NWP training material 2015

In this lecture we will give you a brief history of ECMWF and present the main areas of NWP research that is currently being carried out in the centre. We then look at current research challenges and present some of the latest developments that will soon become operational.

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

• List the main research areas at ECMWF and describe the latest model developments.

The aim of this lecture is to introduce the concept of the EnKF in the context of atmospheric data assimilation. Strengths and weaknesses of the algorithm will be discussed and results of the ECMWF implementation will be presented.

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

•    Describe the basic EnKF algorithm and its connections with    the Kalman Filter;

•    Discuss some of the advantages and the limitations of EnKF algorithms with respect to more established variational algorithms;

•    Be aware of recent developments in hybrid variational-EnKF data assimilation

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

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 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

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.

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 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

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.

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

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

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

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.

This one-hour lecture will identify the challenges associated with the use of physical parametrizations in the context of four-dimensional variational data assimilation (4D-Var). 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 be briefly presented. Examples of the use of physical parametrizations in variational data assimilation and its impact on forecast quality will be given.

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

• to tell why physical parametrizations are needed in data assimilation.
• to recognize the importance of the regularization of the linearized code

The goal of this session is to provide an overview of the use of generalised curvilinear coordinates in atmospheric numerical models.

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

• describe some important aspects of the formulation and implementation of the governing equations in generalised coordinates

• describe various vertical coordinates employed in atmospheric models

• indicate the use of generalised coordinates to employ moving mesh adaptivity

Recently, there is in increasing interest in trying to understand the properties of coupled atmosphere, ocean-wave, ocean/sea-ice models with an ultimate goal to start predicting weather, waves and ocean circulation on time scales ranging from the medium-range to seasonal timescale. Such a coupled system not only requires the development of an efficient coupled forecasting system but also the development of a data assimilation component.

During the two lectures I will briefly describe the components of the coupled system. It will be made plausible that ocean waves are an essential element of such a coupled system as through the wave action, momentum and heat are transferred from atmosphere to ocean. Also, the sea state determines to a considerable extent the efficiency with which momentum is transferred from atmosphere to waves, while ocean waves also play a decisive role in the evolution of the sea-ice edge. Results showing the importance of ocean waves on upper-ocean mixing and on atmospheric circulation are discussed as well, while I will finish the lectures by presenting preliminary results from coupled data assimilation experiments.  

By the end of this session, the student will be able to:

• discuss the impact of ocean waves on the coupled system
• describe the different wave processes that are modelled in the ECMWF system
• describe the impact of ocean circulation on the atmosphere

The aim of this lecture is to systematically build theoretical foundations for Numerical Weather Prediction at nonhydrostatic resolutions. In the first part of the lecture, we will discuss a suite of all-scale nonhydrostatic PDEs, including the anelastic, the pseudo-incompressible and the fully compressible Euler equations of atmospheric dynamics. First we will introduce the three sets of nonhydrostatic governing equations written in a physically intuitive Cartesian vector form, in abstraction from the model geometry and the coordinate frame adopted. Then, we will combine the three sets into a single set recast in a form of the conservation laws consistent with the problem geometry and the unified solution procedure. In the second part of the lecture, we will build and document the common numerical algorithm for integrating the generalised set of the governing PDEs put forward in the first part of the lecture. Then, we will compare soundproof and compressible solutions and demonstrate the efficacy of this unified numerical framework for two idealised flow problems relevant to weather and climate.

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

• explain the form, properties and role of alternative systems of nonhydrostatic PDEs for all scale atmospheric dynamics;

• explain the importance and key aspects of continuous mappings employed in all-scale atmospheric models;

• explain the difference between the explicit and semi-implicit algorithms for integrating nonhydrostatic PDEs, the importance of consistent numerical approximations, and the fundamental role of transport and elliptic solvers.

