Transcript
Page 1: Reading Parametrizations and data assimilation Marta JANISKOVÁ ECMWF marta.janiskova@ecmwf.int

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Parametrizations and data assimilation

Parametrizations and data assimilation

Marta JANISKOVÁ ECMWF

[email protected]

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Parametrizations and data assimilation

• Why is physics needed in data assimilation ?

• How the physics is applied in variational data assimilation system ?

• Which parametrization schemes are used at ECMWF ?

• What are the problems to be solved before using physics in data assimilation ?

• What is an impact of including the physical processes in assimilating model ?

• How the physics is used for assimilation of observations related to the physical processes ?

• Parametrization = description of physical processes in the model.

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Parametrizations and data assimilation

POSITION OF THE PROBLEM

IMPORTANCE OF THE ASSIMILATING MODEL

the better the assimilating model

(4D-Var consistently using the information coming from the observations and the model)

the better the analysis (and the subsequent forecast)

the more sophisticated the model

(4D-Var containing physical parametrizations)

the more difficult the minimization (on-off processes, non-linearities)

DEVELOPMENT OF A PHYSICAL PACKAGE FOR DATA ASSIMILATION

= FINDING A TRADE-OFF BETWEEN:

Simplicity and linearity

(using simplified linear model is a basis of incremental variational approach)

Realism

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Parametrizations and data assimilation

IMPORTANCE OF INCLUDING PHYSICS IN THE ASSIMILATING MODEL

• using an adiabatic linear model can be critical especially in the tropics,

planetary boundary layer, stratosphere

• missing physical processes in assimilation systems can lead to the so-called

spin-up/spin-down problem

• using the adjoint of various physical processes should provide an initial

atmospheric state for NWP models which is:

– more consistent with physical processes

– producing better agreement between the model and data

• inclusion of such processes is a necessary step towards:

– initialization of prognostic variables related to physical processes

– the use of new (satellite) observations in data assimilation systems (rain, clouds, soil moisture, …)

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Parametrizations and data assimilation

STANDARD FORMULATION OF 4D-VAR

• the goal of 4D-Var is to define the atmospheric state x(t0) such that the “distance” between

the model trajectory and observations is minimum over a given time period [t0, tn]

finding the model state at the initial time t0 which minimizes a cost-function J :

1 10 0 0 0 0

0

1 1( ) y ( ) y

2 2

no o

i i i i i i ii

J H H

T T

x x R x x x B x xb b

xi is the model state at time step ti such as:

00, xx ttM ii

M is the nonlinear forecast model integrated between t0 and ti

H is the observation operator

(model space observation space)

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Parametrizations and data assimilationINCREMENTAL FORMULATION OF 4D-VAR

1 10 0 0

0

1 1( ) d ( ) d

2 2

n

i i i i i i ii

H HJ

TTx x B x x R x' '

boiiii Hy xd

• 4D-Var can be then approximated to the first order as minimizing:

where is the innovation vector

00 , xx ttM ii'

• In incremental 4D-Var, the cost function is minimized in terms of increments:

with the model state defined at any time ti as: bbb00, , xxxxx ttM iiiii

tangent linear model

ii'ii

n

iii Htt d)(,

2

1 1

000

1

0

xRHMxB TTx

• Gradient of the cost function to be minimized:

0J x

id

ix

0J x

computed with the non-linear model at high resolution using full physics M

computed with the tangent-linear model at low resolution using simplified physics M’

computed with a low resolution adjoint model using simplified physics MT

Adjoint operators

Tangent-linear operators

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Parametrizations and data assimilationVALIDATION OF THE LINEARIZED SCHEMES

• classical one (TL - Taylor formula, AD - test of adjoint identity)

Comparison:

finite differences tangent-linear integration

• examination of the accuracy of the linearization - TL integrations propagating in time finite-size analysis increments with the trajectory computed using the full nonlinear model

'

,an analysis fg first guess

x x x xan anfg fgM M M

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Parametrizations and data assimilation

ECMWF LINEARIZED PHYSICS

vertical

diffusion

gravity

wave drag radiation

dry processes

deep

convection

large-scale

condensation

mass fluxconvection

statisticalcloud scheme

to be

replaced by

to be

replaced by

moist processes already used in 1D-Var precipitation assimilation

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Parametrizations and data assimilation

SIMPLIFICATIONS OF THE LINEARIZED PHYSICS

done with the aim to have a physical package for data assimilation:

• simple – for the linearization of the model equations

• regular – to avoid strong non-linearities and thresholds

• effective – to reduce the computational cost for operational applications

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Parametrizations and data assimilation

• physical processes are characterized by:

* threshold processes:

• discontinuities of some functions describing the physical processes

(some on/off processes: condensation, precipitation formation, …)

• discontinuities of the derivative of a continuous function

* strong nonlinearities

IMPORTANCE OF THE REGULARIZATION OF TL MODEL

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Parametrizations and data assimilation

WHY REGULARIZATION IS IMPORTANT

Without adequate treatment of most serious threshold processes, the TL approximation can turn to be useless.

89.651

86.428

6.593

3.103

3.0792.761

2.525

2.296

2.240

2.179

2.166

1.998

1.819

1.340

1.238

1.232

1.204

*******

-11.257

-8.562-5.838

-4.039

-3.314

-2.279

-2.163

-2.061

-2.041

-1.891

-1.782

-1.572

-1.318

-0.988

89.651

86.428

6.593

3.103

3.0792.761

2.525

2.296

2.240

2.179

2.166

1.998

1.819

1.340

1.238

1.232

1.204

*******

-11.257

-8.562-5.838

-4.039

-3.314

-2.279

-2.163

-2.061

-2.041

-1.891

-1.782

-1.572

-1.318

-0.988

lv31 T* 1999-03-15 12h fc t+6 - TL with vdif (no regularization applied) [cont.int: 0.5e+07]

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Parametrizations and data assimilation

dyNL

dx

dyTL

Potential source of problem (example of precipitation formation)

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Parametrizations and data assimilation

dx

dy N

L

dy T

L1

dy T

L2

Possible solution, but …

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Parametrizations and data assimilation

dx1

dy N

L

dy T

L2

… may just postpone the problem and influence the performance of NL scheme

dy T

L3

dx2

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Parametrizations and data assimilation

dx

dy N

L

dy T

L1

dy T

L2

However, the better the model the smaller the increments

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Parametrizations and data assimilation

EXAMPLES OF REGULARIZATIONS AND SIMPLIFICATIONS (1)

In NWP – a tendency to develop more and more sophisticated physical parametrizations they may contain more discontinuities

For the “perturbation” model – more important to describe basic physical tendencies while avoiding the problem of discontinuities

Level of simplifications and/or required complexity depends on:

• which level of improvement is expected (for different variables, vertical and horizontal

resolution, …)

• which type of observations should be assimilated

• necessity to remove threshold processes

Different ways of simplifications:

• development of simplified physics from simple parametrizations used in the past

• selecting only certain important parts of the code to be linearized

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Parametrizations and data assimilation

Regularization of vertical diffusion scheme:

• perturbation of the exchange coefficients (which are function of the Richardson

number Ri) is neglected, K’ = 0 (Mahfouf, 1999)

• reduced perturbation of the exchange

coefficients (Janisková et al., 1999):

– original computation of Ri modified in

order to modify/reduce f’(Ri), or

– reducing a derivative, f’(Ri), by factor 10

in the central part (around the point of

singularity )

-20. -10. 0. 10. 20.

Ri number

0.010

0.000

f(Ri)

-0.010

-0.020

Function of the Richardson number

EXAMPLES OF REGULARIZATIONS AND SIMPLIFICATIONS (2)

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Parametrizations and data assimilation

• selective regularization of the exchange coefficients K based on the linearization

error and a criterion for the numerical stability (Laroche et al., 2002)

• reduction of the time step to 10 seconds to guarantee stable time integrations

of the associated TL model (Zhu and Kamachi, 2000)

EXAMPLES OF REGULARIZATIONS AND SIMPLIFICATIONS (3)

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Parametrizations and data assimilation

operational version of ECMWF

EXAMPLES OF REGULARIZATIONS AND SIMPLIFICATIONS (4)

SW: 2 spectral intervalsLW:neural network+mean Jacob.

