Vaughan Pratt, : Springer raises a good point. The crucial question here is whether this decrease in lapse rate driven by increasing absolute humidity (quantity of water vapor) overwhelms the greenhouse effect or is too tiny to be significant.
The theoretical decrease in lapse rate for a global warming (increase in surface temperature) of 10 °C is plotted on the left of Figure 5 of An Analytical Model for Tropical Relative Humidity by David Romps, J. Climate, 27, 7432-7449 (1 Oct. 2014). Romps plots two cases: no evaporation of precipitation (α = 0), and 50% evaporation (α = 0.5).
thank you for the link to the Romps paper
From the abstract: An analytical model is derived for tropical relative humidity using only the Clausius–Clapeyron relation, hydrostatic balance, and a bulk-plume water budget. This theory is constructed for radiative–convective equilibrium and compared against a cloud-resolving model. With some reinterpretation of variables, it can be applied more generally to the entire tropics.
The principle limitation of these lapse rate computations is that they are based on a thermodynamic equilibrium (C-C) that never exists. There is a persistent transfer of energy and water (hence latent energy) from the surface to the upper troposphere via evaporation and wet thermals, and none of the models is a model of that rate of energy and water transport. The total energy transported that way, evapotranspiration, is greater than the energy transported by radiation (Stephens et al, Trenberth et al energy flow diagrams), so the omission is non-negligible. How that transport changes with CO2 or temperature change has hardly been studied. The Romps et al science paper on changes in lightning strike rate is just one of only a few beginnings. The C-C approximation is not necessarily always bad (may be good on cool, sunny, cloudless days), but it is wretched when there are squalls, thunderclouds, and rain storms — i.e. when the rate of non-radiative transfer of energy from surface is greatest.