Author(s): V. Jothiprakash
Linked Author(s): V. Jothiprakash
Keywords: Chaos; Phase space construction; Correlation integral (Cr); Correlation exponent; Pan Evaporation
Abstract: In the present study, it is aimed to study the behaviour of daily pan evaporation time series data using chaos theory. The correlation dimension method (CDM), one of the most common methods of chaotic analysis is used in the present study. Ten years of daily pan evaporation data collected from a meteorological station located at Tirunelveli, Tamil Nadu, India is employed in the present study. In CDM, Heaviside step function is used to find out the correlation integral (Cr) for various steps in terms of radius (r). The next step is finding the slope of the curve (log r Vs log Cr) namely correlation exponent (υ) for various embedding dimension (m). The scaling region (the most linear part of log r Vs log Cr curve) in the Heaviside step function has to be identified to find the correlation exponent (υ). Based upon the relationship between “m” and “υ”, the behaviour of the system can be classified as chaotic (increasing correlation exponent with embedding dimension and finally saturating), stochastic (increasing correlation exponent with increase in embedding dimension) or deterministic (constant correlation exponent for all embedding dimension). From the present study it is found that correlation dimension method gives three different observations, (i) The correlation dimension is around six in the present case (ii) the correlation exponents are changing in a particular pattern for an embedding dimension up to 10 and then changing to some other pattern for the embedding dimension ranging from 11 to 20, (iii) However, both the groups are merging towards a single number (six in the present case). Thus, the correlation dimension method (CDM) provides not only the behavioral study but also gives an indication on number of dimensions required to model the pan evaporation process successfully.
Year: 2013