The aim of this session is to learn about recent developments in discontinuous higher order spatial discretization methods, such as the Discontinuous Galerkin method (DG), and the Spectral Difference method (SD). These methods are of interest because they can be used on unstructured meshes and facilitate optimal parallel efficiency. We will present an overview of higher order grid point methods for discretizing partial differential equations (PDE's) with compact stencil support, and illustrate a practical implementation.

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

• ell what are the advantages offered by discontinuous higher order methods

• describe how to solve PDE's with discontinuous methods

• identify the key elements that contribute to a PDE solver

The goal of this session is to provide an overview of the use of generalised curvilinear coordinates in atmospheric numerical models.

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

• describe some important aspects of the formulation and implementation of the governing equations in generalised coordinates

• describe various vertical coordinates employed in atmospheric models

• indicate the use of generalised coordinates to employ moving mesh adaptivity

The aim of this lecture is to systematically build theoretical foundations for Numerical Weather Prediction at nonhydrostatic resolutions. In the first part of the lecture, we will discuss a suite of all-scale nonhydrostatic PDEs, including the anelastic, the pseudo-incompressible and the fully compressible Euler equations of atmospheric dynamics. First we will introduce the three sets of nonhydrostatic governing equations written in a physically intuitive Cartesian vector form, in abstraction from the model geometry and the coordinate frame adopted. Then, we will combine the three sets into a single set recast in a form of the conservation laws consistent with the problem geometry and the unified solution procedure. In the second part of the lecture, we will build and document the common numerical algorithm for integrating the generalised set of the governing PDEs put forward in the first part of the lecture. Then, we will compare soundproof and compressible solutions and demonstrate the efficacy of this unified numerical framework for two idealised flow problems relevant to weather and climate.

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

• explain the form, properties and role of alternative systems of nonhydrostatic PDEs for all scale atmospheric dynamics;

• explain the importance and key aspects of continuous mappings employed in all-scale atmospheric models;

• explain the difference between the explicit and semi-implicit algorithms for integrating nonhydrostatic PDEs, the importance of consistent numerical approximations, and the fundamental role of transport and elliptic solvers.

The aim of this session is to learn about recent developments in discontinuous higher order spatial discretization methods, such as the Discontinuous Galerkin method (DG), and the Spectral Difference method (SD). These methods are of interest because they can be used on unstructured meshes and facilitate optimal parallel efficiency. We will present an overview of higher order grid point methods for discretizing partial differential equations (PDE's) with compact stencil support, and illustrate a practical implementation.

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

• ell what are the advantages offered by discontinuous higher order methods

• describe how to solve PDE's with discontinuous methods

• identify the key elements that contribute to a PDE solver

During this presentation, we will discuss two of the questions faced by numerical weather prediction scientists as forecast models reach horizontal resolutions of 6 to 2 km:

• Do we need to abandon the primitive equations for a non-hydrostatic system of equations?

• Do we still need a deep convection parametrisation?

• and we will show what answers to these questions are given by very high resolution simulations of the IFS.

By the end of the presentation, you should be able to:

• discuss the limits of the hydrostatic approximation for numerical weather prediction

• explain the dilemma of parametrizing deep convection versus permitting explicit deep convection at resolution in the grey zone of convection

The aim of two lectures is to introduce basis of finite volume and continuous finite element discretisations and relate them to corresponding data structures and mesh generation techniques. The main focus will be on unstructured meshes and their application to global and local atmospheric models. Flexibility, communication overheads, memory requirements and user friendliness of such meshes with be contrasted with those of structured meshes. The most commonly used mesh generation techniques will be highlighted, together with mesh manipulation techniques employed in mesh adaption approaches and will be followed by a discussion of alternative geometrical representations of orography. An example of unstructured meshes’ implementation to non-hydrostatic and hydrostatic atmospheric solvers will provide an illustration of their potential and challenges.

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

• understand applicability, advantages and disadvantages of selected mesh generation techniques for a given type of application.

• appreciate importance of data structures in relation to atmospheric models and mesh generation.

• gain awareness of issues related to flexible mesh generation and adaption.

