Line integral

From Glossary of Meteorology



line integral

The integral of a function along a given curve.

Mathematically, if s is a linear coordinate along the curve, the line integral of a function f(s) between points A and B on the curve is
ams2001glos-Le19
where f(s) is evaluated on the curve. The line integral of a vector field F along the same curve is
ams2001glos-Le20
where dr is a vector element along the curve of magnitude ds. In general the integral will depend on the curve; in the special case where the field F is irrotational, it depends only on the points A and B and therefore vanishes for a closed curve. In meteorology, line integrals are of frequent occurrence, for example, in the circulation, and in the averaging of a quantity along a latitude circle.


Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact permissions@ametsoc.org. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.