Published online 29 June 2007
Published in Soil Sci Soc Am J 71:1371-1380 (2007)
DOI: 10.2136/sssaj2005.0142
© 2007 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
SOIL & WATER MANAGEMENT & CONSERVATION
Digital Elevation Accuracy and Grid Cell Size: Effects on Estimated Terrain Attributes
Robert H. Erskinea,*,
Timothy R. Greena,
Jorge A. Ramirezb and
Lee H. MacDonaldc
a USDA-ARS, Agricultural Systems Research Unit, 2150 Centre Ave., Bldg. D, Suite 200, Fort Collins, CO 80526
b Dep. of Civil Engineering, Colorado State Univ., Fort Collins, CO 80523
c Dep. of Forest Rangeland, and Watershed Stewardship, Colorado State Univ., Fort Collins, CO 80523
* Corresponding author (Rob.Erskine{at}ars.usda.gov).
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ABSTRACT
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Terrain attributes are commonly used to explain the spatial variability of agronomic, pedologic, and hydrologic variables. The terrain attributes studied here (elevation, slope, aspect, and curvature) are estimated readily from digital elevation models (DEMs), but questions remain about how the accuracy and sample spacing of the elevation data affect the estimated attributes. The main objective of this study was to quantify differences in each terrain attribute due to factors affecting DEM accuracy and grid cell size. Three data sources were compared: (i) real-time kinematic global positioning system (RTKGPS); (ii) satellite-differentially corrected global positioning system (DGPS); and (iii) U.S. Geological Survey (USGS) 30-m DEMs. The GPS data from three undulating agricultural fields in northeastern Colorado were interpolated onto 5-, 10-, 20-, and 30-m grid DEMs. The DGPS and USGS DEMs produced similar elevation differences relative to RTKGPS DEMs, but elevation differences in USGS DEMs were more spatially correlated. Estimates of curvature were highly sensitive to DEM differences and the sensitivity of slope, aspect, and curvature estimates decreased as grid cell size increased. The impacts of DEM accuracy and grid cell size were investigated using correlations between wheat (Triticum aestivum L.) grain yields and estimated terrain attributes. The highest correlation coefficients were obtained using RTKGPS data, and decreasing the sample spacing or grid cell size below 30 m did not consistently improve the correlations. These analyses on agricultural lands indicate the importance of accurate elevation data for detailed terrain analyses on grid cell sizes of 30 m or less.
Abbreviations: DEM, digital elevation model • DGPS, satellite-differentially corrected global positioning system • GPS, global positioning system • RMSD, root mean squared difference • RMSE, root mean squared error • RTKGPS, real-time kinematic global positioning system
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INTRODUCTION
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Terrain attributes have been used widely to help explain the spatial variability in soil water (Zaslavsky and Sinai, 1981; Burt and Butcher, 1985; Moore et al., 1988; Tomer et al., 1994; Nyberg, 1996; Western et al., 1999), agronomic and pedologic variables (Moore et al., 1993; Bell et al., 1994; Odeh et al., 1994; Florinsky et al., 2002), and crop yields (Simmons et al., 1989; Halvorson and Doll, 1991; Yang et al., 1998; Kravchenko and Bullock, 2000; Kaspar et al., 2003; Green and Erskine, 2004). The terrain attributes studied here (elevation, slope, aspect, profile curvature, and plan curvature) characterize the land surface geometry and are fundamental to other derived terrain attributes. Moore et al. (1991) defined various primary terrain attributes and identified their significance in hydrologic processes (Table 1).
Terrain attributes are readily estimated from DEMs, but the estimated values are sensitive to DEM accuracy (Sasowsky et al., 1992; Bolstad and Stowe, 1994; Giles and Franklin, 1996; Hunter and Goodchild, 1997; Endreny et al., 2000; Holmes et al., 2000; Raaflaub and Collins, 2006) and grid cell size (Chang and Tsai, 1991; Jenson, 1991; Panuska et al., 1991; Wolock and Price, 1994; Zhang and Montgomery, 1994; Thieken et al., 1999; Thompson et al., 2001). Digital elevation model accuracy and grid cell size are related intrinsically to the data source and sampling method.
