ELEVATION SURFACE INTERPOLATION OF POINT DATA USING DIFFERENT TECHNIQUES A GIS APPROACH

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1 ELEVATION SURFACE INTERPOLATION OF POINT DATA USING DIFFERENT TECHNIQUES A GIS APPROACH Kulapraote Prathuchai Geoinforatics Center, Asian Institute of Technology, 58 Moo9, Klong Luang, Pathuthani, Thailand Phone: , Fax: kulapra@ait.ac.th Lal Saarakoon Earth Observation Research Center, Japan Aerospace Exploration Agency, Triton Square Office Tower-X 23F, Harui, Chuo-ku, Tokyo, JAPAN lal@ait.ac.th KEYWORDS: Interpolation, Elevation, GIS ADBSTRACT: Interpretation of real-world occurrences or particular conditions is generally based on observed in-situ data. Whatever the phenoena or a given condition can be easured with very advanced easuring techniques available today, it is iportant to ention that these easuring represents are carried out on given location on the earth surface. Considering the cost and the tie that need to carryout easureents, it is ipossible to iagine of continuous easureents representing every physical location on the earth surface. It is the interest of everybody to know the exact aount or quantity of a given phenoenon or a given conditions such as elevation, precipitation, water quality, air pollution, in reality quantification is based on approxiations. Measureents are in discrete nature but inforation need to be soewhat continuous. In order to achieve inforation continuity over space, it is necessary to carryout soe for of interpolation to fill gaps.various interpolation techniques are available based on atheatical forulas and approxiations but need to apply the carefully to the given phenoenon in hand and aount and distribution of real-world inforation. This paper presents results that obtained interpolating elevation data to create a digital elevation odel. A study area in Lao PDR was selected and interpolation was carried out using Inverse Distance Weighting (IDW), Spline and Kriging functions available in ArcGIS. Results were copared with each other and present as statistic graphs. Finally, paper describes prospects and constraints of each interpolation technique over elevation data. 1. INTRODUCTION In the atheatical subfield of nuerical analysis, interpolation is a ethod of acquiring new data points fro a discrete set of known points. In the context of GIS, it is a ethod to estiate values for cells in a raster fro a liited nuber of saple data points. Its application is, therefore, to calculate unknown values of any geographic point data, for exaple, elevation, rainfall, cheical concentration, noise levels, and so on. Data collection fro every location a study area to deterine the height, agnitude or concentration of a physical property, ay not generally be practically feasible and econoically viable. Therefore, interpolation is use to create a continuous surface, by acquiring new values of paraeters at points that have not been directly sapled. The interpolation theory is concerned with spatial autocorrelation, ost interpolation places are affected on saple points that are close to the unknown location than those are further away fro it. This is based on the principle of spatial autocorrelation; i.e. the relationship aong values of a single variable/paraeters that coes fro the geographic arrangeent of the areas

2 in which these values occur; in other words, things that are close together are ore coparable than those are far apart. Given a set of coparable data points, the Spatial Analyst interpolation tools in ArcGIS software, deterines a z-value for an epty cell using the z-values of the nearby saple points. This study, the experient was applied in three difference ethods; Inverse Distance Weighting (IDW), Spline and Kriging were approached though out the three different sapling ethods. These were Regular Sapling, Stratified Rando Sapling and Rando Sapling. 2. OBJECTIVES Objectives of the study were to; Exaine the elevation surfaces obtained fro difference data saple characteristic Copare the elevation surface obtained fro difference ethods and thereby to identify the better interpolation technique to obtain elevation on surface 3. SAMPLE AREA, DATA AND METHODOLOGY An area in between Xiengkhuag and Xaysoboun provinces in Lao PDR was selected for the study. Approxiate diension of the area was 17 k x 13 k. Location was latitude N and longitude E, highly undulated. Figure1 shows the Methodology of the study. Creation of Elevation Saple point data Contour TIN&DEM Creation Grid to Point Regular Saple sets points 2 points Adjust X,Y positions Stratified Saple sets (884,18,63,2 points) Rando Saple sets (18,63,2 points sets) Interpolation Inverse Distance Spline Kriging Statistic Calculation/ Visualized Analysis Result & Discussion Figure1 Flowchart depicting ajor steps of analysis 3.1 Creation of Elevation Saple points data Locations of saple points are iportant for interpolation. Ideally, for apping, points should be located evenly over the area. However, saples can be regularly or randoly spaced. More the input points and greater their distribution, ore reliable of the results can be achieved. In this study, contour ap of 1 interval was used, the source of the data was the National Geography Departent of Lao PDR. As one of the objectives of the study was to exaine the

