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 , in a pressure coordinate measuring height the atmosphere. Mathematically, , where 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 in altitude coordinate z.
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