(These are the further notes and references that used to be on my home page, revised to recognize more clearly, for instance, the distinction between natural fluctuations in atmospheric CO2 and anthropogenic CO2 inputs.)
Note added 1 March 2014: I've recently found a more concise and cogent way of arguing the following points. It's now available in the form of a Postlude to a book in preparation.
The last numbered point in the little factsheet, `effects set to last for many millennia', can be put more plainly: on human timescales, the `added CO2', the CO2 we pump into the Earth system, will stay there forever in one or another of the chemical forms that affect climate. The old idea that atmospheric CO2 has a single, finite `lifetime' of the order of a few centuries, after which the system would revert to its pre-industrial state, is now recognized to be profoundly wrong.
The carbon cycle is complicated, and not all its details are accurately known. However, from chemical and geological evidence it seems very clear that some of the added CO2 is converted into what might be called `hidden CO2' within non-gaseous parts of the Earth system. This `hidden CO2' takes a multitude of forms including bicarbonate ions in the oceans and soils but excluding `passive', mineral carbon (coal, oil, kerogen, continental limestone etc). The total inventory of atmospheric CO2 plus `hidden CO2' -- for want of a better term I'll call it the total `active carbon' -- hangs around for many tens of thousands of years, with a portion of it recirculating through the atmosphere as CO2 gas along with certain other, less stable forms of active carbon such as methane, CH4. For practical purposes, tens of thousands of years is forever.
The evidence for timescales of this order is overwhelming, with no dependence on the big climate models used by IPCC. See for instance the 2005 Royal Society Policy Document on ocean acidification, and the clear discussion in this open-access paper published in 2008 one of whose authors, carbon-cycle expert David Archer, has also published in 2009 a short book of outstanding accessibility as well as importance, The Long Thaw: How Humans Are Changing the Next 100,000 Years of Earth's Climate. See especially pages 88-89 on the PETM (the Paleocene-Eocene Thermal Maximum), also page 25 of Challenged by Carbon by oil geologist Bryan Lovell, published early in 2010. Lovell's book gives a more detailed account of the PETM and its far-reaching implications, as seen by leading thinkers in the oil industry. The evidence now to hand is a powerful and sober answer to all the accusations of climate-model inadequacy and `climate alarmism'.
It's not always recognized that the Earth system acts as a slowly-responding amplifier, in its reaction to to the input of added CO2. Some scientists now call this input a `climate control knob' or, more precisely, the `CO2 control knob' of the climate system. An ordinary electronic amplifier responds to an input current that's smaller than the amplifier's internal currents. Similarly, though less promptly, the Earth system responds to the input of added CO2, even though larger amounts of water flow within the system and, in vapour form, produce a stronger greenhouse effect -- part of the amplifier mechanism. Contrary to what some `climate skeptics' like to suggest, water vapour behaves as an internal variable or `feedback', and not as an input variable.
CO2 is more complicated: it too behaves as an internal variable as well as an input variable, the input signal being the added CO2. So in the electronic amplifier analogy, the human input of CO2 is more closely analogous to taking a low-current internal feedback circuit within the amplifier -- a circuit that already carries internal fluctuations -- and connecting it to an input terminal through which a small but persistent current can be added, i.e., injected from outside. Realistically, one has to regard the notional `amplifier' as extremely noisy: unlike a good electronic amplifier it has a high level of spontaneous internal, or natural, fluctuations including fluctuations in the internal CO2 `circuit', or more precisely the active-carbon `circuit'. The most familiar such fluctuation is the large annual cycle due to exchange with land plants; and, as has been known for many years, there are others associated with interannual phenomena such as El Niño and large volcanic eruptions. We may safely assume that the whole biosphere is involved, animals as well as plants. The better known examples include cattle and termites as sources of methane, CH4, most of which is oxidized to CO2 within a decade or so, in the lower atmosphere.
(In a recent study that illustrates the above, Professor Murry Salby has presented evidence from satellite data, adding to a body of older evidence from Robert B. Bacastow and others, that interannual atmospheric CO2 fluctuations are highly correlated with surface temperature and soil moisture, and in such a way that the whole biosphere might produce an additional positive, global-scale feedback. This would add to the water-vapour and other feedbacks, further amplifying the long-term effects of the added CO2. Professor Salby has a different interpretation, with which I disagree. The satellite date shows fluctuations on timescales up to several years only; so whether this particular feedback might operate on longer timescales is an open question. Here is some relevant further discussion.)
