Symbol sequence analysis of climatic time signals

Abstract

The conditional entropy of two symbolic sequences encoded faithfully from different chaotic time signal data is minimised at zero relative shift of the two signals if the signals have their origin in same underlying dynamics. We show that this minimum in conditional entropies E(Z/X) and E(X/Z) obtained after suitably 'coarse-graining' the time signals of, say, variables X and Z have marked differences depending upon the degree of dynamical coupling of the variables in the model. This technique has also been shown to be useful in studying delayed dependences of time signals. Application is made to climate data of four meteorological stations in India, namely New Delhi, Jaipur, Sundernagar and Chennai in order to determine (a) the commonality of underlying dynamics, (b) relative strength of dynamical coupling of different variables and (c) the delay implicit in the dynamics. The method appears robust to measurement noise.