President Reagan departs today for a two-day summit meeting with Canadian Prime Minister Brian Mulroney that has been scripted to play to their Irish ancestry on St. Patrick's Day but promises to be dominated by one of the great environmental controversies of the last decade -- acid rain.

Canada has made elaborate preparations for the 24-hour visit, dubbed the "Shamrock Summit," down to remodeling the three-room presidential suite in Quebec City's Chateau Frontenac hotel for the Reagans with a marble, handmade four-poster bed. Tonight, the two leaders are to star in a skit highlighting a St. Patrick's Day gala at the Quebec Grand Theater.

The summit script also includes a new agreement to share the costs of a $1.3 billion modernization of the aging Distant Early Warning (DEW) Line radar across northern Canada. Reagan and Mulroney also are to ratify a Pacific salmon fishing treaty, sign a new legal cooperation agreement, discuss Canadian participation in the U.S. manned space station project and ways to improve trade between the two large North American economies.

"We are going to Canada now for one simple reason -- no country is more important to the United States," Reagan said yesterday, devoting his weekly radio address to the summit meeting.

Reagan also will be looking to fellow conservative Mulroney for support on arms limitation and the "Star Wars" antimissile defense system just five days after resumption of arms control negotiations and the ascension of Mikhail Gorbachev as the new Soviet leader.

Gorbachev will figure in the two leaders' discussions; Mulroney just returned from a meeting with him after the Moscow funeral of Konstantin Chernenko, which Reagan decided not to attend.

Mulroney, who campaigned last year on a theme of bringing increased U.S. investment to Canada, hopes to demonstrate that his rapport with Reagan can produce substantive gains for Canada's environment and its economy, which is suffering higher unemployment and inflation than the United States.

For all their personal camaderie -- Reagan referred to Mulroney as "the other North American Irishman" when the prime minister visited the White House last Sept. 24, eight days after his election -- the problem of acid rain looms as a major irritant.

"The problem of acid rain concerns both our countries and I'm anxious to hear the prime minister's views on that subject," Reagan said yesterday.

Acid rain is caused by emissions of sulfur dioxide and other chemicals from factories, power plants, automobiles and natural sources in the United States and Candada. Smelters in Canada, and U.S. power plants burning high-sulfur coal are chief sources. The emissions then mix with water vapor to produce weak solutions of nitric and sulfuric acids that then fall to earth and are believed to cause extensive damage to lakes and forests in the northeastern United States and Canada.

Fulfilling a campaign promise, Mulroney's government on March 6 announced a major acid-rain cleanup program designed to reduce sulfur dioxide emissions by 50 percent over the next six years in eastern Canada. The plan includes government financial aid to the smelting industry for pollution control and stricter auto-emission standards.

But Canada also is looking to the United States for help, saying half the emissions come from the south. "It is a common problem," Mulroney said Friday in an NBC interview. "We have to do something about it."

But Reagan has resisted a common approach. He ran for president in 1980 seeking relaxed air-pollution standards, and his administration has refused to support any costly, federally financed cleanup program for acid rain, saying more research is needed first.

The federal budget crunch has been one reason for Reagan's recalcitrance. Furthermore, Congress and U.S. industry are sharply divided over how to share cleanup costs.

But White House officials also say that Reagan, in private conversations, has been skeptical that acid rain is caused mostly by manmade pollution, and instead blames much of it on natural causes.

Although Mulroney said he wanted to put acid rain at the "top of the agenda," the Reagan administration has tried in advance to play down any friction over the issue. White House officials said Reagan will stress the progress made by the United States over the last 12 years in controlling air pollution, and a big increase in his budget for acid rain research.

That would not be enough, however, for Mulroney, who needs "a promise of some sort of movement beyond just research," said Charles Doran, director of the Center of Canadian Studies at the School of Advanced International Studies, Johns Hopkins University.

Reagan's image-conscious advisers, particularly Michael K. Deaver, departing deputy chief of staff, realized that a stalemate at the summit could spell political trouble for the prime minister, White House officials said.

The result: The leaders are expected to announce a "joint effort" between their countries to examine the problem, satisfying Mulroney's need for progress on the issue and Reagan's desire not to substantially switch his policy, at least for now.

This is Reagan's first foreign trip of his second term, and his reception in Canada is expected to be more friendly than that from the hecklers who greeted him on his first visit to Ottawa four years ago. On a personal level, Reagan says, "I like Brian Mulroney a lot," as he apparently did not feel about former Prime Minister Pierre Elliott Trudeau, whose 1983 peace initiative, when superpower arms talks were stalled, angered the White House.

A successful summit could rekindle Reagan's moribund proposal for a "North American accord," linking the United States, Canada and Mexico, which got a chilly reception in his first term.

Reagan hopes the summit also will send important signals around the globe: setting a positive tone for another round of international trade talks and demonstrating to Moscow the cohesion of the West as arms talks begin.

The summit will produce an agreement to modernize the DEW Line, a 3,000-mile string of radar stations built in the late 1950s to detect nuclear-armed Soviet bombers if they appeared over the horizon. The 31 obsolete stations will be replaced with at least 52 capable of scanning low enough to spot advanced, low-flying bombers and ground-hugging cruise missiles. It will be renamed the North Warning System; Canada is to pay 40 percent of the modernization cost.

Reagan and Mulroney also will touch on the $120 billion, two-way trade relationship between the two countries. Congress last year approved legislation that opened the way for the creation of a free-trade zone with Canada.