Omega equation

The omega equation is a culminating result in synoptic-scale meteorology. It is an elliptic partial differential equation, named because its left-hand side produces an estimate of vertical velocity, customarily expressed by symbol $\omega$, in a pressure coordinate measuring height of the atmosphere. Mathematically, $\omega ={\frac {dp}{dt}}$, where ${d \over dt}$ represents a material derivative. The underlying concept is more general, however, and can also be applied to the Boussinesq fluid equation system where vertical velocity is $w={\frac {dz}{dt}}$ in altitude coordinate z.