The geometries of alluvial fans and their upland catchments subject to known rates of basin subsidence V and upland precipitation P, respectively, are compared with predictions from a quantitative analysis of an idealized landscape. We find that the dimensionless ratio V/P explains systematic trends in relative fan size and source catchment relief previously reported from environmentally wide-ranging regions worldwide, and contributes to the interpretation of recently reported observations of fan-like phenomena on Mars.

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