1. Implementation of Ensemble Data Assimilation in Global NWP
Dale Barker, Adam Clayton, Andrew Lorenc
WMO Sub-seasonal to Seasonal Prediction Workshop, 2 December 2010
© Crown Copyright Source: Met Office

2. Outline of Talk 1. Ensemble DA (EnDA) Basics
2. Examples of EnDA in Global NWP:
a. Met Office
b. ECMWF (Lars Isaksen, Massimo Bonavita)
c. Environment Canada (Mark Buehner, P Houtekamer)
d. POP-DART (Raeder, Anderson)
3. Summary

3. 1. Ensemble DA Basics

4. Flow-Dependent Forecast Error Covariances
From Hamill (2006)

5. Ensemble Data Assimilation (EnDA)
Forecast Step
Forecast Step
Assimilation Step E n D A
Observation(s) t
Ne = Ensemble Size (typically for real-world NWP).
EnDA algorithm varies greatly between different implementations.

6. Example: The Stochastic Ensemble Kalman Filter
Forecast step (for ensemble member n, observation time i):
Update step:
are observations perturbed with random noise (called stochastic EnKF).
Only nonlinear model M and observation operator H used. No linear/adjoint.

7. 4D Variational Data Assimilationx
(new)
(initial condition for NWP)
(old forecast)
© Crown copyright Met Office Dale Barker

8. Dynamical Aspects Of 4D-Var
The cost function J is typically
M is nonlinear model. M is linear model (not usually tangent linear). B0 is the background error covariance (includes variable transformation e.g. streamfunction, potential vorticity, etc).
Efficient minimization of cost function requires gradient
MT is the transpose (adjoint) of M.

9. Limitations Of Ensemble DA
Limited ensemble size:
Leads to underestimated forecast error variance and eventual divergence of filter from observations. An empirical covariance inflation factor is typically applied to boost forecast error variance.
Also causes spurious forecast error correlations, typically dealt with via covariance localization.
Treatment of model bias.
Limitations of working in Kalman filter framework:
Non-Gaussianity.
Nonlinearity.

10. 2. Examples of EnDA In Global NWP

11. Operational NWP Models: Nov 2010 (PS25)
Global
25Km 70 L (80km top)
4DVAR (60km inner-loop)
60 hour forecast twice/day
144 hour forecast twice/day
24member 60km MOGREPS-G
NAE (North Atlantic
and Europe)
12Km 70 L (80km top)
4DVAR (36km inner-loop)
60 hour forecast
4 times per day
24member 18km MOGREPS-R
UK4/V
4/1.5km 70 L (40km top)
3DVAR
36 hour forecast
4 times per day
Our current suite of operational NWP models are shown here along with future configurations. The numbers refer to typical horizontal grid spacings in mid- latitudes. This grid spacing is often referred to as resolution. 11

12. One-Way Coupled 4D-Var/MOGREPS
UM1 E T K F . . .
OPS .
UMN
OPS
MOGREPS
N=23
(UM = Unified Model)
(OPS = Observation Preprocessing System)
Deterministic UM
OPS
4D-VAR

13. Ensemble Transform Kalman Filter (ETKF)
Xa= Xf T Pn ( ) -
x I + = ( - )
x I + = ( - )
x I + =
Inflation
factor
Control analysis
Perturbed analysis
T+12 perturbed forecast
T+12 ensemble mean forecast
Transform matrix

14. Met Office: EnDA = Hybrid 4D-Var/ETKF
Scientific Motivations:
4D-Var provides flow-dependent covariances via the linear (perturbation forecast) model. However, still limited by climatological background error covariance.
Flow-dependent perturbations from 23 member ETKF-based MOGREPS likely to suffer from significant sampling error for DA.
Numerous studies indicate benefit of ‘hybrid’ covariances over pure EnKF or Var.
Practical motivations
MOGREPS ensemble forecasts ‘paid for’. We should use them in DA!
Make use of 4D-Var parallelism, simultaneous treatment of all observations, etc.
Hybrid algorithm very easy to code.
Evolutionary, rather than revolutionary strategy for operational EnDA.

15. Current System MOGREPS Deterministic UM1 E T K F . . . OPS . UMN OPS
(UM = Unified Model)
(OPS = Observation Preprocessing System)
Deterministic UM
OPS
4D-VAR

16. Hybrid Varational/Ensemble DA
UM1 E T K F . . .
OPS .
UMN
OPS
MOGREPS
N=23
(UM = Unified Model)
(OPS = Observation Preprocessing System)
Hybrid
Deterministic UM
OPS
4D-VAR

17. Hybrid DA: Single Observation Tests: <u u>h
Ensemble Increment, A=I
3D-Var Increment
Ensemble Spread
4D-Var Increment (middle of 6hr time window)
Ensemble Increment, A=Ah

18. Initial Hybrid Results
First tests of impact of hybrid in a full observation 4D-Var.
Initial month-long trials performed (May 2008 period). Verification:
Positive benefit vs. 3D-Var mode, neutral in 4D-Var.
Reasonably pleasing result given system has not yet been tuned at all.
Plans to increase ensemble size to member (to T+12) for DA application.
Impact on NWP Index
3D-Var Hybrid vs. 3D-Var
4D-Var Hybrid vs. 4D-Var
4D-Var vs. 3D-Var
Verification vs. Obs
+0.78%
-0.39%
+2.7%
Verification vs. Analysis
+0.94%
+1.33%
+1.3%
Single u pseudo ob added at level 15 at the middle of the VAR window, in a region where the ensemble spread is large due to the presence of an unstable frontal structure.
3D-Var increments show the lack of sensitivity to the presence of the frontal instability.
4D-Var increments represent a 3-hr evolution of the 3D-Var static covariances by the PF model. We begin to see the vertical tilt in the unstable modes.
Hybrid run uses a weighting between the static and ensemble covariances. Increments are bigger because the ensemble is suggesting particularly large variance in the background error in this region. Again we see the vertical tilt typical of baroclinically unstable modes.
(A 4D-Var hybrid gives very similar results, because the ensemble covariances are dominating in this region.)

