Physical context for theoretical approaches to sediment transport magnitudefrequency analysis in alluvial channels

Theoretical approaches to magnitude-frequency analysis (MFA) of sediment transport in channels couple continuous flow probability density functions (PDFs) with power law flow-sediment transport relations (rating curves) to produce closed-form equations relating MFA metrics such as the effective discharge, Qeff, and fraction of sediment transported by discharges greater than Qeff, f1, to statistical moments of the flow PDF and rating curve parameters. These approaches have proven useful in understanding the theoretical drivers behind the magnitude and frequency of sediment transport. However, some of their basic assumptions and findings may not apply to natural rivers and streams with more complex flowsediment transport relationships or management and design scenarios, which have finite time horizons. We use simple numerical experiments to test the validity of theoretical MFA approaches in predicting the magnitude and frequency of sediment transport. Median values of Qeff and f1 generated from repeated, synthetic, finite flow series diverge from those produced with theoretical approaches using the same underlying flow PDF. The closed-form relation for f1 is a monotonically increasing function of flow variance. However, using finite flow series, we find that f1 increases with flow variance to a threshold that increases with flow record length. By introducing a sediment entrainment threshold, we present a physical mechanism for the observed diverging relationship between Qeff and flow variance in fine and coarse-bed channels. Our work shows that through complex and threshold-driven relationships sediment transport mode, channel morphology, flow variance, and flow record length all interact to influence estimates of what flow frequencies are most responsible for transporting sediment in alluvial channels.