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Is the world getting warmer?

It's invisible and insidious and sounds like science fiction. But a series of recently published studies is lending new weight to the theory that mankind's industrial activities are changing the climate.

Even a small change in Earth's complicated weather system could alter the face of the globe. A slight temperature increase, for instance, could cause portions of the polar ice caps to melt, scientists say. Water would lap against the steps of the Capitol. The American grain belt would shift north. Camels would graze on rich grass in the Sahara.

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All these changes could stem from a poorly understood phenomenon known as the greenhouse effect. In it, gases and water vapor in the atmosphere trap heat and send it back to Earth. While this is not exactly how glass in a greenhouse collects and traps heat, the term greenhouse effect is used for this atmospheric phenomenon. A component in this heat trap is carbon dioxide, a colorless, odorless gas produced by all combustion. Researchers say the amount of carbon dioxide has increased so much since the Industrial Revolution (its quantity will double by the middle of the next century) that it will magnify the greenhouse effect and raise the world temperature.

Few researchers agree on how much change will occur. Because only a slight warming is expected over the next hundred years, that temperature change has been very difficult to measure and predict.

Now some researchers believe they have measured the beginnings of that flux. And while they hesitate to sound the alarm, their findings add a new and controversial immediacy to the theory.

The most recent report appeared in the respected journal Science. Carried out by Dr. George S. Kukla and his associates at Columbia University's Lamont-Doherty Geological Observatory, the study reports one of the first direct observations that the world is getting warmer: the melting of the Antarctic ice.

These findings apparently fit with the theory that, if the Earth becomes warmer, the most obvious melting will occur at the icecaps. As snow and ice melt , the theory says, newly exposed ground collects heat, and a cycle of more and more heating occurs. The theory was developed in part by Dr. V. Ramanathan, a staff scientist at the National Center for Atmospheric Research in Boulder, Colo. Ramanathan said spring and summer is when you'd find the most heating.

Kukla found further evidence that Ramanathan was right. Summer surface temperatures in northern snow areas were about 0.9 of a degree Celsius warmer than during the century's warmest years. Yet he warns that factors not fully understood could also play a role.

''Those changes are in the right places in the right seasons to fit the theory,'' Kukla says. ''But we are still unable to prove the positive relationship.''

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Kukla's study followed soon after an equally startling report by a team of NASA scientists in New York. In August, the researchers reported that the average climate temperature of the world had increased by about a half degree centigrade over the last century and will increase with the ''unprecedented magnitude'' of six to nine degrees Celsius over the next hundred years. The team based its findings on temperatures recorded for the last century at hundreds of locations throughout the world. What makes their study so significant, NASA researchers say, is that no previous studies had directly measured the world temperature increase, even though the increase in carbon dioxide was well known.

Scientists estimate that a century ago there were 280 to 300 parts per million of carbon dioxide in the air, vs. 335 to 340 parts per million today. Today's figure will probably double if people keep burning fuel at the presently increasing rate of 4 percent per year.

''There is sound evidence at this point that something is happening,'' said Dr. David Rind, a staff scientist at NASA's Goddard Institute for Space Studies in New York City. ''By the end of this decade there could be no doubt about the warming.''

The NASA team went a step further. With the increased temperature, they said, enough ice would melt to produce floods covering a quarter of Florida and Louisiana, 10 percent of New Jersey, and would inundate many low-lying countries.

Perhaps because of those predictions the NASA theory attracted some opposition.

Dr. William Kellogg, senior scientist at the National Center for Atmospheric Research in Boulder, Colo., said that while he generally agreed with the temperature projections, the changes would not occur as quickly as they predicted.

Dr. Sherwood Idso, a climate specialist with the US Department of Agriculture in Phoenix, Ariz., says NASA's world temperature forecast ''is about 10 times too great,'' and that the team did not look carefully enough at their data.

Idso's studies predict only a 0.3 degree Celsius world temperature increase with a doubling of carbon dioxide. ''There are some very positive outcomes of CO 2 increase in the atmosphere,'' he adds. ''There would be a tremendous enhancement of agriculture everywhere.''

Dr. Reginald Newell of the Massachusetts Institute of Technology also predicts a small temperature increase. Newell bases his predictions on the ability of the oceans to disperse heat.

Most climatologists say the Kukla study is too new to dissect. Yet if anything, their criticisms emphasize the complexity of the research. Predicting requires researchers to design a computer ''model'' of the atmosphere. But no one understands all the factors involved. Is the amount of heat the air holds constant or does it change? What is the buffering effect of the Earth's massive, heat-absorbing oceans? No models have accounted for changing cloud cover, which may affect how much heat the atmosphere reflects or passes on.

Then there are complex variations of the weather itself. No one can explain the Earth's general cooling trend that preceded the warming scientists are currently measuring; some say it may have to do with solar cycles or an increase in volcanic particles high in the air. Kukla's study inexplicably found that fall and winter temperatures dropped in the same northern areas where they increased in the summer. Despite these unexplained variations, researchers agree the general trend is toward the warm.

In an effort to resolve some of these differences, Congress last summer authorized the National Academy of Science to review the changing greenhouse effect. That study - due in early 1982 - predicts an estimated three-degree rise in the next hundred years, according to Dr. John Perry, executive director of the academy's climate board.

Meanwhile, other researchers are planning what to do. Citing ''the grave uncertainty of the timing'' of a climate change, Dr. Walter Roberts of the Aspen Institute in Colorado said he places ''primary emphasis on those things that will pay off even if there is no climate change.'' Roberts, who directs the institute's program of Food, Climate, and World Futures, recommends improving irrigation, developing heat and drought-resistant crops, and planting a greater diversity of crops in developing countries.

''I don't think there's any way to stop the climate warming,'' he says. ''It's driven by an energy requirement and a global policy that will not be affected by uncertain data.''

Dr. V. Ramanathan, who developed the computer model with which Kukla correlated his results, says that no matter whose theory you believe reseachers should see positive results, ''by the mid to late 1990s.'' ''But our problem in terms of policy is in the next five to 10 years,'' he added.