Song, Jae Young (2012-08). Investigation of Non-homogenous hidden Markov models and their Application to Spatially-distributed Precipitation Types. Master's Thesis.
Thesis
Precipitation is an important element in the hydrological cycle. To predict and simulate large-scale precipitation, Global Circulation Models (GCMs) are widely used. However, their grid scale is too big to apply to local hydrologic fields. In this study, non-homogenous hidden Markov models (NHMM) are explored as a means of generating the probability of precipitation occurrence in small scale given large-scaled weather patterns. Three different spatial models: (1) independent (2) auto-logistic (3) Chow-Liu tree, are also explored, along with methods and steps for parameter estimation. From this exploration, independent models with NHMM are recommended for very small precipitation networks, and the maximum likelihood method is found to be the most practical fitting method. If there are many points for downscaling, Chow-Liu tree models with the Expectation-Maximization (EM) algorithm are recommended. If more exact solutions are needed, auto-logistic models can be employed. If many points are considered in auto-logistic models, the (EM) algorithm should be used to estimate parameters separately and global optimization methods should be used for emission matrix. The major problem found with the NHMM model in this study is matching the rainfall amount for each year or month. This problem can be addressed by whether combining occurrence models with amount modes or by improving only occurrence models.
