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Physics - Dynamics Interface

Physics - Dynamics Interface. The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR-10000 Zagreb, Croatia tudor@cirus.dhz.hr. Physics - dynamics interface. general considerations mass conservation issues AROME equations

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Physics - Dynamics Interface

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  1. Physics - Dynamics Interface The 14th ALADIN Workshop Innsbruck, 1-4 June 2004 Martina Tudor Meteorological and Hydrological Service, Grič 3, HR-10000 Zagreb, Croatia tudor@cirus.dhz.hr

  2. Physics - dynamics interface • general considerations • mass conservation issues • AROME equations • predictor - corrector scheme

  3. 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

  4. 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 variable

  5. (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 dry air prec. flux dry air water vapour

  6. (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 evaporation of precipitation water vapour

  7. (2) When the mass of the dry air is conserved (2) prec. flux advection qE (1-q)E turbulence (1-q)E -(1-q)E prec. flux dry air water vapour dry air water vapour

  8. Equations horisontal wind • Impact of the variable mass assumption on the evolution of the model variables vertical velocity temperature moisture

  9. 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

  10. Arome

  11. Barycentric velocity • velocities of the different atmospheric constituents cloud water and ice dry air rain snow

  12. 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.

  13. Arome - Velocity equation

  14. Arome - Enthalpy equation • The evolution equation for enthalpy is

  15. Arome - Temperature equation • The evolution equation for temperature is

  16. 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

  17. Aladin - barycentric velocity • with the Aladin assumptions, the barycentric velocity is

  18. Aladin - barycentric velocity (2)

  19. Aladin - barycentric velocity (3)

  20. Aladin - Continuity equation • The continuity equation becomes

  21. Aladin - Conservation of water species

  22. Aladin - Velocity equation

  23. Aladin - Temperature equation

  24. Aladin - Temperature equation (2)

  25. Aladin - Temperature equation (3)

  26. PC scheme The way it is coded now but, Under LPC_FULL, the position of the O points is recomputed and the values are re-interpolated.

  27. And a few figures • Stratiform precipitation woth 5 km resolution over Alps, August 10th 2002.

  28. Conclusion • both options for the mass conservation assumptions may be kept

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