This December, world leaders will meet in Copenhagen to add more hot air to efforts to combat climate change. That is so because although the impacts humanity would like to avoid—fire, flood and drought, for starters—are clear, the right numbers to halt global warming are not. Despite decades of effort, scientists do not know precisely what temperatures or greenhouse gas concentrations in the atmosphere constitute a danger.

When it comes to defining the climate's sensitivity to forcings like rising atmospheric carbon dioxide levels, "we don't know much more than we did in 1975," says climatologist Stephen Schneider of Stanford University, who first defined the term climate sensitivity in the 1970s. "What we know is if you add watts per square meter to the system it's going to warm up."

Greenhouse gases add those watts by acting as a blanket, trapping the sun's heat; they have warmed Earth by roughly 0.75 degree Celsius over the last century. Scientists can measure how much energy greenhouse gases now add (roughly three watts per square meter), but what eludes precise definition is how much other factors—the response of clouds to warming, the cooling role of aerosols, the heat and gas absorbed by oceans, human transformation of the landscape, even the natural variability of solar strength—diminish or strengthen that effect. "We may have to wait 20 or 30 years before the data set in the 21st century is good enough to pin down sensitivity," says climate modeler Gavin Schmidt of the NASA Goddard Institute for Space Studies (GISS).

Despite all these variables, scientists from Svante Arrhenius to those on the United Nations Intergovernmental Panel on Climate Change have noted that doubling preindustrial concentrations of CO2 in the atmosphere from 280 parts per million (ppm) would likely result in a world with average temperatures roughly 3 degrees C warmer.

But how much heating and added CO2 is safe for human civilization remains a judgment call. European politicians have agreed that global average temperatures should not rise more than 2 degrees C above preindustrial levels by 2100, which equals a greenhouse gas concentration of roughly 450 ppm. "We're at 387 now and we're going up at two ppm per year," says geochemist Wallace Broecker of Columbia University's Earth Institute. "That means 450 is only 30 years away. We'd be lucky if we could stop at 550."

The GISS's James Hansen argues that atmospheric concentrations must be brought back to 350 ppm or lower—quickly. "Two degrees Celsius [of warming] is a guaranteed disaster," he says, noting the accelerating impacts that have manifested in recent years. "If you want some of these things to stop changing—for example, the melting of Arctic sea ice—what you would need to do is restore the planet's energy balance."

Other scientists, such as physicist Myles Allen of the University of Oxford, examine the problem from the opposite side: How much more CO2 can the atmosphere safely hold? To keep warming to below 2 degrees C, humanity can afford to put one trillion metric tons of CO2 in the atmosphere by 2050, according to Allen and his team—and humans have already emitted half of that total. Put another way, only one quarter of the world's remaining known coal, oil and natural gas reserves can be burned. "To solve the problem, we need to eliminate net emissions of carbon dioxide entirely," Allen says. "Emissions need to fall by 2 to 2.5 percent per year from now on."

Climate scientist Jon Foley of the University of Minnesota, who is part of a team of researchers that defined safe limits for 10 planetary systems, including climate, argues for erring on the side of caution. "Conservation of mass tells us if we only want the bathtub [water level] so high either we turn down the faucet a lot or make sure the drain is bigger. An 80 percent reduction [in CO2 by 2050] is about the only path we go down to achieve that kind of stabilization."

The National Academy of Sciences, for its part, has convened an expert panel to deliver a verdict on the appropriate "stabilization targets" for the nation, a report expected to be delivered by summer 2010. Of course, perspectives on what constitutes a danger may vary regionally and locally, depending on whether one resides in coastal Florida or landlocked Minnesota, let alone in the U.S. or the Maldives.

Keeping atmospheric concentrations of greenhouse gases below 550 ppm, let alone going back to 350 ppm or below, will not only require a massive shift in human society—from industry to diet—but also, most likely, new technologies, such as capturing CO2 directly from the air. "Air capture can close the gap," argues physicist Klaus Lackner of the  Earth Institute, who is looking for funds to build such a device.

Closing that gap is important as the best existing data—observations over the last century or so—show that the climate is sensitive to human activity. "There are thresholds of irreversible change out there, we don't know where they are," Stanford's Schneider notes. "What we do know is the more warming out there, the more dangerous it gets."