Reading, UK Parametrizations and data assimilation © ECMWF 2010 Marta JANISKOVÁ ECMWF [email protected] Parametrizations and data assimilation

Reading, UK

Parametrizations and data assimilation

© ECMWF 2010

Marta JANISKOVÁ

ECMWF

[email protected]


Reading, UK


© ECMWF 2010

• 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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© ECMWF 2010

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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© ECMWF 2010

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 can increase the so-called spin-up/spin-down

problem

• using the adjoint of various physical processes should provide:

– initial atmospheric state more consistent with physical processes

– 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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© ECMWF 2010

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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© ECMWF 2010

WHY AND WHERE ARE PHYSICAL PARAMETRIZATIONS NEEDED IN DATA ASSIMILATION?

• In 1D-Var, physical parametrizations can be needed in observation operator, H (no time evolution involved).

• In 4D-Var, physical parametrizations are involved in the observation operator, H, but also in the forecast model, M.

• Physical parametrizations are needed in data assimilation (DA):

– to link the model state to the observed quantities,

– to evolve the model state in time during the assimilation

(trajectory, tangent-linear (TL) and adjoint (AD) computations in 4D-Var)

Example: to assimilate reflectivity profiles, H must perform the conversion:

Model state (T, q, u, v, Ps )

Cloud and precipitation

profiles

Simulated reflectivity

profile

moist physics reflectivity model

Reading, UK


© ECMWF 2010

OPERATIONAL 4D-VAR AT ECMWF – INCREMENTAL FORMULATION

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

Reading, UK


© ECMWF 2010

WHY SIMPLIFIED PHYSICS?

• One of the main assumptions in variational DA is that parametrizations and

operators that describe atmospheric processes should be linear.

otherwise, the use of the tangent-linear and adjoint approach is inappropriate

and the analysis is suboptimal

• In practise, weak nonlinearities can be handled through successive trajectory

updates (e.g., 3 outer loops in ECMWF 4D-Var)

• Physical parametrizations used in DA (TL and AD) are usually simplified

versions of the original parametrizations employed in the forecast models:

– to avoid nonlinearities (see further),

– to keep the computational cost reasonable,

– but they also need to be realistic enough !

• ECMWF TL and AD models are coded using a manual line-by-line approach.

Automatic AD coding softwares exist (but far from perfect and non-optimized).

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© ECMWF 2010

• Variational assimilation is based on the strong assumption that the analysis is performed in quasi-linear framework.

• However, in the case of physical processes, strong nonlinearities or thresholds can occur in the presence of discontinuous/non-differentiable processes (e.g. switches or thresholds in cloud water and precipitation formation, …)

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

LINEARITY ISSUE

Thursday 15 March 2001 12UTC ECMWF Forecast t+12 VT: Friday 16 March 2001 00UTC Model Level 44 **u-velocity

-12

-8

-4

-2

-1

-0.50.5

1

2

4

8

12Thursday 15 March 2001 12UTC ECMWF Forecast t+12 VT: Friday 16 March 2001 00UTC Model Level 45 **u-velocity

-12

-8

-4

-2

-1

-0.50.5

1

2

4

8

12 finite difference (FD) TL integration

u-wind increments fc t+12, ~700 hPax 105

Reading, UK


© ECMWF 2010

• 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

TL increments correspond well to finite differences

Thursday 15 March 2001 12UTC ECMWF Forecast t+12 VT: Friday 16 March 2001 00UTC Model Level 44 **u-velocity

-12

-8

-4

-2

-1

-0.50.5

1

2

4

8

12Thursday 15 March 2001 12UTC ECMWF Forecast t+12 VT: Friday 16 March 2001 00UTC Model Level 44 **u-velocity

-12

-8

-4

-2

-1

-0.50.5

1

2

4

8

12

u-wind increments

fc t+12, ~700 hPaTL integrationfinite difference (FD)

