VERTICAL ACCURACY

OF DIGITAL ELEVATION MODELS

AGU Spring Meeting, 1996

Poster T31A - 10

CONTENTS

Problem statement and objectives
Study background
Available DEMs
Previous investigations
Study approach
Study site
USGS standard 7.5' DEM
High resolution DEM
DEM aggregation
Topographical parameters
Digital elevation data residuals
Vertical error structure
Summary of findings and future investigations
References

Problem statement

Evaluation of the expected accuracy of Digital Elevation Models (DEMs) is required to assess the prediction error of distributed hydrologic models associated with digital elevation data.

Objectives

• to compare statistical properties of two digital elevation models of different vertical resolution
• to assess the vertical accuracy of these digital elevation models
• to develop a model of the spatial error structure of digital elevation models

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Study background

The widespread availability of digital topographic data has given rise to a new generation of spatially distributed hydrologic models based on topographic information.

Distributed models such as DHSVM, Distributed Hydrology-Soils-Vegetation Model (Wigmosta et al, 1994), use digital elevation data to model topographic controls on meteorological data and down-slope water movement for each grid cell:

• short-wave radiation varies with topography due to the effects of shading, shadowing and reflection from surrounding terrain
• air temperature varies with elevation according to a lapse rate
• precipitation is distributed over the basin using either a lapse rate or an orographic model which simulates air flow over the topography
• water is distributed between adjacent grid cells according to the local hydraulic gradients which are approximated by local ground surface slope
• rate of discharge is calculated as the product of the soil transmissivity, ground surface slope between cells, and the width of the flow path

Figure 1. Schematic for a distributed hydrologic model

Topography-based models such as TOPMODEL (Beven and Kirkby, 1979) use topographic indices calculated from the DEM to represent the spatial distribution of soil moisture, surface saturation and runoff generation process.

Previous investigations have examined horizontal resolution and found that it strongly affects errors in computed slope and hence simulated hydrologic fluxes.

Although problems with the performance of topographically-based models due to vertical inaccuracy is recognized, the requisite accuracy of DEMs for these models has yet to be assessed. Higher resolution digital elevation data is becoming available from space and airborne radar and laser altimetry and it is unknown what effects this will have on the hydrological prediction errors introduced by inaccuracy of the digital elevation data.

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Available digital topographical products

Digital elevation data is widely available in different formats, horizontal and vertical resolutions and accuracy:

• USGS standard DEM products:
  1) 30-x-30 m data resolution DEMs over 7.5-minute UTM grids are available for selected USGS quadrangles and are used for hydrologic models of small to moderate size catchments
  2) 3-x-3 arc-second DEMs over 1-x-1 degree blocks have been produced by the Defense Mapping Agency (DMA) for the entire US and are widely used for models of 100 to 1000 sq.km. catchments
  3) 30-x-30 arc-second DEMs are being compiled by the EROS Data Center for the entire world, these data are used in macro-scale models
• enhanced DEMs via additional ground control points or low altitude aerial photography are available for experimental watersheds
• airborne radar and laser altimetry, such as the NASA/JPL Topographic Synthetic Aperture Radar (TOPSAR) and Scanning Lidar Imager of Canopies by Echo Recovery (SLICER) are currently under development
• radar altimetry on board SPOT, ERS-1 and ERS-2, and other satellites are currently under development

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Previous investigations of the influence of DEM resolution on hydrologic models

Zhang and Montgomery (1994):

• increasing cell size resulted in increased contributing areas (a), decreased slopes (tan b) and increased the TOPMODEL topographic index, ln (a/tan b)
• topography-based TOPMODEL predicted increased peak discharges with a coarser grid size

Wolock and Price (1994):

• coarser resolution was associated with higher minimum, mean, variance, and skew values of the topographic index distribution
• TOPMODEL predictions of mean depth to the water table decreased while the ratio of overland flow to total flow and the maximum, variance and skew of simulated daily flows increased in response to a coarser grid

Gyasi-Agyei et al (1995):

• effect of vertical resolution on geomorphological parameters was examined by successively truncating the last digit of the elevation data
• slope, area and topographic index of individual pixels varied with vertical resolution however the distribution of the topographic index did not show any significant differences

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Study approach

The accuracy of digital elevation models was assessed by comparing two DEMs of different vertical accuracy for a selected study site.

