The predicted rise in the burning of [WORD ILLEGIBLE] to make up for the shortage of oil [WORD ILLEGIBLE] natural gas in the next 50 years will, according to one academician, raise the earth's temperature by 4 degrees fahrenheit.

The scientist making that precise forecast yeaterday is Columbia University's Dr. Wallace S. Broecker, who based it on the fact that one ton of burned coal produces three tons of carbon dioxide and on the assumptions that in 10 years much of our electricity will begin to come from coal, many o four automobiles will start to be powered by liquid coal chemicals and our houses heated by gasified coal.

"The often used analogy of the green-house is apt, where carbon dioxide is transparent to incoming sunlight but somewhat opaque to outgoing earthlight," Broecker told the annual meeting of the American Geophysical Union. "The primary effect of more carbon dioxide in the atmosphere will be a warmer planet."

Broecker said his forecast assumes a doubling of the world's population to 8 billion by the end to the century and a turning to coal, "whose environmental hazards seem more acceptable to the public than those associated with nuclear reactors."

The geologist from Columbia's Lamont-Doherty Observatory said that based on these assumptions the atmosphere will double its carbon dioxide content in the next 50 years, thereby raising the average temperature of the earth from 60 to 64 degrees. He said his 4-degree rise comes from "widely accepted" computer models of how much heat carbon dioxide can reflect back to the earth's surface.

"From the point of view of personal comfort this might not have much impact, just less opportunity to ski and more to swim," Broecker went on. "But it is not our personal comfort which is a stake but the whole web of life . . . the ecosystem."

Broecker conceded that a rise in carbon dioxide content could increase the earth's cloud over, but he challenged the view that the increase in cloud over would cool the earth enough to offset the temperature rise from carbon dioxide.

"I see no evidence to support this optimism," Broecker said. "While there is certainly room for debate, in my view it would be irresponsible to discount the possible effects of carbon dioxide . . ."

Among the effects of a 4-degree rise in the earth's temperature would be slow melting of the polar ice caps that would raise the earth's sea level by 18 feet in the next century.

"Although posing no threat, such a rise would be a very expensive nuisance," Broecker said. "Enormous expenditures would have to be made for the protection or relocation of the low-lying portions of coastal cities."

The melting of thin floating ice in the Arctic Ocean would change regional rainfall patterns, Broecker said, because an ice-free Arctic would provide the earth with a new source of atmospheric moisture. The warming trend might also reduce the ocean's fish populations, which Broecker said are maintained by the mixing of the oceans that come from the changes between warm and cold waters.