IMPORTANCE OF THE REGULARIZATION OF TL MODEL

© ECMWF 2010

Reading, UK


© ECMWF 2010

dyNL

dyTL

Potential source of problem (example of precipitation formation)

dx

Reading, UK


© ECMWF 2010 dx

dy N

L

dy T

L1

dy T

L2

Possible solution, but …

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© ECMWF 2010 dx1

dy N

L

dy T

L2

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

dy T

L3

dx2

Reading, UK


© ECMWF 2010 dx

dy N

L

dy T

L1

dy T

L2

However, the better the model the smaller the increments

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© ECMWF 2010

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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© ECMWF 2010

Regularization of vertical diffusion scheme:

• 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

10.0

0.0

f(Ri)

- 10.0

- 20.0

Function of the Richardson number

EXAMPLES OF REGULARIZATIONS (1)

• reduction of the time step to 10 seconds to guarantee stable time integrations of the associated TL model (Zhu and Kamachi, 2000) not possible in operational global models

Exchange coefficients K are function of the Richardson number:

2UK l f Ri

z

Reading, UK


© ECMWF 2010

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

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

-20 -15 -10 -5 0 5 10 15 20Ri

-10

0

10

20

30

f(|R

i)

f(Ri) - trajectoryf(Ri) - perturbationreduction factor up to 3kmreduction factor above 3km

• New operational ECMWF version:

using reduction factor for perturbation

of the exchange coefficients

• perturbation of the exchange coefficients neglected, K’ = 0 (Mahfouf, 1999) in

the operational ECMWF version used to the middle of 2008

EXAMPLES OF REGULARIZATIONS (2)

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© ECMWF 2010

ECMWF LINEARIZED PHYSICS (as operational in 4D-Var)

Currently used in ECMWF operational 4D-Var minimizations (main simplifications with respect to the nonlinear versions are highlighted in red):

• Radiation:

– TL and AD of longwave and shortwave radiation [Janisková et al. 2002] – shortwave: only 2 spectral intervals (instead of 6 in nonlinear version)

– longwave: called every 2 hours only.

• Vertical diffusion:

– mixing in the surface and planetary boundary layers,

– based on K-theory and Blackadar mixing length,

– exchange coefficients based on Louis et al. [1982], near surface,

– Monin-Obukhov higher up,

– mixed layer parameterization and PBL top entrainment recently added.

– Perturbations of exchange coefficients are smoothed out.

• Gravity wave drag: [Mahfouf 1999]

– subgrid-scale orographic effects [Lott and Miller 1997],

– only low-level blocking part is used.

• No evolution of surface variables

Dry

p

roce

sses

:

Reading, UK


© ECMWF 2010

ECMWF LINEARIZED PHYSICS (as operational in 4D-Var)

• Convection scheme: [Lopez and Moreau 2005]

– mass-flux approach [Tiedtke 1989],

– deep convection (CAPE closure) and shallow convection (q-convergence)

– perturbations of all convective quantities included,

– coupling with cloud scheme through detrainment of liquid water from updraught,

– some perturbations (buoyancy, initial updraught vertical velocity) are reduced.

• Large-scale condensation scheme: [Tompkins and Janisková 2004]

– based on a uniform PDF to describe subgrid-scale fluctuations of total water,

– melting of snow included,

– precipitation evaporation included,

– reduction of cloud fraction perturbation and in autoconversion of cloud into rain.

After solving the threshold problems

clear advantage of the diabatic TL evolution of errors compared to the adiabatic evolution

Mo

ist

pro

cess

es:

Reading, UK


© ECMWF 2010

VALIDATION OF THE LINEARIZED PARAMETRIZATION SCHEMES

Non-linear model:

• Forecast runs with particular modified/simplified physical parametrization schemes

• Check that Jacobians (=sensitivities) with respect to input variables look reasonable

(not too noisy in space and time)

• classical validation: TL - Taylor formula,

AD - test of adjoint identity

Tangent-linear (TL) and adjoint (AD) model:

• examination of the accuracy of the linearization:

comparison between finite differences (FD) and tangent-linear (TL) integration

Singular vectors:

• Computation of singular vectors to find out whether the new schemes do not

produce spurious unstable modes.

