Do the math! Because climate sensitivity is logarithmic, 1.5 degrees target was already breached at 400 ppm – if you look at CO2 only (& assume ECS = 3C)

According to ‘conventional climate science’ the currently already emitted amount of CO2 (404 ppm) leads to a committed warming of 1.56 degrees Celsius. To keep ‘the promise of Paris’ – the CO2 concentration must go down, down to below 400 ppm on the decades timescale, and (yes, Hansen was right there too) closer to 350 ppm to also prevent ‘the slow climate catastrophe’.

Climate inertia, the timescale of different climate feedbacks
Understanding climate science (and for that matter any Earth science) is very much about understanding timescales – the fact that very many processes that influence each other run at different speeds, for different lengths of time, and may also have different thresholds. All in all these feedback loops determine both the extent of a new equilibrium state and the length of time it takes the system to get there, after an initial disturbance – in this case massive human emissions of greenhouse gases. This giant complexity we try to fit in the phrase ‘climate inertia’. But let’s just for a moment be very simplistic and say there are ‘two types of climate inertia’. Decades-timescale climate inertia (close to the defintion of ‘Equilibrium Climate Sensitivity’) and the longer timescale climate inertia (‘Earth System Sensitivity’). Both add extra warming (ECS in the order of 0.5 degrees, ESS possibly an additional 1-2 degrees) to the currently observed temperatures, without requiring a further rise in CO2 – as explained (we hope!) in our previous article. In this article we look at the relatively short-term thermal inertia – to conclude at the 400 ppm CO2 level (official measurement during COP21 climate summit) we had already breached the 1.5 degrees target. To be more precise: 400 ppm equals 1.53 degrees, and at 404 we’re currently already at 1.56 degrees! This is if you stick to rather conventional estimates of climate sensitivity (3 degrees warming for a doubling of CO2) and still ignore other climate forcers we’re emitting (not a bad simplification, in the long run the climate problem is very much a CO2 problem). The above image (from ‘Making sense of paleoclimate sensitivity,’ a PALEOSENS article published in Nature in 2013) nicely illustrates that the Earth system is always far more complex – and climate inertia is indeed a diffuse mix of processes on overlapping timescales. Elephant in the room are the carbon feedbacks – that we’ve ignored in our series (because we see them as emissions – a rise in carbon concentration – and for the concept of our series we assumed fixed concentrations). Over at Real Climate a climate website hosted by actual climate scientists Gavin Schmidt (NASA GISS) made the below adaptation of the same image of climate feedbacks. We’d like to point to the three vertical green lines he drew  one at ‘zero climate feedbacks’, one after the time lag of your regular (IPCC) definition of climate sensitivity (decades time scale) the other to help define ‘Earth System Sensitivity’ – the very long time scale climate inertia.
climate sensitivity vs Earth system sensitivity - climate inertia
This article focuses on that second line (Charney climate sensitivity) – what we call ‘conventional climate science’ in our introduction. It’s the stuff that politicians are supposed to base their climate policies on. Conservative, non-alarmist (especially when you go for median value, as we do) and very solid. Yet still they seem to be fully unaware of even this foundation of modern climate science – as it shows we need to lower CO2 concentration to the level of before the big UN climate conference of December 2015 – back to below 396 ppm to be precise (the atmospheric CO2 trend level of mid-2013).

Politicians and climate science, part – well, let’s just get to it. At the end of 2015 in Paris the world’s state leaders agreed we should try to limit atmospheric warming to 1.5 degrees (a target we strongly support, to prevent catastrophic climate change). Small detail: the CO2 concentration that (after a thermal climate inertia of a few decades) leads beyond that 1.5 degrees warming was already breached one year earlier, in 2014 – when the atmosphere passed the 400 ppm mark for CO2.

That is if you still ignore the other greenhouse gases. And if you stick to the more conservative part of climate science – summarised in the very IPCC reports that were especially written to make these same politicians understand what exactly their words on climate mean.

Haven’t we all overlooked something? Simple math + 1 odd characteristic of greenhouse gases?

Let’s call this piece a short supplement on our ‘Real’ Global Temperature Trend series. Because it’s too important – and everyone seems to have overlooked something that is politically quite relevant: if you assume Equilibrium Climate Sensitivity is 3 degrees (which is IPCC’s median value – and seems a good yet slightly conservative number judging by our expert survey) at the current CO2 concentration of 404 ppm we already have a committed warming (‘Real’ Global Temperature) of 1.56 degrees Celsius.

The reason is a rather odd characteristic of greenhouse gases: they warm the climate logarithmically. That means linear growth of temperature is reached after exponential growth of the concentration of heat-absorbing gases in the atmosphere. Therefore climate sensitivity is expressed as a certain amount of warming (probably close to/somewhat above 3 degrees [second link to our expert survey – give it a read]) for every doubling of the CO2 concentration. You get that amount of warming from 280 (pre-industrial CO2) to 560 – and again from 560 to 1120 ppm of CO2.

We actually knew this (no proof but our word) when we made our special climate inertia global temperature graph (that we think still offers a nice visualisation and proper indication of committed warming (at different climate inertia time scales) at various CO2 levels/year!), but chose to ignore it – and drew a linear line instead, between 280 and (3 degrees warming at) 560 ppm. ‘Because how big can the difference be,’ if you zoom out a bit.

