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Nonlin. Processes Geophys., 25, 335-353, 2018
https://doi.org/10.5194/npg-25-335-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
02 May 2018
Idealized models of the joint probability distribution of wind speeds
Adam H. Monahan School of Earth and Ocean Sciences, University of Victoria, P.O. Box 3065 STN CSC, Victoria, BC, Canada, V8W 3V6
Abstract. The joint probability distribution of wind speeds at two separate locations in space or points in time completely characterizes the statistical dependence of these two quantities, providing more information than linear measures such as correlation. In this study, we consider two models of the joint distribution of wind speeds obtained from idealized models of the dependence structure of the horizontal wind velocity components. The bivariate Rice distribution follows from assuming that the wind components have Gaussian and isotropic fluctuations. The bivariate Weibull distribution arises from power law transformations of wind speeds corresponding to vector components with Gaussian, isotropic, mean-zero variability. Maximum likelihood estimates of these distributions are compared using wind speed data from the mid-troposphere, from different altitudes at the Cabauw tower in the Netherlands, and from scatterometer observations over the sea surface. While the bivariate Rice distribution is more flexible and can represent a broader class of dependence structures, the bivariate Weibull distribution is mathematically simpler and may be more convenient in many applications. The complexity of the mathematical expressions obtained for the joint distributions suggests that the development of explicit functional forms for multivariate speed distributions from distributions of the components will not be practical for more complicated dependence structure or more than two speed variables.
Citation: Monahan, A. H.: Idealized models of the joint probability distribution of wind speeds, Nonlin. Processes Geophys., 25, 335-353, https://doi.org/10.5194/npg-25-335-2018, 2018.
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Short summary
Bivariate probability density functions (pdfs) of wind speed characterize the relationship between speeds at two different locations or times. This study develops such pdfs of wind speed from distributions of the components, following a well-established approach for univariate distributions. The ability of these models to characterize example observed datasets is assessed. The mathematical complexity of these models suggests further extensions of this line of reasoning may not be practical.
Bivariate probability density functions (pdfs) of wind speed characterize the relationship...
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