Modeling Elevation Uncertainty Using Stochastic Simulation

Chuck Ehlschlaeger, Ashton Shortridge

NCGIA

Perspective view of the study area: San Marcos Pass, above Santa Barbara

This work uses a stochastic simulation approach to explore the impact of uncertainty in USGS digital elevation data within the context of the least-cost path algorithm. By incorporating information from higher accuracy sources, coarser resolution data of lower reliability can be modeled more accurately, providing applications with a more realistic depiction of the impact of terrain uncertainty on analysis.

Left: 30 meter (7.5") DEM / Right: 90 meter (3 arc-second) DEM

A simple visual comparison of the two images above suggests that there is a great deal of additional information about the terrain which captured in the more densely sampled 30 meter data set (See the link to "difference map" below for more on this topic). The additional complexity at the higher sampling interval is confirmed by statistical analysis. Additionally, the accuracy specifications for these datasets indicate that the 30 meter DEM is more reliable. Under these circumstances, why would anyone use the coarser, less accurate 90 meter data?

30 meter data is generally more difficult and more expensive to obtain. Moreover, coverage of the United States is not complete at the 30 meter interval. Three-arc second DEMs, which correspond roughly to 90 meter sampling, are available at no charge over the internet for the entire contiguous U.S. The technique developed here takes advantage of partial 30 meter coverage by developing an error model for the 90 meter data set. Using this error model, areas not covered by the 30 meter dataset can be simulated at 30 meter terrain "roughness".

The 90 meter data was resampled to 30 meters and a difference map was created. Data about differences between non-spatially autocorrelated points were used to calculate parameters for the error model. None of these datapoints were from the study area itself. A series of 247 random fields were generated using these parameters; when added to the 3 arc-second surface, each one is a realization of the terrain surface using what we know about the more accurate 30 meter dataset. Several of these are displayed for comparison with the actual terrain data.

A least-cost path generated on each of these realizations. Two endpoints (at the same coordinate-referenced location in each dataset) were chosen, and the algorithm was tasked with finding the path that minimized a cost function incorporating both distance and elevation changes.

Distribution of paths across the San Marcos Pass area

The first image shows the routes generated on the original 30 meter data (in white) and the original 90 meter data (in blue). The white trail is longer and more complex, because it is reflecting the increased complexity captured by the 7.5" dataset. The second map shows the 247 trails generated from the potential realizations, superimposed over the original two trails.

Two observations are of particular importance. First of all, a majority of the trails generally follow the white route, although none of the 30 meter data in the study area was used to calculate error parameters. This is an indication that this method does capture the impact of terrain features. Secondly, several other corridors are suggested by the distribution of the remaining trails. The resulting spatial distribution is complex, and could not easily be detected without resorting to the stochastic simulation method.

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