Allan Harvey responded>>>>>>>>>>
>One can always reduce roundoff errors and their propagation by making the
numerical algorithms better, and good scientific work will always take steps
to ensure that these errors are not significant to the work.
In the case of climate change predictions, recent predictions are indeed
different from predictions of 5 years ago, primarily because they are run on
more powerfull computers. Climate (and weather) predictions divide the
atmosphere up into small pieces & model the variables (temperature, air
pressure, humidity, solar radiation, gases, etc.) within each cell. There's
relatively few equations actually modeled in the models, which relate the
variables to each other and the neighboring cells.
A large computer can compute both more cells and more equations--hence, more
accuracy. Recent models incorporate the cooling effects of man-made
pollution (i.e., more equations), which accounts for much of the discrepency
in the earlier climate models (which were showing more warming that
observed). A good intro. to this topic is "Sulfate Aerosol and Climatic
Change." Scientific American, February 1994.
Sadly, many naive critics claim the climate models are "flawed" because of
the discrepencies between early models and the data--while ignoring the
increasing accuracy in later models.
A discussion of mathematical models would be appropriate at this point (but
I must defer).
>>The problem with predictions of some dynamical systems is their extreme
sensitivity to initial conditions and parameters. If we don't know a
parameter (like maybe the IR absorption behavior for a given atmospheric
species) or an initial condition (like maybe the current distribution of
that species in the atmosphere) precisely enough, those factors (not the
computing precision) will limit the ability to make predictions. Good
scientific work will also recognize these limitations.
Amen. Indeed, while Chaos is a trendy topic in many ways, one of the basic
mathematical definitions is indeed "sensitive dependence on initial
conditions".
Chaos is particularly an issue with weather predictions, where one is
concerned with questions like "where is the hurricaine going to go", or
"What will tomorrow's temperature be". Weather predictions are a small
scale issue. On the other hand, climate predictions are on a grander scale.
For instance, we know that warm ocean water breeds hurricaines. We can't
predict exactly when & where, but we know about how many to expect (with
some empirical probability distribution) for given ocean temperatures, based
on past observations of ocean & atmosphere conditions and resultant
hurricaines. The when & where of hurricaines is chaotic.
Climate models examine the interchange of heat, solar radiation, ocean
currents, etc., to arrive at a overall predicted set of ocean & atmospheric
conditions. These in turn control the chaotic generation of hurricaines.
So a 2F to 6F rise in average global temperature doesn't sound like much,
but when the ocean warms by that amount (slowly, but surely), the hurricaine
nursery will be both broader (wider zone of warm water) and more intense
(warmer water implies more energy implies stronger storms).
Also, weather can be thought of as a global heat redistribution mechanism
(solar heat warms different parts of the globe differentially). The more
greenhouse gases, the more trapped heat, the more heat to be redistributed.
So even if the heat redistribution system (i.e., weather) is so effective
as to stop any global warming, the heat must still flow (i.e., more severe
weather), and we still have a problem.
So, climate sets the stage for weather. If you know the climate, you know
what kind of weather to expect, but not exactly where or when.
It is a marvelous system God put together for us. As Elihu put it, "He
loads the clouds with moisture; he scatters his lightning through them. At
his direction they swirl around over the face of the whole earth to do
whatever he commands them. He brings the clouds to punish men, or to water
his earth and show his love. Listen to this, Job; stop and consider God's
wonders. Do you know how God controls the clouds and makes his lightning
flash?" Job 37:11-15
Grace & peace,
Dennis Sweitzer