Comparing Single-Objective Optimization Protocols for Calibrating the Birds Nest Aquifer Model—A Problem Having Multiple Local Optima

Abstract

To best represent reality, simulation models of environmental and health-related systems might be very nonlinear. Model calibration ideally identifies globally optimal sets of parameters to use for subsequent prediction. For a nonlinear system having multiple local optima, calibration can be tedious. For such a system, we contrast calibration results from PEST, a commonly used automated parameter estimation program versus several meta-heuristic global optimizers available as external packages for the Python computer language—the Gray Wolf Optimization (GWO) algorithm; the DYCORS optimizer framework with a Radial Basis Function surrogate simulator (DRB); and particle swarm optimization (PSO). We ran each optimizer 15 times, with nearly 10,000 MODFLOW simulations per run for the global optimizers, to calibrate a steady-state, groundwater flow simulation model of the complex Birds Nest aquifer, a three-layer system having 8 horizontal hydraulic conductivity zones and 25 head observation locations. In calibrating the eight hydraulic conductivity values, GWO averaged the best root mean squared error (RMSE) between observed and simulated heads—20 percent better (lower) than the next lowest optimizer, DRB. The best PEST run matched the best GWO RMSE, but both the average PEST RMSE and the range of PEST RMSE results were an order of magnitude larger than any of the global optimizers.

Evaluating the Impacts of Pumping on Aquifer Depletion in Arid Regions Using MODFLOW, ANFIS and ANN

“…This value of NSE lies in the range of "very good" according to the criteria adopted by Rauf and Ghumman [54]. Furthermore, our results are similar to those of Mohanty et al [55] and Lyons et al [16], although the hydraulic conductivity and specific storage were the most sensitive parameters in the calibration phase of their groundwater hydraulic model, but adjustment of the boundary condition was most crucial issue in our case. The resultant predicted vs. observed line was close to the 45-degree line, which also showed that the results of calibration were "very good".…”

“…Similar results were observed by previous studies [30,41,42,49]. This is most probably because a stronger optimization scheme was used in the scaled conjugate gradient to get a better global minimum with the minimum possible number of trials [16,54]. Further, the performance of the Scaled Conjugate Gradient training function was better than that of the Levenberg-Marquardt and Bayesian Regularization training functions for the three-layer architecture with 10 neurons (Figure 11a-d).…”