development of a 4denvar-based ensemble at the met office ...€¦ · and rescaling within the...

Development of a 4DEnVar-based ensemble at the Met Office, and experiments with the new ensemble covariances in hybrid DANeill Bowler, Adam Clayton (presenter), Mohamed Jardak, Peter Jermey, Eunjoo Lee, Andrew Lorenc, Chiara Piccolo, Stephen Pring, Marek Wlasak, Dale Barker, Gordon Inverarity and Richard Swinbank

Outline of talk

•

• 4DEnVar-based ensemble: Design, tuning and performance.

• Results from low-res hybrid DA trials:

• Ensemble update: ETKF-based → 4DEnVar-based.

• Ensemble processing: (a) Time-lagging and time-shifting.

(b) “waveband” localisation.

• Summary and future work.

Global systems Operational NewData assimilation Hybrid-4DVar 4DEnVar*Ensemble ETKF-based 4DEnVar*-based

*Actually, hybrid-4DEnVar.

PF →

Global systems Operational New

Data assimilation Hybrid-4DVar 4DEnVarEnsemble ETKF-based 4DEnVar-based

T+0 T+3T-3

T+0 T+3T-3

↓

+

𝛽𝑒 %&

'()∘𝒘′' = 𝒘' − 𝒘0 𝐾 − 1�⁄

𝛿𝒘

=

𝛽6𝑼𝒗

↓

↓Reconfigure

𝛿𝒙

VAR

Det. forecast

Ensemble

𝜶' = 𝑼;𝒗';



• World-class performance, but

• Linear propagation of analysis increments, so physics must be linearised.

• Expensive: ~100 forward and adjoint forecasts run in serial for each analysis.

• Forecasts don’t scale well as processor numbers increase, so may be unsustainable as resolution and computer core counts increase.

PF →



T+0 T+3T-3

T+0 T+3T-3

↓

+

𝛽𝑒 %&

'()∘𝒘′' = 𝒘' − 𝒘0 𝐾 − 1�⁄

𝛿𝒘

=

𝛽6𝑼𝒗

↓

↓Reconfigure

𝛿𝒙

VAR

Det. forecast

Ensemble

𝜶' = 𝑼;𝒗';



T+0 T+3T-3

T+0 T+3T-3

↓

+

𝛽𝑒 %&

'()∘

𝒘′'<=

𝜶'

𝛿𝒘<=

=

𝛽6𝑼𝒗

↓

↓Reconfigure

𝛿𝒙<=↓

+

𝛽𝑒 %&

'()∘

𝒘′'>

𝜶'

𝛿𝒘𝟎

=𝛽6𝑼𝒗

↓

↓Reconfigure

𝛿𝒙𝟎↓

+

𝛽𝑒 %&

'()∘

𝒘′'@=

𝜶'

𝛿𝒘@=

=

𝛽6𝑼𝒗

↓

↓Reconfigure

𝛿𝒙@=

VAR

Det. forecast

Ensemble

← Same

← Same



• 4DEnVar uses an external “4DIAU” scheme to control gravity waves:

• Hybrid-4DVar uses an internal digital filter 𝐽6 term:

High-pass time filter

µcJ

Increment trajectory:

𝛿𝒙<= 𝛿𝒙𝟎 𝛿𝒙@=Det. forecast



• No PF model, so much cheaper: > 5 times faster. (Also scales better.)

• Perturbations propagated by full nonlinear model.

• Analysis quality not as good as hybrid-4DVar*:

• Climatological part of the increment is 3DVar-like.

• Localisation is (currently) fixed in time - not flow-following.

• External 4DIAU not as good as internal 𝐽6 term.

• Operational at ECCC and NCEP, but Met Office version ~2% behind its hybrid-4DVar system, so no plans for operational implementation.

• But, we can also use it as the basis for a new, relatively cheap ensemble…

* Full details in Lorenc et al (2015), Mon. Wea. Rev., 143, 212-229.



“MOGREPS-G”:

• Generates analysis perturbations by transforming the forecast perturbations (rotating and rescaling within the perturbation subspace).

• Calculate transform matrix using observations local to a limited set of points, approximately evenly distributed around globe.

• Interpolate transform matrix to intermediate grid points.

• Adaptive level-dependent inflation to maintain spread.



Main weaknesses:

• Very basic horizontal localisation. No vertical localisation.

• Doesn’t use the variational framework, so poorer assimilation of satellite data.

• Kalman Gain much different from that of hybrid-4DVar.

