Despite the increasing accuracy of weather forecasts, there is an element of uncertainty in all predictions. In 1992, ECMWF pioneered an ensemble prediction system, which now provides a vast range of products to help forecasters deal quantitatively with the day-to-day variations in the predictability of the atmosphere.

ECMWF continues to commit a substantial research effort to the assessment of predictability at all forecast ranges (medium-range, monthly and seasonal timescales), and to the investigation of methods to appropriately represent forecast uncertainty.

In any given weather forecast, there are two factors that lead forecast skill to decrease as forecast lead-time increases:

• Inevitable uncertainties in the initial conditions
• Necessary approximations in the construction of a numerical model of the exact laws of physics

Both of these cause errors that amplify with time. In fact, these two sources of error cannot be considered independently, since the initial conditions are themselves partly constructed through integration of the underlying numerical model (and thereby include errors resulting from the numerical model) as part of the initialisation process by data assimilation. The ECMWF ensemble forecasting system comprises the Ensemble Prediction System (ENS) for medium-range and monthly forecasts, and System 4 (S4) for seasonal forecasts, which are used to estimate the uncertainty in a forecast.

An ensemble forecast comprises multiple realisations for a single forecast time and location. The different realisations are generated through applying different perturbations to a single control forecast. For the ECMWF medium-range forecasting system, the control forecast is a coarser-resolution realisation of the HRES forecast (the high-resolution forecast). The perturbed forecasts are generated through:

## Perturbations to the initial conditions

The ECMWF weather prediction model is run 51 times from slightly different initial conditions. One forecast, called the ENS control forecast, is run from the HRES ECMWF analysis. An additional 50 integrations, the perturbed members, are made from slightly different initial conditions which are designed to represent the uncertainties inherent in the HRES analysis (for more details, see Leutbecher and Palmer, 2008). The initial perturbations are constructed using the singular vector technique and perturbations generated from the ensemble of data assimilations (Buizza et al., 2008).

• Buizza, R., Leutbecher, M., & Isaksen, L., 2008: Potential use of an ensemble of analyses in the ECMWF Ensemble Prediction System. Q. J. R. Meteorol. Soc., 134, 2051-2066.
• Leutbecher, M., & Palmer, T. N., 2008: Ensemble forecasting. J. Comp. Phys., 227, 3515-3539.

## Perturbations introduced at each model integration

Errors in the underlying numerical model arise from approximations in the discretisations and from assumptions in the parametrizations of sub-grid physical processes. The resulting errors give rise to inherent uncertainty in the accuracy of the model solutions, and in the ECMWF ensemble forecasting system, that uncertainty is simulated by the inclusion of two stochastic parametrization schemes: the Stochastically Perturbed Parametrization Tendency scheme (SPPT, Palmer et al., 2009; Buizza et al., 1999) and the Stochastic Kinetic Energy Backscatter scheme (SKEB, Berner et al., 2009; Shutts, 2005). SPPT represents the uncertainty from the sub-grid parametrization schemes by stochastically perturbing the net tendency from those schemes. Meanwhile, SKEB is designed to simulate the otherwise unresolved upscale transfer of energy from sub-grid scales to the resolved scales, by introducing a stochastic streamfunction forcing. A more detailed discussion of the stochastic parametrizations used at ECMWF and their impact on forecast skill is presented in Shutts et al. (2011).

• Berner, J., Shutts, G. J., Leutbecher, M., & Palmer, T. N., 2009: A spectral stochastic kinetic backscatter scheme and its impact on flow-dependent predictability in the ECMWF ensemble prediction system. J. Atmos. Sci., 66, 603-626.
• Buizza, R., Miller, M., & Palmer, T. N., 1999: Stochastic representation of model uncertainties in the ECMWF Ensemble Prediction System. Q. J. R. Meteorol. Soc., 125, 2887-2908.
• Palmer, T. N., Buizza, R., Doblas-Reyes, F., Jung, t., Leutbecher, M., Shutts, G. J., Steinheimer M, & Weisheimer, A., 2009: Stochastic parametrization and model uncertainty. ECMWF Research Department Technical Memorandum. 598, pp. 42
• Shutts, G. J., 2005: A kinetic energy backscatter algorithm for use in ensemble prediction systems. Q. J. R. Meteorol. Soc., 131, 3079-3102.
• Shutts, G. J., Leutbecher, M., Weisheimer, A., Stockdale, T., Isaksen, L., & Bonavita, M., 2011: Representing model uncertainty: stochastic parametrization at ECMWF. ECMWF Newsletter No. 129, 19-24.