Proper orthogonal decomposition of two vertical profiles of full-scale nonstationary downburst wind speeds[lzcl]

The paper proposes a novel analysis framework for nonstationary wind speeds, from which accumulated results can potentially lead to or enhance empirical nonstationary wind speed models such as the hybrid one for downbursts in (Eng. Struct. 26 (2004) 619). This framework is motivated by the proper orthogonal decomposition (POD) technique and consists of four major steps: separation, POD, approximation and property inference. In the first step, the original wind speed time histories are separated into their time-varying mean speeds and fluctuating speeds through wavelet shrinkage, which is a promising new tool for smoothing; fluctuating speeds are further expressed as the product of their time-varying standard deviations and normalized fluctuating speeds with unit variance. In the second step, the POD is applied to the time-varying means, standard deviations and normalized fluctuation. In the third step, by properly selecting the number of retained modes, the original time series can be approximated to a numerical model. Finally, wind properties such as velocity vertical profiles and turbulence vertical profiles can be calculated from the model. The POD employed herein is a specific POD for arbitrary multivariate data representation. The normalized fluctuations are characterized by both their power spectral densities (PSD) and evolutionary power spectral densities (EPSD). The concept of EPSD for nonstationary processes is briefly presented and one EPSD estimator is given. Specifically, the PSD/EPSD of an original process is related to the PSD/EPSD of the principal coordinate process obtained by the POD. This framework is applied to two sets of nonstationary full-scale thunderstorm downburst wind speed time series. Many appealing downburst properties are obtained and the benefit of the POD is demonstrated.