• Adaptive inflation scheme gives an unphysical semi-diurnal variation in spread.

• Software completely separate from the hybrid-4DVar software.



New 4DEnVar-based ensemble addresses the main weaknesses:

• Very basic horizontal localisation. No vertical localisation.

Ø Inherits the sophisticated model-based localisations built into the VAR code.

• Doesn’t use the variational framework, so poorer assimilation of satellite data.

Ø Variational scheme.

• Kalman Gain much different from that of hybrid-4DVar.

Ø Can use hybrid covariances that are similar to those used in hybrid-4DVar.

• Adaptive inflation scheme gives an unphysical semi-diurnal variation in spread.

Ø Total overhaul of the inflation methods.

• Software completely separate from the hybrid-4DVar software.

Ø 4DEnVar is an option in the VAR code, with additions to support ensemble updates.

Ensemble of data assimilations (i.e. the En-4DEnVar step):• Perturbed observations.• “Mean-pert” method, to reduce computational cost.• “Simple self-exclusion” method to prevent inbreeding.

Inflation to account for DA deficiencies:• RTPP: Relaxation to Prior Perturbations.• RTPS: Relaxation to Prior Spread.

To account for model uncertainties:• Random parameters in physics.• SKEB: Stochastic Kinetic Energy Backscatter.• Additive inflation based on scaled historical analysis increments, plus bias

correction.To account for other uncertainties:

• Random perturbations to SST, soil moisture and soil temperature.

4DEnVar-based ensembleKey design features

1. Calculate the ensemble mean analysis using full nonlinear analysis equations.

2. Calculate the perturbations from the mean analysis for each member, using linear equations and a reduced iteration count.

4DEnVar-based ensemble“Mean-pert”

• No significant effect on the analysed perturbations.

• Ensemble covariance used to analyse member 𝑖 includes the forecast from its own member:

• “In-breeding”:

• 𝜶C generally larger than 𝜶'DC.

• Analysis spread smaller than it should be.

• Should:

1. Remove index 𝑖from the sum.

2. Remove member 𝑖 from 𝒘E.

3. Scale with 𝐾 − 2.�

• To fit in with mean-pert, we just do 1, neglecting 2 and 3.

4DEnVar-based ensemble”Simple self-exclusion”

𝛿𝒘CE = 𝛽6𝑼𝒗 + 𝛽H %𝜶' ∘ 𝒘'

E − 𝒘E 𝐾 − 1�⁄&

'()

4DEnVar-based ensembleInflation to account for DA deficiencies

1. RTPP†: Relaxation to Prior Perturbations:

2. RTPS*: Relaxation to Prior Spread:• Multiplicative inflation such that

• Inflates more in well-observed regions, accounting for impact of sampling error.

• (Applied after RTPP.)

additivemultiplicative

† Zhang, Snyder and Sun (2004), Mon. Wea. Rev., 132, 1238–1253.* Whitaker and Hamill (2012), Mon. Wea. Rev., 140, 3078–3089.

1. AddInfX: Randomly selected historical analysis increment. (With scaling.)

2. From 3-month archive for the same season, but a different year.

3. Also add in the 3-month mean increment, as a bias correction. (No scaling.)

4DEnVar-based ensembleAdditive inflation

AddInf1 AddInf2 AddInf3 AddInf4 AddInf5

6 hours

4DEnVar-based ensemble250hPa temperature. Northern extra-tropics

• Without model uncertainty schemes spread is very small

• Spread grows much faster with additive inflation

• Combining with RTPP (0.85) gives respectable spread

• Seasonal mean correction reduces RMSE

RMS ensemble spreadRMSE of the ensemble mean

4DEnVar-based ensembleInitial configuration after tuning

• 50/50 hybrid covariances.

• Perturbed observations.

• Mean-pert.

• Simple self-exclusion.

• RTPP factor: 𝛼 = 0.5 in • RTTP good at maintaining ensemble spread.• Makes perturbations too large-scale and too balanced.

• RTPS factor:𝛼 = 0.9 in • More realistic effect on scale and balance of perturbations.• Relatively poor at maintaining ensemble spread.

• Additive inflation, with 0.5 scaling, including bias correction.

4DEnVar-based ensembleOverall performanceETKF-based → 4DEnVar-based ensemble

• “Ensemble scorecard”, based on CRPS: Continuous Ranked Probability Score.

• Area of plotted triangle proportional to percentage change in score

• Grey outline indicates 20% change in score

• 4DEnVar-based ensemble generally worse than ETKF-based:

• ETKF-based forecasts are recentredaround a high-resolution operational analysis every cycle.

