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Introduction

The ECMWF operational ensemble forecasts for the western Mediterranean region exhibited high uncertainty while Hurricane Nadine was slowly moving over the eastern N. North Atlantic in Sept. September 2012. Interaction with an Atlantic cut-off low produced a bifurcation in the ensemble and significant spread, influencing both the track of Hurricane Nadine and the synoptic conditions downstream.

The HyMEX (Hydrological cycle in Mediterranean eXperiment) field campaign was also underway and forecast uncertainty was a major issue for planning observations during the first special observations period of the campaign.

This interesting case study examines the forecasts in the context of the interaction between Nadine and the Atlantic cut-off low in the context of ensemble forecasting. It will explore the scientific rationale for using ensemble forecasts, why they are necessary and how they can be interpreted, particularly in a "real world" situation of forecasting for an observational field campaign.

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titleThis case study is based on the following paper which is recommended reading

Pantillon, F., Chaboureau, J.-P. and Richard, E. (2015), 'Vortex-vortex interaction between Hurricane Nadine and an Atlantic cutoff dropping the predictability over the Mediterranean, http://onlinelibrary.wiley.com/doi/10.1002/qj.2635/abstract

In this case study

In the exercises for this interesting case study we will:

  • Study the development of Hurricane Nadine and the interaction with the Atlantic cut-off low using the ECMWF analyses.
  • Study the performance of the ECMWF high resolution (HRES) deterministic forecast of the time.
  • Use the operational ensemble forecast to look at the forecast spread and understand the uncertainty downstream of the interaction.
  • Compare a reforecast using the May/2016 ECMWF operational ensemble with the 2012 ensemble forecasts.
  • Use manual clustering to characterize the behaviour of the ensembles and compare the results with clustering based on principal component analysis (PCA; see Pantillon et al.).
  • Study the performance of the ECMWF ensemble forecasts trough RMSE curves.


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Table of contents

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Note

If the plotting produces thick contour lines and large labels, ensure that the environment variable LC_NUMERIC="C" is set before starting metview.



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Note
titleCaveat on use of ensembles for case studies

In practise many cases are aggregated in order to evaluate the forecast behaviour of the ensemble. However, it is always useful to complement such assessments with case studies of individual events, like the one in this exercise, to get a more complete picture of IFS performance and identify weaker aspects that need further exploration.

Obtaining the exercises

The exercises described below are available as a set of Metview macros with the accompanying data. This is available as a downloadable tarfile for use with Metview. It is also available as part of the OpenIFS/Metview virtual machine, which can be run on different operating systems.

For more details of the OpenIFS virtual machine and how to get the workshop files, please contact: openifs-support@ecmwf.int.

ECMWF operational forecasts

In 2012, at the time of this case study, ECMWF operational forecasts consisted of:

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Please follow this link to see more details on changes to the ECMWF IFS forecast system (http://www.ecmwf.int/en/forecasts/documentation-and-support/changes-ecmwf-model)

Virtual machine

If using the OpenIFS/Metview virtual machine with these exercises the recommended memory is at least 6Gb, the minimum is 4Gb. If using 4Gb, do not use more than 2 parameters per plot.

These exercises use a relatively large domain with high resolution data. Some of the plotting options can therefore require significant amounts of memory. If the virtual machine freezes when running Metview, please try increasing the memory assigned to the VM.

Starting up Metview

To begin:

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titleType the following command in a terminal window
metview &

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For saving images and animations please see the Appendix.


Exercise 1: Hurricane Nadine and the cut-off low

ECMWF analyses to the 20th September 2012

In this exercise, the development of Hurricane Nadine and the cut-off flow up to the 20th September 2012 is studied.

Begin by entering the folder labelled 'Analysis':

Task 1: Mean-sea-level pressure and track

This task will look at the synoptic development of Hurricane Nadine and the cutoff cut-off low up to 00Z, 20th September 2012. The forecasts in the next exercises start from this time and date.

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Warning
titleClose unused plot windows!

