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A comparison between the Met Office ETKF (MOGREPS) and an ensemble of 4DEnVars

Marek Wlasak, Stephen Pring, Mohamed Jardak, Neill Bowler

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Introduction to 4DVar and 4DEnVarDemonstrate need to improve our ensembleCompare re-centered ensemble of 4DEnVar

• Relaxation To Prior Spread (RTPS)• Additive inflation

Look at• spread• balance• vertical correlations • horizontal length scales

Table of contents

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4D-Ensemble-Var (4DEnVar):4D ensemble covariances without using a linear model

• Should be much more efficient on next-generation supercomputers with much larger numbers of processors.

• Model forecasts can be done in parallel beforehand rather than sequentially during the 4D-Var iterations (No PF model)

• Much higher I/O.• Generalises to a unified deterministic / ensemble analysis

system.

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4DEnVar44 v hybrid-4DVar44

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4DEnVar relies more heavily on the quality of the ensemble.

To get deterministic 4DEnVar to be more competitive we need to improve our ensemble.

Improving the ensemble should also improve the properties of the static background error covariance model.

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• MOGREPS training data performed poorly when used to generate static B.

• Verification is consistently poor with significantly larger RMSEs in fit to observations in southern hemisphere.

• Verification signals similar to 4DEnVar vs hybrid 4DVar tests.

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Trials / Training data

1.Ensemble 4DEnVar with RTPS• 0% Bc / 100% Be • RTPS inflation (relaxation parameter

0.93)• Re-centering to deterministic• Perturbed observations• 22 ensemble members• 506 samples over 5.75 consecutive

days2.Ensemble 4DEnVar with Additive inflation

• 0% Bc / 100% Be• Additive inflation 100%• Re-centering to deterministic• Perturbed observations• 22 ensemble members• No stochastic physics• 528 samples over 6 consecutive

days.

1.ECMWF training data from an ensemble of 4DVar analyses –

• 10 ensemble members• 300 samples over 15 days• Time-mean removed

2.MOGREPS• Adaptive inflation• 44 ensemble members• 440 samples from a month’s

worth of data, every 3 days

TRIALS TRAINING DATA

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Spread of ensemble of 4DEnVar 2 day spread: Europe 500hPa height

ETKFRTPSAdditive inflation

Spread comparable

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Spread of ensemble of 4DEnVar 2 day spread: Europe 850hPa wind

ETKFRTPSAdditive inflation

Spread comparable

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Key differences in the properties of training data for static B calibration (Balance 1)

• MOGREPS ETKF• ECMWF training data (used for static B in 4DVAR)• Ensemble of 4DEnVars RTPS• Ensemble of 4DEnVars additive inflation

• MOGREPS is unusually balanced, especially at the surface;• 4DEnVar with additive inflation is closer to ECMWF training data (additive inflation closest)

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Key differences in the properties of training data for static B calibration (Vertical Correlations)

MOGREPS ECMWF training data

Vertical correlation of hydrostatic pressure

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Key differences in the properties of training data for static B calibration (Vertical Correlations)

Ensemble 4DEnVar RTPS Ensemble 4DEnVar Additive inflation

Vertical correlation of hydrostatic pressure is tighter, more like ECMWF data

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Key differences in the properties of training data for static B calibration (Horizontal length scales)

• MOGREPS ETKF• ECMWF training data

(used for static B in 4DVAR)

• Ensemble of 4DEnVars RTPS

• Ensemble of 4DEnVars additive inflation

• ECMWF data has significantly more power in the lowest horizontal wave-numbers.

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Conclusion & future work

• Vertical correlations of ensemble of 4DEnVar are closer to those from the ECWMF training data set, than MOGREPS – GOOD SIGN!

• Latest trials in ensemble of 4DEnVars are getting closer to MOGREPS spread/skill

• Test different inflation schemes• Move away from re-centring• Generate further diagnostics from the perturbations:

• Look at PV diagnostics• Look at minimum-spanning rank tree histograms• Look at more spatially localised statistics• Run non-hybrid / hybrid 4DVar trials with static B generated from

ensemble of 4DEnVars (as well as the error modes) to verify quality of ensemble

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Thanks for your attention