Evaluation of Computational Techniques for Parameter Estimation and Uncertainty Analysis of Comprehensive Watershed Models

The structural complexity of comprehensive watershed models continues to increase in order to incorporate inputs at finer spatial and temporal resolutions and simulate a larger number of hydrologic and water quality responses. Hence, computational methods for parameter estimation and uncertainty analysis of complex models have gained increasing popularity. This study aims to evaluate the performance and applicability of a range of algorithms from computationally frugal approaches to formal implementations of Bayesian statistics using Markov Chain Monte Carlo (MCMC) techniques. The evaluation procedure hinges on the appraisal of (i) the quality of final parameter solution in terms of the minimum value of the objective function corresponding to weighted errors; (ii) the algorithmic efficiency in reaching the final solution; (iii) the marginal posterior distributions of model parameters; (iv) the overall identifiability of the model structure; and (v) the effectiveness in drawing samples that can be classified as behavior-giving solutions. The proposed procedure recognize an important and often neglected issue in watershed modeling that solutions with minimum objective function values may not necessarily reflect the behavior of the system. The general behavior of a system is often characterized by the analysts according to the goals of studies using various error statistics such as percent bias or Nash-Sutcliffe efficiency coefficient. Two case studies are carried out to examine the efficiency and effectiveness of four Bayesian approaches including Metropolis-Hastings sampling (MHA), Gibbs sampling (GSA), uniform covering by probabilistic rejection (UCPR), and differential evolution adaptive Metropolis (DREAM); a greedy optimization algorithm dubbed dynamically dimensioned search (DDS); and shuffle complex evolution (SCE-UA), a widely implemented evolutionary heuristic optimization algorithm. The Soil and Water Assessment Tool (SWAT) is used to simulate hydrologic and water quality processes in a 248 square kilometer watershed in the Midwestern United States. In the first case study, when only streamflow response at the watershed outlet was considered, the six methods performed similarly. However, the computationally frugal DDS method outperformed all other methods when the evaluation was conducted for multiple responses including nitrate loads at various locations within the watershed in the second case. The results reveal the limitations of these methods for multisite many-response modeling studies with highly nonlinear objective function space encompassing many local minimum solutions.