Demetra E. Voyadgis and William H. Ryder

Measuring the Performance of Ground Slope Generation

Abstract - Calculation of ground slope is fundamental to many traditional Geographical Information System's (GIS) applications. Slope is an important component in scientific, military and civilian analyses. Various methods exist for calculating slope. Manual slope generation, based upon contour line information, is a long established and generally acceptable method. However, with automated tools for doing analysis, analysts assume that the algorithm in use is accurate and comparable to the manual method of slope generation. The Digital Concepts and Analysis Center (DCAC) at the U. S. Army Topographic Engineering Center (TEC), the Army's center of expertise for digital topographic data, has conducted a study of the accuracy of slope generation.

The purpose of this study was to field test the well- established method of slope generation used by Army terrain analysts, the manual slope-wedge method, and the more recently available slope algorithm embedded in the ArcInfo GRID module. Manual slope maps compiled from a 1:24000 and 1:50000 scale topographic maps were digitized for analysis in ArcInfo. The elevation data used for slope generation in GRID were produced at TEC and covered the Yakima Training Center, Yakima, Washington. The elevation data were collected at 5-meter post spacing and were thinned to allow further comparisons at resolutions that are generally available to terrain analysts (30 and 100 meters). Rapid field collection of point slope data, a key aspect of this study, was made possible through Global Positioning System (GPS) and laser range-finding technology. To assess slope accuracy, field slope measurements were compared with manual and GRID-generated slope values. The results are summarized and discussed in the paper.

INTRODUCTION

Many spatial analyses are reliant upon ground slope. As traditional methods of spatial analysis are being automated, so too is the production of slope. The automation of slope production raises the question "How does the automated result differ from the manual result?". This study seeks to answer this question by quantifying the accuracy of slope produced by automated and manual methods.

PURPOSE

The majority of slope maps that are available to the Army terrain analyst are compiled from the contours of a Defense Mapping Agency's (DMA) 1:50000 scale Topographic Line Map (TLM). Recently, analysts acquired the capability to generate slope from a grid of elevation data that is available at various resolutions. The purpose of this study was to examine the performance of the algorithm in ArcInfo GRID and the manual method of slope generation to determine the relative accuracy of the results. Slope data collected in the field provided the control for the study. The analysis compared the predicted value with the actual value to derive a measure of reliability.

METHODOLOGY

The methodology employed in this study was to compare computer generated slope ranges with field data. The field data measured slope at pre-selected points. These values were compared with the predicted slope ranges to produce a confusion matrix. A measure of accuracy was established by obtaining the percentages of accurately and inaccurately measured points. This methodology required the following three criteria:

a highly accurate, high-resolution, elevation data set over a fairly large and topographically diverse area
an area which was accessible to field survey work
a slope map for the selection of field points that was better than typically employed by an analyst.

The Topographic Engineering Center (TEC) possessed a recent and highly accurate elevation data set at 5-meter post spacing over the Yakima Training Center, Yakima, Washington. A subset of this data set, covering an area of four by four kilometers was selected. It was sufficiently large to contain areas of diverse topographical features and was accessible to the field surveyors.

The objective of the field data collection effort was to obtain a representative sample of 50 locations from each slope category. An existent United States Geological Survey (USGS) Quad sheet at a scale of 1:24000 was used to create a slope polygon map from which the selection of field points was made. This streamlined the field work by having pre-selected points and provided for greater accuracy in slope selection than could be attained from the 1:50000 TLM.

DATA

Elevation Data

The generation of slope requires reliable elevation data. The Yakima data set was derived from 9" x 9" aerial photography that had a high degree of ground control. The extraction of elevation points was performed on a Digital Photogrammetric Work Station (DSPW). The elevation points were extracted in a matrix formatat 5-meter intervals. Typically, the elevation data that are available for Army applications are at 100-meter, and less frequently, 30-meter post spacing. Although prohibitive to collect over large areas due to time and cost constraints, the possibility of using 5-meter spacing is under consideration for small areas and special projects. Therefore, the 5-meter data set was used in this evaluation. To simulate 30 and 100-meter data, the 5-meter data set was thinned to 30 and 100-meter spacing using the resample command.