During this presentation, we will discuss two of the questions faced by numerical weather prediction scientists as forecast models reach horizontal resolutions of 6 to 2 km:

• Do we need to abandon the primitive equations for a non-hydrostatic system of equations?

• Do we still need a deep convection parametrisation?

• and we will show what answers to these questions are given by very high resolution simulations of the IFS.

By the end of the presentation, you should be able to:

• discuss the limits of the hydrostatic approximation for numerical weather prediction

• explain the dilemma of parametrizing deep convection versus permitting explicit deep convection at resolution in the grey zone of convection

The aim of this session is to understand the main issues and challenges in parallel computing, and how parallel computers are programmed today.

By the end of this session you should be able to

• explain the difference between shared and distributed memory

• describe the key architectural features of a supercomputer

• describe the purpose of OpenMP and MPI on today’s supercomputers

• identify the reasons for the use of accelerator technology

The aim of two lectures is to introduce basis of finite volume and continuous finite element discretisations and relate them to corresponding data structures and mesh generation techniques. The main focus will be on unstructured meshes and their application to global and local atmospheric models. Flexibility, communication overheads, memory requirements and user friendliness of such meshes with be contrasted with those of structured meshes. The most commonly used mesh generation techniques will be highlighted, together with mesh manipulation techniques employed in mesh adaption approaches and will be followed by a discussion of alternative geometrical representations of orography. An example of unstructured meshes’ implementation to non-hydrostatic and hydrostatic atmospheric solvers will provide an illustration of their potential and challenges.

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

• understand applicability, advantages and disadvantages of selected mesh generation techniques for a given type of application.

• appreciate importance of data structures in relation to atmospheric models and mesh generation.

• gain awareness of issues related to flexible mesh generation and adaption.

Recently, there is in increasing interest in trying to understand the properties of coupled atmosphere, ocean-wave, ocean/sea-ice models with an ultimate goal to start predicting weather, waves and ocean circulation on time scales ranging from the medium-range to seasonal timescale. Such a coupled system not only requires the development of an efficient coupled forecasting system but also the development of a data assimilation component.

During the two lectures I will briefly describe the components of the coupled system. It will be made plausible that ocean waves are an essential element of such a coupled system as through the wave action, momentum and heat are transferred from atmosphere to ocean. Also, the sea state determines to a considerable extent the efficiency with which momentum is transferred from atmosphere to waves, while ocean waves also play a decisive role in the evolution of the sea-ice edge. Results showing the importance of ocean waves on upper-ocean mixing and on atmospheric circulation are discussed as well, while I will finish the lectures by presenting preliminary results from coupled data assimilation experiments.  

By the end of this session, the student will be able to:

• discuss the impact of ocean waves on the coupled system
• describe the different wave processes that are modelled in the ECMWF system
• describe the impact of ocean circulation on the atmosphere

The aim of this session is to understand the main issues and challenges in parallel computing, and how parallel computers are programmed today.

By the end of this session you should be able to

• explain the difference between shared and distributed memory

• describe the key architectural features of a supercomputer

• describe the purpose of OpenMP and MPI on today’s supercomputers

• identify the reasons for the use of accelerator technology

In this lecture we will give you a brief history of ECMWF and present the main areas of NWP research that is currently being carried out in the centre. We then look at current research challenges and present some of the latest developments that will soon become operational.

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

• List the main research areas at ECMWF and describe the latest model developments.

This module aims to introduce the fundamentals of radiative transfer theory and its role within the global atmospheric circulation. The lectures will also cover the techniques of numerical modelling of the radiative transfer equations in global-circulation models with a particular focus on the code in use in the ECMWF Integrated Forecasting System.

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

•    Identify the key processes controlling the atmospheric radiative balance

•    Recognize the role of the radiative transfer in the Earth energy balance

•    Estimate the impact of changes in the radiative parameterizations on climate

Additional outcomes:

•    Develop skills in data analysis and numerical modelling

This module aims to introduce the fundamentals of radiative transfer theory and its role within the global atmospheric circulation. The lectures will also cover the techniques of numerical modelling of the radiative transfer equations in global-circulation models with a particular focus on the code in use in the ECMWF Integrated Forecasting System.

