The temperature on the surface of the sun fell 11 degrees last year, the first such drop ever recorded and one that could trigger changes in the earth's climate in the next few years.

An 11-degree drop in the sun's surface temerature is a change of only one-half of 1 percent, said Dr. William C. Livingston of the Kitt Peak National Observatory in Tucson, Ariz., where it was measured. Scientists have said that a 2 percent decline in the sun's surface temperature over a period of as little as 50 years would be enough to form glaciers over most of the earth.

"We presume the changes we see are cyclic and that the temperatures will stop fading sometime in the near future," Livingston said yesterday. "I can't image anything else happening."

The decline in solar surface temperature began in January 1977, around the time the 11-year sunspot cycle passed its period of minimum activity and began to increase. More and more sunspots have broken out on the sun's surface since the start of last year. The period of maximum sunspot activity is expected late next year or early in 1980.

"We think we're seeing a direct correlation here, that as solar activity goes up the sun's surface temperature goes down," Livingston said. "It's the opposite of what you might guess but we believe that when you have a rise in sunspot activity the total temperature must go down as an adjustment to conserve solar energy."

Whatever it is that Kitt Peak scientists saw, it was for the first time. Their observations were made using the McMahon solar telescope, which is the newest and largest of its kind in the world.

The solar telescope tracks the sun with a 80-inch telescope tracks the sun unblurred image of the sun more than three feet across to a device called a spectroscope that analyzes sunlight. The device breaks down sunlight into a continuous rainbow of color where temperature changes can be identified in individual chemical elements as they burn on the sun's surface.

The most sensitive element on the sun is carbon, which flares up if the sun gets hotter and dims if the sun cools. Iron also is sensitive, but opposite the way carbon is. Should the sun cool iron would stand out a little brighter on the sun's surface."

"Iron tends to form in a cooler environment," Livingston explained. "More iron atoms would show up on the sun in a cooler state."

Livington said the solar telescope first began to watch for temperature changes in January 1975. For the next two years, the telescope saw no change in the sun's temperature, which remained constant at 9,820 degrees fahrenheit.

The carbon began to dim in January last year. At precisely the same time, iron grew stronger.Livingston said the iron observation was confirmation that the sun was cooling, since it meant that the telescope was not misreading the carbon change.

If Livingston's theory that the temperature will continue to fall as sunspot activity rises is right, then the temperature should continue declining until late next year or early in 1980.

Livington said that it almost surely means some climatic change, because declining solar temperatures mean less heat will reach the earth. But at the time, rising sunspot activity means more ultraviolent light and X-rays will strike the outer boundaries of the earth's atmosphere, triggering changes of their own.

"It would be premature to look for climate changes right now," Livington said. "By that, I mean I don't think you can blame the last two winters on what we're seeing on the sun right now. But I do think we can look ahead to some change, whatever it might be."

A growing number of scientists believe that changes in the sun trigger changes in the earth's climate. Scientists now believe the 11-year sunspot cycle has a strong connection with drought on the earth. The drought in southern New Mexico that ended in August 1972 came to an end at the same time that large solar flares appeared on the surface of the sun. A second drought ended two years later when flares again streaked from the sun's surface.