Beyond equilibrium climate sensitivity

Since I’ve written about climate sensitivity before, and since I have a few free moments, I thought I would briefly highlight a new paper by Knutti, Rugenstein, and Hegerl called Beyond Equilibrium Climate Sensitivity. It’s really a review of a large number of estimates for the Transient Climate Response (TCR) and the Equilibrium Climate Sensitivity (ECS).


In case you don’t know, the TCR is essentially how much we will have warmed when we’ve doubled atmospheric CO2, and the ECS is how much we will eventually warm once the system has returned to equilibrium after a doubling of atmospheric CO2 (technically, these are model metrics and consider fast feedbacks only, but let’s ignore those details for now). There are a large number of different estimates for the TCR and ECS, and the paper doesn’t really try to reconcile them; it simply discusses the various methods.


Essentially, there is reasonably agreement between the various estimates for the TCR; most are consistent with the likely range of 1 to 2.5oC and suggest that it is extremely unlikely above 3oC. There is some disagreement amongst the estimates for ECS, but this is mostly due to those that use the observed warming. The method that uses the observed warming essentially assume that the feedback response will remain constant as we warm to equilibrium; there now seems to be a reasonable amount of agreement that this is unlikely to be the case and that we will likely warm more as we approach equilibrium than we did initially.


Credit: Knutti et al. (2017)

This is illustrated quite nicely by the figure on the right, which shows the surface temperature anomaly, on the x-axis, and top-of-the atmosphere radiative imbalance, on the y-axis. The black line is the case in which we assume feedbacks remain constant; this produces what is typically referred to as the Effective Climate Sensitivity. We expect, however, that temperature dependent feedbacks and the pattern of the warming could lead to more warming in future than we would expect based on an assumption of constant feedbacks; this will eventually lead to the Equilibrium Climate Sensivity being larger than the Effective Climate Sensitivity. There are also other factors, like internal variability, the base state climate, the magnitude of the forcing, and what produces the change in forcing, that could also influence the overall warming. On top of this, there are slower feedbacks that will ultimately further amplify the warming, producing the Earth System Sensitivity.


Okay, I’m running out of time, as I have to head out to dinner with some colleagues, so will just wrap up, by quoting some of the conclusions of the paper

Our overall assessment of ECS and TCR is broadly consistent with the IPCC’s, but concerns arise about estimates of ECS from the historical period that assume constant feedbacks, raising serious questions to what extent ECS values less than 2oC are consistent with current physical understanding of climate feedbacks. A value of around 3 °C is most likely given the combined evidence and the recognition that feedbacks change over time.

The argument that an ECS value less than 2oC is inconsistent with our physical understanding of climate feedbacks is presented nicely in a video by Andrew Dessler, that I included in this post. I also wanted to quote from the paper’s abstract, which ends with

Newer metrics relating global warming directly to the total emitted CO2 show that in order to keep warming to within 2oC, future CO2 emissions have to remain strongly limited, irrespective of climate sensitivity being at the high or low end.

What this is referring to is the Transient Climate Response to Emissions (TCRE) which I discuss in this post. This attempts to include both radiative feedbacks and carbon cycle feedbacks and suggests that our warming depends linearly on emissions. Essentially, this suggests that if we want to keep warming below 2oC then – approximately – the total amount we can emit in future, is less than we’ve emitted so far. I think this is quite an important metric that probably isn’t discussed enough, but since I need to rush out, I won’t say any more about it now.


