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

As a smooth dynamical field, Although geopotential height at 500hPa at 00 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.

Warning

TODO: update macro image below.

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The eof.mv macro computes the EOFs and the clustering.

Warning

Always use the eof.mv first for a given parameter, step and ensemble forecast (e.g. ens_oper or ens_2016) to create the cluster file.

Otherwise cluster_to_anref.mv and other plots with clustering enabled will fail or plot with the wrong clustering of ensemble members.

If you change step or ensemble, recompute the EOFS and cluster definitions using eof.mv. Note however, that once a cluster has been computed, it can be used for all steps with any parameter.

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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Panel
titleCompute EOFs and clusters

Edit 'eof.mv'.

Set the parameter to use, choice of ensemble and forecast step required for the EOF computation:

Code Block
param="z500"
expId="ens_oper"
steps=[2012-09-24 00:00]

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 (same as in Pantillon et al). If desired it can be changed in eof.mv.

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Panel
titleEOF cluster definition file

The eof.mv macro will create a text file with the cluster definitions, in the same format as described above in the previous task.

The filename will be different, it will have 'eof' in the filename to indicate it was created by using empirical orthogonal functions.

Code Block
languagebash
titleCluster filename created for ensemble 'ens_oper' using eof.mv
ens_oper_cluster.eof.txt

If a different ensemble forecast is used, for example ens_2016, the filename will be: ens_2016_cluster.eof.mv

This cluster definition file can then be used to plot any variable at all steps (as for task 1).

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Panel
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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?


 

Panel
titlePlot 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_anref.mv (TODO: renamed?)  can be used to plot maps of parameters as clusters and compared to the analysis and HRES forecasts.

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

Edit cluster_to_anref.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 the total precipitation (tp) over France and PV/320K.

 

Cluster 1 corresponds to a cutoff low moving eastward over Europe and cluster 2 to a weak ridge over western Europe. Cluster 1 exhibits a weak interaction between Nadine and the cut-off low over Europe. In cluster 2, there is a strong interaction between the cutoff and Nadine in which Nadine makes landfall over the Iberian penisula.
Panel
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Q. How similar is the PCA EOF computed clusters to your manual clustering?
Q. Which cluster best represents the analysis?
Q. How useful is the cluster analysis as an aid to forecasting for HyMEX?
Q. 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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Panel
titleChanging the number of clusters

To change the number of clusters created by the EOF analysis, find the file in the folder 'base' called base_edit eof.mv.

Edit this file and near the top, changeChange:

Code Block
  clusterNum=2

to

Code Block
  clusterNum=3

then select 'File' and 'Save' to save the changes.

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_anref.mv macro, for example:

Code Block
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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