Advanced Building Simulation

68 Degelman
therefore be 310. Then, we do the same for each month of the year, resulting in
a database of a mean and standard deviation for daily mean, daily maximum, and
daily minimum values for each of the 12 months.
A less accurate, though sometimes essential, alternative to calculating the standard
deviation is to estimate it. For many weather stations, detailed historical records of
daily data are not available—daily records simply were never kept. For those sites,
another statistic needs to be available if one is to develop a simulation model sufficient
enough to produce a close representation of the temperature distributions. The
statistic that is required is called the “mean of annual extremes.” This is not the average
of the daily maximums; rather, it is a month’s highest temperature recorded each
year and then averaged over a number of years. The “mean of annual extremes” usually
incorporates about 96.5% of all temperature values, and this represents 2.11
standard deviations above the mean maximum temperature. Once the “mean of
annual extremes” is derived, one can estimate the standard deviation by the equation:
mean of annual extremes�mean maximum temperature
� (est.)�
2.11
(3.5)
What if the “mean of annual extremes” value is not available? All is not lost—one
more option exists (with additional sacrifice of accuracy). It is called “extreme value
ever recorded.” This value is frequently available when no other data except the mean
temperature is available. This is common in remote areas where quality weather
recording devices are not available. The “extreme value ever recorded” is approximately
3.1 standard deviations above the mean maximum temperature, so the equation
for estimating this becomes
extreme value recorded�mean maximum temperature
� (est.)�
3.1
(3.6)
As with previous calculations, these standard deviation values need to be calculated
for each month of the year.
3.4.3 Random number generation
At this point, we have described how to derive hourly temperatures once minimum
and maximum temperatures have been declared. We have seen that the daily average
temperatures and daily maximum temperatures are distributed in a Normal
Distribution pattern defined by a mean and a standard deviation. Next, we explained
that 31 daily values of average temperature could be selected from a cumulative distribution
curve (which is also defined by the mean and standard deviation). To select
these daily average temperatures, we could simply step through the PDF curve from
day 1 through day 31. This would mean the coldest day always occurs on the first
day of the month and the hottest day always occurs on the last day of the month,
followed by the coldest day of the next month, etc. We realize this is not a realistic
representation of weather patterns. So, we need a calculation model to randomly
distribute the 31 daily values throughout a month. We might expect to have a
few warm days, followed by a few cool days, followed by a few colder days, followed
by a few hot days, and finally a few moderate days before the month is over.