Modeling the Effect of Data Errors on FeatureExtraction from Digital Elevation ModelsJay LeeDepartment of Geography, Kent State University, Kent, OH 44242-0001Peter K. SnyderDepartment of Geography, University of Georgia, Athens, GA 30602Peter F. FisherDepartment of Geography, University of Leicester, Leicester LEI 7RH, United Kingdom

ABSTRACT: Controlled simulations were used to document the impact that errors in a digital elevation model (OEM)have o.n the accur~cy of the procedures for the extraction of terrain features. A set of procedures was devised for~xtractin~ floodplam cells fr~m a OEM, the most common data source for terrain analysis, with a raster geographicalmformahon system (GIS). It IS obse~ed that ~he magnitudes and the spatial patterns of errors in a OEM significantlyaffect the results of the tested terram analySIS. Maps showing the probabilities of OEM cells being classified as thefloodplain cells are included.

INTRODUCTION

I N RECENT DECADES, DIGITAL ELEVATION MODELS (OEM) haveb,een developed and provided to users for performing a wide

vanety of terrain analyses. The digital elevation models usuallytake the for~ of a regular matrix in which elevations are spacedevenly apart In two orthogonal directions. Reviews of the meth­ods for creating OEMs and various applications for OEMs can befound in Burrough (1986).

Published OEMs are usually supplied with reports of accuracylevels as a reference for users. As an example, the accuracy ofthe OEMs by U. S. Geologic Survey (USGS) is measured by ther~)Qt-~ean~square-error(RMSE or RMS error) (USGS, 1987). Dif­ficulties eXlst, however, when users wish to assess the reliabilityof the results from performing terrain analyses given the oc­~ur~e.nce of error in the OEM. Specifically, how much more re­liability can be placed on the results from a OEM with a 7-metreRMS error as compared with the results from a OEM with a 15­metre RMS error?

In addition, the geometric accuracy of photogrammetricallysampled digital elevation models is mainly dependent on theterrain type and the sampling procedures (Torlegard et aI., 1984;Fred~rik~en et al., 1984; Ostman 1987). For a OEM, the pointdenSity IS usually homogeneous while the terrain type can bevery heterogeneous. This means that one cannot assume theerror~ in the interpol~ted elevation to be a stationary randomfunction over the entire OEM. Therefore, it is important to ex­amine the impact tha.t spatially c~rrelated (or, more correctly,autocorrelated) elevatIon errors might have on terrain analysesthat might be performed.

To assist in the understanding of the roles that elevation er­rors in OE~S play' in t~rrain analyses, this paper outlines a pro­cedure for Imposing Simulated elevation errors with controlledmagnitudes and spatial patterns onto a OEM. These simulatedsurfaces are used in the extraction of floodplain cells from theOEM: T~is operation is chosen because it has a wide variety ofapplicatIon for many purposes. Cells identified as floodplainare then analyzed with respect to the magnitude and the spatialpattern of the simulated elevation errors to examine the impactof these errors on the classification accuracy.

ALGORITHMS FOR EXTRACTING DRAINAGE FEATURES

A large body of literature relevant to the extraction of a flood­plain exists in the earlier research on automated extraction of

PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING,Vol. 58, No. 10, October 1992, pp. 1461-1467.

drainage networks. This work was pioneered by Peucker andDouglas (1975) who analyzed topographic features of grid cellsaccording to the patterns of elevation changes between neigh­bor cells. Later on, Mark (1983), O'Callaghan and Mark (1984),Band (1986), Morris and Heerdegen (1988), Jensen and Dom­inque (1988), Hutchinson (1989), Smith et al. (1990), and Skid­mo:e (1990) developed various algorithms for extracting thedrainage network based on raster OEMs. These algorithms per­formed to different degrees of success but all encountered prob­lems with single cell pits in flat areas due to high signal-to-noiseratio, as described in O'Callaghan and Mark (1984). Further­more, these algorithms extract drainage networks but with onecell in width. The inconsistency shown among these algorithmsis partly due to the fact that the Single-cell drainage networksare more likely to be affected by error in OEMs.

It was not until Tribe's (1990) work that an algorithm wasspecifically constrained to extract drainage networks with a widthof one cell. Tribe's approach employs two stages and uses bothelevation changes and slopes between grid cells to derive morerealistic drainage networks. First, a drainage network, one cellin width, is found, and then Tribe's algorithm attempts to ex­pand feature width in all directions by examining the slopes ofthe cells adjacent to the identified drainage channels, and in­cluding them if the slope is within a specified threshold. Tribe'sapproach that drainage networks may have more than one cellin width is adapted here. In fact, the areas that drainage net­works have more than one cell concur to a more practical terrainfeature-a floodplain.