Please close any unused plot windows if using a virtual machine. This case study uses high resolution data over a relatively large domain. Multiple plot windows can therefore require significant amounts of computer memory which can be a problem for virtual machines with restricted memory.

Task 2: MSLP and 500hPa geopotential height

Right-click the mouse button on the an_1x1.mv icon and select the 'Edit' menu item.

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titleAdditional tasks

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For changing the map geographical area please see the Appendix.

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For visualizing multiple variables on multiple maps please see the Appendix.


Exercise 2: Operational ECMWF HRES forecast

HRES performance

Exercise 1 looked at the synoptic development up to 20-Sept-2012. This exercise looks at the ECMWF HRES forecast from this date and how the IFS model developed the interaction between Hurricane Nadine and the cut-off low.

Enter the folder 'HRES_forecast' in the 'openifs_2018' folder to begin.

Recap

The ECMWF operational deterministic forecast is called HRES. At the time of this case study, the model ran with a spectral resolution of T1279, equivalent to 18km grid spacing.

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Before looking at the ensemble forecasts, first understand the behaviour of the operational HRES forecast of the time.

Available forecast

Data is provided for a single 10 day forecast starting from 20th September 2012.

Data is provided at the same resolution as the operational model, in order to give the best representation of the Hurricane and cut-off low iterations. This may mean that some plotting will be slow.

Available parameters

A new parameter is total precipitation: tp.

The parameters available in the analyses are also available in the forecast data.

Available plot types

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For this exercise, you will use the Metview icons in the folder 'HRES_forecast' shown above.

hres_1x1.mv & hres_2x2.mv : these work in a similar way to the same icons used in the previous task where parameters from a single lead time can be plotted either in a single frame or 4 frames per page.
hres_xs.mv
                                        : this plots a vertical cross section and can be used to compare the vertical structure of Hurricane Nadine and the cut-off low.

     : for this exercise, this icon can be used to overlay the forecast track of Nadine (and not the track from the analyses as in Exercise 1)

Task 1: Synoptic development

Study the forecast scenario to day+10, focus on:

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To add the forecast track of Hurricane Nadine drag and drop the mv_track.mv icon onto any map.

Precipitation over France

Choose a hres macro (hres_1x1 or hres_2x2) and plot the total precipitation (parameter: tp), near surface wind field (parameter: wind10), relative humidity (parameter: r).

Change the area to France by setting 'maptype=2' in the macro script.

Other suggested isobaric maps

Using either the hres_1x1.mv or hres_2x2.mv macro plot some of these other maps to study the synoptic development.

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titleAdditional tasks

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To study the precipitation over France please see the Appendix.

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To study the vertical structure please see the Appendix.


Exercise 3: Operational ensemble forecasts

Recap

  • ECMWF operational ensemble forecasts treat uncertainty in both the initial data and the model.
  • Initial analysis uncertainty: sampled by use of Singular Vectors (SV) and Ensemble Data Assimilation (EDA) methods. Singular Vectors are a way of representing the fastest growing modes in the initial state.
  • Model uncertainty: sampled by use of stochastic parametrizations. In IFS this means the 'stochastically perturbed physical tendencies' (SPPT) and the 'spectral backscatter scheme' (SKEB)
  • Ensemble mean : the average of all the ensemble members. Where the spread is high, small scale features can be smoothed out in the ensemble mean.
  • Ensemble spread : the standard deviation of the ensemble members, represents how different the members are from the ensemble mean.

The ensemble forecasts

In this case study, there are two operational ensemble datasets, one from the original 2012 operational forecast, the other from a reforecast of the event using the 2016 operational ensemble.

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  • Control forecast (unperturbed)
  • Perturbed ensemble members. Each member will use slightly different initial data conditions and include model uncertainty pertubations.

2012 Operational ensemble

ens_oper: This dataset is the operational ensemble from 2012 and was used in the Pantillon et al. publication. A key feature of this ensemble is use of a climatological SST field (seen in the earlier tasks).

2016 Operational ensemble

ens_2016: This dataset is a reforecast of the 2012 event using the ECMWF operational ensemble of March 2016.

