WIND ENERGY SYSTEMS - Cd3wd

Chapter 2—Wind Characteristics 2–52
1.1ū for the median (50 percentile) standard deviation and between 0.85ū and 1.15ū for the
90 percentile standard deviation. As expected, these are narrower confidence intervals than
were observed for the single monthly mean.
Example
The yearly mean speed at Dodge City was 11.44 knots at 7 m above the ground level in 1973.
Assume a 50 percentile standard deviation and determine the 90 % confidence interval for the true
long term mean speed.
The confidence interval extends from 11.44/1.1 = 10.40 to 11.44/0.9 = 12.71 knots. We can
therefore say that the long term mean speed lies between 10.40 and 12.71 knots with 90 % confidence.
Our estimate of the long term mean speed by one year’s data can conceivably be improved
by comparing our one year mean speed to that of a nearby National Weather Service station.
If the yearly mean speed at the NWS station was higher than the long term mean speed there,
the measured mean speed at the candidate site can be adjusted upward by the same factor.
This assumes that all the winds within a geographical region of similar topography and a
diameter up to a few hundred kilometers will have similar year to year variations. If the long
term mean speed at the NWS station is ū, the mean for one year is ū a , and the mean for the
same year at the candidate site is ū b , then the corrected or estimated long term mean speed
ū c at the candidate site is
ū c =ū b
ū
ū a
(66)
Note that we do not know how to assign a confidence interval to this estimate. It is a single
number whose accuracy depends on both the accuracy of ū and the correlation between ū a and
ū b . The accuracy of ū should be reasonably good after 30 or more years of measurements, as
is common in many NWS stations. However, the assumed correlation between ū a and ū b may
not be very good. Justus[14] found that the correlation was poor enough that the estimate of
long term means was not improved by using data from nearby stations. Equally good results
would be obtained by applying the 90 % confidence interval approach as compared to using
Eq. 66. The reason for this phenomenon was not determined. One possibility is that the type
of anemometer used by the National Weather Service can easily get dirty and yield results
that are low by 10 to 20 % until the next maintenance period. One NWS station may have a
few months of low readings one year while another NWS station may have a few months of
low readings the next year, due to the measuring equipment rather than the wind. This would
make a correction like Eq. 66 very difficult to use. If this is the problem, it can be reduced
by using an average of several NWS stations and, of course, by more frequent maintenance.
Other studies are necessary to clarify this situation.
The actual correlation between two sites can be defined in terms of a correlation coefficient
r, where
Wind Energy Systems by Dr. Gary L. Johnson November 20, 2001