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Let me first explain a little more clearly what I'm trying to do by means of this bit of analysis, and then I'll try and and address some particular concerns.

First and foremost, I am trying to understand the temperature record of the previous millennium or so prior to the Industrial Revolution, a period which still saw substantial global surface temperature variability, but for which atmospheric CO2 was nearly constant (at 275 ppm). That constancy removes the effect of variable emissivity of the Earth + atmosphere (i.e., global warming considerations) from the equation. I do this because we now understand the magnitudes of all the other possible radiative forcings, and so we should be able to use this information to "calibrate" the response of the climate system to these known effects (thereby establishing the climate sensitivity).

My assumptions are this: (1) the Earth is in radiative equilibrium with solar insolation, at least on decadal or longer timescales, and (2) the Earth's climate is stable (in the strict physical sense that a small change in external conditions leads to a small change in climate outcomes, and not to a climate runaway). This means that the observed decadal temperature variability was *caused* by some change in radiative forcings -- these temperature changes didn't just occur without cause.

There are only a few ways that external forcings can result in variations in radiation absorbed by the Earth: (1) intrinsic solar variability, (2) variations in the Earth's orbit, (3) variable transmission of the Earth's atmosphere (due to aerosols), (4) variable albedo of the Earth's atmosphere + surface, and finally (5) variable emissivity of the Earth + atmosphere due to greenhouse gases. The latter is constant for this period.

Volcanoes put aerosols into the atmosphere but these are flushed out after about 2-3 years, resulting in a short-term effect only. The strongest example in the past 1000 years was probably the Tambora eruption of 1815. In this analysis, I only consider effect lasting a decade or longer, so the impact of volcanic activity can be ignored.

I assume that albedo variations are unimportant, except as part of feedbacks due to other effects. So, e.g., an increase in snow cover due to solar cooling would be viewed as a feedback to solar forcing and not an albedo effect.

The climate trend since the Holocene Climatic Optimum around 7000 BC has been that of a slow cooling trend but with substantial decadal variability superimposed. I assume that the slow trend is due to orbital forcing -- the timescale and direction are correct. That leaves only intrinsic solar variability to explain the shorter, decadal variations, so I explicitly assume that these are of solar origin. There does seem to be correlation (but the data are limited) of historical global temperature with sunspot activity, and longer term temperature reconstructions correlate with Be^10 isotope ratios (a measure of cosmic ray flux, which anticorrelates with solar activity).

The Schroeder et al. paper establishes the Maunder minimum (MM) TSI at about 1360 W/m^2, and therefore the range of peak-to-peak (or more accurately, peak-to-trough) TSI at about 2 W/m^2. Interestingly, the short 11-yr solar cycle does not appear to leave its imprint in the climate record (although, it has been speculated for many years that this cycle drives the ENSO cycle -- mostly because no-one really understands ENSO and the period is similar to that of the solar cycle). Instead, it is the longer 90-yr grand solar cycle that shows up in the climate record.

SO I examined the 1000 years of temperature data from 800 to about 1850, and here I used the reconstruction of Mann et al. (2008), which has the drawback of being only northern hemisphere data, and so probably slightly overestimates the actual global effect. Fig 3 of Mann et al. is here:

The mean of the reconstructed temperatures range from a minimum of about -0.6 C in the depths of the LIA around 1700 AD to about maximum of about -0.1 C in the MWP around 1000 AD (with a lot of scatter between the reconstructions), where the zero point is the temperature in 1950. [Sorry, Loren, I do actually make use of the LIA/MWP here!]. That gives me the peak-to-trough range of 0.5 C. This actually isn't that different from the 0.1-0.15 C effect others mentioned. Dividing the peak-to-trough range by two to get an amplitude yields 0.25 C. If a standard deviation was used instead of a peak amplitude that would further reduce the value to about 0.15 C. Finally, allowing for global instead of northern hemisphere temperatures might further reduce this value to 0.10-0.12 C. I don't do this here because I don't readily have these figures available -- the Pages 2K temperature reconstruction (Nature Geoscience, 6, 339: May 2013) does include the southern hemisphere (but not the oceans yet) but you still need to combine these data to get an overall land effect.

Loren is also correct in that, properly, a regression analysis should be carried out instead of simply comparing peak-to-trough quantities, as I have done. The reason I didn't do this regression of TSI vs global temperature (or, at least, vs northern hemisphere temperature) is because this requires a TSI reconstruction. (Directly measured TSI data only go back about 3 decades, and even compiling a consistent dataset from the different satellites has been the subject of much controversy). I don't trust the available reconstructions fully,although many look reasonable, because none make use of the Schroeder et al. Maunder minimum TSI result. But I now know the TSI range (2 W/m^2), which allows me to carry out the present peak-to-trough analysis, but then I need to use comparable peak-to-trough temperatures from the Mann et al. reconstruction (the 0.5 C range).

As Loren points out, the ratio of the observed 0.5 C range to that calculated from radiative equilibrium from the TSI range (0.11 C) gives an estimate of the total multiplicative (short-term) feedback ratio: 0.5/0.11= 4.55. This is probably an overestimate because of the use of only northern hemisphere temperature data. If I had to estimate, I would say that the overall global temperature response would probably be about 2/3 of that of the northern hemisphere, or about 0.35 C peak-to-trough over the 800-1800 AD period. That gives a smaller feedback ratio of 0.35/0.11= 3.2.

One simple way of comparing to the standard CO2 climate sensitivities is to assume that the forcing due to CO2 affects the climate system in a similar way to the other forcings. The direct effect on global temperature due to doubling CO2 alone (from radiative transfer models) is about 1.1 C. Multiplying this direct CO2 sensitivity by the above feedback ratio of 3.2 gives a total climate sensitivity (including all the short-term feedbacks) of about 1.1*3.2= 3.5 C for doubling CO2. So the climate sensitivity derived assuming the short-term, pre-industrial decadal temperature variability was of solar origin agrees with the IPCC climate sensitivity of 2 to 4.5 C. The overall consistency of this result provides confirmation that the pre-industrial decadal temperature variability was mostly due to intrinsic solar variability.

Sorry for the lengthy post, but I think this is an interesting result.

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