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© ECMWF 2010

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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© ECMWF 2010

TLADIAB – adiabatic TL model

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

TLWSPHYS TLADIAB

FD

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

Reading, UK


© ECMWF 2010

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

Reading, UK


© ECMWF 2010 adiabsvd || vdif

EXP - REF

EXP

relative improvement

REF = ADIAB

[%]

X

80N 60N 40N 20N 0 20S 40S 60S 80S60

50

40

30

20

10

Temperature - 15/03/2001 12 h t+12Error difference: SPHYSvdif - ADIAB: -5.81 %

-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

10

20

30

40

50

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

Temperature Impact of operational vertical diffusion scheme

© ECMWF 2010

Reading, UK


© ECMWF 2010 adiabsvd || vdif + gwd + radold + lsp + conv

EXP - REF

EXP

relative improvement

REF = ADIAB

[%]

X

80N 60N 40N 20N 0 20S 40S 60S 80S60

50

40

30

20

10

Temperature - 15/03/2001 12 h t+12Error difference: WSPHYSold_oper - ADIAB: -9.72 %

-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

10

20

30

40

50

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

Temperature Impact of dry + moist physical processes (1st used setup)

© ECMWF 2010

Reading, UK


© ECMWF 2010

16

adiabsvd || vdif + gwd + rad + cloud+conv current

new new new cycle

EXP - REF

REF = ADIAB

EXP

10

20

30

40

50

60

Temperature Impact of all physical processes (including improved schemes)

80N 60N 40N 20N 0 20S 40S 60S 80S60

50

40

30

20

10

Temperature - 15/03/2001 12 h t+12Error difference: WSPHYSnew_oper - ADIAB: -14.73 %

-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

relative improvement [%]

X X X X

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

|FD|

|FD - TL|

adiab

adiabsvd

vdif

oper_old

oper_2007

© ECMWF 2010

Reading, UK


© ECMWF 2010

Zonal wind

|FD|

|FD - TL|

EXP - REF

|FD|

|FD - TL|

Impact of all physical processes


XXX X

conv currentnew cycle

adiab

adiabsvd

vdif

oper_old

oper_2007

adiab

adiabsvd

vdif

oper_old

oper_2007

EXP - REF 20

18 Specific humidity

X X Xconv currentnew cycle


Reading, UK


© ECMWF 2010

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

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

– positive impact on analysis and forecast

– 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

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© ECMWF 2010

1-DAY FORECAST ERROR OF 500 hPa GEOPOTENTIAL HEIGHT

OPER (very simple radiation) vs. NEWRAD (new linearized radiation) (27/08/2001 12h 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 PHYSICAL PROCESSES IN 4D-VAR (2)

impact of new linearized radiation

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© ECMWF 2010

• June 2005 – March 2009 – 1D+4D-Var assimilation of SSM/I brightness temperatures (TBs) in regions affected by rain and clouds. (Bauer et al. 2006 a, b)

• Since March 2009 – active all-sky 4D-Var assimilation of microwave imagers

AIRS – Advanced Infrared Sounder ARM – Atmospheric Radiation Measurement programme

GPS – Global Positioning System SSM/I – Special Infrared Sounder

Operational:

Experimental:

• 1D-Var assimilation of cloud-related ARM observations. (Janisková et al. 2002)‒ surface downward LW radiation, total column water vapour, cloud liquid water path

• Investigation of the capability of 4D-Var systems to assimilate cloud-affected satellite infrared radiances – using cloudy AIRS TBs. (Chevallier et al. 2004)

