The use of computers, sensors, and science to predict weather dates back to the 1950s. This numerical weather prediction is an endeavor that the U.S. National Academy of Sciences called one of the most significant scientific, technical, and political accomplishments of the 20th century.

Around the world, about a dozen major and countless smaller facilities perform numerical weather forecasting. Among the largest within their regions are the Centro de Previsão de Tempo e Estudos Climáticos, in São Paulo, Brazil; the European Centre for Medium-Range Weather Forecasts, in Reading, England; the Japan Meteorological Agency, in Tokyo; the National Centers for Environmental Prediction, in Camp Springs, Md.; and the South African Weather Service, in Pretoria. Forecasts start with observations: temperature, humidity, pressure, wind speed and direction, and cloud properties—how much water does the cloud contain, is it liquid or ice, how big are the drops or ice crystals?

Collecting the data is not a trivial task. Observers gather it from weather stations, from balloons, from aircraft, from ships at sea, and from more than a dozen satellites that circle the globe transmitting images of clouds and measurements of the radiation emitted by the clouds and the atmosphere. Forecasters use specialized software to derive data about temperature, winds, and moisture from the radiation measurements.

As wide-ranging as it is, the weather data pool today is a patchwork collection coming from different sources, taken at different times, with different accuracies, random errors and biases, and a variety of gaps. That’s because most data collection tools provide information only on wind, temperature, or some other variable, rather than a full picture of the weather at a particular point.

To create a three-dimensional weather model of the world, the computer models require in principle that all individual pieces of data for the 1 billion or so points on the globe refer to the same instant in time. In practice, of course, they never do.

The means by which meteorologists bring all the data together and put it into a form that can be used by the models is called assimilation. It’s an iterative process: scientists use previous weather predictions as a first guess of atmospheric conditions, comparing them with actual data to spot potential problems. They also exploit the relationships among different variables to account for parameters that aren’t measured—for example, they use the horizontal distribution of temperature to calculate how fast the wind is blowing.

Forecasters use supercomputers to plot the data on a 3-D map of the earth’s atmosphere. This resulting grid of data sets the initial state of a weather model. The computer systems apply basic physics equations to determine how different parameters will change during a period of days and affect the weather in a particular place. The equations include Newton’s second law of motion, which states that a force acts on a mass and produces an acceleration; the first law of thermodynamics, which relates temperature changes in a mass to heat added or removed from that mass; and the law of conservation of mass, which precludes mass in the atmosphere being either created or destroyed. Another is the equation of state, which relates the pressure, temperature, and density of a fluid.

Repeated over and over on the barrages of data flowing in from global sensors, the equations take myriad fluctuations in data and compute effects. An increase or decrease in the temperature of a section of the atmosphere leads to changes in barometric pressure—which, in turn, change the direction and speed of the winds, and so on. Typically, the modeling computers run the set of equations 5000 times to project weather conditions one day ahead; it takes about 10 minutes on a 2-teraflop computer.

Global and regional weather models feed off each other. The regional models take the output of global ones and fine-tune it to predict local weather. Forecasters combine the results of both global and regional models to create the weather predictions you see on television and in newspapers. The global model gives the basic picture, and the regional models fill in local details. For example, in the Katrina forecast, the global model predicted the storm track and provided the regional model with the information needed for it to give the specifics about the storm’s intensity and evolution.

The process is not as straightforward as it might seem, because the atmosphere is a nonlinear system—that is, it can behave chaotically and therefore be impossible to model with complete accuracy. In a nonlinear system, a minor alteration of initial conditions is typically magnified into an enormous change. The most nonlinear weather phenomena, and therefore the most difficult to forecast, are low-pressure systems, fronts, and thunderstorms—the weather events that people are most concerned with.

Whether your picnic is ruined by a tumultuous summer thunderstorm or is undisturbed by a fat cumulus cloud drifting overhead can be determined by a factor as minor as a 2 °C temperature difference or a 5 percent difference in relative humidity 12 hours before you spread out your blanket. If that thunderstorm forms, it can change the local winds, atmospheric pressure, and temperature for such a short time and on such a small scale that its effect is not picked up by sensors and therefore not included in the data that forecasters input to set a model’s initial conditions. Because of nonlinearity, the imperfection created by that missing data grows unpredictably over time and makes subsequent forecasts wrong.

That is one example of the so-called butterfly effect, the hypothetical idea that, under the right circumstances, small changes such as the flapping of a butterfly’s wings can eventually cause a huge weather disturbance thousands of kilometers away.

Weather models, like everything else in the digital world, are discrete. They compute key meteorological parameters such as temperature and relative humidity—the amount of moisture in the air as a fraction of the amount it could hold at that temperature—at regularly spaced points on a 3-D grid enveloping the Earth. The distance between the points on that global grid defines the resolution of the model. And just as in today’s digital cameras, the higher the resolution of a model, the clearer the picture of future weather it produces.

Today’s global models typically use a 35-km horizontal resolution; the resolution of regional models can be as small as 5 km. Three such regional models cover the continental United States.

Today’s resolution, however, is often not good enough. For example, even 5 km is too coarse to accurately simulate a typical thunderstorm. Sometimes, too, the models miss more serious weather conditions, including tornadoes, squalls, floods, or the location of the line separating rain and snow in a major winter storm.