Ramble: What is the purpose of an ensemble forecast? The dominant philosophy at the moment is that ensemble forecasts provide uncertainty information.

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Presentation transcript:

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

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

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

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

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.

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!

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

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

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

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

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

 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)

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

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

References Hybrid Anderson’s filter MOGREPS/ETKF 4D VAR 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

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 44 600km 600km Low Res Hybrid 44 900km 900km Low Res Hybrid 44 1500km 1500km horizontal localisation via Guassian exp[ -r2 / (2 L2 ) ] r – dist, L –scale L  0.3 (2c) – Gaspari & Cohn zero if r>2c