# Surface integral

From Glossary of Meteorology

## surface integral

In rectangular Cartesian coordinates, the integral where

*f*(*x*,*y*,*z*) is a single-valued continuous function of*x*,*y*and*z*in a region in which*S*is a surface given by*z*= φ(*x*,*y*), and*R*is the projection of*S*on the*xy*-plane.Similar surface integrals exist over surfaces where

*x*= φ(*y*,*z*) and*y*= φ(*z*,*x*). In vector notation the surface integral of a single-valued continuous vector**F**over the surface*s*can be written**n**is an outward directed unit vector normal to the surface. The surface integral for a closed surface may be related to a volume integral by the divergence theorem.*See*line integral.