Prediction of ozone levels using a Hidden Markov Model (HMM) with Gamma distribution

Ground level ozone, generated by the photochemical reaction between nitrogen oxides and volatile hydrocarbons, is harmful to humans and the environment. Prediction and forecasting play an important role in the regulatory policies aimed at the control and reduction of surface ozone. Belonging to the family of model-driven statistical models, Hidden Markov Models (HMMs) provide a rich mathematical structure and perform well in many applications. While conventional HMM applications assume Gaussian distribution for the observation statistics, several key meteorological factors and most ozone precursors exhibit a non-Gaussian distribution, which would weaken the performance of a conventional HMM in modeling ozone exceedances. We propose a method based on a HMM with a Gamma distribution (HMM-Gamma) where each monitoring day is pre-labeled according to its maximum 8-h average ozone concentration and monitoring days are further grouped into zones with different ozone levels. Then, HMMs associated with each zone are trained using air quality monitoring data where the model parameters are estimated by a modified Expectation–Maximization (EM) algorithm. We derive a new re-estimation formula for the model parameters for observation sequences that exhibit a Gamma distribution. The trained HMM-Gamma models are used to predict ozone exceedances in two geographic areas, Livermore Valley near San Francisco, CA and Houston Metropolitan Area, TX. Compared to the conventional HMM (HMM-Gaussian), HMM-Gamma for the ground level ozone in Livermore Valley can reduce false alarms by 77% and HMM-Gamma for that in Houston Metropolitan Area can reduce false alarms by 32%.

► A Hidden Markov Model with Gamma distribution is derived in this paper.
► It is applied on ozone prediction in Livermore Valley near San Francisco, CA and Houston Metropolitan Area, TX.
► Results show that HMM-Gamma can predict all exceedances correctly and reduce false alarms significantly.