3 perforance of interpolation output with suitable data sapling and hence the unifority of input data need to be controlled. Thus initially, contour data was used to generate elevation surface using TIN odel then it was converted to grid. Subsequently, the grid result with 26 rows and 34 coluns were converted to equal esh points. Total data points were 884. Then the nuber of points were reduced to 18, 63 and 2 respectively, to exaine whether the nuber of the ight affected to interpolation ethods. These sets of data were called as Regular saple, representing a perfect selection of saple point. The next step was creation of Stratified Rando Saple i.e. the saple points in between the cases of regular. These sets of data were created by shifting X,Y locations of regular saple points. The last data set was Rando Saple, it was selected randoly fro Stratified Rando Saple points. Figure 2 shows the steps adopted in the creation of sapling points. DEM TIN Surface Contour Regular 884 Regular 18 Regular 63 Regular 2 Stratified 884 Stratified 18 Stratified 63 Stratified 2 Rando 18 Rando 63 Rando 2 Figure 2 Creation of Saple points data sets 3.2 Interpolation Techniques This study was developed in ArcGIS software, which allows any techniques available, three of those difference techniques were selected for this study. Options and paraeters pertaining to particular ethod were depended upon default setting of the software. Inverse Distance Weighting (IDW) IDW assues that each easured point has a local influence which is inversely proportional to a selected power of the distance&hence the nae of the ethod is Inverse Distance Weighting. The output value for a cell using IDW is liited to the range of the input values used to interpolate. It should be noted that since IDW is a weighted distance average, the average cannot be greater than the values of saples. Therefore, it cannot create ridges or valleys if these extrees have not already been sapled. Also, the output surface will not pass through the saple points. Spline Spline is an interpolation ethod that estiates values using a atheatical function that iniizes overall surface curvature, resulting in a sooth surface that passes exactly through

4 the input points. Theoretically, the saple points are extruded to the height of their agnitude; spline bends a sheet of rubber which passes through the input points while iniizing the total curvature of the surface. It fits a atheatical function to a specified nuber of nearest input points while passing through the saple points. This ethod is best for generating gently varying surfaces such as elevation, water table heights, or pollution concentrations. Kriging Kriging assues that the distance or direction between saple points reflects a spatial correlation that can be used to explain the variation in the surface. Kriging fits a atheatical function to a specified nuber of points, or all points within a specified radius, to deterine the output value for each location. Kriging is a ultistep process; it includes exploratory statistical analysis of the data, variogra odeling, creating the surface, and (optionally) exploring a variance surface. Kriging is ost appropriate when we know there is a spatially correlated distance or directional bias in the data. It is often used in soil science and geology. 4. RESULTS AND DISCUSSION 4.1 Visualized surface perforance Coparison of interpolations surfaces created fro axiu nuber points (884) and difference interpolation ethods. Figure4 shows surface outputs corresponding to IDW, Spline and Kriging interpolations for the axiu nuber of regular and stratified data points. It could be seen fro Figure4 that both regular and stratified rando saple points provide siilar surfaces for each interpolation technique. According to tie of processing used, it was found that Kriging ethod with 884 points of regular saple and stratified rando saple took longest processing tie(5 inutes). IDW regular884 points Spline regular884 points Kriging regular884 points IDW stratified rando 884 points Spline stratified rando 884 points Kriging stratified rando 884 points Figure 4 Coparing Maxiu nuber points (884) Coparison of interpolations surfaces created fro different nuber of saple points, saple types and interpolated ethods Elevation surface odels corresponding to different nuber of saple points, saple type and interpolation ethods are illustrated in figure5 These results were copared to Figure4 which assued as coplete dataset. Deonstrating the less detail appearance when nuber of points was reduced. Aong different Interpolation ethodologies available, Spline and Kriging give a ore sooth surface than that given by IDW, which gave ore single hills appearance. 63 nuber of saple points provided a little differences surface copared to 18 saple points. Unlike 2 points returned less and rare detail of surface.

