Implementation of Hybrid Variational-ETKF Data Assimilation at the Met Office

1. Implementation of Hybrid Variational-ETKF Data Assimilation at the Met Office Peter Jermey Dale Barker, Neill Bowler, Adam Clayton, Andrew Lorenc, Mike Thurlow

2. 4D-VAR Data Assimilation • Increments to background forecast obtained by minimising Background error cov at t0 Increment at t0 • Same error covariance used in every cycle • Represents climatological features • Does not represent daily variation in the error covariance Obs Obs error cov Model equivalent of obs • A covariance estimate featuring “errors of the day” can be obtained from the ensemble prediction system (MOGREPS) … High frequency penalty

3. Hybrid 4D-VAR Data Assimilation • Increments to background forecast obtained by minimising • Error covariance varies with cycle • Still represents climatological features • Also represents daily variation Covariance of ensemble member-mean differences

4. 4D VAR 4D VAR Deterministic Forecast Deterministic Forecast Analysis Analysis Ensemble Forecast Ensemble Forecast Implementation Ensemble Forecast • Static 4D VAR and MOGREPS • Static 4D VAR and MOGREPS • Hybrid System Ensemble Forecast Ensemble Forecast

5. Results • Assess impact of change via “NWP Index” • Impact is weighted sum of skill differences of PMSL, geopotential heights and wind speeds • Uses observations or analyses as ‘truth’ • Following results use static system as control.

6. Verification • Traditionally verify impact of changes on a “NWP Index” – weighted sum of skill scores – taking observations and then analyses as ‘truth’. Control is static. • (Own) analyses should not be used as ‘truth’ to verify the impact of changes to B!

7. Verification • Use ECMWF analyses as ‘truth’.Independent of change & trustworthy • Unusually good/consistent results!

8. Hybrid Vs Static • PMSL 11th June 2010 00Z • North China 60-85N, 70-140E • ECMWF Analysis • Static T+120 • Static T+120 • Hybrid T+120 Results from low resolution experiments

9. Development • Hybrid operational July 2011 • Ensemble from 12Hr cycling to 6Hr operational March 2012 • Ensemble from 22 members to 44 members ~Oct 2012 • Expect improved forecast (sampling error reduced) • UM N320(50km) VAR N216(60km) • UM N216(60km) VAR N108(70km) • ~10 days • ~40 days • disappointingly neutral

10. Many tuneable parameters & different flavours… • Raw ensemble covariance is low rank (22 or 44) and has sample error • Ensemble size • Horizontal Localisation Scheme/Scale • Ameliorate by element-wise multiplication with localisation matrix C • Vertical Localisation Scheme/Scale • Covariance weighting • C localises horizontally and vertically, but not between variables. • Ensemble forecast time • Hybrid domain • Expected: increased ensemble size allows increased scale • Relaxation to prior in ensemble • Previous experiments suggest Gaussian with scale 1200km near-optimum for 22 members • Can we improve on this? Is this appropriate for 44 members? Is this restricting the ability of the 44 member hybrid? • Vertical Smoothing

11. Anderson’s Hierarchical Ensemble Filter • Taken from • Hierarchical ensemble of ensembles to estimate optimum value of each element of C • Applied horizontally to 44 member hybrid control variables • Obtained 100 ensembles by randomly sampling the static cov matrix to make the filter affordable

12. Anderson’s Hierarchical Ensemble Filter • Est optimum scale for covariances with a surface point in stream function against distance

13. Anderson’s Hierarchical Ensemble Filter • Estimated optimum scale at surface  Stream Function 1175km  Velocity Potential 1959km Pa Ageostrophic Pressure 1162km  Moisture 335.1km • Gaussian Appropriate • Scale varies with variable • Scale increases with height (not shown)

14. Length Scale Trials (Low Res.) • NH-PMSL&H500NH-W250Tp-WindsSH-PMSL&H500SH-W250 • Overall optimum scale is ~ 800km for some variables, ~1500km for others • 2/3rds of weight in the index is for NH & SH so use ~800km? • Control is 22 member hybrid • Control is 22 member hybrid • Tropics are all wind scores, extra tropics mainly PMSL and geopotential height at 500hPa • ‘Maxima’ at 900km and 1500km • ‘Maxima’ at 900km and 1500km • NH wind – ‘Maximum’ at 600km or lower • Tropics & SH wind - Maximum at 1500km or larger • NH & SH - ‘Maximum’ between 600km to 900km

15. Summary • Hybrid uses ensemble forecasts to improve B estimation • Hybrid improves forecast in tropics and extratropics • Verification Vs own analyses inappropriate for testing changes in error cov • Can use analyses from another center as an alternative • Increasing size of ensemble does not necessarily improve the deterministic fc • Many parameters to tune including horizontal localisation • Anderson’s hierarchical filter can be used to investigate optimum localisation • Optimum horizontal localisation depends on variable, region and level • Overall optimum scale is unclear~800km for some, ~1500km for others • Thank you for listening

16. References • Hybrid Clayton AM, Lorenc AC, Barker DM. submitted Feb. 2012. Operational implementation of a hybrid ensemble/4D-Var global data assimilation system at the Met Office Q. J. Roy. Meteor. Soc. • Anderson’s filter • MOGREPS/ETKF • 4D VAR

17. Experiment Specifications • horizontal localisation via Guassian exp[ -r2 / (2 L2 ) ] r – dist, L –scale • L  0.3 (2c) – Gaspari & Cohn zero if r>2c