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^[1] expressed by symbol ${\displaystyle \omega }$, in a pressure coordinate measuring height the atmosphere. Mathematically, ${\displaystyle \omega ={\frac {dp}{dt}}}$, where ${\displaystyle {d \over dt}}$ represents a material derivative. The underlying concept is more general, however, and can also be applied^[2] to the Boussinesq fluid equation system where vertical velocity is ${\displaystyle w={\frac {dz}{dt}}}$ in altitude coordinate z.