Stochastic weather generators (SWGs) are designed to create simulations of synthetic weather data and are frequently used as input into physical models throughout many scientific disciplines. While the field of SWGs is vast, the search for better methods of spatiotemporal simulation of meteorological variables persists. We propose techniques to estimate SWG parameters based on an emerging set of methods called Approximate Bayesian Computation (ABC), which bypass the evaluation of a likelihood function. In this thesis, we begin with a review of the current state of ABC methods, including their advantages, drawbacks, and variations, and then apply ABC to the simulation of daily local maximum temperature, daily local precipitation occurrence, and daily precipitation occurrence over a spatial domain.;For temperature, we model the mean and variance as following a sinusoidal pattern which depends on the previous day. A similar approach is used for precipitation, but instead use a probit regression to model the probability that it rains on a given day of the year, based on an oscillatory mean function. For spatiotemporal precipitation occurrence, we employ a thresholded Gaussian process which reduces to our methods for local occurrence. In each scenario, we identify appropriate ABC penalization criteria to produce simulations whose statistical characteristics closely resemble those of the data. For our numerical case studies, we use daily temperature and precipitation records Colorado and Iowa, collected over the course of hundreds of years.
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