Editor's note: Although we don't make a habit of reposting old content, some things just seem to stay relevant. In recent discussions on global warming, various commenters have made comments to the effect of "If you can't predict the weather, you can't predict the climate." To try and remind people why this simply isn't true, we are reposting this article from 2006. Enjoy.

One of the things we have noticed here at Nobel Intent is how some topics tend to generate the same forum comments. These are usually topics for which there is some emotional connection, such as embryonic stem cells or climate change. It means that the forum debate doesn't focus on what is new in the article; instead, it generally covers the same ground over and over again.

I personally stay away from such forum discussions for precisely this reason, even though I may think the findings are interesting and may be willing to comment on them. In an effort to move the debate beyond certain hurdles, we felt that articles that outlined in detail why scientists hold to a certain opinion were appropriate. I don't hold the hope that these articles will change anyone's opinion. Rather, by understanding why someone believes something to be true, the discussion can move beyond those issues and onto new terrain.

In this article I take a look at climate modeling and in particular why the comment "They can't predict the weather, therefore climate models are not good" is just plain wrong. It represents a fundamental misunderstanding of what climate modelers are trying to achieve, what is achievable and why the weather is unpredictable.

Reaching phase space

In this article there is very little about the climate, weather patterns, or the physical and chemical properties of the atmosphere. That is because our understanding of what is predictable and unpredictable comes from an underlying knowledge of the general properties of nonlinear dynamical systems. Thus, this article focuses on those general principles and then relates them back to the earth's climate.

A dynamical system is one that changes, such as a weight on a spring, planets orbiting a sun, some chemical reactions, and the weather. It is generally described by a system of one or more mathematical equations that relate particular features of the system. No matter how complicated a system might be, it can often be described using a small set of overall properties and the behavior of the system can be understood by how these properties vary in time.

This is often done by viewing the properties in what mathematicians and physicists call "phase space." This is best understood by example, the simplest of which is a mass attached to a spring. We know that if we take the spring and extend it, then it will bounce up and down. The size of the bounces will get smaller and smaller until it finally stops bouncing, and the spring and weight will return to their original position, called the equilibrium position.

For any given spring and mass system, there are only two properties that go into the phase space; the position of the mass, and the velocity with which it is moving. When we draw a graph of the mass' velocity and its position, we find that it makes a spiral. The spiral starts at the initial extension and ends at the equilibrium position, when the mass is at rest.

That graph is the phase space of the spring and mass dynamical system; the spiral is called the trajectory of the system through phase space.

Set phase space on stun

Note that no matter where the system starts in phase space, it always ends up in the same position, which is called a point attractor. Attractors take more than one form and the phase space can be much more complicated than a simple two dimensional space. However, phase space and the shape of attractors are the key ideas behind understanding climate models.

To further illustrate the idea of attractors and to demonstrate the idea of a basin of attraction, let's take a look at the orbit of a planet around a star. In this case, our phase space is given by the planet's distance from the star and its velocity. Tracing these out in time, we find that the attractor looks like an ellipse.

However, not all starting locations in phase space lead to the same result. If we start our planet closer to the star, moving slower and in a dense dust cloud, then it spirals into the star, which is another point attractor. If the planet's velocity is too high, then the star will fail to capture the planet and it will head off into space, never to be seen again. The range of phase space locations that lead to a stable orbit define a basin of attraction for the elliptically shaped attractor of the orbit. The range of coordinates that lead to the planet spiraling into the star defines the basin of attraction for the point attractor.

The consequence of the attractor is one of predictability. Returning to the planet example, a planet in a stable orbit will repeat its trajectory through phase space, which makes it predictable over long periods of time. This is because, even if we don't measure the location and velocity very accurately, the system is bounded by a very narrow range of values, meaning that it never gets very far from predicted values.

To summarize, a phase space is a space in which each location defines a unique configuration for the system. The phase space of a system may contain attractors, which limit the range of configurations that are available to the system. All attractors are associated with a basin of attraction; if the system is within the basin then it will end up at the attractor. Once on an attractor, the system becomes predictable since it is bound to repeat itself.

