Sigma coordinate system

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

σ

{\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.

Description

Pressure at a height

p

{\displaystyle p}

may be scaled with the surface pressure

p

0

{\displaystyle p_{0}}

, or less often with the pressure at the top of the defined domain

p

T

{\displaystyle p_{T}}

. The sigma value at the scale reference is by definition 1: i.e., if surface-scaled,

σ

0

=

1

{\displaystyle \sigma _{0}=1}

.

In a sigma coordinate system, if the sigma scale is divided equally, then at every point on the surface, each horizontal layer above that point has the same thickness in terms of sigma, although in terms of metres each next higher equal sigma-thickness layer is thicker than the previous one. The sigma-thickness of each layer decreases with surface altitude, the sigma-levels being compressed together (in terms of metres) as the total vertical range is reduced.

The sigma coordinate system allows sigma-surfaces to follow model terrain; where terrain is sharply sloped, so are the sigma surfaces. This allows for continuous fields, such as temperature, to be represented especially smoothly at the lowest layers in the model. Further, with the exponential decaying nature of density within the atmosphere, sigma coordinates provide a greater vertical resolution (in terms of metres) near the surface.