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CLIMATE/EARTH 401�Geophysical Fluid Dynamics�Dynamical Meteorology

Richard B. Rood

rbrood@umich.edu

https://clasp.engin.umich.edu/people/richard-b-rood/

https://openclimate.org/

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Thermodynamic Equation in Pressure Coordinate

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Vertical motion in pressure coordinates

  • Definition:

​

​

​

  • Pressure decreases with height.
  • What is the sign of Dp/Dt (change in pressure following the motion)?
    • for upward motion?
    • for downward motion?

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Vertical motion in pressure coordinates

  • ω is negative for upward motion
  • ω is positive for downward motion

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Thermodynamic equation (in p coordinates)

From Holton, we can

Derive two forms of �the thermodynamic �equation

Expand the material derivative and use

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Thermodynamic equation (in p coordinates)

Collect terms in ω and divide through by cp

Use the equation of state (ideal gas law)

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Thermodynamic equation (in p coordinates)

Define the static stability parameter Sp

What is static stability?

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Thermodynamic equation (in p coordinates)

If there is no advection, then the time rate of change of temperature is due to…?

Diabatic heating

(radiation, condensation)

Adiabatic rising/sinking

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End: Thermodynamic Equation in Pressure Coordinate

Richard B. Rood

rbrood@umich.edu

https://clasp.engin.umich.edu/people/richard-b-rood/

https://openclimate.org/