Elevation data can be measured very accurately using a dual-frequency RTKGPS, which is comprised of an on-site base GPS for differential correction and a rover GPS for data collection. The RTKGPS data are typically accurate within 0.01 m RMSE horizontally and 0.02 m RMSE vertically based on static measurements. Rapid data acquisition is possible by mounting the rover GPS on a vehicle and taking measurements while driving the terrain. Using this approach, RTKGPS can be used to create DEMs in agricultural lands. Elevation errors for RTKGPS-derived elevation contours were <0.1 m when driving transects spaced up to 33 m apart (Clark and Lee, 1998). Note that elevation errors in derived elevation contours or grid DEMs will be higher than the typical RTKGPS accuracy at a point (0.02 m RMSE) because of required data interpolation. Currently, the application of RTKGPS in precision farming is limited by equipment costs, but we expect that data of similar accuracy will become more readily available as GPS technology advances.
The present technology for most precision farming operations incorporates single-frequency, real-time DGPS. These DGPS data are typically accurate within 0.5 m RMSE horizontally and 1 m RMSE vertically. A DGPS provides a more efficient means than RTKGPS for DEM production on agricultural lands because these data are already being collected during precision farming operations. Previous studies have shown that DGPS accuracy can be improved by averaging data from multiple data collections. Averaging 10 sets of DGPS data yielded elevations differences of less than 0.15 m relative to RTKGPS measurements (Yao and Clark, 2000). Averaging DGPS data from six data collections produced elevation differences of <0.4 m relative to RTKGPS measurements (Schmidt et al., 2003). Under normal agricultural practices, several years may be needed to acquire six or more data sets. Therefore, the DGPS data sources evaluated here were from single operations.
Due to their public availability and broad use, USGS DEMs were also compared with the GPS data sources. At these sites, 30-m grid DEMs derived from 1:24000 contour maps were available. Systematic errors are common with these photogrammetric methods and the USGS specifies 900f these DEMs to have elevation errors <7 m RMSE. Relative to RTKGPS elevations, absolute vertical differences can exceed 18 m and exhibit spatial autocorrelation (Holmes et al., 2000). Estimated terrain attributes such as slope, aspect, and curvature are sensitive to the elevation errors associated with USGS DEMs (Holmes et al., 2000). Slope and aspect were less sensitive to simulated DEM errors as the spatial autocorrelation of these errors increased (Hunter and Goodchild, 1997; Raaflaub and Collins, 2006).
The accuracy and grid cell size of DEMs derived from GPS data will depend on the sampling method. On an undulating agricultural field, varying the density or pattern of RTKGPS data collection changed the mean elevation for the field by <0.05%, but the mean slope changed by up to 25% (Wilson et al., 1998). On average, slope estimates from DEMs decrease with increasing grid cell size across a wide range of scales and land types (Chang and Tsai, 1991; Jenson, 1991; Panuska et al., 1991; Wolock and Price, 1994; Zhang and Montgomery, 1994; Thieken et al., 1999; Thompson et al., 2001). Slope differences were greatest in steep areas (Chang and Tsai, 1991; Zhang and Montgomery, 1994). Aspect was most sensitive to grid cell size where slopes were relatively low (Chang and Tsai, 1991). The range of curvature values decreased as grid cell size increased up to 30 m (Thompson et al., 2001).
The main objective of this study was to quantify relative differences in land surface elevation, slope, aspect, and curvature due to factors affecting DEM accuracy and grid cell size over undulating agricultural lands. Terrain attributes estimated from these DEMs will be used for ongoing research on the spatial variability of agronomic and hydrologic variables on these lands. The present analyses may also be used to guide the design of future elevation data collection efforts and terrain analyses on similar agricultural landscapes.
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MATERIALS AND METHODS
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Site Description
Three cropped fields in northeastern Colorado (40.48°N, 103.03oW) were surveyed. These fields are referred to as the North, South, and West fields, and they are 63, 70, and 64 ha, respectively (Fig. 1). The climate is semiarid with an average annual precipitation (1961–1990) of 440 mm and an average pan evaporation of approximately 1600 mm per growing season (Peterson et al., 2000). The undulating terrain was formed by aeolian deposition, with slopes reaching a maximum of 0.15 m m–1 on the North field.
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Fig. 1. The location and terrain of the three study fields in northeastern Colorado (contour interval = 3.0 m, source data from USGS). The three-dimensional image of each field was created from real-time kinematic global positioning system (RTKGPS) data with a vertical accuracy of 0.02 m.
