Firstly, your links on historic sea ice are interesting for an on topic discussion of how far north and west Holland's destroyers had to search. I can quite easily believe that the pack ice limit marked on our maps of the Bismarck sortie were copied from data from just before the map was drawn rather than from May 1941 data (note that the pack ice limit should be further north and west of the limit of drifting sea ice, which interests climatologists but which Bismarck could possibly sail through).
Secondly, I have learnt a few things about the science of climate change over the last week for which many thanks to the other posters, which I may try to explain below but, alas, without many references (I suspect Dave understands most of it but it may carry this a little further). Unfortunately, there is still a great deal well beyond the competence of this retired biochemist.
I remain convinced that the observed warming over the last forty years (the period for which we have good satellite data) is real. There was one site that pointed out that simply moving heat from the Southern Hemisphere to the North would raise global average temperatures because more of the South is ocean but the warming is seen in both hemispheres and is also seen if we look just at sea surface temperatures.
The clearest signal that this is due to greenhouse gases is the warming of the troposphere together with a slight cooling of the stratosphere which suggests that that Earth has put on a slightly thicker overcoat. If we were seeing something caused by a change in solar flux, the stratosphere would be warming rather than cooling, which is a good job because direct measurement suggests that the Sun has kept the same average radiance over the last three sunspot cycles (the Sun does vary about 0.1% over a sunspot cycle, which excites some sceptics but that can probably be ignored if it averages out).
As an aside, one reason that this debate is so difficult is that global warming involves so many different fields from measurement of sea ice to solar physics to infrared spectroscopy. Clearly nobody understands everything that is going on.
The actual “greenhouse effect” is also not quite obvious. Sunlight hits the ground or the sea and may be reflected or absorbed. If it is absorbed, the surface becomes hotter and emits more infrared radiation. Although the atmosphere is mostly nitrogen, oxygen and argon, none of those absorbs infrared. Thus, only gases such as water vapour, carbon dioxide, methane and ozone can absorb infrared and also liquid water in clouds, which I understand not at all. I am probably unusually happy about that point as I can remember sleeping through lectures about fifty years ago where the lecturer explained that the symmetric modes were only in Raman Spectroscopy whilst the asymmetric modes were seen in an infrared spectrum and I measured some infrared spectra in practicals. After the gases absorb the heat, they swap it by collision and also re-radiate it up or down as well as carrying the heat up or down by convection (mostly up).
The water vapour is by far the most important greenhouse gas as it is on average at a much higher concentration. However, there are windows of frequencies that water vapour cannot absorb. Carbon dioxide has a strong effect despite being at only about 400 ppm because it partially blocks some of the windows, catching radiation that would otherwise escape towards space. Methane similarly blocks some extra windows. Thus, although one can talk about a "forcing" due to either CO2 or methane alone, you actually get the strongest greenhouse effect with a mixture. The scientists don't like to talk about a forcing due to water vapour because while CO2 lasts over a century and methane years or decades, water vapour only last on average 14 days in the atmosphere. Thus, the models need to calculate how much water vapour is present and also what is happening to clouds limiting my understanding. However, one point is that raising the concentrations of the absorbers together will keep the heat nearer the ground than simply having one gas at high concentration and leaving windows in the spectrum to let the heat out.
Thus, I hope that I have explained why any calculation depends on models that are sufficiently complex that they can easily hide the biases of their creators. We cannot escape using such models and they will always fit the data used to design them. We can only hope that the code is published and hope that biases can be removed. However, any good model should predict the observed warming from 1980.
The most optimistic article that I found today was at http://www.innovations-report.com/html/ ... event.html
and suggests that 50 million years ago, 2000 ppm of CO2 only raised the temperature about 5º C. Of course, the Sun was not quite so bright then but hopefully we may escape some of the runaway greenhouse events leading to Venus like conditions.
Unfortunately, even more limited temperature rises may make it unwise to buy land in Florida or worse the Maldives unless you are hoping to run a SCUBA school.