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The analysis was not rerun for 20-Sept-2012. This means the reforecast using the 2016 ensemble will be using the original 2012 analyses. Also only 10 ensemble data assimilation (EDA) members were used in 2012, whereas 25 are in use for 2016 operational ensembles, so each EDA member will be used multiple times for this reforecast. This will impact on the spread and clustering seen in the tasks in this exercise.

Ensemble exercise tasks

Key parameters: MSLP and z500.  We suggest concentrating on viewing these fields. If time, visualize other parameters (e.g. PV320K).

Available plot types
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this will plot (a) the mean of the ensemble forecast, (b) the ensemble spread, (c) the HRES deterministic forecast and (d) the control forecast.

 this plots all of the ensemble forecasts for a particular field and lead time. Each forecast is shown in a stamp sized map. Very useful for a quick visual inspection of each ensemble forecast.

this useful macro allows two individual ensemble forecasts to be compared to the control forecast. As well as plotting the forecasts from the members, it also shows a difference map for each.

this will plot the difference between the ensemble control, ensemble mean or an individual ensemble member and the HRES forecast for a given parameter.


Group working

If working in groups, each group could follow the tasks below with a different ensemble forecast. e.g. one group uses the 'ens_oper', another group uses 'ens_2016'.

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Code Block
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titleEnsemble forecast datasets available in the macros
#The experiment. Possible values are:
# ens_oper = operational ENS
# ens_2016 = 2016 operational ENS

expId="ens_oper"
Ensemble forecast uncertainty

In these tasks, the performance of the ensemble forecast is studied.

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titleQuestions to consider

Q. How does the ensemble mean MSLP and Z500 fields compare to the HRES forecast?
Q. Examine the initial diversity in the ensemble and how the ensemble spread and error growth develops.  What do the extreme forecasts look like?

Task 1: Ensemble spread

Use the ens_maps.mv icon and plot the the MSLP and z500. This will produce plots showing: the mean of all the ensemble forecasts, the spread of the ensemble forecasts and the operational HRES deterministic forecast.

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Q. When does the ensemble spread grow the fastest during the forecast?

Task 2: Visualise ensemble members

Stamp maps are used to visualise all the ensemble members as normal maps. These are small, stamp sized contour maps plotted for each ensemble member using a small set of contours.

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Make sure clustersId="off" for this task. Clustering will be used later.

Compare ensemble members to the deterministic and control forecast

After visualizing the stamp maps, it can be useful to animate a comparison of individual ensemble members to the HRES and ensemble control deterministic forecasts.

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Compare the control forecast scenario to the HRES:

Q. Try to identify ensemble members which are the closest and furthest to the HRES forecast.
Q. Try to identify ensemble members which are the closest and furthest to the ensemble control forecast.

Sea-surface temperature

Compare the SST parameter used for the ens_oper and ens_2016 ensemble forecasts. The 2016 reforecast of this case study used a coupled ocean model unlike the 2012 ensemble and HRES forecast that used climatology for the first 5 days.

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titleAdditional tasks

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forfurtherplots
To study the ensemble forecast further please see the Appendix.

Exercise 4: Cluster analysis

The paper by Pantillon et al, . describes the use of clustering to identify the main scenarios among the ensemble members.

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  • Construct your own qualitative clusters by choosing members for two clusters.,
  • Generate clusters using principal component analysis.

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Enter the folder 'Clusters' in the openifs_2018 folder to begin working.

Task 1: Create your own clusters

Clusters can be created manually from lists of the ensemble members.

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You can choose any parameter to construct the clusters from, if you think another parameter shows a clear clustering behaviour.

How to create your own cluster

Right-click 'ens_oper_cluster.example.txt' and select Edit (or make a duplicate)

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The filename is important !
The first part of the name 'ens_oper' refers to the ensemble dataset and must match the name used in the plotting macro. 
The 'example' part of the filename can be changed to your choice and should match the 'clustersId'.
As an example a filename of: ens_both_cluster.fred.txt would require 'expId=ens_both', 'clustersId=fred' in the macro

Plot maps of parameters as clusters

The macro cluster_to_ref.mv can be used to plot maps of parameters as clusters and compared to the ensemble control forecast and the HRES forecast.

