Markovian approach to the frequency of tropical cyclones and subsequent development of univariate prediction model

Abstract

A tropical cyclone is one of the most devastating meteorological events. In recent years, we faced some very severe cyclones to a super cyclone successively that caused heavy damages to life and property during the helpless situations of the global pandemic. In this paper, we studied the frequency of cyclones from the years 1891 to 2019, i.e., for 129 years, on the Arabian Sea Basin, Bay of Bengal Basin, and land. We have categorized the cyclones according to their wind speeds: (i) cyclonic storms and severe cyclonic storms (CS + SCS) and (ii) depressions, cyclonic storms, and severe cyclonic storms (D + CS + SCS) where depressions, cyclonic storms, and severe cyclonic storms have wind speeds of more than or equal to 17 knots, 34 knots, and 48 knots respectively. We examined the Markovian dependence of the discretized time series of the two categories mentioned earlier for the first, second, third, and fourth order of a two-state Markov chain model. It is found that CS + SCS represents the first-order two-state (FOTS) model of Markov chain and D + CS + SCS represents the second-order two-state (SOTS) model of Markov chain. Thereafter, we have developed autoregressive models for the two categories and checked their goodness of fit using Willmott’s indices of orders 1 and 2. It is found that CS + SCS best represents the autoregressive model of order 5, whereas D + CS + SCS could not be efficiently represented by the developed autoregressive models. So we further developed autoregressive neural networks for D + CS + SCS and obtained a significant hike in the prediction yield. Nevertheless, it is found that both categories are not serially independent.