and this graph
Well, the idea is interesting enough. As I get it, the proposal is that ocean heat capacity allows small (fractions of a W/m2) variations in TSI to be integrated to produce a larger forcing. The oceans acting as enthalpy computers for cumulative small changes in solar variance. Something like that I guess.
The description on Tattersall's site is pretty minimal, but the impression I'm left with is that, whatever mathematical transformation was employed for the TSI data set, the form of the data in the end remains W/m2 for the TSI proxy and °C for Mann's data. That may explain why no units are provided on the y-axis; it should presumably be depicted as a double y-axis plot. If that's right, its important to note that the magnitude of change along the y-axis between the two data sets cannot be directly compared.
However, if you are a fan of this type of model, a more robust presentation can be found here; I had this bookmarked from something or other at some point.
http://climatechange90.blogspot.com/2013/05/natural-climate-change-has-been.html
Pangburn does a better job describing his approach for integrating TSI variance and how he goes about converting these differences to a temperature anomaly that can be compared to AGT data sets (see his Fig. 1 in the link). If you look at the equations what's notable is the use of several coefficients, the use of which he describes (in a slightly redacted form) as follows:
"A,B,C and D are calibration coefficients which have been determined to maximize the coefficient of determination, R2....some have mistakenly interpreted these coefficients to indicate mathematical curve fitting.....instead, the coefficients allow the rational estimation of the (contribution)...to the total temperature change".
One's consideration of the model obviously rests on how willing one is to buy this explanation. The coefficients are argued to derive from fundamental thermodynamic considerations, but, at the end of the day, they are still user defined values to make the curves fit. As described, there is nothing empirical about them, and the "integration" model (as well as much of the admittedly fun stuff produced by the I was right about the comet crowd) suffers, IMO, from this limitation. At some point, somebody has to propose an experiment.
At any rate, this idea has been around since at least 2008/2009. Cycle 24 is well underway and has been weak. If the entrainment between AGT and TSI/sunspot # variance is as tight as suggested in the model (Fig 1 in the link shows virtually no lag between changing TSI and changing temp) an obvious prediction seems to be that we should be observing considerable global cooling right about now. Although I would not be surprised if by proper adjustment of the coefficients in the equation one could produce a slower response to make it work.