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Euclidean Distance Based Permutation Methods in Atmospheric Science

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Abstract

The majority of existing statistical methods inherently involve complex nonmetric analysis spaces due to their least squares regression origin; consequently, the analysis space of such statistical methods is not consistent with the simple metric Euclidean geometry of the data space in question. The statistical methods presented in this paper are consistent with the data spaces in question. These alternative methods depend on exact and approximate permutation procedures for univariate and multivariate data involving cyclic phenomena, autoregressive patterns, covariate residual analyses including most linear model based experimental designs, and linear and nonlinear prediction model evaluations. Specific atmospheric science applications include climate change, Atlantic basin seasonal tropical cyclone predictions, analyses of weather modification experiments, and numerical model evaluations for phenomena such as cumulus clouds, clear-sky surface energy budgets, and mesoscale atmospheric predictions.

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Authors and Affiliations

  1. Department of Statistics, Colorado State University, Fort Collins, CO, 80523-1877, USA

    Paul W. Mielke Jr.

  2. Department of Sociology, Colorado State University, Fort Collins, CO, 80523-1784, USA

    Kenneth J. Berry

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  1. Paul W. Mielke Jr.
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  2. Kenneth J. Berry
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Mielke, P.W., Berry, K.J. Euclidean Distance Based Permutation Methods in Atmospheric Science. Data Mining and Knowledge Discovery 4, 7–27 (2000). https://doi.org/10.1023/A:1009824531876

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