Method Comparison for Hyporheic Zone Transport Model Parameter Estimation using Tracer Tests Conducted in East Fork Poplar Creek, Tennessee, USA

Abstract:

Quantifying the hyporheic zone exchange rate coefficient, α, (the diffusive mass transfer between surface and groundwater) and the dispersion coefficient, D, (in-stream concentration spreading due to diffusion and velocity variations) typically relies on inverse modeling through comparison to in-stream tracer test data. Measuring both parameters in the field has been challenging. Several researchers have commented on the nonuniqueness and nonidentifiability of a and D in parameter estimation. This study assesses several different nonlinear least square methods for estimating a and D. Four nonreactive tracer tests were conducted in East Fork Poplar Creek, Tennessee. The widely used 1D transient storage model for solute transport, OTIS, was used with the parameter estimation routine distributed with the code via OTIS-P to estimate a and D for each test. Other model parameters were directly measured or estimated from field methods. OTIS-P includes an adaptive nonlinear regression algorithm for parameter estimation (NL2SOL) within the standards time series and regressions package (STAR-PAC). The results obtained from multiple nonlinear regression methods Newton Raphson, Gauss-Newton, Marquardt-Levenberg, Fletcher-Reeves’s Conjugate-Gradient, and Nelder-Mead) were compared to those generated from OTIS-P. Each method was evaluated for its performance in determining the global objective function minimization or optimization solution for α and D. The percentage of deviation from the root mean square error of OTIS-P solution to the solution from the another parameter estimation algorithm was the evaluation metric used to quantify parameter estimation performance. The parameter estimates acquired from various parameter estimation algorithms were comparable. Whereas, the parameter estimation performance of the Newton Raphson method was significantly improved relative to the NL2SOL method used within OTIS-P. The Newton Raphson parameter estimation method provided an improved determination of the global objective function minimum, which might reduce the nonuniqueness and nonidentifiability of a and D parameter estimation for hyporheic zone characterization and simulation.