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Analyzing surface air temperature and rainfall in univariate framework, quantifying uncertainty through Shannon entropy and prediction through artificial neural network

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Abstract

The current research reports a univariate analysis of 2 important climatological parameters surface air temperature and rainfall over North East India over annual scale characterized by various degrees of non-linearity. An Autocorrelation study reveals that although the surface air temperature is characterized by an approximate sinusoidal pattern, the rainfall has no apparent pattern. As both the time series have continuous random variables associated with it we need a discretization to make them suitable for study in time domain. First, we test for Markovian behavior against serial independence. By appropriate discretization of both the time series the transition probabilities are computed to test for Two State Markov Chain model with different orders. A chi square test reveals that although the surface air temperature time series follows the Markov Chain model of 1st Order, the annual rainfall is serially independent. The steady state transition probabilities are computed for surface air temperature and subsequently autoregressive models upto order 4 with the help of Yule-Walker Equations. It was further observed that the 2nd order model satisfied the stationarity conditions. Subsequently to have a general overview of the stationarity, Unit Root Test is carried out for both the time series. For surface air temperature a root was found to exist inside the circumference of the unit circle while for rainfall time series finds a root of the characteristic equation outside unit circle. This indicates stationarity of the surface air temperature time series for its 1st order differences and non-stationarity of rainfall time series. Based on this, Autoregressive Integrated Moving Average (ARIMA(p,q,d)) model is fitted to the rainfall time series for various orders of Autoregression and differencing. Subsequently the performance of ARIMA has been compared to univariate artificial neural network model with 4 successive realizations as predictor and the 5th one as predictand. In order to test the relative contributions to these meteorological phenomenon, maximization of Shannon entropy is used.

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Acknowledgements

The authors acknowledge the supportive comments from the anonymous reviewers.

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  1. Department of Mathematics, Amity University Kolkata, Major Arterial Road, Action Area II, Newtown, Kolkata, 700135, India

    Samayita Nag Ray & Surajit Chattopadhyay

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  1. Samayita Nag Ray
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Correspondence to Surajit Chattopadhyay.

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Ray, S.N., Chattopadhyay, S. Analyzing surface air temperature and rainfall in univariate framework, quantifying uncertainty through Shannon entropy and prediction through artificial neural network. Earth Sci Inform 14, 485–503 (2021). https://doi.org/10.1007/s12145-020-00555-5

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