ECS is 2.5

[Ned W]

[This thread is a work in progress, and some later posts have affected the discussion of this first post.  So I'll add some notes (in bold, red text) as updates.  -Ned]

ECS is "equilibrium climate sensitivity" and recall that it's defined as the temperature change per doubling of CO2 concentration.

If preindustrial CO2 was 278 ppmv, then ECS = dT/dlog2(CO2/278), where dT is a change in temperature and dlog2 is the change (over the same time period) in the base-2 log of [the CO2 concentration divided by 278]. 

To borrow an idea from David Appell's blog (here) and this climate graphs site (here, but no longer maintained?) ... let's plot temperature as a function of number of doublings of CO2 concentration, over the past half-century:

The temperature data are NASA GISTEMP land/ocean, modified by Tamino to compensate for the effects of ENSO, solar variation, and volcanic aerosols.

Note the slope of the linear regression line: 2.5 degrees C per doubling.  That's an estimate of climate sensitivity ... except there are two problems:

• This ascribes all the temperature change to CO2, but there are other forcings as well.
• This is only the transient climate response (TCR).  ECS (equilibrium climate sensitivity) is higher, due to slow feedbacks.

[It's worth noting that this is not the formal definition of TCR, and we haven't yet established whether the slope of this line is close to the "official" value of TCR, or too low, or too high.]

The absolutely nifty thing is that these two "problems" cancel each other out perfectly:

• Per the CMIP5 forcings database here, from 1967 to 2017 the forcing from CO2 was 0.74 of the total anthropogenic forcing (Tamino's temperature data were already corrected for non-anthro forcings).
• Per this 2017 paper, the best estimate of the ratio of TCR to ECS is ... 0.74. 

[The fact that those two ratios happened to have the same value (0.74) and thus canceled out when calculating ECS is purely coincidental.  Using different time periods, or different representations of total radiative forcing, or different studies about the TCR/ECS ratio, can give ratios that don't match like this.  It's not a problem -- nothing in this analysis depends on them matching.  At the time this was written, the author was surprised and amused by the fact that they canceled out, but it is merely a point of curiosity.]

So we have an initial estimate of TCR (2.5 C/doubling).  We multiply by 0.74 (because CO2 is only 0.74 of the total forcing) and find that TCR is 1.85.  Then, to convert from TCR to ECS, we divide by 0.74, getting us right back where we started.  So ... ECS is 2.5.

This is rather cool, because it provides a simple and intuitive way to estimate climate sensitivity, and it gives a value that is well within the middle of the IPCC's range, and it's also exactly the same as one widely used estimate of climate sensitivity from paleoclimate studies:

Hargeaves et al., 2012, "Can the Last Glacial Maximum constrain climate sensitivity?"  GRL, 39(24).

https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2012GL053872

We have found evidence in the PMIP2 ensemble of a relationship between LGM cooling in the tropics, and equilibrium climate sensitivity. Based on this result, we estimate climate sensitivity to be around 2.5°C with a high probability of lying below 4°C.

[Other paleoclimate studies give different values for ECS (higher or lower) and in addition it's worth noting that ECS may not in fact be stationary over time; it is possible that at the LGM, ECS was either higher or lower than it is today.]

The bottom line: based on 50 years of observational data, a simple and intuitive method of calculating climate sensitivity suggests that ECS is 2.5.  This nicely agrees with paleoclimate data as well.

In the longer term, Earth System Sensitivity (ESS) is probably higher than ECS, so ESS will be greater than 2.5.   

Again, thanks to David Appell and the climate graphs site (linked above) for suggesting this.


[The title of this thread ("ECS is 2.5") was only half-serious.  As will be seen below, using this same methodology with different time periods or different temperature data sets will give different estimates of ECS.  At the time of this update, alternative versions of this calculation shown in subsequent posts in this thread find values for ECS of 2.3, 2.5, 2.7, 2.8, and 3.0 ... and that is without even considering several other issues that could produce higher or lower values.

All that said, the official position of the author of this thread is that ECS is probably around the range of 2.5 to 3.0; it could be slightly lower or more than slightly higher.]

