Digeman

Uncertainty in spatial information and its effect on spatial modelling has become an increasingly important research issue in the last decade.  The data models implemented within GIS contains various errors; and frequently inexperienced users are capable of performing complex analyses without considering issues of data quality.  Uncertainty analysis provides the means to quantitatively examine the impact of input and model error on the outputs of modelling processes.

A digital elevation model (DEM) represents the spatial distribution of elevation in a landscape.  Analogous to a DEM, a digital terrain model (DTM) is an ordered array of numbers that represent the spatial distribution of terrain attributes in a landscape. Digital elevation model is the basis for calculation of surface attributes, which include slope, aspect, and curvatures. For primary attributes that are derived locally (using the local neighbourhood points), a quadratic trend local surface is usually fitted to the surface. The standard method involves calculating the parameters of a central cell and its 8 neighbourhood in a moving 3 × 3 cells window. The purpose of this fitting is that it enables the easy calculation of the first and second derivative of the surface, and these values can be used to calculate slope, aspect and various curvatures. Calculation of the first and second derivatives using local window is scale dependent. The derived parameters are only relevant to the resolution of the DEM and the neighbourhood cells used for calculation.

The model uncertainty is mainly a function of how well a quadratic function fits the ‘real’ surface and the approximation of the finite-differences.  At present most research in the uncertainty analysis of digital terrain modelling has focused on DEM input uncertainty rather than model error.  While studies have attempted to compare methods for calculating terrain attributes, the major obstacle is obtaining estimates of ‘true’ values, for example how do we measure the ‘true’ upslope area of a point?  Therefore, the uncertainty within a DTM is dependent on the algorithm used to calculate a particular terrain attribute and the uncertainty of the DEM.

We implement the uncertainty analysis of terrain attributes as a result of elevation uncertainty and model uncertainty in a program called Digeman. The algorithm is presented in Figure 1. The model used a generalisation of Wood (1996) for multiple windows to calculate the surface attributes. For the estimation of input uncertainty, it was assumed that the Mean Error = 0, and the uncertainty had a Gaussian distribution, therefore the RMSE was equal to the standard deviation of uncertainty.  Monte-Carlo simulation with Latin hypercube sampling of correlated variables (LHS)  was used to create spatially correlated uncertainty. Model uncertainty was estimated by fitting a quadratic function to the DEM surface and estimating the standard error of the parameters.  Monte-Carlo simulation with LHS was used to generate multiple realisations of the attributes. With this approach we can examine the individual and the combined impacts of input and model uncertainty.

References

Bishop, T.F.A., Minasny, B., McBratney, A.B., 2006. Uncertainty analysis for soil-terrain models. International Journal of Geographical Information Science 20, 117-134.

Algorithm in Digeman

See Jo Wood's thesis