The two main methods of producing future climates scenarios are:
About 20 of these ocean-atmosphere climate models now exist, four times as many as a decade ago. They are the principal tools available to researchers who are trying to understand how the global climate is changing.
By pumping data on temperature, winds, solar radiation, ocean currents and a host of other climatic factors into a model and then setting it in motion, scientists can simulate what could happen over time if emissions of greenhouse gases increase.
Not a lot of stock should be placed in a single "run" of a single model, or even in many runs.
But many runs of many models present the same picture: models show a general global fidelity to reality but also pervasive regional error.
They also continue to yield the same general conclusion their much cruder predecessors first yielded nearly two decades ago: that a doubling of carbon dioxide concentrations in the atmosphere would raise the earth's average surface temperature by three to eight degrees Fahrenheit.
The wide range is a measure of the differences among model projections, and thus of the uncertainty inherent in climate modeling.
The models are exhibiting "a progressive convergence toward what has happened in nature," said Dr. W. Lawrence Gates, a climatologist at the Lawrence Livermore National Laboratory in California who has long been a leader of systematic international efforts, including those of the intergovernmental panel, to evaluate the models.
For making long-term predictions of climatic change on a continental scale or greater, Gates said, "the ensemble of existing modern models is reliable" and "provides a firm scientific base for policy."
Not everyone agrees. Some skeptics, like Dr. Richard S. Lindzen of MIT, have always considered the models worthless as prognosticators, and still do. "I'm not saying the model output bears no resemblance at all to nature; in the gross figures, it looks plausibly similar," Lindzen said. But that, he said, "does not give you forecast ability."
No model, by definition, will ever match the real world perfectly. "It's never going to happen," said Hansen, the director of the Goddard Institute.
A decade ago, Hansen became the first scientist to go on record before Congress and say that the greenhouse effect was probably the cause of global warming.
Models will always fail to mimic nature exactly, he says, even though today's smaller but much faster computers make possible a precision unapproached by the lumbering mainframe that occupied an entire floor some 20 years ago.
For one thing, the atmosphere's normal internal churnings are to some extent unpredictable; some variations are never repeated exactly.
The atmosphere is far too complex to be completely captured in any computer program. The essence of modeling is to simplify but to retain the processes most important in driving the climate.
Nevertheless, proponents of the models say, they are the most powerful tools available for analyzing climate.
Why turn to computers? The atmosphere is simply too complex for any other mode of analysis, and the virtual climate made possible by computers is far closer to reality than any model that might be generated in anyone's head.
Some things about climate are simple and certain enough, needing no computer analysis.
Scientists know, for instance, that a doubling of carbon dioxide, by itself, would warm the earth's surface by about two degrees. They also know that atmospheric concentrations of the gas are increasing as a result of industrial activity.
But simplicity ends there. The warming touches off feedback processes, some of which increase the warming and some of which decrease it.
For instance, a warmer atmosphere melts snow and sea ice, both of which cool the planet by reflecting sunlight; less ice and snow means further warming. On the other hand, warming also increases low-level clouds, which cool the planet.
Modeling is in large measure an exercise in representing enough of these competing influences faithfully enough to estimate their net effect.
A climate model is a computer program containing mathematical equations that express fundamental laws of atmospheric physics. These laws govern the interlinked workings of the sun, atmosphere, oceans, land and other elements of the climate system.
The various feedback influences are also expressed mathematically. The computer calculates the extent to which the basic physical laws dictate changes in things like temperature and precipitation over time and under different conditions.
One big limitation of the models in predicting the climate decades ahead is that despite the growing speed of computers, they are unable to calculate climatic changes everywhere in the atmosphere.
Instead, they make the calculations only at widely separated points. The points form a three-dimensional grid typically rising 10 or 12 miles above the earth. A typical spacing between grid points is about 150 miles horizontally and less than half a mile vertically.
This "resolution," as scientists call it, is about twice as fine as a decade ago. But it still misses many processes that happen between grid points -- cloud formation, for example.
Coarse resolution is also the major reason why the models are not very good at simulating climate at the regional scale. They simply miss too many small-scale climatic influences, like topography, vegetation and regional atmospheric churnings.
An even bigger limitation of the models than coarse resolution is the incomplete knowledge of the atmosphere's functioning, Hansen says. Gates agrees, saying, "How the natural world works -- that's always going to be our problem."
The biggest gap in knowledge, many scientists believe, is that the net effect of clouds on the planet's temperature is still unknown.
While low-level clouds reflect heat, high-level clouds trap it. Moreover, experts do not fully understand how water vapor behaves when the atmosphere warms. The amount by which vapor amplifies the warming therefore remains uncertain.
In sum, the models are still cloudy crystal balls. But they are getting clearer, and they offer some answers.
"Despite all the uncertainties, I think you can make useful estimates" of climatic change using the models, said Dr. Andrew P. Ingersoll, a planetary scientist at the California Institute of Technology who employs them to investigate the climates of other planets.
"You just have to be aware of the uncertainties," he said. "It's just like any other scientific process."