Identifying transient storage model parameters in karst conduits using the normal-score ensemble smoother with multiple data assimilation

Abstract

Transient storage model (TSM) is widely used to describe solute transport processes in karst areas. Accurately identifying model parameters is essential for predicting and mitigating groundwater contamination. This paper employs the normal-score ensemble smoother with multiple data assimilation (NS-ES-MDA) algorithm to automatically identify model parameters (cross-sectional area of main channel A, dispersion coefficient D, cross-sectional area of storage zone As, and exchange coefficient α), while evaluating their uncertainty across four cases: identification of only model parameters (case 1), model parameters alongside tracer parameters (case 2), model parameters with conduit length (case 3), and all three –model parameters, tracer parameters, and conduit length (case 4). We examine the variations in uncertainty of model parameters when tracer parameters and/or conduit length are known or unknown. We further investigate the effects of concentration observation limits and observation error variance on the identification performance. The results demonstrate that the proposed method can successfully identify model parameters, even in cases where tracer parameters and/or conduit length are unknown, although with a certain level of uncertainty. However, the calibration of tracer parameters leads to an increase in uncertainty for A and D, and a slight rise in uncertainty for α. The calibration of conduit length significantly elevates the uncertainties of A and As and causes an increase in uncertainty for D. Compared with tracer parameters, conduit length causes larger uncertainty in A and As. The identification performance significantly deteriorates when the tail of observed breakthrough curve (BTC) is truncated, and reaches its peak at an observation error variance of 1 × 10-4. This implies that it is crucial to monitor the tail in BTC and to assign a reasonable observation error when using this method to identify model parameters. Although these findings are derived from a synthetic karst conduit, they offer valuable insights for identifying model parameters as tracer data and/or conduit length are uncertain in field conditions.