Where the certainties of physics meet the unruly real world -- at that spot is weather forecasting.

That intersection, in this part of the world, is in suburban Maryland, where the National Weather Service daily passes millions of numbers about behavior at 15 levels of the atmosphere -- temperatures, speeds, pressures -- through huge computers, and a few human brains as well.

On the top floor of a nondescript building in Camp Springs the desktops are littered with atmospheric maps with contour bars, circles, flags and numbers depicting in simple form a single moment in the great fluid flow of air and moisture over the continent and the world.

Though the maps have their roots in the great laws of physics, and the translation from equations to numerical models has been worked out by scholars, these maps piled on desks are not products of slow scholarship. They are live, hours-old snapshots of massive air movements, and will be superseded by new maps in hours.

The weather forecast that comes from the National Weather Service is one of the few products of government work that daily affects the lives of many, perhaps most, citizens. Weather is a universally hot topic, so hot that even bitter politics between nations does not stop the trade in weather data.

During the Cuban missile crisis, said the Weather Service's Don Witten, there was a period when nothing passed between the United States and Cuba but a steady trade of weather information. Through the fierce blasts of noncooperation in the Cold War, weather data continued to be passed daily between the United States and the Soviet Union.

At Camp Springs, each desk has someone responsible for making the crucial calls that may end up sending people scurrying from their homes or heading for cover in their basements. "This is tough, but that's what makes it exciting," said Ron McPherson, chief of the meteorological operations division at the National Meteorological Center there.

On the evening of Aug. 1 last year, for example, Cheyenne, Wyo., was hit, in succession, by a tornado, a severe thunderstorm, a hailstorm with stones up to an inch in diameter and accumulations on the ground of up to four feet, then more tornadoes, and finally flash floods, with people alerted at each step by broadcast warnings.

Not every day is that exciting.

Ross La Porte, meteorologist in charge of the Washington forecast office, said a man called to say he needed to know whether it was raining in Phoenix because he had a cactus in the house and intended to water it when it rained in Phoenix. Contractors call, members of Congress call, the White House calls when heads of state are arriving.

"And people let us know when we miss one," La Porte said.The Agency's Early Years

The National Weather Service, with 5,000 employes, 300 offices, five satellites and one supercomputer, is a part of the National Oceanic and Atmospheric Administration within the Commerce Department. Despite its central importance to government and civilians, its budget is only about $600 million per year.

The service came together as a governmental function in the last century when concern built up in 1874 about storms on the Great Lakes that were disrupting commerce, and the opportunity appeared for a takeover of a network of weather observers that Joseph Henry of the Smithsonian Institution had established in 1849.

Henry and his hundreds of observers had begun issuing daily weather forecast maps, or "probabilities" as they were called, in 1871.

In the early years, the service was placed in the Army signal service, and its chief mission was to give forecasts to sugar and cotton producers and, later, to signal storm warnings for the Atlantic. Forecast by Computer

The service was later moved to the Agriculture Department, and, in 1940, to the Commerce Department when it became clear that the service's prime mission was changing from farm forecasts to specialized aviation forecasts for wartime.

Probably the single most significant event in Weather Service history came in 1954 when forecasting went from "observational" to "numerical."

At the turn of the century, key actions in the atmosphere could be specified and physical equations could be used to give precise predictions of its future state, just as scientists were able to do on a small scale with moisture, gas, and heat in the closed space of a laboratory flask.

In 1904, Norwegian meteorologist Vilhelm Bjerknes created a series of equations that acted as a model of the atmosphere. By 1922, Lewis F. Richardson, a British physicist, was able to make weather predictions by using a mathematical model.

He inserted current weather data into the appropriate equations, describing the motion of air and moisture and the action of heat on them. When calculated, the results would yield a new set of numbers that would state future temperature, moisture and wind speeds.

The model worked badly. There was too little data available to work with, and the computation, which was done on adding machines, took far longer than the weather to form.

