Readers have recently discussed the correlation through time between global temperature on the one hand, and CO2 concentration on the other. Close examination shows that the correlation is stronger during some time intervals, weaker during others, and although it’s strong overall, there seems to be a lot happening to temperature other than mimicry of the CO2 changes.
One suggestion was to study the relationship, not with CO2 concentration, but with its logarithm. This is because climate forcing — a measure of the ultimate climate-changing impact — is proportional to the logarithm of the CO2 concentration, not to the concentration itself. The idea is to look for correlation between temperature and climate forcing — and it makes sense.
The fascinating thing is: there are many different climate forcings. A lot more than just CO2.
For one thing, there are other greenhouse gases beside CO2. Methane (CH4) has a surprisingly large effect, and bringing up the rear is a host of others, including N2O, chloroflourocarbons, hydroflourocarbons, and others. And, these gases can interact with each other; the climate forcing of methane, e.g., depends on the concentration of N2O, and vice versa. NASA has estimated the total greenhouse gas forcing, from all gases combined, and came up with this:
An important thing to note is that although water vapor (H2O) is a potent greenhouse gas, and the most abundant in our atmosphere, it’s not a climate forcing. That’s because it is controlled by temperature; if we tried to increase or decrease global water vapor artificially, it would quickly rain back out of or evaporate back in to the atmosphere. Water vapor doesn’t hang around long enough be a climate forcing, it adjusts to temperature (and other things) too quickly. It is, however, a climate feedback (we’ll leave that discussion for another day).
Greenhouse gases just get us started. Ozone is it’s own thing, working differently high in the stratosphere than lower in the troposphere. When the sun gets hotter, so does Earth, when the sun cools off we do too, so changes in solar output make another climate forcing. Land use is crucial; when we replace forest with cropland (or cities) it affects the climate. Albedo is the reflectivity of Earth’s surface, and when it decreases because ice and snow are replaced by open land or water, more solar energy is absorbed and we heat up — albedo is another forcing. There are even small forcings due to changes in Earth’s orbit. Then there are the aerosols, which, low in the troposphere, have both a direct and an indirect effect, and which, high in the stratosphere (from volcanic eruptions) make one of the strongest cooling effects. NASA has estimated all these forcings (data through the year 2012):
The two strongest forcings are the thick black line on top, for well-mixed greenhouse gases, and the thin black line on the bottom, stratospheric aerosols from volcanic eruptions. NASA also provides estimates of the total climate forcing, from 1850 through 2012:
Rather than look for the correlation between global temperature and just CO2 concentration, let’s see how it relates to total climate forcing.
Climate forcing means more energy coming in to the system, which heats things up, and it takes time for the heat to accumulate, so it’s just the laws of physics that the climate doesn’t respond to a forcing instantaneously. The simplest physical model is the energy balance model. It’s quite simple really, and can’t (in my opinion) compete with the fancy supercomputer models that run the details, but it does reflect some of the basic physics that’s happening.
It tells us to seek correlation between temperature and exponentially smoothed climate forcing. An exponential smooth has a “time scale” — short for a “fast” smooth”, long for a “slow” smooth. If the climate system has low thermal inertia then it will respond quickly — maybe with a time scale as short as one year. Let’s correlate global temperature with a 1-year exponentially smoothed climate forcing, by making a model of temperature (we’ll call it the “fast-response model”). I’ll use the temperature data from Berkely Earth, and the model looks like this:
The first thing we notice is that the large downward spikes (from volcanic eruptions) in the model actually correspond to downward spikes in the temperature data — but the model spikes are much too large. It’s like the effect of climate forcing is being magnified too much by this model.
But the overall pattern is actually quite close, so the scaling factor for forcing looks about right in the long term, but far off in the short-term stuff.
The land surface, and the atmosphere, might respond to climate forcing that quickly, but the oceans take longer with so much thermal inertia. Just the upper ocean, let alone the deep abyss, is sluggish compared to land and air. Let’s try a model using a more long-term smooth, say a 22-year exponential smooth (I’ll call it the “slow-response model”):
It follows the long-term pattern excellently, and the unrealistic huge downward spikes are now gone. We still see drops when volcanic eruptions happened, but nothing like a spike, and not as deep a dive as is seen in real data. Even so, this model is at least realistic, and avoids nonsense features.
Those energy balance models only use one “compartment” to the system. You can treat it like a land-atmosphere system and get fast response, or like an upper-ocean system with slow response, but the former exaggerates the fast response (to match the slow) while the latter subdues it too much. A more realistic model, both mathematically and physically, is to use two (or more) “compartments” for a model — a two-box energy balance model.
