A New Approach to Estimate the Parameters of the Joint Distribution of the Wind Speed and the Wind Direction, Modelled with the Angular–Linear Model

Samuel Martínez-Gutiérrez (), Alejandro Merino, Luis A. Sarabia, Daniel Sarabia and Ruben Ruiz-Gonzalez
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Samuel Martínez-Gutiérrez: Department of Digitalization, Higher Polytechnic School, University of Burgos, Avda. Cantabria, s/n, 09006 Burgos, Spain
Alejandro Merino: Department of Digitalization, Higher Polytechnic School, University of Burgos, Avda. Cantabria, s/n, 09006 Burgos, Spain
Luis A. Sarabia: Department of Mathematics and Computing, Faculty of Science, University of Burgos, Plaza Misael Bañuelos, s/n, 09001 Burgos, Spain
Daniel Sarabia: Department of Digitalization, Higher Polytechnic School, University of Burgos, Avda. Cantabria, s/n, 09006 Burgos, Spain
Ruben Ruiz-Gonzalez: Department of Digitalization, Higher Polytechnic School, University of Burgos, Avda. Cantabria, s/n, 09006 Burgos, Spain

Mathematics, 2025, vol. 13, issue 8, 1-22

Abstract: In order to assess the potential and suitability of a location to deploy a wind farm, it is essential to have a model of the joint probability density function of the wind speed and direction, f V , Θ ( v , θ ). The angular–linear model is widely used to obtain the analytical expression of the joint density from the parametric estimation of the probability density functions of wind speed, f V ( v ), and wind direction, f Θ ( θ ). In previous studies, the parameters of the marginal distributions were obtained by fitting the wind measurements to the cumulative distribution function (CDF) using the least squares method and then calculating the probability density function (PDF). In this study, we propose to directly fit the probability density function and then calculate the cumulative distribution function. It is shown that it has both computational and goodness-of-fit advantages. In addition, previous studies have been expanded, analysing the effect of the number of intervals on which wind speed and direction ranges are divided. The new parameter fitting method is evaluated and compared with the original proposal in terms of goodness of fit, using the coefficient of determination R 2 as an estimator both in the probability density function ( R 2 pdf ) and in the cumulative distribution function ( R 2 cdf ). The computational times required to estimate the parameters using both methods will also be compared. The new approach is faster, and the goodness of the fitting is satisfactory for both estimators: it produces a better R 2 pdf , without significantly affecting the R 2 cdf , in contrast to the initial one where the R 2 pdf is smaller.

Keywords: wind speed; wind direction; joint probability distributions; parameter estimation; computation time (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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