But by 1954, computers had arrived, and weather observers and rapid communications systems were in place. The precision of physics was applied to the unruly action of the atmosphere, and truly national forecasts were made for the first time.

Improvements in scientific models have made weather forecasting considerably more accurate. In the late 1940s, for example, the weather office in Salt Lake City was making temperature forecasts that were within a few degrees of correct on most days. But on about 70 days during the year, the forecasts were off by 10 degrees or more.

The same office now sends its regional weather soundings to Washington and gets in return forecasts created on the Weather Service's supercomputer. There are now only about 15 days a year when the citizens of Salt Lake are given forecasts that are off by more than 10 degrees.

In the Weather Service as a whole, only 3 percent of the two-day forecasts (made twice daily) are off by that much.

To produce Weather Service forecasts, about 300 stations report in several times a day. A network of civilian observers as well as government offices, airport towers, and military bases are part of the network.

The data is sent to the National Meteorological Center in Camp Springs, where about 1,000 charts per day are cranked out by the computer, which makes about 300 billion calculations for the twice-a-day forecasts of the next two days' weather.

The new numerical models run on the Cyber 205 computer include the amount of evaporation from the ocean and from earth, the amount of heat from the sun, the effect of the clouds on the incoming heat, and so on. Because every part of the earth's weather affects every other part, the model also takes into account details of weather over the globe, in finer detail over the northern hemisphere and in the greatest detail over the continental United States and nearby ocean areas.

From all the observations, the computer calculates weather conditions at points 50 miles apart on a nationwide grid. Using those points, a series of national weather charts are produced and sent to regional offices around the country, where forecasters may add in local observations before sending the forecast to newspapers, radio and television stations. Trailing the Competition

As in several other fields of science and commerce, the United States has fallen behind world competitors in weather forecasting. While U.S. forecasts for the next 48 hours are accurate and comparable to those being produced in the European Center for Mid-Range Forecasting, the forecasts for between three and six days are not.

The chief difference is simple, said Richard E. Hallgren, an assistant NOAA administrator and head of the National Weather Service. The Europeans have a faster computer -- the American-designed Cray X-MP.

Because weather forecasts must be cranked out on deadline, speed in a computer allows more observations to be put in and more detailed calculations to be made before the deadline arrives.

In an interview, Hallgren avoided the question of whether a bigger computer has been budgeted for future years. He said that instead of concentrating on better three-to-six-day forecasts, the service concentrates on giving better warnings of severe weather.

"There is more severe weather and flooding here than in any nation on earth," Hallgren said.

The country annually can experience as many as 10 hurricanes, a thousand tornadoes, 500 flash floods, and numerous other bits of severe weather. "By contrast Europe has no weather," Hallgren said. "A few dozen tornadoes, no hurricanes, few flash floods."

To improve the Weather Service's ability to provide emergency warnings, some major new high-tech equipment will be put in place between now and the middle 1990s.

To replace 1950s-vintage radar that reads only a gross picture of heavy weather areas, the service will install a nationwide system of "Doppler" radars called NEXRAD, for next-generation radar.

The radar can not only read signals that bounce off moisture droplets but can also determine the speed and direction of the droplets' movement, enabling clearer pictures of severe fronts and the even faster, tighter spirals that make tornadoes.

In tests in the Midwest, the new radars have given more than 20 minutes' warning on average for tornadoes, instead of the usual two minutes now given the public.

In the future, the stream of weather information now being funneled into Washington will be translated into data that is immediately accessible at regional weather offices around the country in a system called AWIPS, the Advanced Weather Interactive Processing System. Current weather charts, now printed out on paper, will be put on computer video screens for easier reading and manipulation.

William Bonner, director of the National Meteorological Center, which is the forecasting heart of the Weather Service, calls the new system extraordinary when applied to short-term forecasts.

The decision on whether to take the leap to the next size computer and accurate three-to-10-day forecasts "will have to come soon," he said. "We are probably not far from making that decision."