Error propagation of DEM-based surface derivatives

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.