Exploring Equifinality in a Numerical Landscape Evolution Model
Abstract
Over the last ten years, geomorphologists have shown increasing interest in the use of numerical simulation models to investigate landscape evolution. An advantage of these models is that they make evident the consequences of theories about past landscape changes, and the processes that have produced them. This is helpful in attempting to test (i.e. falsify) specific theories of landscape evolution. A difficulty in using such models, however, lies in selecting appropriate values for the empirical parameters used to calculate process rates and define process thresholds. These parameter values have to be derived from field data or, more frequently, model calibration. Whichever method is used, the process of selecting a calibration parameter value is uncertain, and the value may therefore take any point within an acceptable range. The large number of empirical calibration parameters typically included in landscape evolution models therefore allows for the possibility of differing combinations of model parameters generating similar output, a phenomenon known as model equifinality. A significant degree of model equifinality is problematic because it implies the model is ambiguous, and hence difficult to falsify, thereby hampering the development of more complete theories of landscape evolution. Although the potential for model equifinality in complex, spatially-distributed, models with numerous calibration parameters has long been recognised, the actual extent of the problem has not previously been quantified. To address this issue, we herein outline a method to determine the extent to which a representative landscape evolution model (GOLEM, see Tucker and Slingerland, 1997) produces equifinal results. Each simulation is initialised with a landscape DEM taken from a catchment (c. 40 km2) in the Oregon Coast Range. In this study, GOLEM is analysed by varying ten specific parameter values, which between them cover most of the main processes in the chosen landscape setting. However, even a sample of just three values to represent each parameter would require >59,000 simulations to fully explore the parameter space. To make the search for equifinality tractable, we have therefore implemented a special computational sampling technique. Simulations are run using different parameter value combinations, with an initial sampling of these being decided according to a central composite experiment design of resolution V (see Wu and Hamada, 2000). Each model result is then compared with every other, to determine the standard deviation of elevation differences between simulated landscapes. This is then regressed against parameter value combinations up to the quadratic, with solutions to the regression equation used to indicate new parameter value combinations in the next run of simulations. By repeating this procedure, patterns of more nearly equifinal solutions emerge, and a robust assessment of overall equifinal model behaviour may be attempted based on a practical number (< 1000) of simulations.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2002
- Bibcode:
- 2002AGUFM.H12B0923O
- Keywords:
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- 1815 Erosion and sedimentation;
- 1824 Geomorphology (1625);
- 3210 Modeling