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If your cluster definition file has another name, e.g. ens_oper_cluster.fred.txt, then members_1=["cl.fred.1"].

Plot ensembles with clusters

In this part of the task, redo the plots from the previous exercise which looked at ways of plotting ensemble data, but this time with clustering enabled.

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If time, also try the ens_part_to_all.mv icon. This compares the spread and mean of part of the ensemble to the full ensemble.

Plot other parameters

Use the stamp.mv icon and change it to plot the total precipitation over France with clusters enabled.e.g.

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Q. Are two clusters enough? Do all of the ensemble members fit well into two clusters?
Q. What date/time does the separation of the clusters (e.g. z500 maps) become apparent and grow significantly?

Task 2: Empirical orthogonal functions / Principal component analysis

A quantitative way of clustering an ensemble uses empirical orthogonal functions from the differences between the ensemble members and the control forecast and then using an algorithm to determine the clusters from each ensemble as projected in EOF space (mathematically).

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Q. What do the EOFs plotted by eof.mv show?
Q. Change the parameter used for the EOF (try the 'total precipitation' (tp) field). How does the cluster change?


Plot ensemble and cluster maps

Use the cluster definition file computed by eof.mv to the plot ensembles and maps with clusters enabled (as above, but this time with the 'eof' cluster file).

The macro cluster_to_ref.mv  can be used to plot maps of parameters as clusters and compared to the HRES forecast.

Use cluster_to_ref.mv to plot z500 and MSLP maps of the two clusters created by the EOF analysis.

Edit cluster_to_ref.mv and set:

Code Block
languagebash
#ENS members (use ["all"] or a list of members like [1,2,3]
members_1=["cl.eof.1"]
members_2=["cl.eof.2"]

Run the macro.

If time also look at other parameters such as PV/320K.

 

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If time, change the date/time used to compute the clusters. How does the variance explained by the first two clusters change? Is geopotential the best parameter to use?

Changing the number of clusters

To change the number of clusters created by the EOF analysis, edit eof.mv.

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titleCluster method code

For those interested:

The code that computes the clusters can be found in the Python script: aux/cluster.py.

This uses the 'ward' cluster method from SciPy. Other cluster algorithms are available. See http://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.linkage.html#scipy.cluster.hierarchy.linkage

The python code can be changed to a different algorithm or the more adventurous can write their own cluster algorithm!


Exercise 5: Assessment of forecast errors

In this exercise, the analyses covering the forecast period are now available to see how Nadine and the cut-off low actually behaved.

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Enter the 'Forecast errors' folder in the openifs_2018 folder to start work on this exercise.

Task 1: Analyses from 20th September

Now look at the analyses from 20th September to observe what actually happened.

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If time, use the other icons such as an_2x2.mv and an_xs.mv to look at the cross-section through the analyses and compare to the forecast cross-sections from the previous exercises.

Task 2: RMSE "plumes" for the ensemble

This is similar to the previous exercise, except the RMSE curves for all the ensemble members from a particular forecast will be plotted.

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Change 'expID' for your choice of ensemble (either ens_oper or ens_2016).

Clusters

First plot the plumes with clustering off:

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Q. How do the HRES, ensemble control forecast and ensemble mean compare?
Q. How do the ensemble members behave, do they give better or worse forecasts?
Q. Is the spread in the RMSE curves the same in using other pressure levels in the atmosphere?

Task 3: Difference stamp maps

Use the stamp_diff.mv plot to look at the differences between the ensemble members and the analysis. It can be easier to understand the difference in the ensembles by using difference stamp maps.

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Q. Using the stamp and stamp difference maps, study the ensemble. Identify which ensembles produce "better" forecasts.
Q. Can you see any distinctive patterns in the difference maps?


