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M. M. Carter and J. B. Elsner

Abstract

Using results from a factor analysis regionalization of nontropical storm convective rainfall over the island of Puerto Rico, a statistical methodology is investigated for its potential to forecast rain events over limited areas. Island regionalization is performed on a 15-yr dataset, while the predictive model is derived from 3 yr of surface and rainfall data. The work is an initial attempt at improving objective guidance for operational rainfall forecasting in Puerto Rico. Surface data from two first-order stations are used as input to a partially adaptive classification tree to predict the occurrence of heavy rain. Results from a case study show that the methodology has skill above climatology—the leading contender in such cases. The algorithm also achieves skill over persistence. Comparisons of forecast skill with a linear discriminant analysis suggest that classification trees are an easier and more natural way to handle this kind of forecast problem. Synthesis of results confirms the notion that despite the very local nature of tropical convection, synoptic-scale disturbances are responsible for prepping the environment for rainfall. Generalizations of the findings and a discussion of a more realistic forecast setting in which to apply the technology for improving tropical rainfall forecasts are given.

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J. B. Elsner and A. A. Tsonis
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A. A. Tsonis and J. B. Elsner

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In a recent paper Mohan et al. presented a reanalysis of climatic data using concepts from the theory of dynamical systems. The data is the oxygen isotope ratio 18O/16O record of the V28-238 deep sea care covering a period of a million years at a sampling time of 2 Kiloyears. This dataset was first analysed by Nicolis and Nicolis who reported that the dynamics of the records may be explained by a low-dimensional dynamical system. We take this opportunity to bring to the attention of the scientific community some major problems involved with the reanalysis of the data hoping that this comment will serve as a reference for other analyses of different datasets in the future.

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J. B. Elsner and A. A. Tsonis

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Recent studies have shown how concepts from information theory can be applied to climate models to better understand the problem of climate prediction. This paper describes how information theory, specifically the concept of entropy, can be used in the analysis of short-term precipitation records. The ideas are illustrated through analysis and comparisons of two long, hourly precipitation records. From the results it is concluded that the records are not periodic and are definitely more complex than records of random origin. This complexity, however, arises from underlying deterministic rules indicating the potential for predictability.

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A. A. Tsonis and J. B. Elsner
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J. B. Elsner and C. P. Schmertmann

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This study shows that hindcasts of seasonal numbers of intense Atlantic hurricanes made using a nonlinear statistical model are superior to those made by linear statistical models previously described in the literature. A fully cross-validated Poisson model achieves an increase of nearly 40% in hindcast skill when compared to a fully cross-validated linear model. Improvements are most evident for years with relatively large numbers of intense hurricanes. It is suggested that a significant improvement in forecast skill is possible with the Poisson model. A prediction for the 1993 season is made, and calls for two intense hurricanes to visit the Atlantic basin.

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A. A. Tsonis and J. B. Elsner

Some of the basic principles of the theory of dynamical systems are presented, introducing the reader to the concepts of chaos theory and strange attractors and their implications in meteorology. New numerical techniques to analyze weather data according to the above theory are also presented.

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J. B. Elsner and C. P. Schmertmann

Abstract

This study explains the method of cross validation for assessing forecast skill of empirical prediction models. Cross validation provides a relatively accurate measure of an empirical procedure's ability to produce a useful prediction rule from a historical dataset. The method works by omitting observations and then measuring “hindcast” errors from attempts to predict these missing observations from the remaining data. The idea is to remove the information about the omitted observations that would be unavailable in real forecast situations and determine how well the chosen procedure selects prediction rules when such information is deleted. The authors examine the methodology of cross validation and its potential pitfalls in practical applications through a set of examples. The concepts behind cross validation are quite general and need to be considered whenever empirical forecast methods, regardless of their sophistication are employed.

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J. B. Elsner and A. A. Tsonis

We present a brief overview of some new methodologies for making predictions on time-series data. These ideas stem from two rapidly growing fields: nonlinear dynamics (chaos) theory and parallel distributed processing. Examples are presented that show the usefulness of such methods in making short-term predictions. It is suggested that such methodologies are capable of distinguishing between chaos and noise. Implications of these ideas and methods in the study of weather and climate are discussed.

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