Well, that was a bit silly of us. We had a little chat with atmospheric scientist Bart Verheggen (please also read his special blog post about climate inertia!), who pointed out that –because at 400 ppm we are close to the middle between 280 and 560!– the difference between a logarithmic line and a linear one is now relatively large: not 43% of climate sensitivity, but 51% – a difference between 1.29 and 1.53 degrees.

Wow. +0.24 degrees! That is such a big difference that we immediately added the information in a disclaimer as part of the original article (before open publication). But we felt we also needed to do a bit more than that. And that is because 1.53 is more than 1.50 – and that means that at the current CO2 concentration, judging by conventional climate science, we had already passed the target the moment the political promise was made. Odd, considering the fact that at the UN climate summit none of the world leaders mentioned the fact that establishing their 1.5 degrees ambition requires effective lowering of the CO2 concentration. Instead there came pledges to cut some of the emissions, leading to further growth of the CO2 concentration (to 670 ppm CO2/860 ppm CO2eq!) and bringing the world on a path towards 3.5 degrees warming (if all the pledges will in fact be translated to actual (national) energy policies, indeed another risk factor).

Climate sensitivity is logarithmic – but why again? And what are the consequences?

Yes, we needed to get back to that part. And a good question. Also because no one seems to know exactly. That’s because it’s not a direct consequence of some universal law of physics, but rather (as in many cases) just a feature of Earth’s climate system (which is also why CO2′s warming effect is probably not perfectly logarithmically distributed).

dT = NOT λ x ((CO2 – CO2ref)/CO2ref)
with λ = climate sensitivity = assumed at 3 degrees Celsius
(and CO2 = 404 & CO2ref = 280)

dT = λ x RF (%)
with RF = radiative forcing = 5.35*ln(CO2/CO2ref)
with 100% λ = 3.7 W/m2, equals 3 degrees Celsius

At 400 ppm CO2 (official during COP21) RF = 51% of λ => 1.53 degrees climate warming
At 404 ppm CO2 (current value) RF = 52% => 1.56 degrees warming

The 1.5 threshold was actually already breached in mid-2013, at a CO2 concentration of 396 ppm => 50% of λ => 1.5 degrees climate warming(!)

*) All the above based on IPCC AR4, ECS = 3C = 3.7W/m2, constant at 5.35. (Good to note that these assumptions and constants can of course evolve over time, so all calculations are indications.)

Perhaps a very simple way to understand the process is as follows: greenhouse gases absorb infrared energy (solar radiation transformed into infrared energy at Earth’s surface, en route to return to the cosmos, until it bumps into… a CO2 molecule). Now imagine a wave of infrared energy passing through the atmosphere on its way to outer space. Not so fast, says CO2 molecule number 1 – that happens to be in exactly the right collision course. You won’t reach the stars tonight – I’m going to eat [absorb] you! But what if there are two CO2 molecules in exactly the flight path of the initial energy wave? Molecule one will absorb the energy – but also prevent molecule 2 from doing the same (effectively making it an idle greenhouse gas). The chance that this scenario happens increases with the amount of greenhouse gases in the atmosphere. Therefore warming will continue to go up with rising CO2 (and for that matter any other greenhouse gas) – but for warming to increase linear in time, the concentration would have to increase exponentially.

(The above is intended to help illustrate a logarithmic connection. Reality is more complex still. The infrared wavelength section at which CO2 can act as a greenhouse gas is already saturated, implying all of the outgoing radiation in that wavelength section of infrared energy is already being absorbed by CO2 at some place in the atmosphere. There is indeed competition between CO2 molecules, but (as all infrared energy of the relevant wavelength is already absorbed) the only difference is the atmospheric altitude of heat absorption. If this happens at a low atmospheric altitude (more likely when there are more CO2 molecules), more of the energy is kept in the Earth’s climate system. High-altitude absorption allows for a larger portion of re-emitting to the cosmos, therefore a relatively cooler planet Earth.)

Because climate sensitivity is logarithmic, 1.5 degrees is at 400 ppm CO2!
Shown above is a basic graph – to help you get an understanding of a logarithmic connection. On x=1, you could visualise preindustrial CO2 (280 ppm). x=2 would be 560 ppm and 3 degrees warming. We’re somewhere in the middle between those two dots, which is why a linear line between x=1 and x=2 would now lead to underestimation of warming (and why 400 ppm equals a 1.5 degrees temperature rise). But if you would look beyond 560 ppm, the fact that there’s a logarithmic connection is actually good news, wouldn’t you say? You’d have to keep doubling the CO2 concentration for every 3 degrees of further temperature rise (please let’s not).

True. In a sense that’s good news. You need massive emissions (or should we say runaway carbon feedbacks) to get from 3 to 6 degrees warming. But it also leads to a skewed perception of climate change, as in fact climate change is an accelerating process, which is why we need to get back to climate inertia – and another graph, made famous by a now 15-year old IPCC report. Talking about time scales. What we are emitting will have increasing consequences for a long as we live. That is a picture of escalation – not of a logarithmic connection:
Climate inertia according to IPCC report 2001
Yes, it’s complex, but the conclusion is very simple. We need to lower the CO2 concentration

We’d just like to repeat the very clear conclusion to draw in the here and now: the CO2 concentration must go down – down to below 400 ppm – and further still (closer to 350 ppm) to also put a lock on the very inert and very unwanted climate processes, like icesheet melting, and possible ocean current changes.

© Rolf Schuttenhelm |

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