Error propagation of DEM-based surface derivatives

• Authors: Juha Oksanen;Tapani Sarjakoski
• Venue: Computers & Geosciences
• Year: 2005

This paper presents research showing how random errors in a fine toposcale digital elevation model (DEM) are propagated to DEM-based surface derivatives. The focus was on two constrained derivatives, slope and aspect, and one unconstrained derivative, drainage basin delineation. The error propagation was explored by using numerical and analytical methods, and in both approaches the DEM error was modelled as a second-order stationary Gaussian random process. The results were summarised in the case study, in which 32 realistic scenarios of DEM error models were used. The scenarios were based on exponential and Gaussian spatial autocorrelation models with four sills (0.0625, 0.25, 1.00, and 4.00m^2) and practical ranges (0, 30, 60, and 120m). We found that, as expected, increase in DEM error increased the error in surface derivatives. However, contrary to expectations, the spatial autocorrelation model appears to have varying effects on the error propagation analysis depending on the application. In constrained surface derivatives, such as slope and aspect, the maximum error in results appeared to exist when the practical range of the error's spatial autocorrelation was roughly equal to the size of the surface derivative's calculation window. In unconstrained terrain analysis, such as drainage basin delineation, the variance of the results appeared to increase while the spatial autocorrelation range increases. Until now, the use of spatially uncorrelated DEM error models have been considered as a 'worst-case scenario', but this opinion may now be challenged because none of the DEM derivatives investigated in the study had maximum variation with spatially uncorrelated random error. In addition, the study revealed that the role of the appropriate shape of the spatial autocorrelation model, either exponential or Gaussian, was not as important as the choice of appropriate autocorrelation parameters: practical range and sill. However, the shape of the spatial autocorrelation model appeared to have more influence on the calculation of slope and aspect than on the drainage basin delineation. For error propagation analysis purposes an analytical approach appears to be more useful for constrained derivatives, while the Monte Carlo method is appropriate for analysing both constrained and unconstrained derivatives.