Appendix

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Saving images and animations

Info

The macros described in this tutorial can write PostScript and GIF image files to the 'figures' directory in the 'openifs_2019' folder.

To save the images, use the 'Execute' menu option on the icon, rather than 'Visualise'. The 'okular' command can be used to view the PDF & gif images.

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convert -delay 75 -rotate "90<" in.ps out.gif

Back to the tutorial

Additional tasks of exercise 1

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Changing the map geographical area

Right-click on an_1x1.mv icon and select 'Edit'.

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Animate the storm on this smaller geographical map.

Back to the tutorial

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Plotting multiple variables on multiple maps

The an_2x2.mv icon plots up to 4 separate figures on a single frame.

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Q. What do you notice about the SST field?

Back to the tutorial

Additional tasks of exercise 2

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Precipitation over France

Choose a hres macro (hres_1x1 or hres_2x2) and plot the total precipitation (parameter: tp), near surface wind field (parameter: wind10), relative humidity (parameter: r).

Change the area to France by setting 'maptype=2' in the macro script.

Back to the tutorial

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Vertical structure and forecast evolution

This task focuses on the fate of Nadine and examines vertical PV cross-sections of Nadine and the cut-off low at different forecast times.

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Q. Look at the PV field, how do the vertical structures of Nadine and the cut-off low differ?

Changing forecast time

Cross-section data is only available every 24hrs until the 30th Sept 00Z (step 240).

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steps=[2012-09-26 00:00]

Changing cross-section location

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#Cross section line [ South, West, North, East ]
line = [30,-29,45,-15]

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titleQuestions to consider

Q. What changes are there to the vertical structure of Nadine during the forecast?
Q. What is the fate of the cut-off and Nadine?
Q. Does this kind of Hurricane landfall event over the Iberian peninsula happen often?

Suggestions for other vertical cross-sections

A reduced number of fields is available for cross-sections compared to the isobaric maps: temperature (t), potential temperature (pt), relative humidity (r), potential vorticity (pv), vertical velocity (w), wind-speed (speed; sqrt(u*u+v*v)) and wind vectors (wind3).

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  • "pt", "pv"              : potential temperature + potential vorticity  -  to characterize the cold core and warm core structures of Hurricane Nadine and the cut-off low.
  • "r", "w"                  : humidity + vertical motion  -  another view of the cold core and warm core structures of Hurricane Nadine and the cut-off low.
  • "pv", "w" ("r")      : potential vorticity + vertical velocity (+ relative humidity)  -  a classical cross-section to see if a PV anomaly is accompanied with vertical motion or not.

Back to the tutorial

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Additional tasks of Exercise 3

Additional plots for further study

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this plots a 'spaghetti map' for a given parameter for the ensemble forecasts compared to the reference HRES forecast. Another way of visualizing ensemble spread.

 this plots a vertical cross-section through the forecasts in the same way as the cross-section plots for the analyses.

this comprehensive macro produces a single map for a given parameter. The map can be either: i/ the ensemble mean, ii/ the ensemble spread, iii/ the control forecast, iv/ a specific perturbed forecast, v/ map of the ensemble probability subject to a threshold, vi/ ensemble percentile map for a given percentile value. For example, it is possible to plot of a map showing the probability that MSLP would be below 995hPa.

this macro can be used to plot the difference for two ensemble members against the HRES forecasts. As ensemble perturbations are applied in +/- pairs, using this macro it's possible to see the nonlinear development of the members and their difference to the HRES forecast.


Back to the tutorial



Further reading

For more information on the stochastic physics scheme in IFS, see the article:

Shutts et al, 2011, ECMWF Newsletter 129.

Acknowledgements

We gratefully acknowledge the following for their contributions in preparing these exercises. From ECMWF: Glenn Carver, Gabriella Szepszo, Sandor Kertesz, Linus Magnusson, Iain Russell, Simon Lang, Filip Vana. From ENM/Meteo-France: Frédéric Ferry, Etienne Chabot, David Pollack and Thierry Barthet for IT support at ENM.

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