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/

Potential Temperature

Potential Temperature (AMS Glossary)

• Potential temperature is the temperature that an unsaturated parcel of dry air would have if brought adiabatically and reversibly from its initial state to a standard pressure, p_s, typically 1000 hPa.

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• In oceanography it is the temperature that a water parcel would have if brought adiabatically to the sea surface.

Return to meteorological form of the thermodynamic equation

Thermodynamic equation�(conservative, no heating, adiabatic)

conservative, no heating, adiabatic all mean J=0

Thermodynamic equation (conservative, no heating, adiabatic)

We will move the parcel by using integration

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Thermodynamic equation conservative, no heating, adiabatic �(solve, perfect differential)

Know how to do this mathematical manipulation.

Definition of potential temperature

This is the temperature a parcel would have if it was moved adiabatically from some pressure and temperature to the surface.

This is Poisson’s equation.

Quantitative problem

• The temperature at the top of the continental divide is �-10 degrees celsius (about 263 K)
• The pressure is 600 hPa, R=287 J/kg/K, c_p=1004 J/kg/K
• Compute
1. potential temperature at the continental divide
2. The temperature the air would have if it sinks to the plains (pressure level of 850 hPa) with no change in potential temperature

304 K

Average vertical temperature structure

This cooling with height is related to dynamics – vertical mixing. The change of temperature with height is called the lapse rate.

End: Potential Temperature

Richard B. Rood

rbrood@umich.edu

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

https://openclimate.org/