To deal with the immense complexity of the climate system, scientists turn to comprehensive global climate models. The word model means many different things to different people and in different contexts. (I once asked a new graduate student how she had spent her undergraduate years. She told me she had done some modeling. “Computational fluids dynamics?” I asked. Looking puzzled, she replied, “No, clothes.”) Climate models, like models used for predicting weather, are computational devices for solving large sets of equations. These equations include those governing radiative transfer and the fluid equivalent of Newton’s laws of motion. Using a computer to solve these equations is very similar to using a computer to, say, precisely land a spacecraft on Mars. In this case, the computer is primarily solving equations encoding Newton’s laws. These laws and equations that describe them are exact, which makes it possible to direct a spacecraft with great precision to a soft landing on a distant planet.
This type of modeling is quite different from, for example, economic modeling. Economic models also solve equations, but unlike with climate models, the equations are not fundamental but rather constructs based mostly on data from past economic behavior. For example, there are no known equations governing human behavior, so we have to, in essence, guess what they might look like if they existed, based on how economies have performed in the past. The reader may judge how successful such models have been. No one pretends that economic models may be made arbitrarily exact, even given many resources and much time over which to improve them.
Yet the comparison of climate models with the “models” used to land spacecraft is a little misleading. Although the equations governing climate are known rather precisely, there is no way they can be solved exactly using present-day computers. We cannot even begin to track each molecule of the climate system but must average over big blocks of space and time. For example, today’s climate models typically average over blocks of the atmosphere that are 100 kilometers square and perhaps 1 kilometer thick, and over time intervals of several tens of minutes. This averaging introduces errors and skips over important climate processes. For example, cumulus convection—thunderstorms, for example—is the main way, other than radiation, that heat is transmitted vertically though the atmosphere. But cumulus clouds are only a few kilometers wide and so cannot possibly be simulated by models that average over 100 kilometer squares. Nevertheless, they must be accounted for, and so we turn to a technique awkwardly called parameterization to do so. Parameterizations represent processes that cannot be resolved by the model itself, and they attempt to be faithful to the equations underlying those processes. But many assumptions have to be introduced, and their efficacy is usually judged by how well they simulate past events. In many ways, parameterizations are closer in spirit to economic modeling than to programming spacecraft.
Thus climate and weather models are hybrids of strictly deterministic modeling (like programming spacecraft) and somewhat ad hoc parameterizations (closer to economic modeling). Weather models can be tested over and over again, every day, and thereby progressively refined. Today’s weather models are far superior to those of a generation ago, partly because of improved computational technology, partly because of increased know-how, and partly because they can be repeatedly tested against observations and refined. But climate evolves slowly, and so there are not that many climate states against which to test models. So, in contrast with weather forecasting, in climate modeling we have neither the history of success nor the confidence that comes with it. But the fundamentally chaotic nature of weather imposes a predictability horizon on weather forecasting, whereas with climate we are trying to predict the slow response of the longterm average statistics of the weather to changes in sunlight, CO2, and other factors. For this kind of prediction, there may not be a fundamental predictability horizon. (We can say with confidence that summer will be warmer than winter for as many years in advance as we care to.)
Even here, though, we are on shaky ground. Very simply mathematical models of climate-like systems can exhibit sudden, unpredictable shifts, even though the evolution of the system between these shifts can be quite predictable. (The great mathematician and atmospheric scientist Edward Lorenz, the father of chaos theory, was fascinated by such systems.) We do not know for sure whether our climate is an example of such a system, but there is evidence encoded in ice cores from Greenland that ice age climates can jump rather quickly from one state to another. This evidence, together with behavior of some simple models, puts mathematical teeth on the idea of tipping points—sudden and largely unpredictable shifts in the climate state. This idea keeps many a climate scientist awake at night.