[sidd]

TCR integrates for  60 to 80 years (average temperature response over a twenty-year period centered at CO2 doubling in a transient simulation with CO2 increasing at 1% per year (compounded), i.e., 60 – 80 years following initiation of the increase),  and ECS over centuries (but with icesheets held constant, allows deep ocean equilibration)).

But the time period of the data is 50 yrs.

sidd

[oren]

Ned W, I must say the certainty implied in your thread title is not compatible with the information contained herein. There are lots of unknowns in this business - even a layman such as me knows that. Don't be surprised when criticism shows up.

[AbruptSLR]

Dessler & Forster (2018) demonstrate rather convincingly that the likely range for ECS in the period from 2000 to 2017 was 2.4 to 4.6C (with a mode and a mean of 2.9 and 3.3C, respectively) as opposed to AR5's cited likely range of 1.5 to 4.5C.

Furthermore, it is important to remember that ECS is not a fixed value but rather is projected to increase with continued global warming, this century:

A. E. Dessler and P.M. Forster (07 August 2018), "An estimate of equilibrium climate sensitivity from interannual variability', Journal of Geophysical Research Atmospheres, https://doi.org/10.1029/2018JD028481

https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2018JD028481?campaign=wolacceptedarticle

Abstract
Estimating the equilibrium climate sensitivity (ECS; the equilibrium warming in response to a doubling of CO2) from observations is one of the big problems in climate science. Using observations of interannual climate variations covering the period 2000 to 2017 and a model‐derived relationship between interannual variations and forced climate change, we estimate ECS is likely 2.4‐4.6 K (17‐83% confidence interval), with a mode and median value of 2.9 and 3.3 K, respectively. This analysis provides no support for low values of ECS (below 2 K) suggested by other analyses. The main uncertainty in our estimate is not observational uncertainty, but rather uncertainty in converting observations of short‐term, mainly unforced climate variability to an estimate of the response of the climate system to long‐term forced warming.

Plain language summary
Equilibrium climate sensitivity (ECS) is the amount of warming resulting from doubling carbon dioxide. It is one of the important metrics in climate science because it is a primary determinant of how much warming we will experience in the future. Despite decades of work, this quantity remains uncertain: the last IPCC report stated a range for ECS of 1.5‐4.5 deg. Celsius. Using observations of interannual climate variations covering the period 2000 to 2017, we estimate ECS is likely 2.4‐4.6 K. Thus, our analysis provides no support for the bottom of the IPCC's range."

You can obtain a copy of the paper here:

https://drive.google.com/file/d/1nt4YEMLc0AwWEAHtHAcwDEVzHkyKj1G-/view
"

[Ned W]

Ned W, I must say the certainty implied in your thread title is not compatible with the information contained herein. There are lots of unknowns in this business - even a layman such as me knows that. Don't be surprised when criticism shows up.

Yes, sorry, that was sort of a joking title.  One could propagate the uncertainty through the calculations (e.g., the 2017 paper I linked to on TCR/ECS ratio has a range of values, not just a central tendency) and the result would be a range of possible ECS's. 

That range is probably asymmetric -- it probably can't be much lower than 2.5, but could be substantially higher. 

At least I didn't say "ECS is 2.500".  And actually, in real life I would probably just round it up to 3.0 and leave it at that.

But ... I do think the method, and the way it works out, is rather cool, and very user-friendly.

TCR integrates for  60 to 80 years (average temperature response over a twenty-year period centered at CO2 doubling in a transient simulation with CO2 increasing at 1% per year (compounded), i.e., 60 – 80 years following initiation of the increase),  and ECS over centuries (but with icesheets held constant, allows deep ocean equilibration)).

But the time period of the data is 50 yrs.

sidd

Yes, the slope of the curve in the above figure is a lower-case "transient climate response" but it definitely does not meet the official criteria of "Transient Climate Response". 

50 years is actually a pretty long time, though.  And it's impressive (to me, anyway) how linear the relationship is in that figure, and how little noise there is.  Not much in climate actually works out this cleanly.

Furthermore, it is important to remember that ECS is not a fixed value but rather is projected to increase with continued global warming, this century:

I think the nonstationarity of ECS is a rather complicated and different studies have found different relationships between climate regime and ECS.  But the broader point -- that ECS is not necessarily fixed -- is reasonable.

