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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.
When it is thought of as vertical (e.g., re density or pressure of
an atmosphere above a body's surface,
or density of stars in a galaxy above/below its plane),
it may be referred to as a **vertical scale height**.

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