The climate system is extremely complex. Consequently, there is no simple way of determining how much the climate will change in response to rising greenhouse gas levels. If temperature were the only thing to change, it would be relatively straightforward to predict a warming of around 1°C for a doubling of carbon dioxide concentrations. But this "direct response" would be almost meaningless because it would be physically impossible for the climate system to warm up by over 1^oC without changes in clouds, water vapour, snow and ice, and so forth.

Complex computer simulations are therefore essential for understanding climate change. Computers allow scientists to model the many interactions between different components of the climate system. The most detailed projections are based on coupled atmosphere-ocean general circulation models (AOGCMs). These are similar to the models used to predict the weather, in which the physical laws governing the motion of the atmosphere are reduced to systems of equations to be solved on supercomputers. However, climate models must also include equations representing the behaviour of the oceans, land vegetation, and the cryosphere (sea ice, glaciers, and ice caps).

"Positive feedbacks" involving water vapour, snow, and ice may amplify the direct response to greenhouse gas emissions by a factor of two to three. Snow and ice reflect sunlight very effectively. If a small warming melts snow earlier in the year, more energy will be absorbed by the ground exposed underneath it, in turn causing more warming. This is the main reason wintertime northern regions are expected to warm the most. The water vapour feedback is even more important: water vapour is itself a powerful greenhouse gas, and models project that global warming will raise water vapour levels in the lower atmosphere.

Changes in cloud cover, ocean currents, and chemistry and biology, may either amplify or reduce the response. Models generally predict that cloudiness will change in a warmer world, but depending on the type and location of the clouds, this could have various effects. Clouds reflect sunlight, implying that more clouds would have a cooling effect. But most clouds, particularly those at high altitudes, also have an insulating effect: being very cold, they shed energy to space relatively ineffectively, thus helping to keep the planet warm. So the net cloud feedback could go either way. Clouds are the main reason for the large uncertainty about the size of warming under any given emissions scenario.

The speed and timing of climate change strongly depends on how the oceans respond. The uppermost layers of the oceans interact with the atmosphere every year and so are expected to warm along with the earth's surface. But it takes over 40 times as much energy to warm the top 100 m of the ocean as to warm the entire atmosphere by the same amount. With ocean depths reaching several kilometres, the oceans will therefore slow down any atmospheric warming. How much they slow it down depends on how deeply the warming penetrates. The latest climate models are only just beginning to represent the processes which exchange energy between the atmosphere and ocean depths, so this remains an important source of uncertainty.Although major improvements have been made in modeling some ocean processes, the exchange of heat between the atmosphere and ocean depths remains an important source of uncertainty.

Climate projections must begin from a stable and realistic simulation of the present-day climate, which is not easy to obtain. Ideally, scientists would like to allow a model to settle down with pre-industrial levels of greenhouse gases and then increase greenhouse gas levels to examine the response. But the inevitable approximations mean that the model generally starts to drift away from the present climate at a rate comparable to, or even larger than, the warming expected due to changing greenhouse gas levels. There are various ways of correcting for this "climate drift" to obtain a stable model climate before starting a climate change experiment. None of these correction schemes is completely satisfactory, since they are covering up model errors that might be important for climate change. The size of these corrections is diminishing as models improve, however, which suggests that it may be possible to eliminate them altogether in the relatively near future.

Confidence in the ability of models to project future climate is growing. The representation of many processes, such as water vapour and the horizontal transport of heat in the oceans, has improved. Climate models provide credible simulations of climate, at least down to sub-continental scales. They have been able to reproduce, for example, the 20^th century’s warming trends, as well as some aspects of ancient climates and the El Niño/Southern Oscillation. As a result of these improvements, several climate models have now been run successfully without the need for non-physical adjustments (flux adjustments or flux corrections) to keep their climates stable. However, models cannot yet simulate all aspects of climate. For example, they still cannot account fully for the observed trend in the temperature difference between the surface and the lower atmosphere. There are also significant uncertainties regarding clouds and their interaction with radiation and aerosols.

Climate models are scientific tools, not crystal balls. Large climate modeling experiments consume enormous computing resources and are so expensive that each year only a handful of such experiments can be performed world-wide. Then the work involved in interpreting the results of a computer simulation is often greater than the work needed to perform the experiment in the first place. All of this work and expense can give models the aura of truth. But even the most sophisticated models are approximate representations of a very complex system, so they will never be an infallible guide to the future. So think of climate models as sophisticated tools for extending our knowledge of present and past climate into an unexplored future. Since climate change will only happen once, they are the best tool we have.