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Parametrizations and data assimilation

• physical processes are characterized by:

* threshold processes:

• discontinuities of some functions describing the physical processes

(some on/off processes)

• discontinuities of the derivative of a continuous function

* strong nonlinearities

• regularizations help to remove the most important threshold processes in

physical parametrizations which can effect the range of validity of

the tangent linear approximation

• after solving the threshold problems

clear advantage of the diabatic TL evolution of errors compared to

the adiabatic evolution

IMPORTANCE OF THE REGULARIZATION OF TL MODEL

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Parametrizations and data assimilation

Comparison:

finite differences (FD) tangent-linear (TL) integration

TANGENT-LINEAR DIAGNOSTICS

'

,an analysis fg first guess

x x x xan anfg fgM M M

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Parametrizations and data assimilation

Zonal wind increments at model level ~ 1000 hPa [ 24-hour integration]

FD TLADIAB

TLADIABSVD TLWSPHYS

TLADIAB – adiabatic TL model

TLADIABSVD – TL model with very simple vertical diffusion (Buizza 1994)

TLWSPHYS – TL model with the whole set of simplified physics (Mahfouf 1999)

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Parametrizations and data assimilation

Diagnostics:

• mean absolute errors:

• relative error

fganfgan MMM xxxx

%100.

REF

REFEXP

TANGENT-LINEAR DIAGNOSTICS

Comparison:

finite differences (FD) tangent-linear (TL) integration

'

,an analysis fg first guess

x x x xan anfg fgM M M

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Parametrizations and data assimilation

80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60

50

40

30

20

10

Temperature - 15/03/2001 12 h t+12Error difference: WSPHYSexp2 - ADIAB: -4.55 %

-0.8

-0.4

-0.2

-0.1

-0.05

-0.025

-0.010.01

0.025

0.05

0.1

0.2

0.4

Temperature

adiabsvd

10

20

30

40

50

60 80N 60N 40N 20N 0 20S 40S 60S 80S

EXP - REF

relative improvement

EXP

REF = ADIAB

[%]

Impact of very simple vertical diffusion scheme

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Parametrizations and data assimilation

80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60

50

40

30

20

10

Temperature - 15/03/2001 12 h t+12Error difference: WSPHYSexp2 - ADIAB: -6.22 %

-0.8

-0.4

-0.2

-0.1

-0.05

-0.025

-0.010.01

0.025

0.05

0.1

0.2

0.4

Temperature Impact of dry physical processes

adiabsvd || vdif + gwd + radold

80N 60N 40N 20N 0 20S 40S 60S 80S

10

20

30

40

50

60

EXP - REF

EXP

relative improvement

REF = ADIAB

[%]

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Parametrizations and data assimilation

80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60

50

40

30

20

10

Temperature - 15/03/2001 12 h t+12Error difference: WSPHYSexp2 - ADIAB: -10.41 %

-0.8

-0.4

-0.2

-0.1

-0.05

-0.025

-0.010.01

0.025

0.05

0.1

0.2

0.4

Temperature

adiabsvd || vdif + gwd + radold + lsp + conv

80N 60N 40N 20N 0 20S 40S 60S 80S

10

20

30

40

50

60

EXP - REF

EXP

relative improvement

REF = ADIAB

[%]

Impact of dry + moist physical processes

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Parametrizations and data assimilation

80ON 60ON 40ON 20ON 0O 20OS 40OS 60OS 80OS60

50

40

30

20

10

Temperature - 15/03/2001 12 h t+12Error difference: WSPHYSexp2 - ADIAB: -14.38 %

-0.8

-0.4

-0.2

-0.1

-0.05

-0.025

-0.010.01

0.025

0.05

0.1

0.2

0.4

Temperature

adiabsvd || vdif + gwd + conv + radnew + cl_new

80N 60N 40N 20N 0 20S 40S 60S 80S

10

20

30

40

50

60

EXP - REF

|FD|

|FD - TL|

REF = ADIAB

EXP

relative improvement [%]

Impact of physical processes (including improved schemes)

X X

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Parametrizations and data assimilation

Zonal wind

Specific humidity

Impact of all physical processes

relative improvement

relative improvement

|FD|

|FD - TL|

|FD|

|FD - TL|

[%]

[%]

EXP - REF

EXP - REF

X X

X X

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Parametrizations and data assimilation

IMPACT OF THE LINEARIZED PHYSICS IN 4D-VAR (1)

• comparisons of the operational version of 4D-Var against the version without linearized physics included shows:

FORECAST VERIFICATION – 500 hPa GEOPOTENTIAL period: 15/11/2000 – 13/12/2000

root mean square error – 29 cases

N.HEM S.HEM

oper RD

4v no phys

– positive impact on analysis and forecast

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Parametrizations and data assimilation

– reducing precipitation spin-up problem when using simplified physics in 4D-Var minimization

