Numerical modelling of landscape evolution on geological time-scales: a parameter analysis and comparison with the south-eastern highlands of Australia

Surface-process models (SPMs) have the potential to become an important tool in predicting sediment flux to basins, but currently suffer from a lack of quantitative understanding of their controlling parameters, as well as difficulties in identifying landscape properties that can be used to test model predictions. We attempt to constrain the parameter values that enter a SPM by comparing predictions of landscape form (as expressed by hypsometric and fractal measures) and process rates obtained for different parameter sets with observations from the south-eastern Australian highlands, a rifted margin mountain belt that has remained tectonically stable during Cenozoic times. We map the hypsometry and fractal characteristics of south-eastern Australia and find that the roughness amplitude (G) correlates well with local relief, whereas the hypsometric integral (H ) correlates slightly better with elevation than with relief. The fractal dimension (D) does not correlate with any other morphometric measure and varies randomly throughout the region. Variograms generally show three kinds of scaling behaviour of topography with increasing wavelength, with topography only being truly self-affine at wavelengths between ～1 and 10 km. From a review of the available data on long-term denudation rates in south-eastern Australia, we infer that these have been 1–10 m Myr^?1, and average escarpment retreat rates 0.2–1.0 km Myr^?1, throughout the Cenozoic. Model predictions, using a SPM that includes hillslope diffusion and long-range fluvial transport, suggest that landscape form evolves with time; after an initial phase where D, G and relief increase, all morphometric measures decrease with increasing denudation. The behaviour of GandH in the models is qualitatively compatible with the observations; D, however, varies predictably in the models, in contrast with its random behaviour in the real world. The observed present-day morphology of SE Australia does not impose quantitative constraints on parameter values. The fractal analyses do impose general conditions of relative parameter values that have to be met in order to create ‘realistic’ topographies. They also suggest that there is no theoretical basis for including hillslope diffusion in SPMs with a spatial resolution coarser than 1 km. A comparison of the observed denudation and retreat rates with model predictions places order-of-magnitude constraints on parameter values. Thus, data pertaining to landscape evolution are much more valuable than static present-day topography data for calibrating SPMs.