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titleData Assimilation

 


 

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Monday

TuesdayWednesdayThursdayFriday
9.15
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titleIntroduction. 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.

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

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

Erland Källén, Sarah Keeley

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titleAssimilation Algorithms: (2) 3D-Var

 

Mike Fisher


PDF
nameTC_lecture_2.pdf

 

 

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titleAssimilation Algorithms: (3) 4D-Var

 

Mike Fisher


PDF
nameTC_lecture_3.pdf

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titleData Assimilation Diagnostics: Forecast Sensitivity

 

Carla Cardinali - Lecture will be given by Andras Horanyi

View file
nameFSOI_Lecture_AHCC.pptx
pageNWP Training Material 2016
spaceOPTR
height250


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titleParameterization and Data Assimilation

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

View file
nameTC_DA_lopez_2016_main.ppt
pageNWP Training Material 2016
spaceOPTR
height250



10.35
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titleAssimilation Algorithms (1): Basic Concepts

 

 

TC_lecture_1.pdf

Mike Fisher

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titleLand Data Assimilation - Soil moisture

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

View file
nameLand_data_assimilation_2016_part2.pptx
pageNWP Training Material 2016
spaceOPTR
height250


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titleEnsemble of Data Assimilations and uncertainty estimation

The Ensemble of Data Assimilations (EDA) technique is used for the estimation of the analysis and background errors of the ECMWF assimilation system. This lecture describes the EDA formulation and implementation, and how it interacts with ECMWF 4DVar analysis and ECMWF Ensemble Prediction System.

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

  • Describe the theoretical basis and practical implementation of the EDA
  • Explain the use of the EDA in the ECMWF analysis and ensemble prediction systems

Massimo Bonavita

 

PDF
nameBonavita_EDA_TC2016.pdf


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titleAnalysis of Satellite Data

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

View file
nameDA_TC_satellite.pptpageNWP Training Material 2016
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titleOcean Data Assimilation

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.

Magdalena Alonso-Balmaseda

View file
nametcourse16_da_ocean.pptx
pageNWP Training Material 2016
spaceOPTR
height250


11.45
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titleThe Global Observing System

The aim of this session is to present an overview of the current observing systems used in Numerical Weather Prediction. We will discuss our observational requirement, and how close the current observing system is to meeting our needs. We will also discuss areas where our requirements are evolving. We will learn about WMO's OSCAR database that describes the Global Observing System. We will learn how the large diversity of observations now available, are monitored to ensure only good observations are presented to an operational system.

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

  • be able to describe the main types of observations used in data assimilation for Numerical Weather Prediction;
  • be aware of how large volumes of observations are exchanged, implemented and monitored in operational systems;
  • be aware of WMO's OSCAR database, how to access it and what type of information it can provide.

Steve English

View file
nameGlobalObservingSystem.pptxpageNWP Training Material 2016
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titleBackground error modeling and non-Gaussian aspects of data assimilation

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

View file
nameBGErr_lecture_2016.pptpageNWP Training Material 2016
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titleEnsemble Kalman filters
 

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

 

PDF
nameBonavita_ENKF_TC2016.pdf

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titleModel error

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.


Yannick Tremolet - Lecture will be given by Mike Fisher

 


PDF
nameWeak4DVar2015.pdf

 

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titleData Assimilation of Atmospheric Composition

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

View file
nameEnvMoni_2016.pptxpageNWP Training Material 2016
spaceOPTR
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14.00
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titleAspects of using observations in data assimilation

 

Lars Isaksen

View file
nameLI_DA_TC_2016_Observations1.pptx
pageNWP Training Material 2016
spaceOPTR
heightheight250

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titleBias Correction

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.

Dick Dee

View file
nameDee_2016_TC_BiasCorrection.pptx
pageNWP Training Material 2016
spaceOPTR
height250

Toy Model Practice Session (1) 

Mike Fisher, Yannick Tremolet, Martin Leutbecher

OR

 

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titleTangent Linear and Adjoints

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

 

Toy Model Practice Session (1) 

Mike Fisher, Yannick Tremolet, Martin Leutbecher

OR

 

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titleTangent Linear and Adjoints

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

 

View file
nameTraining_course_2016_TLAD.pptx
pageNWP Training Material 2016
spaceOPTR
height250



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titleReanalysis

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

PDF
nameLaloyaux_Reanalysis_2016.pdf

15.30
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titleLand Data Analysis System - screen level parameters and snow