Then the math tells us to model something like surface temperature as a combination of two different exponential smooths with two different time scales. I found that the best combination of time scales was 1 and 22 years, leading to this two-box model:
Now we have a rather good model, based on extremely simple physics (it certainly omits a lot of detail!). It matches the global data well, matches the response to volcanic eruptions well, and even has a plausible physical interpretation. The land+atmosphere system responds quickly (time scale 1 year), the upper ocean more slowly (time scale 22 years), and observed surface temperature is a manifestation of both (like the physics says).
Efforts to correlation global temperature with CO2 alone, are often interesting, sometimes persuasive, sometimes informative. I encourage getting to know how these things are related to each other. But let’s not lose sight of the fact that with so many other forcings, and with nature’s never-ceasing fluctuation even in the most constant of times, this is one of those cases where deeper understanding deserves closer examination.
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Open Mind 
For my understanding as a barely scientifically literate citizen, I would like to see what’s happening translated into dollars, i.e., does a dollar of economic activity equal about one pound of CO2 added to the atmosphere?
This is really excellent. It reminds me of the simple things considered in Ray Pierrehumbert’s Principles of Planetary Climate or J Tuzo Wilson’s introductions to plate tectonics.
Very helpful Tamino
Not the first time you have answered a question I was struggling with in a follow up post. The effect of volcanic aerosols during the early period 1900 to 1920 .
I also see the anomaly that is measured sea surface temperatures during and after the war seems to stand out as unresolved by your simple two-box model.
These two factors appear to be what Currys monkeys are gibbering about rather than the warming due to mans actions during the 1910 to 1945 interval.
Neglected to describe the seasonal/annual forcing and the daily forcing. There are also the tidal forcings — see this recent paper on developing models with explicit tidal forcing
https://www.geosci-model-dev-discuss.net/gmd-2018-5/
@WHUT,
Appreciate that, Paul, but the point is that you can get this far with two windows or “boxes”. That simplicity is pretty compelling.
I know it’s worth going the rest of the way for just the science, but as a hard-nosed data guy, I’d like to see the negative partial of the mean-squared-error with respect to additional CPU cycles remain high with any additional work.
And to the general science audience, quoting from RayP who quoted about Arnold E Ross:
Specifically, regarding the Ross Program:
Jan,
I didn’t mean anything more deep than pointing out some forcing terms that are so obvious that they tend to be forgotten.
Reblogged this on jpratt27 and commented:
Time to put a price on carbon pollution
It would be interesting to subtract out an estimated temperature response to ENSO variability from the observed data, which would get rid of a lot of the wiggles, and improve the match even more.
It would also be interesting to perform a similar exercise in some climate-model world: first, fit the function from 1900-2018 and see how well that does, but then also see how well the function handles future projected climate change in the model. If it performs well, then maybe we have a very simple model for calculating global average surface temperature from a forcing time series! I do, however, wonder if this model would fall short like some of Nic Lewis’ work, where fitting simplified models to observed data seems to lead to underestimates of the long-term climate response…
-MMM
How does your simple model work for negative forcing and feedback, say, for the onset of glaciation?
@mandarin etto,
That’s a different thing, and is out-of-scope for the present model, because those forcings are low level and consistent over a long period of time. Tamino addressed those in 2011. You should read. See:
Glacial cycles, part 1
Glacial cycles, part 1b
Glacial cycles, part 2
Milankovitch cycles
This was also addressed by Eli Rabett in 2012.
Indeed, the only thing startling is the degree to which the repeated and insistent set of warnings by scientists to government has been systematically ignored. And this hasn’t all been due to fossil fuel company nefariousness, although they jumped on that bandwagon in the late 1970s:
There are no surprises here. Haven’t ever been. Knowledgeable people have been explaining the same thing over and over again.
I’ve personally concluded the problem is in the audience, meaning a set of people who don’t want to accept the ethical implications of the reality for their lifestyles.
Obviously, that’s just my opinion. I do not speak for Tamino and I do not “work” here. I have my own gig.
But it’s more than a little more than irritating to see people trying to wriggle out of the aforementioned ethical implications by engaging in cheap shots.
Thanks for the response. I’m familiar with these. I’m much more curious about how models replicate the real world, using past data for comparison. Not sure about the oil company conspiracy theory add on and really don’t care. I just want the objective science, and I know I’m missing a lot of good work out there.
