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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:
- HRES : spectral T1279 (18km grid) highest resolution 10 day deterministic forecast.
- ENS : spectral T639 (36km grid) resolution ensemble forecast (50 members) is run for days 1-10 of the forecast, T319 (70km) is run for days 11-15.
In 2016, the ECMWF operational forecasts was upgraded compared to 2012 and consisted of:
- HRES/2016 : spectral T1279 with an octahedral grid configuration providing highest resolution of 9km.
- ENS/2016 : spectral T639 with an octahedral grid configuration providing highest resolution of 18km for all 15 days of the forecast.
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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metview & |
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Please enter the folder 'openifs_2019' to begin working. |
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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 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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an_1x1.mv : this plots horizontal maps of parameters from the ECMWF analyses overlaid on one plot. an_2x2.mv : this plots horizontal maps of parameters from the ECMWF analyses four plots to a page (two by two). |
Right-click on the an_1x1.mv
icon and select the 'Visualise' menu item (see figure)
After a pause, this will generate a map showing mean-sea-level pressure (MSLP).
Drag and drop the mv_track.mv
icon onto the map to add the track of Hurricane Nadine.
In the plot window, use the play button in the animation controls
to animate the map and follow the development and track of Hurricane Nadine.You can use the 'Speed' menu to change the animation speed (each frame is every 6 hours).
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If the contour lines appear jagged, in the plot window, select the menu item 'Tools -> Antialias'. |
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Q. What is unusual about Hurricane Nadine? |
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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.
An edit window appears showing the Metview macro code used to generate the plot. During these exercises you can change the top lines of these macros to alter the choice of parameters and plot types.
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# Available parameters: # mslp,t2,wind10,speed10,sst # t,z,pt,eqpt [850,700,500,200] # wind,speed,r[925,850,700,500,200] # w700, vo850, pv320K |
The surface fields (single level) are:
- mslp (mean-sea-level-pressure),
- t2 (2-metre temperature),
- wind10 (10-metre wind arrows),
- speed10 (wind-speed at 10m: sqrt(u^2+v^2)),
- sst (sea-surface temperature).
The upper level fields are:
- t (temperature),
- z (geopotential),
- pt (potential temperature),
- eqpt (equivalent potential temperature),
- wind (wind arrows),
- speed (wind-speed as contours),
- r (relative humidity).
The upper level fields have a list of available pressure levels in square brackets.
To plot upper level fields, specify the pressure level after the name, e.g. z500 would plot geopotential at 500hPa.
Some extra fields are also provided:
- w700 (vertical velocity at 700hPa),
- vo850 (relative vorticity at 850hPa) and
- pv320K (potential vorticity at 320K).
Wind fields are normally plotted as coloured arrows. To plot them as wind barbs add the suffix '.flag', e.g. "wind10.flag" will plot 10m wind as barbs.
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With the edit window open for an_1x1.mv, find the line that defines 'plot1':
Change this line to:
The '.s' means plot the 500hPa geopotential as a shaded plot instead of using contours (this style is not available for all fields). Make sure Click the play button and then animate the map that appears |
Use the an_1x1.mv
(or the an_2x2.mv
) to plot fields of your choice.
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Change the value of
You might add the mslp or z500 fields to this plot e.g.
Note that the fields are plotted in the order specified in the list! |
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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.
Only a single forecast is run at this resolution as the computational resources required are demanding. The ensemble forecasts are run at a lower resolution.
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_1x1.mv & : 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:
- the evolution of Nadine,
- the fate of the cut-off low.
You can use the hres_1x1.mv
and hres_2x2.mv
icons in the same way as Exercise 1 when looking at the analyses.
For example, to plot geopotential at 500hPa and MSLP using the hres_1x1.mv
macro, right click, select Edit and put:
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plot1=["z500.s","mslp"] |
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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Q. How strongly does Nadine appear to interact with the cut-off low? |
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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.
An ensemble forecast consists of:
- 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.
Two key differences between the 2016 and 2012 operational ensembles are: higher horizontal resolution, and coupling of NEMO ocean model to provide forecast fields of SST (sea-surface temperature) from the start of the forecast.
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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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'.
Choose your ensemble dataset by setting the value of 'expId', either 'ens_oper' or 'ens_2016' for this exercise.
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#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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Q. How does the ensemble mean MSLP and Z500 fields compare to the HRES forecast? |
Task 1: Ensemble spread
Use the ens_maps.mv
icon and plot 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.
Change 'expId'
if required to select either the 2012 ensemble expId="ens_oper"
or the reforecast ensemble expId="ens_2016"
.
Animate this plot to see how the spread grows.
This macro can also be used to look at clusters of ensemble members. It will be used later in the clustering tasks. For this task, make sure all the members of the ensemble are used.
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#ENS members (use ["all"] or a list of members like [1,2,3] members=["all"] #[1,2,3,4,5] or ["all"] or ["cl.example.1"] |
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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.
Use stamp.mv to plot the MSLP and z500 fields in the ensemble.
The stamp map is slow to plot as it reads a lot of data. Rather than animate each forecast step, a particular date can be set by changing the 'steps' variable.
