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Time | Monday | Tuesday | Wednesday | Thursday | Friday |
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9.15 | Introductions | The aim of this set of lectures 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 lectures you should be able to:
Piotr Smolarkiewicz see first lecture for handout | 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 you should be able to:
Michail Diamantakis
| 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:
Willem Deconinck | 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
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10.45 | 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:
Nils Wedi
| The aim of this set of lectures 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 lectures you should be able to:
Piotr Smolarkiewicz see first lecture for handout | Practical Session Willem Deconinck, Christian Kühnlein |
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:
Sarah Keeley and Erland Källén | The aim of this session is to understand how numerical precision can be traded against computational performance in Earth System modelling. It will be discussed how a reduction in numerical precision will influence model quality and how the minimal level of precision that will still allow simulations at high accuracy can be identified. We will give an overview about existing hardware options to adjust numerical precision to the need of the application. By the end of this session you should be able to
Peter Düben |
11.55 | The aim of this set of lectures 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 lectures you should be able to:
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Practical Session (elliptic solvers) Andreas Müller, Willem Deconinck, Christian Kühnlein | Practical Session Willem Deconinck, Christian Kühnlein | 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:
| Course wrap up and Certificates |
14.00 | 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:
Nils Wedi | The aim of this session is to describe Eulerian based numerical techniques for integrating the equation sets encountered in NWP models. We will present an overview of different time-stepping techniques and discuss the advantages and disadvantages of each approach. By the end of the session you should be able to:
Michail Diamantakis | 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:
By the end of the presentation, you should be able to:
| 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:
Joanna Szmelter | |
15.30 | 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:
| 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:
Christian Kühnlein See first lecture for handout | 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:
By the end of the presentation, you should be able to:
| 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:
Joanna Szmelter |
Time | Monday | Tuesday | Wednesday | Thursday | Friday |
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9.15 | In this session we will sort out general house keeping for the course, such as computing accounts as well as introducing ourselves to one another. Andy Brown, Sarah Keeley |
Sebastien Massart
| The aim of this lecture is to By the end of the lecture the participants should be able to:
Massimo Bonavita | 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:
Niels Bormann | 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:
Patricia de Rosnay |
10.45 | The goal of the ECMWF Earth System data assimilation is to provide an accurate and physically coherent description of the state of the atmosphere, ocean, sea ice and land surface as an initial point for our forecasts. This requires blending in a statistically optimal way information from a huge variety of observations and our prior knowledge about the physical laws of the Earth system, which is encapsulated in our models. In this lecture we will lay the general conceptual framework on how to achieve this from a Bayesian perspective. We will then highlight the approximations and hypotheses which are required to make the assimilation problem computationally tractable and which underlie the practical data assimilation algorithms which will be described in detail in this training course. By the end of lecture you should be able to:
Massimo Bonavita | 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:
Tony McNally | 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:
| A single observation can under some conditions undermine the quality of a global analyses. The lecture will go through methods used to make the analysis more robust against oulier or wrong observations, with focus on variational quality control. Elias Holm
| 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:
Hao Zuo |
11.55 | This lecture will explain the basic concepts of the assimilation algorithms. The terminology used in the next lectures will be introduced. Simple examples will conduce towards the formulation of the optimal minimum-variance analysis. The optimal interpolation method will finally be presented. By the end of the lecture the participants should be able to:
| 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 Massimo Bonavita |
Cristina Lupu
| 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:
Patrick Laloyaux
| 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:
Antje Inness |
14.15 | This lecture will introduce how observations are an essential part of the data assimilation system. It will focus on in situ (also called conventional) observations, from surface stations, drifters, aircraft and radiosondes. They are important both for direct use in the data assimilation system and for diagnostics. Radiosonde and surface observations also help to control the biases in the assimilation system. However they are diverse and hey can be complex, so close attention to quality control, observation uncertainty and (in some cases) bias correction is needed to optimise their use. The use of new BUFR format high resolution radiosonde data will also be presented. The lecture will also introduce the actively sensed satellite observations used for data assimilation at ECMWF: radio occultation data, scatterometer winds, and altimeter wind/significant wave height. By the end of the lecture the student should be able to:
Lars Isaksen | 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:
| The background error is central to the performance of the analysis system and tells how much confidence to put in the best available forecast which is to be updated with new observations. The lecture will review how background errors are estimated and represented for current variational algorithms. Elias Holm | 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:
Philippe Lopez
| At ECMWF we are striving to move towards an Earth System approach to our data assimilation techniques. We currently have models not only of the atmosphere, but of the ocean, the land surface, sea ice, waves, and atmospheric composition. These systems interact with each other in different ways and all need to be initialised through the incorporation of observational data.
The aim of this lecture is to recognise the benefits and challenges associated with data assimilation in coupled models.
By the end of the lecture the participants should be able to:
Phil Browne
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15.45 | This lecture will present the 3D-Var assimilation algorithm. This algorithm is based in the formulation of a cost function to minimize. Minimization methods will be presented together with some information on how to improve their efficiency. By the end of the lecture the participants should be able to:
Sebastien Massart Followed by drinks reception and poster session | Practical Session: Tangent Linear and Adjoints
| Practical Session with OOPS Marcin Chrust Sebastien Massart Patrick Laloyaux
| Practical Session with OOPS Marcin Chrust Sebastien Massart Patrick Laloyaux | Question/answer session Course evaluation 16:-16:30 Sarah Keeley |
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