Dino Manalis Added Sep 11, 2017 - 3:54pm
The climate is evolving, like everything else, we don't have all the answers, but there's nothing wrong in admitting it, but we shouldn't go bonkers over it either.  Instead of generalizing about climate change and global warming, we should specifically reduce pollution and waste as much as possible without ruining the economy.
opher goodwin Added Sep 11, 2017 - 6:48pm
Dino - I agree with that - as well as reversing Trump's short-sighted decision to shut down all the monitoring agencies.
Flying Junior Added Sep 12, 2017 - 2:35am
Interesting article.  I had mistakenly claimed that perhaps we had already hit the doubling point since 1800.  But upon further looking I realized that the level has only increased from around 280 ppm at the close of the 17th century to around 410 ppm today.  Surely not a doubling.  But my crude estimate was not off by more than 40%.  Still very alarming.
Even A Broken Clock Added Sep 12, 2017 - 10:31am
Physics - (love the name) - Good to see someone post on this site with a background in math and science. One note that I have on your chart is that there are likely to be discontinuities in the emission rate of methane as warming continues. In particular, I expect the arctic warming will result in accelerated permafrost melting, and the concomitant release of methane from that will greatly increase the methane concentration rise.
Then there's the possibility of ocean warming releasing the clathrates, especially in the continental shelf regions. This too would act to greatly increase the CO2 concentration in a very short time. That would amplify the earth system feedback line shown on your graph.
Edward Miessner Added Sep 12, 2017 - 1:43pm
Interesting article. From elsewhere, I've read that the Equilibrium Climate Sensitivity was 3 deg C and the longer term, Earth Systems Sensitivity was 6 deg C.
Edward Miessner Added Sep 12, 2017 - 1:44pm
Other research such as paleoclimatic data suggests a higher sensitivity than the ECS.
And Then There's Physics Added Sep 12, 2017 - 2:06pm
Flying Junior,
We've emitted enough CO2 to have doubled atmospheric CO2 if it had all remained in the atmosphere.  However, more than 50% of what we've emitted has been taken up by the oceans and biosphere, and so atmospheric CO2 has increased by just over 40%.
Evan a Broken Clock,
Technically, the ECS is defined as being the equilibrium warming through fast feedbacks only, so doesn't really include the impact of carbon cycle feedbacks.  There is another term called the Transient Climate Response to Emissions which does take some of the carbon cycle feedbacks into account and suggests that we will warm by about 2C for every 1000 GtC emitted.  To date we've emitted about 600GtC and warmed by about 1C.
The Earth System Sensitivity is indeed probably higher than the ECS.  However - given our current climate state - it is probably not as high as 6C because the ice sheets are smaller now than they were during previous  glacial periods. 
Nicholas Schroeder Added Sep 12, 2017 - 7:42pm
No doubt many of you are tired of seeing this post and yet I persist. Just explain per traditional scientific etiquette and dialogue why my methods and conclusions are wrong and I will have to stop until corrections are made. Simple and in your hands. 
If it had not been for "deniers" challenging the "consensus" doctors and surgeons would still be going from patient to patient with infectious hands and clothing.
Here's an excellent example of fake news.
"97% of scientists (implying ALL!!! scientists) believe in man-caused climate change." 
What the MSM meant to say is 97% of all CLIMATE scientists (similar to aroma-therapists and horse whisperers) actively researching and publishing in that field (At this point insert getting paid.) consider the evidence compelling - all 82 of them "cherry picked" out of the 10,500 surveys that were sent out. (Doran and Zimmerman) 
Demonizing, marginalizing, silencing and censoring the skeptics and critics (Union of Concerned "Scientists" & Disqus & FB & USA Today & MSN) is the real anti-science. Science without doubt, science without uncertainty, becomes religion. 
Believing that 0.04% of the atmospheric gases magically influences weather and dominates the climate takes a real sci fi flight of fantasy (or article of faith). 
The upwelling/down welling/"back" radiation of greenhouse theory is comic book science, Saturday morning cartoon science, cinematic shape-shifting, mutant superhero science defying six of the three most fundamental laws of thermodynamics and physics. 
Believing in the upwelling/downwelling/"back" radiation GHG/GHE theory is like believing in the X-men, but without the kewl movies. Not surprising since they share a common fan base. 
4,300!!!! (plus 2,500 since 6/9) views collected on the following three papers and NOBODY has disputed my methods or conclusions. 
Step right up, be the first, take 'em apart. 
Bring science, I did.
Nicholas Schroeder Added Sep 13, 2017 - 12:02am
"We've emitted enough CO2 to have doubled atmospheric CO2 if it had all remained in the atmosphere.  However, more than 50% of what we've emitted has been taken up by the oceans and biosphere, and so atmospheric CO2 has increased by just over 40%."
The amount of CO2 fossil fuels and cement added to the atmosphere between 1750 and 2011 represent 0.34% of the total biospheric carbon cycle. Since the amounts of carbon sinks/sources, ebbs/flows, are wild ass guesses, numbers just pulled out of various PhD butts, the uncertainty, "We really haven't got a clue." in where CO2 comes from, where it goes, and what sector is responsible is ten times larger than that puny 0.34%.
Source: IPCC AR5 Figure and Table 6.1.
Earth's carbon cycle contains 46,713 Gt (E15 gr) +/- 850 Gt (+/- 1.8%) of stores and reservoirs with a couple hundred fluxes Gt/y (+/- ??) flowing among those reservoirs. Mankind's gross contribution over 260 years was 555 Gt or 1.2%. (IPCC AR5 Fig 6.1) Mankind's net contribution, 240 Gt or 0.53%, (dry labbed by IPCC to make the numbers work) to this bubbling, churning caldron of carbon/carbon dioxide is 4 Gt/y +/- 96%. (IPCC AR5 Table 6.1) Seems relatively trivial to me. IPCC et. al. says natural variations can't explain the increase in CO2. With these tiny percentages and high levels of uncertainty how would anybody even know? BTW fossil fuel between 1750 and 2011 represented 0.34% of the biospheric carbon cycle.
Flying Junior Added Sep 13, 2017 - 2:45am
BTW fossil fuel between 1750 and 2011 represented 0.34% of the biospheric carbon cycle.
Good work.  What you say is true.  As Star Trek taught us, we are carbon-based life forms.  Maybe that's why I like good bread so much.

