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H. Waelbroeck

Abstract

An 11-year dataset from the tropical weather station of Tlaxcala, Mexico, is examined. It is found that mutual information drops quickly with the delay, to a positive value that relaxes to zero with a timescale of 20 days. The mutual dependence of the observables is also examined and it is concluded that the dataset gives the equivalent of eight variables per day, known to a precision of 2%. It is determined that the effective dimension of the attractor is D eff ≈ 11.7 at the scale 3.5% < R/R max < 8%. Evidence is found that the effective dimension increases as R/R max → 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. A local reconstruction of the dynamics in phase space is performed; 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.

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H. Waelbroeck, R. López-Pen̄a, T. Morales, and F. Zertuche

Abstract

The authors propose a weather prediction model based on a local reconstruction of the dynamics in phase space, using an 11-year dataset from Tlaxcala, Mexico. A vector in phase space corresponds to T consecutive days of data; the best predictions are found for T = 14. The prediction for the next day, x 0f L(x 0), is based on a local reconstruction of the dynamical map f in an η ball centered at x 0. The high dimensionality of the phase space implies a large optimal value of η, so that the number of points in an η ball is sufficient to reconstruct the local map. The local approximation f Lf is therefore not very good and the prediction skill drops off quickly at first, with a timescale of 2 days. On the other hand, the authors find useful skill in the prediction of 10-day rainfall accumulations, which reflects the persistence of weather patterns. The mean-squared error in the prediction of the rainfall anomaly for the year 1992 was 64% of the variance, and the early beginning of the rain season was correctly predicted.

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