1. Ramble:
What is the purpose of an ensemble forecast? The dominant philosophy at the moment is that ensemble forecasts provide uncertainty information that supplements a deterministic forecast. In that sense an ensemble forecast is always the bridesmaid, but never the bride.
However, there are some murmurings in the ensemble and data assimilation communities that maybe one day we will no longer have deterministic forecasting systems. This may happen when global models reach the gap around 10km where modellers fear to tread. It may also happen at very high resolution where predictability is lost extremely quickly.
What I’m going to talk about today is a different criterion for making that transition – when an ensemble forecasting system provides a better deterministic forecast than can be achieved using a single model alone. Combining forecasts from models with different resolutions can already meet this criterion, so in some sense that day has already come, even though we still base our output on a single model run. On the way we also take in the more familiar poor-man’s ensembles. Only at the end of the talk do we return to genuine ensemble prediction systems, and using some of these ideas in that more traditional context.
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. 4D-VAR Data Assimilation
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. Implementation Static 4D VAR and MOGREPS Static 4D VAR and MOGREPS
Ensemble Forecast
Static 4D VAR and MOGREPS
Static 4D VAR and MOGREPS
4D VAR
Deterministic Forecast
Ensemble Forecast
Analysis
Hybrid System
Ensemble Forecast
4D VAR
Deterministic Forecast
Ensemble Forecast
Analysis
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.  Stream Function 1175km  Velocity Potential 1959km Pa 1162km 
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&H500 NH-W250 Tp-Winds SH-PMSL&H500 SH-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?
Can improve H44 by reducing or increasing scale.
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. Thank you for listening
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 Anderson’s filter MOGREPS/ETKF 4D VAR
Clayton AM, Lorenc AC, Barker DM. submitted Feb 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
Name
UM Res.
VAR Res.
Ens. Res.
Ens. Size
H. Loc. Scale
Dec09 Static
N320 (~50km)
N216(~60km)
None
Dec09 Uncoupled 23 (12Hr cycling)
N320
N216 23
1200km
Jun10 Static
Jun10 Coupled (12Hr cycling)
Dec09 Uncoupled 47 47
Low Res Static
N108
Low Res Hybrid 22
N144 (~65km) 22
Low Res Hybrid 44
N144 44
Low Res Hybrid km
600km
Low Res Hybrid km
900km
Low Res Hybrid km
1500km
horizontal localisation via Guassian exp[ -r2 / (2 L2 ) ] r – dist, L –scale
L  0.3 (2c) – Gaspari & Cohn zero if r>2c