It’s not a “conspiracy” when an industry fights to protect its business model. Tobacco, asbestos, leaded gas, fluorocarbons, sulfur dioxide-producing industries etc., etc., etc, ALL show this. ALL engaged in disinformational campaigns to protect and extend their profits. But it’s not a conspiracy over power and world domination which is usually associated with the meaning.
@jgnfld,
But if any of these are publicly traded companies, as many are, disinformation campaigns or, equivalently, saying one thing publicly but operating the company inconsistently with that, is, ethically speaking, defrauding their shareholders. They have a fiduciary duty to be transparent as much as they have a fiduciary duty to profit.
I qualified this with “ethically speaking” because U.S. SEC laws and case law are fuzzy on what exactly constitutes securities fraud, where “fuzzy” means “it’s not what you think”. That U.S. laws have been amended over time to diverge from the common notion ethics does not recommend them.
jgnfld, for once I think I disagree with you on this. I don’t think there’s any clean distinction between money and power–money per se confers power, and holders generally seek power of various sorts when they wish to amass or protect money. And I think many activities connected with both can reasonably be categorized as ‘conspiring.’
There’s a distinction I’m trying to get at here, but I guess I’m not communicating it well. Conspiracy theories in general usage usually implies some sort of lack of reality contact somewhere in the chain to me at least. Don’t know how to phrase this better.
That said, yes there is a special place down in the 9th Circle of Hell for people like Robert Kehoe of “lead is no threat” fame. And while there were very likely some conspiratorial elements where the industry apparently tried to buy off Clair Patterson, it’s somehow in a slightly distinct area of my brain/semantic space. Maybe the distinction is along the lines of “crank conspiracies” versus “disinformational conspiracies” or some such thing.
There is never a post here which does not inform and stimulate: my thanks again for making my old grey cells work harder! As ever you have written a comprehensible, informative post – just as you did recently on change-point analysis. Forgive me if i betray too much of my ignorance in trying to set these two posts side by side. If the temperature trend change-points are more than just a statistical phenomenon, would we not expect to see change-points at around the same time in the trend of total forcings? Sorry to have to use eyeball analysis, but one might perceive a change-point in the NASA data around 1910, and one around the late 1970s – but not one around 1940-45.
As ever, I’d be very interested in your comments.
Why isn’t there more of a conversation about the resulting temperature change when aerosol levels decline?
The IPCC SR1.5 estimates a warming of 0.5C by ~2060 from aerosol loss (well, 70-8% of 0.5C). The paper that the IPCC cites actually suggests 0.5-1.1 with a median value of 0.7C.
Can anyone tell me why this large forcing due to aerosols isn’t included in any “pathways” to 1.5C or 2C. Even if the IPCC low estimate is correct, we are already at ~ 1.5C once the aerosols decline, let alone a higher 0.7 or 1.1 value which would put us at 1.7-2.1C current warming.
I just don’t understand how that extra half a degree C+ of warming isn’t part of the mitigation/adaptation numbers.
This is because the deep oceans provide us with a free lunch.
When we stop emitting carbon dioxide then concentrations of carbon dioxide in the atmosphere will decrease a fair bit as the deep ocean continues to absorb carbon dioxide. This will compensate for the lost cooling effect from aerosols.
That other issue is that the cooling effect from aerosols is the most uncertain term in the work presented here by tamino. So it’s hard to use it to make policy recommendations.
@Timothy,
True, but note, it won’t be quick, and the associated warming won’t drop for a long time even when CO2 concentrations do, due to thermal inertia of oceans:
D. Archer, et al, “Atmospheric Lifetime of Fossil Fuel Carbon Dioxide”, 10.1146/annurev.earth.031208.100206
S. Solomon, et al, “Irreversible climate dioxide emissions”, http://www.pnas.org/cgi/doi/10.1073/pnas.0812721106
The above article’s Abstract opens with:
S. Solomon, et al, “Persistence of climate changes due to a range of greenhouse gases”, http://www.pnas.org/cgi/doi/10.1073/pnas.1006282107
Is it probable to get to zero emissions?
Cement and steel production along with intensive agriculture all result in emissions of greenhouse gasses .
In the next 50years we will be lucky to halt the rise in the keeling curve let alone reduce human emissions to zero and see it decline. It is probable we will see aerosols reduce to a negligible effect long before we see a halt in C02 rise.
An extra 0,5C to 1C from aerosol reductions above the underlying 0.2C a decade warming trend may result in feed backs in the CO2 cycle that make our efforts moot.
