Monte Carlo Methods (technical)
Ill-conditioned mathematical Models and the "Butterfly Effect"
While astrologers talk about the Zodiac cycles (12-month Western Zodiac and 12-year Chinese Zodiac), scients talk about another celestial cycle that is important to human
health and prosperity. That is the The Ice Age cycle, which is one that occurs every multi-thousand years.
Geologists tell us that there have been many cycles of global cooling called
"ice ages" that are all followed by periods of warming (called inter-glacial periods).
In general, life on Earth prospers during the warm phase of each cycle, and suffers during the cold phase.
There are various theories about why this happens, but the most compelling is the explanation put forth
by a NASA scientist in his book "Hot Talk, Cold Science,"
which is that global temperature changes are causes by variations in the sun's output
(similar to the sunspot cycle, but much slower and not as regular).
Unfortunately, we currently have no model that reliably predicts changes in solar output, which limits our ability to
construct a reliable model of global climate change.
See also a more recent book,
"Unsettled: What Climate Science Tells Us, What it Doesn't, and Why it Matters"
As we have previously discussed on our show
What is Truth?
the Scientific Method requires that scientific findings must be published (made public) with a sufficiently detailed
description of the methods used (for example the computer program source code) and the data used
(for example the temperature and other measurements used as inputs to the program)
in order for independent researchers to validate and repeat the experiment to obtain independently verified results
that support the originally published conclusions.
"Climategate: The Crutape Letters" documents a breakdown of the scientific
method in at least one major climate research lab.
A credible climate-change model should be able to reproduce the global temperature changes over,
let's say, the past 2,000 years (which includes periods of both warming and cooling),
and predict perhaps the next 10 years of climate change, without adding or changing any input data beyond the
data available today, and without any "hacks" (ad-hoc constraints) that force a particular future outcome.
Furthermore, if based on this 10 year "trial" of the model, trust is placed in it's ability to project further into
future, that trust should be immediately withdrawn at any point in time at which the model's predictions
begin to vary significantly from observed reality.
In addition, climate models are what computational mathematicians call "ill-conditioned systems" (subject to what is
sometimes called the "butterfly effect"). This means that very small changes in inputs can cause dramatic changes in
outputs. In practice, all the input data is measured to only a few decimal places of precision. For example,
suppose a particular temperature measurement is reported as 25.00 degrees Celsius. What this really means is we do not
know the exact true temperature, but the true temperature most likely is somewhere 24.99 degrees and 25.01 degrees.
An important technique for evaluating the stability of any mathematical model is the
Monte Carlo Method.
In this method, all the input data by is randomly changed by a tiny amount of "wobble" for each measurement
(in this example, by randomly changing each temperature measurement to a random number chosen between 24.99 and 25.01
degrees etc). The model is then re-run with this randomly chosen input data.
[Full disclosure: Dr. Weyrich used Monte Carlo methods to study ill-conditioned non-linear chemical models as
part of his PhD dissertation in Chemistry].
If this process is repeated many times, then if the model is stable then we will arrive at a distibution of
results which will all cluster near the same outcome. We therefore conclude that the model is at least stable
(gives consistent answers), and may also be reliable.
On the other hand, if the results are wildly different for the different runs, then the model is
unreliable and should not be used for public policy decisions.
To the best knowledge of Dr. Weyrich, all this has never been done for the climate models
currently being touted in the news media and proposed as a basis for public policy decisions,
and which may have been politicized. See also
What is Truth? Part 3, Lysenko and the Politicization of Science.