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Elevation Data Collection
Two types of GPS data were collected in this study. A RTKGPS with an Ashtech Z-Surveyor (Magellan Navigation, Santa Clara, CA) provided static measurements accurate to within 0.02 m in each dimension relative to National Geodetic Survey control points. Elevation data were collected by mounting the rover GPS to an all-terrain vehicle. For the North field, transects were spaced 5 m apart and driven at approximately 5 m s–1. For the South and West fields, transects were spaced 10 m apart and driven at approximately 10 m s–1. One GPS position was recorded each second. This method allowed rapid acquisition of elevation data; however, dynamic measurements were less accurate than static measurements since the rover GPS antenna height varied slightly on the vehicle platform while driving. Microtopographic effects of the cropping system on elevation measurements were considered negligible because the vehicle platform tended to mask microtopographic features. To simulate larger sample spacing, up to approximately 30-m spacing, data points were systematically removed from the original data sets (Fig. 2).
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Fig. 2. Global positioning system sample points for each data set on the (a–e) North, (f–i) South, and (j–m) West fields using real-time kinematic global positioning system (RTKGPS) or satellite-differentially corrected global positioning system (DGPS) data source.
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The second type of GPS data, DGPS data, was collected in 1999 by an OmniStar 7000 (Omnistar, Houston, TX) with a harvester-mounted yield monitor (Fig. 2e, 2i, and 2m). The average sample spacing of approximately 9 m was controlled by the yield monitor configuration and the swath width of the harvester. Further details are given below.
Data Interpolation to Digital Elevation Models
Because GPS sampling on a regular grid is inefficient and not feasible for the data collection methods described above, data interpolation was necessary. Irregularly spaced elevation data were interpolated to 5-, 10-, 20-, and 30-m grid DEMs by ordinary kriging based on the eight nearest neighbors. Semivariogram models were fit to separation distances required to achieve eight neighboring elevation values. Cross validation, where each measured elevation point was removed individually and recomputed by the interpolation method, was used to evaluate interpolation errors. The semivariogram models and parameters were chosen to minimize these errors. Gaussian models were optimal for all fields and data sets except for the West field DGPS data, for which an exponential model was chosen.
Estimation of Terrain Attributes
First and second derivatives of the DEM were estimated using central finite differences (Mitasova and Hofierka, 1993). For grid cell (i,j) the derivatives are
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where z is elevation and d is the grid cell size. Slope can then be estimated by
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where SFD is the central finite difference estimate for slope at the center grid cell, expressed as a dimensionless gradient. Aspect (
FD) was measured in degrees clockwise from the north and was estimated by
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Aspect was only estimated for grid cells with non-zero slope. Profile (Kp) and plan (Kc) curvatures [L–1] were estimated by
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Positive curvature values are concave upward and are characterized by decelerating and converging flows (Mitasova and Hofierka, 1993). Curvatures could only be estimated where the slope was non-zero using this method. If SFD was near zero, extreme curvature values were possible. One curvature value from the West field's DGPS 30-m DEM was discarded for this reason, as results were sensitive to its inclusion.
Digital Elevation Model Comparisons
The DEMs were produced to isolate the effects of data source, sample spacing, and grid cell size on terrain attribute estimations at three sites. The horizontal extents of the DEMs were defined to allow for overlapping grid cell centers regardless of data source and grid cell size. This allowed point comparisons of attributes and quantification of relative differences between attributes by root mean squared differences (RMSDs) and bias (mean difference). A summary of these DEMs and an explanation of the naming convention are given in Table 2
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Table 2. Summary of digital elevation models (DEMs) and the naming conventions used in this study. Single-letter abbreviations for fields and data sources are given in parentheses and used the data set and DEM names.
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Differences in data sources were measured relative to RTKGPS, the most accurate data source. At a 30-m grid cell size, differences in attributes estimated from DGPS and USGS DEMs were measured relative to the attributes estimated from RTKGPS DEMs. Since 10-m USGS DEMs were unavailable at these sites, only the DGPS-derived attributes were compared with the attributes estimated from RTKGPS data at a 10-m grid cell size.
The effects of sample spacing and grid cell size were evaluated using only the RTKGPS DEMs. The DEMs interpolated from the smallest sample spacing, approximately 5 m for the North field and approximately 10 m for the South and West fields, were assumed to be the most accurate because interpolation errors were smallest. Therefore, for a given DEM grid cell size, differences in each attribute estimated by DEMs derived from 10- (North field only), 20-, and 30-m sample spacing were computed relative to attributes estimated by DEMs derived from the smallest sample spacing.