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

•    Identify the key processes controlling the atmospheric radiative balance

•    Recognize the role of the radiative transfer in the Earth energy balance

•    Estimate the impact of changes in the radiative parameterizations on climate

Additional outcomes:

•    Develop skills in data analysis and numerical modelling

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

• recognise land elements relevant to weather,
• review land modelling strategies to heterogeneity

This short lecture is an introduction to the questions of time splitting and process splitting in a numerical weather prediction model and to the problems resulting from the interaction of different numerical solvers inside the same model.

After this introduction, you should

•    be fully aware that each parametrisation is only a small part of a much larger system, usually one term in the full system of equations which needs to be solved by the forecast model,

•    remember, when working on your own parametrisation(s), that parametrisations are also subject to the constraints imposed by numerical analysis and algorithmic, as is the solver in the dynamical core.

This session is a short course of atmospheric thermodynamics.

The following basic concepts are reviewed

•    energy conservation

•    phase changes

•    thermodynamic diagrams

Convection affects all atmospheric scales. Therefore, the convection session aims to provide a deeper understanding of the atmospheric general circulation and its interaction with convective heating and vertical transports. The notions and techniques acquired during the course should be useful for developers of convective parametrizations, forecasters and for analysing ouput from high-resolution convection resolving models.

By the end of the session you should become familiarised with

•    the interaction between the large-scale circulation and the convection including  radiative-convective equilibrium and convectively-coupled large-scale waves

•    the notion of convective adjustment and the mass flux concept in particular

•    the basic concepts behind the ECMWF convection parametrization and some useful numerical tricks

•    forecasting convection including convective systems and the diurnal cycle

•    diagnose forecast errors related to convection.

Convection affects all atmospheric scales. Therefore, the convection session aims to provide a deeper understanding of the atmospheric general circulation and its interaction with convective heating and vertical transports. The notions and techniques acquired during the course should be useful for developers of convective parametrizations, forecasters and for analysing ouput from high-resolution convection resolving models.

By the end of the session you should become familiarised with

•    the interaction between the large-scale circulation and the convection including  radiative-convective equilibrium and convectively-coupled large-scale waves

•    the notion of convective adjustment and the mass flux concept in particular

•    the basic concepts behind the ECMWF convection parametrization and some useful numerical tricks

•    forecasting convection including convective systems and the diurnal cycle

•    diagnose forecast errors related to convection.

Convection affects all atmospheric scales. Therefore, the convection session aims to provide a deeper understanding of the atmospheric general circulation and its interaction with convective heating and vertical transports. The notions and techniques acquired during the course should be useful for developers of convective parametrizations, forecasters and for analysing ouput from high-resolution convection resolving models.

By the end of the session you should become familiarised with

•    the interaction between the large-scale circulation and the convection including  radiative-convective equilibrium and convectively-coupled large-scale waves

•    the notion of convective adjustment and the mass flux concept in particular

•    the basic concepts behind the ECMWF convection parametrization and some useful numerical tricks

•    forecasting convection including convective systems and the diurnal cycle

•    diagnose forecast errors related to convection.

Convection affects all atmospheric scales. Therefore, the convection session aims to provide a deeper understanding of the atmospheric general circulation and its interaction with convective heating and vertical transports. The notions and techniques acquired during the course should be useful for developers of convective parametrizations, forecasters and for analysing ouput from high-resolution convection resolving models.

By the end of the session you should become familiarised with

•    the interaction between the large-scale circulation and the convection including  radiative-convective equilibrium and convectively-coupled large-scale waves

•    the notion of convective adjustment and the mass flux concept in particular

•    the basic concepts behind the ECMWF convection parametrization and some useful numerical tricks

•    forecasting convection including convective systems and the diurnal cycle

•    diagnose forecast errors related to convection.

