## gradient

- The space rate of decrease of a function.

The gradient of a function in three space dimensions is the vector normal to surfaces of constant value of the function and directed toward decreasing values, with magnitude equal to the rate of decrease of the function in this direction. The gradient of a function*f*is denoted by -**∇***f*(without the minus sign in the older literature) and is itself a function of both space and time. The ascendent is the negative of the gradient. In Cartesian coordinates, the expression for the gradient isFor expressions in other coordinate systems, see Berry et al. (1945).

- Often loosely used to denote the magnitude of the gradient or ascendent (i.e., without regard to sign) of a horizontal pressure field.

Berry, F. A., E. Bollay, and N. Beers 1945. Handbook of Meteorology. 224–225.

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