To paraphrase a common saying: Everybody complains about the weather forecast, but nobody does anything about it. Of course meteorologists have been trying to make better forecasts since they invented meteorology as a separate branch of science, but sometimes it seems the cards are just stacked against them.

## First Forecasting Problem: The Equations

The atmosphere is not so terribly hard to describe, either physically or mathematically: There are seven well-known equations that have seven variables. Theoretically the equations have a solution. However, modern mathematical techniques are totally inadequate to solve them.

So, we must give up our dream of predicting the weather for all time as though we were predicting the flight of a baseball given the speed of the ball, the trajectory and angular momentum of the slugger’s swing, the air resistance, the weight of the ball, and the possibility of the ball hitting a bird. Enter the computer.

## How Computers Can Substitute for an Analytical Solution to the Equations

The equations of motion describe the change in the movement of air with time, so if we know the conditions at time zero, we can use the equations to determine the conditions at some later time. The smaller we make the time increment, the better our results will be. We can take the results after a short time interval and use those values to repeat the calculation. Each step is called an iteration, and the more iterations, the better the forecast — theoretically.

Back in the 1960s, there was great optimism that computers would make forecasting easy — just plug in some numbers and grind out the forecast. The numbers went in and the forecasts came out, but they (the forecasts) were maddeningly inaccurate. Even with today’s vastly increased computing power, meteorologists struggle to make medium-range forecasts that are better than a simple prediction of the historical average.

## Forecasting the Weather’s Second Problem: The Whole Atmosphere is Interconnected

Let’s go back to the baseball analogy. If David Ortiz hits a home run in Fenway Park, we can calculate the trajectory of the ball without any concern about whether Hanley Ramirez has gotten a hit or struck out in Los Angeles. But the atmosphere circles the globe, and if we want an accurate forecast for a week from now over the United States, we care very much whether there’s a storm in China. We need to make a forecast for the whole atmosphere, and this is made more difficult by the sparsity of data from far-off and sometimes unfriendly countries.

## Third Problem With Forecasting: The Boundary

To model the whole atmosphere, we have to consider the boundaries. Horizontally, there is no problem except the fact that the system is curved, but we can handle that. The top is not so much of a concern because the weather we care about takes place at the bottom — and that’s where the trouble comes in. The surface of the earth is not flat; it is not of a uniform material (in particular it is sometimes water and sometimes not). Furthermore, the non-uniformity has no particular pattern. Whatever model we use, the boundary condition is pretty much arbitrary.

## Finally, Some Good News

The jet stream, a powerful river of air roughly four miles up, is an important factor in forecasting the weather. Because the jet stream is, except near the earth’s highest mountains, far removed from the boundary, forecasts that isolate this level in the atmosphere are pretty accurate out as many as ten days.

We humans, of course, are interested in the weather at the surface, very close to the boundary, but the jet stream pattern is highly correlated with weather at the surface, so experienced weathermen can use jet stream forecasts to make ground level predictions.

## Major Weather Forecasting Models:

**The American Model: **The United States National Centers for Environmental Protection (NCEP) uses a model called the Global Forecast System (GFS). The GFS has a horizontal resolution of about 18 miles and runs one hour iterations for 24 hours and 3 hour iterations after that up to 8 days. The NCEP also issues forecasts based on an ensemble of lower resolution models, called the Global Ensemble Forecasting System (GEFS).

Waves that ripple through the jet stream are the primary cause of weather at the surface of the earth. The GFS tends to over-amplify these waves, and the forecast, especially at the longer time scale, is often inaccurate. The ensemble, though based on lower resolution, is frequently better. Since the GFS is the only forecast that is available free in its entirety, it is used by such forecasting entities as the Weather Channel, Weather Underground, and AccuWeather. The GFS will be upgraded in 2014 to use a nine mile horizontal grid.

**The European Model:** The Integrated Forecast System (IFS) is a model run by the European Centre for Medium-Range Weather Forecasts (ECMWF). The IFS uses a variable horizontal resolution of generally 15 to 30 miles; some of the information about the model is proprietary, as is some of its output.

**Other Models: **Three other global models are in general use, though they, like the IFS, are proprietary and not always available to the public. The Global Environmental Multiscale Model (GEM) is run by the Canadian Meteorological Center; the Navy Global Environmental Model (NAVGEM) is put out by the Naval Research laboratory; the Unified Model is published by the United Kingdom Meteorological Office (UKMET).

## Accurate Weather Forecasting

Will computers ever be able to accurately predict mid-range and long-range weather patterns? If current techniques advance significantly, it’s possible. Until then, the short term and jet-stream-based forecasts will be most accurate.

Decoding Science. One article at a time.