I would hope that Joss Hagallaar’s graphic and my more wordy version speak for themselves and you can go to the science for more.

As to policy, my graphic in part tries to show that we are, right now, making critical choices that will affect the amount of greenhouse gases that will add to the accumulation of CO2 in the atmosphere that causes global warming. Certainly, the current path means there is a very high risk of extremely dangerous warming of 4ºC above pre-industrial temperatures, strongly indicating that radical emissions reduction is needed from now on, especially beginning immediately in wealthy countries.

For more look at the research of Kevin Anderson and Alice Bows.

]]>How does your graphic of the latest science inform policy?

]]>changed last line in “Ess. Facts” plus other minor stuff:

https://docs.google.com/file/d/0B5NgIqKD_aX4aFdHZnRodVQtTVE/edit ]]>

Many thanks to both of you for all of your help, especially in resolving my lin/log confusion. Now I understand the basic compensation reason but I will try to get into reading the references you have kindly given me.

Somehow messaging climate to citizens and policy makers needs to get better so by working on it together like this we can hopefully improve that communication.

Here is a link to a new draft, https://docs.google.com/file/d/0B5NgIqKD_aX4RmxjUXFjYkQxaWM/edit?ups=drive_web

As you can see it has taken a few hours (obviously it is intended as a Commons effort).

Inevitably this poster/graphic is a balance between too much and too little information especially as the intention is too convey the science to people who, like myself, not fully aware of the detailed climate science.

The presentation in this draft is ‘doomy’ but it seems to be what the science is saying in precautionary terms. If either of you have suggestions, corrections, thoughts I would welcome them. For example, temp anomaly date range may be wrong on left hand side of chart. Warming dates are from Stocker, 2012 as above.

Thanks again,

Paul

]]>This is a good on-line textbook that should help clarify the kinds of questions you have: http://www.climate.be/textbook/index.html

The quote you give is about total (i.e. integrated over time; cumulative) amount of CO2 emitted being proportional to eventual T-rise. That is correct, and has been found by multiple authors (e.g. Nature Climate Crunch few years ago, Allen et al, Meinshausen et al). If you talk about “emissions” sec, I interpret that to mean instantaneous emissions, and in that case it is not at all correct.

]]>When doing calculations with gigatonnes of carbon, you must keep in mind that 1 Gt carbon comes down to 1 * 44/12 = 3.7 Gt CO2 (the difference in molecular mass).

Also from the weight of the atmosphere it can be calculated that 1 ppm CO2 relates to ~2.13 Gt carbon or 7.81 Gt CO2.

From the abstract it follows that Matthews et al takes the carbon cylce response into account: how much of the emitted CO2 is absorbed by oceans or used for the growth of the trees/plants when the temperature and CO2 concentration will go up. But probably also an estimate is made of the amount of CO2 that will be released by the warming of the permafrost et cetera.

I can’t tell exactly how they reach their results: for every trillion tones of carbon emitted there is an increase of 1 to 2.1 °C independent from the background CO2. Doing some math:

1000 Gt carbon = 1000/2.13 = 470 ppm CO2. Assuming that about 50% is taken up by the ocean+land sink, the increase in CO2 is 235 ppm from 280 ppm in pre-industrial times, which comes down to ~515 ppm CO2 total.

Meinshausen et al mentions 1000 Gt / 1440 Gt CO2 above the 2000 level when I’m correct. This comes down to 50% of 128/184 ppm = 64/92 ppm CO2 above the 2000 level of 370 ppm or ~434/462 ppm CO2 total. Roughly comparable to Matthews.

The relationship between CO2 and the amount of energy (and therefore temperature) it adds to the atmosphere is logarithmic as Bart says. It is described by this formula for the change in forcing with reference to a starting CO2 concentration: dF = 5.35 * ln(CO2/CO2-start) in W/m2.

A doubling in CO2 means CO2/CO2-start = 2, this comes down to 3.71 W/m2 per doubling of the CO2 concentration in the atmosphere. Taking all the feedbacks into account, which amplify or reduce the CO2 effect, you will end up with a rise in temperature of 2 – 4.5 °C per doubling of the CO2 concentration. This 2 – 4.5 °C is the equilibrium climate sensitivity and it will take a while until equilibrium is reached, centuries to millennia. See this RealClimate post: http://www.realclimate.org/index.php/archives/2013/01/on-sensitivity-part-i/

Some references regarding the logarithmic relationship:

http://www.grida.no/publications/other/ipcc_tar/?src=/climate/ipcc_tar/wg1/222.htm

http://folk.uio.no/gunnarmy/paper/myhre_grl98.pdf

If I’m correct, the linear relationship in e.g. Rapauch between the cumulative total CO2 emissions and temperature is based on exponentially growing CO2 emissions that compensate the logarithmic relationship between CO2 and temperature. The abstract says:

*“This implies that, if the carbon-climate system is idealised as a linear system (Lin) forced by exponentially growing CO2 emissions (Exp), then all ratios of responses to forcings are constant.”*.

Hope this helps a little.

]]>I am now very puzzled because the references I have and talks I have heard have seemed to make it very clear that there is linear relation of temperature to CO2 emissions. Please could you give me a reference or two for the logarithmic relation that you describe?

In this paper by Raupach http://www.earth-syst-dynam.net/4/31/2013/esd-4-31-2013.pdf Fig 6 bottom right gives a very linear relation of Temperature to CO2.

I received an email from a senior climate scientist here in Ireland saying that Matthews above and this reference by Stocker

http://www.climate.unibe.ch/~stocker/papers/stocker12scix.pdf

It starts with this on the relationship:

“Robust evidence from a range of climate–carbon cycle models shows that the maximum warming relative to pre-industrial times caused by the emissions of carbon dioxide is nearly proportional to the total amount of emitted anthropogenic carbon (1, 2). This proportionality is a reasonable approximation for simulations covering many emissions scenarios for the time frame 1750 to 2500 (1). This linear relationship is remarkable given the different complexities of the models and the wide range of emission scenarios considered.”

These references point to the relationship being linear but I may have not asked you correctly or we may be talking about different things. Many thanks for the help in this.

I understand that these are ‘eventual’ temperatures, but also that other non-linear effects may apply, potentially accelerating warming.

]]>That’s not entirely true. The temperature effect of CO2 is logarithmic, ie each doubling of CO2 has the same effect (eg from 280 to 560 ppm has the same T-effect as going from 560 to 1120 ppm). It is thus not correct to state that each 100 ppm would correspond to 1 degree C eventual (it takes time!) rise in T. The error in the linear assumption would be small though if you only apply it over a small range.

]]>Thanks very much for your reply. As you can probably tell I am not ‘deep climate science aware’ enough to trust myself to deal with the raw data, though I will look at it.

Communicating the likely implications of ongoing emissions right now is what I’m aiming at, the current and future warming. If you can give me an idea of the ranges that would be great.

For example if ECS = 3ºC that implies that for a 280 ppm CO2 increase over pre-industrial every 95 ppm increase roughly corresponds to 1ºC in equilibrium temperature rise. If Meinshausen (above) figure is used then 1TtCO2 for 2ºC rise (25% chance) implies 500 GtCO2 per 1ºC.

So: each 1ºC rise = about 100 ppm = 500 GtCO2

You can see how rough I am being but I think this is how policy-makers have to be approached if the idea of ‘safe’ emission paths and carbon budgets are to be conveyed with any impact.

Paul

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