# Del operator

From AMS Glossary

## 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 where differentiation with respect to If the quasi-hydrostatic approximation is justified, as in most meteorological contexts, pressure is a useful coordinate, and where with differentiation carried out in isobaric surfaces, and

**∇**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*x*and*y*is understood as carried out on surfaces of constant*σ*(the subscript usually being omitted). The horizontal component is now*g*is the acceleration of gravity and*ρ*is the density. Here**∇**_{z}is the horizontal gradient operator in Cartesian-altitude coordinates.*Term updated 8 March 2017.*