This session gives a theoretical introduction of the planetary boundary layer, including its definition, classification, notions about turbulence within the boundary layer, differences between clear and cloudy boundary layers, and equations used to describe the mean state in a numerical model.

Expected outcomes:

•    understand what is the boundary layer, its characteristics and why it is important to study it and represent it correctly in numerical models

•    understand the difference between the various boundary layer types

This session focuses on representation of the surface layer, i.e. the layer between the surface and the first model level. More particularly, it explains how the surface fluxes are parametrized, and it gives insights on the representation of the surfaces roughness lengths which are one of the crucial aspects of the formulation of the surface fluxes.

Expected outcomes:

•    be aware of the difficulties related to the representation of the surface layer in a numerical model

•    understand how the surface fluxes are parametrized

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 session gives a detailed overview of the processes controlling the evolution of stratocumulus clouds. It also explains how these clouds are represented in the ECWMF model, and points out the remaining challenges.

Expected outcomes:

•    grasp the complexity of processes and interactions controlling the lifetime of these clouds

•    understand why is it  so difficult to represent these clouds in a numerical model

This session will give an overview of techniques and data sources used for the verification of the boundary layer scheme. We will use examples from the IFS to explore how verification methods can help to identify systematic errors in the model's boundary layer parameterization, and guide future model development.

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

•    Identify data sources and products suitable for BL verification

•    Recognize the strengths and limitations of the verification strategies discussed

•    Choose a suitable verification method to investigate model errors in boundary layer height, transport and cloudiness.

This module aims to introduce the fundamentals of radiative transfer theory and its role within the global atmospheric circulation. The lectures will also cover the techniques of numerical modelling of the radiative transfer equations in global-circulation models with a particular focus on the code in use in the ECMWF Integrated Forecasting System.

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

•    Identify the key processes controlling the atmospheric radiative balance

•    Recognize the role of the radiative transfer in the Earth energy balance

•    Estimate the impact of changes in the radiative parameterizations on climate

Additional outcomes:

•    Develop skills in data analysis and numerical modelling

This session gives a brief overview of cloud parametrization issues and an understanding of the basic microphysics of liquid, ice and mixed phase cloud and precipitation processes.

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

•    recall the basic concepts for the design of a cloud parametrization

•    describe the key microphysical processes in the atmosphere

•    recognize the important microphysical processes that need to be parametrized in a global NWP model.

In addition to the efforts devoted to the parametrization of individual physical and dynamical processes, there is need to investigate how well these all fit together to create the forecast model. With the help of a few examples, this lecture discusses some of the diagnostic tools used to identify key deterministic and probabilistic weaknesses in the forecast system.

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

• Describe some of the key weakness of our forecast system
• List some of the diagnostic tools used to identify and understand these weaknesses

In this lecture we will give you a brief history of ECMWF and present the main areas of NWP research that is currently being carried out in the centre. We then look at current research challenges and present some of the latest developments that will soon become operational.

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

• List the main research areas at ECMWF and describe the latest model developments.

This module aims to introduce the fundamentals of radiative transfer theory and its role within the global atmospheric circulation. The lectures will also cover the techniques of numerical modelling of the radiative transfer equations in global-circulation models with a particular focus on the code in use in the ECMWF Integrated Forecasting System.

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

•    Identify the key processes controlling the atmospheric radiative balance

•    Recognize the role of the radiative transfer in the Earth energy balance

•    Estimate the impact of changes in the radiative parameterizations on climate

Additional outcomes:

•    Develop skills in data analysis and numerical modelling

On the basis of simple gravity wave theory, the concepts of sub-grib turbulent form drag, flow blocking, and gravity wave excitation will be introduced. The ECMWF formulations will be described, and the impact will be discussed.

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

•    Describe the relevant physical mechanisms related to sub-grid orography that have impact on flow in the atmosphere.

•    Describe the impact of sub-grid orography.  

Building on the previous two Cloud sessions, the practical implementation of acloud parametrization is described, using the ECMWF global model as an example appropriate for global weather forecasting.

