So, a whole lot of hot air has passed, and maybe the dust is starting to settle. Mt noted that the Klotzbach et al work is "Pielkes all the way down", and several references have been made to the Pielke and Matsui 2005 paper which underpins a lot of this work. Mention of this prompted a distant memory, so I checked my mailbox (amazing the power of computers to recover old memories these days). I also re-read the PM05 paper more critically, in light of its current relevance and the previous emailed comment.
Well, well. That was...enlightening.
PM05 examines the near-surface lapse rate that arises on calm and windy nights, with a simple one-dimensional analytical model. They further calculate the changes in lapse rate as the cooling rate varies.
In all this work, they apply the radiative cooling at the surface, even though they explicitly portray this forcing as being representative of the effect that arises from a change in GHG concentrations. Standard climate theory holds that the radiative forcing is applied the top of the atmosphere - indeed this is the level at which the forcing is defined. It is simply wrong to claim that a doubling of CO2 will generate a forcing of 3.7Wm-2 at the surface, for example.
The startling impact of this odd application of "bottom of the atmosphere" forcing is apparent from their Table 1. A change in this "forcing" of a mere 1Wm-2 leads to a temperature difference of a whopping 1.5C (at the 2m level) over a single calm night! This is the simple result of applying 1Wm-2 of cooling to the fairly shallow layer at the bottom of the atmosphere, which has relatively low heat capacity due to its shallowness.
Consider a simple thought experiment. Start with a pre-industrial atmosphere, wait for a calm night, and instantaneously double the CO2 level. According to PM05's interpretation of GHG forcing, this will result in a temperature rise of about 6C (compared to the unforced case) in the space of 12 hours. This simply doesn't pass the sniff test, not by a million miles. It's not just wrong, it's several orders of magnitude wrong!
Remember, PM05 is the celebrated theoretical underpinning for this entire night-time warming edifice.
For the standard approach, check out this article which compares various radiation models. Here's their plot of depth-varying warming rate due to an increase in GHGs (from 1860 to 2000 values) holding everything else constant:
Note the warming rate is basically uniform in the bottom 200hPa of the atmosphere, in stark contrast to the PM05 assumption that the forcing acts at ground level. Thus, a large increase in GHGs generates a warming rate of about 0.04K per day across the boundary layer, as compared to the Pielkian ~1K over a single night (depending on wind speed).
This paper (pdf here), co-authored by all the big names in the field, ("The radiative effects from increased concentrations of well-mixed greenhouse gases (WMGHGs) represent the most significant and best understood anthropogenic forcing of the climate system.") has essentially the same plot in their Figure 12. There does not appear to be the slightest bit of debate over this subject.
So I don't think that the PM05 calculations can have any relevance to the response of the lower part of the atmosphere to changes in GHG forcing.