WIND ENERGY SYSTEMS - Cd3wd

Chapter 2—Wind Characteristics 2–49
The monthly mean wind speeds at Dodge City for 1958 were 11.78, 13.66, 11.16, 12.94, 12.10,
13.47, 12.56, 10.86, 13.77, 11.76, 12.44, and 12.55 knots. Find the yearly mean (assuming all months
have the same number of days), the standard deviation, and the wind speeds one and two standard
deviations from the mean. What monthly mean will be exceeded 95 % of the time? What is the 90 %
confidence interval?
By a hand held calculator, we find
ū =12.42
σ =0.94
The wind speeds one standard deviation from the mean are 11.48 and 13.36 knots, while the speeds
two standard deviations from the mean are 10.54 and 14.30 knots. From Table 2.4 we see that F (u)
= 0.05 (indicating 95 % of the values are larger) for q = -1.645. From Eq. 65 we find
u =12.42 + (−1.645)(0.94) = 10.87 knots
Based on this one year’s data we can say that the monthly mean wind speed at Dodge City should
exceed 10.87 knots (5.59 m/s) for 95 % of all months.
The 90 % confidence interval is given by the interval 12.42 ± 1.645(0.94) or between 10.87 and
13.97 knots. We would expect from this analysis that 9 out of 10 monthly means would be in this
interval. In examining the original data set, we find that only one month out of 12 is outside the
interval, and it is just barely outside. This type of result is rather typical with such small data sets. If
we considered a much larger data set such as a 40 year period with 480 monthly means, then we could
expect approximately 48 months to actually fall outside this 90 % confidence interval.
We might now ask ourselves how confident we are in the results of this example. After all,
only one year’s wind data were examined. Perhaps we picked an unusual year with mean and
standard deviation far removed from their long term averages. We need to somehow specify
the confidence we have in such a result.
Justus, Mani and Mikhail examined long term wind data[14] for 40 locations in the United
States, including Alaska, Hawaii, and Wake Island. All sites had ten or more years of data
from a fixed anemometer location and a long term mean wind speed of 5 m/s or greater.
They found that monthly and yearly mean speeds are distributed very closely to a normal or
Gaussian distribution, as was mentioned earlier.
The monthly means were distributed around the long term measured monthly mean ū m
with an average standard deviation of 0.098ū m where ū m is the mean wind speed for a given
month of the year, e.g. all the April average wind speeds are averaged over the entire period
of observation to get a long term average for that month. For a normal distribution the 90 %
confidence interval would be, using Table 2.5, ū m ± 1.645(0.098)ū m or the interval between
0.84ū m and 1.16ū m . We can therefore say that we have 90 % confidence that a measured
monthly mean speed will fall in the interval 0.84ū m to 1.16ū m . If we say that each measured
Wind Energy Systems by Dr. Gary L. Johnson November 20, 2001