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In this session the generation of the perturbed initial condition of the ECMWF ensemble will be presented. We will discuss the ratio behind using singular vectors in the ensemble and how they are calculated. Then it will be explained how the singular vectors are combined with perturbations from the ensemble of data assimilations to construct the perturbations for the ensemble.

By the end of the session you should be able to:

• explain the idea behind using singular vectors in the ensemble

• describe how singular vectors are calculated

• describe the construction of the ensemble perturbations

The aim of this session is to introduce the ECMWF ensemble of data assimilation (EDA). The rationale and methodology of the EDA will be illustrated, and its use in to simulate initial uncertainties in the ECMWF ensemble prediction system (ENS) will be presented.

By the end of the session you should be able to:

• know what is the ECMWF EDA

• illustrate how the EDA is used to simulate initial uncertainty in ensemble prediction

• understand the main differences between singular vectors and EDA-based perturbations

Abstract: The lectures introduce methods of ensemble verification. They cover the verification of discrete forecasts (e.g. dry/wet) and continuous scalar forecasts (e.g. temperature). Various scores such as the Brier score and the continuous ranked probability score are introduced.

After the lectures you should be able to

• explain what a reliable probabilistic forecast is and how to measure reliability

• understand why resolution and sharpness of a probabilistic forecast matter

• compute several of the standard verification metrics used for ensemble forecasts

 The aim of this session is to introduce the idea of chaos.  We will discuss the implications this has for numerical weather prediction.

By the end of the session you should be able to:

• describe what limits the predictability of the atmosphere
• understand the need for probabilistic forecasting

The aim of this session is to illustrate the key characteristic of the nine operational global, medium-range ensemble systems. These are the ensembles available also within the TIGGE (Thorpex Interactive Grand Global Ensemble) project data-base. Similarity and differences in the approaches followed to simulate the sources of forecast uncertainties will be discussed, and their relevance for forecast performance will be illustrated.

By the end of the session you should be able to:

• illustrate the main similarities and differences of the 9 TIGGE global ensembles

• link the performance differences of TIGGE ensemble to their design

• describe the main differences between singular vectors and EDA-based perturbations

The aim of this session is to introduce the main sources of uncertainty that lead to forecast errors. The weather prediction problem will be discussed, and stated it in terms of an appropriate probability density function (PDF). The concept of ensemble prediction based on a finite number of integration will be introduced, and the reason why it is to be the only feasible method to predict the PDF beyond the range of linear growth will be illustrated.

By the end of the session you should be able to:

• explain which are the main sources of forecast error

• illustrate why numerical prediction should be stated in probabilistic terms

• describe the rationale behind ensemble prediction

Abstract: The lectures introduce methods of ensemble verification. They cover the verification of discrete forecasts (e.g. dry/wet) and continuous scalar forecasts (e.g. temperature). Various scores such as the Brier score and the continuous ranked probability score are introduced.

After the lectures you should be able to

• explain what a reliable probabilistic forecast is and how to measure reliability

• understand why resolution and sharpness of a probabilistic forecast matter

• compute several of the standard verification metrics used for ensemble forecasts

The aim of this session is to understand the ECMWF clustering products.

By the end of the session you should be able to:

• explain how the cluster analysis works
• use the ECMWF clustering products

This lecture covers the essentials of building a numerical seasonal forecast system, as exemplified by the present prediction system at ECMWF.

  By the end of this lecture, you should be able to:

• explain the scientific basis of seasonal forecast systems
• describe in outline ECMWF System 4 and its forecast performance
• discuss the critical factors in further improving forecast systems

The aim of this session is to understand how we are able to provide forecasts at long time horizons given the chaotic nature of the atmosphere.

After this session you should be able to:

• describe the Lorenz idea of Predictability of the first and second kind
• list examples of the elements of the Earth system that provide predictability on longer timescales
• understand the type of forecast that we are able to provide beyond the deterministic limit

After this lecture, students will be able to:

• explain the physical and practical motivations for using stochastic physics in an ensemble forecast;

• describe the two stochastic parameterization schemes used in the IFS ensemble, and their respective purposes;

• be able to identify the improvement in forecasting skill from the inclusion of stochastic physics.

This lecture gives an overview of ensemble and post-processing and calibration techniques. The presentation is made from the medium-range forecast perspective. The (relative) benefits of calibration and multi-model combination for medium-range forecasting are also discussed.

  By the end of this lecture, you should be able to:

• describe a wide range of possible calibration methods for ensemble systems
• explain which methods are suitable in which circumstances
• discuss the merits of calibration and multi-model combination

The latest medium, monthly and seasonal forecasts will be discussed in terms of out look and performance.

This is a combined event with the weekly weather discussion that ECMWF staff attend.

You get the opportunity to experiment yourself with an ensemble prediction system for a chaotic low-dimensional dynamical system introduced by Edward Lorenz in 1995. Experiments permit to study the role of the initial condition perturbations and the representation of model uncertainties. Various metrics introduced in the ensemble verification lectures will be applied in this session.

After the practice session, you will be able to use the toy model as an educational tool.

Abstract: The lecture is a short introduction to operational hydrological ensemble prediction systems, with focus on flooding. The European Flood Awareness System (EFAS) is described. The lecture also contains a short interactive exercise in decision making under uncertainty using prbabilistic forecasts as an example.

By the end of the session you should be able to:

• Describe the components in hydrological ensemble prediction systems (HEPS).

• Describe the major sources of uncertainty in HEPS and how they can be reduced.

• Explain the difficulties in using probabilistic flood forecasts in decision making.