Analytical solution and analysis of solute transport in rivers affected by diffusive transfer in the hyporheic zone

SummaryA model is presented for solute transport in rivers including transient storage in hyporheic zones. The model consists of an advection–dispersion equation for transport in the main channel with a sink term describing diffusive solute transfer to the hyporheic zone. This system of equations is solved analytically for instantaneous injection of a conservative tracer in an infinite uniform river reach with steady flow. The solution enables to estimate the temporal and spatial evolution of tracer concentrations downstream of the injection point with fewer parameters than any other model before. The solution is linked to a non-linear least squares optimisation algorithm to analyse breakthrough curves and estimate solute transport parameters. The model is applied to tracer experiments conducted in the Chillán River, Chile, which were previously analysed with a model including mass exchange between the river and a stagnant storage zone. The fit between observations and model results is good, except for some experiments where the tailing of the fitted curves is more pronounced than observed. Estimates of the water flow velocity are practically identical with previous findings, but the estimates of the cross-sectional area and the dispersion coefficient are markedly different. Estimated values for the diffusion coefficient in the hyporheic zone agree with values cited in literature and with the magnitude of chemical diffusion coefficients in porous media.