[1] Soil erosion and the associated nutrient fluxes can lead to severe degradation of surface waters. Given that both sediment transport and nutrient sorption are size selective, it is important to predict the particle size distribution (PSD) as well as the total amount of sediment being eroded. In this paper, a finite volume implementation of the Hairsine-Rose soil erosion model is used to simulate flume-scale experiments with detailed observations of soil erosion and sediment transport dynamics. The numerical implementation allows us to account for the effects of soil surface microtopography (measured using close range photogrammetry) on soil erosion. An in-depth discussion of the model parameters and the constraints is presented. The model reproduces the dynamics of sediment concentration and PSD well, although some discrepancies can be observed. The calibrated parameters are also consistent with independent data in the literature and physical reason. Spatial variations in the suspended and deposited sediment and an analysis of model sensitivity highlight the value of collecting distributed data for a more robust validation of the model and to enhance parametric determinacy. The related issues of spatial resolution and scale in erosion prediction are briefly discussed.

[1] This paper presents a finite volume scheme for coupling the Saint-Venant equations with the multiparticle size class Hairsine-Rose soil erosion model. A well-balanced monotone upstream-centered schemes for conservation laws-Hancock (MUSCL-Hancock) method is proposed to minimize spurious waves in the solution arising from an imbalance between the flux gradient and the source terms in the momentum equation. Additional criteria for numerical stability when dealing with very shallow flows and wet/dry fronts are highlighted. Numerical tests show that the scheme performs well in terms of accuracy and robustness for both the water and sediment transport equations. The proposed scheme facilitates the application of the Hairsine-Rose model to complex scenarios of soil erosion with concurrent interacting erosion processes over a nonuniform topography.

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The upper free surface z = u(x, y) of a static fluid with gravity acting in the z direction, occupying a volume V , satisfies the Laplace-Young equation. The fluid wets the vertical boundaries of V so that the usual capillary contact conditions hold. This paper considers wedge shaped volumes V with corner angle 2α, that belong to the intermediate corner angle case of π/2 − γ < α < π/2 where γ is the contact angle, and determines explicitly, a regular power series expansion for the height u(r, θ) of the fluid near the corner, r = 0, to all orders in r. Miersemann (1988) shows that it is possible to have logarithmic terms for a general corner expansion of the Laplace-Young equation, with appropriate boundary conditions. However, we suggest that the usual practical cases do not possess any singular terms near the corner, and we analytically and explicitly produce a non-singular series to any order in r, and propose that near the corner the far field effects are lost through any "interior or inner flat" region in exponentially small terms. We give computational solutions for these regular (energy minimising) cases based on a numerical finite volume method on an unstructured mesh, which fully support our assertions and our analytical series results, including the (minor) influence of the far field on local corner behaviour.

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