Fractal-based numerical simulation of multivariate typhoon wind speeds utilizing weierstrass mandelbrot function

Abstract

This paper proposes a fractal-based technique for simulating multivariate nonstationary wind fields by the stochastic Weierstrass Mandelbrot function. Upon conducting a systematic fractal analysis, it was found that the structure function method is more suitable and reliable than the box counting method, variation method, and R/S analysis method for estimating the fractal dimension of the stochastic wind speed series. Wind field measurement at the meteorological gradient tower with a height of 356 m in Shenzhen was conducted during Typhoon Mandelbrot (1983). Significant non-stationary properties and fractal dimensions of typhoon wind speed data at various heights were analyzed and used to demonstrate the effectiveness of the proposed multivariate typhoon wind speed simulation method. The multivariate wind speed components simulated by the proposed fractal-based method are in good agreement with the measured records in terms of the fractal dimension, standard deviation, probability density function, wind spectrum and cross-correlation coefficient.