Wednesday, September 3, 2014

Climate Change: Models and Proofs

Every now and then I still run into the argument that climate science is far from settled, that we cannot rely on the fact that the vast majority of scientists in the field are in fundamental agreement and that “real” science requires proof. Models, people taking this view, are imperfect, and not “real” science, which is not a popularity poll.

Let’s examine how science actually works.

First, what is a model? It is an abstraction of reality that allows you to make predictions. A good model will make accurate predictions; a useful model makes predictions accurate enough to allow reasonable action ahead of knowing the correct result. Weather models, for example, are not 100% accurate, but good enough to allow us to do things like plan whether to do laundry, or to evacuate a city ahead of a major storm.

We need two things of model predictions to be sure it is useful. We need error bounds and evidence that those error bounds are accurate. Error bounds are a measure of how much our model varies from reality. If the error bounds are too big, any model predictions may be no better than guesses. If the bounds are not accurate, we do not know how much confidence to put in the accuracy of any prediction.

Nothing in science is ever proved except in pure mathematics.

Take an example: Newton’s Laws of Motion and his theory gravity. These all look nice and mathematical, but they ultimately rest on matching prediction to models. Those models are relatively simple – a bunch of 1-line formulae, but these formulae result from observations, not mathematical proofs. Take gravity, for example. Newton came up with a formula, then used that formula to calculate movement of planets and found it matched.

Newton’s formulae are models. They are an abstraction of an aspect of the universe that can be used to predict outcomes including many Newton would never have though of – whether a space probe reaches Jupiter, whether a car stops in a certain distance when you hit the brakes, and so on.

Since his time, millions of measurements have fitted his models so well, they have become accepted as correct – mostly. Late in the 19th century, the puzzling problem that the speed of light did not vary according to the relative speed of the source and the observer arose. Only with Einstein’s intuition that an invariant speed of light required rewriting Newton’s Laws did we solve this conundrum. Even so, Newton’s formulae still work well enough in most situations that we still use them.

Consensus in science

Models of complex real-world systems cannot provide the accuracy that Newton’s Laws do. Nonetheless they can be useful – even if the results have significant unknowns as well as known sources of error.

How do we determine if a model is sufficiently accurate to be useful? By taking lots of measurements. If the model consistently gives answers close enough to reality that we are confident that the accuracy we predict for the model is correct (the difference from prediction is within accepted error limits), our confidence in the model grows.

That is how consensus in science works. Einstein’s theories, for example, were not fully accepted, despite their mathematical logic, until they could be verified by measurement.

Michelson-Morley set up (source: Wikipedia)
On the other hand, it only takes one measurement that completely contradicts a theory to call it into question. Staying with Einstein and Newton, the starting point was the Michelson–Morley experiment, first published in 1887, which demonstrated that the speed of light is a constant. This was followed by the Lorentz transformations, developed over 1887 to 1905, which became the basis for Einstein’s special relativity.

Despite these radical changes, Newton’s Laws still apply because a Einstein’s new theories come out with the same numbers in most cases where we are not dealing with speeds close to light speed, or gravitation on a relatively small scale.

So despite Einstein’s radical new theories, Newton’s theories still stand – even if we now know they are not totally accurate.

How this relates to climate science
Climate science is not a simple collection of formulae but is based on complex models that are hard to understand a piece at a time. Even so, the same basic concept applies. If you can make predictions that, when later tested against reality, are within the predicted error bounds, you can make claims about the accuracy and usefulness of the theory.

Where are we now?

Some have made a big deal of the relatively slow rate of global temperature increase since the late 1990s. The models do not claim that all temperature variation is human-caused. A major factor is solar variation. Another factor is inaccuracy of models of how the oceans take up increased energy.

In the first half of the twentieth century, the sun was on a slow warming trend, which made it hard to pick out the effect of anthropogenic global warming (AGW: human-caused warming). The most recent solar cycle, on the other hand, has been relatively cool. That alone is a big factor in the apparent slowdown in warming, and is not a factor we can rely on because either the sun will return to its long-term relative warmth, or the AGW trend will rise sufficiently to mask this effect.

The oceans absorb 90% of any change in the planet’s energy balance in the short term, because a temperature change in water can be mixed into lower layers, since water is constantly in motion. A small perturbation in the way the oceans take up heat can have a huge effect on surface temperature. There is increasing evidence that the oceans are warming a little faster than predicted, and that effect too can explain an apparent slowdown in surface warming.

Arctic sea ice volume trend (April and September).
Source: PIOMAS
There is plenty of evidence that the Earth is not in balance with energy flows in from the sun, such as growing ice loss both on land and Arctic sea ice, and that energy imbalance can only ultimately be corrected by a higher surface temperature.

And finally, the apparent slowdown is within the error limits of the commonly accepted models though at the lower end of the predicted range. Other published predictions that have held up well include predictions of extreme weather in the US, and that is the sort of prediction we need to worry about.

So the argument that the models are fundamentally flawed is wrong: they are not totally accurate, but they are accurate enough to be useful.