Analytical solution for solute transport resulting from instantaneous injection in streams with transient storage

An analytical solution is presented for solute transport in rivers including the effects of transient storage. The traditional advection–dispersion equation for transport in the main channel is linked to a first order mass exchange term between the main channel and the transient storage zones. This system of equations is solved analytically for the case of an instantaneous injection of a tracer mass in a river with constant and uniform flow. The solution enables to estimate the temporal and spatial evolution of the tracer concentration downstream of the injection point. The correctness of the solution is verified by comparison with the numerical model OTIS (USGS). The solution is programmed in MATLAB and linked to a non-linear least squares optimisation algorithm to obtain an effective and reliable method to estimate solute transport parameters from observed breakthrough curves. The procedure is successfully applied to the Chillán River, Chile, where five tracer experiments were conducted. The observed concentration profiles vs. time at the different measuring locations are well reproduced by the model. In all cases the exchange of solute between the main flow channel and transient storage zones is markedly present.