Sigma coordinates

The sigma coordinate system is a common coordinate system used in computational models for oceanography, meteorology and other fields where fluid dynamics are relevant. This coordinate system receives its name from the independent variable ${\displaystyle \sigma }$ used to represent a scaled pressure level.

Models that use a sigma coordinate system include the Princeton Ocean Model (POM), the COupled Hydrodynamical Ecological model for REgioNal Shelf seas (COHERENS)[1], the ECMWF Integrated Forecast System, and various other numerical weather prediction models.

Pressure at a height ${\displaystyle p}$ may be scaled with the surface pressure ${\displaystyle p_{0}}$, or less often with the pressure at the top of the defined domain ${\displaystyle p_{T}}$. The sigma value at the scale reference is by definition 1: i.e., if surface-scaled, ${\displaystyle \sigma _{0}=1}$.

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