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The Ensemble of Data Assimilations (EDA) technique is used for the estimation of the analysis and background errors of the ECMWF assimilation system. This lecture describes the EDA formulation and implementation, and how it interacts with ECMWF 4DVar analysis and ECMWF Ensemble Prediction System.

By the end of the lecture the participants should be able to:

• Describe the theoretical basis and practical implementation of the EDA
• Explain the use of the EDA in the ECMWF analysis and ensemble prediction systems

The primary purpose of this lecture is explore the implications of the fact that satellites can only measure radiation at the top of the atmosphere and do not measure the geophysical variables we require for NWP (e.g. temperature, humidity and wind). The link between the atmospheric variables and the measured radiances is the radiative transfer equation - the key elements of which are discussed. It is shown how - with careful frequency selection - satellite measurements can be made for which the relationship to geophysical variables is greatly simplified. Despite these simplifications, it is shown that the extraction of detailed profile information from downward looking radiance measurements is a formally ill posed inverse problem.

Data assimilation is introduced as the solution to this inverse problem, where background information and satellite observations are combined to produce a best or optimal estimate of the atmospheric state. The main elements of the assimilation scheme (such as the chain of observation operators for radiances) and its key statistical inputs are examined. In particular it is shown that incorrect specification of observation errors (R) and background errors (B) can severely limit the successful exploitation of satellite data.

By the end of this lecture you will:

• understand exactly what a satellite actually measures (radiance)
• appreciate the complex relationship between what is measured and what we wish to know for NWP
• how information is extracted from satellite measurements in data assimilation

This lecture provides an overview of a typical ocean data assimilation system for initialization and re-analyses application. The lecture uses as an example the ECMWF ocean data assimilation system, which is based the NEMOVAR (3Dvar FGAT). This will be used to discuss design of the assimilation cycle, formulation of error covariances, observations assimilated and evaluation procedure, among others.

By the end of the lecture students should be able to:

• describe the different components involved in a an ocean data assimilation system
• list the commonalities and and differences between ocean and atmosphere data assimilation
• describe the basics of the physical ocean observing system
• explain the essential multivariate relationships between ocean variables
• identify the limitations of the existing systems.

The aim of this session is to present an overview of the current observing systems used in Numerical Weather Prediction. We will discuss our observational requirement, and how close the current observing system is to meeting our needs. We will also discuss areas where our requirements are evolving. We will learn about WMO's OSCAR database that describes the Global Observing System. We will learn how the large diversity of observations now available, are monitored to ensure only good observations are presented to an operational system.

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

• be able to describe the main types of observations used in data assimilation for Numerical Weather Prediction;
• be aware of how large volumes of observations are exchanged, implemented and monitored in operational systems;
• be aware of WMO's OSCAR database, how to access it and what type of information it can provide.

The background error is central to the performance of the analysis system and tells how much confidence to put in the best available forecast which is to be updated with new observations. The lecture will review how background errors are estimated and represented for current variational algorithms.

In this lecture, the impact of model error on variational data assimilation will be presented. This lecture will introduce weak-constraint 4D-Var as a way to account for model error in the data assimilation process. Several examples of results from simplified implementations in the IFS will be shown.

By the end of the lecture the participants should be able to:

• describe the impact of model error on the data assimilation process,
• explain the difficulties in properly accounting for model error in data assimilation.

At ECMWF atmospheric composition data are assimilated into the IFS as part of the MACC-II project. On a global scale, atmospheric composition represents the full state of the global atmosphere covering phenomena such as desert dust plumes, long-range transport of atmospheric pollutants or ash plumes from volcanic eruptions, but also variations and long-term changes in the background concentrations of greenhouse gases.

The aim of this lecture is to give an overview of the work that is carried out at ECMWF regarding the assimilation of atmospheric composition data, and to address why this is of interest and which special challenges are faced when assimilating atmospheric composition data.

By the end of the session you should:

• have some understanding of the work carried out at ECMWF to assimilate data of atmospheric composition

In this lecture the variational bias correction scheme (VarBC) as used at ECMWF is explained. VarBC replaced the tedious job of estimating observation bias off-line for each satellite instrument or in-situ network by an automatic self-adaptive system. This is achieved by making the bias estimation an integral part of the ECMWF variational data assimilation system, where now both the initial model state and observation bias estimates are updated simultaneously.

