Jacobian

The determinant formed by the n² partial derivatives of n functions of n variables, when the derivatives of each function occupy one row of the determinant. For the case of two functions f(x, y) and g(x, y), the Jacobian J(f, g) is

sometimes also written

The geostrophic advection of any scalar ψ may be written

where g is the acceleration of gravity, f the Coriolis parameter, and z the isobaric contour height.