Editing Area density (section)

== Column density ==
A special type of area density is called ''column density'' (also ''columnar mass density'' or simply ''column density''), denoted ''ρ''<sub>A</sub> or ''σ''. It is the [[mass]] of [[chemical substance|substance]] per unit [[area]] [[integral|integrated]] along a path;<ref name="Boeker_vanGrondelle2000">
{{cite book
 |author1=Egbert Boeker |author2=Rienk van Grondelle | title=Environmental Physics 
 | edition=2nd
 | year=2000
 | publisher=Wiley
}}</ref> It is obtained integrating [[density|volumetric density]] <math>\rho</math> over a column:<ref>{{Cite book  | last1 = Visconti | first1 = Guido | title = Fundamentals of physics and chemistry of the atmosphere | year = 2001 | publisher = Springer | location = Berlin  | isbn = 978-3-540-67420-7 | pages = 470 }}</ref>
<math display="block">\sigma=\int \rho \, \mathrm{d}s.</math>

In general the integration path can be slant or oblique incidence (as in, for example, [[line of sight propagation]] in [[atmospheric physics]]). A common special case is a vertical path, from the bottom to the top of the medium:
<math display="block">\sigma = \int \rho \, \mathrm{d}z,</math>
where <math>z</math> denotes the vertical coordinate (e.g., height or depth).

Columnar density <math>\rho_A</math> is closely related to the vertically averaged volumetric density <math>\bar{\rho}</math> as
<math display="block">\bar{\rho} = \frac{\rho_A}{\Delta z},</math>
where <math display="inline">\Delta z = \int 1 \, \mathrm{d}z</math>; <math>\bar{\rho}</math>, <math>\rho_A</math>, and <math>\Delta z</math> have units of, for example, grams per cubic metre, grams per square metre, and metres, respectively.