Time evolution of total precipitation in the tropical belt [30S, 30N] averaged over 14 forecasts issued from 4D-Var assimilation

IMPACT OF THE LINEARIZED PHYSICS IN 4D-VAR (2)

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Parametrizations and data assimilation

1-DAY FORECAST ERROR OF 500 hPa GEOPOTENTIAL HEIGHT OPER (very simple radiation) vs. NEWRAD (new linearized radiation) (27/08/2001

t+24)

A1:

FC_OPER –

ANAL_OPER

A2:

FC_NEWRAD –

ANAL_OPER

A2 – A1

500hPa Z* 2001-08-27 12h fc t+24 A1: fc_oper - anal_oper 500hPa Z* 2001-08-27 12h fc t+24 A2: fc_e7gm - anal_oper

0.2

500hPa Z* 2001-08-27 12h fc t+24 A2 - A1

4.3

0.5

-5.3

500hPa Z* 2001-08-27 12h INIT: anal_e7gm - anal_oper

75.4

-30.3

63.8

-23.3

500hPa Z* 2001-08-27 12h fc t+24 A1: fc_oper - anal_oper 500hPa Z* 2001-08-27 12h fc t+24 A2: fc_e7gm - anal_oper

0.2

500hPa Z* 2001-08-27 12h fc t+24 A2 - A1

4.3

0.5

-5.3

500hPa Z* 2001-08-27 12h INIT: anal_e7gm - anal_oper

-17.9

-10.0

IMPACT OF THE LINEARIZED PHYSICS IN 4D-VAR (3)

impact of new linearized radiation

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Parametrizations and data assimilation

B = background error covariance matrix

R = observation and representativeness error covariance matrix

H = nonlinear observation operator (model space observation space) (physical parametrization schemes, microwave radiative transfer model, reflectivity model, …)

• For a given observation yo, 1D-Var searches for the model state x=(T,qv) that minimizes the cost function:

Background term Observation term

1D-Var assimilation of observations related to the physical processes

• The minimization requires an estimation of the gradient of the cost function:1 1( ) ( ) ( ( )H )J Tx B x x H R x yb o

• The operator HT can be obtained:

– explicitly (Jacobian matrix)

– using the adjoint technique

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Parametrizations and data assimilation

Schematic description of forward modelling of physical outputs and their corresponding adjoint modelling

controlvariablesT, q, ps

physicsoutput

departures

physical

parametrization

schemes

physicsoutput

adjoint

of physical

parametrization

schemes

controlvariables

increments

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Parametrizations and data assimilationPrecipitation assimilation at ECMWF

A bit of history:

• Work on precipitation assimilation at ECMWF initiated by Mahfouf and Marécal.

• 1D-Var on TMI and SSM/I rainfall rates (RR) (M&M 2000).

• Indirect ‘1D-Var + 4D-Var’ assimilation of RR more robust than direct 4D-Var.

• ‘1D-Var + 4D-Var’ assimilation of RR is able to improve humidity but also the dynamics in the forecasts (M&M 2002).

Goal: To assimilate observations related to precipitation and clouds in ECMWF 4D-Var system including parameterizations of atmospheric moist processes.

More recent developments:

• New simplified convection scheme (Lopez & Moreau 2005) • New simplified cloud scheme (Tompkins & Janisková 2004) used in 1D-Var• Microwave Radiative Transfer Model (Bauer, Moreau 2002)

Assimilation experiments of direct measurements from TRMM and SSM/I (TB or Z) instead of indirect retrievals of rainfall rates, in a ‘1D-Var + 4D-Var’ framework.

TMI – TRMM Microwave Imager, TRMM – Tropical Rainfall Measuring Mission SSM/I – Special Sensor Microwave/Imager

OPERATIONAL USE: assimilation of precipitation affected microwave radiancess since June 2005 (Bauer et al. 2006)

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Parametrizations and data assimilation“1D-Var+4D-Var” assimilation of observations related to precipitation

4D-Var

1D-Varmoist physics

moist physics + radiative transfer

background T,qv

background T,qv

“Observed” rainfall rates

Retrieval algorithm (2A12,2A25)

1D-Var on TBs or reflectivities 1D-Var on TMI or PR rain rates

Observations interpolated on model’s T511 Gaussian grid

TMI TBs or

TRMM-PR reflectivities

“TCWVobs”=TCWVbg+∫zqv

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Parametrizations and data assimilation

Background

PATER obs 1D-Var/RR PATER

1D-Var/TB

1D-Var on TMI data (Lopez and Moreau, 2003)

Tropical Cyclone Zoe (26 December 2002 @1200 UTC)

1D-Var on TMI Rain Rates / Brightness Temperatures

Surface rainfall rates (mm h-1)

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Parametrizations and data assimilation

2A25 Rain Background Rain 1D-Var Analysed Rain

2A25 Reflect. Background Reflect. 1D-Var Analysed Reflect.