I hope I are not seen as needlessly alarmist.
We have been looking at this problem globally since the inception of the IPCC in 1988 and done SFA.
There is no free get out of jail card for humanity.
Whether it is probable to get to zero emissions is a political question. It is necessary to get to zero emissions, or we see escalating impacts that are untenable.
There has been lots of emphasis on electricity generation in terms of the policy response because it’s one of the easier changes to make, but agriculture, steel, cement, etc, will all need to change too.
I think these are problems that human ingenuity can find solutions to, but it’s not going to be easy.
@Timothy,
Yes, all needs to go to zero, but in the case of agriculture, even if planting, maintenance, harvesting, transport, and processing are all electrified and driven from zero Carbon sources, there is a residual 1.5-2 GtC per annum (out of a total of nearing 11 GtC per annum) which is intrinsic to agriculture. Rice paddies as well as cows produce a lot of GHGs.
This is why any realistic solution needs some negative emissions deployment. But negative emissions can’t fix the rest — except after we’ve zeroed — because it cannot in even the wildest conception keep up with close to 11 GtC per annum.
We could have tried to switch much more of the world’s population to ocean produce, but we’re doing a pretty good job of killing that off too, with pollution of all kinds (not merely plastic, whose date in oceans is not yet understood), development, as well as using it for a big thermal sink.
I mean, don’t get me wrong, it’s good that it’s there because otherwise we”d be dealing with the effects of excess heat energy sooner. But it does foreclose on other options, and means cleaning up this mess will be horrifically expensive, way more than taking the hit and shutting off all fossil fuel production in 5 years.
But like Trump says, he won’t be around so it’s not his problem. So thinks a lot of the relatively wealthy (read averagely wealthy) people on the planet..
ecoquant, I’ve been hearing more and more claims that agriculture can actually be restructured to provide negative emissions, essentially by reversing the current ‘mine the soil’ approach to one in which topsoil building is the norm. Some high carbon sequestration rates have been projected.
I think the science is still a bit sparse, though, and not without controversy, so it’s difficult for me to say just how great the promise of such approaches may be. There’s been a fair amount of discussion about it at RC at various times. Perhaps you already are aware of this, though; if so, any thoughts?
@Doc Snow,
Regarding agriculture, yes, some progress can definitely be made there. There have been large scale controlled experiments, both in agriculture and also plantings. I don’t have access to my files of papers (I’m at work) so I unfortunately cannot give references here. (I’ll take a note and provide tomorrow.) But I do remember a recent related paper from PNAS on reforestation, Nave, Domke, et al, 2018: https://www.pnas.org/content/pnas/115/11/2776.full.pdf. One result from there which shows the magnitude of the problem is that reforesting 5e5 km^2 will offset 1% of all U.S. GHG emissions.
If I recall, global adoption of advanced agriculture techniques and aggressive reforestation could offset something like 30% of emissions tops, so that would do the trick. But, and this is another reason why mitigating climate change is such a Wicked Problem, this has to be done with care: Setting aside the political and social implications of such a project, as far as I know, no one has looked at the effects of albedo change when doing this. I know planting massive numbers of Jatropha curcas in arid regions is not a win for this reason. (Sorry, don’t recall reference either, but can look it up.)
By the way, these kinds of side effects are not limited to agriculture and reforestation: It is believed that a dense array of wind turbines off the eastern U.S. will steal enough energy from winds to affect local climate. This doesn’t mean it oughtn’t be done, it’s just that when engineering at big scales y’need to think and model at big scales. This is also true of massive area of PV arrays, although there it’s more complicated. If I recall, the albedo change is fine — it’s higher than house and building roofs, I believe, certainly higher than grass and forest — but these tend to change local climate, too, making it drier. (Again, apologies for lacking the appropriate pointers.)
Just to illustrate the sorts of claims being made, Dr. Christine Jones stated in a 2008 article that it is possible to achieve “rates of soil carbon sequestration in the order of five to 20 tonnes of CO 2 per hectare per year…”
The amount of cultivated land globally is on the order of 48 million square kilometers. So if even 5 tonnes is sequestered p.a., that’s 500 tonnes per square kilometer, or notionally 24 billion tonnes globally–quite close to the 29 gigatonnes we are estimated to emit each year. But that doesn’t consider how amenable all those millions of agricultural hectares may be to the techniques used in Australia and investigated by Dr. Jones.
