| Time | Monday | Tuesday | Wednesday | Thursday | Friday |
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| 9.15 | Introductions | | Expand |
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| title | Algorithms for semi-implicit integrations of nonhydrostatic PDEs of atmospheric dynamics (1) |
|---|
| 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.
|
Piotr Smolarkiewicz
| | Expand |
|---|
| title | Hydrostatic/Non-hydrostatic dynamics, resolved/permitted convection and interfacing to physical parameterizations | The semi-Lagrangian, semi-implicit technique of the ECMWF model |
|---|
| The aim of this session is to describe the numerical technique used in the ECMWF model for integrating the transport equations of the hydrostatic primitive equation set. We will present an overview of the semi-Lagrangian method and how it is combined with semi-implicit time-stepping to provide a stable and accurate formulation for the ECMWF Integrated Forecasting System (IFS) 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, this session you should be able to: discuss limits of the hydrostatic approximation for numerical weather predictionexplain the dilemma of parametrizing deep convection versus permitting explicit deep convection at resolution in the grey zone of convection - fundamental concepts of semi-Lagrangian advection schemes, their strengths and weaknesses
- describe semi-implicit time-stepping and its use in IFS
- explain the important role these two techniques play for the efficiency of the current IFS system
- explain the impact that future super-computing architectures may have in the applicability of the semi-Lagrangian technique in high resolution non-hydrostatic global NWP systems.
|
Michail DiamantakisSylvie Malardel
| | Expand |
|---|
| title | Discontinuous higher order discretization methods |
|---|
| 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
|
Willem Deconinck | 10.35 | | Numerics + Discretization in NWP today | Using the 30-year history of ECMWF's Integrated Forecasting System (IFS) as an example, thelecture is an introduction to the development and current state-of-the-art of global numerical weather prediction (NWP), as well as to the challenges faced in the future. It is intended to provide
an overview and context for the topics covered in more detail during the course.
| Massively parallel computing for NWP and climate |
| 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 |
| By the end of the session you should be able to |
| :- describe the development of global NWP, the current-state-of-the-art, and future challenges
- identify relevant areas of research in numerical methods for Earth-System Modelling
- put into context every subsequent lecture and its purpose
Nils Wedi
| Expand |
|---|
| title | Algorithms for semi-implicit integrations of nonhydrostatic PDEs of atmospheric dynamics (2) |
|---|
|
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.
|
Piotr Smolarkiewicz
| Expand |
|---|
| title | Mesh adaptivity using continuous mappings |
|---|
|
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
|
Christian Kühnlein
| Expand |
|---|
| title | Discontinuous higher order discretization methods |
|---|
| 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
|
Willem Deconinck | 11.45 | | Expand |
|---|
| title | Introduction to semi-implicit integrations of nonhydrostatic PDEs of atmospheric dynamics |
|---|
| By the end of this session you should be able to: |
Piotr Smolarkiewicz | 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
|
Andreas Müller |
| 10.35 | | Expand |
|---|
| title | Numerics + Discretization in NWP today |
|---|
| Using the 30-year history of ECMWF's Integrated Forecasting System (IFS) as an example, thelecture is an introduction to the development and current state-of-the-art of global numerical weather prediction (NWP), as well as to the challenges faced in the future. It is intended to provide an overview and context for the topics covered in more detail during the course.
By the end of the session you should be able to: - describe the development of global NWP, the current-state-of-the-art, and future challenges
- identify relevant areas of research in numerical methods for Earth-System Modelling
- put into context every subsequent lecture and its purpose
|
Nils Wedi | | Expand |
|---|
| title | Algorithms for semi-implicit integrations of nonhydrostatic PDEs of atmospheric dynamics (2) |
|---|
| 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.
|
Piotr Smolarkiewicz | Practical Session Practical Session (elliptic solvers) Andreas Müller, Willem Deconinck, Christian Kühnlein | | Expand |
|---|
| title | Massively parallel computing for NWP and climateDiscontinuous higher order discretization methods |
|---|
| The aim of this session is to understand the main issues and challenges in parallel computing, and how parallel computers are programmed todaylearn 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 this the 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
|
George Mozdzynski 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
|
Willem Deconinck | | Expand |
|---|
| title | Reduced Precision Computing for Earth System Modelling |
|---|
| The aim of this session is to By the end of this session you should be able to |
Peter Düben |
| 11.45 | | Expand |
|---|
| title | Introduction to semi-implicit integrations of nonhydrostatic PDEs of atmospheric dynamics |
|---|
| By the end of this |
| Course wrap up and Certificates | 14.00 | | Expand |
|---|
| title | The spectral transform method |
|---|
| The success of the spectral transform method in global NWP in comparison to alternative methods has been overwhelming, with many operational forecast centres (including ECMWF) having madethe spectral transform their method of choice. The lecture will introduce the basic elements of the spectral transform, explain why it has been successful and describe recent developments such as the fast Legendre transform. By the end of the session you should be able to: |
Piotr Smolarkiewicz explain what the spectral transform method is, how it is applied, and describe the latest developments at ECMWF.- give reasons why it is successful for global NWP and climate.
