Intelligent Calibration of the Transient Storage Model by Integrating Genetic Algorithm and Finite Difference Method for Solute Transport Simulation

Mirnaseri, Mohammad; Divband Hafshejani, Laleh; Khoshravesh, Mojtaba

doi:10.22059/ijswr.2025.401515.670002

Intelligent Calibration of the Transient Storage Model by Integrating Genetic Algorithm and Finite Difference Method for Solute Transport Simulation

Document Type : Research Paper

Authors

Mohammad Mirnaseri ¹

Laleh Divband Hafshejani ²

Mojtaba Khoshravesh ³

¹ Assistant professor of water engineering department, Faculty of agricultural engineering, Sari agricultural sciences and natural resources university.

² Department of Environmental Engineering, Faculty of Water and Environmental Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

³ Water Engineering Department, Faculty of Agricultural Engineering, Sari Agricultural Sciences and Natural Resources University, Sari. Iran.

10.22059/ijswr.2025.401515.670002

Abstract

Simulating solute transport in rivers is significantly challenged by the complex phenomenon of transient storage. This study develops an integrated numerical model that couples an explicit Finite Difference Method (FDM) with a Genetic Algorithm (GA) to automate the calibration of key parameters in the one-dimensional Transient Storage Model (TSM). The governing advection-dispersion equations for the main channel and storage zones were discretized using an Upwind-Central scheme. A GA-based optimization framework was implemented to estimate four critical parameters—longitudinal dispersion coefficient (D), storage exchange coefficient (α), main channel cross-sectional area (A), and storage zone area (Aₛ)—by minimizing the Root Mean Square Error (RMSE) between simulated and experimental concentration data. The model incorporates flexible boundary conditions, including constant concentration, time-varying input, and mass flux at the upstream end, and zero-gradient or advective flux at the downstream end. Advanced numerical stability mechanisms (CFL, diffusion, and exchange criteria) ensure robust performance. Validation against experimental data from a simulated flume demonstrated the model's superior performance (R² > 0.90, NSE > 0.90) over the standard OTIS-P software. Beyond high accuracy, the model offers novel capabilities: 3D concentration output visualization, systematic parameter sensitivity analysis via the Morris method, and uncertainty assessment based on the Damköhler number (Da). This approach provides a powerful, automated tool for realistically simulating solute transport in river systems, effectively incorporating transient storage dynamics.

Keywords

Genetic Algorithm (GA)

Numerical Modeling

Parameter Calibration

Solute Transport

Transient Storage Model (TSM)

Subjects

Introduction

The simulation of solute transport in rivers is fundamentally challenged by transient storage, whereby solutes are temporarily retained within hyporheic zones and other low-velocity recirculation areas before re-entering the main channel. This process materially influences contaminant dispersion, nutrient cycling, and ecosystem dynamics. While the One-Dimensional Transport with Inflow and Storage (OTIS) model and its software implementation (OTIS-P) provide a standard theoretical framework, their practical use often hinges on manual parameter calibration. Such calibration is labor-intensive, subjective, and liable to converge to suboptimal local minima, thereby introducing avoidable uncertainty into predictions. There is thus a clear need for an automated, robust calibration framework to enhance the accuracy and reliability of the Transient Storage Model (TSM).

Materials and Methods

This study developed an integrated numerical framework that couples an explicit finite-difference solver with a genetic algorithm (GA) to automate calibration of the one-dimensional TSM. The governing advection–dispersion equations for the main channel and the storage zone were discretized using an upwind scheme for advection to promote stability and a central-difference scheme for dispersion to preserve accuracy, with time integration via the forward Euler method. The GA-based optimizer minimizes the root mean square error (RMSE) between simulated and observed breakthrough curves (BTCs) by evolving populations of candidate parameter sets for four key coefficients: longitudinal dispersion (D), storage exchange (α), main-channel cross-sectional area (A), and storage-zone area (A_s).

To accommodate diverse field and laboratory settings, the model supports flexible boundary conditions: at the upstream boundary, constant concentration (Dirichlet), time-varying input, or inflow mass-flux; at the downstream boundary, zero-gradient (Neumann) or advective outflow. A central feature of the framework is a triple stability check embedded in the GA fitness evaluation that enforces numerical stability and physical plausibility: the Courant–Friedrichs–Lewy (CFL) condition for advection, a diffusion stability criterion for dispersion, and an exchange stability criterion for inter-zone mass transfer. Candidate solutions that fail any criterion are penalized, guiding the search toward stable, admissible parameterizations.

For validation, high-resolution experimental data were collected in a controlled laboratory flume (12 m length, 0.5 m width) with a natural gravel bed. Instantaneous NaCl tracer injections were performed under three discharges (10, 12.5, and 15 L/s), and concentration BTCs were recorded at two downstream stations. Model performance was evaluated against OTIS-P using the coefficient of determination (R²), Nash–Sutcliffe efficiency (NSE), and RMSE.

Results and Discussion

The integrated GA–FDM model delivered consistently superior performance relative to OTIS-P across all experimental scenarios, achieving close agreement with observations, with (R²>0.9) and (NSE>0.9). The automated calibration efficiently identified physically meaningful parameter sets, removing the need for subjective, iterative manual tuning.

Parameter trends were robust and physically coherent. The exchange coefficient (α) exhibited a strong inverse relationship with discharge, decreasing by approximately 97% as flow increased, indicating reduced hydrological connectivity with storage zones at higher velocities. In contrast, the storage-zone area (A_s) showed a non-monotonic response, initially decreasing from 0.030 m² to 0.018 m² and then increasing to 0.037 m², consistent with a dynamic activation–deactivation of sub-zones within the sediment bed. The Damköhler number (Da) served as an informative diagnostic: (0.1<Da<10) corresponded to reliable parameterizations, whereas (Da>100) or (Da < 0.01) flagged regimes more susceptible to uncertainty. A Morris elementary-effects sensitivity analysis further indicated that (α) and (A_s) dominate solute retention and the characteristic tailing of the BTCs.

Conclusions

This work presents an automated, robust computational framework for simulating solute transport with transient storage in riverine environments. By fully automating calibration, the GA–FDM approach improves objectivity, efficiency, and numerical robustness over conventional workflows such as OTIS-P. Its diagnostic capabilities (via the Damköhler number) and its global sensitivity analysis provide insight beyond standard outputs, making the framework a practical tool for contaminant fate assessment, tracer-test design and interpretation, and restoration planning where transient storage is consequential. The framework is extensible and provides a solid foundation for future incorporation of reactive transport processes.

Author Contributions

All authors contributed equally to the conceptualization of the article and writing of the original and subsequent drafts. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data is available on reasonable request from the authors.

Ethical considerations

The authors avoided data fabrication, falsification, plagiarism, and misconduct.

Conflict of interest

The author declares no conflict of interest.

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