Parameter uncertainty estimation of transient storage model using Bayesian inference with formal likelihood based on breakthrough curve segmentation

Abstract

The transient storage model (TSM) for the analysis of pollutant mixing in rivers has been hampered by parameter uncertainties due to the equifinality problem. The generalized uncertainty estimation method, which was frequently used to quantify the parameter uncertainty of TSM, has been criticized because this method uses informal likelihood which can cause overestimation of the uncertainty. Thus, in this study, we suggest a Bayesian inference method using a segment mixture (SM) likelihood, which is a formal likelihood based on the mixture distribution of the segmented breakthrough curve. The uncertainty estimation was conducted using three synthetic data and the real tracer test data achieved from Uvas Creek in the USA. The results show that the SM likelihood estimated uncertainties of TSM appropriately by correctly representing the error distribution of the TSM and identifying the behavioral parameters.