Utah farmers and ranchers have begun applying for payments under the $3.9 billion drought relief measure President Reagan signed into law Aug. 11.

The program is designed to compensate farmers for losses suffered in this year's record drought, which is expected to cut U.S. harvests by more than 30 percent.The largest number of Utahns seeking relief funds is expected to come from the state's northern counties, said Koze Hallows, program specialist from the Utah Agricultural Stabilization and Conservation Service office in Salt Lake City.

He said the southern third of Utah did not suffer from drought nearly as much as the rest of the state. "Somewhere between $250,000 and $500,000 is expected to be paid to an estimated 500 Utah farmers, most of them from Provo north.

"We anticipate another 1,500 farmers will apply for other kinds of relief associated with the drought even though they are not eligible for direct cash payments," Hallows said.

"In order to qualify for cash payments under the drought relief plan, a farmer must have had a drought-related production loss of more than 35 percent of his normal yield.

"In order to prove such a loss, farmers can use production statistics already formulated for their county and area or they can bring in production records for three years prior to 1988. Most farmers are waiting until all their harvesting is completed, since they have until March 31, 1989, to apply for drought relief payments."

Another relief program, an emergency program for livestock feeders, is also available for ranchers and farmers who suffered from the drought. Hallows said farmers can get payments from either one of the drought programs, but not both.

Farmers who suffered losses of 35 percent or less can apply for credit on loans they obtained earlier this year through other government crop subsidy programs, officials said. More than 1,500 Utah farmers and ranchers are expected to apply for these kinds of "forgiveness" credits, Hallows said.

Utah agricultural experts say dry-land wheat yields in northern Utah this year may be down 30 to 40 percent. Other statewide forecasts indicate winter wheat will be down 23 percent, spring wheat down 22 percent, barley down 15 percent, dry bean production down 23 percent, hay production down 18 percent and corn down 2 percent.

Nationwide, peanuts and tobacco may be the only crops with yields larger than last year. U.S. peanut production is expected to top last year's crop by 20 percent and tobacco output is forecast at about 10 percent above the 1987 level.

Among the principal grains, corn is expected to be down nationally by 37 percent of the 1987 figure; sorghum grain, down 27 percent; soybeans, down 23 percent; and wheat, down 14 percent from last year.