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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

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 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

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

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 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.

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

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.

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 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.

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

• Identify the main processes associated with snow in the climate system
• Describe the main components of the snow scheme in the ECMWF model

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

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

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 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

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 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

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 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 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 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

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.

Building on the previous two Cloud sessions, the practical implementation of a cloud 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 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 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.

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 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.

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.  

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

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

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.