Calculation of the volume of an alluvial fan

Abstract

Calculation of the volume of a lithostratigraphic unit within an alluvial fan allows a longterm denudation rate to be calculated for the fan's catchment, where sediment is not transported beyond the fan. The calculation of denudation rates in this case depends upon accurate estimates of the volume of sediment in a lithostratigraphic unit of known age. Two methods of volume calculation and their approximations are presented. The first method sums the volume of discrete blocks used to approximate a variety of fan shapes. The second method integrates a quadratic function that approximates both the surface and lower boundary of a lithostratigraphic unit where the edges of the fan are assumed to be vertical. For fans that satisfy these restrictive assumptions, the integration method should be more accurate than the summation method. However, the summation method is more generally applicable and calculations using the two methods, and their approximations, yield remarkably similar results.