There's another useful analogy with noisy electronic amplifiers. Over the past million years or more, long before we began adding CO2, the Earth's climate-system amplifier was responding mainly to another input. That was the input from small changes in the Earth's orbit. On the long, multi-millennial timescales of the orbital changes, positive feedback through the active-carbon circuit became very important indeed, essentially because on those timescales the circuit expands to include the deep oceans. Atmospheric CO2 concentrations swung back and forth between values within a range of about 180 and 290 ppmv (parts per million by volume), roughly every 100,000 years, as large amounts of active carbon flowed back and forth between the atmosphere and oceans. In round numbers, a 100 ppmv change in the atmosphere corresponds to just over 200 billion tons of carbon, or 800 billion tons of CO2.
The atmospheric CO2 concentrations over these timescales are well determined from air trapped in ice cores. (Here is a summary of why the ice-core-records are credible.) The accompanying climate changes were huge. Sea levels went up and down by hundreds of feet, again and again, as the great ice sheets responded. The surprisingly large magnitude of this response to a small orbital input must have depended on many things including poorly-understood ice-sheet dynamics and, crucially, the positive feedback from the active-carbon circuit. New insight into the workings of that sensitive part of the climate-amplifier circuitry -- including new information about the timings of changes in temperature and atmospheric CO2 that kick in after an orbital change -- can be found in an important recent paper by Shakun et al (2012), Global warming preceded by increasing carbon dioxide concentrations during the last deglaciation, Nature 484, 49-54, © Macmillan.
So if you think that our new input of added CO2 is small by any natural measure, then please think again. Our new input has already forced the atmospheric concentration far beyond its recent natural range of 180--290 ppmv. It has now risen past 400 ppmv. The atmosphere now contains well over 200 billion tons more carbon than it did in pre-industrial times. The total CO2 added from fossil-fuel burning and cement production is known from available statistics, and now corresponds to well over 300 billion tons of carbon, an order of magnitude that can account for the bulk of what's measured in the atmosphere with some left over to go elsewhere, such as the oceans. And this is happening with unprecedented rapidity. As a recent Science article puts it (15 Oct. 2010, Lacis et al, Science 330, 356-359, © AAAS), the CO2 control knob `is now being turned faster than at any time in the geological record'.
What's sometimes lost sight of in the complexities is what the Science article correctly emphasizes, and what I emphasize in my little factsheet: in the atmosphere CO2 is distinguished as the most important non-condensing greenhouse gas. Among all the non-condensing greenhouse gases that are found in the atmosphere, CO2 is by far the most abundant, and has the strongest warming effect. It is also the chemically most stable, as a gas in the atmosphere, apart from a few other gases such as perfluorocarbons that are present in relatively tiny amounts.
So what does all this mean for us humans? Fossil-fuel burning turns passive into active carbon. Unless we remove it the extra active carbon will stay forever in the atmosphere, plants, soil, and oceans, all of them critical parts of our life support system. Ways to slow the buildup of active carbon are set out in two more outstanding books. One is from an eminent scientist:  Sustainable Energy - Without the Hot Air by David J. C. MacKay FRS, free online at http://withouthotair.com).  MacKay's book documents the numerical magnitudes and makes it clear why, for instance, governments are reckless to favour short-haul air travel over rail travel. The other book is from an eminent economist:  Blueprint for a Safer Planet by Nicholas Stern.  Lord Stern argues that low-carbon economic growth is not only possible, but also commercially attractive -- a proposition endorsed by the high-powered business leaders in the `Carbon War Room', whose vision is that `entrepreneurial solutions to climate change... make economic sense right now.' The government of China has a similar vision, aiming for low-carbon leadership.
For more on the scientific and technical background, including the removal of active carbon, I recommend Fixing Climate: What Past Climate Changes Reveal About the Current Threat -- and How to Counter It by Wallace S. Broecker ForMemRS and Robert Kunzig. The main forum for serious public debate is the vast but valuable website www.realclimate.org.
Some accusations of `climate alarmism' invoke the climate-model inadequacies as if that somehow justified inaction. Yes, the models are inadequate. And in particular they cannot tell whether today's active-carbon burden is, or is not, already enough to send the Earth system into a new Eocene, with sea level rising slowly but unstoppably to more than 200 feet higher than at present. It simply isn't known.
Did I say unstoppably? There's one and only one safe way to stop it. We need to capture CO2 and reconvert it to passive carbon. Instead of tar-sand canyons we could have mountains of gleaming white limestone and dolomite. Simple, doable, and quite a tourist attraction. Seriously, take a look at the Royal Society report on geoengineering of 1 September 2009, especially pages 15-16 (pdf pages 29-30).