The effects of grid cell size on terrain attribute estimations were evaluated using the RTKGPS data with the smallest sample spacing (5 m for the North field and 10 m for the South and West fields) to ensure that the most accurate DEMs were used. Unlike the effects of data source and sample spacing, there were no differences in elevation, or accuracy, when evaluating grid cell size effects. Differences in slope, aspect, and curvature estimated from 10- (North field only), 20-, and 30-m DEMs were computed relative to these attributes estimated from a 5-m DEM on the North field and 10-m DEMs on the South and West fields. Table 3 provides a summary of all DEM comparisons.
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Table 3. Summary of the digital elevation model (DEM) comparisons used to determine the effects of data source (DS), sample spacing (SS), and grid cell size (CS) on terrain attribute estimations. Differences in attributes estimated from DEM B are measured relative to the attribute estimated from DEM A. The DEM abbreviations are defined in Table 2.
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Crop Yield Application
After analyzing the effects of DEM accuracy and grid cell size on estimated terrain attributes, impacts of DEM accuracy and grid cell size on a regression model application were demonstrated by correlating dryland winter wheat grain yields with terrain attributes estimated by the different DEMs. Yield data were collected in 1997 using a harvester-mounted yield monitor. The yield monitor was configured to compute an average yield for each incremental area formed by the swath width (8.84 m) and an incremental distance (10 m) driven by the harvester. Based on the average driving speed of approximately 2 m s–1, with yield data recorded each second, five yield values were typically averaged for a sample area. We represented the average yield for an area with a yield value located at the centroid of that area. Each yield data point was then assigned to the DEM grid cell containing it, and univariate linear correlation coefficients, r, were computed between yield and each terrain attribute across each DEM. When multiple yield values were contained by a single grid cell, each yield value was analyzed individually rather than averaging yield across the grid cell area. This method avoided any grid cell size effects on r based on averaging across different grid cell areas.
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RESULTS AND DISCUSSION
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Elevation Distributions
The North field had the widest range of elevations, with 21 m between the highest and lowest points. The South and West fields had ranges of 11 and 9 m, respectively. The probability density function (pdf) of each field displays some degree of multimodality and distinct differences between these undulating fields are apparent (Fig. 3a). The pdfs of RTKGPS and USGS elevations on the West field have bimodal distributions that are not captured by the DGPS data (Fig. 3d). Overall, differences between elevation distributions due to data source are greater than differences due to the different RTKGPS sample spacing (Fig. 3b, 3c, and 3d).
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Fig. 3. Probability density functions for the elevation data: (a) a comparison of all three fields from real-time kinematic global positioning system (RTKGPS) data at 10-m sample spacing; (b) a comparison of all data sets for the North field; (c) a comparison of all data sets for the South field; and (d) a comparison of all data sets for the West field.
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Elevation Data Interpolation
Digital elevation model accuracy is affected by measurement error for a given data collection method and interpolation error. For the data collection method used in this study, measurement error included GPS instrumental error and variable GPS antenna height above the ground surface caused by movement of the all-terrain vehicle. The semivariogram nugget variance is an indirect measure of the measurement error variance plus small-scale terrain variability, and was <0.014 m2 for the RTKGPS data on all fields and at all sample spacings up to 30 m. The maximum value of the square root of nugget variance (0.12 m) may be interpreted as an estimate of the maximum measurement error for elevation data collected with dynamic RTKGPS on an all-terrain vehicle. Therefore, 0.10 m or less error was added to the static RTKGPS measurement error (0.02 m) by the all-terrain vehicle method.
Interpolation errors, based on cross validation, ranged from 0.04 to 0.16 m for the RTKGPS elevation data, with errors increasing with sample spacing. Interpolation errors for the DGPS elevation data ranged from 1.09 to 1.33 m across the three fields. These higher interpolation errors corresponded to higher nugget variances, 0.4 to 0.9 m2, for the semivariogram models of the DGPS data. The cross-validation errors were not sensitive to changes in the semivariogram model selection or parameters; however, kriging produced lower cross-validation errors than the inverse squared distance weighted method (Erskine, 2005).
Differences in Estimated Terrain Attributes
Effects of Elevation Data Source
Relative to RTKGPS DEMs, RMSDs for the DGPS DEMs ranged from 0.89 m on the North field to 1.27 m on the South field (Table 4). On the South and West fields, the USGS DEMs were more accurate than DGPS, with RMSDs of 0.61 and 0.58 m, respectively. On the North field, the USGS DEM had a RMSD of 1.49 m and underestimated elevation by a mean value of 0.96 m. The USGS DEM differences were relatively unbiased for the South and West fields.
