Advanced Building Simulation

(b) Compute today’s average temperature by
Simulation and uncertainty: weather predictions 71
Table 3.1 The 31 values of deviations from the mean for a Normal Distribution’s Cumulative
Distribution Curve
Left half of curve including the mid point
x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
f(x) �2.11 �1.70 �1.40 �1.21 �1.06 �0.925 �0.808 �0.70 �0.60 �0.506 �0.415 �0.33 �0.245 �0.162 �0.083 0.0
Right half of curve
x 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
f(x) 0.083 0.162 0.245 0.33 0.415 0.506 0.60 0.70 0.808 0.925 1.06 1.21 1.40 1.70 2.11
T ave�T Mave�� * FNORMAL(X) (3.8)
where, Tave is the average temperature for today; TMave, the average temperature
for this month; and �, the standard deviation for average daily temperatures.
Computation of Equations (3.7) and (3.8) is performed 31 times until all the days
of the month are completed. The result will be a sequence similar to the pattern
shown in Figure 3.5. The pattern will appear to be a bit choppy, so the software
developer may wish to apply some biasing to how the 31-day sequence is generated.
Usually, there should be 2–4 warm days grouped together before the weather moves
to colder or hotter conditions. It is convenient to force the simulation to begin the
month at near average conditions and end the month in a similar condition. This prevents
large discontinuities when moving from one month to the next, where the mean
and standard deviation will take on new values.
If the selection of the days from the cumulative distribution curve is left totally to
the random number generator, usually several days will be omitted and several days
will be repeated. To obtain the best fit to the normal distribution curve, and thus the
best representation of the historical weather, all 31 days should be utilized from the
table, and used only once. The methods to do this can be varied. One simple method
is to introduce a biased ordering of the day sequence when performing the computer
programming. Better conformance to the local climate can be done if the sequence of
day selections is correlated to other variables such as solar, humidity, and wind. This
requires more extensive analysis of the local climate conditions and may present some
rather formidable tasks. This issue will be addressed later in this chapter after the
solar simulation techniques have been presented.
3.4.5 Simulation of humidity
The most convenient value to use to represent humidity is the dew-point temperature.
It tends to be rather flat during any one day, and its mean value is tightly correlated
to the daily minimum temperature. Mean monthly dew-point temperatures are frequently
published by the weather stations, but if these are unavailable, they can still
be computed from a psychrometric chart assuming that either relative humidity or
wet-bulb temperatures are published. One or the other of these is necessary if the
dew-point temperature is to be simulated.