# Ensemble Forecasting

Ensemble forecasting is a numerical prediction method that is used to attempt to generate a representative sample of the possible future states of a dynamical system. Ensemble forecasting is a form of Monte Carlo analysis: multiple numerical predictions are conducted using slightly different initial conditions that are all plausible given the past and current set of observations, or measurements. Sometimes the ensemble of forecasts may use different forecast models for different members, or different formulations of a forecast model. The multiple simulations are conducted to account for the two usual sources of uncertainty in forecast models: (1) the errors introduced by the use of imperfect initial conditions, amplified by the chaotic nature of the evolution equations of the dynamical system, which is often referred to as sensitive dependence on the initial conditions; and (2) errors introduced because of imperfections in the model formulation, such as the approximate mathematical methods to solve the equations. Ideally, the verified future dynamical system state should fall within the predicted ensemble spread, and the amount of spread should be related to the uncertainty (error) of the forecast.

Consider the problem of numerical weather prediction. In this case, the dynamic system is the atmosphere, the model is a numerical weather prediction model and the initial condition is represented by an objective analysis of an atmospheric state. Today ensemble predictions are commonly made at most of the major operational weather prediction facilities worldwide, including the National Centers for Environmental Prediction (US), the European Centre for Medium-Range Weather Forecasts (ECMWF), the United Kingdom Met Office, Meteo France, Environment Canada, the Japanese Meteorological Agency, the Bureau of Meteorology (Australia), the China Meteorological Administration, the Korea Meteorological Administration, and CPTEC (Brazil). Experimental ensemble forecasts are made at a number of universities, such as the University of Washington, and ensemble forecasts in the US are also generated by the US Navy and Air Force. There are various ways of viewing the data such as spaghetti plots, ensemble means or Postage Stamps where a number of different results from the models run can be compared.

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