[wehappyfew]

Ned,

I absolutely applaud your efforts to highlight the relationship between CO2 and temp, instead of time vs temp. The scatter plot is spot on. I have used the same graph many times when putting denier trolls in their place.

That said, your data do not support your calculation. Specifically, the RCP forcing data you linked to show that the ratio between CO2 forcing and total anthro forcing is not now and has not ever been as low as 0.74.

I believe the error comes from failing to account for non-GHG anthro forcings like aerosols, land-use albedo, cloud albedo due to particulate pollution, etc.

From your data source:

Year 1967
Total anthro forcing (col 4) = 0.6985 W/m^2
CO2 forcing (column 8 )    =   0.7989 W/m^2

Ratio = 1.14


Year 2017
Anthro = 2.398
CO2 = 2.061

Ratio = 0.859

A simple average of the ratios at these 2 end points is almost exactly 1.00, not 0.74

Updating your final conclusion with these corrected values gives us an ECS of 3.37

This is a number fully in line with many other estimates, and even more alarming than the already dangerous value of 2.5.

[AbruptSLR]

I think the nonstationarity of ECS is a rather complicated and different studies have found different relationships between climate regime and ECS.  But the broader point -- that ECS is not necessarily fixed -- is reasonable.

In a constantly changing world, reality is as much a function of the trend as of one's last observation:

Kate Marvel, Robert Pincus, Gavin A. Schmidt & Ron L. Miller (29 January 2018), "Internal Variability and Disequilibrium Confound Estimates of Climate Sensitivity From Observations", Geophysical Research Letters, https://doi.org/10.1002/2017GL076468

https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2017GL076468

Extract: "An emerging literature suggests that estimates of equilibrium climate sensitivity (ECS) derived from recent observations and energy balance models are biased low because models project more positive climate feedback in the far future. Here we use simulations from the Coupled Model Intercomparison Project Phase 5 (CMIP5) to show that across models, ECS inferred from the recent historical period (1979–2005) is indeed almost uniformly lower than that inferred from simulations subject to abrupt increases in CO2 radiative forcing. However, ECS inferred from simulations in which sea surface temperatures are prescribed according to observations is lower still. ECS inferred from simulations with prescribed sea surface temperatures is strongly linked to changes to tropical marine low clouds. However, feedbacks from these clouds are a weak constraint on long‐term model ECS. One interpretation is that observations of recent climate changes constitute a poor direct proxy for long‐term sensitivity."

[AbruptSLR]

Furthermore, Marvel's January 30, 2018, twitter feed indicates:

https://twitter.com/DrKateMarvel

Extract: "So the future is not the past. We're heading toward conditions we've never experienced. There may be no historical analog for what lies ahead.

We have reason to believe that this far future may be hotter, as the Southern Ocean starts to warm up and (perhaps) shed some of its reflective cloud cover.
…
And we seem to have gotten lucky on this front. We've experienced weird cool conditions in the tropical oceans that seem to have resulted in more low cloud cover, which reflected sun & cooled the planet.

This might have just been due to chance (and, at any rate, these weird cool waters have warmed up now). But it led us to an especially low estimate of eventual climate warming.

In summary: the past is not the future. Models don't "run hot". We got lucky. But our luck's run out. Happy Tuesday!"

[Ned W]

Ned,

I absolutely applaud your efforts to highlight the relationship between CO2 and temp, instead of time vs temp. The scatter plot is spot on. I have used the same graph many times when putting denier trolls in their place.

Great! 

That said,

Uh oh...

your data do not support your calculation. Specifically, the RCP forcing data you linked to show that the ratio between CO2 forcing and total anthro forcing is not now and has not ever been as low as 0.74.

I believe the error comes from failing to account for non-GHG anthro forcings like aerosols, land-use albedo, cloud albedo due to particulate pollution, etc.

From your data source:

Year 1967
Total anthro forcing (col 4) = 0.6985 W/m^2
CO2 forcing (column 8 )    =   0.7989 W/m^2

Ratio = 1.14


Year 2017
Anthro = 2.398
CO2 = 2.061

Ratio = 0.859

A simple average of the ratios at these 2 end points is almost exactly 1.00, not 0.74

Updating your final conclusion with these corrected values gives us an ECS of 3.37

This is a number fully in line with many other estimates, and even more alarming than the already dangerous value of 2.5.

