Improved Stockwell transform on the estimation of the evolutionary spectrum for nonstationary typhoons

Abstract

Accurate evolutionary power spectral density (EPSD) estimation for monitored typhoon winds is of significance in studying time-varying properties. Current estimation approaches, such as Priestley-based and wavelet-based approaches, all have certain limitations in their widespread practical applications. In this study, an improved Stockwell-transformed-based (IST) approach was proposed to enhance its estimation accuracy and applicability. A novel window function, called the k-th power half cosine function, was adopted to represent the traditional Gaussian window in the traditional ST, which could adaptively control the window size by selecting different parameters of k. To reduce the estimation error, the even k was recommended, and the series expansion was also employed. Two numerical cases that represented uniformly modulated winds and non-uniformly modulated winds were simulated to investigate the estimation performance of the proposed IST. Moreover, the Priestley-based and wavelet-based approaches were also applied to compare the estimated results with IST. The comparison demonstrated greater accuracy of the IST, which indicated that IST outperformed the Priestley-based and wavelet-based approaches. Finally, the IST was successfully carried out to estimate time-varying spectra for monitored typhoon Jongdary (2018) atop the Shanghai Tower (ST). The investigation for monitored typhoon spectra revealed that typhoon winds displayed remarkably time-varying spectra. A time-varying Von Karman spectrum model was utilized to characterize the estimated EPSDs by the IST, and its characterization performance was evaluated in detail. Therefore, this study could provide a valuable route to study nonstationary typhoon spectra.