Topographic Scaling Reflects Process Differences on Alluvial and Fluvial Fans

Fans are dominant landforms in sedimentary basins and vary considerably in terms of size, dynamics and resultant morphology and stratigraphy. Fan dynamics (including avulsion and floodplain evolution) are difficult to observe directly due to the long timescales on which they operate. However, fan surface topography is the time-integrated result of fan dynamics and provides a promising avenue for investigating avulsion and floodplain processes indirectly.

Here we leverage recent high-precision bare earth elevation data to characterize the topographic scaling for a set of globally distributed alluvial and fluvial fans. Transverse elevation profiles were collected for each fan of interest, and "topographic spectra" calculated using the Fourier Transform. Breaks in scaling are identified from spectra through visual inspection and corroborated by comparison to semi-variograms (plots comparing variance across scales).

Our results highlight the interdependence of topography and depositional processes on fans and inform conceptual and rule-based models of fan evolution. The topography of both alluvial and fluvial fans exhibit classic "1/fβ" scaling where variance roughly follows a power-law decrease with scale (also called "red noise"). However, fluvial fans exhibit a characteristic break in scaling that corresponds with the average width of alluvial ridges as measured from satellite imagery.

We hypothesize that the differences in topographic scaling are due to differences in flow and avulsion styles. Alluvial fans tend to emanate from small catchments with highly variable discharge and aggrade through successive sheet flows and shallow channelized flows. The deposits from these ephemeral flows scale with the events that created them, where magnitude is inversely related to frequency (i.e. red noise). By contrast, topography on fluvial fans is constructed by perennial rivers with banks and levees of a roughly constant width. Deposits from these rivers thus exhibit a characteristic horizontal (strike-parallel) scale corresponding to the width of the "alluvial ridge" (the channel-levee complex). Below this characteristic scale, fluvial fan topography exhibits scaling associated with red noise due to the presence of crevasse splays and avulsion deposits of varying scale on the floodplain.