In this study, we devised a set of procedures using IORISI(Eastman, 1990), a raster GIS, to determine which grid cells arepart of the floodplain. In this fashion, a more meaningful rep­resentation of drainage pattern can be achieved instead of hav­ing a drainage network that is highly suspectable to error as isthe case of the one-cell networks.

SAMPLE DEM

We used a USGS OEM which covers the area of Herbert Do­main, Tennessee and is located in the Appalachian PlateauProvince. The spatial resolution of this OEM is 30 metres andthe OEM covers an area of 9 krn2, giving a 100 by 100 cell subset.The minimum elevation in the OEM is 474.6 metres and themaximum elevation is 569.0 metres. Figure 1 shows the contourmap and a 3D diagram for the studied area. An oblique T-shape

0099-1112/92/5810-1461$03.00/0©1992 American Society for Photogrammetry

and Remote Sensing

1462 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1992

FIG. 1. Contour map and 3D diagram of Herbert Domain, Tennessee.

floodplain can be easily identified in both the contour map andthe 30 diagram.

The process of generating the errors with specified spatialautocorrelation (Goodchild, 1986) onto the OEM surface was out­lined by Goodchild (1980) and implemented by Fisher (1991a).First, for each cell in the OEM, a set of random numbers is drawnfrom a normal distribution with a mean of zero and a specifiedstandard deviation. Then, the spatial autocorrelation of the er­ror matrix is calculated and stored for later comparison. Next,two cells are randomly identified and swapped. Then the newspatial autocorrelation of the errors is calculated. If the newspatial autocorrelation is closer to the specified spatial autocor­relation, then the swap is retained; otherwise, the two cells areswapped back and two other cells are tried. This process iscontinued until the spatial autocorrelation is within a certainthreshold. After an error matrix is generated, it is added to theOEM and the simulation is complete. In the analysis presentedhere, 30 simulations were run per test: 480 simulations in total.Discussion of an appropriate number of tests and the uniformityof random numbers generated can be seen in Fisher (1991b).

To assess how the magnitudes and the spatial patterns ofelevation errors impact the accuracy of the results of terrainanalysis, we conducted two sets of simulations. The first set ofsimulations was run to generate errors of varying magnitudesfrom ± 1 metres to ± 7 metres (standard deviations of 1 and 7metres) with no spatial autocorrelation (Moran's I = 0.0). Thesecond set of the simulations were run to generate errors ofvarying spatial autocorrelation from Moran's I = 0.0 to 0.9 witha fixed magnitude of ± 7 metres. In this manner, we can observethe effects that errors in magnitude or spatial autocorrelationhave on the accuracy of terrain analysis.

THE EXTRACTION OF FLOODPLAIN CELLS

The third stage extracted floodplain cells from the OEM throughthe use of several IDRISI programs. First, an examination of theoriginal OEM and the elevation ranges was made to determineat what elevations the drainage channels were located. Becausethe OEM of this area is located in a physiographic region char­acterized by flat plateaus and deeply incised river channels (Fig­ure 1), we assumed that the floodplain can be defined by acertain elevation range. Therefore, the elevation range of thefloodplain cells was defined to occur between 474.6 metres(minimum elevation in the OEM) and 505 metres. The elevationimage was then reclassified, using RECLASS in IDRISI, assigninga value of 1 to those cells with elevations from 474.6 metres to505 metres and a value of 0 to cells with elevation 506 metresor above.

Next, a slope image was created from the OEM image usingthe SURFACE program in IDRISI and again reclassified to assigna value of 1 to those cells with slopes between 0 and 10 degreesand a value of 0 to those cells with slopes of 11 degrees or above.The range for the slope map was chosen subjectively becauseit is assumed that the floodplain cells are relatively flat areas(i.e., slope under 11 degrees). Again, this should not affect thevalidity of the study here as long as they are kept consistentover all test runs.

The third step was to overlay the reclassified elevation andslope maps using the MULTIPLY option in IDRISI's OVERLAY. Cellswith both a slope less than 11 degrees and an elevation between474.6 metres and 505 metres were classified as a floodplain cell.Finally, the AREA program in IDRISI was used to find the numberof cells classified as floodplain for analysis in the results.

