Perturbation of Perturbation of Parametrized TendenciesParametrized Tendenciesand Surface Parametersand Surface Parameters

in the Lokal-Modellin the Lokal-Modell

Susanne Theis

Andreas Hense

Ulrich Damrath

Volker Renner

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

The LAM “Lokal-Modell“The LAM “Lokal-Modell“

• operational high-resolution model of the DWD

• nested within the GME

• horizontal gridsize: 7 km

• lead time: 48 hours

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Why are we looking into EPS?Why are we looking into EPS?

DMO of a

single simulation

noise-reduced forecast

and

probabilistic forecast

Development of a Postprocessing Method:

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Why are we looking into EPS?Why are we looking into EPS?

DMO of a

single simulation

noise-reduced forecast

and

probabilistic forecast

Development of a Postprocessing Method:

calibrationby an experimental ensemble

uncertainty inlateral boundary

conditions

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Aims of a LAM EPSAims of a LAM EPS

modeluncertainty uncertainty in

surface parameters

uncertainty inLAM output

?

uncertainty ininitial conditions

uncertainty inlateral boundary

conditions

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Selecting Certain Aspects Selecting Certain Aspects

modeluncertainty uncertainty in

surface parameters

uncertainty inLAM output

?

uncertainty ininitial conditions

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Perturbation of Roughness LengthPerturbation of Roughness Length

original perturbation

jhh

mm

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Perturbation of Roughness LengthPerturbation of Roughness Length

jj hhh

where jh = 0

STDV jh 0.05 h

E

and

Set-up of the ensemble (6 members):

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Case Study (July 4th, 1994)Case Study (July 4th, 1994)

mm/h

Ensemble Mean Standard Deviation

perturbation of roughness length (only)

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

„„Stochastic Physics“: MethodStochastic Physics“: Method

Perturbation of parametrized tendencies:

dttetedtt

ete

t

t

t

t

00

;;)( )P() A(

Unperturbed simulation:

dttxtetetet

t

jjjj )(r)P( A(

0

;;);)(

Ensemble member:

(Buizza et al, 1999)

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

„„Stochastic Physics“: NumericsStochastic Physics“: Numerics

Caveat: Stochastic differential equations need a different numerical scheme(Kloeden and Platen, 1999) -- we are still using the traditional scheme!

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Consistency with Surface RadiationConsistency with Surface Radiation

Perturbation of the temperature tendency should be consistent with the solar radiation flux at the surface:

z

Q

t

T

RAD

z

Q

z

Q

perturbationof tendency

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

„„Stochastic Physics“: Set-up No.1Stochastic Physics“: Set-up No.1

1.25 , 0.75 )(r; tx j

D = 5T = 4

x t

„low ampl.“

Set-up of the ensemble (10 members):

consistent perturbation of the solar radiation at the surface

+

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Roughness LengthRoughness Length

where jh = 0

STDV jh 0.05 h

E

and

jj hhh

Additionally, we keep the perturbation of the roughness length:

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Roughness Length: The BugRoughness Length: The Bug

where jh = 0

STDV jh 0.05 h

E

and

jj hhh

roughness length is too low (by a factor of 6)SORRY

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Case Study (July 10th, 2002)Case Study (July 10th, 2002)

mm/h

Ensemble Mean Standard Deviation

stochastic physics (low-amplitude)

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Verification of Ensemble MeanVerification of Ensemble Mean

ENSMEANORIGINAL

stochastic physics (low-amplitude)

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

„„Stochastic Physics“: Set-up No.2Stochastic Physics“: Set-up No.2

2.0 , 0.0 )(r; tx jD = 10T = 16

x t

„highamplitude“

Set-up of the ensemble (10 members):

consistent perturbation of the solar radiation at the surface

+

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Case Study (July 10th, 2002)Case Study (July 10th, 2002)

mm/h

Ensemble Mean Standard Deviation

stochastic physics (high-amplitude)

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Verification of Ensemble MeanVerification of Ensemble Mean

ENSMEANORIGINAL

stochastic physics (high-amplitude)

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Perturbation of Initial ConditionsPerturbation of Initial Conditions

Start of the LM-Simulations: 00 UTC

Initialize LM-simulation with the „wrong“ time of the nudged assimilation run:

Analysisof 01 UTC

Analysisof 00 UTC

Analysisof 23 UTC(prev.day)

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Set-up of the EnsembleSet-up of the Ensemble

0.75,1.25 )(r; tx j

D = 5T = 4

x t

„low ampl.“

consistent perturbation of the solar radiation at the surface

+

Additionally, the parametrizedtendencies are perturbed:

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Set-up of the EnsembleSet-up of the Ensemble

Analysisof 01 UTC

Analysisof 00 UTC

Analysisof 23 UTC(prev.day)

3 simulations per analysis+ 1 unperturbed simulation

= 10 ensemble members

3 simulations3 simulations 3 simulations 3 simulations

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Case Study (July 10th, 2002)Case Study (July 10th, 2002)

mm/h

Ensemble Mean Standard Deviation

initial conditions &stochastic physics (low-amplitude)

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

Verification of Ensemble MeanVerification of Ensemble Mean

ENSMEANORIGINAL

ínitial conditions & stochastic physics (low-amplitude)

OUTLINE

Introduction

Surface Parameters

Parametrized Tendencies

Initial Conditions

Conclusion

ConclusionConclusion

• the precipitation forecast is sensitive to the perturbation of roughness length, parametrized tendencies and initial conditions

• the sensitivity is largest on the scale of a few gridboxes in size

• the ensemble mean achieves better verification results than the unperturbed forecast (initial cond.!)