sigma vertical coordinate

Two links below seem to on the same page. 

http://glossary.ametsoc.org/wiki/Sigma_vertical_coordinate

http://www.met.tamu.edu/class/metr452/models/2001/vertres.html

sigma vertical coordinate

A vertical coordinate for atmospheric models defined as pressure normalized by its surface value, or as the difference in pressure and its value at the top of the model atmosphere normalized by the surface value of this difference.

 

Thus, σ = (p - p_T)/(p_S - p_T) 

 

where p is pressure, and the subscripts T and S stand for the top and the ground surface values of the model atmosphere, respectively. 

 

p_S :  pressure on the ground surface

p_{T :}  pressure on the top of atmosphere

 

Range: [ 0 , 1 ]

_Benefits:

With the sigma coordinate, the lowest coordinate surface follows the model terrain, resulting in significant simplification of the equations compared to pressure or to an unmodified geometric height coordinate.  

 

 

What does "normalized" mean???

normalized : multiply (a series, function, or item of data) by a factor that makes the norm or some associated quantity such as an integral equal to a desired value (usually 1).