Second-Order Autoregressive Model-Based Likelihood Function for Calibration and Uncertainty Analysis of SWAT Model

Abstract

Second order autoregressive [AR(2)] model has been adopted in the likelihood function to calibrate the soil and water assessment tool (SWAT) model for the Canard River watershed, southwestern Ontario, Canada. The Bayesian approach is used for uncertainty analysis of SWAT modeling. The performance of AR(2) model for uncertainty estimation is evaluated by the index called Percentage of observations bracketed by the unit confidence interval (PUCI) for 95% confidence limits. The results are compared with the simple least square (SLS) method of calibration. In the SLS method, the modeling errors are assumed to be uncorrelated. The study reveals that the model parameter uncertainty is high and there exists local optimum values in the parameter space. The reliability of streamflow simulation uncertainty due to parameter uncertainty is increased when AR(2) model is implemented in the calibration process. The comparison of PUCI values between AR(2) method and SLS method shows that the estimation of streamflow simulation uncertainty is more reliable in AR(2) model-based calibration method. But the lower values of PUCI indicate very high uncertainty in 95% confidence limits estimation. The residuals are observed to have nonnormal distribution with nonconstant variance. Therefore, appropriate transformation of data might improve the uncertainty estimation. The model structural uncertainty is high for simulating streamflow in the study area during low-flow and high-flow periods. Therefore, the study suggests applying separate statistical error models in the likelihood function for representing the modeling errors in low-flow and high-flow periods.