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 entropyK ₂ of the approximation of Kolmogorov’s entropy, the fractional dimensionD = 7.7 ∼ 7.9 and the positive valueK ₂ ≈ 0.1 are obtained. This shows that the attractor for the short-term weather evolution in the monsoon region of China exhibits a chaotic motion. The estimate ofK ₂ yields a predictable time scale of about ten days. This result is in agreement with that obtained earlier by the dynamic-statistical approach. The effects of the lag time τ on the estimate ofD andK ₂ are investigated. The results show thatD andK ₂ 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.