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Table 4. Absolute and normalized measures of root mean squared difference (RMSD) and bias between digital elevation models (DEMs) of varying data sources. Normalized measures are the absolute measures divided by the field standard deviation of attributes estimated by DEM A. For absolute measures, spatial autocorrelation of elevation differences between DEMs is indicated by the isotropic Moran's I based on a separation distance equal to the grid cell size. The DEM abbreviations are defined in Table 2.
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The normalized measures of RMSD and bias show that differences in attribute estimations generally increased with higher order derivatives of the DEM, with profile curvatures being the most sensitive to the DEM data source (Table 4). On the South and West fields, the RMSDs in profile curvature from the 10-m DGPS DEMs were more than 10 times the standard deviation of the RTKGPS-derived profile curvatures within each field. This sensitivity of curvature estimation decreased with increasing grid cell size. With the exception of the normalized RMSD for plan curvature on the South field, absolute and normalized RMSDs for all attributes were less at 30-m grid cell size than at 10-m grid cell size (Table 4).
The differences in the estimated terrain attributes depend on the spatial distribution of the elevation differences. On the North field, the elevation RMSD for the USGS DEM was nearly twice as large as the RMSD for the 30-m DGPS DEM, but the USGS DEM yielded smaller differences in all other attributes (Table 4). Isotropic estimates of Moran's I (Moran, 1950) indicate that the spatial autocorrelations of elevation differences for the USGS DEMs were higher than for the DGPS DEMs (Table 4). For the USGS DEM on the North field, the 30-m separation Moran's I was 0.96 vs. 0.45 for the DGPS data. Mapping the elevation differences relative to RTKGPS clearly shows this difference in spatial autocorrelation (Fig. 4). Holmes et al. (2000) also reported a high spatial autocorrelation of USGS DEM errors. The random nature of differences between RTKGPS and DGPS elevations produced a positive bias in slope estimates (Table 4) and a wider range of curvature values for DGPS-derived attributes.
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Fig. 4. Elevation residuals for the (a) 30-m USGS digital elevation model (DEM) and (b) 30-m satellite-differentially corrected global positioning system DEM (DGPS) relative to the 30-m real-time kinematic global positioning system (RTKGPS) DEM on the North field.
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Effects of Global Positioning System Sample Spacing
Increasing the sample spacing of GPS data collection increased the interpolation error, thus decreasing DEM accuracy. For the RTKGPS data, these differences in interpolation errors produced RMSDs in DEM elevations of 0.05 m or less (Table 5). A comparison of Tables 4 and 5 indicates that all differences in attribute estimations due to increased sample spacing were much smaller than differences due to the data sources used here. The normalized RMSDs increased with the higher order derivatives, indicating that curvature estimates were most sensitive to DEM errors due to increased GPS sample spacing (Table 5). The maximum normalized RMSD was 1.03 for plan curvature on the South field when comparing 20- to 10-m sample spacing. The absolute RMSD, being slightly greater than the standard deviation of the RTKGPS-derived plan curvatures on the South field, resulted from an RMSD in elevation of only 0.03 m (Table 5). The differences in attribute estimations due to increased GPS sample spacing were all essentially unbiased, and like the effects of data source, sensitivity of terrain attribute estimations to GPS sample spacing generally decreased with increasing DEM grid cell size.
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Table 5. Absolute and normalized measures of root mean squared difference (RMSD) and bias between digital elevation models (DEMs) of varying real-time kinematic global positioning system (RTKGPS) sample spacing. Normalized measures are the absolute measures divided by the field standard deviation of attributes estimated by DEM A. The DEM abbreviations are defined in Table 2.
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Effects of Digital Elevation Model Grid Cell Size
As shown above, there was a general reduction in the sensitivity of estimated slopes, aspects, and curvatures to DEM differences with increasing grid cell size. Another result of increasing grid cell size was an increase in RMSD for estimated slopes, aspects, and profile curvatures on all three fields based on RTKGPS data (Table 6). The RMSDs for estimated plan curvatures also increased with increasing grid cell size except for the incremental increase from 20- to 30-m grid cell size on the North field. In this case, both were greater than the field standard deviation (normalized RMSD >1; Table 6).
