 max mean 88,8 11,9 87,7 11,6 86,6 11,4 54,8 11,3 53,5 10,7 61,8 10,5 54,5 9,5 5,7 2,9

stDEV 4,8 4,6 4,5 4,0 4,0 3,6 3,4 1,1 stDEV 12,5 12,3 12,1 11,2 11,6 11,0 10,5 3,1 stDEV 8,1 7,9 7,6 6,9 6,9 6,2 6,0 2,8 stDEV 9,3 9,1 8,9 8,1 8,0 7,5 7,2 1,3

Comparison with 5 m DEM i-max i-mean i-stD 1,00 1,00 1,00 0,83 0,98 0,96 0,76 0,95 0,93 0,67 0,97 0,84 0,54 0,91 0,82 0,53 0,93 0,74 0,47 0,81 0,70 0,10 0,34 0,23 i-max i-mean i-stD 1,00 1,00 1,00 0,91 0,98 0,98 0,88 0,97 0,97 0,79 0,95 0,90 0,73 0,91 0,93 0,80 0,90 0,88 0,74 0,83 0,84 0,17 0,29 0,25 i-max i-mean i-stD 1,00 1,00 1,00 0,81 0,98 0,97 0,69 0,96 0,94 0,72 0,90 0,85 0,86 0,94 0,85 0,79 0,88 0,76 0,62 0,81 0,74 0,21 0,38 0,34 i-max i-mean i-stD 1,00 1,00 1,00 0,99 0,98 0,98 0,98 0,96 0,96 0,62 0,95 0,88 0,60 0,90 0,86 0,70 0,89 0,81 0,61 0,80 0,77 0,06 0,24 0,14

Values of standard deviations are also very characteristic. If index of 0.9 (10% drop of value) is taken as a lower limit, only 10 m and 15 m interpolated MAFWE DEM's are satisfactory accurate for slope modelling aside of reference 5 m DEM. 1"ASTER GDEM and 3"SRTM are far away from that limit and can't be used for detailed analyses. When interpolated DEM's from same source are taken into considerations instead of totally different original DEM's, much smaller deviations appears. In our sample, 7 downscaled DEM's interpolated from original 5 m MAFWE are analyzed: 10 m, 15 m, 20 m, 30 m, 60 m, 90 m and 900 m. The 20 m interpolated DEM have same resolution as 20 m SAC DEM, 30 m with ASTER, 90 m with SRTM and 900 m with SRTM30 DEM. Evidently, deviations rises on more sloped terrains compared to flatted areas. Based on these data, as a good cell resolutions 5 m - 20 m DEM's can be considered, where standard deviation is below 5%. After that, slope accuracy drastically downgrade especially in regard to maximal or extreme values.

Table 3, Slope values of the test area for the interpolated 5 m DEM's of MAFWE.


Quadr. Skopje 5m 10 m 15 m 20 m 30 m 60 m 90 m 900 m Matka 5m 10 m 15 m 20 m 30 m 60 m 90 m 900 m Vodno 5m 10 m 15 m 20 m 30 m 60 m 90 m 900 m Zeden 5m 10 m 15 m 20 m 30 m 60 m 90 m 900 m

max 54,7 45,6 41,8 44,0 37,6 27,9 26,1 10,2 max 78,8 72,1 69,4 71,1 68,0 59,7 56,3 34,6 max 57,2 46,2 39,3 43,2 38,6 36,4 35,6 17,6 max 88,8 87,7 86,6 87,5 86,9 84,4 82,7 14,0

Slope values mean 4,7 4,6 4,5 4,5 4,4 4,1 3,9 1,9 mean 17,2 17,0 16,7 16,9 16,5 15,7 15,0 8,3 mean 10,0 9,8 9,6 9,7 9,4 8,8 8,3 5,4 mean 11,9 11,6 11,4 11,5 11,3 10,5 10,0 4,7

stDEV 4,8 4,6 4,5 4,6 4,4 4,0 3,7 1,8 stDEV 12,5 12,3 12,1 12,2 11,9 11,4 11,0 6,0 stDEV 8,1 7,9 7,6 7,7 7,5 6,8 6,4 4,0 stDEV 9,3 9,1 8,9 9,0 8,8 8,2 7,8 2,8

