physics - dynamics interface the 14th aladin workshop innsbruck, 1-4 june 2004 martina tudor...

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Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR-10000 Zagreb, Croatia [email protected]

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Page 1: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Physics - Dynamics Interface

The 14th ALADIN WorkshopInnsbruck, 1-4 June 2004

Martina Tudor

Meteorological and Hydrological Service, Grič 3, HR-10000 Zagreb, Croatia

[email protected]

Page 2: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Physics - dynamics interface

• general considerations

• mass conservation issues

• AROME equations

• predictor - corrector scheme

Page 3: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

General considerations

• total tendency is a sum of the linear contribution from dynamics, the non-linear part of the dynamics and the physics part

• we compute the physics tendency before the dynamical one and interpolate it to the origin point

Page 4: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Mass conservation

• In ALADIN/ARPEGE, two options exist:• (1) the total mass of the atmosphere is conserved

(NDPSFI=0 in NAMPHY)

• (2) the mass of the dry air is conserved (NDPSFI=1)

– is a prognostic variabletotal

vvq

Page 5: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

(1) When the total mass of the atmosphere is conserved

• the mass of water removed from the atmosphere is replaced by the dry air

• the mass of water vapour evaporated from the bottom surface (or falling precipitation) is compensated by a removal of the dry air

dryair

prec.flux

watervapour

dryair

Page 6: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

(2) When the mass of the dry air is conserved

• the total mass of the atmosphere changes due to the precipitation - evaporation budget

• condensation produces a local mass deficit

• evaporation produces a local mass increase

prec.flux

watervapour

evaporation of precipitation

Page 7: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

(2) When the mass of the dry air is conserved (2)

prec.flux

watervapour

prec.flux

watervapour

dryair

dryair

advection

qE (1-q)E

turbulence

(1-q)E -(1-q)E

Page 8: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Equations

• Impact of the variable mass assumption on the evolution of the model variables

p

VgP

t

VpRTVfk

dt

Vdm

phy

ln

gPdp

Vt

Bp

ms

0

p

TP

C

Cg

pgP

t

T

pC

RT

dt

dT

p

pdmm

phyp

1

p

Pgq

t

q

p

Pg

dt

dqm

phy

horisontalwind

verticalvelocity

temperature

moisture

Page 9: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Vertical co-ordinate

• in the case of condensation, and precipitation we have a removal of mass here

• but this precipitation may evaporate on the way to the ground so we have extra mass here

• we get vertical velocity due to a mass flux due to precipitation-evaporation budget

cloud

Page 10: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Arome

Page 11: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

snowrain

Barycentric velocity

• velocities of the different atmospheric constituents

cloud water and ice

dry air

Page 12: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Arome - Conservation of species

• The conservation equation for the species k is

• species: dry air, water vapour, liquid water, cloud ice, rain, snow and graupel.

Page 13: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Arome - Velocity equation

Page 14: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Arome - Enthalpy equation

• The evolution equation for enthalpy is

Page 15: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Arome - Temperature equation

• The evolution equation for temperature is

Page 16: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Aladin

• all the non-precipitating species move with the same speed• mass and volume of precipitation is neglected• velocity of precipitation is infinite• we define the product of mass to the velocity of precipitation as

• where P is a precipitation flux

Page 17: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Aladin - barycentric velocity

• with the Aladin assumptions, the barycentric velocity is

Page 18: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Aladin - barycentric velocity (2)

Page 19: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Aladin - barycentric velocity (3)

Page 20: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Aladin - Continuity equation

• The continuity equation becomes

Page 21: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Aladin - Conservation of water species

Page 22: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Aladin - Velocity equation

Page 23: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Aladin - Temperature equation

Page 24: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Aladin - Temperature equation (2)

Page 25: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Aladin - Temperature equation (3)

Page 26: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

PC schemeThe way it is coded now

but,

Under LPC_FULL, the position of the O points is recomputed and the values are re-interpolated.

Page 27: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

And a few figures

• Stratiform precipitation woth 5 km resolution over Alps, August 10th 2002.

Page 28: Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR- 10000

Conclusion

• both options for the mass conservation assumptions may be kept