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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:

  • 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

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:
  • 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



 

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


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

Andreas Müller


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:
  •   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






 

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:

  • 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

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:

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

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

  • describe how rounding errors will impact model simulations that show chaotic dynamics

  • describe the connection between numerical precision, computational performance and predictability
  • recall how a trade off between precision and performance can be realised in Earth System modelling today and in the future

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:

  • 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 (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:

  • 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



 

 

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:
  •   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



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:
  • obtain a good understanding of the minimum theoretical properties required by time-stepping schemes
     
  • 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

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.

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:

  • 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


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

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:

  • 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.

Joanna Szmelter


 

Time

Monday

TuesdayWednesdayThursdayFriday
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:

  • 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.

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:

  • 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

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:

  • understand the basics of how a geophysical data assimilation system works;
  • understand the main approximations and hypotheses which are required to build practical data assimilation algorithms for large geophysical systems

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:

  • 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

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:

  • 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


Patrick Laloyaux

 

 

Cristina Lupu


 

 

 


 

 

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


 





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:

  • Recognize the notations used for the rest of the week
  • Solve the optimal minimum-variance analysis problem
  • Apply the optimal interpolation method


Sebastien Massart



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





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

Philippe Lopez


 


 

 

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.

Patrick Laloyaux


 




14.15

The aim of this lecture is to

 

By the end of the lecture the participants 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:

  • 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.
Angela Benedetti

 

 

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.

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

Antje Inness


 



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:

  • Recall the challenges associated with variational data assimilation in systems with different timescales and computer codes.
  • Describe the benefits of having more consitently balanced coupled systems from coupled data assimilation.
  • Explain the differences between weakly and strongly coupled data assimilation approaches.
  • Discuss the various methods that are in use at ECWMF and explain the planned developments of the systems.

 

Phil Browne


 



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:

  • Recognize the 3D-Var cost function
  • Explain the various terms of the cost function
  • Question the efficiency of methods designed to find the mimimum of the cost function

Sebastien Massart

Followed by drinks reception and poster session



Practical Session: Tangent Linear and Adjoints


 

Practical Session with OOPS continued


 

Practical Session with OOPS

Marcin Chrust

Sebastien Massart

Patrick Laloyaux

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.

Hao Zuo

Question/answer session
Elias Holm, Lars Isaksen, Tony McNally, Massimo Bonavita



Course evaluation 16:-16:30

Sarah Keeley


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