We study the geophysical controls on the size of alluvial fans. Simple relationships between catchment characteristics, sediment yield, subsidence patterns and fan size are developed. As predicting fan size is essentially a conservation of mass problem, our analysis is general, applying to all types of fan landform. The importance of spatially variable subsidence rates has gone largely unrecognized in previous studies of modern fans. Here we stress that the distribution of subsidence rates in the depositional basin is a primary control on relative fan size. Both free coefficients in the oft-cited power-law correlation of fan area and catchment area can be shown to be set primarily by the tectonic setting, taken to include source area uplift rate and the subsidence distribution in the depositional basin. In the case of a steady-state landscape, relative fan size is shown to be independent of both climate and source lithology; only during times of significant departure from steady state can relative fan size be expected to vary with either climate or source lithology. Transients associated with (1) a sudden increase in rock uplift rate, (2) a sudden change in climate and (3) the unroofing of strata with greatly differing erodibilities may produce variation of relative fan areas with both climate and source lithology. Variation of relative fan size with climate or lithology, however, requires that catchment-fan system response to perturbations away from steady state is sensitive to climate and lithology. Neither the strength of transient system responses nor their sensitivity to climate or lithology are known at present. Furthermore, internal feedbacks can significantly dampen any climatic or lithological effect. Thus theoretical considerations of the importance of climatic and lithological variables are inconclusive, but suggest that climatic and lithological effects are probably of secondary importance to tectonic effects. Field data from an unsteady landscape in Owens Valley, California, support and illustrate theoretical predictions regarding tectonic control of fan size. Field data from Owens Valley allow, but do not prove, a secondary dependence on source lithology. In addition, the Owens Valley field data indicate no relationship between relative fan size and climate. Headward catchment growth and enhanced sediment bypassing of fans during times of increased sediment yield (glacial) are put forward as plausible explanations.
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