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

• many observations are biased, and that the characteristics of bias varies widely between types of instruments
• separation between model bias and observation bias is often difficult
• the success of an adaptive system implicitly relies on a redundancy in the underlying observing system.

The goal of this lecture is to familiarise the student with the notion of tangent linear and adjoint models, and their use in variational data assimilation.  A general overview of the current use of tangent linear and adjoint models in the ECMWF system will also be provided. Theoretical definitions and practical examples of tangent liner and adjoint models will be given. The student will be invited to work some simple tangent linear and adjoint derivations together with the instructor. A brief introduction to automatic differentiation software will also be given./

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

• define what tangent linear and adjoint models are
• derive tangent linear and adjoint equations for a simple nonlinear equation
• describe the use of tangent linear and adjoint codes within the ECMWF's 4D-VAR system.

The aim of this session is to understand how data assimilation can improve our knowledge of past weather over long time-scales. We will present recent advances that help capture changes over time in observing system networks, and project this variation in information content into uncertainty estimates of the reanalysis products. We will also discuss the applications of reanalysis, which generally put weather events into the climate context.

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

• explain what are the goals of data assimilation in a reanalysis data assimilation system
• list the key aspects that require particular attention in reanalysis, as compared to numerical weather prediction
• describe the most common problems in reanalysis products

The aim of these sessions is to understand the role of land surface data assimilation on medium range weather forecasts.

We will give an overview of the different approaches used to assimilate land surface data and to initialise model variables in NWP.  We will  present the current observing systems and describe the land data assimilation structure within ECMWF system.

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

• identify the different observations used for snow and soil moisture data assimilation
• define land surface data assimilation approaches used for NWP
• describe the role of land surface data assimilation on medium-range weather forecasts

A single observation can under some conditions undermine the quality of a global analyses. The lecture will go through methods used to make the analysis more robust against oulier or wrong observations, with focus on variational quality control.

This three-hour lecture will start by explaining the role and main ingredients of data assimilation in general. The widely used framework of variational data assimilation will then be gradually introduced. The challenges associated with the necessary inclusion of physical parametrizations in the data assimilation process will be highlighted. The concept of adjoint model as well as the techniques to derive it will be introduced. The importance of the linearity constraint in 4D-Var and the methods to address it will be detailed. The set of linearized physical parametrizations used at ECMWF will then be briefly presented. Finally, various examples of the use of physical parametrizations in variational data assimilation and its impact on weather forecast quality will be given.

By the end of the session, the students should be able:

•    to name the main ingredients of a data assimilation system.

•    to tell why physical parametrizations are needed in data assimilation.

•    to identify the role of the adjoint code in 4D-Var.

•    to recognize the importance of the regularization of the linearized code.

This session explains the different approaches used in numerical models to parametrize the turbulent mixing taking place at the subgrid scale, above the surface layer. Various turbulence closures are presented before describing closure currently used in the ECMWF model.

Expected outcomes:

•    understand what a turbulence closure is and what are the types of closures encountered in numerical models

•    have an overview of the parameterization of turbulent mixing in the ECMWF model

This three-hour lecture will start by explaining the role and main ingredients of data assimilation in general. The widely used framework of variational data assimilation will then be gradually introduced. The challenges associated with the necessary inclusion of physical parametrizations in the data assimilation process will be highlighted. The concept of adjoint model as well as the techniques to derive it will be introduced. The importance of the linearity constraint in 4D-Var and the methods to address it will be detailed. The set of linearized physical parametrizations used at ECMWF will then be briefly presented. Finally, various examples of the use of physical parametrizations in variational data assimilation and its impact on weather forecast quality will be given.

By the end of the session, the students should be able:

•    to name the main ingredients of a data assimilation system.

•    to tell why physical parametrizations are needed in data assimilation.

•    to identify the role of the adjoint code in 4D-Var.

•    to recognize the importance of the regularization of the linearized code.

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

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