The pause and its affect on temperature predictions

Yesterday I realised that I could work out the statistics of 1/f noise which is the form of natural variation (NV) we see in the climate. I worked out that this means that natural variation (NV) is more than likely going to tend to cool the climate. In contrast man-made warming (MW) will have the other effect. But which will dominate?
I have now realised that depending on the scale of Man-made warming and Natural variation, we get different predictions of the likely warming in the next decade.
So, this is my first rough calculation to try to understand how the different scale of MW and NV will have on our prediction of future climate. I hope to finish this with a nice conclusion along the lines of “if it cools next decade – this proves”…
Terminology

• NV – Natural variation
• MW – Man-made warming
• |NV| – the root mean square value
• v NV – the maximum value (or to be more accurate √2 x |NV| because this relates to a sin wave as a Gaussian has no theoretical limit). [ A v B apparently means “maximum of A & B]
• Where warming/cooling is given it is (roughly) equivalent to those stated by the IPCC in this statement:
  ” This range of implied radiative forcing gives rise to an estimated global warming from 1990 to 2100 of 1.4-5.8°C, assuming a range of climate sensitivities. ” (link)

I’m going to try to put some figures on these different scenarios. I will base these on the following assumptions:

• Based on 1970-2000 trend of 0.48C/30 years, the “unprecedented” trend was 0.12C/decade.
• The IPCC used a figure of ~1C for doubling of CO2 which equate to positive feedbacks of 1.4 to 6x.
• Although CO2 output is supposed to be exponential increase, effect of CO2 is logarithmic, so assume a linear relationship with time.
• I will calculate the effect of increasing NV by the effect on the rough mid point value of 3C/decade or 1C from CO2 and 3x feedback.
• The IPCC work using an out of date HITRAN database suggesting around 1C warming for a doubling of CO2. As I’ve repeated before, if the latest data for IR absorption is used, this figure comes down by around 30% to about 0.6C

Conclusion
This article took much longer than I expected, because typically natural variation creates a trend around 0 to 0.2C/decade. But this means a 0.2C/decade or 2C/century trend stopped trends that were supposed to go up to 6C.
Eventually, the only way I could make the figures stack up with MW lower than NV, was to significantly decrease the scale of MW using the Harde work showing about a 30% reduction in predicted CO2 effects.