The WE-38 experimental watershed on Mahantango Creek, PA, was chosen as the study site. The standard USGS 7.5', 30 x 30 m DEM was compared to a higher resolution product developed from stereo pairs obtained from low altitude aerial photography.

Vertical errors were calculated as the difference or residual between the standard and high resolution DEMs. The spatial structure of the residuals was analyzed to relate errors to topographic parameters.

Figure 2. USGS Standard DEM and High Resolution DEM

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Study site: Mahantango Creek, WE-38

WE-38, is a USDA-Agricultural Research Service (ARS) experimental watershed on Mahantango Creek, located near Klingerstown in eastern Pennsylvania. The station has been operated since 1968, recording weir flow, maximum and minimum daily temperature and precipitation. Mahantango Creek is a tributary to the Susequehanna River approximately 50km north of Harrisburg, PA.

Figure 3. Mahantango Creek, WE-38, study site

• 7.19 sq.km drainage area
• 8000 pixels at 30 x 30 m resolution
• elevations range from 215 to 500 m
• moderate to steep slopes, 0 to 20%
• very low surface roughness; vegetation is predominantly corn fields

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USGS standard 7.5' DEM

30 x 30 m horizontal resolution, 1 m vertical resolution

max absolute error of 50 m, max relative error of 21 m

The standard 30 m, 7.5' DEM available for the Mahantango Creek is classified as Level 1, the least accurate of the USGS DEMs. This DEM was developed from high altitude aerial photography using the Gestalt Photo Mapper II as part of an orthophoto production process as follows:

• a 47 x 52 regularly distributed grid of points is measured for each 9 x 8 mm area of each diapositive
• an iterative process is used to scan and correct parallax at each of the 2444 points until parallax values stabilize
• points are compared to overlapping areas of previous patches (20-50%) to ensure edge-matching
• parallax values are converted to ground heights with corresponding horizontal coordinates
• patches are combined to cover a USGS 7.5' quadrangle and are regridded to the standard format
• DEMs are smoothed to remove any large edge effects

Currently 70-80% of USGS 7.5' DEMs are classified as Level 1. Efforts to construct more accurate DEMs from digital line graphs or tagged vector contours are focused on updating the 3 arc-second DEMs.

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High resolution DEM

5 x 5m horizontal resolution densified from 15 m scan lines

0.1 m vertical resolution

estimated max error of 0.5 m except under closed canopy

A high resolution DEM was developed for the WE-38 experimental watershed by Photo Sciences, Inc:

• low altitude photography was acquired on April 21, 1994 from flights at 3600 feet above mean terrain
• stereomodels were scanned in sections, creating separate models for each photo pair set up
• scans were performed along east-west lines separated x 15 meters, with elevation values recorded every 15 meters along each scan
• models were selected with UTM northings and eastings at some multiple of 5 m
• data were densified to 5 meter resolution using bilinear interpolation along each scan line, and at right angles to scan lines
• data was combined onto a uniform 5 x 5 m grid
• scale and quality of the photography and the parameters used while scanning with an analytical stereoplotter were such that errors should not exceed 0.5 m except under closed canopy

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DEM aggregation

The high resolution DEM had to be aggregated from a 5 to 30 m resolution for comparison with the standard 30 m USGS DEM. Aggregation using standard methods affects the spatial structure of elevation and orographic gradients.

Blindish and Barros (1995) proposed a modified fractal interpolation scheme to aggregate topographical data while preserving the spatial structure of the elevations and orographic gradients. The high resolution DEM was aggregated using this scheme as follows:

• the fractal dimension, D, and roughness of the 5m data were calculated from the slope and intercept of the log-log plot of the mean power spectral density function
• a Brownian surface was created at a 5 m resolution and transformed to match the fractal dimension and roughness factor as the 5 m high resolution DEM
• this surface is used as a weighting function to aggregate the domain to a coarser resolution
• a correction term based on the standard deviation of the elevations is added to the aggregated DEM

Figure 4. Power spectral density function for high resolution DEM

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Topographical parameters

Hypsometry, contributing upstream area, slope and the TOPMODEL topographic index were calculated for the study site using both the USGS standard DEM and the aggregated high resolution DEM.

