You may shift the goalposts if you like buy I like to be precise in mathematical terminology. The fractral refers to the similarlity of the power law behaviour at all scales.
‘In this article, a multi-scale climate response model was fitted to temperature records encompassing time scales ranging from a year to a millennium. On assumption of the correctness of a strongly modulated solar irradiance (Shapiro et al. 2011) and by using recent data on SO2
emissions (Smith et al. 2011) the model provides tentative explanations for conspicuous trends in global average temperature from Middle Ages up to now (Figs. 5, 7a, b,8).’
21st century SO2 forcing is 0.1 W/m^2 – either from volcanic or anthropogenic aerosols. It is a little more complex for anthopogenic aerosols because of the interactions of sulphate and black carbon. http://www.nature.com/ngeo/journal/v3/n8/full/ngeo918.html
So it doesn’t explain the period for which there is the best data available. It is curve fitting – and as I say is reliant on knowing all of the forcing functions. This is obviously not the case. It doesn’t for instance reference the CERES data at all at the near scale and we don’t know about snow, ice and cloud going back to 1200AD. Don’t you see? The mathematics doesn’t change anything fundamentl about what is known about forcings. So tentative is entirely the correct interpretation. Claiming more than this is I am afraid just climate warrior claptrap.
This is indeed what Webby does – fits a power law to a curve. This paper is world’s more sophisticated. Webby’s relationships are hopelessly simplistic based always on some insanely misconceived conceptual model. Fat tailed ot thin tailed is entirely irrelevant is the context of a curve that is fitted by incomplete or incorrect forcing functions.