The influence of input data design on terrain morphometric parameters quality and accuracy Mgr. Radoslav Bonk bonk@fns.uniba.sk Katedra fyzickej geografie a geoekológie, Prírodovedecká fakulta Univerzity Komenského, Mlynská dolina 1, Bratislava, 842 15, Slovenská republika With the advent of the geographic information science, geographic information systems (GIS), as its software implementation, became a routine tool for geoscientists. Especially, modules for digital elevation model (DEM) production and analysis have special importance for geomorphologists as they make morphometric terrain analysis faster, and its limitations is truly represented only by sophistication and the degree of users' profesionality. If the analysis of such an geomorphic phenomena as natural disasters and hazards has to be widely applicable at various scales, repeatable by other scientists, and finaly comparable independent from various locations, strong theoretical framework has to be established. Such a famework, including basic logical rules, and principles may became integral part of DEM generation process and its subsequent analysis. However, as the implementation of algorithms is in progress, basic theoretical and practical rules regarding the correct morphometric analysis, are not well applicable within the wider geoscientific and student community yet. This fact makes to comparison of results of different morphometric analysis problematic, moreover different approaches in morphometric analysis produce the courses which are not applicable at different scales or terrain types. In the paper a special attention will be given to factors influencing DEM production and analysis. Particularly, the effect of input data design and scale on morphometric parameters accuracy will be addressed here.the DEM generation and analysis is influenced by several factors as it is a complex task (Figure 1). Georelief -simple primary geomorph. parameters -complex primary geomorph. parameters -combined primary geomorph. parameters. Input Data Design -accuracy -density -design (spatial distribution) Interpolation Function -global interpolators -local (moving window approach) -interpolators based on geostatistical approach Scale -cell size -geographic scale -operational scale DEM Quality -smooth DEM versus edge detecting DEM -artificial undulations -high frequency data variations DEM Accuracy -horizontal accuracy -vertical accuracy -cell size PURPOSE & TIME & MONEY Figure 1. Basic factors influencing DEM generation and analysis. Gerelief factor are based on Schmidt and Dikau (1999). To completely address this problem one has consider all factors at once. However, that would produce task too complex, and probably with results not specific enough regarding the subproblems. Instead scientific community tries to address the problems analysing its subsets such as: georelief and its attributes (Dikau, 1990; Krcho, 1990, 2001; Minár, 1998; Schmidt and 24
Dikau, 1999), effect of input data design (Li, 1991, 1992), effect of interpolation function (Hofierka, 1997; Mitášová, 1993), and effect of scale and resolution (Cao, 1997; Band, 1995). Partitioning the problem allows scientists to focus on one aspect. Furthermore, as the practical scientific tasks usually requires less than four of the factors to focus on, such an approach seems to be correct. The Devinska Kobyla region at Bratislava area was used as the testing region. That region was used bacause of the fact, that due to the intensive geoecological research performing by the scientists and students from the department, variety of data were collected (Minar, 2001). Especially, geodetic measurements of 75 points distributed along the transect are of serious importance as they were used as ground truth points. Specifically, the effect of two input data designs (regular grid distribution, and random area-equal distribution), varying in scale, on the accuracy of morphometric parameters (elevation, slope angle, profile curvature) was investigated.. It was hypotetized that the magnitude of error rises with enlarging degree of elevation derivatives. At this research only numerical analysis was performed, spatial distribution, and spatial autocorreation of the error was not a part of the analysis. At the begining, as it was necessary to compare various resulted surfaces with the reference one, and to extract various height data sources with specific design, the reference DEM was generated. There were contours digitized from the S-JTSK map with the scale of 1:10000. Using the site data obtained from digitized contours, interpolation method was used such that the resulted surface matched the original contours, so that the surface deviation from the contours was equal to zero. Before further analysis 75 ground truth points representing elevation were compared with the reference DEM, as for the vertical accuracy. Errors varying from -14m to +11m were obtained. That fact did not have an impact of further analysis, but provided an interesting information on vertical accuracy of original 1:10000 map. Furthermore the correlation analysis between vertical error, and terrain s local relief (computed by 3x3 cells moving window) was performed. However the correlation coefficient of 0.21 did confirm low numerical correlation between the variables. Using the reference DEM, GRASS Open Source GIS system was used to extract eight height data points designs. Specifically, the same number of height data points were used, with different spatial distribution (Figure 2.). Figure 2. Input data design. From upper lef to lower down, grid data design 10 m grid size, 25 m, 50 m, 100 m, random data design 6568, 1036, 257, and 68 height points. Height points were extracted from the reference DEM. Then for each of the input data designs the surface representing elevation, slope angle and profile curvature was computed, using the same 2m cell resolution, and the same interpolation 25
