Wind resource and site assessment - Wind Power Generation and Wind Turbine Design - page 66

application. Here the emphasis should be on the energy containing part of the
spectrum. Thus a moment fi tting method is normally used with focus on medium
to high wind speeds but not extreme wind speeds. The requirements for determin-
ing the two Weibull parameters are that the total wind energy in the fi tted Weibull
distribution and the observed distribution are equal. Additionally the frequencies
of occurrence of the wind speeds higher than the observed average wind speed
have to be the same for both distributions. The combination of these two require-
ments leads to an equation in k only, which can be solved by a standard root-
fi nding algorithm.
As a rough approximation, the relationship between the Weibull parameter A
and k and the mean wind speed can be described as follows:

1/ k

0.434

⎛ ⎞

UA ≈ 0.568 + (5)

⎜ ⎟

⎝ ⎠

k

4 Spatial extrapolation

4.1 Introduction

Analyses of wind speed measurements lead to a detailed description of the wind
climate at one point. In order to calculate the energy yield of the whole wind fi eld,
the results from the measurements have to be extrapolated horizontally to cover
the wind farm area, and vertically if the measurements were not performed at hub
height. Normally for the spatial extrapolation, computer models are used which
are primed with wind speed data measured on site.
In the following section, parameters affecting the vertical extrapolation are
described. This is followed by a description of the concept of fl ow models, and
particularly WAsP as the most commonly used model in the industry.

4.2 Vertical extrapolation

4.2.1 Introduction
The planetary boundary layer (PBL), also known as the atmospheric boundary
layer (ABL), is the lowest part of the atmosphere and its behaviour is directly
infl uenced by its contact with the planetary surface. Above the PBL is the "free
atmosphere" where the wind is approximately geostrophic (parallel to the iso-
bars) while within the PBL the wind is affected by surface drag and turns across
the isobars. The free atmosphere is usually non-turbulent, or only intermittently
turbulent. The surface layer is the lowest part of the ABL. Its height is normally
taken as around 10% of the ABL height but varies signifi cantly during seasons and
day times.
The change of wind speed with height is described by the vertical wind pro-
fi le, which is the key for extrapolation of the measured wind speed to hub height.
Generally the wind speed increases with increasing height above the ground.