• 4DEnVar-based ensemble spread generally less.

• Adding recentring reduces the gap.

• But scores still significantly worse for some fields, mainly because of relatively low spread.

4DEnVar-based ensembleOverall performanceETKF-based → Recentred 4DEnVar-based ensemble

4DEnVar-based ensembleUpcoming QJ papers

Low-res hybrid DA trialsExperimental setup

• Data from ETKF-based ensemble (44 members) and 4DEnVar-based ensemble (44 and 200 members).

• 00Z 24 February to 00Z 14 March 2014. (First week discarded for verification, so 6 weeks verified.)

• “Deterministic” forecasts: ~40 km, 70 levels.

• Ensemble forecasts: ~60 km, 70 levels.

• Analyses: ~60 km, 70 levels.

% change in obs-based NWP index(Relative to operational-like system)

% change in RMSE vs. ECMWF analyses(Outer triangle = 5% change)

( slightly below the line because vertical localisation differs from operational scheme)

4DVar (non-hybrid) → hybrid-4DVar44-member ETKF-based ensembleLow weight on ensemble covariance

ETKF-based → 4DEnVar-based ensemble44-member ensemblesLow weight on ensemble covariance



ETKF-based → 4DEnVar-based ensemble44-member ensemblesHigh weight on ensemble covariance



44 → 200-member 4DEnVar-based ensembleLow weight on ensemble covariance

(Horizontal and vertical localisation scales multiplied by 4/3)



44 → 200-member 4DEnVar-based ensembleHigh weight on ensemble covariance



Total improvement: ~1.5 %

Hybrid-4DVar → 4DEnVar44-member 4DEnVar-based ensembleHigh weight on ensemble covariance



(Baseline for ensemble processing experiments)

Time-lagging and time-shiftingCoding and experiments by Andrew Lorenchttp://www.isda2016.net/assets/posters/LorencThebenefit.pdf

• Time-lagging:

• Add ensemble perturbations with longer lead-times, but the correct validity time.

• Time-shifting:

• Add ensembles perturbations that are displaced in time.

• (Equivalent to a smoothing in time)

• Can be used in combination to give large increases to the effective ensemble size.

• Tuned for 4DEnVar, using the 44-member 4DEnVar-based ensemble:

“T+3” “T+6” “T+9”

Effective ensemble size: 44 * 6 = 264

Add time-lagging and time-shifting4DEnVar44-member 4DEnVar-based ensembleHigh weight on ensemble covariance



Waveband localisationCoding and experiments by Andrew Lorenchttp://www.isda2016.net/assets/posters/LorencThebenefit.pdf

• Buehner (2012), MWR “Evaluation of a Spatial/Spectral Covariance Localization Approach for Atmospheric Data Assimilation”:

• Correlations decrease with distance between horizontal wavenumbers, so split ensemble error modes into wavebands and assume they are uncorrelated.

• Apply shorter localisation scales to shorter-scale bands.

• Performance improvement in hybrid-3DVar with 48 members, similar to improvement from doubling the ensemble size to 96 members.

• Coded into Met Office 4DEnVar system and trialed with the following settings:

Band: Scale (km)1: 81152: 6653: 2304: 120

Add waveband localisation4DEnVar44-member 4DEnVar-based ensembleHigh weight on ensemble covariance



Total improvement: ~1.0 %

Upcoming QJ papers

• Summary:

• Initial version of the new 4DEnVar-based ensemble a little worse than the current ETKF-based ensemble on standard ensemble metrics.

• Low-resolution trials showed significant DA improvements from1. The new 4DEnVar-based ensemble.2. Larger ensembles, used with higher weight.3. Time-lagging and time-shifting (in 4DEnVar).4. Waveband localisation (in 4DEnVar).

• Recently:

• Further tuning of inflation settings has made the new ensemble competitive with the current one.

• Trial suites upgraded ready for further development testing. (The new 4DEnVar-based ensemble may benefit from general VAR upgrades.)

• Parallelisation of En-4DEnVar minimisations gives large reductions in run time.

Summary and future work

• Aimed for inclusion in parallel trial by March 2018:

• 4DEnVar-based ensemble, with 100 members and ~20 km grid spacing. (~40 km spacing for the En-4DEnVar update.)

• Time-lagging/shifting and waveband filtering of the ensemble data, to further improve the performance of hybrid-4DVar.

Summary and future work

Questions and answers

development of a 4denvar-based ensemble at the met office ...€¦ · and rescaling within the...

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