19. Operational NWP Models: Dec 2012 (Tentative)
Global
16-18km 70L (80km top)
Hybrid 4DVAR (50km inner-loop)
60 hour forecast twice/day
144 hour forecast twice/day
48/24member 40km MOGREPS-G
MOGREPS-R
12Km 70 L (40km top)
4DVAR or NoDA?
48 hour forecast
4 times per day
UKV
1.5km 70L (40km top)
3DVAR (hourly)
36 hour forecast
4 times per day
3-4 member 1.5km ensemble
Our current suite of operational NWP models are shown here along with future configurations. The numbers refer to typical horizontal grid spacings in mid- latitudes. This grid spacing is often referred to as resolution. 19

20. Operational NWP Models: Dec 2016 (VERY Tentative!)
Global
12-14km 110L (80km top)
Hybrid 4DVAR or EnDA?
60 hour forecast twice/day
144 hour forecast twice/day
192/24member 30km MOGREPS-G
MOGREPS-R
12Km 110L (40km top)
NoDA
48 hour forecast
4 times per day
UKV
1.5km 110L (40km top)
Hybrid 4DVAR (or EnDA)
36 hour forecast
4 times per day
~10 member 1.5km ensemble
Our current suite of operational NWP models are shown here along with future configurations. The numbers refer to typical horizontal grid spacings in mid- latitudes. This grid spacing is often referred to as resolution. 20

21. VAR v EnDA (future scheme) with current IBM HPC scaling
Rick Rawlins

22. Analysis (schematic) Main run (N216) QG12
OPS
(QG12) UM
(QG12) UM
(QU06)
model
background
analysis
increment
vguess
VAR
N108
VAR
N216
Hessian
eigenvectors
GMT
Preconditioning N108 4D-Var reduces final N216 4D-Var cost from 21mins to 13mins
Rick Rawlins

23. MetO Longer-Term Strategy
Scalability of 4D-Var on next-generation architectures a concern – significant algorithmic changes already underway.
EnDA has practical advantages: less tied to dynamics, more amenable to parallelism, etc. However, cannot yet beat 4D-Var.
EnDA system to 2015 likely to be expanded ensemble hybrid 4D-Var/EnKF.
Current 4D-Var system closely tied to dynamics. Probable radical core redesign on 5-10yr timeframe.
New EnDA group created to focus on next-gen EnDA system for 5-10yr timeframe. Initial recommendations due 03/2011.

24. ECMWF: EnDA = Ensembles of 4D-Var (Courtesy Lars Isaksen)
Forecast Error Variance Post-processing:
xa+εia
Analysis
Forecast
SST+εiSST
y+εio
xb+εib
xf+εif
i=1,2,…,10
EDA Cycle: 10 x Low-Res T95/159 4D-Var. Perturbed obs/SSTs:
εif raw variances
Variance Recalibration
Variance Filtering
EDA scaled variances
High-Resolution Deterministic 4D-Var Cycle: xa
EDA scaled Var xb
Slide 24 24

25. Ensemble spread and Ensemble mean RMSE (+) for 850hPa T
Use of EDA in ECMWF EPS
(Lars Isaksen, ECMWF)
The Ensemble Prediction System benefits from using EDA based perturbations. Replacing evolved singular vector perturbations by EDA based perturbations improve EPS spread, especially in the tropics.
The Ensemble Mean has slightly lower error when EDA is used.
N.-Hem.
Tropics
EVO-SVINI
EDA-SVINI
EVO-SVINI
EDA-SVINI
Ensemble spread and Ensemble mean RMSE (+) for 850hPa T

26. Use of EDA in ECMWF 4D-Var DA
(Lars Isaksen, ECMWF)
Blue=☺ ☺ ☺

27. EC: EnDA = Stochastic EnKF, 4D-Var and combinations…
4D-Var operational since March 2005.
Stochastic EnKF for EPS operational since January members.
Buehner et al (2010) tested a variety of configurations:
Pure EnKF
Pure 4D-Var with climatological covariances: 4D-Var Bnmc
4D-Var with ensemble covariances from EnKF: 4D-Var Benkf
4D-Var with TL/adjoint replaced by 4D ensemble covariances: En-4d-Var

28. Comparison of 4D-Var/EnKF (Mark Buehner)
***Verifying analyses from 4D-Var with Bnmc***
Northern hemisphere
Southern hemisphere
Daley and Barker, 2001, NAVDAS sourcebook.
4D-Var Bnmc
4D-Var Benkf
EnKF mean analysis
4D-Var Bnmc
4D-Var Benkf
EnKF mean analysis
Conclusion: Combined 4D-Var + EnKF covariances->~10hrs SH skill

29. POP-DART (NCAR – Raeder et al)
Daley and Barker, 2001, NAVDAS sourcebook.

30. Summary
1. Ensemble DA (EnDA) Basics – EnDA has scientific and practical pros/cons but devil is in the detail.
2. Examples of EnDA in Global NWP shown:
a. Met Office – 4D-Var/ETKF hybrid.
b. ECMWF: EnDA = Ensembles of 4D-Var
c. EC: EnDA = 4D-Var/EnKF hybrid but EnKF sufficient?
d. POP-DART: EnDA: Coupled Atmos/Ocean EnKF
3. Many centres evaluating options for next-gen DA for new cores, applications, coupling, etc.