An accurate numerical solution to the Saint-Venant-Hirano model for mixed-sediment morphodynamics in rivers

We present an accurate numerical approximation to the Saint-Venant-Hirano model for mixed-sediment morphodynamics in one space dimension. Our solution procedure originates from the fully-unsteady matrix-vector formulation developed in [54]. The principal part of the problem is solved by an explicit Finite Volume upwind method of the path-conservative type, by which all the variables are updated simultaneously in a coupled fashion. The solution to the principal part is embedded into a splitting procedure for the treatment of frictional source terms. The numerical scheme is extended to second-order accuracy and includes a bookkeeping procedure for handling the evolution of size stratification in the substrate. We develop a concept of balancedness for the vertical mass flux between the substrate and active layer under bed degradation, which prevents the occurrence of non-physical oscillations in the grainsize distribution of the substrate. We suitably modify the numerical scheme to respect this principle. We finally verify the accuracy in our solution to the equations, and its ability to reproduce one-dimensional morphodynamics due to streamwise and vertical sorting, using three test cases. In detail, (i) we empirically assess the balancedness of vertical mass fluxes under degradation; (ii) we study the convergence to the analytical linearised solution for the propagation of infinitesimal-amplitude waves [54], which is here employed for the first time to assess a mixed-sediment model; (iii) we reproduce Ribberink's E8-E9 flume experiment [46].Environmental Fluid MechanicsRivers, Ports, Waterways and Dredging Engineerin

A regularization strategy for modeling mixed-sediment river morphodynamics

A notable drawback in mixed-size sediment morphodynamic modeling is the fact that the most commonly used mathematical model in this field (i.e., the active layer model Hirano, 1971) can be ill-posed under certain circumstances. Under these conditions the model loses its predictive capabilities, as negligible perturbations in the initial or boundary conditions produce significant differences in the solution. In this paper we propose a preconditioning method that regularizes the model to recover well-posedness by altering the time scale of the sediment mixing processes. We compare results of the regularized model to data from four new laboratory experiments conducted under conditions in which the active layer model is ill-posed. The regularized active layer model captures the change of bed elevation and surface texture averaged over the passage of several bedforms. Neither the active layer model nor the regularized one account for small scale changes due to individual bedforms.Rivers, Ports, Waterways and Dredging Engineerin

Unaccounted CO₂ leaks downstream of a large tropical hydroelectric reservoir

Recent studies show that tropical hydroelectric reservoirs may be responsible for substantial greenhouse gas emissions to the atmosphere, yet emissions from the surface of released water downstream of the dam are poorly characterized if not neglected entirely from most assessments. We found that carbon dioxide (CO2) emission downstream of Kariba Dam (southern Africa) varied widely over different timescales and that accounting for downstream emissions and their fluctuations is critically important to the reservoir carbon budget. Seasonal variation was driven by reservoir stratification and the accumulation of CO2 in hypolimnetic waters, while subdaily variation was driven by hydropeaking events caused by dam operation in response to daily electricity demand. This “carbopeaking” resulted in hourly variations of CO2 emission up to 200% during stratification. Failing to account for seasonal or subdaily variations in downstream carbon emissions could lead to errors of up to 90% when estimating the reservoir’s annual emissions. These results demonstrate the critical need to include both limnological seasonality and dam operation at subdaily time steps in the assessment of carbon budgeting of reservoirs and carbon cycling along the aquatic continuum.Rivers, Ports, Waterways and Dredging Engineerin