Comparison with 5 m DEM i-max i-mean i-stD 1,00 1,00 1,00 0,83 0,98 0,96 0,76 0,95 0,93 0,80 0,97 0,94 0,69 0,94 0,91 0,51 0,87 0,83 0,48 0,83 0,77 0,19 0,41 0,37 i-max i-mean i-stD 1,00 1,00 1,00 0,91 0,98 0,98 0,88 0,97 0,97 0,90 0,98 0,97 0,86 0,96 0,96 0,76 0,91 0,91 0,71 0,87 0,88 0,44 0,48 0,48 i-max i-mean i-stD 1,00 1,00 1,00 0,81 0,98 0,97 0,69 0,96 0,94 0,76 0,97 0,96 0,68 0,94 0,92 0,64 0,88 0,84 0,62 0,83 0,79 0,31 0,54 0,50 i-max i-mean i-stD 1,00 1,00 1,00 0,99 0,98 0,98 0,98 0,96 0,96 0,99 0,97 0,97 0,98 0,95 0,95 0,95 0,88 0,89 0,93 0,84 0,84 0,16 0,39 0,30

In Fig. 3, graphs of maximum and mean slope values for different DEM's are presented. It is interesting that in some cases 1"ASTER GDEM show in first sight better results than 15 m or 20 m models. The reason is not because of higher quality, but because of many artifacts and pseudo-slopes in the model from the processing procedure. When artifacts removing tool is used in SAGA GIS (Mesh Denoise), slope deviations increased significantly. It is evidently also that deviations of mean slope are much less expressed except in case of coarsest SRTM30 model, thus the last is inappropriate for any kind of slope estimation and calculation, even of largest areas. On Fig. 4, two topographic profiles of same terrain are given with representation of correlated slope differences. Clearly, on the top profile from 5 m reference DEM, profile line is much more irregular reflecting even small changes of slope, while the second (bottom) profile from 3"SRTM DEM is more "soft" and generalized. Previously mentioned empiric procedures, slightly improve the situation.


100 90 80 70 60 50 40 30 20 10 0

100 90 80 70 60 50 40 30 20 10 0

Skopje Vodno Matka Zeden


20 18 16 14 12 10 8 6 4 2 0

20 18 16 14 12 10 8 6 4 2 0



Figure 3, Graphs of maximal (left) and mean (right) slope values for each of 4 quadrants.

Figure 4, Topographic profile of the south slope of Vodno Mountain on 5 m DEM (top) and 90 m SRTM DEM.