Site Selection Points

To test the prediction of slope, selection of field locations was a critical component. To attempt to ensure a good correlation between the selected points and their ground truth, the largest scale slope map available, a 1:24000, was used for site selection. Ultimately, the combination of pre-selected points and daily restrictions on the firing range resulted in sample sizes of less than 50 in three of the six slope category ranges, and especially in the two highest slope range categories. (See Table 1)

The distribution of points was critical in the selection process. The goal was to ensure adequate representation of points in all slope categories. Attention to the distribution of points also ensured that the slope at the selected site was not an anomaly, but representative of the larger terrain. To meet these criteria the following rules were established:

points had to be separated by at least 125 meters
the point must be at the center of a homogeneous circular area, 125 meters in radius.

The first rule ensured that there would be no overlapping of slope areas when testing points at 100 meters. The second rule ensured that the point contained only the slope category being tested.

FIELD WORK

Point Location

Locating the pre-selected points in the field was accomplished using Global Positioning System (GPS) technology. A Precision Lightweight Global Positioning System Receiver (PLGR) with a military key was used in the field to navigate to the pre-selected point. The military key allows the reading of coordinate positions at accuracies only available to military users (+- 10-meter). Although sufficient for the 30 and 100-meter evaluations, greater precision was needed for the 5-meter evaluation. Thus, differential GPS (DGPS) was used. Differential GPS employs a base station over a surveyed coordinate point that tracks the ephemeris of satellites. A computer program is used to compare the known position with the satellite data. A measure of the amount of ephemeris dithering is calculated. This information is used to correct the data collected by the receiver units that are used in the field. The result is a coordinate position with +-2.5 meter accuracy.

Once the positions were collected, a laser range-finder was used to measure the slope. The range finder sends out a signal that rebounds off a (preferably highly reflective) object, and calculates various properties, such as slope and distance. Field personnel visually estimated the direction of maximum slope and one person paced off the distance to be measured (5, 30 or 100 meters). The range-finder was used to fine tune the distance measurement and the slope was recorded. In areas where the direction of maximum slope was not apparent, the procedure was repeated several times. To maintain accuracy in the slope measurement, measured poles were used to ensure that the height of the laser range-finder's beam was the same height as the reflector.

MANUALLY GENERATED SLOPE METHODOLOGY

Historically, slope was manually generated using the slope-wedge method according to the Defense Mapping Agency's (DMA) specifications for generating slope. The slope-wedge is a template of graduated circles. Each circle represents one of the six slope categories found in the DMA's slope specifications. (See Table 2)

Using a topographic map, this method requires fitting the circles on the template between the contour lines. The value of the largest circle that fits between two contour lines determines the maximum slope. According to the DMA specifications, the axes of a slope polygon must measure at least 250 meters in ground distance for the polygon to be retained. Two slope polygon maps derived by the manual method were used in this study. One map was created at a scale of 1:24000 and was also used for the selection of field sites. The other map was obtained from the DMA and was generated by an analyst at the conventional 1:50000 scale. Slope information on both of the maps was digitized as slope polygons, and converted to GRID format for analysis.

COMPUTER GENERATED METHODOLOGY

The computer generated methodology consisted of using the embedded algorithm in ArcInfo GRID to generate a slope map. The slope is calculated using a 3 x 3 roving window algorithm that calculates the average maximum slope. It is a third order finite difference method with a weighting factor of 2 for cells in the cardinal directions. This slope map was then reclassified into slope categories. The slope values for the field locations were extracted and the two grids were used in a confusion matrix. This last step was also used on the manually produced maps that had been gridded. A detailed account of the process follows. A matrix of elevation points from the DSPW system was output in ASCII format.

The ARC generate command was used to generate a point coverage, which was brought into the GRID module through the pointgrid function. Next, the field locations were downloaded from the differential GPS in ASCII format. Again, the generate command was used to create a point coverage, and the pointgrid command used to create a grid coverage.

The original elevation data set, at 5-meter spacing, was thinned to 30-meter and 100-meter using the resample command. For each of these three data sets, the following procedures were performed:

define the projection
calculate the slope
classify the data
extract the slope category values for the field locations. (This was also performed on the manually compiled data set.)

The slope was calculated using the slope command. A remap table of values, using the DMA specified slope categories, was created and used with the reclass function to produce the slope polygon map. Finally the combine command was used to extract the slope category values. The combine command combines two or more coverages and outputs a coverage of unique values. The database table associated with the resulting coverage contains the values from each of the original coverages. Therefore, when the reclassified slope grid and the field location grid are input to the combine function, the resulting grid coverage contains only those grid cells that are common to both input grids. The database table for the resulting grid contains the value of the slope category and the number of the field location. These numbers were then used in the statistical comparisons.