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

View file
page
nameLand_data_assimilation_2016_part1.pptxNWP Training Material 2016
spaceOPTR
height250

Followed by drinks reception and poster session


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titleQuality Control of observations

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

View file
nameVarQC_lecture.pptx
pageNWP Training Material 2016
spaceOPTR
height250

 

Toy Model Practice Session (2)

Mike Fisher, Yannick Tremolet, Martin Leutbecher

OR

Tangent linear and adjoint practical session

Angela Benedetti


Toy Model Practice Session (2)

Mike Fisher, Yannick Tremolet, Martin Leutbecher

OR

Tangent linear and adjoint practical session

Angela Benedetti

View file
nameTraining_course_2016_AD_handson.pptx
pageNWP Training Material 2016
spaceOPTR
height250


Question/answer session
Elias Holm, Lars Isaksen, Tony McNally, Mike Fisher

Course evaluation 16:-16:30

Sarah Keeley

...

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titleParametrization of sub-grid scale processes

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MondayTuesdayWednesdayThursdayFriday

Introduction to the course

Erland Källén / Students

 


 

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titleClouds (2)

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.

Richard Forbes

TC2016_Forbes_L2_cloud_coldphase.pptx

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titleLand Surface (2):Snow
This session will have two mains components:
  • An overview of the role of snow in the climate system from observations, models and forecasts.
  • Description of the current representation of snow in the ECMWF model, evaluation examples and ongoing developments.

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

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

Emanuel Dutra

pa_surf_2_cold_20160518.pptx

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titleLand Surface (3): Surface Energy, Water Cycle

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

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

Gianpaolo Balsamo

surf2.pptx

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titleParametrization and Data Assimilation

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.

Philippe Lopez

TC_PA_lopez_2016_main.ppt


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titleRadiation (1)

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

 

Robin Hogan

hogan_ecmwf_radiation_lecture1.pptx

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titleConvection (1)

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.

Peter Bechtold

CONVECTION_T1_2016.ppt

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titleRadiation (3)

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

Robin Hogan

hogan_ecmwf_radiation_lecture2.pptx

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titleConvection (3)

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.

Peter Bechtold

CONVECTION_T3_2016.ppt

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titleNumerics of Parameterization

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.

Sylvie Malardel

PDC_2016.pdf

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titleBoundary Layer (1)

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

Irina Sandu

pbl1_is_2016.pdf

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titleRadiation (2)

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

Alessio Bozzo

Bozzo_Radiation_Lecture3.pptx

Expand
titleConvection (2)

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.

Peter Bechtold

CONVECTION_T2_2016.ppt

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titleClouds (3)

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.

Richard Forbes

TC2016_Forbes_L3_cloud_subgrid.pptx

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titleModel Evaluation: Clouds and Boundary Layer

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.

Maike Ahlgrimm

CldPblVeri2016.ppt

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titleClouds (1)

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.

Richard Forbes

TC2016_Forbes_L1_cloud_warmphase.pptx

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titleBoundary Layer (2)

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

Irina Sandu

pbl2_is_new.pdf

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titleBoundary Layer (3)

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

Irina Sandu

pbl3_is_2016.pdf


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titleParametrization and Data Assimilation

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.

Philippe Lopez




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titleParameterization of Sub-grid Orography

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.  

 

Anton Beljaars

subgrid_orography_2016.ppt

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titleLand Surface (1): Introduction

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

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

Gianpaolo Balsamo

surf1.pptx

Introduction to the Single Column Model

Filip Vana

Lecture2016.pdf

Radiation exercises

Alessio Bozzo and Robin Hogan

 

 

Land Surface exercises

Gianpaolo Balsama and Emanuel Dutra


 

 

Boundary Layer & Cloud exercises

Irina Sandu, Maike Ahlgrimm and Richard Forbes

 

 

 

Moist Processes Exercises

Richard Forbes and Peter Bechtold


Moist Processes Games

Richard Forbes and Peter Bechtold

Radiation exercises

Alessio Bozzo and Robin Hogan

Land Surface exercises

Gianpaolo Balsama and Emanuel Dutra

Boundary Layer & Cloud exercises

Irina Sandu, Maike Ahlgrimm and Richard Forbes

Course wrap up and certificates

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titlePredictability and ocean-atmosphere ensembles

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