1 of 13

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/

2 of 13

Lapse Rate

Lapse rate: The decrease of an atmospheric variable with height, the variable being temperature, unless otherwise specified. From (AMS Glossary)

3 of 13

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.

4 of 13

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.

5 of 13

Dry Adiabatic Lapse Rate: Change in Temperature with Height

  • For a dry adiabatic, hydrostatic atmosphere the potential temperature θ does not vary in the vertical direction:�

​

​

  • In a dry adiabatic, hydrostatic atmosphere the temperature T must decrease with height.
    • How quickly does the temperature decrease?

6 of 13

Derive the dry adiabatic lapse rate

  • Remember that you own the equation, but you have to treat the equation according to the rules.
    • You must respect the “equal sign.”

​

  • Think of the derivations that we do as exploration, not as prescription.

7 of 13

(take the vertical derivative)

(logarithm of �potential temperature)

(Definition of d lnx and �derivative of a constant)

(Multiply through by T)

(Hydrostatic balance)

(Equation of State)

= 1

8 of 13

Dry adiabatic lapse rate (AMS Glossary)

The adiabatic change in temperature with height is��

​

​

For dry adiabatic, hydrostatic atmosphere

Γd: dry adiabatic lapse rate (approx. 9.8 K/km)

9 of 13

Average vertical temperature structure

  • In a dry atmosphere, this profile should be very close to the adiabatic lapse rate.

10 of 13

To remember

  • Adiabatic does not mean isothermal. It means that there is no external heating or cooling.
  • If the atmosphere is in adiabatic balance, the temperature changes with height.
  • Even in adiabatic motion, with no external source of heating, if a parcel moves up or down its temperature changes.

​

11 of 13

Definition of potential temperature

  • This is the thermodynamic energy equation under the assumption of adiabatic motion.
  • If the atmosphere were stirred adiabatically, then this is how the temperature would evolve.

This is Poisson’s equation.

12 of 13

Average vertical temperature structure

  • In actuality, the observed temperature decline is not the dry adiabatic lapse rate.
  • What are the physical reasons for the difference?

13 of 13

End: Lapse Rate

Richard B. Rood

rbrood@umich.edu

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

https://openclimate.org/