## 1. Introduction

Wind fluctuations on time scales of several minutes to several hours are interesting because they fall in the part of the wind speed spectrum which separates turbulent flow from the mean flow (Stull, 1988). This part of the spectrum is often referred to as the ‘spectral gap’, since many authors have identified a local minimum in the wind speed spectrum at a period close to half an hour (for example, Van der Hoven, 1957; Petersen, 1975; Courtney and Troen, 1990; Yahaya *et al.*, 2003). Based on the assumption of the spectral gap, we might expect there to be little variability in the wind speed on these time scales, but it has been shown that the spectral gap is not always well defined, and that in certain atmospheric conditions it may not exist at all (Gjerstad *et al.*, 1995; Heggem *et al.*, 1998). Wind speed fluctuations on these time scales are not a constant feature of the wind, and therefore exhibit climatological patterns with regard to time of year and other explanatory variables. Atmospheric processes that contribute to the generation of variance in the spectral gap region of the spectrum include large cumulus clouds (Stull, 1988), convective cells (Gjerstad *et al.*, 1995; Heggem *et al.*, 1998) and horizontal roll vortices (Heggem *et al.*, 1998).

Large fluctuations in wind speed on time scales of minutes to hours also present important practical challenges, particularly for offshore engineering and construction projects in locations such as the North Sea. For example, episodes of severe wind variability can have serious implications for large offshore wind farms, because the high concentration of turbines within a small geographical area means that fluctuations in wind speed can be closely coupled to severe power fluctuations (Akhmatov *et al.*, 2007). In particular, large amplitude wind speed variability with periods of several minutes up to several hours has been identified as a recurring and problematic feature in the wind speeds at the Horns Rev offshore wind farm off the west coast of Denmark (Akhmatov, 2007). The time evolving nature of the spectral properties of wind speed and other meteorological variables are also of relevance to statistical forecasting models. For example, the time evolving fluctuations in wind speeds on time scales of minutes to hours must be considered in the application of models which rely on a basic assumption of stationarity of the time series. Therefore, the existence and implications of severe wind fluctuations on time scales of minutes to hours cannot be ignored.

Turbulent fluctuations and wind speed profiles in the North Sea region have been the subject of a number of investigations, due to the importance of turbulent loading on wind turbines and other structures, and to the importance of knowing the hub height wind speed based on measurements at a different height (e.g. Tambke *et al.*, 2005; Peña *et al.*, 2008). Wind resource mapping over the sea (or the climatological average of the wind speed) has also been studied in detail due to its importance for the siting and planning of wind farms (e.g. Barthelmie and Pryor, 2006; Hasager *et al.*, 2006). However, wind variability on time scales of several minutes to several hours falls between these two areas and has received less attention. The problem needs to be studied in a different framework from turbulence (which could be well described by classical spectral analysis given a nearly stationary set of atmospheric conditions), and from climatological averages (in which temporal variation does not play a role).

Several authors have recently addressed the problem of wind and power fluctuations on time scales of minutes to hours, and each has chosen a different technique to study the problem. Akhmatov (2007) investigated power fluctuations (which are assumed to be mainly driven by wind speed fluctuations) at the Horns Rev wind farm by calculating the maximum 10-min change in power and discovered that the largest power fluctuations were experienced when the wind direction was from the westerly sector. Sørensen *et al.* (2008) used the spectral properties of wind speed time series to create models of power production to be used in planning and siting of wind farms, focusing on scales of several minutes to several hours. Vigueras-Rodríguez *et al.* (2010) studied the importance of including both low-frequency wind speed fluctuations and the spatial correlations between them in an aggregated model of wind farm power fluctuations. Studying the problem of fluctuating wind power production on the east coast of Australia, Davey *et al.* (2010) created a metric of wind variability using a moving average of the standard deviation of the band-pass filtered wind speed, then related their metric to large-scale meteorological fields using a random forest model. They found that important predictors of wind variability included fields such as planetary boundary layer height, vertical velocity, wind speed and geopotential height.

The study of wind fluctuations lends itself to treatment in the spectral domain because we are interested in the variability over a certain range of frequencies. However, to isolate certain times when there is enhanced variability on these frequencies, an adaptive spectral analysis method which can uncover the time-evolving spectral behaviour of the time series is needed. A classical Fourier spectrum can either be applied to a long time series to give the best fit, on average, of a set of harmonics to the data, or can be applied to short segments of the data where it is limited by the difficulty of finding particular atmospheric regimes that last long enough to create a meaningful spectrum. Neither of these options is satisfactory if one wishes to describe the evolution in time of certain classes of statistical behaviour. Therefore, for this analysis, an adaptive spectral analysis method called the Hilbert-Huang transform (HHT) was adopted (Huang *et al.*, 1998). The HHT is based on an empirical decomposition of the time series in such a way that instantaneous frequencies and amplitudes in the data can be calculated and combined to form a time-evolving spectrum. It is ideal for this analysis, since it describes the changing statistical properties of the time series. The potential of using the HHT for analysing wind speed time series has been demonstrated and extensively discussed in Vincent *et al.* (2010).

Here, the HHT is used to study wind fluctuations at the Horns Rev wind farm on temporal scales of 1 min to 10 h. To analyse fluctuations with periods of 1–10 h, a 4-year time series of 10 min wind speed observations is used, while the analysis of fluctuations with periods of 1–60 min is based on a 10-month time series of sonic anemometer measurements of frequency of 12 Hz. The flexibility of the method in creating time-evolving and conditionally averaged spectra is exploited to demonstrate climatological patterns between wind fluctuations and several potential explanatory variables including wind direction, time of year, pressure tendency, precipitation and stability. These explanatory variables are footprints of the physical conditions which may be the real underlying cause of particular classes of wind speed behaviour. For example, the wind direction relates to upstream surface conditions as well as the synoptic situation, heavy precipitation is suggestive of generally convective conditions, pressure tendency is a simple proxy for the synoptic cycle and stability is a measure of the buoyancy and shear in the boundary layer. Wind variability as a function of wind speed was also explored, but it was found that there was no strong relationship between wind variability on scales of 1–10 h and wind speed.

The structure of the paper is as follows. In Section 2, the measurement site and the data are described. In Section 3, the background of the HHT and its specific use in this study are discussed. In Section 4, the results are presented. In particular, it is shown that there is a strong directional dependence in wind variability, that the most severe wind variability occurs in autumn and winter, that variability is enhanced when precipitation is observed and that the spectral gap is better defined for stable than for unstable conditions.