A stochastic daily weather generation model at multiple sites
Stochastic generation of daily precipitation at multiple sites is frequently needed to evaluate the long-term effects of hydrologic and climate-change in design and operation of water resources systems. Capturing the spatial dependence of precipitation at multiple sites into a stochastic model presents a great challenge because of the non-normal bivariate distributions of precipitation-amounts. Without normalizing the precipitation amounts, many models have attempted to establish spatial dependence through alternative methods that tended to be cumbersome. In contrast, representing precipitation in Gaussian fields provides a generic structure that is well-amenable to statistical analyses facilitating easy implementation of models. The thrust of this thesis is to generate normalized precipitation data and transform them back into the original domain for applications and analyses. A multivariate censored distribution (MCD) and a multivariate autoregressive censored process (MACP) are developed to formulate two weather generation (WG) models. Parameters of censored distributions were estimated by using the maximum likelihood method. To reduce the magnanimity in the number of parameters and their temporal variation, elements of covariance matrices of models were represented by periodic functions. The performance of models was evaluated by comparing discrepancies in attributes. Three performance measures (i.e., the coefficient of determination, the coefficient efficiency and the root mean square error) suggested that simulated data to be indistinguishable from the historical precipitation sequences. The models were implemented with other techniques to address the three most common problems encountered in daily precipitation records. The first implementation is related to simulation of precipitation at un-gauged sites using the WG-MACP model with general regression neural networks or Kriging methods. The second implementation was related to infilling of missing observations a using the WG-MCD and WG-MACP models with Gibbs sampling. The third implementation was related to downscaling of monthly and daily output of the Canadian regional climate model (CRCM) using traditional and parametric Delta change methods.