Scale-based Simulation of Topography

A model of natural terrain is proposed, which describes topography as the summation of scale-dependent periodic spatial structure, and scale-independent fractional noise. These two elements can be varied, and appear related to each other by the sampling theorem and the scale at which the model is applied. The scale-dependent component of the model can be calibrated for any given landscape using Fourier analysis, as can the scale-independent component by measurement of the fractal dimension of a specific piece of terrain. The model is invertible, allowing simulation of terrain with specific surface characteristics. This paper develops the model mathematically, gives a description of the advantages and disad vantages of the model, shows examples of the use of the model for terrain simulation using a test data set, and discusses the cartographic uses of the model in automated mapping sys tems.