• 1D-Var assimilation of precipitation radar data. (Benedetti and Lopez 2003)

• 1D-Var assimilation of cloud radar reflectivity – retrieved from 35 GHz radar at ARM site. (Benedetti and Janisková 2004)

• 2D-Var assimilation of ARM observations affected by clouds & precipitation – using microwave TBs, cloud radar reflectivity, rain-gauge and GPS TCWV. (Lopez et al. 2006)

• 4D-Var assimilation of cloud optical depth from MODIS. (Benedetti & Janisková 2007)

•1D+4D-Var assimilation of NCEP Stage IV hourly precipitation data over USA – combined radar + rain gauge observations. (Lopez and Bauer 2007)

• 1D-Var of cloud radar reflectivity from CloudSat (QuARL project)

Reading, UK

Assimilation of rain and cloud related observations at ECMWF

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© ECMWF 2010

Impact of the direct 4D-Var assimilation of SSM/I all-skies TBs on the

relative change in 5-day forecast RMS errors (zonal means).

Period: 22 August 2007 – 30 September 2007

Wind Speed

4D-Var assimilation of SSM/I rainy brightness temperatures (Geer, Bauer et al.)

0.10.0500.05-0.1

forecast is better forecast is worse

Relative Humidity

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© ECMWF 2010

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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© ECMWF 2010

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

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

TRMM – Tropical Rainfall Measuring Mission TMI – TRMM Microwave Imager PR – Precipitation Radar

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© ECMWF 2010

Background

PATER obs 1D-Var/RR PATER

1D-Var/TB

Tropical Cyclone Zoe (26 December 2002 @1200 UTC)

1D-Var on TMI Rain Rates / Brightness Temperatures

Surface rainfall rates (mm h-1)

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

Reading, UK


© ECMWF 2010

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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© ECMWF 2010

Background term Observation term

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

the cost function:

1D-Var assimilation of cloud related observations (1)

H(x): moist physics or

+ radar/lidar radiative model

(+ radiation scheme)x_b:

Background

T,q

1D-Var (analyzed T, q)

Y: retrieved cloud parameters

(level-2 products)or

backscatter cross-sections,

reflectivities (level-1 products)

Reading, UK


© ECMWF 2010

REF_AT AN - refl

c)

60 N 50 N 40 N 30 N 20 N 10 N 0 10 S 20 S 30 S 40 S 50 S 60SLat

175W 170W 165W 160W 155W 150W 145W 140WLon

1.1

1.9

3.1

4.5

6.1

7.9

9.6

11.2

12.9

14.5

Heig

ht (km

)

-24 - -21 -21 - -18 -18 - -15 -15 - -12 -12 - -9 -9 - -6 -6 - -3 -3 - 0 0 - 3 3 - 6 6 - 9 9 - 12 12 - 15 15 - 19

REF_AT FG

c)


175W 170W 165W 160W 155W 150W 145W 140WLon

1.1

1.9

3.1

4.5

6.1

7.9

9.6

11.2

12.9

14.5

Heig

ht (km

)

-24 - -21 -21 - -18 -18 - -15 -15 - -12 -12 - -9 -9 - -6 -6 - -3 -3 - 0 0 - 3 3 - 6 6 - 9 9 - 12 12 - 15 15 - 19

REF_AT OBS averaged

b)


175W 170W 165W 160W 155W 150W 145W 140WLon

1.1

1.9

3.1

4.5

6.1

7.9

9.6

11.2

12.9

14.5

Heig

ht (km

)

-24 - -21 -21 - -18 -18 - -15 -15 - -12 -12 - -9 -9 - -6 -6 - -3 -3 - 0 0 - 3 3 - 6 6 - 9 9 - 12 12 - 15 15 - 19

1D-Var assimilation of cloud related observations (2) (QuARL project)

OBS – CloudSat (94 GHz radar)