1D-Var on TRMM/ Precipitation Radar data (Benedetti and Lopez, 2003)

Tropical Cyclone Zoe (26 December 2002 @1200 UTC)

Vertical cross-section of rain rates (top, mm h-1) and reflectivities (bottom, dBZ): observed (left), background (middle), and analysed (right).

Black isolines on right panels = 1D-Var specific humidity increments.

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Parametrizations and data assimilation1D+4D-Var assimilation of microwave radiances affected by precipitation (Bauer et al. 2006)

120

120 120 12060°S60°S

30°S 30°S

0°0°

30°N 30°N

60°N60°N

120°W

120°W 60°W

60°W 0°

0° 60°E

60°E 120°E

120°E

Wednesday 1 September 2004 00UTC ECMWF Forecast t+24 VT: Thursday 2 September 2004 00UTC 850hPa **geopotential heightECMWF Analysis VT:Thursday 2 September 2004 00UTC 850hPa **geopotential height

-1-0.7-0.6-0.5-0.4-0.3-0.2-0.1-0.050.050.10.20.30.40.50.60.71

rms error differences between RAIN (run with precipitation assimilation) and REF (reference run)

geopotential height at 850 hPa (t+24) – mean over 30 days (September 2004)

negative values = RAIN improved w.r.t. REFrms rms REFRAIN

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Parametrizations and data assimilation

ARM SGP, May 1999 - observations: - surface downward longwave radiation (LWD),

- total column water vapour (TCWV) - cloud liquid water path (LWP)Observation operator includes: - shortwave and longwave radiation schemes - diagnostic cloud scheme

1D-Var assimilation of cloud related ARM observations (1) (Janisková et al., 2002)

positive values = improvement

TCWV LWD

LWP SWD

| FG - OBS | - | ANAL - OBS |

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Parametrizations and data assimilation1D-Var assimilation of cloud related ARM observations (2) (Benedetti and Janisková, 2004)

ARM – Atmospheric Radiation Measurement

RefdBZ

0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.

Days since 20010101 00UTC

984. 977. 962.

939. 905.

861. 807.

745. 676. 603.

528. 454. 383.

316. 256.

201. 154. 113.

80. 55.

Pre

ssu

re (h

Pa)

-12 - -11 -11 - -10 -10 - -9 -9 - -8 -8 - -7 -7 - -6 -6 - -5 -5 - -4 -4 - -3 -3 - -2 -2 - -1 -1 - 0 0 - 1 1 - 2 2 - 3 3 - 4

RefdBZ

0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.

Days since 20010101 00UTC

984. 977. 962.

939. 905.

861. 807.

745. 676. 603.

528. 454. 383.

316. 256.

201. 154. 113.

80. 55.

Pre

ssu

re (h

Pa)

-12 - -11 -11 - -10 -10 - -9 -9 - -8 -8 - -7 -7 - -6 -6 - -5 -5 - -4 -4 - -3 -3 - -2 -2 - -1 -1 - 0 0 - 1 1 - 2 2 - 3 3 - 4

RefdBZ

0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.

Days since 20010101 00UTC

984. 977. 962.

939. 905.

861. 807.

745. 676. 603.

528. 454. 383.

316. 256.

201. 154. 113.

80. 55.

Pre

ssu

re (h

Pa)

-12 - -11 -11 - -10 -10 - -9 -9 - -8 -8 - -7 -7 - -6 -6 - -5 -5 - -4 -4 - -3 -3 - -2 -2 - -1 -1 - 0 0 - 1 1 - 2 2 - 3 3 - 4

OBS

FG

AN -12 -10 -8 -6 -4 -2 0 2dBZ / 10.