STATISTICAL ANALYSIS

The slope's accuracy was the confusion matrix. A confusion matrix compares known values to predicted values. Each axis of the matrix is labeled with the six categories of slope (See Table 3).

The accuracy of predicted values is determined by selecting a category of known slope and reading across the matrix to the equivalent column of predicted values. The value at this juncture indicates the number of times the computer predicted points agreed with the ground truth. The total number of surveyed locations for that slope category is tallied by adding all the values across the row; this number is found in the column labeled "Row Total". The accuracy percentage is obtained by dividing the number of correctly identified values into the total number of values.

RESULTS

The results of this analysis are summarized in Table 4.

As expected, at all three resolutions the GRID generated slope performed better than the manual method. Due to inability to collect sufficient field slope measurements in the "E" and "F" slope categories, accuracy figures in these categories are not as reliable as the categories "A-D".

ArcInfo Performance

The performance at 30-meter and 100-meter resolutions was almost identical, the exception being in the "A" slope category. Prediction accuracy in the "A" category was nearly 7% higher (93.5% vs. 86.7%) for the 100 meter compared to 30-meter resolution.

Surprisingly, the 5-meter data set performed worse than the other resolutions. In every slope category, the 30-meter resolution data set outperformed the 5-meter data set. The magnitude of this difference in performance ranged from 12.3% for the "A" slope category to 6% for the "B" slope category. The 100-meter data set also performed better than the 5-meter data set in every category, except for the "E" slope category. This latter observation must be tempered by the overall lower reliability of the "E" slope information.

Manual Method Performance

Of the two manual methods, the larger-scale map produced slightly better results except in the "A" category. An explanation can be attributed to a polygon collection criterion. This criterion involved the elimination of polygons whose axes measure < 250 meters in length. This criterion was adopted from the DMA slope specification that was designed for 1:50000 scale maps, but at a larger scale it appears to have eliminated micro-features in the terrain.

CONCLUSIONS

The automated slope generation method performed better than both instances of the manual method. Of the manually generated maps, the larger the map scale from which the slope was produced, the higher the percentage of accuracy.
At 5-meter resolution, performance of the GRID algorithm was degraded when compared with the 30-meter and 100-meter resolutions. This may be due to positional inaccuracies in the ground collected slope data and inability of the algorithm to locate micro-terrain features.
At 30-meter and 100-meter resolutions, the GRID algorithm performed at approximately the 75% accuracy level.
At all resolutions and with all methods, there was a trend towards decreasing prediction accuracy when progressing from low ground slope, i.e., category "A" slope, to high ground slope, i.e., category "F" slope.

ACKNOWLEDGMENTS

The authors of this paper would like to thank Mr. Louis Fatale and Mr. James Ackeret for their excellent field support, and Mr.Patrick Nguyen for his system support. We also greatly appreciate the leadership and support of Mr. Jeffrey Messmore.

REFERENCES

Burrough, P.A. 1986. Principles of Geographical Information Systems for Land Resources Assessment, New York, NY: Oxford University Press, pp. 39-56

Environmental Systems Research Institute. 1994. Help documentation for ArcInfo 7.0.2, Redlands, CA.

Horn, B.K.P. 1989. Hill shading and the reflectance map. Proceedings of the I.E.E.E., pp. 14-47.

Skidmore, A.K. 1989. A comparison of techniques for calculating gradient and aspect from a gridded digital elevation model, International Journal of Geographical Information Systems, Vol. 3, No. 4. pp. 323-334.

AUTHOR INFORMATION

Demetra E. Voyadgis, Geographer
Army Topographic Engineering Center
Attn: CETEC-PD-DT
7701 Telegraph Rd.
Alexandria, VA 22315-3864
Phone: (703) 428-6760, FAX: (703) 428-6176
email: dvoyadgi@tec.army.mil

William H. Ryder, Physical Scientist
Army Topographic Engineering Center
Attn: CETEC-PD-DT
7701 Telegraph Rd.
Alexandria, VA 22315-3864
Phone: (703) 428-6759, FAX: (703) 428-6176
email: wryder@tec.army.mil