Eta vertical coordinate

From Glossary of Meteorology

eta vertical coordinate

A vertical coordinate for atmospheric models defined with a steplike representation of topography, having mountains formed of grid boxes of the model.

The vertical coordinate surfaces are quasi-horizontal, intersecting model mountains or forming their nearly horizontal upper sides. It is defined by
where p is pressure; the subscripts T and S stand for the top and the ground surface values of the model atmosphere, respectively; z is geometric height; and pref(z) is a suitably defined reference pressure as a function of z. The ground surface heights zS are permitted to take only a discrete set of values, those of elevations at which the interfaces of the chosen model layers are located when pressure is equal to the reference pressure pref(z). The "Eta Model" using the eta coordinate became the primary short-range operational forecasting model of the U.S. National Weather Service in 1993.
See sigma vertical coordinate, isentropic vertical coordinate, hybrid vertical coordinate, vertical coordinate system.