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

•    explain the key sources and sinks of cloud and precipitation required in a parametrization

•    describe the main components of the ECMWF stratiform cloud parametrization

•    recognise the limitations of approximating complex processes.

This session describes different methodologies for diagnosing model cloud and precipitation errors to help improve parametrization. Uncertainties and limitations of evaluating models with observations are discussed.

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

•    identify the different observation types that can be used for model cloud evaluation

•     describe the different evaluation methodologies that can be used to inform parametrization development

•    recognise the limitations of model evaluation due to uncertainties and differences in observed and modelled quantities.

The lecture will give an overview on how and why the ECMWF model system was extended to forecast atmospheric composition. We focus on the use of physical parametrisation to represent the sources and sinks of atmospheric trace gases and aerosols such as photolysis, deposition, lightening and chemical conversion.

By the end of the session:

• you can draw a basic sketch of the processes to be considered  in atmospheric composition modelling
• you can relate chemical and meteorological time scales
• you have better knowledge of the activities at ECMWF on atmospheric composition modelling

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

• relate flux and storage
• recognise land surface predictors and land diagnostic quantities

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

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 is about the physical processes and the circulation in the middle atmosphere. Having a realistic middle atmosphere is of major importance for data assimilation and long-range forecasts. Vertically propagating gravity waves including those not generated by orography strongly modulate the middle atmospheric through wave braking effects.

By the end of the session you should become familiarised with

•    effects of ozone and greenhouse gases in the middle atmosphere

•    the polar vortex and thermal wind balance

•    the influence of background wind and the dissipation of non-stationary (non-orographic) gravity waves

•    a simple spectral scheme for the wave flux

•    the quasi-biennal oscillation

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 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 describes the representation of subgrid-scale variability of humidity, cloud and precipitation and how this can be parametrized in atmospheric models.

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

•    recognise the reasons for representing the subgrid variability of humidity and cloud in an atmospheric model

•    explain how the key quantity of cloud fraction is related to subgrid heterogeneity assumptions

•     describe the different types of subgrid cloud parametrization schemes.

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

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

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

In this lecture we will give you a brief history of ECMWF and present the main areas of NWP research that is currently being carried out in the centre. We then look at current research challenges and present some of the latest developments that will soon become operational.

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

• List the main research areas at ECMWF and describe the latest model developments.

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

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

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.

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.

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.

This lecture will give an overview of the general circulation of the atmosphere as a refresher. Starting from a radiative energy balance perspective the dominating atmospheric circulation systems will be described. The coupling between Hadley cell dynamics and surface friction will be covered as well as midlatitude jets and baroclinic instability. Orographic steering of large scale Rossby waves and flow regime behaviour will also be discussed.

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

• Describe the overall energy balance of the atmosphere.
• Explain the dynamics of the Hadley cell circulation.
• Describe factors that determine midlatitude flow variability.

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

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.

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 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 aim of this session is to understand the role of sea ice for medium to extended range forecasts. We will discuss the mechanisms that give rise to sea ice predictability on seasonal to interannual timescales. We will present an overview of the current observing systems and the representation of sea ice within ECMWF system.

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

• explain the impact of sea ice cover on atmospheric and oceanic circulation
• describe the sources of predictability for Arctic sea ice
• describe the representation of sea ice within ECMWF forecast systems.

The aim of this session is to provide a general overview of the application of probabilistic medium-to-long-range forecasts in meteorological drought applications. We will review the main drought concepts and how probabilistic forecast can be adapted to typical drought indicators.

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

• explain the benefit of using drought indicators

• describe the forecast products that can be used for drought monitoring and forecasting

• understand the different sources of drought indicators predictability

This lecture looks at calibration and multi-model ensembles from a seasonal forecasting perspective. The theoretical basis is given, followed by research results that strongly motivated a multi-model approach for these timescales. The operational EUROSIP multi-model system is described.

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

• explain the difference between a model distribution and a pdf
• discuss why a multi-model approach is powerful for seasonal forecasts in particular
• outline the methods used by the EUROSIP multi-model system