0

100

200

300

400

500

600

700

800

900

1000

pres

sure

leve

ls

BIAS - reflectivity for ARM SGPPeriod: 1 - 31 January 2001

background departure (o - b)analysis departure (o - a)

period: January 2001 (retrieved from 35 GHz radar) Cloud reflectivity in dBZ/10

> 20 dBZ

0 dBZ<Z< 10 dBZ

-10 dBZ<Z< 0 dBZ

< -20 dBZ

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Parametrizations and data assimilation

-20 -15 -10 -5 0 5

0

100

200

300

400

500

600

700

800

900

1000

pres

sure

leve

lsBIAS - Temp-RH for ARM SGP

Period: 1 - 31 January 2001

first-guess departure (o - b)analysis departure (o - a)_1

-20 -15 -10 -5 0 5

0

100

200

300

400

500

600

700

800

900

1000

pres

sure

leve

lsBIAS - Temp-RH for ARM SGP

Period: 1 - 31 January 2001

analysis departure (o - a)_2

-20 -15 -10 -5 0 5

0

100

200

300

400

500

600

700

800

900

1000

pres

sure

leve

lsBIAS - Temp-RH for ARM SGP

Period: 1 - 31 January 2001

analysis departure (o - a)_3

Synergy of active and passive observations for cloud assimilationAN1= Reflectivity only AN2= Total Column Water Vapor

+ Surface LW radiative flux

RELATIVE HUMIDITY BIAS

The combination of passive and active observations gives the lowest analysis bias at all levels with respect to radiosoundings

%

1D-Var of cloud related ARM observations (3a) (Janisková 2004, Benedetti & Janisková 2004)

AN3 = Reflectivity + Total Column Water Vapor + Surface LW radiative flux

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Parametrizations and data assimilation

• Main objective: to investigate the possibility to assimilate observations affected by cloud and/or precipitation over a certain time window (12 hours), using measurements either with a high temporal resolution (30 min) or that are accumulated or averaged in time

• 2D-Var framework using ECMWF Single Column Model (SCM, M. Köhler) → much more simple to run and to interpret than 4D-Var

• So far, test with MW TBs, cloud radar reflectivities, rain-gauge and GPS TCWV data

2D-Var assimilation of ARM observations affected by clouds and precipitation (Lopez et al., 2005)

x0 = profile of temperature and

specific humidity at initial time

B = error covariance matrix for background

Ri = error covariance matrices for observations at time ti Hi = “observation operator” (model

space observation space) = O Mti

1

1

minimize

1( ) ( ) ( )

21

( ( ) ( ( )2

-i i i i i

i

J

H ) H )

T0 0 0 0 0

T0 0

x x x B x x

x y R x y

b b

o o

i

b0ti

OM x

tiy

2D-Var

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Parametrizations and data assimilation2D-Var on 23.8 and 31.4 GHz TBs & mean profiles of cloud radar reflectivities (Lopez et al., 2005)

Mean Reflectivity

23.8 GHz TB

31.4 GHz TB

TCWV

ARM SGP site

4 February 2001

– Assimilation of half-hourly MW TBs over 12 hours is feasible, provided a proper screening is applied ( i.e. |guess – obs| < 3 K )

– Better to assimilate reflectivity profiles averaged over the assimilation window (despite the obvious lost of information) than half-hourly reflectivity profiles due to the sometimes large model-obs departures at such “high” temporal resolution

Conclusions:

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Parametrizations and data assimilation

SUMMARY AND PERSPECTIVES

• Positive impact from including linearized physical parametrization schemes

into the assimilating model has been demonstrated.

• Physical parametrizations become important components in current variational

data assimilation systems

• Recently, improvement/development of the schemes for the linearized moist

processes with emphasis on:

– moist convection (Lopez and Moreau 2005)

– parametrization of large-scale condensation and clouds (Tompkins and Janisková 2004)

• Some care must be taken when deriving the linearized parametrization schemes

linearity, regularity & efficiency realism

• This is particularly true for the assimilation of observations related to precipitation,

clouds and soil moisture, to which a lot of effort is currently devoted.

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Parametrizations and data assimilation

REFERENCES

Bauer, P., Lopez, P., Benedetti, A., Salmond, D. and Moreau, E., 2006: Implementation of 1D+4D-Var assimilation of precipitation affected microwave radiances at ECMWF. Part I: 1D-Va. Quart. J. Roy. Meteor. Soc., accepted.

