Wavelet Scale Variance Analysis of Wind Extremes in Mountainous Terrains

Abstract

The 10-min average wind speed series recorded at 130 stations distributed rather homogeneously in the territory of Switzerland are investigated. Fixing a percentile-based threshold of the wind speed distribution, a wind extreme is defined as the duration of the sequence of consecutive wind values above the threshold. This definition allows to analyze the sequence of extremes as a temporal point process marked by their duration. Representing the sequence of wind extremes by the inter-extreme interval series, the wavelet variance, a useful tool to investigate the variance of a time series across scales, was applied in order to find a link between the wavelet scales and several topographic parameters. Our findings suggest that the mean duration of wind extremes and mean inter-extreme time are positively correlated and that such relationship depends on the threshold of the wind speed. Furthermore, the threshold of the wind speed distribution correlates best with a terrain parameter related to the Laplacian of terrain elevations; and, in particular, for wavelet scales less than 3, the terrain exposure may explain the formation of extreme wind speeds.

Wavelet Packet Decomposition for IEC Compliant Assessment of Harmonics under Stationary and Fluctuating Conditions

“…The main advantage of DWT is that, while DFT requires a stationary, perfectly periodic sinusoidal signal to work properly, this is not a requirement for DWT. This signal processing tool has a wide range of applications, including power systems, where it proved to be extremely useful in signal denoising, short time predictions, fault detection, and energy management [9][10][11][12][13][14], as well as for Power Quality [15][16][17][18][19]. From WT, Wavelet Packet Decomposition (WPD) was derived, generalizing the link between wavelets and Multiresolution Analysis (MRA).…”