## Numerical Model Forecasts: A Caveat

Beware: the accuracy of numerical weather forecast models typically declines the farther into the future they go.

This is true because of a characteristic of many nonlinear, "chaotic" systems such as the atmosphere: they are sensitive to initial conditions. This means that if the same system were to start out in two, slightly different states, the small initial differences between them would tend to become larger over time. Eventually, the states would become quite different from each other. The implications for weather forecasting are huge.

To understanding why, note first that that numerical (computer model) weather forecasts must start with as accurate an analysis as possible of the state of the atmosphere (temperature, pressure, winds, moisture content), in three dimensions everywhere in the atmosphere, simultaneously. The models then solve an approximate set of nonlinear, coupled, partial differential equations that express the basic physical principles that govern atmospheric behavior. (These principles consist of the ideal gas law plus conservation laws for momentum, energy, and mass). These equations describe how the atmosphere changes with time, given some initial state (the analysis).

An analysis of the state of the atmosphere requires measurements. Measurements of the atmosphere are made regularly around the earth by a variety of in situ and remote instruments. Inevitably, however, these instruments can't make perfect measurements--that is, there is always some, usually small measurement error. Moreover, instruments can't measure the state of the atmosphere everywhere and all at once. Hence, the state of the atmosphere where there are no measurements must be interpolated from places where there are measurements. No interpolation scheme is perfect, so there are more errors.

This means that the analysis of the state of the atmosphere, from which every forecast starts, is inevitably a little bit different from the actual state of the atmosphere. As is true of any "chaotic" system, a forecast that starts with that slightly erroneous initial state will sooner or later drift away from what the real atmosphere actually does, because the atmosphere, and the numerical model of the atmosphere, are "sensitive to the initial conditions".

Moreover, the equations that numerical weather forecast models solve are only approximations to the nonlinear, coupled, partial differential equations that describe the evolution of the atmosphere. Hence, the model itself introduces certain errors to the forecast, and these additional errors contribute to the divergence of the forecast from what the real atmosphere does.

For these reasons, it will never be possible to make weather forecasts beyond about two weeks or so that are any better than educated guesses. Weather forecasts have gradually improved over the decades as a result of many ongoing research and development efforts, and forecasts that are better than educated guesses can now be made out to a week or so, depending on the state of the atmosphere. (Note that this stands in constrast to climate forecasts, which are a different story in many respects. Climate forecasts with some value can be made decades into the future--they just can't be used to make specific weather forecasts for any particular place and time.)

Ensemble Forecasting. One way in which forecasters try to take into account the sensitivity of forecasts to the initial conditions, is to make an ensemble of forecasts. Each member of the ensemble starts with a slightly different analysis of the atmosphere at the same starting time. The differences among the analyses are similar to those that measurement and interpolation errors typically introduce in such analyses. (Sometimes, some members of the ensemble might be generated by different forecast models or different configurations of the same model.) The extent to which the forecasts by the individual members of the ensemble diverge from each other tells forecasters something about the reliability of the model forecasts: highly divergent forecasts by the ensemble means low forecast reliability; modestly divergent forecasts means higher reliability. As a general rule, the farther into a forecast the ensemble goes, the more the forecasts tend to diverge from each other and the less reliable any individual forecast will be.

The jet stream forecast maps offered by the California Regional Weather Server (CRWS) are based on output of the Global Forecast System (GFS) model, which is developed, run, and maintained by the National Centers for Environmental Prediction (NCEP) in Camp Springs, Maryland. NCEP makes a "control run" of the GFS model four times a day, based on analyses of data gathered at 00Z, 06Z, 12Z, and 18Z (that is, midnight, 6 am, 12 noon, and 6 pm standard time in Greenwich, England). The California Regional Weather Server shows forecasts from the control run. In addition to the control run, twice a day (at 00Z and 12Z) NCEP runs an ensemble of 20 forecasts for the same time period, as does the Canadian Meteorological Center. Note that the control run is nothing more than one member of the ensemble--it's forecast isn't necessarily any better or worse than that of any other member.

The results of the ensemble of forecasts are available on the Web via the NCEP Ensemble Products page.

To learn more about ensemble prediction systems, see for example "Ensemble Prediction Systems", a basic training manual for operational meteorologists.

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