A model for forecasting large-scale patterns of soil erosion and deposition from Landsat MSS data in arid grazing lands is presented. The model is based on the erosion cell mosaic approach and exploits the high degree of temporal and spatial autocorrelation in the erosion process on flat alluvial plains. Erosion and deposition are first mapped using Pickup and Nelson's soil stability index. As a landscape degrades, the variance and autocorrelation function of this index change. These trends represent changes in the physical behaviour of the system and can be explained by it. The model used for forecasting change is a first-order simultaneous autoregressive (s.a.r.) process which can reproduce changes in mean, variance and spatial autocorrelation. This model expresses each pixel value as a function of those of its neighbours plus a noise term. The forecasting procedure involves fitting a s.a.r. model to an area, obtaining the values of the underlying pattern (noise) series by inverse filtering and then obtaining a forecast by filtering the underlying pattern series using a prototype s.a.r. model for a more (or less) degraded state. The prototype s.a.r. model is obtained by fitting to a similar area in a different erosional condition. Testing of the model against observed change indicates that it is reasonably accurate as long as the underlying pattern series is obtained from imagery in which there is sufficient vegetation cover for the soil stability index to be a sensitive indicator of the state of the landscape.
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