I often make mistakes and always try to cheerfully acknowledge them, but in this case I think my work above was actually correct.

The value that you want is not the average of the forcings from 1765-1967 and 1765-2017.  You want the forcings from 1967-2017, i.e., the forcings from the same period during which the temperature change occurs.

So, using your numbers above, which are the same as what I used:

CO2 forcing = 2.061 - 0.7989 = 1.2617 W/m2
Total anthro forcing = 2.398 - 0.6985 = 1.6996 W/m2

Ratio = 1.2617 / 1.6996 = 0.7423 W/m2

Hope that's clear enough.  And thanks for checking my work!

[sidd]

Re: 50 years is actually a pretty long time, though. 

If this method is taken seriously, then the points at the hi end of the graph would be closest to TCR definition. And indeed we see the slope of the last three points increasing ... but i dont think the noise is small enuf to say so definitively.

But a more important reason to doubt this approach is that not only does CO2 have effect on T, the reverse is also true ... so disentangling the two calls for a more subtle argument, as, say, in vanNes(2015) doi: 10.1038/NCLIMATE2568

Although i note that vanNes worked with much longer timescales and did not explicitly calculate a climate sensitivity ...

sidd

[Ned W]

One more note on the question of the CO2/total-anthro forcing ratio:

Here's a graph showing the ratio calculated in rolling 30-year windows centered on a given year (i.e., the CO2 forcing from X+15 to X-15 years, divided by the total anthro forcing during the same time window):



Some crazy spikes in the pre-1950s period, but then circa 1960 it settles in to around 0.75, for the rest of the 20th and first half of the 21st centuries.

BUT ... different data sets for forcings will give somewhat different values for this ratio.  GISS has their own, for example.  And others too, I assume.

Meanwhile ...

But a more important reason to doubt this approach is that not only does CO2 have effect on T, the reverse is also true ... so disentangling the two calls for a more subtle argument, as, say, in vanNes(2015) doi: 10.1038/NCLIMATE2568

I'll take a look at that, but there's no inherent reason why the fact that CO2 is a feedback as well as a forcing should cause a problem for this method.  The definition of climate sensitivity is based on forcing from all CO2 in the atmosphere, whether anthropogenic in origin or from a feedback process.  It's not an emissions-based metric.

[Ned W]

Missed this:

And indeed we see the slope of the last three points increasing ... but i dont think the noise is small enuf to say so definitively.

Eh, I am dubious.  The last three points are above the trendline, but the three points right before them are below the trendline.  My guess is that it's just noise. 

Tamino's method of compensating for ENSO, solar, and volcanics is nice, and it definitely reduces the noise, but it doesn't eliminate it.

That said ... I'll be curious to see where 2018 and 2019 and 2020 fall. 

[wehappyfew]

Indeed, we all make mistakes, and it was my turn to demonstrate the cliche, apparently!

While you've got the spreadsheet fired up, can I suggest another graph?

How about graphing the ECS calculated from your method (ratio of delta forcings) over time, just as you did above to show the changing ratio of RF(CO2)/RF(total anthro)?

And maybe try varying time period from 30 years rolling windows to larger timespans, too.

[sidd]

Re: problems with using T and CO2 regressions for climate sensitivity

in context of ESS, i commented in

https://forum.arctic-sea-ice.net/index.php/topic,1053.msg123247.html#msg123247

In addition to the link listed there i add some realclimate discussions which are quite good, even the comments(?!)

http://www.realclimate.org/index.php/archives/2016/09/why-correlations-of-co2-and-temperature-over-ice-age-cycles-dont-define-climate-sensitivity/

http://www.realclimate.org/index.php/archives/2017/07/climate-sensitivity-estimates-and-corrections/

and there are others posts on realclimate that speak of related matters.

sidd

[Ned W]

Thanks for the links, sidd.  Sounds interesting.

While you've got the spreadsheet fired up, can I suggest another graph?

How about graphing the ECS calculated from your method (ratio of delta forcings) over time, just as you did above to show the changing ratio of RF(CO2)/RF(total anthro)?

