Deterministic Chaos in Tropical Atmospheric Dynamics

We examine an 11-year data set from the tropical weather station of Tlaxcala, Mexico. We find that mutual information drops quickly with the delay, to a positive value which relaxes to zero with a time scale of 20 days. We also examine the mutual dependence of the observables and conclude that the data set gives the equivalent of 8 variables per day, known to a precision of $2\%$. We determine the effective dimension of the attractor to be $D_{eff} \approx 11.7$ at the scale $3.5\% < R/R_{max} < 8\%$. We find evidence that the effective dimension increases as $R/R_{max} \to 0$, supporting a conjecture by Lorenz that the climate system may consist of a large number of weakly coupled subsystems, some of which have low-dimensional attractors. We perform a local reconstruction of the dynamics in phase space; the short-term predictability is modest and agrees with theoretical estimates. Useful skill in predictions of 10-day rainfall accumulation anomalies reflects the persistence of weather patterns, which follow the 20-day decay rate of the mutual information.