in the model initialization, the equations are too complex to run in real-time, even with the use of supercomputers. The practical importance of ensemble forecasts derives from the fact that in a chaotic and hence nonlinear system, the rate of growth of forecast error is dependent on starting conditions. An ensemble forecast therefore provides a prior estimate of state-dependent predictability, i.e. an estimate of the types of weather that might occur, given inevitable uncertainties in the forecast initial conditions and in the accuracy of the computational representation of the equations. These uncertainties limit forecast model accuracy to about six days into the future. The first operational ensemble forecasts were produced for sub-seasonal timescales in 1985. However, it was realised that the philosophy underpinning such forecasts was also relevant on shorter timescales – timescales where predictions had previously been made by purely deterministic means. Edward Epstein recognized in 1969 that the atmosphere could not be completely described with a single forecast run due to inherent uncertainty, and proposed a stochastic dynamic model that produced means and variances for the state of the atmosphere. Although these Monte Carlo simulations showed skill, in 1974 Cecil Leith revealed that they produced adequate forecasts only when the ensemble probability distribution was a representative sample of the probability distribution in the atmosphere. It was not until 1992 that ensemble forecasts began being prepared by the European Centre for Medium-Range Weather Forecasts (ECMWF) and the National Centers for Environmental Prediction (NCEP). Methods for representing uncertainty There are two main sources of uncertainty that must be accounted for when making an ensemble weather forecast: initial condition uncertainty and model uncertainty. Initial condition uncertainty Initial condition uncertainty arises due to errors in the estimate of the starting conditions for the forecast, both due to limited observations of the atmosphere, and uncertainties involved in using indirect measurements, such as satellite data, to measure the state of atmospheric variables. Initial condition uncertainty is represented by perturbing the starting conditions between the different ensemble members. This explores the range of starting conditions consistent with our knowledge of the current state of the atmosphere, together with its past evolution. There are a number of ways to generate these initial condition perturbations. The ECMWF model, the Ensemble Prediction System (EPS), uses a combination of singular vectors and an ensemble of data assimilations (EDA) to simulate the initial probability density. The singular vector perturbations are