Markov Chain Modeling of Sequences of Lagged NWP Ensemble Probability Forecasts: An Exploration of Model Properties and Decision Support Applications

Abstract

It is shown that sequences of lagged ensemble-derived probability forecasts can be treated as being realizations of a discrete, finite-step Markov chain. A reforecast ensemble dataset is used to explore this idea for the case in which the Markov chain has 12 states and 15 steps and the probability forecasts are for the event for which the 500-hPa geopotential height exceeds the climatological value at a specified point. Results suggest that the transition probabilities of the Markov chain are best modeled as first order if they are obtained from the reforecast ensemble dataset using maximum likelihood estimation. Most of the first-order-estimated transition probabilities are statistically significant. Also, the transition probabilities are inhomogeneous, and all states in the chain communicate. A variety of potential decision support applications for the Markov chain parameters are highlighted. In particular, the transition probabilities allow calculation of the conditional probability of taking protective action and calculation of the conditional expected expense when used with static cost?loss decision models. Also, the transition probabilities facilitate optimized decisions when incorporated into dynamic decision models. Decision model test scenarios can be obtained using cluster analysis and conditional most likely sequences, and these scenarios reveal the key patterns traced by the Markov chain.