Space time rainfall modeling using hidden markov model

Abstract

Statistical modeling of rainfall in space-time scales is essential in providing information on the behavior of the rainfall process at a particular region. One of the conventional ways of rainfall modeling is done through studies of the probabilistic structure of the rainfall. In the last decade, many statistical rainfall models were done regardless of the atmospheric information. A model which succeeded in incorporating atmospheric information will be useful in studies of climate variability or climate change. Therefore, this study applied the hidden Markov model (HMM) and non-homogeneous hidden Markov model (NHMM) to model daily rainfall of 40 stations in Peninsular Malaysia over a period of 34 years during the Northeast monsoon and Southwest monsoon. Four different models for rainfall amounts namely single exponential distribution, mixture of two exponential distributions, single gamma distribution and mixture of two gamma distributions were examined for the non-zero rainfall amount. The relationship between the local rainfall process and the large scale atmospheric process were investigated through the behavior of the composite wind anomalies at 850hPa with omega vertical velocity at 500hPa on each hidden state from HMM. The HMM was then extended to NHMM by including the time-varying covariates (atmospheric variables) into the model. So far, the most popular algorithm used for the parameter estimation of HMM was Baum-Welch algorithm, but it was only guaranteed to find a local maximum with a high dependency on initial parameters chosen. Hence, this study also proposed a parameter estimation, segmental K-means algorithm that sacrifices some of Baum- Welch's generality for computational efficiency. The findings here showed that the segmental K-means algorithm is able to improve the conventional model with a reduced computational time. The performances of the HMM and NHMM are assessed through the comparison between the observed rainfall data with the simulated rainfall data. For the rainfall occurrences, the HMM is considered as a very well fit for the tropical regions because it can capture fairly well the rainfall data in Peninsular Malaysia. It is found that the rainfall process in Peninsular Malaysia is associated to the atmospheric composites: low rainfall probabilities are characterized by a high pressure system and high rainfall probabilities are accompanied by a low pressure system. The HMM is able to reproduce the wet/dry spells for most of the stations but overestimated on the short duration of the wet/dry spell (one or two days wet/dry spell). For the rainfall amount, the NHMM has exploited all the mechanisms related to the atmospheric information and rainfall data, and able to reproduce and predict the interannual variability during the Northeast monsoon.