Determination of Kolmogorov Entropy of Chaotic Attractor Included in One-Dimensional Time Series of Meteorological Data

The 1970-1985 day to day averaged pressure dataset of Shanghai and the extension method in phase space are used to calculate the correlation dimension D and the second-order Renyi entropy K2 of the approximation of Kolmogorov’s entropy, the fractional dimension D = 7.7~7.9 and the positive value K2 ≈ 0.1 are obtained. This shows that the attractor for the short-term weather evolution in the monsoon region of China exhibits a chaotic mo-tion. The estimate of K2 yields a predictable time scale of about ten days. This result is in agreement with that ob-tained earlier by the dynamic-statistical approach.The effects of the lag time τ on the estimate of D and K2 are investigated. The results show that D and K2 are convergent with respect to τ. The day to day averaged pressure series used in this paper are treated for the extensive phase space with τ = 5, the coordinate components are independent of each other; therefore, the dynamical character quantities of the system are stable and reliable.