In the first thorough analysis of the familiar gloomy view of humankind's future on this planet, a special report to President Carter yesterday confirmed it: widespread hunger, polluted air, water shortages and poverty on an overcrowded earth unless major steps are taken very soon.

The Global 2000 Report to the President summarized its findings as "disturbing. They indicate the potential for global problems of alarming proportions by the year 2000," Carter responded by appointing a task force on world resources "to ensure that high priority attention" is given within the government to the problems.

Many such reports call for limits to economic expansion, but this one holds that continued economic development worldwide is essential to braking the slide into real trouble. Population pressures are foremost in the problem and seem to respond only to an improved social and economic condition, the report explained.

"We're not going to solve these problems without it," said Gus Speth, chairman of the Council on Environmental Quality, which drew up the report along with the State Department. The United States should take the lead in tackling the situation, which is an interlocking "vicious circle of causality," the study said.

The numbers show a world population of 6.35 billion by 2000 compared to 4 billion today, with 5 billion in the less developed countries and the number going up faster than it is now.Food production is expected to be up by 90 percent and gross national product up by 145 percent, but mostly in countries that are already relatively rich.

"For every $1 increase in GNP per capita in the less developed countries, a $20 increase is projected for the industrialized countries," the study said. "Disparities between the rich and poor [within] many LDC's are equally striking."

Food shortages in central Africa will be "calamitous," and very bad in much of Asia and the Middle East -- "insufficient [supplies] to permit children to reach normal body weight and intelligence" -- while the overall number of malnourished people is likely to triple the current 400 million.

Deforestation is projected to proceed worldwide until, "by 2020, virtually all of the physically accessible forest in the LDCs is expected to have been cut." Poor people will resort to burning dung and crop residues for fuel rather than leaving them on the soil, further harming crop output. Deserts will continue to spread at or faster than the current rate that takes an area the size of Maine every year.

Urban sprawl is likely to eat much more land. Mexico City, with 30 million persons, will be among many that are "almost inconceivably large and crowded."

Water use, especially for irrigation, is expected to increase 200 to 300 percent in the next two decades, with population growth alone accounting for a doubling of water demand in nearly half the countries of the world. But siltation and salinization already plague half the planet's irrigated land and are likely to get worse.

Among the most urgent problems will be a 15 to 20 percent loss of all the species of creatures on earth, mainly because of deforestation but also because of growing air and water pollution.

In general, "there will be fewer resources to go around . . . the tensions that could lead to war will have multiplied." And all this, the study said, is an optimistic assessment because it assumes continue rapid technological advance no serious social resistance to their adoption, no new plant or human health scourges and no major disruptions of international trade like war or financial collapse.

"Few if any of the problems addressed . . . are amenable to quick technological or policy fixes; rather they are inextricably mixed with the world's most perplexing social and economic problems," the report concludes.

Speth and coauthor Thomas R. Pickering of the State Department told Washington post Editors and reporters that, although the report's conclusions were not new, many Washington decision-makers do not yet believe them. "We have time if we make the right commitments to address these problems," speth said. A subsequent study will recommend some actions that governments could take worldwide, he said.