The forecast is for continued cool weather through the mid-1980s, with a global warming trend for the rest of the century -- followed by a severe cold snap after 2000 that might last the first half of the 21st century.

That's the way that Drs. Leona A. Libby and Louis J. Randolfi project the world's climate for roughly the next 70 years. They base this forecast upon a detailed analysis of old trees.

Libby, an adjunct professor of engineering at the UCLA, and Randolfi, formerly a graduate student in Libby's laboratory and now a research scientist with the Global Geochemistry Corp. of Santa Monica, Calif., have made chemical analyses of tree rings ranging in age from a few hundred years to more than 1,800 years, since a tree lays down a new ring each year from the rainwater, carbon dioxide and other nutrients it absorbs during the course of that year.

Tree ring-sizes have long been interpreted as indicators of climatic conditions for any year -- a wide ring suggesting ample supplies of water and nutrients, along with benign temperatures. Libby and Randolfi extended this concept by calculating such factors as the ratio of certain isotopes (different forms of the same element), like oxygen-16 to oxygen-18, from atree ring of say, 800 or 900 years agi, and comparing it to a more recent ring for which the annual average temperature is known.

These tree measurements reflect, for example, the "Little Ice Ages" of the 15th and 18th centuries, when the annual average temperatures dropped one to two degrees Fahrenheit. That slight temperature drop was enough for glaciers in the Alps, Scandinavia, Alaska and New Zealand to extend much farther down into their valleys. The growing season was also shorter and cooler and life generally was difficult.

The Libby/Pandolfi tree-ring studies indicate the same sort of climatic hard times in the 4th century AD, a time for which there is little information available. Still it is known that the Emperor Diocletain imposed price controls on key commodities such as wheat, and Libby thinks maybe poor weather caused shortages.

Now she and Pandolfi have found additional evidence that not only corroborates their earlier work on past climates, but also suggests possible climatic trends in the future. For example, the annual catch of blue crabs in the Chesapeake Bay varies in much the same way as the more conventional factors do.

Drawing upon morle than 50 years of catch yields for the crabs, they set up some complex mathematical equations of the crab tonnage figures, along with maximal air temperatures and minimal rainfall measurements from nearby and the variations in high tides recorded in the bay, all for the same 50-year span. When these factors were plotted on a graph, they showed the same periodicity -- they appeared to rise and fall almoslt in union.

"The explanation we offer for the agreement among the periods," the researchers wrote, "is that high tides wash nutrients into the surface waters of the bay, and higher temperatures warm the surface waters, and minimum rainfall allows the surface waters to become more saline, all of which factors are salubrious for crab growth." (Incidentally, their curves accurately caught the up-turn in the crab yield observed in 1977. Looking further ahead, the UCLA theam has forecast increased catches until 1982-perhaps as much as 90 million pounds of crabs annually -- and continued high yields until the late 1980s.)

Their trace of the isotopic variations in very old tress from around the world coincides almost perfectly with a trace of temperatures made in England with mercury thermometers since the early 1700s. This corroborated record shows the trees -- German oaks, Japanese cedar and American sequoia -- with reduced ozygen -18 concentrations in the first and last decades of the 18th century, decades that thermometer records show as colder than average.

Both the isotope record and the thermometer record show neat agreement for the cold decades at the ends of the 17the and 18th centuries, when temperatures fell by 1/10th to 2/10th of a degree. They also show corresponding parallel tracks during the 1700-1730 and 1890-1940 periods when temperatures rose by 3/10ths and almost 5/10ths of a degree.

Is it coincidence that so many of Europe's great palaces and chateaus were built in the early 1700s when temperatures, according to the tree-ring data, were mild? Libby thinks not. She feels that because of many consecutive years of warm sunshine and abundant rain, there were ample supplies of food and other raw materials. People, especially the ruling classes, prospered and commissioned the construction of their magnificent structures.

More recently, the worlld has enjoyed an agricultural boom during the past 70 years. The earth's annual average temperature has risen by about 1 to 1 1/2 degrees, and never has so much food been produced.

And when Libby and Pandolfi project their curves into the future, they show lower average temperatures from now through the mid 1980s. Then," Libby said, "we see a warming trend (by about a quarter of a degree Fahrenheit) globally to around the year 2000. And then it will really get cold -- if we can believe our projections. This has to be tested."

How cold? "Easily one to two degrees, and maybe even three or four degrees. It only takes [a shift of] 10 degrees to bring on an Ice Age. It was less than a half-degree drop in the annual temperature that led to the little Ice Age during the late 1700s. So this drop, after the start of the next century, could be very significant for the world if our projections are correct."