Implementation of Hybrid Variational-ETKF Data Assimilation at the Met OfficePeter Jermey

Dale Barker, Neill Bowler, Adam Clayton, Andrew Lorenc, Mike Thurlow

Background error cov at t0

• Increments to background forecast obtained by minimising

4D-VAR Data Assimilation

Increment at t0

Obs error covObs

Model equivalent of obs

High frequency penalty

• Same error covariance used in every cycle

• Represents climatological features

• Does not represent daily variation in the error covariance

• A covariance estimate featuring “errors of the day” can be obtained from the ensemble prediction system (MOGREPS) …

• Increments to background forecast obtained by minimising

Hybrid

Covariance of ensemble member-mean differences

• Error covariance varies with cycle

• Still represents climatological features

• Also represents daily variation

4D-VAR Data Assimilation

Implementation

4D VAR

Deterministic Forecast

Ensemble Forecast

Analysis

• Static 4D VAR and MOGREPS

• Hybrid System

4D VAR

Deterministic Forecast

Ensemble Forecast

Analysis

Ensemble Forecast

Ensemble Forecast

Ensemble Forecast

• Static 4D VAR and MOGREPS

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.

• Traditionally verify impact of changes on a “NWP Index” – weighted sum of skill scores – taking observations and then analyses as ‘truth’. Control is static.

Verification

• (Own) analyses should not be used as ‘truth’ to verify the impact of changes to B!

Verification

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

Hybrid Vs Static

• PMSL 11th June 2010 00Z

• North China 60-85N, 70-140E

• Static T+120

• Hybrid T+120

• ECMWF Analysis

• Static T+120

Results from low resolution experiments

• Expect improved forecast (sampling error reduced)

Development

• Hybrid operational July 2011

• Ensemble from 12Hr cycling to 6Hr operational March 2012• Ensemble from 22 members to 44 members ~Oct 2012

• UM N320(50km) VAR N216(60km)• ~10 days

• UM N216(60km) VAR N108(70km)• ~40 days

• disappointingly neutral

• Expected: increased ensemble size allows increased scale

• Previous experiments suggest Gaussian with scale 1200km near-optimum for 22 members

Many tuneable parameters & different flavours…

• Ensemble size

• Horizontal Localisation Scheme/Scale

• Vertical Localisation Scheme/Scale

• Covariance weighting

• Ensemble forecast time

• Hybrid domain

• Relaxation to prior in ensemble

• Raw ensemble covariance is low rank (22 or 44) and has sample error

• Ameliorate by element-wise multiplication with localisation matrix C

• C localises horizontally and vertically, but not between variables.

• Can we improve on this? Is this appropriate for 44 members? Is this restricting the ability of the 44 member hybrid?

• Vertical Smoothing

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

Anderson’s Hierarchical Ensemble Filter

• Est optimum scale for covariances with a surface point in stream function against distance

335.1kmMoisture

1162kmAgeostrophic PressurePa

1959kmVelocity Potential1175kmStream Function

• Estimated optimum scale at surface

• Gaussian Appropriate

• Scale increases with height (not shown)

Anderson’s Hierarchical Ensemble Filter

• Scale varies with variable

Length Scale Trials (Low Res.)

• Control is 22 member hybrid

• ‘Maxima’ at 900km and 1500km

• Tropics are all wind scores, extra tropics mainly PMSL and geopotential height at 500hPa

• NH & SH - ‘Maximum’ between 600km to 900km

• ‘Maxima’ at 900km and 1500km

• Control is 22 member hybrid

• Tropics & SH wind - Maximum at 1500km or larger

• NH wind – ‘Maximum’ at 600km or lower

• NH-PMSL&H500 NH-W250 Tp-WindsSH-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?

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

References

• HybridClayton 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

Experiment Specifications

Name UM Res. VAR Res. Ens. Res. Ens. Size

H. Loc. Scale

Dec09 Static N320 (~50km) N216(~60km) None None None

Dec09 Uncoupled 23 (12Hr cycling) N320 N216 N216 23 1200km

Jun10 Static N320 N216 None None None

Jun10 Coupled (12Hr cycling) N320 N216 N216 23 1200km

Dec09 Uncoupled 47 N320 N216 N216 47 1200km

Low Res Static N216 N108 None None None

Low Res Hybrid 22 N216 N108 N144 (~65km) 22 1200km

Low Res Hybrid 44 N216 N108 N144 44 1200km

Low Res Hybrid 44 600km N216 N108 N144 44 600km

Low Res Hybrid 44 900km N216 N108 N144 44 900km

Low Res Hybrid 44 1500km N216 N108 N144 44 1500km

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