Calibration, sensitivity and uncertainty analysis in surface water quality modeling

QUAL2K (or Q2K) is a USEPA sponsored river and stream water quality model that was recently developed at Tufts University to represent a modernized version of the QUAL2E (or Q2E) model. Compared to empirical models, process-based models are often favored for being able to perform better in extrapolations but they also suffer higher computational burden and lack of identification in calibration and parameter uncertainty analysis. The parameter uncertainty estimation was casted in Bayesian framework. Because normally an analytic solution is unavailable, Markov Chain Monte Carlo (MCMC) algorithm is applied to directly sample from the joint posterior distribution of the model parameters. It was shown that the Coefficients of Variation (CVs) of the posterior distribution from MCMC simulation can be used to tell which parameter can be well estimated from a given data set. To help practitioners to better apply QUAL2K in their modeling practice, automatic calibration tools were developed that can take advantage the speed of computer and recent advances in global searching algorithms. Two robust global search algorithms, Genetic Algorithm (GA) and Shuffled Complex Evolution (SCE-UA) were compared in their performance to calibrate a real data set from Boulder Creek. SCE-UA is favored for being more efficient and effective in finding the best parameter set. The result of finding best parameter set can be used to guide MCMC to more efficiently estimate the parameter posteriors. For parameters that cannot be estimated from data, a practical way is to use a more constrained prior distribution from expert knowledge. To enable Sensitivity and Uncertainty Analysis in QUAL2K, QUAL2K-UNCAS was developed that enables calculating elasticity and performing first-order error analysis (FOEA), Monte Carlo simulation (MCS) with Latin hypercube sampling (LHS).