Indeed, there isn't, moreover the processes are not linear. You could compare the double effect of heating and cooling with a tap opening a bit more (heating) to fill a bucket with a hole in the bottom, which we make a bit bigger (cooling). there is no way to tell what the water level is going to do, without quantification.
Although you could quantify both warming and cooling rates logaritmically proportional to the density of the greenhouse gas, but quantifying the increase in convection rate would be rather complicated especially when the role of water evaporation and condensation is taken into consideration.
It may be noted that problems in the basic mechanisms of the greenhouse idea have been signalled by Miskolsci here
as well as Douglass et al here
Bottom line however from the study remains that it makes a case that the atmosphere is primarily heated by convection instead of radiative effects. It appears that this would reduce the effect of radiative forcing heating or greenhouse effect considerably.