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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.

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

By the end of this session you should be able to

• explain the difference between shared and distributed memory

• describe the key architectural features of a supercomputer

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

• identify the reasons for the use of accelerator technology

The aim of 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.

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 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

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 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 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 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

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.

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 session we will sort out general house keeping for the course, such as computing accounts as well as introducing ourselves to one another. 

The aim of this lecture is to

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

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.

The aim of these sessions is to understand the role of land surface data assimilation on medium range weather forecasts.

We will give an overview of the different approaches used to assimilate land surface data and to initialise model variables in NWP.  We will  present the current observing systems and describe the land data assimilation structure within ECMWF system.

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

• identify the different observations used for snow and soil moisture data assimilation
• define land surface data assimilation approaches used for NWP
• describe the role of land surface data assimilation on medium-range weather forecasts

The goal of 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

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

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

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.

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.

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

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.

At ECMWF atmospheric composition data are assimilated into the IFS as part of the MACC-II project. On a global scale, atmospheric composition represents the full state of the global atmosphere covering phenomena such as desert dust plumes, long-range transport of atmospheric pollutants or ash plumes from volcanic eruptions, but also variations and long-term changes in the background concentrations of greenhouse gases.

The aim of this lecture is to give an overview of the work that is carried out at ECMWF regarding the assimilation of atmospheric composition data, and to address why this is of interest and which special challenges are faced when assimilating atmospheric composition data.

By the end of the session you should:

• have some understanding of the work carried out at ECMWF to assimilate data of atmospheric composition

The 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.

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.

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

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.

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

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.

This session will have two main components:

• An overview of the role of snow in the climate system from observations, models and forecasts; with a description of the current representation of snow in the ECMWF model.
• An overview of the role of vegetation in NWP with a description of the evolution of vegetation representation in the ECMWF model, supported by some evaluation examples.

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

• Identify the main processes associated with snow and vegetation in NWP
• Describe the main components related to snow and vegetation scheme in the ECMWF land surface 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