PROCEEDINGS OF ICC&GIS 2014 |8 CONCLUSION In this paper 3 types of freely available global (or nearly global) DEM's (1"ASTER GDEM, 3"SRTM DEM and SRTM30) which cover also the area of the Republic of Macedonia are compared and evaluated together with 2 national digital elevation models (5 m MAFWE DEM and 20 m SAC DEM). As a reference for the comparisons and analyses 5 m DEM of the MAFWE of Republic of Macedonia is used. That is because according to our tests, until now this model is closest to real topography with incredible horizontal and vertical accuracy (+/- 2 m max.). This resolution of DEM will be upper limit for reasonable terrain modelling and processing of areas larger than 1 km2 keep in mind good spatial cover and amount of data cells for processing. Presented analyses show that because of resolution and some systematic errors, all of freely available DEMs have some degree of deviations in elevation or slope values. Highest inaccuracy shows 30"SRTM DEM which is normal because of very coarse resolution. However, our results suggests that in regard to mean elevation, it is possible to use SRTM30 model for large even country areas comparison. Also, 1"ASTER GDEM (v2) is generally better than 3"SRTM, but there are some issues with DEM quality, especially in regard to high noise, many artifacts and pseudo-slopes (for that reason it is yet considered as "research grade"). This problem is partially resolved with denoise software modules like those in SAGA GIS. 3"SRTM DEM is a good compromise between the quality and spatial resolution for large areas. In the extent of Macedonia the resolution of this model is 72*90m, which is enough for coarse-scale modellings on country level. There are significant shifts of steep slopes, but with use of correction equation in form: a*1+(a/125) where a is slope angle, slope values can be acceptable. Some procedures of bicubic polynomial reinterpolation to 30 m may improve the overall quality closely to the original 1"SRTM DEM (Keeratikasikorn & Trisirisatayawong 2008). Because of that this model is widely used by many institutions in Macedonia. References Chang. K., Tsai. B. 1991. The effect of DEM resolution on slope and aspect mapping. Cartography and Geographic Information Systems. 18. pp. 69 77. Chaplot, V., Walter, C., Curmi, P., 2000. Improving soil hydromorphy prediction according to DEM resolution and available pedological data. Geoderma 97, 405–422. Deng Y., Wilson P.J., Bauer B.O., 2007. DEM resolution dependencies of terrain attributes across a landscape. International journal of Geographical Information Science, Vol. 23, Nos. 1-2, 187-213. Guth P.L. 2010. Geomorphometric comparison of ASTER GDEM and SRTM. A special joint symposium of ISPRS Technical Commision IV&AutoCarto in conjuction with ASPRS/CaGIS 2010 Fall Specialty Conference, Orlando, Florida, 1-9 Hengl, T., Reuter, H. 2011. How accurate and usable is GDEM? A statistical assessment of GDEM using LiDAR data. In Hengl, T., Evans, S. I., Wilson, P. J., Gould, M., eds. Geomorphometry 2011 - Proceedings (Redlands, CA, USA, 7–11 Huber M., Gruber A., Wendleder A., Wessel B., A. Roth and Schmitt A. 2012. The Global TANDEM-X DEM: Production status and first validation results. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012 XXII ISPRS Congress, 25 August – 01 September 2012, Melbourne, Australia Jarvis, A., H.I. Reuter, A. Nelson, E. Guevara, 2008. Hole-filled SRTM for the globe Version 4, available from the CGIAR-CSI SRTM 90m Database (http://srtm.csi.cgiar.org). Keeratikasikorn C. Trisirisatayawong I. 2008 Reconstruction of 30m DEM from 90m SRTM DEM with bicubic polynomial interpolation method. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B1. Beijing 2008 Milevski, I. 2005. Using 3"SRTM DEM for geomorphometrical analysis. In Stamenkovic, S., ed. Proceedings: Serbia and modern processes in Europe and World (Tara, Serbia, 26–27 May 2005). Faculty of Geography, University of Belgrade, Serbia, 825 – 832. (in Serbian). Milevski I., Gorin S., Markoski M., Radevski I. (2013): Comparison of Accuracy of DEM’s Available for the Republic of Macedonia. Proceedings from the 3rd International Geographic Symposium - GEOMED 2013, Antalya, 165-172 Rexer, M.; Hirt, C. (2014). "Comparison of free high-resolution digital elevation data sets (ASTER GDEM2, SRTM v2.1/v4.1) and validation against accurate heights from the Australian National Gravity Database.". Australian Journal of Earth Sciences 61 Thompson, J.A., J.C. Bell, and C.A. Butler.2001. Digital elevation model resolution: effects on terrain attribute calculation and quantitative soil-landscape modeling. Geoderma 100:67-89. Wilson, J.P, Repetto, P.L., Snyder, R.D., 2000. Effect of data source, grid resolution, and flow routing method on computed topographic attributes. In: Wilson, J.P., Gallant, J.C. (Eds.),Terrain Analysis: Principles and Applications. John Wiley & Sons, New York, pp. 133–161. Zhang, W., Montgomery, D.R., 1994. Digital elevation model grid size, landscape representation, and hydrological simulations. Water Resour. Res. 30, 1019–1028.