Directional Wind Spectrum Description using Bivariate L1 Norm RBFs

In this paper, the simplest directional wind spectrum description is given using surrogate bivariate polynomial radial basis functions (PRBF) with L1 norm smoothed by dense boundary points distribution, which enables an accurate description of the geometry and the calculation of the volume below the observed surface when belonging double integral is known.For that purpose, the direct solution of double integral below the descriptive surface is given for bivariate polynomial RBFs with integer exponents, which is examined for accuracy on two examples, for Franke's 2D function and upper hemisphere.After proven accurate in those examples, the direct description of the directional wind spectrum and the calculation of the joint density function of the wind spectrum is done in the paper, thus proving PRBFs as an efficient method for wind spectrum description.In that way, it is possible to calculate the joint density function (JDF) of the actual measured directional wind spectrum analytically, instead of the theoretical calculations used so far.