Physical context for theoretical approaches to sediment transport magnitude‐frequency analysis in alluvial channels

Abstract

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, Q eff , and fraction of sediment transported by discharges greater than Q eff , 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 Q eff 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 Q eff 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.

Sub-Bankfull Flow Frequency versus Magnitude of Flood Events in Outlining Effective Discharges. Case Study: Trotuș River (Romania)

“…Subsequent to the publication of the study by Wolman and Miller [7], a whole array of studies approached the magnitude-frequency analysis (MFA) of flow discharge, which is an essential part of determining the effective discharge [16,39,40]. Although Wolman and Miller [7] suggested that a theoretical probability density function (PDF) can be employed to illustrate the flow regime, it was only after the 1990s that the theoretical MFA approach was perfected [8,19,23,40,41,42].…”

Quantifying River Channel Stability at the Basin Scale

“…This is perhaps now regarded as a more general model with an emerging body of evidence suggesting that variability in the flow regime, drainage basin size, bed material type and other factors might be responsible for the observed variation in the frequencies of geomorphologically effective flows (for a detailed review, see [57]). It is recognised that in some cases low flows can make a significant contribution to the total annual sediment load, as discussed by Soar and Thorne [17,57] and corroborated by Sholtes et al [58], and with climate and land-use change the higher magnitude events in humid, temperate environments might become more significant, geomorphologically, in the future.…”

Sub-Bankfull Flow Frequency versus Magnitude of Flood Events in Outlining Effective Discharges. Case Study: Trotuș River (Romania)

“…Subsequent to the publication of the study by Wolman and Miller [7], a whole array of studies approached the magnitude-frequency analysis (MFA) of flow discharge, which is an essential part of determining the effective discharge [16,39,40]. Although Wolman and Miller [7] suggested that a theoretical probability density function (PDF) can be employed to illustrate the flow regime, it was only after the 1990s that the theoretical MFA approach was perfected [8,19,23,[40][41][42].…”

“…The assessment of effective discharge using an analytical approach was performed according to the indications provided by Nash [19]; Vogel et al [8]; Goodwin [41]; Quader and Guo [42]; Klonksy and Vogel [23]; and Sholtes et al [40]. According to this method, the sediment transport mechanics are represented by a power function:…”