User:Peterlean/Ensemble forecasting Work In Progress

Ensemble forecasting is a method used by modern operational weather forecast centers to account for the uncertainty present in the forecasts (effectively adding error bars to the forecast). Many different forecasts ("ensemble members") are made using slightly different represntations of the current state of the atmosphere and/or different versions of numerical forecast model. For any given forecast time a range of possible outcomes are forecast. This allows the generation of probabilistic weather forecasts. The first operational ensemble forecasts were produced in 1992 independently at ECMWF and NCEP.

Uncertainty in weather forecasts
Weather forecasts contain errors. In the modern weather forecasting system, observations and computer models are used to make an estimate ("analysis") of the current state of the atmosphere in terms of atmospheric pressure, temperature, moisture and wind across the entire globe including above the surface. A weather forecast can then be made using a numerical model based on the fluid dynamics and atmospheric physics to predict how the state of the atmosphere will evolve with time.

Initial condition error
Unfortunately, an analysis of the current weather conditions always contains errors. Instruments used to make observations introduce errors and observations are not made of every molecule in the atmosphere. The grid onto which the analysis is made cannot resolve scales smaller than the gird length (typically many kilometers across). Finally, the data assimilation system used to make the analysis is not perfect and inevitably introduces errors.

The atmosphere is a chaotic system and therefore exhibits sensitive dependence on initial conditions. Therefore, a forecast made using an analysis of current conditions containing errors will become increasingly different from the real atmosphere with time. In other words the forecast errors inevitably grow with time.

Model error
However, even if an analysis of the current weather across the globe was perfect, a weather forecast made using it would still contain errors due to the imperfect representation of the atmosphere in numerical models. Various approximations are used to simulate the atmospheric dynamics in a numerical model which cause errors in the forecast. Also, very small processes which are too small to be resolved by the model are "parameterised" to simulate the effects of those processes without modelling them directly. These introduce further forecast errors. Finally, numerical errors introduced by the discrete represenatation of continuous mathematical equations lead to further forecast errors.

Ensemble forecasting methodology
Ideally, an ensemble of forecasts should fully sample the initial condition uncertainty by running a separate weather forecast starting from every possible combination of initial conditions possible given the estimated analysis uncertainty. By running each of these forward using many different forecast models which fully sample the estimated model uncertainty, the full extent of the forecast uncertainty would be estimated.

However, each weather forecast require billions of calculations to be performed which takes a supercomuter several hours to complete. Given the vast number of different forecasts (or "ensemble members") required to fully sample the forecast uncertainty it is not possible to do this and a selective sample must be made.

Perturbation strategy
The method used to generate initial condition perturbations to produce a good sample of the initial condition uncertainty is still an area of active research and the different operational centers currently use different methods.

Benefits of ensemble forecasts
Ensemble forecasts allow probabilistic forecasts to be made e.g. Instead of saying the noon temerature in Hong Kong tommorow will be 25C, a probabilistic forecast might say there is 20% chance of the temperature being less than 24C, 70% chance of between 24C and 26C and 10% chance of it being hotter than 26C (given the uncertainty in our estimate of the current conditions and our forecast model errors).

Probabilistic forecasts are useful because they indicate if an event (e.g. high wind speeds) is merely a slight possibility or a virtual certainty. This type of information is not present in a single forecast.

Ensemble forecasts have also been shown to be better at forecasting the possibility of extreme events further in advance. (Ken Mylne reference)

See also: chaos theory