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#Define forecast steps steps=[2012-09-24 00:00,"to",2012-09-24 00:00,"by",6] |
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.
This can help in identifying individual ensemble members that produce a different forecast than the control or HRES forecast.
Use the ens_to_ref_diff.mv
icon to compare an ensemble member to the HRES forecast. Use pf_to_cf_diff.mv
to compare ensemble members to the control forecast.
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To animate the difference in MSLP of an individual ensemble member 30 to the HRES forecast, edit the lines:
and visualise the plot. To compare the control forecast, change:
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This will show the forecasts from the ensemble members and also their difference with the ensemble control forecast. To animate the difference in MSLP with ensemble members '30' and '50', set:
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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. |
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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Q. What is different about SST between the two ensemble forecasts? |
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Exercise 4: Cluster analysis
The paper by Pantillon et al. describes the use of clustering to identify the main scenarios among the ensemble members.
Using clustering will highlight the ensemble members in each cluster in the plots.
In this exercise you will:
- Construct your own qualitative clusters by choosing members for two clusters,
- Generate clusters using principal component analysis.
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.
Choose members for two clusters. The stamp maps are useful for this task.
From the stamp map of z500 at 24/9/2012 (t+96), identify ensemble members that represent the two most likely forecast scenarios.
It is usual to create clusters from z500 as it represents the large-scale flow and is not a noisy field. However, for this particular case study, the stamp map of 'tp' (total precipitation) over France is also very indicative of the distinct forecast scenarios.
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)
The file contains two example lines:
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1# 2 3 4 9 22 33 40 2# 10 11 12 31 49 |
The first line defines the list of members for 'Cluster 1': in this example, members 2, 3, 4, 9, 22, 33, 40.
The second line defines the list of members for 'Cluster 2': in this example, members 10, 11, 12, 31, 49.
Change these two lines!.
Put your choice of ensemble member numbers for cluster 1 and 2 (lines 1 and 2 respectively).
You can create multiple cluster definitions by using the 'Duplicate' menu option to make copies of the file for use in the plotting macros..
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.
Use cluster_to_ref.mv
to plot z500 maps of your two clusters.
If your cluster definition file is called 'ens_oper_cluster.example.txt', then Edit cluster_to_an.mv
and set:
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#ENS members (use ["all"] or a list of members like [1,2,3] members_1=["cl.example.1"] members_2=["cl.example.2"] |
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.
Stamp maps: the stamp maps will be reordered such at the ensemble members will be grouped according to their cluster. This will make it easier to see the forecast scenarios according to your clustering. |
Use the clusters of ensemble members you have created in ens_oper_cluster.example.txt
.
Set clustersId='example'
in the stamp.mv to enable cluster highlighting.
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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param="tp" expId="ens_oper" mapType=2 clustersId="example" |
If you choice of clustering is accurate, you should see a clear separation of precipitation over France between the two clusters.
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Q. Are two clusters enough? Do all of the ensemble members fit well into two clusters? |
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).
As a smooth dynamical field, geopotential height at 500hPa at 00Z 24/9/2012 is recommend (it used in the paper by Pantillon et al.), but the steps described below can be used for any parameter at any step.
The eof.mv
macro computes the EOFs and the clustering.
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Always use the Otherwise If you change step or ensemble, recompute the EOFS and cluster definitions using Note that the EOF analyses is run over the smaller domain over France. This may produce a different clustering to your manual cluster if you used a larger domain. |
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Edit Set the parameter to use, choice of ensemble and forecast step required for the EOF computation:
Run the macro. The above example will compute the EOFs of geopotential height anomaly at 500hPa using the 2012 operational ensemble at forecast step 00Z on 24/09/2012. A plot will appear showing the first two EOFs. The geographical area for the EOF computation is: 35-55N, 10W-20E. If desired it can be changed in |
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The The filename will be different, it will have 'eof' in the filename to indicate it was created by using empirical orthogonal functions.
If a different ensemble forecast is used, for example This cluster definition file can then be used to plot any variable at all steps (as for task 1). |
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Q. What do the EOFs plotted by |
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:
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#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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Q. What are the two scenarios proposed by the two clusters? |
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?
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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.
Various methods for presenting the forecast error are used in the tasks below. The clusters created in the previous exercise can also be used.
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.
Right-click an_1x1.mv
, Edit and set the plot to show MSLP and geopotential at 500hPa:
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plot1=["z500.s","mslp"] |
Click the play button and animate the plot to watch how Nadine and the cut-off low behave.
Drop the mv_track.mv
icon to overlay the track of Nadine onto the map.
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.
Right-click the ens_rmse.mv icon, select 'Edit' and plot the curves for 'mslp' and 'z500'.
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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clustersId="off" |
There might be some evidence of clustering in the ensemble plumes.
There might be some individual forecasts that give a lower RMS error than the control forecast.
Next, use the cluster files created from the earlier exercise. You can use either your own created cluster file as before, or use the EOF generated file.
