Del operator

From Glossary of Meteorology
Revision as of 12:56, 8 March 2017 by imported>Bcrose (→‎del operator)

del operator

The operator (written ) is used to transform a scalar field into the ascendent (the negative of the gradient) of that field.

In Cartesian coordinates the three-dimensional del operator is
and the horizontal component is
Expressions for in various systems of curvilinear coordinates may be found in any textbook of vector analysis. In meteorology it is often convenient to use a thermodynamic function of state, such as pressure or potential temperature, as the vertical coordinate. If the chosen function is σ, then
where differentiation with respect to x and y is understood as carried out on surfaces of constant σ (the subscript usually being omitted). The horizontal component is now
If the quasi-hydrostatic approximation is justified, as in most meteorological contexts, pressure is a useful coordinate, and
where g is the acceleration of gravity and ρ is the density. Here
with differentiation carried out in isobaric surfaces, and z is the horizontal gradient operator in Cartesian-altitude coordinates.

Term updated 8 March 2017.

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact 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.