One-Dimensional Variational Assimilation of SSM/I Observations … · 2006-10-27 · One-Dimensional Variational Assimilation of SSM/I Observations in Rainy Atmospheres at Environment

One-Dimensional VariationalAssimilation of SSM/IObservations in RainyAtmospheres atEnvironment Canada (EC)Science & Technology Branch

G. DeblondeJ.-F. MahfoufB. BilodeauD. Anselmo6 October 2006

www.ec.gc.ca

10/6/2006 Page 2

Motivation

• Development at EC of an assimilation system ofsatellite radiances in cloudy and rainy regions (overopen oceans)

• Operational NWP centers– JMA : Mesoscale 4D-Var assimilation of radar

precipitation– NCEP : Global 3D-Var assimilation SSM/I and TMI

derived rainfall rates– ECMWF : Towards a global 4D-Var assimilation of

SSM/I radiances in rainy areas• Two step method (1D-Var+4D-Var) operational since

June 2005 (Bauer et al. 2006 a and b, QJRMS)

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Proposed strategy

ObservationsMW Brightness

Temperature

Control variables Profiles of T and Q

1D-Var

Observation operator (1)Precipitation Schemes

ObservationsSurface

Rainfall Rate

Observation operator (2)Radiative Transfer Model

Integrated Water Vapor

Marécal and Mahfouf (2000,2002) -SRRMoreau et al. 2004 -Tb

QC 4D-Var

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Experimental set-up• Control variable : T and ln(q) profiles (58 levels)• Observations : SSM/I brightness temperatures (Tb) or derived

surface rain rates (SRR) (Bauer et al. 2002)• Observation operator :

– Moist physical processes : same as in EC globalforecast model (GEM) –jacobians obtained by finitedifference

– Radiative transfer model : RTTOV with scattering effects(Bauer and Moreau, 2002) –jacobians obtained by adjointmethod

• Background error statistics : “NMC” method (lagged forecasts)as in EC operational 4D-Var (incremental)

• Two case studies (40S-40N):– Tropical Cyclone Zoe (F15) & Typhoon Chaba (F14)

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Background Term

• Forecast Model:

– Global Environmental Multi-Scale (GEM) MESOGLOBAL -research– Model Resolution: 0.45o longitude x 0.3o latitude grid– 58 vertical levels, model lid at 10 hPa, time-step = 15 minutes

• Moist physical schemes:

– Shallow Convection: KuoTrans -> only cloud liquid water– Non-convective (or stratiform): CONSUN (Sundqvist variant)– Deep Convection: Kain-Fritsch (CAPE) ->highly non-linear

• 12-h precipitation spin-up: 1D-Var background field = 12-h forecast

10/6/2006 Page 6

HclearVclear

HV

TbTb

TbTbP

3737

3737

!

!"

)cos(/22 !"# $%& eP

• P is a measure of visibility of sea-surface relative to expected value inabsence of clouds P=0 => completely opaque rain cloud P=1 => cloud-free ocean sceneIf P > 0.15 ( =Transmittance > 0.4) then Use (19V,H,22V, 37 V,H)Else Use 19V,H, 22V ONLY

!

(Petty 1994)

Number of SSM/I Tb channels assimilated

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Brightness Temperature (K)at 19 GHz V 2002 12 27 000 UTC

Tropical Cyclone Zoe

GEM Mesoglobal 12h Forecast SSM/I F15 ObservationsK

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Experiments

• 1D-Var Tb – Small ObservationErrors (SOE)– (O+F) = 3 K for V channels &

6 K for H channels (as inMoreau et al. 2004)

• 1D-Var Tb – Large ObservationErrors (LOE)– (O+F) = HBHT

• 1D-Var SRR (Surface RainfallRate) –Observation errorprovided by retrieval algorithm

0

10

20

30

40

50

60

70

19v 19h 22v 37v 37h

SSM/I channel

Ob

serv

ati

on

Err

or

(K)

SOE

LOE

1D-Var Tb Observation Error (K)

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Zoe Case: 0000 UTC 27 Dec 2002

N=1414 for 3 channels –more opaqueN=3098 for 5 channels –less opaque

(HBHT)1/2 in Kelvin

19V 19H

22V 37V

37H

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TC Zoe: Analyzed Surface Rain Rate (mm/h)

1D-Var LOE

b)

c)

a)

d)

1D-Var SOE

1D-Var SRR PATER observations SSM/I F15

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Analyzed fields vs SSM/I retrievals basedon regression equations

O=LWP (Weng & Grody, 1994)

O=IWV (Alishouse et al. 1990)

O=SRR (Bauer et al. 2002 , PATER)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

(O-P) bias (O-P) SD (O-A) bias (O-A) SDSR

R (

mm

/h)

Tb SOE(N=4512)

Tb LOE (N=4288)

SRR (N=4038)

-10

-8

-6

-4

-2

0

2

4

6

8

(O-P) bias (O-P) SD (O-A) bias (O-A) SD

NO

N-R

AIN

Y IW

V (

kg/m

2)

Tb SOE (N=1242)

Tb LOE (N=1166)

SRR (N=1840)

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

(O-P) bias (O-P) SD (O-A) bias (O-A) SD

LW

P (

kg

/m2

)

Tb SOE (N=4507)

Tb LOE (N=4283)

SRR (N=4034)

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Integrated Wapor Vapor (IWV) increments(kgm-2)

TYPHOON CHABA CASE

-3

-2

-1

0

1

2

3

4

5

6

Mean SD

IWV

In

cre

me

nts

(kg

/m2

)

Tb SOE

Tb LOE

Tb LOE2

SRR

TROPICAL CYCLONE ZOE

-3

-2

-1

0

1

2

3

4

5

6

7

Mean SD

IWV

In

cre

me

nts

(kg

/m2

)

Tb SOE

Tb LOE

Tb LOE2

SRR

Increment = (Analysis-Background)

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Analyzed IWV error estimateChaba Zoe

A = [ B-1 + HTR-1H ] -1, Rodgers (2000)

Tb SOE TB LOE

SRR

Tb SOE Tb LOE

SRR

10%5% 5%

10%

10%

10% 10%

10%

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Size of temperature and humidityincrements (normalized by backgrounderrors) for Zoe

1D-Var Tb SOE1D-Var Tb LOE

T

lnQ

TlnQT

lnQ

TlnQ

(Analysis-Background)

10/6/2006 Page 15

Conclusions

• 1D-Var Tb and SRR developed (RTTOVSCATT-SSM/I or TMI) with GEM moist physicalschemes

• Successful analyses for Tropical Cyclone Zoe and Typhoon Chaba (> 95% convergence).• 1D-Var Tb SOE experiment: weight given to observations is too large and leads to large water

vapor increments. • Largest contribution of observation error comes from the moist physics (in particular deep

convection scheme) and hence affects the 1D-Var behavior– Explicit scheme favored (larger sensitivity to humidity)

• Assimilation of Tb, rather than SRR, should be favored in the variational assimilation context dueto the direct dependence of Tb on cloud liquid water path and integrated water vapor.

• Correlation of observation error between different channels is important for five channel set (lessopaque atmosphere implies more parameters to define).

• Applying moist physical schemes (“linearized”) from other NWP centers (developed specificallyfor DA) not trivial because schemes need to be tuned for model of center. Evaluate the impact ofassimilating 1D-Var IWV in the EC global 4D-Var

– Need to improve the computing efficiency of the 1D-Var– Tb bias correction

• Paper accepted to appear in Monthly Weather Review

10/6/2006 Page 16

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