Parameter uncertainty with flow variation of the one-dimensional solute transport model for small streams using Markov chain Monte Carlo

Abstract

The transient storage model (TSM) is a popular solute transport model among hydrologists and ecologists for characterizing solute retention potential of small headwater streams. TSM parameters are most commonly estimated in an inverse modeling framework using tracer breakthrough data. A key challenge in interpreting TSM parameters is the inherent difficulty in the estimation process and relating these parameters with the physical characteristics of streams. While often recognized that multiple sources of uncertainty impact transient storage modeling, rigorous evaluation of TSM parameter uncertainty is rare. Stream flow magnitude has been identified as a key variable in characterizing stream solute transport dynamics, yet no study has shown the impact of flow magnitude on TSM parameter uncertainty. In this paper we study the impact of flow magnitude on TSM parameter uncertainty by using tracer data from repeated tracer studies with changing stream flow magnitudes, and introduce a software tool to perform Markov chain Monte Carlo based parameter estimation and uncertainty evaluation. The software tool developed is capable of performing thousands of model runs within a few hours, which is necessary for Monte Carlo based parameter estimation, and provides a potentially attractive framework for model testing and improvement. TSM parameters were found to be relatively less important during higher flows with large uncertainty bounds and clear evidence of parameter correlations. The importance of TSM parameters on solute transport seemed to increase as flow decreased with seasonal baseflow recession. Our findings highlight the need for improved field methodologies to reduce parameter uncertainty and the need for further improvement in the model structure for successful stream characterization.