5 4.2 Graph Statistic Characteristics Coparison of statistics of interpolations surfaces created fro axiu nuber points (884) Figure 6 shows the statistical graph associated with the axiu nuber of saple points, corresponding to Figure 4, Statistics values; iniu, ean and axiu of regular saple surface were alost sae with regular saple input points, and stratified rando saple point were sall difference at iniu value, which was fro spline ethodology. Coparison of interpolations surfaces created fro different nuber of saple points, saple types and interpolated ethods Figure7,8 and 9 show graphs of statistics of interpolations surfaces created fro different nuber of saple points; 18, 63 and 2, for each type of saple; regular, stratified rando and rando as well as difference interpolation ethods; IDW, Spline and Kriging. In ters of nuber of saple points, it is realized the fact that ore nuber of points and ore regular saple points would generate new values which are coparative to input data points (original data). However, this trend reduces with rando saple point type using Spline ethod, which generate inus values. Regular and Stratified rando saple points generated stable and oderately stable surfaces respectively. Rando saple points produced ore artificial values on all three saple set points, Figure 9. Preliinary testing for the accuracy of a surface The best way to test the quality of surface is to generate the reoved saple point against the reaining saple and exaine the interpolated surface whether it could predict the issing saple (ESRI). For this study, due to tie liitation, those steps were not prepared. However, preliinary testing of the accuracy of a surface, provided soe significant results. Figure1 depicts graph bars of the testing surface obtained for different interpolation ethods using 63 points rando saple, the set that ost probably siilar to real sapling collection, against the 884 points stratified rando saple which was the initial saple data. It could be seen that the IDW ethod generates the ost statistic values close to the full data points, i.e. 884 stratified rando saple points. Therefore, it could be assessed that IDW would be the best ethod for this rando saple 63 points dataset. 5. CONCLUSION In the context of GIS, interpolation is a functional ethod to create surface with inadequate saple data. The ore input saple data and the ore distribution and regular saples created, higher the reliablity of results. Spline ethod produced soothest surface, enabling good visualization and contour line conversion. However, the ethod returns the synthetic results because of its curvature and sooth processing, while IDW and Kriging, generated ore preservative statistic values of original saple points. Based on statistics, IDW ethod would be the best ethod for this study area with 63 rando saple points. Testing of the accuracy of surface, however, require ore exhaustive process. Future work on this study would consider output surface, odel and option testing.

Inverse Distance Weighting Regular 18 points Regular 63

Stratified rando 63 points Stratified rando 2 points

18 points Regular 63 points Regular 2 points Regular 18

Spline Stratified rando 18 points Rando 18 points

points Rando 18 points Rando 63 points Rando 2 points

6 Inverse Distance Weighting Regular 18 points Regular 63 points Regular 2 points Stratified rando 18 points Stratified rando 63 points Stratified rando 2 points Rando 18 points Rando 63 points Rando 2 points Regular 18 points Regular 63 points Regular 2 points Regular 18 points Regular 63 points Regular 2 points Kriging Spline Stratified rando 18 points Stratified rando 63 points Stratified rando 2 points Rando 18 points Rando 63 points Rando 2 points Stratified rando 18 points Stratified rando 63 points Stratified rando 2 points Rando 18 points Rando 63 points Rando 2 points Figure5 Coparing of different nuber points, saple types and interpolated ethods

7 3 by Regular Saple by Straitified Rando Saple 884 Saple points stat. values IDW stat. values Spline stat. value Kriging stat.value Statistic Values Statistic Values Figure 6 Statistic of different interpolation ethods using 884 saple points 2 by Regular Saple 18 Points 2 by Regular Saple 63 Points 2 by Regular Saple 2 Points Statistc values Statistc values Min. (.) Mean (.) Max.(.) Statistc values Figure 7 Statistic of different interpolation ethods using 16,63 and 2 regular saple points 2 by Straitified Rando Saple 18 Points 25by Straitified Rando Saple 63 Points 2by Straitified Rando Saple 2 Points Min. Mean Max.(. Statistc Min. Mean Max.(. Statistc Min. Mean Max.(. Statictic Figure 8 Statistic of different interpolation ethods using 16,63 and 2 stratified rando saple i 3 by Rando Saple 18 Points 3 by Rando Saple 63 Points 3 by Rando Saple 2 Points Statistic Statistic Statistic Figure 9 Statistic of different interpolation ethods using 16,63 and 2 rando saple points Testing Surface of Difference Interpolation Methods using Rando Saple 63 Points Against Stratified Rando Saple 884 Points 466. Std Max.(.) Mean (.) Stratified Saple points_884 Kriging_63rd Min. (.) Spline_63rd IDW_63rd Figure 1 depicts graph bars of the testing surface of difference interpolation ethods using rando saple 63 points against to stratified rando saple 884 points

8 REFERENCES Environental Systes Research Institute, 21.Working with ArcGIS Spatial Analyst, Interpolation tool, Session 7 pp Ji McCoy, Environental Systes Research Institute, 24. Using ArcGIS Spatial Analysis, ArcGIS8. pp Peter A.Burrough and Rachael A.McDonnell, 1998, Principles of Geographical Inforation Syste, Oxford University Press, pp Suwanwerakatorn. R,2.Coparison of Interpolation Methods for Spatial Rainfall Pattern using GIS: A case Study of Na Choen Watershed, Journal of Reote Sensing and GIS Association of Thailand, ISSN , Vol.1. No.3.pp.35-48

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