THE CLIMATE ADJUSTMENT PROCESS - Wind Resource Assessment: A Practical Guide to Developing a Wind Project - page 169

deviations between prediction and reality. As a result, just a few outlying data points,
such as may occur in wind data that have not been properly quality-controlled, can
pull the fitted line significantly to one side. For this reason, professional statisticians
often prefer other, more robust fitting methods, but for ordinary users, the simplicity
and ease-of-use of the linear regression usually make it the method of choice.
Linear regression does not assume a perfect correlation. When the correlation is
weak, the slope tends to be small, so variations in the reference wind speed have little
effect on the predicted target speed. Another advantage of linear regression is that
it can easily incorporate more than one reference station at a time (a multiple linear
regression). Sometimes different reference stations capture different aspects of the
target site's wind climate; for example, a coastal station may be more representative
of the target site than an inland station when the winds come from over the ocean,
while the reverse is true when the winds originate from over land. The weight given
to each reference station in the fit depends on that station's correlation with the target
site and its statistical independence from other stations. A multiple linear regression
can be a handy way of improving the overall correlation and allowing an objective
determination of the relative value of different stations. However, if too many reference
stations are used in multiple linear regression, and especially if they are strongly
correlated, there is a risk that the regression will be overspecified. This can produce
poor results.

12.4.3 Predicting the Speed Frequency Distribution
A significant drawback of linear regression is that it tends to understate the degree
of variation of the target wind speeds, especially when the correlation is weak. For a
given linear equation y

= mx + b , the variance, or standard deviation squared, of the

predicted speeds is given by

2
y

m 2

2
x

σ = σ (12.5)

The weaker the correlation, the smaller the slope m and therefore the smaller the
variance of the predicted wind speeds. To accurately predict the speed frequency
distribution, in general, something other than a linear regression is required.
One simple but often effective approach is to scale the observed target site's wind
speeds to the predicted long-term mean. Each speed value in the target data set is
multiplied by the ratio of the predicted long-term mean to the observed mean:

v ( pred )
v ( obs )

v ( obs )
i

v ( pred )
i

= (12.6)

This assumes, in effect, that the data measured at the site accurately capture the relative
variation of the wind, so only the mean needs to be adjusted. In practice, this is usually
a good assumption: rarely does the estimated power production vary by more than
1 - 2% because of variations in the wind speed distribution at the same tower, from
one year to another, for the same mean.