Effect of noise reduction in nonlinear dynamic analysis of maximum daily temperature series in Kerman station

Climate could be known as a set of atmospheric conditions of a dynamic and chaotic system. However, a fundamental problem in estimating the chaotic time series dimension is dealing with the fact that a temporal signal of any natural phenomenon is always contaminated by noise. The objectives of this study are: a) investigating the effect of noise reduction in daily maximum temperature time series on the reconstructed phase space, time delay and embedding dimension; b) quantifying chaos for both time series before and after noise reduction, by using methods such as maximal Lyapunov exponent and correlation dimension; and c) comparing the prediction accuracy in both time series. For this study, we used daily maximum temperature time series of Kerman station for 25 years (1984-2008 AD). The results showed that the embedding dimension and delay time in time series after the noise was reduced (respectively, 5 and 76 days) from those of before (respectively 7 and 82 days). In both time series, the positive maximal Lyapunov exponent (respectively, 0.011 and 0.019) and low correlation dimension (respectively, 2.78 and 2.85) resemble the chaotic system. However, noise reduction can have some effects on quantifying chaos and the accuracy of prediction by reducing the random component, so, for the analysis of nonlinear dynamics of time series, noise reduction is essential, but this reduction should not destroy the determinism component of the system.