Transient Storage Model Parameter Optimization Using the Simulated Annealing Method. Issue 7 (19th July 2022)

• Record Type: Journal Article
• Authors: Tsai, C. H.; Rucker, D. F.; Brooks, S. C.; Ginn, T.; Carroll, K. C.
• Is Part Of: Water resources research. Volume 58:Issue 7(2022)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-07-19
• Subjects: simulated annealing -- transient storage model -- parameter optimization -- hyporheic -- TSM -- parameter estimation; Hydrology -- Periodicals; 333.91
• DOI: 10.1029/2022WR032018
• Languages: English
• ISSNs: 0043-1397

Abstract

Abstract: Hyporheic exchange in streams is critical to ecosystem functions such as nutrient cycling along river corridors, especially for slowly moving or small stream systems. The transient storage model (TSM) has been widely used for modeling of hyporheic exchange. TSM calibration, for hyporheic exchange, is typically used to estimate four parameters, including the mass exchange rate coefficient, the dispersion coefficient, stream cross‐sectional area, and hyporheic zone cross‐sectional area. Prior studies have raised concerns regarding the non‐uniqueness of the inverse problem for the TSM, that is, the occurrence of different parameter vectors resulting in TSM solution that reproduces the observed in‐stream tracer break through curve (BTC) with the same error. This leads to practical non‐identifiability in determining the unknown parameter vector values even when global‐optimal values exist, and the parameter optimization becomes practically non‐unique. To address this problem, we applied the simulated annealing method to calibrate the TSM to BTCs, because it is less susceptible to local minima‐induced non‐identifiability. A hypothetical (or synthetic) tracer test data set with known parameters was developed to demonstrate the capability of the simulated annealing method to find the global minimum parameter vector, and it identified the "hypothetically‐true" global minimum parameter vector even with input data that were modified with up to 10% noise without increasing the number of iterations required for convergence. The simulated annealing TSM was then calibrated using two in‐stream tracer tests conducted in East Fork Poplar Creek, Tennessee. Simulated annealing was determined to be appropriate for quantifying the TSM parameter vector because of its search capability for the global minimum parameter vector. Plain Language Summary: Hyporheic exchange is critical for biogeochemical and ecological processes in river corridors, and in‐stream tracer testing and modeling are commonly used for exchange characterization. Non‐uniqueness of inverse modeling parameter estimation is a concern for the transient storage model (TSM) for hyporheic exchange as gradient‐based parameter estimation methods tend to get trapped in local minima of the difference between observation and model results, which limits our ability to locate global minimum parameters that provide the closest match between model and data. We used a hypothetical (or synthetic) tracer test data set with known parameters to test simulated annealing as an alternative inverse modeling approach, which was also compared to the results of the commonly used TSM code, OTIS‐P, a modified version of one‐dimensional transport with inflow and storage (OTIS) code, couples the solution of the governing equation of OTIS with a nonlinear regression package (Runkel, 1998a). The simulated annealing method identified the "hypothetically‐true" global minimum parameter vector even with variations in initial guesses of the parameter vector values and input observation data that were modified to include up to 10% noise to account for experimental error. The simulated annealing inverse TSM was also able to identify reasonable/comparable parameters for two tracer tests conducted in East Fork Poplar Creek, Tennessee, which suggests that simulated annealing is a reasonable approach for TSM inverse modeling. Key Points: Simulated annealing with random initial guesses was able to identify correct parameter values for synthetic case with known parameter vector Acceptable parameter estimation (without increased iteration requirement) for Transient Storage Model (TSM) even with 5 and 10% noise was added Simulated annealing method was successfully applied with random initial guesses of the parameter vector for model calibration of two in‐stream tracer test data sets