Richard T. Wetherald and Syukuro Manabe calculated atmospheric radiative-convective equilibrium with a prescribed relative humidity distribution. Allowing the water-vapour content to adjust with temperature changed the sensitivity compared with fixing absolute humidity.[ref]
Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity by Syukuro Manabe and Richard T. Wetherald. 1967 Abstract: humidity assumptions and equilibrium sensitivity
The calculation demonstrates why a humidity constraint is a physical modelling assumption: it controls part of the radiative feedback as the atmosphere warms.
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