FG

AN – 1D-Var of cloud reflectivity

Cloud reflectivity [dBZ] – 23/01/2007 over Pacific

QuARL – Quantitative Assessment of Operation.Value of Space-Borne Radar and Lidar Measurements of Cloud and Aerosol Profiles

Reading, UK


© ECMWF 2010

1D-Var assimilation of cloud related observations (3) (QuARL project)

0 50 100 150 200 250 300 350 400 450 500 550 600 650 7000

20

40

60

80

100

clo

ud o

ptical depth

a)

opt_MODISopt_AN_reflopt_AN_refloptopt_FG

Comparison of the first guess and analysis against cloud optical depth

FG departure

AN-refl departure

AN-reflopt departure

BIAS - reflectivity

FG departure

AN-refl departure

AN-reflopt departure

STD.DEV. - reflectivity

Reading, UK

Bias and standard deviation of first-guess vs. analysis departures for reflectivity

hei

gh

t [k

m]

hei

gh

t [k

m]

profile number

Reading, UK


© ECMWF 2010

Experimental 4D-Var assimilation of cloud optical depth from MODIS (1) (Benedetti and Janisková, 2008)

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5FG

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

OB

S

Period = 2006040500 to 2006042000Scatterplot of OBS versus FG

125102040751251502002505007501000150020002500

Maximum number per bin = 1908Total number = 2393230

corr. coef. = 0.480RMS = 0.57BIAS (y-x)= 0.22

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5ANA

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

OB

S

Period = 2006040500 to 2006042000Scatterplot of OBS versus ANA

125102040751251502002505007501000150020002500

Maximum number per bin = 2235Total number = 2393205

corr. coef. = 0.672RMS = 0.51BIAS (y-x)= 0.21

Period: 2006040500 - 2006042000

Assimilation of cloud optical depth at 0.55 m from MODIS – fit to observations Scatter-plot of OBS versus FG Scatter-plot of OBS versus

ANA

BIAS = 0.22 RMS = 0.57 corr. coef. = 0.480

BIAS = 0.21 RMS = 0.51

corr. coef. = 0.672

‒ Positive impact on the distribution of the ice water content, particularly in the Tropics.

‒ Impact on 10-day forecast positive for upper level temperature in the Tropics and neutral for the model wind.

‒ ECMWF 4D-Var is approaching a level of the technical maturity necessary for global assimilation of cloud related observations.

Conclusions:

MODIS – Moderate Resolution Imaging Spectroradiometer © ECMWF 2010

Reading, UK


© ECMWF 2010

MLS retrievals: Ice Water Content at 215 hPa

ECMWF model – CNTRL run

CNTRL run – MLS obs

ECMWF model – EXP run

EXP run – MLS obs

MLS = Microwave

Limb Sounder

Courtesy of F. Li, Jet Propulsory Laboratory, CA, USA

IWC [mg/m3]

Experimental 4D-Var assimilation of cloud optical depth from MODIS (2) Comparison with independent cloud observations

Reading, UK


© ECMWF 2010

• Physical parametrizations become important components in current variational

data assimilation systems as they are needed:

‒ to link the model state to the observation quantities

‒ to evolve the model state in time during the assimilation

• Positive impact from including linearized physical parametrization schemes

into the assimilating model has been demonstrated.

• However, there are several problems with including physics in adjoint models:

– development and thorough validation require substantial resources

– computational cost may be very high

– non-linearities and discontinuities in physical processes must be treated with care

• Constraints and requirements when developing new simplified parametrizations

for data assimilation:

– find a compromise between realism, linearity and computational cost

– evaluation in terms of Jacobians (not too noisy in space and time)

– systematic validation against observations

– comparison to the non-linear version used in forecast mode (trajectory)

– numerical tests of tangent-linear and adjoint codes for small perturbations

– validity of the linear hypothesis for perturbations with larger size (typical of analysis increments)

GENERAL CONCLUSIONS

© ECMWF 2010

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