# Sigma vertical coordinate

From AMS Glossary

## 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. 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.*See*eta vertical coordinate, hybrid vertical coordinate, isentropic vertical coordinate, pressure vertical coordinates, height vertical coordinate.