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Table 6. Absolute and normalized measures of root mean squared difference (RMSD) and bias between real-time kinematic global positioning system (RTKGPS) DEMs of varying grid cell sizes. Normalized measures are the absolute measures divided by the field standard deviation of attributes estimated by DEM A. The DEM abbreviations are defined in Table 2.
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On average, an increase in grid cell size resulted in lower estimated slopes, and this produced a negative bias for all comparisons (Table 6). The magnitude of this bias increased with increasing grid cell size. Similar results have been found in previous studies (Wolock and Price, 1994; Chang and Tsai, 1991; Panuska et al., 1991; Jenson, 1991; Zhang and Montgomery, 1994; Thieken et al., 1999; Thompson et al., 2001).
The normalized values of RMSD were greater for curvature than for slope or aspect (Table 6). The maximum normalized RMSD was 1.16 for plan curvature between 30- and 10-m grids on the West field. This difference was similar in magnitude to the maximum normalized RMSD found with increased GPS sample spacing, but was still an order of magnitude less than the maximum normalized RMSD found with the DGPS data source relative to the RTKGPS data source.
Crop Yield Application
Yield maps from the dryland winter wheat harvest in 1997 suggest a relationship between yield and the terrain (Fig. 5) (c.f., Green and Erskine, 2004). The North field has the greatest terrain relief and the highest standard deviation and coefficient of variation in winter wheat yields (Table 7).
For terrain attributes estimated from DEMs of different data sources, RTKGPS-derived attributes provided the strongest univariate, linear correlations at 10- and 30-m grid cell sizes on each of the three fields (Table 8). The strongest correlation on the North field was an inverse relationship with slope from the RTKGPS 10-m DEM (r = –0.55). The strongest correlations on the South and West fields were with profile curvature from RTKGPS 30-m DEMs (r = 0.36 and 0.41). Based on these results and the sensitivity of terrain attribute estimations to DEM data source reported above, RTKGPS is the preferred data source.
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Table 8. Correlation coefficients between winter wheat yields and the terrain attributes estimated from digital elevation model (DEM) data sources. The highest correlation on each field and at each grid cell size is indicated by italics.
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Terrain attribute estimations were less sensitive to GPS sample spacing and grid cell size than to data source. Differences in the correlations between crop yields and the terrain attributes were not significant when changing the GPS sample spacing. Differences in the correlations between crop yields and the terrain attributes of slope and aspect were also not significant when changing grid cell size. Larger grid cells, however, increased the correlations between crop yields and both profile and plan curvatures for all three fields (Table 8). This result may be physically based, indicating that the scale at which land curvature controls the processes affecting crop yield is closer to 30 than 10 m. This result may also be explained by the high sensitivity of curvature estimates to DEM errors. Since this sensitivity increases as grid cell size decreases, curvature estimates at 10-m cell size are likely less accurate than estimates at 30-m cell size.
Implications and Recommendations
The information gained from the quantification of relative differences in terrain attribute estimations combined with the results of this specific crop yield application provides insight to the GPS data accuracy, sample spacing, and grid cell size necessary for terrain-based modeling in our agricultural applications. In addition, we propose more general guidance and recommendations below.
Questions that arise from this work are: (i) how is the explanatory power of individual terrain attributes related to errors in their estimation, and (ii) is there an error level above which the estimated terrain attributes are not useful for predicting spatial landscape variables (e.g., grain yield) from terrain-based modeling? These questions are addressed here using a combined analysis of the normalized RMSDs due to data source differences (Table 4) and the linear regressions of grain yields vs. different terrain attributes (Table 8). For example on the West field, r = 0.41 between wheat yield and profile curvature derived from RTKGPS data on a 30-m grid (Table 8). This correlation coefficient is reduced by 80% to 0.08 when relating these same yields to profile curvatures derived from DGPS data (Table 8). A relatively high normalized RMSD of 6.78 is computed for these profile curvatures derived from DGPS data on the West field (Table 4). Figure 6 shows the reduction in the absolute value of r as a function of the normalized RMSD due to data source differences. Figure 6 includes only the cases where the absolute value of r exceeds 0.2 between yields and terrain attributes derived from RTKGPS, because changes in r when the absolute value of r is <0.2 (r2 < 0.04) are likely to be coincidental and not valuable for spatial estimation. The graph indicates that the effect of data source on correlation coefficients increases with increasing normalized RMSD up to an asymptotic value approaching 100 0.000000or very high RMSD. In nearly all cases, r is reduced by >50% when the normalized RMSD is >1 and <30% when then normalized RMSD is <1 (Fig. 6).