function (Mitášová 1993). Resulted surfaces, specifically data points located at the same locations as ground truth points, were compared with ground truth points each by each, using both input data designs, and all four scales. Numerical errors statistics, computed as the difference between the morphometric parameters of ground truth points, and resulted surfaces are provided in Table 1. Table 1. Basic statistic on error resulting from ground truth points parameters and resulted morphometric fields. Mean and standard deviation were computed using absolute values of error to eliminate the influence of negative values. GRID DATA DESIGN RANDOM DATA DESIGN Elevation Grid size [m] Mean error Std. Dev. Number of points Mean error Std. Dev. 10 2.12 2.54 6568 2.13 2.54 25 2.26 2.47 1036 2.4 2.72 50 3.27 3.21 257 3.02 2.87 100 4.63 4.6 68 4.98 5.5 Slope angle 10 4.32 3.94 6568 4.44 4.0 25 4.41 4.11 1036 4.42 4.49 50 5.22 4.78 257 4.97 5.23 100 5.42 4.49 68 5.7 5.14 Profile curvature (absolute values) 10 0.0143 0.0175 6568 0.0137 0.0173 25 0.0130 0.0167 1036 0.0130 0.0168 50 0.0130 0.0168 257 0.0131 0.0167 100 0.0132 0.0173 68 0.0132 0.0171 Major part of the analysis was performed using dot-plots between ground truth points and resulted surfaces. The analysis showed that the magnitude of elevation error is increasing with the lower number of points used for interpolation (with increasing sampling interval for grid data design). This is applicable for both grid data design and random data design. Similarly, the magnitude of slope angle error is increasing with larger sampling interval, however the same can not be stated for profile curvature error distribution. Magnitude of profile curvature error is significantly high, but nothing support the assumption it increases with larger sampling size (Figure 3) Figure 3. Boxplots representing magnitude of error for elevation (left), slope angle (middle), and profile curvature (right). Each boxplot from left to right: grid data design - 10 m, 25 m, 50 m, 100m, random data design 6568, 1036, 257, 68 points. Y axe represent magnitude of error. When plotting grid interval (number of sampling points respectively) versus mean error, the trend is obvious only for elevation error statistics. Both curves (representing grid and random data design) for mean, are climbing up. These facts support the previous trend of increasing error with decreasing number of points (while area remains the same). On the other hand, line plots for slope angle, and profile curvature error do not follow the trend so precisely as elevation does. The breaks points on lines can not be explored by simple visual and numerical analysis and spatial data analysis including spatial autocorrelation methods and geostatistics is required (Figure 4). Following conclusions can be made base on the presented research: numerical error is enlarging with decreasing point density, numerical error is enlarging with the 26
increasing degree of elevation derivatives, and there are certain phenomena including the effect of scale and geostatistics which requires further investigations. Figure 4. Mean error of elevation, slope angle, and profile curvature versus grid size. Both grid data design (solid line) and random data design (dashed line) are presented. To completelly understand the relation between input data design and morphometric parameters accuracy, new tools and techniques have to be included in the research. Furthermore, it may be neccessary to recruit other factors presented at Figure 1, to adequately address the topic. Further research is warranted. This research was conducted with support of S. G. A. grant No.: 1/8396/01. References BAND, L. E. (1995): The effect of different terrain representation and resolutions on simulated watershed processes. Zeitschrift für Geomorphologie, /Supplementeband, Advances in Geomorphometry, (82): 187-199. CAO, C., LAM, N. S. (1997): Understanding the scale and resolution effects in remote sensing and GIS. In Quattrochi, D. A. and Goodchild, M. F., editors, Scale in Remote Sensing and GIS, chapter 3, pages 57-73. Lewis Publishers. DIKAU, R. (1990): Geomorphometric landform modeling based on hierarchy theory. In Proceedings of the 4 th International Symposium on Spatial Data Handling, pages 230-239, Zurich. HOFIERKA, J. (1997): Natural phenomena modeling in geographic information systems. Ph.D. thesis, Comenius University, Faculty of Sciences. Bratislava. in Slovak. KRCHO, J. (1990): Morphometric analysis and digital elevation models. VEDA, Bratislava. in Slovak. KRCHO, J. (2001): Modeling of georelief and it geometric structure using DTM. Q111, Bratislava. LI, Z. (1991): Effects of check points on the reliability of the DTM accurracy estimates obtained from experimental tests. Photogrammetric Engineering and Remote Sensing, 57(10): 1333-1340. LI, Z. (1992): Variation of the accuracy of the digital elevation models with sampling interval. Photogrammetric Records. 14(79): 113-127. MINÁR, J. (1998): Georelief and geoecological mapping at large scales. Ph.D. thesis, Comenius University, Faculty of Sciences. Bratislava. in Slovak. MINÁR, J. et. al. (2001): Geoecological (complex physical-geographical) research and mapping at large scales. Geographical Spectrum 3. Geo-grafika, Bratislava. in Slovak. MITÁŠOVÁ, H., HOFIERKA, J. (1993): Interpolation by regularized spline with tension: II. Application to terrain modeling and surface geometric analysis. Mathematical Geology, 25(6): 657-669. 27
SCHMIDT, J., DIKAU, R. (1999): Extracting geomorphometric attributes and objects from digital elevations models- sematics, methods,future needs. In Dikau, R. and Saurer, H., editors, GIS for Earth Surface Systems, pages 154-171. Gebrüder Borntraeger. Súhrn Vplyv vstupného bodového poľa na kvalitu a presnosť morfometrických parametrov reliéfu Príspevok prezentuje vplyv vstupného bodového poľa na presnosť morfometrických parametrov z neho vygenerovaných (nadmorská výška, sklon, a profilová krivosť). Ukázalo sa že, magnitúda chyby morfometrického parametra sa zvyšuje so znižovaním počtu vstupných bodov pre dané územie. Avšak je potrebné použiť sofistikovanejšiu analýzu a nové testovacie územie pre vysvetlenie niektorých nejednoznačností (závislostí strednej chyby sklonu a profilovej krivosti od rozpätia gridu). 28