Evaluation of Implicit and Explicit Methods of Uncertainty Analysis on a Hydrological Modeling
Uncertainty in any hydrological modeling can be quantified either implicitly by lumping all sources of errors or explicitly by addressing different sources of errors individually. This dissertation has evaluated some implicit and explicit methods of uncertainty analysis for a physically based distributed hydrological model called Soil and Water Assessment Tool (SWAT). A multiplicative input error model has been developed considering season-dependent precipitation multipliers for quantifying precipitation uncertainty explicitly in the distributed hydrological modeling. The high-dimensional and computational problems of the existing explicit methods have lead to the development of the seasonal input error model. The model is implemented in the calibration process of SWAT for simulating streamflow in two watersheds of Southwestern Ontario, Canada. The calibration method is based on the Bayesian approach and the Markov Chain Monte Carlo (MCMC) simulations are performed by the Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm to analyze the posterior probability distribution of model parameters. By keeping the number of precipitation multipliers equal to the number of distinct seasons, the seasonal input error model has reduced the number of latent variables in the Bayesian modeling and has reduced the dimension of posterior probability distribution. The study reveals that streamflow prediction uncertainty due to parameter uncertainty is reduced when the autoregressive models are used in the implicit methods to represent the residual errors. However, the model parameters are biased when the Box-Cox transformation of data is used in the calibration process for addressing non-homogeneity and non-normality of the residual errors. The parameter and prediction uncertainties estimated by the seasonal input error model based calibration method are consistent with that of implicit methods. Model structural uncertainty is observed to be dominating over the input and parameter uncertainties in modeling the study area with SWAT. Hence, the autoregressive models as well as the input error models could not provide global optimum values in the parameter space. The seasonal input error model quantifies that the true precipitation is lower than the measured precipitation and the precipitation uncertainty estimated by the model is comparable to that of existing input error models. The effects of seasonal precipitation multipliers on parameter estimation and model prediction are explained by the correlation of estimated model parameters and by the reliability of model prediction uncertainty.