On the other hand, such things presumably are included in an article by Chatterjee and Lal cited in a review article from 2013 which states that:
Still quite helpful, but much less of a silver bullet–and pretty close to the 30% you mentioned.
This is great work. One minor correction.
The albedo change due to melting snow and ice is, I’m pretty sure, a feedback and not a forcing, as it occurs in response to an increase in temperature.
The albedo change related to snow and ice that is included is “SnowAlb_BC” from your list, where the “BC” stands for “Black Carbon” – so that’s soot on snow and ice.
By dividing the temperature by the forcing in Fourrier space, you can extract the true response (Do not forget to remove the mean and aposize the ends. Then extracting the components of the time constant is relatively easy.
Typo: “Efforts to correlation global temperature” -> “Efforts to correlate global temperature”
Typo alert!
“chloroflourocarbons, hydroflourocarbons–”
“chlorofluorocarbons, hydrofluorocarbons”
Fascinating. Does your model mean that if we stopped emit greenhouse gases tomorrow, temperatures would go on rising for another 22 years?
@nickthiswerspoon,
I’ll let Tamino address that in his model, but, in fact, this overshooting phenomenon is indeed the case, although, if I recall, I think it’s much longer than 22 years.
I promised to provide @Doc Snow with references on using enhanced agricultural practices to sequester free CO2. Sorry for the delay.
The scientific consensus is pretty consistent. Improved practices can help, but this far from the kind of “magic bullet” stuff you hear some proponents espouse. One of the references, in fact, from 2016 lamented the existence of a systematic means of assessing efficacy, and devoted their otherwise sympathetic effort to trying to provide one. I quote from the Conclusion of Rosenbrock, et al (2016):
This is from
T. S. Rosenbrock, et al, “The scientific basis of climate-smart agriculture A systematic review protocol“, Working Paper No. 138, CGIAR Research Program on Climate Change Agriculture and Food Security (CCAFS), 2016.
There are three other important works.
The first
E. Wollenberg, et al, “Reducing emissions from agriculture to meet the 2°C target“, Global Change Biology (2016) 22, 3859–3864, doi: 10.1111/gcb.13340
is a major work addressing whether or not the target of reducing GHG emissions intrinsic to agriculture by 1 GtCO2e by 2030 is a reasonable goal. Note present estimates put such intrinsic emissions at 1.5-2 GtC per annum, so this would mean reducing GHG emissions from agriculture to 14%-18% of what they are at present. (1.5-2 GtC is 5.5-7.3 GtCO2 because a single CO2 is 3.67 a C. So 100/7.3 to 100/5.5 is about 14% to 18%.) Note, too, that, as mentioned in my earlier comment, “intrinsic emissions” means those inherent to the agricultural process, setting aside emissions currently made for tilling, planting, harvesting, transport, and processing using, in part, fossil fuel-powered vehicles. Those will presumably be zeroed in their own way.
The second
K. Paustian, et al, “Climate-smart soils“, Nature, 7 April 2016, 532
gives deep insights into the Carbon Cycle relating to agricultural and other soils, and examines the evidence for active measures to enhance sequestration of Carbon in soils. Paustian, et al repeatedly caution that full life cycle assessments need to be done for interventions, including the addition of biochar. They also discuss a little appreciated forcer, N2O, of which arable soils emit more of than any other source. This is important because, in their words, N2O “has no significant terrestrial sink” and emissions are enhanced by applications of fertilizer. Fortunately, the forcing of N2O compared with CO2 is small. They do the same for CH2 emissions. Paustian, et al go on to discuss how soil sequestration might be enhanced in policy and mechanism. It’s interesting, but understandable, that they do not strike out and discuss the idea of Stewart Brand that perhaps we should genetically modify crops so their GHG emissions are attenuated or CO2 sequestering capabilities are enhanced.
The last
S. Luyssaert, et al, “Old-growth forests as global carbon sinks“, Nature, 455, 11 September 2008.
works to remove the misconception that old growth forests cease to sequester CO2. In fact, according to evidence,
See the article for the figures. This is significant, as replantings to compensate for old growth forest destroyed by development or expansion of agriculture are considered legitimate environmental policy. Similarly, felling recently regrown forest to build solar farms is considered by many activists a poor trade because, in part, the regrown forest is erroneously considered a Carbon sink, irrespective of the actual quantitative comparisons.
Many thanks, ecoquant. I’ve added those to my bibliography on the topic. At some point I’m going to have to make some time to really go through this in depth, and really think and compare. It’ll be a bit of a project, for sure!