DOI: 10.4211/hs.eeb3927dbefe4bf3b1ef26e0e897eb76
title: 1D grain-size-specific morphodynamic model for sand bed rivers

description: Morphodynamic model research code for sand bed rivers used in Leonard and Wilcock (2024). Morphodynamic models evolve the bed surface grain size and topography from initial conditions to a steady state using conservation of mass and momentum for open channel flow and sediment mass conservation. We use a simplified version of channel geometry with constant width and no floodplain such that the only adjustment is in bed texture and bed aggradation or degradation. The model starts with a specified slope and bed grain size at each model node and calculates bed shear stress from a specified discharge to predict the transport rate and grain size. Bed topography and grain size adjust based on the difference between the mass of each sediment size fraction delivered to and transported from each node at each timestep. The 1D shallow water equation of mass and momentum conservation describes flow within the rectangular channel. Flow resistance and the skin friction portion of the total boundary stress are specified using the Wright and Parker (2004b) formulation, which accounts for the effects of density stratification and flow resistance over dunes. The grain-size-specific formulation of the Exner equation (Parker et al., 2007), which conserves sediment mass for individual size fractions, determines bed grain size and topography. The channel bed is divided into an upper active layer that exchanges with the bed material load, a lower substrate layer that maintains a constant grain size, and an interface layer that exchanges sediment between the active layer and the substrate as the bed aggrades and degrades (Hirano, 1971). The active layer thickness is specified as the height of the bedforms, predicted as a function of flow depth using the relation of Julien and Klaassen (1995). The grain size of the interface layer evolves as the bed aggrades and erodes using the relation formulated by Hoey and Ferguson (1994) and Toro-Escobar et al. (1996). Grain-size specific volumetric bed material transport rates are calculated using a separate transport relation for bed and suspended loads. Total volumetric bed material transport is the sum of transport of each grain size fraction in the bed and suspended loads. We use the Wright and Parker (2004b) entrainment model (W-P) coupled with a Rouse profile and van Rijn (1984) initiation of suspension criterion to estimate suspended load transport. W-P is a modified version of the Garcia and Parker (1991) (G-P) entrainment model that accounts for reduced mixing due to density stratification in the presence of large suspended loads. G-P and W-P are the only entrainment models with a mixed-size hiding function tested against field data, making this relation ideal for predicting size-selective transport in the suspended load that drives the sorting of bed grain. Bed load is calculated from the Ashida and Michiue (1972) relation (A-M), which includes the Egiazaroff (1965) hiding function. A-M was developed from flume measurements of sand bedload, making this relation ideal for our modeling purpose.