- identify potential disadvantages of the method.
Nils Wedi | Practical Session (elliptic solvers) Andreas Müller, Willem Deconinck, Christian Kühnlein | Practical Session Willem Deconinck, Christian Kühnlein | | Expand |
|---|
| title | Operational and research activities at ECMWF now/in the future |
|---|
| 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 | | Expand |
|---|
| title | The semi-Lagrangian, semi-implicit technique of the ECMWF model |
|---|
| | The aim of this session is to describe the numerical technique used in the ECMWF model for integrating the transport equations of the hydrostatic primitive equation set. We will present an overview of the semi-Lagrangian method and how it is combined with semi-implicit time-stepping to provide a stable and accurate formulation for the ECMWF Integrated Forecasting System (IFS) . By the end of this session the lecture you should be able to: - describe the fundamental concepts of semi-Lagrangian advection schemes, their strengths and weaknesses
- describe semi-implicit time-stepping and its use in IFS
- explain the important role these two techniques play for the efficiency of the current IFS system
- explain the impact that future super-computing architectures may have in the applicability of the semi-Lagrangian technique in high resolution non-hydrostatic global NWP systems.
|
Michail Diamantakis - List the main research areas at ECMWF and describe the latest model developments.
|
Sarah Keeley and Erland Källén | Course wrap up and Certificates |
| 14.00 | | Expand |
|---|
| title | The spectral transform method |
|---|
| The success of the spectral transform method in global NWP in comparison to alternative methods has been overwhelming, with many operational forecast centres (including ECMWF) having madethe spectral transform their method of choice. The lecture will introduce the basic elements of the spectral transform, explain why it has been successful and describe recent developments such as the fast Legendre transform |
| Expand |
|---|
| title | Eulerian time-stepping schemes for NWP and climate |
|---|
| The aim of this session is to describe alternative (to the semi-Lagrangian) numerical techniques for integrating the transport equation sets encountered in NWP models. We will present an overview of different Eulerian time-stepping techniques and discuss the advantages and disadvantages of each approach.
By the end of the session you should be able to: |
- describe the basic features of different time-stepping schemes used in other weather forecasting models such as WRF, ICON
Michail Diamantakis | Expand |
|---|
| title | Introduction to element based computing, finite volume and finite element methods |
|---|
| 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.
|
Joanna Szmelter - explain what the spectral transform method is, how it is applied, and describe the latest developments at ECMWF.
- give reasons why it is successful for global NWP and climate.
- identify potential disadvantages of the method.
|
Nils Wedi
| | Expand |
|---|
| title | Eulerian time-stepping schemes for NWP and climate |
|---|
| The aim of this session is to describe alternative (to the semi-Lagrangian) numerical techniques for integrating the transport equation sets encountered in NWP models. We will present an overview of different Eulerian time-stepping techniques and discuss the advantages and disadvantages of each approach.
By the end of the session you should be able to: - recognize the basic differences between semi-Lagrangian and Eulerian approaches
- describe differences, strengths-weaknesses of different time-stepping approaches such as split-explicit time-stepping, Runge-Kutta time-stepping
- describe the basic features of different time-stepping schemes used in other weather forecasting models such as WRF, ICON
|
Michail Diamantakis | | Expand |
|---|
| title | Hydrostatic/Non-hydrostatic dynamics, resolved/permitted convection and interfacing to physical parameterizations |
|---|
| 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
|
Sylvie Malardel
| | Expand |
|---|
| title | Introduction to element based computing, finite volume and finite element methods |
|---|
| 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.
|
| |
| 15.30 | | Expand |
|---|
| title | Vertical discretisation |
|---|
| 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
|
Christian Kühnlein
| | Expand |
|---|
| title | Mesh adaptivity using continuous mappings |
|---|
| 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
|
Christian Kühnlein | | Expand |
|---|
| title | Hydrostatic/Non-hydrostatic dynamics, resolved/permitted convection and interfacing to physical parameterizations |
|---|
| 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
|
Sylvie Malardel
| | Expand |
|---|
| 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 |
| | Expand |
|---|
| title | Massively parallel computing for NWP and climate |
|---|
| 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
|
George Mozdzynski |
15.30 | | Expand |
|---|
| title | Vertical discretisation |
|---|
|
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
|
Christian Kühnlein
| Expand |
|---|
| title | Mesh adaptivity using continuous mappings |
|---|
| The goal of this session is to provide By the end of the session you should be able to: |
Christian Kühnlein | | Expand |
|---|
| title | Hydrostatic/Non-hydrostatic dynamics, resolved/permitted convection and interfacing to physical parameterizations |
|---|
| 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
|
Sylvie Malardel | Expand |
|---|
| 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.
|
Joanna Szmelter | Expand |
|---|
|