Wednesday, September 2, 2009

Models and Modelling

"All models are wrong. Some models are useful." George Box

Box was a modeller, and the sentiment is widely spread among modellers of all kinds. This might be a surprise to many, who imagine that modellers think they're producing gospel. The reality is, we modellers all acknowledge the first statement. We are more interested in the second -- Some models are useful.

But let's back up a bit. What is a model? In figuring out some of this, we'll see how it is that models can be imperfect, but still useful.

There are several sorts of model, is one thing to remember. On fashion runways or covers of magazines, we'll see fashion models. In hobby shops, we can get a model spacecraft or car. We could head more towards science, and find a laboratory model, or a biological model animal, statistical model, a process model, numerical model, and so on.

Common to the models is that they have some limited purpose. A fashion model is to display some fashion to advantage -- making the dress/skirt/make up/... look good. She's not to be considered an attempt to represent all women accurately. The model spacecraft is not intended to reach the moon. But you can learn something about how a spacecraft is constructed by assembling one, and the result will look like the real thing.

In talking about a laboratory model, read that as being a laboratory experiment. You hope that the set up you arrange in the lab is an accurate representation of what you're trying to study. The lab is never exactly the real thing, but if you're trying to study, say, how much a beam flexes when a weight is put in the middle, you might be able to get pretty close. If you want to know the stability of a full-size bridge with full size beams and welds and rivets assembled by real people, it'll be more a challenge -- represent the 1000 meter bridge inside your lab that's only 10 meters long. It won't be exact, but it can be good enough. Historical note for the younger set: Major bridges like the Golden Gate Bridge, Brooklyn Bridge, Tower Bridge, and such, were designed and built based on scale models like this. The Roman Aqueducts designed over 2000 years ago, still stand, and never came near a computer. They were all derived from models, not a single one of which was entirely correct.

In studying diseases, biologists use model animals. They're real animals of course. They're being used a models to study the human disease. Lab rats and such aren't humans. But, after extensive testing was done, it was discovered that the rats for some diseases, and other animals for other diseases, reacted closely enough to how humans did. Not exactly the same. But closely enough that the early experiments and tests of early ideas could be done on the rats rather than on people. The model is wrong, but useful.

Statistical models seem to be the sort that the most people are most familiar with. My note Does CO2 correlate with temperature arrives at a statistical model, for instance -- that for each 100 ppm CO2 rises, temperature rises by 1 K. It's an only marginally useful model, but useful enough to show a connection between the two variables, and an approximate order of magnitude of the size. As I mentioned then, this is not how the climate really is modelled. A good statistical model is the relationship between exercise and heart disease. A statistical model, derived from a long term study of people over decades, showed that the probability of heart disease declined as people did more aerobic exercise. Being statistical, it can't guarantee that if you walk 5 miles a week instead of 0 you'll decrease your heart disease chances by exactly X%. But it does provide strong support that you're better off if you cover 5 miles instead of 0. Digressing a second: Same study was (and is still part of) the support of the 20-25 miles per week running or walking or equivalent (30-40 km/week) suggestion for health. The good news being that while 20 is better than 10, 10 is better than 5, and 5 is way better than 0. (As always, before starting check with your doctor about your particular situation, especially if you're older, have a history of heart problems already, or are seriously overweight). This model is wrong -- it won't tell you how much better, and in some cases your own results might be a worsening. But it's useful -- most people will be better off, many by a large amount, if they exercise.

Process models started as lab experiments, but also are done in numerical models. Either way, the method is to strip out everything in the universe except for exactly and only the thing you want to study. Galileo, in studying the motion of bodies under gravity stripped the system, and slowed it down, by going to the process model of balls rolling down sloping planes. He did not fire arrows, cannon balls, use birds, or bricks, etc.. Simplified to just the ball rolling down the plane. The model was wrong -- it excluded many forces that act on birds, bricks, and all. But it was useful -- it told him something about how gravity worked. Especially, it told him that gravity didn't care about how big the ball was, it accelerated by the same rules. In climate, we might use a process model that included only how radiation travelled up and down through the atmosphere. It would specify everything else -- the winds, clouds, where the sun was, what the temperature of the surface was, and so on. Such process models are used to try to understand, for instance, what is important about clouds -- is it the number of cloud droplets, their size, some combination, ...? As a climate model, it would be wrong. But it's useful to help us design our cloud observing systems.

Numerical models, actually we need to expand this to 'general computational models' as the statistical, process, and even some disease models now, are done as computational models. These general models attempt to model relatively thoroughly (not as a process model) much of what goes on in the system of interest. An important feature being that electronic computers are not essential. The first numerical weather prediction was done by pencil, paper, and sometimes an adding machine -- more than 25 years before the first electronic computer. Bridges, cars, and planes are now also modelled in this way, in addition or instead of scale models. Again, all of them are wrong -- they all leave out things that the real system has, or treat them in ways simpler (easier to compute) than the real thing. But all can be useful -- they let us try 'what if' experiments much faster and cheaper than building scale models. Or, in the case of climate, they make it possible to try out the 'what if' at all. We just don't have any spare planets to run experiments on.

Several sorts of models, but one underlying theme -- all wrong, but they can be useful. In coming weeks, I'll be turning to some highly simplified models for the climate. The first round will be the four 1-dimensional models. Two are not very useful at all, and two will be extremely educational. These are 4 of the 16 climate models.

1 comment:

naught101 said...

I think it's kind of worth noting that all science is, and all it can ever be, is a collection of models. All hypotheses and all theories ultimately are just representations of reality, which (apparently universally) get proved wrong in certain situations - i.e. Newtonian mechanics is a model that is extremely accurate at representing real world mechanics in most situations, but starts failing when you approach the speed of light.

A model's goodness is proportional to the amount of reality it can describe. A matchbox car is not a great model of a real car, since it doesn't go anywhere. A remote control car is better, because it does, and can even go around corners, approximating the physics of a real car. A Crash test is even better, since it actually uses a real car, and the only models are the bodies, the control, and the wall. But even that isn't excellent, and it's actually impossible to create a real model car, because in reality, cars are driven by variable people with variable loads, and variable driving styles. And no model can account for all of them.

I would even contend that climate models these days are far BETTER than Newtonian mechanics. After all, climate is innately chaotic, and climate models still manage to be able to approximate it. Newtonian mechanics completely ignores nearly all non-linearities, and there are a lot of them, even at low speeds.