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sigma coordinate system : ウィキペディア英語版
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 \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)(), the ECMWF Integrated Forecast System, and various other numerical weather prediction models.
==Description==

Pressure at a height p may be scaled with the surface pressure p_0, or less often with the pressure at the top of the defined domain p_T. The sigma value at the scale reference is by definition 1: i.e., if surface-scaled, \sigma_0 = 1.
In a sigma coordinate system, if the sigma scale is divided equally, then at every point on the surface, each vertical layer above that point has the same thickness. The thickness of each layer decreases with surface altitude, being compressed together as the total vertical range is reduced.
The sigma coordinate system allows 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 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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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