For example:
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clustersId="eof" |
would use the cluster definitions in the file: ens_oper_cluster.eof.txt (for the 2012 operational ensemble).
The cluster files are 'linked' from the Cluster folder, but if they do not work, just copy the cluster file (e.g. ens_oper_cluster.eof.txt) to the Forecast_errors folder.
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Q. How do the HRES, ensemble control forecast and ensemble mean compare? |
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.
Note, stamp_diff.mv
cannot be used for 'tp' as there is no precipitation data in the analyses.
Clustering can also be enabled for this task.
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Q. Using the stamp and stamp difference maps, study the ensemble. Identify which ensembles produce "better" forecasts. |
Appendix
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The macros described in this tutorial can write PostScript and GIF image files to the 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. |
To save any other images during these exercises for discussion later, you can either use:
"Export" button in Metview's display window under the 'File' menu to save to PNG image format. This will also allow animations to be saved into postscript.
or use the ksnapshot
command to take a 'snapshot' of the screen and save it to a file.
If you want to create animations from other images, save the figures as postscript and then use the convert
command:
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convert -delay 75 -rotate "90<" in.ps out.gif |
Additional tasks of exercise 1
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Right-click on an_1x1.mv
icon and select 'Edit'.
In the edit window that appears you can see the map types available covering a different area:
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#Map type: 0=Atl-an, 1: Atl-fc, 2: France mapType=0 |
With mapType=0
, the map covers a large area centred on the Atlantic suitable for plotting the analyses and track of the storm (this area is only available for the analyses).
With mapType=1
, the map also covers the Atlantic but a smaller area than for the analyses. This is because the forecast data in the following exercises does not cover as large a geographical area as the analyses.
With mapType=2
, the map covers a much smaller region centred over France.
Change, mapType=0
to mapType=1
then click the play button at the top of the window.
Repeat using mapType=2
to see the smaller region over France.
These different regions will be used in the following exercises.
Animate the storm on this smaller geographical map.
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The an_2x2.mv
icon plots up to 4 separate figures on a single frame.
Right-click on the an_2x2.mv
icon and select the 'Edit' menu item.
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#Define plot list (min 1- max 4) plot1=["mslp"] plot2=["wind10"] plot3=["speed500","z500"] plot4=["sst"] |
Click the play button
at the top of the window to run this macro with the existing plots as shown above.Each plot can be a single field or overlays of different fields.
Wind parameters can be shown either as arrows or as wind flags ('barbs') by adding '.flag' to the end of variable name e.g. "wind10.flag".
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Animating. If only one field on the 2x2 plot animates, make sure the menu item 'Animation -> Animate all scenes' is selected. Plotting may be slow depending on the computer used. This reads a lot of data files. |
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Q. What do you notice about the SST field? |
Additional tasks of exercise 2
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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.
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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.
Right-click on the icon 'hres_xs.mv'
icon, select 'Edit' and push the play button.
The plot shows the cross-section for the 22nd September, (day 2 of the forecast), for potential vorticity (PV), wind vectors projected onto the plane of the cross-section and potential temperature drawn approximately through the centre of the Hurricane and the cut-off low. The red line on the map of MSLP shows the location of the cross-section.
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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).
This means the 'steps' value in the macros is only valid for the times: [2012-09-20 00:00], [2012-09-21 00:00], .... and so on to [2012-09-30 00:00].
Change the forecast time to day+6 (26th September). Nadine has now intensified as it approaches the coast.
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steps=[2012-09-26 00:00] |
Changing cross-section location
Code Block |
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#Cross section line [ South, West, North, East ] line = [30,-29,45,-15] |
The cross-section location (red line) can be changed by editing the end points of the line as shown above.
If the forecast time is changed, the storm centres will move and the cross-section line will need to be repositioned to follow specific features. This is not computed automatically, but must be changed by altering the coordinates above. Use the cursor data icon
to find the new position of the line.Change the forecast time again to day+8 (28th September), or a different date if you are interested, relocate and plot the cross-section of Nadine and the low pressure system. Use the hres_1x1.mv
icon from task 1 if you need to follow location of Nadine.
If time, try some of the other vertical cross-sections below.
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Q. What changes are there to the vertical structure of Nadine during the forecast? |
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).
Choose from the following (note the cross-section macro hres_xs.mv
uses slightly different names for the parameters).
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Additional plots for further study
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Additional tasks of exercise 4
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To change the number of clusters created by the EOF analysis, edit eof.mv.
Change:
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clusterNum=2 |
to
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clusterNum=3 |
Now if you run the eof.mv
macro, it will generate a text file, such as ens_oper.eof.txt
with 3 lines, one for each cluster. It will also show the 3 clusters as different colours.
You can use the 3 clusters in the cluster_to_ref.mv
macro, for example:
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param="z500.s" expId="ens_oper" members_1=["cl.eof.1"] members_2=["cl.eof.3"] |
would plot the mean of the members in the first and the third clusters (it's not possible to plot all three clusters together).
You can have as many clusters as you like but it does not make sense to go beyond 3 or 4 clusters.
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For those interested: The code that computes the clusters can be found in the Python script: 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! |
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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