[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...

[1] Regional grain size trends in fluvial successions can reveal important information regarding the dynamics of sediment routing systems. Self-similar solutions for downsystem grain size fining have recently been proposed to explore how key variables, such as the spatial distribution of deposition, sediment discharge, and sediment supply characteristics, control spatial distribution of grain size in fluvial successions over time scales of 10 4 -10 6 years. We explore the sensitivity of these solutions to changes in key variables and assess their applicability to ancient fluvial successions. Several sensitivity analyses are presented to investigate the relative control of the key model variables on the spatial pattern of down-system grain size fining in fluvial successions. Sensitivity analyses demonstrate that (1) an increase in the initial value of sediment discharge to a basin causes a decrease in the rate of grain size fining in fluvial successions, an effect that becomes nonlinear for large values of initial sediment discharge; (2) a short-wavelength/ high-amplitude subsidence regime generates a greater rate of down-system grain size fining and a long-wavelength/lower-amplitude subsidence regime generates a lesser rate of down-system grain size fining in fluvial successions; and (3) an increase in the spread of grain sizes in the sediment supply generates a greater rate of down-system grain size fining. We apply this modeling technique to grain size data sets collected from two time surfaces within conglomerates of the Upper Eocene Montsor Fan Succession of the Pobla Basin, Spanish Pyrenees. These data sets exhibit approximately self-similar grain size distributions; further, the observed increase in down-system grain size fining associated with smaller depositional system lengths provides support for the application of self-similar solutions to fluvial successions. By applying these solutions to carefully collected grain size data from fluvial successions, we are able to relate explicitly the initial grain size supplied to the system, the spatial distribution of subsidence and the sediment discharge into the basin to the rate of grain size fining in fluvial successions. This method thus offers a powerful means of elucidating sediment routing system dynamics over time.

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