A Markov chain approach to the predictability of surface temperature over the northeastern part of India
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ORIGINAL PAPER
A Markov chain approach to the predictability of surface temperature over the northeastern part of India Samayita Nag Ray 1 & Sanghita Bose 1 & Surajit Chattopadhyay 1 Received: 16 May 2020 / Accepted: 3 November 2020 # Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract The present study reports a two-state Markov chain approach as well as an autoregressive approach to study the behavior of the surface temperature time series over northeast India. Considering the minimum requirement of the chi-square test, 1998–2007 (> 100 months) have been considered for testing the Markovian and autoregressive behavior. The monthly surface temperature time series involves monthly data that corresponds to a continuous random variable. This random variable has been discretized to binary data, and the transition probabilities have been computed up to the fourth-order Markov chain model. The best order of Markov chain has been derived through the minimization of the Bayesian information criterion (BIC). By analyzing the time series autocorrelation function and the Akaike information criteria (AIC), the autoregressive model of order two has been found to be a representative and the best autoregressive method for the average monthly time series of surface temperatures over northeast India. Keywords Surface temperature . Northeast India . Two-state Markov chain . BIC . Autoregression
1 Introduction Profile of atmospheric temperature has a considerable role to play in meteorology. A plethora of literature, including Dash et al. (2007), Kothawale and Rupa Kumar (2005), Kothawale et al. (2010), and Karmakar et al. (2019), have demonstrated the significance of exploring the atmospheric temperature in various scales. The scales may vary from daily, monthly, to global. In the study of Kothawale and Rupa Kumar (2005), it has been demonstrated how the rising monsoon temperatures led to a weakened seasonal asymmetry of temperature trends in India. In more recent work, a study by Ross et al. (2018) reported the patterns of change in surface temperature in the decadal scale over India. According to Ross et al. (2018), there has been a steady warming over northwestern and southern India and cooling has occurred in northeastern and southwest India. It was explained in their study that the cooling of the underlying surface of northeast India is caused by the absorption of the solar radiation by the adjacent oceanic region and
* Surajit Chattopadhyay [email protected] 1
Department of Mathematics, Amity University, Kolkata, Major Arterial Road, Action Area II, Newtown, Kolkata 700135, India
the brown haze over the country. After carrying out a MannKendall trend analysis, Mondal et al. (2015) reported a significant variation in the minimum temperature in different spatial scales in India. In the last few decades, the idea of the Markov chain (Wilks 2006) has become a potential tool to explore a discrete time series generated as a sequence of realizations of a random variable characterized by dichotomy (yes/n
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