Balanced Coupling Between Vertical Motion and Diabatic Forcing for Variational Data Assimilation

Luc FillionCollaborators:

Monique Tanguay, Nils Ek, Christian Page, Simon Pellerin, Michel Desgagne

Meteorological Service Canada

Dorval, Québec, Canada

Target Grid for Regional 48H Forecast at 10 km using GEM_LAM

Higher resolution nested grids on demand (ex: 2km)

VancouverMontreal

Development of a Limited Area VDAS(Main Focus: Precipitation)

Unified Global/LA Variational analysis code.

Main features (at the present time: 1st Sept 2005):

1. Extension of Meso3D-Var to 4D-Var (june 2005).

2. Coupling of Divergence and Mass fields using Moist

Diabatic Balance Operators directly in the Variational

Analysis.

hPa wind analysis increments: FGAT Versus 4D-Var

UU-Obs at 500 hPa at 0h

Meso 4DVar wind analysis increments at 500 hPaTime Assimilation window: 6h

)(*

)(**

2202

2202 T

p

Rf

p

f

p

fω

vv

OperatorsNonlinearAATAA TT ,;)()( Ω

TTT ;

OperatorsLinearTangentTT TT AAAAΩ ,;),(),(

Adiabatic Balance (Mike Fisher’s approach at ECMWF)

PHYT dt

dT

p

RTAA 2

*)()(

Ω

),,;,( vuqTKdt

dT

Conv

),()()( 2

*qTK

p

RTAA T

Ω

),(),(),( ,2

*qT

p

RTT qTT

KAAΩ

Diabatic Balance (Kasahara & Krishnamurti’s dream!)

Diabatic Balance Included

24 August 2004; 12 UTC

~ 500 hPa Wind Increments

Total μbs at 500 hPa

bs-1

hPa

850 hPa

Kain-Fritsch Temperature Tendency

esovar_L: 50 km; 58 Levels

RHS Convective Forcing of Equation

hPa Wind Increments due to Convective Forcing

hPa Wind Increments due to Convective Forcing

Summary: Benefits of the coupling

1. Better I.C. for NWP over diabatic regions.2. Spin-up effects should be reduced3. Can improve Precipitation Assimilation 4. Can potentially be extended down to Kilometric XD-Var Data Assimilation; i.e. See Christian Page ‘s talk at 12h45 !

Regionalmodel