Fractals and strange attractors

In the example of a planet orbiting a star, the attractor takes on the shape of an ellipse and the dynamic system travels the perimeter; there is only a single orbit available. Even if we were to imagine a similar, spherical attractor, it remains predictable. In this case, the attractor is spherical and the dynamic system can travel anywhere on that surface.

However, the surface area is finite, so eventually the system comes back to a place it has been before. Once it does, it will retrace its previous path—if you observe for long enough, it is predictable. However, there are shapes called fractals which, even though they have a finite volume, have an infinite surface area.

Some dynamical systems, such as the climate, have an attractor with a fractal shape, called a strange attractor. The dynamical system still has a basin of attraction and only passes through a limited range of values in phase space (mathematicians term this "bounded"). However, it can travel anywhere on the surface of the attractor, which means that it will never return to exactly the same point on the surface.

The implication is that the system will never exactly repeat itself. Worse than that, because it will never return the same place in phase space, you cannot expect that a small error in measuring the phase space position to stay small. The weather is unpredictable because the infinite surface area of the strange attractor requires us to know the starting conditions (i.e., temperature, pressure, humidity, etc) exactly, everywhere on the Earth, which is clearly impossible.

Strange attractors in the climate

The question is this: if the local weather in unpredictable, how can a climatologist model the planetary weather and thus make statements about climate change? The answer to this lies in the nature of the strange attractor. Remember that the surface of the attractor is infinite but the volume is finite. This means that there are boundaries to the range of weather conditions available.

In other words, the planet's weather conditions are limited to those contained on the surface of the strange attractor. Although we cannot predict the exact trajectory the system will take over the surface, we can focus on more general features, such as the exact shape of the strange attractor.

More importantly, modelers are interested in how frequently the system visits a particular range of climate conditions. To achieve this, they start simulating the weather and note how often the weather system passes through a small section of the attractor. By doing this for many locations and starting positions, one can determine the statistical averages of the climate for the whole planet.

More succinctly, climatologists are looking at the surface of the attractor and how often the weather passes through particular regions (instead of the particular course the weather takes along the surface). How does this relate to real physical-chemical processes in the atmosphere?

Here is a fake example. I've discovered a new way that carbon dioxide is produced in the atmosphere. We'll call it the politically catalyzed hot air reaction. To find out how significant this new source of carbon dioxide might be, I put the politically catalyzed hot air reaction into my dynamical system and examine changes in the surface of the strange attractor. From these changes, a climatologist can determine the relative significance of each atmospheric process and its effect on average climate values.

Strange, but well-understood

The conclusion is that the modeling itself and its methodology have been intensively studied in multiple systems, and they are sound. So why are climate models the focus of so much attention from those who don't like the conclusions drawn from them?

Mostly, the debate centers around the inclusion of particular processes. Each additional process takes computation time, so climatologists spend a considerable amount of time determining what needs to be explicitly calculated, what can be reduced to a time-averaged value, and what can be left out all together. Climatologists then spend even more time checking the results of these decisions against real world data and alternative models.

However, some of the spurious criticisms tend to ignore this result checking, and focus on the fact that some atmospheric processes are not included in detail. This is compounded by the fact that the Earth's climate is so variable; the significance of some processes can be changed quite a lot while still giving a reasonable average climate. Hence, it takes a lot of time and computer cycles to determine which set of processes and their relative strengths gives the best fit to historical climate averages, and therefore have the best predictive power.

Unfortunately, this means predictions are given by broad ranges, such as an average temperature that may increase by between 0.4 and 7 degrees Celsius over 100 years. Naturally, some will suggest that this prediction range is an example of poor science, rather than as a sign of responsible data reporting.

Still, that's nowhere near as misleading as the suggestion that weather forecasts and climate models are equivalent. As we've described, forecasting the weather is an attempt to get fairly precise information on the state of the atmosphere in the near future. Forecasting the climate, in contrast, involves an attempt to identify the atmosphere's most probable states on far longer time scales. Given that they're such fundamentally different problems, there's no reason to expect that our skill with one (or lack thereof) would translate to the other.