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Fig. 6. The reduction percentage in the absolute value of correlation coefficients, r, due to changing the data source from real-time kinematic global positioning system (RTKGPS) to satellite-differentially corrected global positioning (DGPS) system or USGS is plotted as a function of the normalized root mean squared difference (RMSD) between the different data sources.
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Normalized RMSDs due to sample spacing effects alone were predominantly <1 (Table 5), and there were no significant changes in correlation coefficients in the crop yield application due to sample spacing. Therefore, we suggest that DEM accuracy, which depends on both GPS data source and sample spacing, is poor when the normalized RMSE in the applied terrain attribute relative to ground truth is >1. Note that for this study, we have dealt with differences (RMSD) rather than errors (RMSE), but we assume that our best data (RTKGPS at 5-m sample spacing) serve approximately as ground truth. The threshold of normalized RMSD = 1 is a rough guideline that corresponds with the case where DEM-based errors equal the spatial standard deviation of the terrain attribute in question. For normalized RMSD < 1, the correlation coefficients improve with decreasing RMSD as indicated in Fig. 6.
On agricultural fields such as these, a GPS data source commensurate to the accuracy of RTKGPS and collected at 30-m sample spacing is recommended for detailed terrain analyses that include estimates of higher order derivatives such as slopes and curvature. This recommendation is based on maintaining normalized RMSDs < 1. A 30-m grid cell size is recommended here, specifically due to the highest correlation between crop yields and curvatures at 30 m. Otherwise, finer grid cell sizes, down to the approximate GPS sample spacing, could be interpolated from the GPS data. No recommendations on grid cell size are made based on normalized RMSD because the optimal grid size will be determined by the DEM application. Recalling the potential significance of each terrain attribute to hydrology (Table 1), one might expect fine-scale processes such as topographically focused runoff and erosion to require relatively small grid cell sizes. In such cases, DEM accuracy is even more critical because terrain attributes are more sensitive to DEM errors at smaller grid cell sizes.
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CONCLUSIONS
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DEMs are central to terrain analysis methods and DEM accuracy is shown in this study to be vital. Estimates of terrain attributes, particularly land surface curvatures, are sensitive to DEM errors. Rapid elevation data acquisition in agricultural lands is provided at sufficient sample spacing during GPS-guided precision farming operations such as yield monitoring. The accuracy of the GPS must be commensurate with the accuracy of RTKGPS, however, in order for these data to be used for detailed terrain analyses in these agricultural lands. This level of accuracy is not typical for precision farming operations now, but is growing more typical with advances in technology. The main results of this study are:- Estimates of terrain attributes describing land surface geometry were more sensitive to DEM accuracy due to the data source than to differences in interpolation errors or grid cell size.
- Sensitivity of terrain attribute estimates to DEM accuracy decreased with increasing grid cell size and with spatial autocorrelation of DEM errors, such as the autocorrelation displayed in USGS DEMs.
- Sensitivity of terrain attribute estimates to DEM accuracy and grid cell size increased with increasing order of the land surface derivative, with curvature being the highest order studied.
- Estimates of curvature were sensitive to centimeter-level DEM errors. For example, elevation differences of only 0.03 m RMSD due to increased sample spacing caused an RMSD in plan curvature estimates greater than the field standard deviation (normalized RMSD > 1).
- The example crop yield application showed that correlations between wheat grain yield and terrain attributes deteriorated rapidly as the normalized RMSE in the applied terrain attribute relative to ground truth increased up to a value of
1. DEM accuracy was considered poor when the normalized RMSE in the applied terrain attribute relative to ground truth was >1.
For these agricultural lands, we recommend that RTKGPS data, or another data source of equivalent accuracy, should be used for the generation of DEMs and, subsequently, for performing detailed terrain analyses. For the crop yield application, a 30-m grid cell size is recommended, but specific grid cell size recommendations depend on the application.
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ACKNOWLEDGMENTS
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This research was conducted on lands owned by Gilbert Lindstrom, who provided cooperation throughout the project. We thank Michael Murphy and Daniel Salas for technical support with field data collection. We also thank Gordon Starr and James Thompson for their constructive comments.
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NOTES
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All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.
Received for publication May 4, 2005.
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REFERENCES
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ABSTRACT
INTRODUCTION
