Improving the identifiability of Transient Storage Model parameters to explore process information in solutes breakthrough curve

Transient storage models (TSM) are a valuable tool for investigating the distribution and transport of solutes, nutrients, and pollutants in the stream corridor. The application of TSM is fundamental for understanding the continuous exchange of water between the active stream channel and dead zones, in-stream sediments, and the adjacent groundwater. Despite the large amount of studies, TSM applications are often limited by the lack of information on parameters certainty. Among the available studies, only few addressed sensitivity of TSM parameters and found poor parameter identifiability and substantial model uncertainty, which make the current interpretation of TSM results rather challenging. This issue raises the question if and when TSM parameters are actually meaningful. Addressing identifiability of TSM parameters is pivotal, since uncertainty in parameter estimation and their interpretation limit linking specific physical processes to model parameters.

Here, we apply a step-sampling approach that combines global identifiability analysis with dynamic identifiability analysis to evaluate model sensitivity and uncertainty in a set of tracer breakthrough experiments in a headwater stream reach. Our results demonstrate that limitations in parameter identifiability often found in several TSM studies can be related to: (i) the assumption velocity = velocity_peak; (ii) the large parameter range used for the parameters sampling; and (iii) the relatively low number of sampled parameter sets. While it is generally assumed that advection-dispersion parameters act on the solute arrival time, and that transient-storage parameters control the tail of the breakthrough curve (BTC), our study brings new insights on the role of TSM parameters in controlling the solute transport in streams. The proposed step-sampling approach allowed us to clearly reduce uncertainty of parameters in TSM highlighting the importance of TSM parameters in certain sections of the BTC, where they are usually assumed to be negligible. By targeting the identifiability range of transient-storage parameters on the tail of the BTC, the applied step-sampling approach bears significant potential for substantially increasing TSM parameters identifiability, and for advancing our understanding of hydrological processes involved in solute transport in streams.