Similarity solutions for fluvial sediment fining by selective deposition

Abstract

[1] Current models for downstream sediment sorting by selective deposition generally perform well at describing observed sorting data. However, since most were developed initially for application to modern rivers, they are typically formulated in terms of hydraulic and bed-surface variables that are not readily measurable in the sedimentary record. Moreover, their algebraic complexity obscures some of the underlying simplicity of the segregation process. Here we show how a pair of hydraulically based sorting models developed by Parker et al. can be reformulated, with minimal loss of accuracy, in terms of the size distribution of the supplied sediment and the downstream depositional mass balance. By invoking constant dimensionless shear stress within either the gravel or sand regimes, reach-scale, short-term details of hydraulics and sediment transport are summarized via a pair of dimensionless relative mobility functions, one for gravel and one for sand. Our approach yields simplified similarity solutions in which the long-term longitudinal grain-size distribution of the substrate and the relative mobility functions can be collapsed into self-similar forms in which only local mean and standard deviation of sizes in transport are used as scaling parameters. The formulation we propose offers a simple means to explore the impact of controlling variables on fining profiles and can be easily incorporated in long-term, basin-scale numerical stratigraphic models, avoiding the necessity of modeling the details of hydraulics and sediment transport. The model involves a minimum number of physically based parameters, the numerical values of which can be determined from the spatial distribution of rate of deposition, dimensionless shear stress, and the coefficient of variation of the supply gravel or sand size distributions. Downstream Sediment Fining and the Concept of Similarity: Overview[2] A common geomorphic observation in fluvial systems is their ability to sort sediments via several physical mechanisms. In particular, the tendency of bed material to become finer downstream is a critical property of aggrading rivers that must be accounted for when modeling fluvial systems since it is a primary driver of downstream changes in river planform and depositional facies [Leopold and Wolman, 1957;Heller and Paola, 1992;Paola et al., 1992a;Paola, 2000]. The two most common explanations for fluvial downstream fining are (1) abrasion, a mechanism in which large particles break down into smaller sizes by fracturing and attrition; and (2) selective deposition, a process that can be viewed as a kind of hydraulically driven sediment fractionation [Paola, 1988;Parker, 1991;Paola et al., 1992a;Ferguson et al., 1996;Rice, 1999]. The observations that fining rates are strongly positively correlated with deposition lengths, and that observed fining rates in natural depositional streams are often orders of magnitude higher than those that appear possible by abrasion alone, indicate that selective deposition is the dominant factor that ca...

Dynamics and mechanics of bed-load tracer particles

“…The spatial pattern of diminishing grain size with increasing distance from the headwaters is near universal among gravel rivers, and results from a combination of size-selective sorting and particle abrasion (e.g., Paola et al, 1992;Kodama, 1994;Paola and Seal, 1995;Ferguson et al, 1996;Gasparini et al, 1999Gasparini et al, , 2004Fedele and Paola, 2007;Jerolmack and Brzinski, 2010). For tracer particles, the relatively short distances and timescales involved preclude abrasion as a mechanism for observed downstream fining (Ferguson et al, 1996).…”

Possible threshold controls on sediment grain properties of Peruvian coastal river basins

“…4). Geomorphologists widely accept the notion that the downstream hydraulic geometry of alluvial channels reflects the decrease in particle size within an equilibrated system involving stream flow, channel gradient, sediment supply and transport (Hoey and Ferguson, 1994;Fedele and Paola, 2007;Attal and Lavé, 2009). Sternberg (1875) formalized these relations and predicted an exponential decline in particle size in gravel-bed rivers as a consequence of abrasion and selective transport where the gravel is transported downstream.…”

“…McLaren and Bowles, 1985;Lisle et al, 1993) and numerical models (Hoey and Ferguson, 1994). These studies have mainly been directed towards exploring the controls on the downstream reduction in grain size of gravel beds (Schumm and Stevens, 1973;Hoey and Fergusson, 1994;Surian, 2002;Fedele and Paola, 2007;Allen et al, 2016). In addition, it has been proposed that the grain size distribution, particularly of mountainous rivers, mainly depends on (i) tectonic uplift resulting in steepening of the entire landscape (Dadson et al, 2003;Wittmann et al, 2007;Ouimet et al, 2009), (ii) earthquakes and seismicity causing the release of large volumes of landslides (Dadson et al, 2003;McPhillips et al, 2014), (iii) precipitation rates and patterns controlling river discharge and shear stresses (D'Arcy et al, 2017;Litty et al, 2017), and (iv) bedrock lithology in which low erodibility lithologies are sources of larger volumes of material (Korup and Schlunegger, 2009;Allen et al, 2015).…”

Controls on Pebbles’ Size and Shape in Streams of the Swiss Alps

“…These studies have mainly been directed toward exploring the controls on the downstream grain-size reduction in gravel-bed rivers (e.g., Schumm and Stevens 1973;Hoey and Ferguson 1994;Surian 2002;Fedele and Paola 2007). Here, we report data about grain size and shape that we collected from a large variety of mountainous perennial streams situated in the Swiss Alps.…”