Thus, the change in ocean heat storage with time can be used to calculate
the net radiative imbalance of the Earth (Ellis et al., 1978; Piexoto and Oort, 1992).
The Levitus and Pielke papers show that averaged out for these types of time intervals (> 1 year), this analysis provides a snapshot of
the net radiative imbalance at the top of the atmosphere.
Not exact matches
That's far from the worst flaw in his calculation, since his two biggest blunders are the neglect of the
radiative cooling due to sulfate aerosols (known to be a critical factor in the period in question) and his neglect of the many links in the chain of physical effects needed to translate a top of atmosphere
radiative imbalance to a change in
net surface energy flux
imbalance.
This means that there has been very little actual global warming (or
net TOA
radiative imbalance) in these seven years.
Some of that would result also in a change in the radiation to space, and in particular a change in the
net top of atmosphere
radiative imbalance.
What we're talking about here is basically the amount of unrealized warming, whereas the
radiative forcing tells you the total
net energy
imbalance since your choice of start date (the IPCC uses 1750).
The
radiative forcing (IPCC 2007) is about 1.6 W m − 2 for both carbon dioxide increases alone and also the total with all other effects included (0.6 — 2.4 as 95 % confidence limits), and the
net energy
imbalance of the planet is estimated (Trenberth et al. 2009) to be 0.9 ± 0.5 W m − 2.
You would do better to discuss why FG were not sure of their result for various practical reasons, e.g. the
net radiative flux
imbalance at the top of the atmosphere has only been measured for a very short time, and their study doesn't include albedo forcings from melting ice — if you're actually as interested in their results as you pretend to be.
Irrespective of what one thinks about aerosol forcing, it would be hard to argue that the rate of
net forcing increase and / or over-all
radiative imbalance has actually dropped markedly in recent years, so any change in
net heat uptake can only be reasonably attributed to a bit of natural variability or observational uncertainty.
The TOA
imbalance minus the
net surface flux (from * all * fluxes, latent,
radiative, etc.) gives the rate of change of the atmospheric energy content.