Hey Scott,
'I don't dispute log functions as I don't know such math. I found my ability to function in maths is very limited.I make it a rule to not argue where I know too little.'
Log functions 'compact' either the x or y- values on a graph. You just change the scale of either. For example, the pH scale is log base 10, which means that if you want to alter the pH from 6 to 5 (keep in mind that a lower pH is more acidic), then you need 10x more free H+ than you had at pH 6. If you want to reach a pH of 4 from 6, you'd need 100X more free H+ than at pH 6.
CO2 and absorbance is a base 2 logarithm, meaning that if I want to get 2.2W/m/m more absorbance than I have at 420ppm, I'd have to double the [CO2] to 840ppm. If I want 4.4W/m//m extra, I'd need 1680ppm.
It's taken us since the industrial revolution to build from 280ppm to 420ppm. That's 140 molecules per million more than what we started with, which, by the way, is dangerously close to all-out plant death. Anyway, we haven't quite doubled it, yet, from its 'resting' state of 280ppm. How long would it take us to reach 1120ppm, which is four times 'resting' state? If we do get there, we could expect an extra 4.4W/m/m in the system, which is still negligible compared to how much energy reaches us (~1300W/m/m).
As to your other points:
The little ice age demonstrates climate change without anthropogenic influence. The fact that it's warmer since the little ice age is undeniable.
The urban heat island effect has nothing at all to do with the idea that it's the cities warming the planet. It has everything to do with the fact that it's causing localised warming to the thermometers fixed in expanding urban environments.
What I said about the Tongan volcano was that it definitely affects the system. All that extra H2O is significant. I guess I was also calling out the ABC for stating that the eruption could affect temperature for up to seven years one day, and then reverting back to blaming CO2 for everything the following day. Here's my perception of the ABC: For the next few years, they are doing a disservice to the taxpayers if they mention temperature fluctuations without reminding us about all the extra water in the system due to the Tongan eruption.
Q
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