ABSTRACT
Alluvial fans evolve into distinct planform shapes and topographic surfaces with capricious channel migration, depending on their depositional environments. The plan view of alluvial fans is uniquely organized into a “semicircular” configuration based on their upstream boundary conditions: sediment supply, Qs, and water discharge, Qw. Specifically, the margin of the alluvial fan exhibits its own level of bumpiness, consisting of protrusions and reentrants. We define the degree of this irregularity as a “fan-margin roughness” and investigate whether it varies systematically with and can therefore constrain upstream boundary conditions. To examine the effect of discharge conditions on the planform roughness, we conducted alluvial-fan experiments using a range of sediment and water discharge rates with a bimodal sediment mixture of coarse quartz sand and fine crushed-walnut-shell sediment and quantified the margin roughness using root-mean-square deviation (RMSD). RMSD decreases when local progradation preferentially fills reentrants, while RMSD increases when local progradation preferentially generates margin protrusions. The downstream topography of alluvial fans can be classified into three hierarchical scales: bar, lobe, and basin scale. Our scaling analyses demonstrate that: 1) the characteristic roughness of the fan margin is comparable to the lobe size, 2) roughness tends to decrease exponentially with the Qs/Qw ratio, and 3) substantial spatiotemporal fluctuations of roughness are observed when the Qs/Qw ratio is low. These dependencies occur because upstream Qs and Qw influence the distribution and mobility of channels and distributary lobes. Specifically: 1) the mobility of the channel(s) increases with increasing Qs and decreasing Qw and 2) the reoccupation probability of the channel(s) increases with decreasing Qs and increasing Qw. Quantifying fan-margin roughness may provide a framework for disentangling the upstream boundary conditions of modern and ancient fans in nature.
