Goemetric height at high altitudes (WACCM-X)

[fvitt]

Issue Type

Other (please describe below)

Issue Description

From Hanli Liu:

I went through the derivation again and here are the correct formulations:

(1) Z_gm = 1/(1 - (1+Zs/r) * Z_gp/r) * (Zs + (1+Zs/r) * Z_gp)

Z_gm: geometric height Zs: Surface height Z_gp: model calculated geopotential height (zm and zi in the model)

If we assume Zs/r << 1, then (2) Z_gm ~= 1/(1 - Z_gp/r) * (Zs + Z_gp)

The worst violation is over Mt Everest is 8.8/6370 = 1.4e-3, so this is not a bad assumption. The formulation in ionosphere_interface.F90 Francis sent yesterday is: (3) Z_gm = (1 + Z_gp/r) * (Zs + Z_gp).

To the first order 1/(1-Z_gp/r) ~ 1+Z_gp/r, the error is about 10% at 600 km (1.104 and 1.094 respectively)

I would suggest using either (1) or (2) in the model for calculating Z3GM.

Will this change answers?

I Don't Know

Will you be implementing this yourself?

Yes