ICON defines height-related variables against MSL (Mean Sea Level), e. g.
HHL - Geometric height of model half levels above msl [1]
There’re several height systems in geodesy using different reference surfaces (such as ellipsoidal, orthometric, normal height).
Following the definition of ellipsoidal and orthometric heights [2] I assume the ICON height (“geometric height … above MSL”) to be the ‘orthometric height H’.
Secondly, in order to get the ‘ellipsoidal height h’, as used by global geodetic coordinate frames and reported by GNSSs, the so-called ‘geoid undulation N’ needs to be added, like
h = H + N
Is this right?
References:
[1] D. Reinert, F. Prill, et.al. - “DWD Database Reference for the Global and Regional ICON and ICON-EPS Forecasting System”, Version 2.5.6
[2] Geoid - Wikipedia