Prediction of Tropical Rainfall by Local Phase Space Reconstruction

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  • 1 Instituto de Ciencias Nucleares, UNAM, Mexico
  • | 2 Centro de Ciencias de la Atmósfera, UNAM, Mexico
  • | 3 Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, UNAM, Cuernavaca, Morelos, Mexico
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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, x0fL(x0), is based on a local reconstruction of the dynamical map f in an η ball centered at x0. 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 fLf 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.

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, x0fL(x0), is based on a local reconstruction of the dynamical map f in an η ball centered at x0. 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 fLf 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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