The weather is a chaotic system. Small errors in the initial conditions of a forecast grow rapidly, and affect predictability. Furthermore, predictability is limited by model errors due to the approximate simulation of atmospheric processes of the stateof- the-art numerical models.

These two sources of uncertainties limit the skill of single, deterministic forecasts in an unpredictable way, with days of high/ poor quality forecasts randomly followed by days of high/poor quality forecasts.

Two of the most recent advances in numerical weather prediction, the operational implementation of ensemble prediction systems and the development of objective procedures to target adaptive observations are discussed.

Ensemble prediction is a feasible method to integrate a single, deterministic forecast with an estimate of the probability distribution function of forecast states. In particular, ensemble can provide forecasters with an objective way to predict the skill of single deterministic forecasts, or, in other words, to forecast the forecast skill. The European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS), based on the notion that initial condition uncertainties are the dominant source of forecast error, is described.

Adaptive observations targeted in sensitive regions can reduce the initial conditionsâ€™ uncertainties, and thus decrease forecast errors. More generally, singular vectors that identify unstable regions of the atmospheric flow can be used to identify optimal ways to adapt the atmospheric observing system.

- Introduction
- The Lorenz system
- Numerical weather prediction
- Sources of forecast error
- The ECMWF Ensemble Prediction System
- Targeted observations
- Summary and future developments
- Conclusion
- Acknowledgements
- References

10alecture notes10aNWP1 aBuizza, Roberto uhttps://www.ecmwf.int/node/16927