Chris suggested that maybe I should summarise yesterday’s discussion with Roger Pielke Sr. I may do that but I think I would first need to give it some thought, and I also need to catch my breath slightly. However, as suggested by KR, I have been playing around a little with MODTRAN. In case you don’t know, MODTRAN is a radiation transfer code that simulates the emission and absorption of infrared radiation in the atmosphere.
Using MODTRAN you can vary the type of atmosphere, the CO2 concentration, the methane concentration, the water vapour scale, and the ground temperature. I started with a Tropical atmosphere, a CO2 concentration of 280 ppm, a methane concentration of 0.8 ppb, a ground offset temperature of 0, and a water vapour scale of 1. These were chosen to roughly match the pre-industrial conditions. This gives an upward IR heat flux of 289.82 Wm-2 (which I’ll call the reference value). I then increased the CO2 to 390ppm and the methane to 1.8 ppb, and the upward IR flux decreased to 287.69 Wm-2. This is consistent with the IPCC’s anthropogenic forcings (about 2.2 Wm-2). I appreciate that there is much more than simply CO2 and methane involved, but this is the right ballpark (there are other positives and negatives, but they seem to roughly cancel).
I then increased the ground offset temperature to 0.85 to roughly match the surface warming since pre-industrial times. The upward IR flux increased to 290.76 Wm-2. This is greater than the reference value (289.82 Wm-2). In the absence of other feedbacks, this would imply the we should actually be above equilibrium and be losing more energy into space than we gain from the Sun. However, we actually have an energy imbalance of around 0.7 Wm-2 (i.e., the climate system is currently gaining, rather than losing, energy). This implies a net positive feedback of around 1.6 Wm-2. If I adjust the water vapour scale from 1 to 1.085, the upward IR flux drops to 289.13 Wm-2 (i.e., about 0.7 Wm-2 less than the reference value). So, to match the current conditions seems to require a positive feedback of around 1.6 Wm-2 which, if mainly water vapour, would imply an increase in water vapour of around 8.5% (I think).
I should make clear that I’m not suggesting this is some kind of definitive calculation. I have, however, tried some of the other atmospheres and I get the same basic result. There are, however, reasonably large uncertainties in some of the numbers, which I haven’t considered. This is, also, essentially a local calculation. Globally it is presumably much more complicated. The warming of the land and sea surface is different. There is polar amplification. However, a big part of the discussion with Roger related to positive feedbacks which – based on the IPCC numbers – he seemed to be suggesting were not yet operating. I was arguing that even the IPCC numbers indicated that positive feedbacks needed to be operating at a level similar to the level of the anthropogenic forcings. A fairly simple MODTRAN test seems to confirm this. Of course, I’m not an expert at this so if someone thinks that I’ve misunderstood something or used and interpreted MODTRAN incorrectly, feel free to let me know through the comments.