Modeling Elevation Uncertainty Using Stochastic Simulation

Spatial Autocorrelation in Elevation Datasets

The difference between elevation values at each common point allows the researcher to estimate error statistics for the entire data set of interest, but this procedure is not straightforward due to the complicating factor of spatial dependence, or autocorrelation. Error, like other spatially distributed phenomena, will generally be subject to some degree of autocorrelation, and this should be accounted for in the model. The reason this is significant is that the values at neighboring, dependent points contain less information about the error than the values of independent points; just as in classical non-spatial statistics, the results will be biased. Therefore, sets of points must be selected that are independent of each other; all will be separated by distances greater than the maximum extent of spatial autocorrelation, as measured by the correlogram or variogram.

The correlogram for the elevation data was calculated to determine the maximum distance of spatial dependence. We found that spatial dependence persisted to 3,210 meters. To determine the error statistics for the stochastic simulation, 100 sets of spot locations were selected from the areas covered by the six USGS 7.5-minute DEMs outside of the study area.

Data Sampling Region

The image above is of the Los Angeles - west 1-degree DEM. The rainbow-colored region in the left-central portion of the map is the study area itself. Red polygons indicate the areas in which the locations were sampled.

Each set of samples contained between 75 and 90 points, all of which were separated by more than 3,210 meters. For each set, error statistics -- mean and standard deviation -- were derived. The mean average difference value was -8.60 meters, indicating that the 1-degree DEM underestimated the 7.5-minute DEM by 8.6 meters. The standard deviation of the average difference values was 10.36 meters. The mean of the standard deviation for all sets was 132.55 meters, and the standard deviation of the standard deviation was 11.34 meters.

Using these statistics, a probability distribution model is developed. This model creates a random field with a gaussian distribution using the mean and standard deviation parameters of the difference map, as well as accounting for the spatial autocorrelative characteristics (i.e. the texture) of the more accurate data set.

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Page created by Ashton Shortridge

Last modified on April 10, 1996