Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus...

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Initial perturbations for ensemble forecasting – singular vectors vs. breeding vectors Linus Magnusson Stockholm University Acknowledgements: Erland Källén; Jonas Nycander; Martin Leutbecher; SMHI

Transcript of Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus...

Page 1: Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus Magnusson et al. (2008), Monthly Weather Review Magnusson et al. (2008), Nonlinear processes

Initial perturbations for ensemble forecasting – singular vectors vs. breeding vectors

Linus Magnusson Stockholm University

Acknowledgements: Erland Källén; Jonas Nycander; Martin Leutbecher; SMHI

Page 2: Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus Magnusson et al. (2008), Monthly Weather Review Magnusson et al. (2008), Nonlinear processes

Desirable properties of initial perturbations

•  Sampling analysis uncertainty –  Mean amplitude –  Geographical distribution –  Spatial scale –  ”Error of the day”

•  Sustainable growth

•  High quality of probabilistic forecast

Page 3: Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus Magnusson et al. (2008), Monthly Weather Review Magnusson et al. (2008), Nonlinear processes

Singular vectors

€

α =Δ x (t),Δ x (t)

Δ x (0),Δ x (0)

Optimize perturbation growth for a time interval

M tangent linear operator. Δx(t)=M(t,x0)Δx(0)

Norm dependent!

Singular vector perturbation

Atmospheric state

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Breeding perturbations

Perturbed Forecast +06h Unperturbed Forecast +06h

-

Breeding vector

x normalizing factor =

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Random Perturbations

Random number (-1 to 1) x x global tuning factor

Analysis error estimate

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Random Field (RF) perturbation

Analysis Random date 1 Analysis Random date 2

-

x normalizing factor =

Random Field Perturbation

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Perturbation methods Lorenz-63

  Random pert. ✚ 1st SV ✖ 2nd SV   BV

Initial point

After 1 time unit

Page 8: Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus Magnusson et al. (2008), Monthly Weather Review Magnusson et al. (2008), Nonlinear processes

Exponential perturbation growth

SV – red, BV – blue, Random Field Pert. – Green, Random Pert. - black

NWP-model (ECMWF) Lorenz-63

Page 9: Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus Magnusson et al. (2008), Monthly Weather Review Magnusson et al. (2008), Nonlinear processes

Evolution of ensemble spread (one case, total pert. energy 700 hPa)

Maximum – red,

Initially

Page 10: Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus Magnusson et al. (2008), Monthly Weather Review Magnusson et al. (2008), Nonlinear processes

Evolution of ensemble spread (one case, total pert. energy 700 hPa)

Maximum – red, Scale 48: twice the scale for +00h

+48h

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Connections between perturbations and baroclinic zones

Fastest growth rate of normal modes

Page 12: Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus Magnusson et al. (2008), Monthly Weather Review Magnusson et al. (2008), Nonlinear processes

Correlation Eady index – Ens. Stdev z500

(20N-70N)

SV - Red ET - Blue RF – Green RP - Black

Page 13: Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus Magnusson et al. (2008), Monthly Weather Review Magnusson et al. (2008), Nonlinear processes

SV - Red ET - Blue RF – Green RP - Black

BV

RF

Page 14: Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus Magnusson et al. (2008), Monthly Weather Review Magnusson et al. (2008), Nonlinear processes

+48h

+00h

SV - Red ET - Blue RF – Green RP - Black

Page 15: Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus Magnusson et al. (2008), Monthly Weather Review Magnusson et al. (2008), Nonlinear processes

Zonal mean perturbation energy (sqrt) Initially

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Zonal mean perturbation energy (sqrt) +48h

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Ensemble quality

•  Initial + evolved singular vectors

•  Ensemble transform perturbations (regionally rescaled)

•  90 forecast cases

•  20 ensemble members

•  ECMWF IFS-model TL255L40

Page 18: Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus Magnusson et al. (2008), Monthly Weather Review Magnusson et al. (2008), Nonlinear processes

RMSE of Ensemble mean and Ensemble spread z500

SV – Red ET – Blue RF - Green

N.Hem S.Hem

Spread

RMSE

Page 19: Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus Magnusson et al. (2008), Monthly Weather Review Magnusson et al. (2008), Nonlinear processes

Different Centres (from Park et al.(2008), Courtesy R. Buizza )

Ranked Probability skill score t850

Different initial perturbations (N.Hem)

SV - Red ET - Blue RF – Green RP - Black

Page 20: Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus Magnusson et al. (2008), Monthly Weather Review Magnusson et al. (2008), Nonlinear processes

Summary

Singular Vectors •  Fast transient

perturbation growth •  Strong connection to

baroclinic zones •  Tropics?

Breeding Vectors •  Growth as Lyapunov

exponent •  Mature structures •  Tropics?

Similar properties after the transient period

Page 21: Initial perturbations for ensemble forecasting – singular ...Magnusson et al. (2009), Tellus Magnusson et al. (2008), Monthly Weather Review Magnusson et al. (2008), Nonlinear processes

Discussion

•  Are the singular vectors too explosive? •  Are the breeding vectors too mature? •  Does it matter?

Papers: Magnusson et al. (2009), Tellus Magnusson et al. (2008), Monthly Weather Review Magnusson et al. (2008), Nonlinear processes in geophysics

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Perturbation Energy ratio

SV - Red ET - Blue RF – Green RP - Black


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