Advanced Building Simulation

Simulation and uncertainty: weather predictions 63
Before the Monte Carlo method got its formal name in 1944, there were a number of
isolated instances of similar random sampling methods used to solve problems. As early
as the eighteenth century, Georges Buffon (1707–88) created an experiment that would
infer the value of PI�3.1415927. In the nineteenth century, there are accounts of people
repeating his experiment, which entailed throwing a needle in a haphazard manner
onto a board ruled with parallel straight lines. The value of PI could be estimated from
observations of the number of intersections between needle and lines. Accounts of this
activity by a cavalry captain and others while recovering from wounds incurred in the
American Civil War can be found in a paper entitled “On an experimental determination
of PI”. The reader is invited to test out a Java implementation of Buffon’s method
written by Sabri Pllana (University of Vienna’s Institute for Software Science) at
http://www.geocities.com/CollegePark/Quad/2435/buffon.html.
Later, in 1899, Lord Rayleigh showed that a one-dimensional random walk
without absorbing barriers could provide an approximate solution to a parabolic
differential equation. In 1931, Kolmogorov showed the relationship between Markov
stochastic processes and a certain class of differential equations. In the early part of
the twentieth century, British statistical schools were involved with Monte Carlo
methods for verification work not having to do with research or discovery.
The name, Monte Carlo, derives from the roulette wheel (effectively, a random
number generator) used in Monte Carlo, Monaco. The systematic development of the
Monte Carlo method as a scientific problem-solving tool, however, stems from work
on the atomic bomb during the Second World War (c.1944). This work was done by
nuclear engineers and physicists to predict the diffusion of neutron collisions in fissionable
materials to see what fraction of neutrons would travel uninterrupted
through different shielding materials. In effect, they were deriving a material’s
“shielding factor” to incoming radiation effects for life-safety reasons. Since physical
experiments of this nature could be very dangerous to humans, they coded various
simulation models into software models, and thus used a computer as a surrogate for
the physical experiments. For the physicist, this was also less expensive than setting
up an experiment, obtaining a neutron source, and taking radiation measurements.
In the years since 1944, simulation has been applied to areas of design, urban planning,
factory assembly lines and building performance. The modeling method has
been found to be quite adaptable to the simulating of the weather parameters that
affect the thermal processes in a building. Coupled with other deterministic models,
the Monte Carlo method has been found to be useful in predicting annual energy
consumption as well as peak thermal load conditions in the building.
The modeling methods described herein for weather data generation include the
Monte Carlo method where uncertainties are present, such as day to day cloud cover
and wind speeds, but also include deterministic models, such as the equations that
describe sun–earth angular relationships. Both models are applied to almost all the
weather parameters. Modeling of each weather parameter will be treated in its whole
before progressing to the next parameter and in order of impact on a building’s
thermal performance.
In order of importance to a building’s thermal performance, temperature probably
ranks first, though solar radiation and humidity are close behind. The next section
first describes the simulation model for dry-bulb temperatures and then adds the
humidity aspect by describing the dew-point temperature modeling.