PROBABILITY MAPS OF FLOODPLAIN CLASSIFICATION

To observe the spatial patterns of the impact that elevationerrors may have on the accuracy of the extracted floodplaincells, a series of probability maps will be compiled to computethe probability that any OEM cell would be classified as a flood­plain cell with simulated elevation errors. To do this, we use

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METHODOLOGY

Our procedures for assessing the impacts that the magnitudesand the spatial patterns of elevation errors have on the accuracyof the extracted floodplain can be divided into four main stages:(1) the pre-processing of the OEM, (2) the running of the errorsimulations, (3) the extraction of the floodplain cells, and (4)the mapping the probabilities of cells being classified as part ofa floodplain.

THE PRE-PROCESSING OF DEM

In pre-processing, the 100 by 100 cell OEM was converted intothe IDRISI file format. The size of 100 by 100 was chosen due tothe memory limit imposed by the simulation program. To ex­clude the effect of single-cell pits, we applied a low-pass filtertwice to remove single-cell pits in the flat areas of the OEM. Thevalidity of this study should not be affected by applying thelow-pass filter at this stage because the resulting OEM is to beused as input to all subsequent analyses.

SIMULATIONS OF VARIABLE MAGNITUDES AND SPATIAL PATTERNS

The second stage of the methodology is to simulate differentmagnitudes and spatial patterns of errors onto the OEM surface.The simulation process adds errors with a specified standarddeviation (i.e., magnitude) and a specified spatial autocorrela­tion (i.e., spatial pattern).

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MODELING THE EFFECT OF DATA ERRORS

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FIG. 2. Floodplain cells classified without simu­lated errors.

FIG. 3. Floodplain cells with errors of spatial cor­relation of 0.0 and standard deviation of 2.0metres.

FIG. 4. Floodplain cells with errors of spatial cor­relation of 0.2 and standard deviation of 7.0metres.

TABLE 1. RESULTS OF SIMULATION PERFORMED WITH VARYING SPATIAL

AUTOCORRELATION VALUES AND A FIXED STANDARD DEVIATION OF 7METRES. ABBREVIATIONS: SA (SPATIAL AUTOCORRELATION).

autocorrelation among the errors added, the more commissioncells and the less omission cells would result.

In graphic form, Figure Sa shows the rate of increase in theaverage number of classified floodplain cells when the spatialautocorrelation increases. Figure Sb displays the differences be­tween the avera.ge number of classified floodplain cells againstthe spatial autocorrelation values. It is apparent that the trendfluctuates initially but becomes continuously increasing afterthe spatial autocorrelation value exceeds 0.5 or 0.6.

This analysis seems to suggest that the results of the extractedfloodplain will likely be more reliable if the errors are morespatially autocorrelated (i.e., similar magnitude errors being lo­cated closer to each other). The increase in the number of flood­plain cells corresponding to an increase in the spa lialautocorrelation of the errors is thought to be a result of theclustering of errors. The errors that affect those cells making upthe floodplain may be lessened as the errors become more clus­tered (i.e., high spatial autocorrelation).

It is also evident that spatial autocorrelation (from 0.0 to 0.9)has a stronger impact on the number of cells omitted (287 =741 - 454) (Figure Sc) than on the number of cells committed(88 = 270 - 182) (Figure Sd) to the floodplain.

Linear regression models were run for each measure to ex­amine the relationship between floodplain cells and spatial au­tocorrelation. The results are listed in Table 2 and Figures Sa,Sc, and Sd. Although spatial autocorrelation has a stronger im­pact on the number of omission cells than on the number ofcommission cells, Table 2 suggests that the relationship be­tween spatial autocorrelation and the number of commissioncells is more predictable than the number of omission cells (in-

the AOO option in the OVERLAY program of IORISI to accumulatethe number of times each cell has been classified as a floodplaincell for all simulations in each test. Next, the overlaid imagesare divided by the number of simulations in each test (which is30 in this study) to produce probabilities, using the SCALARprogram of lORIS!.

RESULTS

In order for comparisons to be made between the simulationsperformed and the original OEM, the original OEM needed to beprocessed using the same IDRISI procedures for extracting thefloodplain with the same criteria for RECLASS (as described inthe previous section) to be applied to every test. This processwas first carried out for the original OEM, and the number offloodplain cells classified was found to be 1,137 out of 10,000cells. Figure 2 shows the classified floodplain cells without anyerror applied.

The extracted floodplain seems to agree well with those dis­played on the topographic map (Figure 1). The procedures werethen repeated for every simulated OEM. Two of the floodplainmaps after error simulation in the OEM are shown in Figure 3and Figure 4. It is apparent that the error term causes mis­classification of many floodplain cells.

