The ECMWF operational ensemble forecasts for the western Mediterranean region exhibited high uncertainty while Hurricane Nadine was slowly moving over the eastern N. Atlantic in Sept. 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.
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 principal component analysis (PCA) with clustering techniques (see Pantillon et al) to characterize the behaviour of the ensembles.
If the plotting produces thick contour lines and large labels, ensure that the environment variable
LC_NUMERIC="C" is set before starting metview.
Caveat 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.
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 (34km 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)
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
Please enter the folder 'openifs_2018' to begin working.
Saving images and animations
The macros described in this tutorial can write PostScript and GIF image files to the
'figures' directory in 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
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 low up to 00Z, 20th September 2012. The forecasts in the next exercises start from this time and date.
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 controlsto 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).
If the contour lines appear jagged, in the plot window, select the menu item 'Tools -> Antialias'.
Close 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.
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.
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.
an_1x1.mv (or the
an_2x2.mv) to plot fields of your choice.
Task 3: Changing the map geographical area
an_1x1.mv icon and select 'Edit'.
In the edit window that appears
mapType=1 then click the play button at the top of the window.
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.
Task 4: Wind fields, sea-surface temperature (SST)
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.
Click the play buttonat 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".
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.
Exercise 2: Operational ECMWF HRES forecast
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.
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.
Data is provided for a single 10 day forecast starting from 20th Sept 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.
A new parameter is total precipitation : tp.
The parameters available in the analyses are also available in the forecast data.
Available plot types
Task 1: Synoptic development (day 0-5)
Study the forecast scenario to day+5, focus on:
- the evolution of Nadine,
- the fate of the cutoff low,
- the precipitation over France.
You can use the
hres_2x2.mv icons in the same way as Exercise 1 when looking at the analyses.
Although the macros will animate the data for the whole forecast, for this task concentrate on the forecast for the first 5 days.
For example, to plot geopotential at 500hPa and MSLP using the
hres_1x1.mv macro, right click, select Edit and put:
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_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_2x2.mv macro plot some of these other maps to study the synoptic development.
Task 2: Vertical structure and forecast evolution to day 10
This task focuses on the fate of Nadine and examines vertical PV cross-sections of Nadine and the cutoff 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 Sept., (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.
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 Sept). Nadine has now intensified as it approaches the coast.
To change the forecast length for
hres_2x2.mv, right-click, select Edit and change:
Changing cross-section location
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 iconto find the new position of the line.
Change the forecast time again to day+8 (28th Sept), 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.
Cyclone phase space (CPS) diagrams
An objectively defined cyclone phase space (CPS) is described using the storm-motion-relative thickness asymmetry (symmetric/non-frontal versus asymmetric/frontal) and vertical derivative of horizontal height gradient (cold- versus warm-core structure via the thermal wind relationship). A cyclone's life cycle can then be analyzed within this phase space, providing insight into the cyclone structural evolution.
This allows a classification of cyclone phase, unifying the basic structural description of tropical, extratropical, and hybrid cyclones into a continuum.
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).
Exercise 3: Operational ensemble forecasts
- 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
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.
Ensemble forecast uncertainty
In these tasks, the performance of the ensemble forecast is studied.
Task 1: Ensemble spread
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.
'expId' if required to select either the 2012 ensemble
expId="ens_oper" or the reforecast ensemble
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.
Spaghetti plots - another way to visualise spread
A "spaghetti" plot is where a single contour of a parameter is plotted for all ensemble members. It is another way of visualizing the differences between the ensemble members and focussing on features.
ens_to_ref_spag.mv icon. Plot and animate the MSLP and z500 fields using your suitable choice for the contour level. Find a value that highlights the low pressure centres. Note that not all members may reach the low pressure set by the contour.
The red contour line shows the control forecast of the ensemble.
Note that this may animate slowly because of the computations required.
Experiment with changing the contour value and (if time) plotting other fields.
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.
clustersId="off" for this task. Clustering will be used later.
Precipitation over France
Use stamp.mv and plot total precipitation ('tp') over France (mapType=2) for 00Z 24-09-2012.