Slope and topographic index were computed for each grid cell from the aggregated high resolution DEM. Slope, tan b, was calculated based on the lowest neighboring pixel. The TOPMODEL topographic index was determined from ln(a/tan b) where a is the contributing area per unit contour length.

Figure 5. Basin topographic parameters

Figure 6. Spatial distribution of slope

Figure 7. Spatial distribution of topographic index

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Digital elevation data residuals

• residuals = (high resolution DEM - USGS 7.5' DEM)
• residuals range from -27 to 24 m
• average residual = -7.4 m
• 80% of the residuals are negative
• residuals reflect two factors:
• DEM production process
• local topography

Figure 8. Spatial distribution of residuals

Figure 9. Histogram of residuals

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Vertical error structure

DEM production process

• the spatial structure of the residuals displays a distinct grid-like pattern
• this grid maps ridges where poor correlation resulted in discontinuous topography during the DEM production process
• the smoothing process that is used to correct these edge effects smoothes the ridges in the USGS DEM but does not correct the vertical errors
• certain patches contain much higher average errors than their neighbors, indicating poor correlation

Topographical effect

• the residuals were compared to the topographical parameters for each patch to separate the effects of the topography from the errors due to edge effects in the USGS DEM

Figure 10. Relationship of residuals to topographic parameters in steep terrain

• the error structure of the residuals can be linearly related to the TOPMODEL in steep regions of the watershed, however in low-lying regions, it is not a good indicator of vertical accuracy
• residuals are greatest along stream channels and have a spatial pattern that reflects the topography

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Summary of findings

The USGS standard 30 m DEM was found to contain errors with a distinct spatial structure.

Errors in vertical accuracy occurred due to poor matching of patches during the DEM production.

Errors were also related to topographic index and slope in steep areas where these parameters are well-defined.

Future investigations

The Distributed Hydrology-Soils-Vegetation Model (DHVSM) will be used to simulate flows based on the standard and high resolutions DEMs and artificial DEMs constructed by degrading the high resolution DEM with the known spatial error structure.

Simulation results will be compared to determine the effects of the vertical accuracy of the digital elevation data on the prediction of hydrologic parameters.

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References

Beven, K.J. and M.J. Kirkby, A physically based, variable contributing area model of basin hydrology, Hydrological Sciences Bulletin, 24(1), 43-69, 1979.

Blindish, R. and A.P. Barros, Aggregation of digital terrain data using a modified fractal interpolation scheme, Computers & Geosciences, 1996, in press.

Gyasi-Agyei, Y., G. Willgoose and F.P. De Troch, Effects of vertical resolution and map scale of digital elevation models on geomorphological parameters used in hydrology, Hydrological Processes, 9, 363-382, 1995.

Kelly, R.E., P.R.H. McConnell and S.J. Mildenberger, The gestalt photomapping system, Photogrammetric Engineering and Remote Sensing, 43(11), 1407-1471, 1977.

Mark, D.M. and P.B. Aronson, Scale-dependent fractal dimensions of topographic surfaces: An empirical investigation, with applications in geomorphology and computer mapping, Mathematical Geology, 16(7), 671-683, 1984.

U.S. Geological Survey, Digital elevation models, National Mapping Program, Data users guide 5, 1993.

Wigmosta, M.S., L.W. Vail and D.P. Lettenmaier, A distributed hydrology-vegetation model for complex terrain, Water Resources Research, 30(6), 1665-1679, 1994.

Wolock D.M. and C.V. Price, Effects of digital elevation model map scale and data resolution on a topography-based watershed model, Water Resources Research, 30(11), 3041-3052, 1994.

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