Self‐Affine Fractal Spatial and Temporal Variability of the San Pedro River, Southern Arizona

Abstract

Prevailing mathematical models of alluvial channel evolution generate smooth, idealized longitudinal profiles. Alluvial channel longitudinal profiles in nature, however, have substantial multiscale spatial and temporal variability. In this paper we quantify the spatial and temporal hydrologic and geomorphic variability of a 90-km-long reach of the San Pedro River (San Pedro River) in southeastern Arizona and compare that variability to numerical models designed specifically to honor the spatial and temporal variability of alluvial channel systems in nature. A key motivation of this work is the power law frequency size distribution of wet and dry reaches observed in the San Pedro River. We demonstrate that such a distribution is consistent with self-affine fractal variations of the depth to bedrock and the channel longitudinal profile. At large spatial scales, spatial variations in depth to bedrock control the accommodation space for groundwater, which, in turn, controls spatial variations in surface water discharge. At small spatial scales, the longitudinal profile controls spatial variations in surface water discharge by changing the distance between the channel bed and the water table. These results underscore the complex spatiotemporal behavior of dryland alluvial rivers and the tight coupling that is possible between hydrologic and geomorphic processes in such systems.