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Tropical Cyclone Forecast Errors and the Multimodal Bivariate Normal Distribution

Harold L. CrutcherAsheville, NC, 28804

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Charles J. NeumannNational Hurricane Center, NOAA, Coral Gables, FL 33146

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Joseph M. PelissierNational Hurricane Center, NOAA, Coral Gables, FL 33146

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Abstract

This study focuses on the use of the bivariate normal distribution model to describe spatial distributions of tropical cyclone forecast errors. In this connection, it is found that forecast errors from the entire Atlantic tropical cyclone basin (Gulf of Mexico, Caribbean and North Atlantic) are multimodal and the fitting of these collective data to the usual unimodal bivariate normal distribution will be judged invalid by the usual statistical goodness-of-fit tests. While this is a recognized pitfall in classical statistics, it is often overlooked in meteorological application. The isolation of the clusters (components) and their statistical characteristics permit the issuance of forecast positions accompanied by more representative error ellipses.

The study continues with a bivariate clustering analysis of a set of 979 tropical cyclone 24 h forecast errors for the Gulf of Mexico, Caribbean and North Atlantic. These errors were collected from the entire tropical cyclone basin without regard to season or geography. The analysis shows that these errors could be drawn from two or possibly three parent bivariate normal distributions. A further analysis of the two clusters was made and it is shown that group membership is essentially a function of forecast “difficulty.” One group (essentially storms located in the Caribbean and Gulf of Mexico) has about one-half the component standard errors of the other group (the more northerly storms). A physical interpretation of the more complex three-mode clustering was not accomplished.

The study has application with regard to the future development of statistical prediction models and in connection with a recently inaugurated tropical cyclone “strike” probability concept.

Abstract

This study focuses on the use of the bivariate normal distribution model to describe spatial distributions of tropical cyclone forecast errors. In this connection, it is found that forecast errors from the entire Atlantic tropical cyclone basin (Gulf of Mexico, Caribbean and North Atlantic) are multimodal and the fitting of these collective data to the usual unimodal bivariate normal distribution will be judged invalid by the usual statistical goodness-of-fit tests. While this is a recognized pitfall in classical statistics, it is often overlooked in meteorological application. The isolation of the clusters (components) and their statistical characteristics permit the issuance of forecast positions accompanied by more representative error ellipses.

The study continues with a bivariate clustering analysis of a set of 979 tropical cyclone 24 h forecast errors for the Gulf of Mexico, Caribbean and North Atlantic. These errors were collected from the entire tropical cyclone basin without regard to season or geography. The analysis shows that these errors could be drawn from two or possibly three parent bivariate normal distributions. A further analysis of the two clusters was made and it is shown that group membership is essentially a function of forecast “difficulty.” One group (essentially storms located in the Caribbean and Gulf of Mexico) has about one-half the component standard errors of the other group (the more northerly storms). A physical interpretation of the more complex three-mode clustering was not accomplished.

The study has application with regard to the future development of statistical prediction models and in connection with a recently inaugurated tropical cyclone “strike” probability concept.

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