Techniques for Increasing the Reliability of Estimates of Surface Water Transport Models

The Transient Storage Model (TSM) is widely used to simulate solute transport in stream settings. Within the TSM framework, solute transport is simulated using the advection dispersion equation in the main channel with additional mass transfer terms that represent the transverse exchange with surface water storage zones (dead zones) and the hyporheic zone (subsurface surrounding the stream). The TSM parameters are commonly treated as reach-averages, and they are estimated by fitting a theoretical to an experimental breakthrough curve. The parameters? values suffer from the problem of non-uniqueness whereby many combinations of parameters? values provide essentially the same fit. We explore various techniques for alleviating the problem of non-uniqueness. We use for this purpose stream-tracer studies that we conducted in a 190-m reach of Indian Creek, Philadelphia, Pennsylvania USA, where two stream-tracer studies were conducted and the concentration is monitored at two transects. We also conducted measurements of the cross section area at various transects and incorporated them into the objective function in a Bayesian parameter estimation framework. We found that using multiple stream tracer studies under various hydraulic conditions and/or the Bayesian framework alleviate the problem of non-uniqueness. We fitted the model to the data when the cross section area was treated as a distributed parameter while the other parameters were treated as reach-averages. While the fit was good, many reach-averaged parameters (exchange coefficient, dispersion coefficient) had to take to extreme values. This indicates that additional but incomplete geomorphic information does not necessarily improve the understanding of a particular stream system. The variation of the parameters with scale was also explored.