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.
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.
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.
Cross-sections of an ensemble member
To show a cross-section of a particular ensemble member, use the macro
This works in the same way as the
Exercise 4: CDF, percentiles and probabilities
|Figure 1. The probability distribution function of the normal distribution |
or Gaussian distribution. The probabilities expressed as a
percentage for various widths of standard deviations (σ)
represent the area under the curve.
Figure from Wikipedia.
Figure 2. Cumulative distribution function for a normal
Figure from Wikipedia.
Cumulative distribution function
The figures above illustrate the relationship between a normal distribution and its associated cumulative distribution function. The CDF is constructed from the area under the probability density function.
The CDF gives the probability that a value on the curve will be found to have a value less than or equal to the corresponding value on the x-axis. For example, in the figure, the probability for values less than or equal to X=0 is 50%.
The shape of the CDF curve is related to the shape of the normal distribution. The width of the CDF curve is directly related to the value of the standard deviation of the probability distribution function.
For an ensemble, the width is therefore related to the 'ensemble spread'. For a forecast ensemble where all values were the same, the CDF would be a vertical straight line.
Not all parameters will have a Gaussian distribution in values from the ensemble. This will be apparent in the exercises below.
Percentiles and probabilities
For a specified location, the CDF gives the probability that the parameter (for example, total precipitation) is below or equal to the percentile value, p, from the ensemble forecast. This means that the probability of the precipitation being above the value is 1-p.
A probability map then shows the spatial distribution of the precipitation exceeding a specific threshold, p, for example, a map showing the probability that the precipitation will exceed a threshold of 20mm in a 6hr period. A percentile map is very similar and shows the spatial distribution of the given percentile, for example, a map of total precipitation (in mm) for a percentile of 95%.
In the next tasks, we will look at probabilities of the total precipitation in different ways, highlighting the differences between the two forecast ensembles.
Task 1: Plot probabilities and percentiles of total precipitation
Enter the folder Probabilities in the openifs_2018 folder.
prob_tp_compare.mv icon will produce maps over France showing the probability that total 6-hourly precipitation exceeds a threshold expressed in mm, for both the 2012 and 2016 forecast ensembles.
Maps are produced for 3 forecast times: +90, +96 and +102 hours.
prob_tp_compare.mv and set the probability to 10mm:
location as an empty string for now:
Run the macro and view the map.
Location for CDF
Using the probability map, click the cursor data iconand move the pointer over the map for +96h and choose a location in the region of highest rainfall. Do this for both the 2012 and 2016 ensemble map.
Make a note of the latitude and longitude coordinates. The highest rainfall area was approximately over the Cévennes mountains (
and replot the map. A small purple dot will appear at the location specified. If the dot is not in the right location, change it and replot.
Using the plotted probability map for 10mm precipitation threshold, use the cursor data icon to read the probability at the chosen location for +96 hours. Make a note of this value.
prob_tp_compare.mv, and change the threshold value to 20mm:
Replot the map and make a note of the probability at your chosen location.
Finally change the threshold probability to 30mm and replot:
At your chosen location, using the cursor data icon, make a note of the probability for the 30mm threshold values.
You should now have the probability values that total precipitation will exceed 10mm, 20mm and 30mm, for both the 2012 and 2016 ensembles, for forecast time +96 hours for your chosen location.
Task 2: Plot the CDF
This exercise uses the cdf.mv icon.
Right-click, select 'Edit' and then plot a CDF for your location chosen in Task 1 for the 2012 ensemble forecast:
Make sure the steps value is set correctly to +96 hours (00Z 24th Sept):
Do the same for the 2016 operational ensemble reforecast:
Compare the CDF from the different forecast ensembles.
Compare with probability map values
Using the CDF graph for the 2012 ensemble, read the probability that total precipitation will exceed 10mm. For example, see what percentile value, p, is indicated on the y-axis for x=10mm. The probability that total precipitation exceeds this value is then 100-p.
The value read from the CDF graph in this way should agree with the value you obtained by reading the probability value from the map in Task 1.
