Advanced Building Simulation

Dry-bulb temperature (°F)
60
50
40
30
20
10
0
+
+
+ +
+
Simulation and uncertainty: weather predictions 69
+ + + + +
Figure 3.4 shows a sequence of days from an actual set of recorded month of daily
temperature data.
In thermal energy simulations for building applications, we do not necessarily need
to replicate this exact sequence; however, we need to replicate the same mean values,
the same spread from minimum to maximum, and approximately the same number
of “day types” in between the minimum and maximum. Following the CDF in a
somewhat random fashion will enable us to meet this objective. So, how do we select
the random pattern? It’s simpler than it might first appear. In effect, all we have to do
is scramble 31 numbers and let each number represent a “day type” on the CDF
graph, and thereby derive 31 different temperatures. To randomly order the day
types, we use a computerized random number generator. Most computers have inherent
random number generators, but there may be reasons why you might want to
write your own. The sequence below shows a Fortran code for a random number generator
that generates a flat distribution of numbers between 0 and 1, repeating itself
only after around 100,000,000 selections. The values derived within the code must
have eight significant figures, so double precision variables must be used. Also, an
initial value, called “the seed”, must be entered to start the sequence. Though we only
want 31 numbers, we need to keep internal precision to eight figures, so the sequences
won’t repeat themselves very often—a lot like the weather. This code can be converted
to BASIC with very few modifications.
+
+
+ + +
Ave. max. = 36.0°F
Monthly ave. = 27.8°F
+
+ +
+ +
2 4 6 8 10 12 14 16 18 20
Day of the month (January)
Figure 3.4 Actual record of daily maximum and average temperatures for 20 consecutive days in January.
Fortan code for a random number generator
*** RANDOM NUMBER GENERATOR ********************************
Function RANDOM (B)
Double Precision B, XL, XK, XNEW
XL�B * 1E7
XK�23.*XL
XNEW�INT (XK / 1E8)
B�XK�XNEW*100000001.
B�B/1E8
*** Check to be sure B is not outside the range .00001 to 1.
IF (B.LT.1E-5)B �ABS (B*1000.)
IF (B.GE.1) B�B/10.
RANDOM�B
RETURN
END