Accuracy assessment of digital elevation model using stochastic simulation

Annamaria Castrignanò1, Gabriele Buttafuoco2, Roberto Comolli3 and Cristiano Ballabio3
1 CRA - Agronomic Research Institute
Via Celso Ulpiani, 5 - 70125 Bari, Italy
Tel.: + 39 080 5475024; Fax: + 39 080 5475023
2 CNR - Institute for Agricultural and Forest Systems in the Mediterranean
Via Cavour, 4-6 - 87030 Rende (CS), Italy, 
Tel.: + 39 0984 466036; Fax: + 39 0984 466052
3 Department of Environmental Sciences (DISAT), University of Milano-Bicocca
Piazza della Scienza 1 - 20126 Milano, Italy
Tel.: + 39 02 64482875; Fax: + 39 02 64482994

Various methods have been applied to generate Digital Elevation Models (DEM) but whatever method is used, DEM estimates will always be  affected by errors. Comparing interpolated values with the actual elevation values, obtained with a high precision field survey, allows us to assess DEM accuracy. At every spot height  location it is possible to subtract the actual values from the DEM values to obtain the error at that point. Using this error information, different types of statistics can be computed; however, Root Mean Squared Error (RMSE) is the standard measure of error used by surveyors around the world. Such a way of error reporting uses a single value for the whole DEM and makes several implicit and unacceptable assumptions about the error: it has no spatial distribution and is statistically stationary across a region. An alternative approach is proposed here to achieve an improved estimate of local error. It is based on error  modelling using conditional stochastic simulations to produce alternative values of the data and so result in a probabilistic assessment of DEM accuracy. The study area is a doline of about 1.5 ha in size and is located in the Alps (North Italy) at a mean elevation of 1900 m above sea level. In this study, to test the accuracy of a previously generated DEM, elevation data were measured at 110 randomly  distributed points using a laser distance system linked with an electronic theodolite. Five hundred simulations were generated using conditional and sequential Gaussian simulation algorithms. Statistical information was extracted from the set of simulated error images: 1) averaging the values for each pixel and producing the map of the ‘expected’ error in any considered location and that of standard deviation; 2) counting the number of times that each pixel exceeded the null value and converting the sum to a proportion, in  order to produce the probability maps of overestimation and underestimation. Basic statistics and the histogram of errors showed them to be of approximately normal distribution with a small positive bias. The map of the expected values revealed a clear correlation of errors in the DEM to the slope of the land surface. The highest values were localised on the steepest  areas in the northern half of the doline. The spatial distribution of errors was not random but showed a high probability for overestimation in the northern area, while an  actual probability for underestimation was restricted to the southern area. Multiple DEM results generated by incorporating different images of the error field also allow us to derive a probable version of the products used for subsequent decision- making processes.

Keywords: digital elevation model, geostatistics, stochastic simulation, accuracy

In: Caetano, M. and Painho, M. (eds). Proceedings of the 7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, 5 – 7 July 2006, Lisboa, Instituto Geográfico Português

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