Check your probabilities for 20mm and 30mm total precipitation.
The values may not match exactly as the number of samples (ensembles forecasts in this case) is limited.
Task 3. Plot percentiles of total precipitation
To further compare the 2012 and 2016 ensemble forecasts, plots showing the percentile amount above a threshold can be made for total precipitation.
These can also be compared to the CDF curves from Task 2.
As before, this will use the 6-hourly total precipitation for forecast steps at 90, 96 and 102 hours, plotted over France.
Set the percentile for the total precipitation to 70% and specify the location as in Tasks 1 & 2:
Plot the map. It is very similar to the probability map but now shows precipitation values (in mm) for the specified percentile.
From the CDF graph, read the percentile value of 70% on the y-axis and find the total precipitation value indicated on the x-axis.
Use the cursor data icon on the map, as before, and confirm the CDF value agrees with the value at the location on the map (shown by the purple dot).
Repeat this by setting the percentile to 80% and 95%
Exercise 5: 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:
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 '
clustersId=fred' in the macro
Plot maps of parameters as clusters
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.
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:
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.
Spaghetti maps: with clusters enabled, two additional maps are produced which show the contour lines for each cluster.
Use the clusters of ensemble members you have created in
clustersId='example' in each of the stamp.mv and ens_to_ref_spag.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
stamp.mv icon and change it to plot the total precipitation over France with clusters enabled.e.g.
If you choice of clustering is accurate, you should see a clear separation of precipitation over France between the 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.
eof.mv macro computes the EOFs and the clustering.
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.
cluster_to_ref.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.
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).
cluster_to_ref.mv can be used to plot maps of parameters as clusters and compared to the HRES forecast.
cluster_to_ref.mv to plot z500 and MSLP maps of the two clusters created by the EOF analysis.
cluster_to_ref.mv and set:
Run the macro.
If time also look at other parameters such as PV/320K.
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
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:
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.
Exercise 6. 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: Satellite images
Open the folder 'satellite' (scroll the window if it is not visible).
This folder contains satellite images (water vapour, infra-red, false colour) for 00Z on 20-09-2012 and animations of the infra-red and water vapour images.
Double click the images to display them and watch the observed behaviour of Nadine and the cut-off low.
Task 2: Analyses from 20th Sept.
Now look at the analyses from 20th Sept to observe what actually happened.
an_1x1.mv, Edit and set the plot to show MSLP and geopotential at 500hPa:
Click the play button and animate the plot to watch how Nadine and the cut-off low behave.
mv_track.mv icon to overlay the track of Nadine onto the map.
If time, use the other icons such as
an_xs.mv to look at the cross-section through the analyses and compare to the forecast cross-sections from the previous exercises.
Task 3: Compare forecast to analysis
Plot forecast difference maps to see how and when the forecast differed from the analyses.
hres_to_an_diff.mv icon and plot the differences between the z500, MSLP and other fields to how the forecast differences evolve.
Also try the
ctrl_to_an_diff.mv icon which plots the difference but this time using the ensemble control forecast.
Task 4: Forecast error curve
In this task, we'll look at the difference between the forecast and the analysis by using "root-mean-square error" (RMSE) curves as a way of summarising the performance of the forecast.
Root-mean square error curves are a standard measure to determine forecast error compared to the analysis and several of the exercises will use them. The RMSE is computed by taking the square-root of the mean of the forecast difference between the HRES and analyses. RMSE of the 500hPa geopotential is a standard measure for assessing forecast model performance at ECMWF (for more information see: http://www.ecmwf.int/en/forecasts/quality-our-forecasts).
Right-click the hres_rmse.mv icon, select 'Edit' and plot the RMSE curve for z500.
Repeat for the mean-sea-level pressure mslp.
Repeat for both geographical regions:
mapType=1 (Atlantic) and
Task 5: 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).
First plot the plumes with clustering 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.
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.
Task 6: 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.
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.
For more information on the stochastic physics scheme in IFS, see the article:
Shutts et al, 2011, ECMWF Newsletter 129.
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.