Surface Transient Storage Under Low-Flow Conditions in Streams With Rough Bathymetry

Abstract

In natural and restored rivers, protruding river-bed elements can cause complex flow patterns. We hypothesize that, particularly at very low flows, solute spreading in such streams is controlled by different mechanisms than at high flows, questioning existing parameterizations. We investigate two-dimensional flow and transport in a synthetic channel with rough bathymetry under low-flow conditions with a numerical model solving the full shallow-water equations. Recirculation cells form behind protruding bed elements and trap water, macroscopically acting as transient-storage domain. We fit the one-dimensional mobile-immobile transport model to the concentration breakthrough curves of the two-dimensional model and relate the fitted parameters to easy-to-measure properties of the stream. The velocity in the mobile domain undergoes a power-law relation with the discharge and the channel slope, differing from the relationship expected for normal flow in streams with large water depths. Both the fitted dispersion coefficient and the mass-transfer coefficient between the mobile and immobile domains scale linearly with the velocity in the mobile domain. The ratio of immobile to mobile storage volumes β first increases then decreases with increasing discharge. We suggest measuring the surface area of bed elements protruding the water surface and that of the open water. The product of the corresponding area ratio with the velocity exerts a power-law control on β. Altogether, we can relate the coefficients of the mobile-immobile transport model to a few easy-to-measure properties of the stream. The findings of the present work contribute to the understanding of surface transient storage in natural and restored streams.