Analysis of atmospheric wind and gust prediction

Abstract

This thesis examines how atmospheric wind varies across a broad range of spatial and temporal scales, from fluctuations over seconds to patterns extending hundreds of kilometers. The analysis is based on long-term measurements from the offshore research platform FINO1 in the North Sea. A detailed investigation of scaling features in energy spectra and structure functions is carried out, using the local Taylor hypothesis to relate temporal observations to spatial flow structures. Despite varying weather conditions, the smallest scales below the measurement height consistently exhibit signatures of classical three-dimensional turbulence. At intermediate scales between the measurement height and the typical height of the planetary boundary layer, the influence of the Earth's surface becomes apparent through patterns characteristic of wall-bounded turbulence. On horizontal scales of tens or hundreds of kilometers, buoyancy-driven internal gravity waves and quasi-two-dimensional geostrophic turbulence shaped by Earth's rotation dominate the wind field. The transition between the gravity-wave and the geostrophic regime manifests itself in a remarkably abrupt sign change of the third-order structure function. It occurs at a scale of 500 km, which can be explained by the maximum horizontal length scale permitted by gravity wave dynamics. In both regimes, the scaling of structure functions agrees well with aircraft measurements reported in the literature. The analysis demonstrates that applying the Taylor hypothesis locally is essential for obtaining the correct scaling behavior. Distributions of velocity increments reveal an additional, secondary peak at scales corresponding to the gravity-wave regime. These secondary maxima play a decisive role in producing the observed scaling of structure functions. Moreover, anticorrelations in increment time series are linked to the constraint of finite turbulent kinetic energy. The final part of the thesis focuses on short-term gust prediction. Existing wind gust definitions in the literature are critically reviewed, and gusts are defined on a physical basis as sudden changes in drag force or wind power. Autoregressive models may be used to predict single gust events, but they tend to forecast gusts persistently in gusty phases. To address this problem, ARCH-type models are employed to predict the variance of wind speed increments, which correlates with the number of gusts within a given time window. This approach offers a complementary perspective on short-term gust predictability relevant for wind energy and aviation