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**Scale Height** is a measure of the decrease of
something that falls off exponentially, specifically,
the distance over which it falls by a factor
of **e** (~ 2.718). Examples can include:

- Pressure of some planetary Atmospheres at heights from the surface (a
**Pressure Scale height**or**Atmospheric Scale Height**). - Temperature of a Stellar Atmosphere (
**Temperature Scale Height**). - Stellar density in a Galaxy at distances from its Galactic Center (a
**Density Scale Height**).

For example, a planet's atmosphere might fall
by a factor of *e* every 10km of height.
Despite the word "height", it might be applied
to dimensions not thought of as vertical.

Equation forms associated with scale height:

A = A_{0}e^{-z/H}A z ln —— = - —— A_{0}H dA —— = -HA dz

(The first two are forms of the solution to the differential equation.)

- z - the height.
- H - the scale height.
- A - the quantity, a function of z for which H applies (e.g., pressure).
- A
_{0}- the value of A when z = 0.

Zonal Flow