RESULTS FROM SIMULATIONS WITH VARYING SPATIALAUTOCORRELATION

The results of the first set of simulations with varying spatialautocorrelation values and a fixed standard deviation of 7.0 metresshow that the number of floodplain cells classified increases asa function of the spatial autocorrelation of the errors. The resultsshown in Table 1 include average numbers of classified flood­plain cells, omission cells, and commission cells. The numberof classified floodplain cells for a test was obtained by simplycounting the number of cells that were classified as floodplaincells in each simulation. The number of omission cells was ob­tained by (1) overlaying the floodplain found from the originalOEM and the floodplain found for each simulated surface and(2) counting the number of cells that were not classified asfloodplain cells when they should have been. In a similar fash­ion, the number of commission cells was obtained by overlayingthe floodplain found from the original OEM and from simulatedOEMs and counting those cells that were classified as floodplaincells when they should not have been.

By observing the results listed in 'f.able 1, the average numberof cells classified as floodplain cells decreases when spatial au­tocorrelation decreases. The average number of omission andcommission cells change in different directions when spatialautocorrelation increases. It is clear that the higher the spatial

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Mean of CellsClassified

952829755706653625604593588579

Mean ofOmission Cells

454557616655688707725733735741

Mean ofCommission

Cells270248235224203194191188185182

1464 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING, 1992

OEM ERROR SIMULATIONSHerbert Domain. TN S.D. = 7.0

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(~ (d)FIG. 5. (a) Relationship between spatial autocorrelation and the average number of classified floodplain cells, shown with ± 1 standard deviation.(b) Relationship between spatial autocorrelation and the differences in the number of classified floodplain cells. (c) Relationship between spatialautocorrelation and the average number of Commission cells, shown with ± 1 standard deviation. (d) Relationship between spatial autocorrelationand the average number of omission cells, shown with ± 1 standard deviation.

dicated by a higher r-square value and a lower coefficient ofvariation).

TABLE 2. THE RELATIONSHIP BETWEEN DRAINAGE CELLS AND SPATIALAUTOCORRELATION. V,: AVERAGE NUMBER OF CLASSIFIED DRAINAGE

CELLS. V2 : AVERAGE NUMBER OF OMISSION CELLS. V3 : AVERAGE NUMBEROF COMMISSION CELLS.

TABLE 3. RESULTS OF SIMULATION PERFORMED WITH VARYINGSTANDARD DEVIATIONS AND WITH No SPATIAL AUTOCORRELATION.

ABBREVIATIONS: SA (SPATIAL AUTOCORRELATION).

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RESULTS FROM THE SIMULATIONS WITH VARYING STANDARD

DEVIATIONS

The second set of simulations varied the standard deviationof elevation errors (equivalent to RMS errors) while holding thespatial autocorrelation constant at 0.0. The results of these sim­ulations are listed in Table 3.

From Table 3, it is observed that the average number of class­ified floodplain cells increases when the magnitude of errordecreases, and again, the number of omission cells seems to be

more sensitive to varying error magnitudes than the number ofcommission cells. However, both numbers decrease when thestandard deviation increases. Figure 6 shows three diagrams ofthe relationships between changing standard deviations and theaverage numbers of classified floodplain cells, omission cells,and commission cells.

Linear regression models were also run for this set of simu­lations and are listed in Table 4. It should be noted that, in the

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MODELING THE EFFECT OF DATA ERRORS 1465

TABLE 4. THE RELATIONSHIP BETWEEN DRAINAGE CELLS AND ERRORSTANDARD DEVIATION. V,: AVERAGE NUMBER OF CLASSIFIED DRAINAGE

CELLS. V2 : AVERAGE NUMBER OF OMISSION CELLS. V3 : AVERAGE NUMBEROF COMMISSION CELLS.

simulation of varying error magnitudes with no spatial auto­correlation, the average number of omission cells tends to bemore predictable with a higher r-square value and a lower coef­ficient of variation than the average number of commission cells.

From the results in the second set of simulations, it is obviousthat, as the amount or magnitude of errors decreases, the moresimilar the DEM will be to the original OEM regardless of thespatial patterns of the errors. For instance, errors of one metrein standard deviation applied to the OEM are so small that, re­gardless of the spatial pattern, the OEM closely approximatesthe original OEM. As the magnitude of the errors increases, thesimulated OEM will diverge from the original OEM. This resultcorresponds to our intuitive expectation of deriving more ac­curate results from less errors.

PROBABILITY MAPS

As described earlier, a series of probability maps was pro­duced to show the likelihood of each cell being classified as afloodplain cell under various simulated situations. Figures 7 and8 show the results of these mapping procedures.

A close examination of the maps shown in Figure 7 revealsthat the spatial patterns of error (simulated by various spatialautocorrelation values) affect the extraction of the floodplain.The more clustered the simulated errors the more likely thefloodplain cells are to be correctly extracted, Commission cellsare observed at the middle left portion of the maps, and exhibitincreased clustering when errors are more spatially autocorre­lated.

