Figure 1: Original Sample DEM
With the increasing availability of data for digital elevation models (DEM) and the software capable of processing them, it is important for users of DEM data to be aware of the effect that data accuracy has on the results of their applications.
In this paper, we examined the relationship between simulated errors and the results of extracting hydrological features from DEMs. The simulated errors were controlled to have various degrees of spatial cluterness to allow further investigation of the impact on the extracted hydrological features.
The results of our study suggest that even errors of small magnitudes would significantly affect the quality of extracted hydrological features. It is extremely important for users of DEM data to recognize this limitation and not to overly confident on the results of less accurate data.
The extraction of hydrological features from digital elevation models (DEMs) has become the de facto procedures in many geographic information systems (GIS) due to two recent trends: GIS functions for processing DEM data are becoming easier to use and the DEM data are becoming increasingly available, even over Internet for free. Processing DEM data to extract hydrological features has thus become so routine that users of such data often perform this task without carefully considering the accuracy of data and how that affects the reliability of the extracted hydrological features. We suspect that this is especially true for inexperienced or occasional users who have not been trained to perceive such possible shortfalls.
In this paper, we present the results of a simulation study that analyzed the impact of potential errors on the extracted hydrological features from DEMs. We used a sample DEM (scale: 1 to 24,000; resolution: 30 meters) released by the U. S. Geologic Survey. A series of simulated errors were generated and added to the sample DEM. Moreover, the errors were also controlled to have various degrees of spatial cluterness for testing. We then applied the same set of procedures for extracting drainage cells, networks, and contours using all simulated DEM with added errors. The results of the extracted drainage cells, networks, and contours were then analyzed and compared to those of the original DEM to reveal the impact of data accuracy.
As can be seen in the three dimensional diagram of the original DEM (Figure 1), the sample terrain surface has a river going across the study area with rugged landscape on both sides of the river banks. The sample data set was selected because of the terrain relief and the hydrological features it provides.
Elevation errors were simulated by using the random number generator. The random numbers generated were then re-scaled to be within a specified magnitude. In addition, the errors were swapped and controlled to have various degree of spatial clusterness. The spatial cluterness was represented as spatial autocorrelation measured by Moran's Index (see Goodchild 1986 for further discussion). The details of theses simulation procedures are described in Lee, Snyder, and Fisher (1992).
We generated error surfaces ranging from error magnitudes of 0.5 meter, 1.0 meters, ..., to 7.5 meters and each set were swapped to have spatial cluterness measured as spatial autocorrelation from 0.0 to 0.9 of Moran's Index. The three dimensional diagram below (Figure 2) shows an example of simulated error surfaces at error magnitude of 7.5 meters above or below the listed elevations in the sample DEM.
The extraction of hydrological features was carried out by using the ArcInfo GRID module on an HP9000/770. The extraction of contours was a straightforward procedures with the GRID command of LATTICECONTOUR while the extraction of drainage cells and networks was carried out by using the GRID procedures for computing flow directions, accumulation with a cut-off level at 100 cells. The details of these procedures can be seen in Jensen and Dominque (1988), Tarboton, Bras and Rodriguez-Itube (1991) and the GRID documentation (Esri 1996).
In Figure 3 and Figure 4, we show the results of extracted hydrological features with added error surfaces at the magnitudes of 0.5 meters and 7.5 meters.
Figure 3 and 4 show that the results of extracted hydrological features have been changed significantly even with errors of low magnitude (0.5 meters). In Figure 3, the resulting drainage network was broken at the same cut-off level. This is even more severely shown in Figure 4 which was added with errors up to 7.5 meters.
First, Figure 5 describes the relationship between the length of contours (computed as the percentage of cells on contours over all cells) and the spatial autocorrelation. It is clear that the lengths of contours reduced significantly as spatial autocorrelation of added error increased. Furthermore, the variations represented by the dashed lines also showed to be decreasing when the errors were more spatially clustered.
Figure 6 gives the relationship between the length of the extracted drainage networks and the spatial clustering of errors. The lowest lengths of the extracted drainage networks were occurred when the spatial autocorrelation coefficients of the added errors were around 0.4 as measured by Moran's index.
In conclusion, we have showed that the procedures for extracting hydrological features using DEM data are indeed very sensitive to the potential errors in DEMs. A slight distortion of the terrain measures will lead to dramatic changes in the resulting hydrological features. In addition, the spatial clusterness of the errors as defined by spatial autocorrelation among DEM measures seemed to have only modest effect to the results of extracting drainage cells from DEMs. Based on the above results, it is therefore our suggestion that DEM data be used with careful consideration with regards to their accuracy.
Jensen, S. K. and J. O. Dominque (1988). "Extracting topographic structure from digital elevation data for geographic information system analysis," Photogrammetric Engineering and Remote Sensing, 54(11): 1593-1600.
Goodchild, M. F., 1986. Spatial Autocorrelation, CATMOG 47, Norwich: Geo Books.
Lee, J., P. K. Snyder, and P. F. Fisher, 1992. "Modeling the effect of data errors on feature extraction from digital elevation models," Photogrammetric Engineering and Remote Sensing, 58(10): 1461-1467.
Tarboton, D. G., R. L. Bras, and I. Rodriguez-Itube (1991). "On the extraction of channel networks from digital elevation data," Hydrological Processes, 5: 81-100.