I haven’t done a Watt about post for quite some time, so thought I would repeat it just this once. Roger Pielke Sr has guest post on Watts Up With That claiming to present seven very inconvenient questions that Gavin Schmidt is too afraid to answer (yes, I’m going to link to WUWT, deal with it 
). I’ll ignore the whole rather bizarre “you’re the head of a publicly funded organisation, therefore you need to respond to these questions” framing, and simply address one of Roger’s questions.
Roger refers to a Climate Etc. post, where he discusses an alternative metric to assess global warming. Basically, he just does a simple energy balance calculation which he casts as
Global annual average radiative imbalance [GAARI] = Global annual average radiative forcing [GAARF] + Global annual average radiative feedbacks [GAARFB] (2)
He uses Levitus et al. (2012) to infer a GAARI, since 1955, of 0.39Wm-2 ± 0.031 Wm-2, which is for the oceans only, so it’s increased by 10% to give 0.43Wm-2 ± 0.031 Wm-2. The radiative forcing (GAARF), since 1750, is 2.29Wm-2 (1.13 to 3.33 Wm-2). Since 1950, this becomes 1.72Wm-2. The radiative feedbacks he essentially takes from Soden et al. (2008) and considers the Planck response, water vapour, clouds, and albedo. Together, they sum to -1.21Wm-2K-1. The change in temperature since 1955 is about 0.6K, which gives a net feedback response of -1.21Wm-2K-1 x 0.6K = -0.73Wm-2.
Therefore we have a GAARF of 1.72Wm-2 and a GAARFB of -0.73Wm-2. If we sum these we get 1.72 – 0.73 = 0.99Wm-2, which Roger points out is about twice as large as the value estimated from Levitus et al. (2012). This was one of the things that Roger highlights and asks for Gavin’s best estimates for these terms.
So, why is there an apparent discrepancy between the system heat uptake rate estimated using an energy balance approach, and that estimated from ocean heat content measurements? Well, Roger appears to have made a number of mistakes in his calculation. Firstly, he did not correct for the fact that the oceans are only 70% of the surface. Secondly, it shouldn’t be the global average radiative imbalance, it should be the change in radiative imbalance over the time interval considered (i.e., the difference between what it is at the end of the time interval, and at the beginning). In the most recent decade, Levitus et al. (2012) suggest a radiative imbalance of 0.7Wm-2 (full surface plus increased by 10%). During the earliest decade (1950s) it was probably about 0.2Wm-2. So, the change is around 0.5Wm-2. Roger also forgot to include lapse rate feedback, which – according to Soden et al. (2008) – is probably around -0.75Wm-2K-1. So the feedback is actually -1.96Wm-2K-1, giving a net feedback response of -1.96 x 0.6 = -1.176Wm-2. Combining that with the change in external forcing gives 1.72 – 1.176 = 0.544Wm-2, pretty much the same as that estimated from Levitus et al. (2012). Of course, I’ve just eyeballed some of the numbers, and there are uncertainties to consider, but it certainly seems as though one can come close to reconciling the model-based estimates, and the observations.
So, I think that clears up one of Roger’s questions. The reason for the discrepancy is – I would suggest – simply because Roger’s calculation isn’t correct, not because there really is some kind of major discrepancy between model estimates and observations. Apologies, of course, to Gavin for butting in
Edit and acknowledgement: I’ve just realised – and Chris Colose has confirmed – that the temperature feedback includes the lapse rate, so Roger’s feeback estimate is about right. However, I still maintain the the correct radiative imbalance is the difference between what it is at the end of the time interval and at the beginning, not the average over the time interval. Hence, the discrepancy is not quite as great as Roger’s calculation suggests.