Geopotential

up:: 034 MOC Atmospheric Physics

The geopotential is the amount of Work required to lift an air parcel of unit mass from the Earth’s surface () to a height .

Defined as¹

where it’s defined as at , much like (usually) the gravitational potential.

Alternative formula for ideal gases

Due to the Hydrostatic Law, we have

Supposing it’s an unit mass parcel of air, we can write its specific volume and thus

Using gravitational field formula

Opening up ,² we have

where is the Earth’s (or any planet’s) radius. It’s the same as

When , we have the usual result

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References

• WALLACE, John Michael; HOBBS, Peter Victor. Atmospheric science: an introductory survey. 2nd ed ed. Amsterdam Paris: Academic press, 2006.

Footnotes

1. Seeing it as the work of gravitational force: , where (air parcel of unit mass). ↩

2. Newton’s gravitational law for some mass : gravitational force (on unit mass air parcel) , which is just the gravitational field . ↩