Change in vertical wind intensity in atmospheric modeling
It really depends on whether you're model is hydrostatic or not.

If your model is hydrostatic, then the vertical velocity is found diagnostically. The diagnostic algorithm is called the Richardson Equation.

If your model is nonhydrostatic, often it is presumed that the vertical velocity is 0. The vertical velocity is presumed to be 0 (unless you do some spin-up or model restart, or some other special initialization), and the prognostic equation for vertical velocity is found.