Wind Energy Handbook. Michael Barton Graham
Wind spectrum from Brookhaven based on work by Van der Hoven (1957)
2.2 Geographical variation in the wind resource
Ultimately the winds are driven almost entirely by the sun's energy, causing differential surface heating. The heating is most intense on land masses closer to the equator, and obviously the greatest heating occurs in the daytime, which means that the region of greatest heating moves around the earth's surface as it spins on its axis. Warm air rises and circulates in the atmosphere to sink back to the surface in cooler areas. The resulting large‐scale motion of the air is strongly influenced by Coriolis forces due to the earth's rotation. The result is a large‐scale global circulation pattern. Certain identifiable features of this such as the trade winds and the ‘roaring forties’ are well known.
The non‐uniformity of the earth's surface, with its pattern of land masses and oceans, ensures that this global circulation pattern is disturbed by smaller‐scale variations on continental scales. These variations interact in a highly complex and non‐linear fashion to produce a somewhat chaotic result, which is at the root of the day‐to‐day unpredictability of the weather in particular locations. Clearly though, underlying tendencies remain that lead to clear climatic differences between regions. These differences are tempered by more local topographical and thermal effects.
Hills and mountains result in local regions of increased wind speed. This is partly a result of altitude – the boundary layer flow over the earth's surface means that wind speed generally increases with height above the ground, and hill tops and mountain peaks may ‘project’ into the higher wind speed layers. It is also partly a result of the acceleration of the wind flow over and around hills and mountains and funnelling through passes or along valleys aligned with the flow. Equally, topography may produce areas of reduced wind speed, such as sheltered valleys or areas in the lee of a mountain ridge or where the flow patterns result in stagnation points.
Thermal effects may also result in considerable local variations. Coastal regions are often windy because of differential heating between land and sea. While the sea is warmer than the land, a local circulation develops in which surface air flows from the land to the sea, with warm air rising over the sea and cool air sinking over the land. When the land is warmer, the pattern reverses. The land will heat up and cool down more rapidly than the sea surface, and so this pattern of land and sea breezes tends to reverse over a 24‐hour cycle. These effects were important in the early development of wind power in California, where an ocean current brings cold water to the coast, not far from desert areas that heat up strongly by day. An intervening mountain range funnels the resulting air flow through its passes, generating locally very strong and reliable winds (which are well correlated with peaks in the local electricity demand caused by air conditioning loads).
Thermal effects may also be caused by differences in altitude. Thus, cold air from high mountains can sink down to the plains below, causing quite strong and highly stratified ‘downslope’ winds.
The brief general descriptions of wind speed variations in Sections 2.1–2.5 are illustrative, and more detailed information can be found in standard meteorological texts. Section 10.1.3, in Chapter 10, describes how the wind regimes at candidate sites can be assessed, while wind forecasting is covered in Section 2.9 and Section 11.6.3.
Section 2.6 presents a more detailed description of the high frequency wind fluctuations known as turbulence, which are crucial to the design and operation of wind turbines and have a major influence on wind turbine loads. Extreme winds are also important for the survival of wind turbines, and these are described in Section 2.8.
2.3 Long‐term wind speed variations
There is evidence that the wind speed at any particular location may be subject to very slow long‐term variations. Although the availability of accurate historical records is a limitation, careful analysis by, for example, Palutikof et al. (1991) has demonstrated clear trends. Clearly these may be linked to long‐term temperature variations for which there is ample historical evidence. There is also much debate at present about the likely effects of global warming, caused by human activity, on climate, and this will undoubtedly affect wind climates in the coming decades.
Apart from these long‐term trends, there may be considerable changes in windiness at a given location from one year to the next. These changes have many causes. They may be coupled to global climate phenomena such as el niño, changes in atmospheric particulates resulting from volcanic eruptions, and sunspot activity, to name a few.
These changes add significantly to the uncertainty in predicting the energy output of a wind farm at a particular location during its projected lifetime.
2.4 Annual and seasonal variations
While year‐to‐year variation in annual mean wind speeds remains hard to predict, wind speed variations during the year can be well characterised in terms of a probability distribution. The Weibull distribution has been found to give a good representation of the variation in hourly mean wind speed over a year at many typical sites. This distribution takes the form
(2.1)
where F(U) is the fraction of time for which the hourly mean wind speed exceeds U. It is characterised by two parameters, a ‘scale parameter’ c and a ‘shape parameter’ k, which describes the variability about the mean. The parameter c is related to the annual mean wind speed
(2.2)
where Γ is the complete gamma function. This can be derived by consideration of the probability density function
(2.3)
because the mean wind speed is given by
(2.4)
A special case of the Weibull distribution is the Rayleigh distribution, with k = 2, which is actually a fairly typical value for many locations. In this case, the factor Γ(1 + 1/k) has the value