Advanced Building Simulation

Simulation and uncertainty: weather predictions 65
on–off timers, daylight sensors, motion sensors, and even thermostats that control the
environmental control systems.
That completes the deterministic model for calculating temperatures throughout
the course of each day. It should be pointed out that the selection of 3:00 p.m. for the
peak daily temperature is merely a norm and may not suit exactly every locality on
earth. Also, this value references local standard time, so a 1-h adjustment needs to be
made in summers if daylight savings time is utilized.
To calculate hourly values of dew-point temperature, the same procedure can be
followed, so there is no need to show additional equations. The main difference
between simulation of dew-point temperatures compared to dry-bulb values is that
the diurnal curve will be relatively flat, that is, there is little or no rise in the dewpoint
at 3:00 p.m. Also, one should recognize that the dew-point can never exceed
the dry-bulb value at any single point.
3.4.2 Stochastic model
The stochastic portion of the temperature modeling is more intriguing than the deterministic
portion, because it has a less prescribed pattern. As a matter of fact, no one
knows in advance what the sequence of warm and cold days will be during a month.
We see it only after it has happened. It is not actually guesswork, but things are more
random than the previous method. This part of the model sets the max–min temperature
values for each day and is very much influenced by the uniqueness of the local
climate. Fortunately for the simulation community, nature has provided a very wellbehaved
temperature distribution pattern that nicely fits a bell-shaped curve—better
known to the statistical community as the Normal Distribution curve. Statisticians
are very familiar with working with Normal distributions. When frequency of occurrences
versus the measured variable is plotted, the resulting shape is a bell-shaped
curve. This happens when measuring heights of people, areas covered by numerous
gallons of paint, or fuel efficiencies attained by a sample of automobiles. Essentially,
the highest frequencies of occurrences are around the mean value, while a few are
extremely high and a few are extremely low. Average daily temperatures behave in
exactly the same way. Furthermore, average daily maximum temperatures also form
the same pattern, as do daily minimum temperatures, etc. This distribution pattern is
shown in Figure 3.2, depicting the probability of occurrence on the ordinate axis
versus the average value plotted on the abscissa.
The probability density function (PDF) for dry-bulb temperatures is almost always
Normal (bell-shaped). The mean value is always at the center of the bell, and the
spread (fatness) of the bell is determined by the Standard Deviation (�). As a point of
reference, the region bounded between �1� and �1� always contains 68% of all values.
In Figure 3.2, the mean temperature is shown as 72, and the � is 5.4. The plot
shows that the region from �2� to �2� will contain 95.8% of the temperatures and
they will range from 61 to 83. This means that only 4.2% of the values will lie outside
this range (half above and half below). Research investigations on temperature
occurrences have shown that the “means of annual extremes” (both high and low)
are at 2.11� above and below the mean. This region contains 96.5% of all values.
For purposes of weather simulation for energy and design load prediction, it is
recommended that this region be utilized. More on this later!