What about the delta change in CO2 emitted into the atmosphere?  Did two hundred and fifty-two years of burning fossil fuels change that very much?
And Then There's Physics Added Sep 13, 2017 - 4:00am
The amount of CO2 fossil fuels and cement added to the atmosphere between 1750 and 2011 represent 0.34% of the total biospheric carbon cycle.
No, this is not true.  It is true that if we only consider emissions (not uptake) then anthropogenic emissions are a small fraction of natural emissions.  However, prior to us starting to emit CO2 into the atmosphere, the natural sinks were in balance - they emitted (on average) as much CO2 as they took up.  In other words, the amount in the atmosphere remained (on average) constant even though there were quite large emissions into, and out of, the atmosphere. 
We, however, only emit CO2; we don't also take it up (we're source, but not a sink).  Therefore, we have pushed the natural system out of balance and CO2 is accumulating in the atmosphere because of our emissions.  In fact, the increase in atmospheric CO2 is less than half of what we've emitted, so something has taken up more than 50% of our emissions.  This is the oceans and biosphere.  In other words, the natural sinks (oceans, biosphere) are currently taking up more than they emit and therefore cannot be the source of the increase in atmospheric CO2.
Edward Miessner Added Sep 13, 2017 - 3:20pm
And Then There's Physics,
True we have less ice but we still have ice. I presume our current volume is one-third the Pleistocene maximum volume? Anyway, didn't a similar-magnitude bump to the one I recall to be predicted by the ESS occur at the PETM extinction-level event?
And Then There's Physics Added Sep 13, 2017 - 3:34pm
I'm not sure about the PETM. I did find <a href="">this" target="_blank">discussion on Realclimate</a> which suggests a range of 4.5C to 6C, so it seems that it might be as high as 6C. 
Edward Miessner Added Sep 13, 2017 - 3:38pm
Thanks for the info. So we're looking at a mean long, long term warming of 5.25 C for a doubling of pre-industrial CO2. Not good.
And Then There's Physics Added Sep 13, 2017 - 3:39pm
Yes, on long enough timescales, that's probably what we would get if we doubled atmospheric CO2.
Edward Miessner Added Sep 13, 2017 - 4:05pm
Exactly. I'm thinking at 1,000 years out.
Nicholas Schroeder Added Sep 13, 2017 - 4:55pm
Lots of sound and fury signifying nothing. CO2 doesn't actually do anything. The heating/cooling of the earth is controlled  by the elliptical orbit, tilt, and Malinkovich.
The genesis of RGHE theory is the incorrect notion that the atmosphere warms the surface (and that is NOT the ground). Explaining the mechanism behind this erroneous notion demands some truly contorted physics, thermo and heat transfer, i.e. energy out of nowhere, cold to hot w/o work, perpetual motion.
Is space cold or hot? There are no molecules in space so our common definitions of hot/cold/heat/energy don't apply.
The temperatures of objects in space, e.g. the Earth, Moon, space station, Mars, Venus, etc. are determined by the radiation flowing past them. In the case of the Earth, the solar irradiance of 1,368 W/m^2 has a Stefan Boltzmann black body equilibrium temperature of 394 K, 121 C, 250 F. That's hot. Sort of.
But an object's albedo reflects away some of that energy and reduces that temperature.
The Earth's albedo reflects away about 30% of the Sun's 1,368 W/m^2 energy leaving 70% or 958 W/m^2 to "warm" the surface (1.5 m above ground) and at an S-B BB equilibrium temperature of 361 K, 33 C cooler (394-361) than the earth with no atmosphere or albedo.
The Earth's albedo/atmosphere doesn't keep the Earth warm, it keeps the Earth cool.
And Then There's Physics Added Sep 13, 2017 - 5:14pm
Your numbers are wrong.  Solar insolation is indeed about 1360 W/m^2, and the planet does indeed reflect about 30%, but when you want to estimate what the surface temperature would be if we had no atmosphere and the surface simply radiated as much energy into space as it gets from the Sun, you also need to divide by 4 to account for the Earth being spherical.  This gives a solar forcing of about 240W/m^2 and an effective surface temperature (in the absence of an atmosphere) of about 255K, about 33K cooler than it is now (because of what we call the atmospheric greenhouse effect).
John Minehan Added Sep 13, 2017 - 6:59pm
"However, more than 50% of what we've emitted has been taken up by the oceans and biosphere, and so atmospheric CO2 has increased by just over 40%."
Which is believed to be a factor in the KT Extinction, the Carbon f: volcanism?