A HIERARCHICAL STOCHASTIC-MODEL OF LARGE-SCALE ATMOSPHERIC CIRCULATION PATTERNS AND MULTIPLE STATION DAILY PRECIPITATION

A stochastic model of weather states and concurrent daily precipitation at multiple precipitation stations is described. Four algorithms are investigated for classification of daily weather states: k-means clustering, fuzzy clustering, principal components, and principal components coupled with k-means clustering. A semi-Markov model with a geometric distribution for within-class lengths of stay is used to describe the evolution of weather classes. A hierarchical modified Polya urn model is used to simulate precipitation conditioned on the regional weather type. An information measure that considers both the probability of weather class occurrence and conditional precipitation probabilities is developed to quantify the extent to which each of the weather classification schemes discriminates the precipitation states (rain-no rain) at the precipitation stations. Evaluation of the four algorithms using the information measure shows that all methods performed equally well. The principal components method is chosen due to its ability to incorporate information from larger spatial fields. Precipitation amount distributions are assumed to be drawn from spatially correlated mixed exponential distributions, whose parameters varied by season and weather class. The model is implemented using National Meterological Center historical atmospheric observations for the period 1964-1988 mapped to 5-degrees x 5-degrees grid cells over the eastern North Pacific, and three precipitation stations west of the Cascade mountain range in the state of Washington. Comparison of simulated weather class-station precipitation time series with observational data shows that the model preserved weather class statistics and mean daily precipitation quite well, especially for stations highest in the hierarchy. Precipitation amounts for the lowest precipitation station in the hierarchy, and for precipitation extremes, are not as well preserved.