![Sigma-z-coordinates](https://upload.wikimedia.org/wikipedia/commons/a/a1/Sigma-z-coordinates.svg)
The sigma coordinate system is a common coordinate system used in computational models for
oceanography
Oceanography (), also known as oceanology and ocean science, is the scientific study of the oceans. It is an Earth science, which covers a wide range of topics, including ecosystem dynamics; ocean currents, waves, and geophysical fluid dynamic ...
,
meteorology
Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...
and other fields where
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...
are relevant. This coordinate system receives its name from the independent variable
used to represent a
scaled pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
level.
Models that use a sigma coordinate system include the Princeton Ocean Model (POM), the COupled Hydrodynamical Ecological model for REgioNal Shelf seas (COHEREN
the
ECMWF
The European Centre for Medium-Range Weather Forecasts (ECMWF) is an independent intergovernmental organisation supported by most of the nations of Europe. It is based at three sites: Shinfield Park, Reading, United Kingdom; Bologna, Italy; an ...
Integrated Forecast System The Integrated Forecasting System (IFS) is a global numerical weather prediction system jointly developed and maintained by the European Centre for Medium-Range Weather Forecasts (ECMWF) based in Reading, England, and Météo-France based in Toulous ...
, and various other
numerical weather prediction
Numerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in th ...
models.
Description
Pressure at a height
may be scaled with the surface pressure
, or less often with the pressure at the top of the defined domain
. The sigma value at the scale reference is by definition 1: i.e., if surface-scaled,
.
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. The sloping nature of the coordinate surfaces does require additional interpolation of the pressure gradient force, and the smoothing of terrain can often cause it to extend beyond the true boundaries of land.
Sigma coordinate hybrids
Hybrid sigma-pressure
Some atmospheric models use a hybrid sigma-pressure coordinate scheme, combining sigma-denominated layers at the bottom (following terrain) with
isobaric
Isobar may refer to:
* Isobar (meteorology), a line connecting points of equal atmospheric pressure reduced to sea level on the maps.
* Isobaric process
In thermodynamics, an isobaric process is a type of thermodynamic process in which the pr ...
(pressure-denominated) layers aloft. The isobaric upper layers are generally more numerically tractable (since flatter), and specifically more tractable for
radiative transfer
Radiative transfer is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission, and scattering processes. The equation of radiative tran ...
calculations (important for
assimilating satellite radiance observations). Some models (e.g., the 2009 NAM) have a pure sigma domain at the bottom and a fixed transition level, above which all layers are exactly isobaric. Other models (e.g., GFS) gradually transition from sigma to isobaric.
Hybrid sigma-density
Some oceanographic models uses coordinates which similarly transition from
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
(
isopycnic
An isopycnic surface is a surface of constant density inside a fluid. Isopycnic surfaces contrast with isobaric or isothermal surfaces, which describe surfaces of constant pressure and constant temperature respectively. Isopycnic surfaces are so ...
) to sigma coordinates in shallow
coastal shelf
A continental shelf is a portion of a continent that is submerged under an area of relatively shallow water, known as a shelf sea. Much of these shelves were exposed by drops in sea level during glacial periods. The shelf surrounding an island ...
regions.
References
{{reflist
Synoptic meteorology and weather
Oceanography
Numerical climate and weather models