Bauer, P., Lopez, P., Salmond, D., Benedetti, A., Saarinen, S. and Bonazzola, M., 2006: Implementation of 1D+4D-Var assimilation of precipitation affected microwave radiances at ECMWF. Part II: 4D-Var. ECMWF Technical Memorandum 488

Benedetti, A. and Janisková, M., 2004: Advances in cloud assimilation at ECMWF using ARM radar data. Extended abstract for ICCP, Bologna 2004

Errico, R.M., 1997: What is an adjoint model. Bulletin of American Met. Soc., 78, 2577-2591

Fillion, L. and Errico, R., 1997: Variational assimilation of precipitation data using moist convective parametrization schemes: A 1D-Var study. Mon. Wea. Rev., 125, 2917-2942

Fillion, L. and Mahfouf, J.-F., 2000: Coupling of moist-convective and stratiform precipitation processes for variational data assimilation. Mon. Wea. Rev., 128, 109-124

Klinker, E., Rabier, F., Kelly, G. and Mahfouf, J.-F., 2000: The ECMWF operational implementation of four-dimensional variational assimilation. Part III: Experimental results and diagnostics with operational configuration. Quart. J. Roy. Meteor. Soc., 126, 1191-1215

Chevallier, F., Bauer, P., Mahfouf, J.-F. and Morcrette, J.-J., 2002: Variational retrieval of cloud cover and cloud condensate from ATOVS data. Quart. J. Roy. Meteor. Soc., 128, 2511-2526

Chevallier, F., Lopez, P., Tompkins, A.M., Janisková, M. and Moreau, E., 2004: The capability of 4D-Var systems to assimilate cloud_affected satellite infrared radiances. Quart. J. Roy. Meteor. Soc., in press

Janisková, M., Thépaut, J.-N. and Geleyn, J.-F., 1999: Simplified and regular physical parametrizations for incremental four-dimensional variational assimilation. Mon. Wea. Rev., 127, 26-45

Janisková, M., Mahfouf, J.-F., Morcrette, J.-J. and Chevallier, F., 2002: Linearized radiation and cloud schemes in the ECMWF model: Development and evaluation. Quart. J. Roy. Meteor. Soc.,128, 1505-1527

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Reading

Parametrizations and data assimilation

REFERENCES

Janisková, M., Mahfouf, J.-F. and Morcrette, J.-J., 2002: Preliminary studies on the variational assimilation of cloud-radiation observations. Quart. J. Roy. Meteor. Soc., 128, 2713-2736

Janisková, M., 2004: Impact of EarthCARE products on Numerical Weather Prediction. ESA Contract Report, 59 pp.

Laroche, S., Tanguay, M. and Delage, Y., 2002: Linearization of a simplified planetary boundary layer parametrization. Mon. Wea. Rev., 130, 2074-2087

Lopez, P. and Moreau, E., 2005: A convection scheme for data assimilation purposes: Description and initial test. Quart. J. Roy.. Meteor. Soc., 131, 409-436

Lopez., P., Benedetti, A., Bauer, P., Janisková, M. and Köhler, M.., 2005: Experimental 2D-Var assimilation of ARM cloud and precipitation observations. ECMWF Technical Memorandum 456

Mahfouf, J.-F., 1999: Influence of physical processes on the tangent-linear approximation. Tellus, 51A, 147-166

Marécal, V. and Mahfouf, J.-F., 2000: Variational retrieval of temperature and humidity profiles from TRMM precipitation data. Mon. Wea. Rev., 128, 3853-3866

Marécal, V. and Mahfouf, J.-F., 2002: Four-dimensional variational assimilation of total column water vapour in rainy areas. Mon. Wea. Rev., 130, 43-58

Marécal, V. and Mahfouf, J.-F., 2003: Experiments on 4D-Var assimilation of rainfall data using an incremental formulation. Quart. J. Roy. Meteor. Soc., 129, 3137-3160

Moreau, E., Lopez, P., Bauer, P., Tompkins, A.M., Janisková, M. And Chevallier, F., 2004: Rainfall versus microwave brightness temperature assimilation: A comparison of 1D-Var results using TMI and SSM/I observations. Quart. J. Roy. Meteor. Soc., in press.

Tompkins, A.M. and Janisková, M. , 2004: A cloud scheme for data assimilation: Description and initial tests. Quart. J. Roy. Meteor. Soc., 130, 2495-2518

Zhu, J. and Kamachi, M., 2000: The role of the time step size in numerical stability of tangent linear models. Mon. Wea. Rev., 128, 1562-1572


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