In Figure 8, a distinct contrast can be observed between theprobability maps of SD = 1 metre versus SD = 7 metres. Thiscontrast confirms our intuitive expectation that the lower prob­abilities would be associated with higher magnitudes of simu­lated errors. Similarly, as the simulated error magnitude increases,more commission cells appear in the maps.

It would also appear that the areas of highest probability inthe floodplain form linear ribbons through the image, and mayactually be identifying (or locating) the network of at least pri­mary streams. It is possible that this may enable detection ofthe drainage network through manipulation of error: the usualcause of problems in extraction by standard algorithms.

CONCLUSIONS

Because of the time involved in manually mapping the drain­age patterns, such as a floodplain, from a topographic map, theOEM has been seen as an excellent data source and an effectivealternative for automating this once tedious and specializedprocess. In addition to proposing the procedures for extractinga floodplain, this paper demonstrates how the accuracy of aDEM impacts these procedures by simulating DEM errors undercontrolled circumstances.

By comparing the results of the simulated surfaces with thoseof the original, a better understanding of how the magnitudeand the spatial pattern of the elevation errors can be achieved.The results from the simulations performed in this paper havedemonstrated that there is a strong quantifiable impact of theaccuracy of a OEM on the floodplain extracted.

An understanding of how the accuracy of the procedure forthe extraction of floodplain changes as a function of the mag-

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MODELING THE EFFECT OF DATA ERRORS 1467

nitude and the spatial pattern of the error can give new insightsinto the prediction of how accurate a resulting drainage patternwill be for different levels of accuracy in a OEM. This ability todescribe the level of accuracy of a particular terrain analysisfunction for various OEM accuracies may be valuable to organ­izations wishing to set standards for terrain analysis and GISoperations. By determining the level of accuracy for which re­sults are required, the required accuracy of the data source canbe determined. This would alleviate the need for trial and errortests to be performed on OEMs with different levels of accuracy.

A similar approach can be taken to assess the performanceof various existing algorithms for extracting drainage patternsand other types of terrain analysis. We hope that, by docu­menting the impact of error magnitudes and spatial patterns onthe accuracy of the results of terrain analyses in this paper, moreunderstanding of the relationship between data accuracy andprocedures for analyzing terrain surfaces may be achieved andused for various applications.

REFERENCES

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Burrough, P. A., 1986. Principles of Geographic Information Systems forLand Resources Assessment, Clarendon Press, Oxford.

Eastman, R., 1990. IDRISI: A Grid-Based Geographic Analysis System, ClarkUniversity, Worcester, Massachusetts.

Fisher, P. F., 1991a. Modelling soil map-unit inclusions by Monte Carlosimulation. International Journal of Geographic Information Systems,5(2):193-208.

--, 1991b. First experiments in viewshed uncertainty: the accuracyof the viewshed area. Photogrammetric Engineering & Remote Sensing,57(10):1321-1327.

--, 1992. First experiments in viewshed uncertainty: simulating fuzzyviewsheds. Photogrammetric Engineering & Remote Sensing, 58(4):345­352.

Frederiksen, P., O. Jacobi, and K. Kubik, 1984. Modelling and classi­fying terrain. International Archives of Photogrammetry and RemoteSensing, XXV, Part A3a:256-267.

Goodchild, M. F., 1980. Algorithm 9: simulation of autocorrelation foraggregate data. Environment and Planning A, 12:1073-1081.

---,1986. Spatial Autocorrelation. CATMOG 47, Geo Books, Norwich,United Kingdom.

Hutchinson, M. F., 1989. A new procedure for gridding elevation andstream line data with automatic removal of spurious pits. Journalof Hydrology, 106:211-232.

Jenson, S. K., and J. O. Domingue, 1988. Extracting topographiC struc­ture from digital elevation data for geographic information systemanalysis. Photogrammetric Engineering & Remote Sensing, 54(11):1593­1600.

Mark, D. M., 1983. Automated detection of drainage networks fromdigital elevation models. Proceedings of Auto-Carto 6, 2:288-298.

Morris, D. G., and R. G. Heerdegen, 1988. Automatically derived catch­ment boundaries and channel networks and their hydrological ap­plications. Geomorphology, 1:131-141.

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(Received 25 October 1991; accepted 30 December 1991; revised 6 Jan­uary 1992)

ISPRS Commission IINIIInlemalional Wortshop

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13-17 January 1990Orono, Maine

Advances in Spatial Information

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