And maybe try varying time period from 30 years rolling windows to larger timespans, too.

OK, that is a good idea.  However, there are some constraints:

• Tamino's temperature data start in 1950, but the early years are noisy and I'm reluctant to go back much more than 50 years (1967-ish)
• We can estimate CO2 and temperature for 2018, to add another year.  For 2018 temperature, I'll take the YTD average of Tamino's monthly data.  For 2018 CO2, I'll assume 407.5 (should be close enough).
• I would like the two estimates to be independent, i.e. to use separate windows, not overlapping.

So let's split the 1967-2018 period in half, and have two non-overlapping, 25-year periods (1967-1992 and 1993-2018).  Here is log(CO2) vs temperature:

The slopes are actually not all that different (early = 2.43 and late = 2.64).  During the same two 25-year windows, the CO2/all-forcings ratios are 0.70 (early) and 0.78 (late).  Unfortunately I don't have separate values for the TCR/ECS ratio, so we'll use 0.74 for both periods.

That gives ECS of 2.3 (early) and 2.8 (late).  Not too surprising, since the full period was 2.5.

Now for the million-dollar question: is the increase due to just random noise, or is it the non-stationarity that ASLR alluded to? 

My guess would be ... who knows?  It's well within the noise, and the change in ECS over such a short time period (25 years) should be very small.  So I would bet it's mostly noise, but the noise could be masking a small signal.

Also note:  this is predicated on the TCR/ECS ratio from the 2017 paper cited in the first post.  Using a lower (or higher) value for that ratio would scale both the early and late ECS estimates upward (or downward). 

This is back-of-the-napkin stuff, here, people.  But that's what napkins are for, right?

[Ned W]

Postscript:

Sidd, I don't want you to think I'm ignoring your cautionary comments, which are quite interesting.  Let me give a short answer now, and then think more about it.

The links you are pointing to are about the problems with using an empirical approach like this to relate CO2 and T over the glacial/interglacial cycles.  I think the big problem there is that most of the forcing of T is not coming from CO2, it's coming from the effect of Milankovich cycles on seasonal albedo.  In the approach used in this thread, (a) CO2 is a much larger fraction of the total forcing, and (b) there is a step that explicitly accounts for the ratio of CO2 to total forcing.

So ... I don't think the problems that RealClimate warned about in the Snyder case are particularly meaningful for this one.  But I will think more about it, and would appreciate your thoughts as well.

[AbruptSLR]

The linked reference discusses paleodata to indicate that climate sensitivity increased from 3.3 - 5.6 (mean of 4.45k) at the beginning of the PETM up to 3.7 - 6.5 K (mean of 5.1K) near the peak of the PETM; and that if we burn only the easily accessible carbon reserves then GMST could increase by about 10C.  I note these climate sensitivity values are much higher than those inherent in the CMIP5 projections:

Gary Shaffer, Matthew Huber, Roberto Rondanelli & Jens Olaf Pepke Pedersen (23 June 2016), "Deep-time evidence for climate sensitivity increase with warming", Geophysical Research Letters, DOI: 10.1002/2016GL069243

http://onlinelibrary.wiley.com/doi/10.1002/2016GL069243/full

Abstract: "Future global warming from anthropogenic greenhouse gas emissions will depend on climate feedbacks, the effect of which is expressed by climate sensitivity, the warming for a doubling of atmospheric CO2 content. It is not clear how feedbacks, sensitivity and temperature will evolve in our warming world but past warming events may provide insight. Here we employ paleo-reconstructions and new climate-carbon model simulations in a novel framework to explore a wide scenario range for the Paleocene-Eocene Thermal Maximum (PETM) carbon release and global warming event 55.8 million years ago, a possible future warming analogue. We obtain constrained estimates of CO2 and climate sensitivity before and during the PETM and of the PETM carbon input amount and nature. Sensitivity increased from 3.3 - 5.6 to 3.7 - 6.5 K (Kelvin) into the PETM. When taken together with Last Glacial Maximum and modern estimates this result indicates climate sensitivity increase with global warming."

Also see:

https://www.sciencedaily.com/releases/2016/06/160623112206.htm

Extract: ""Our results show that the amount of carbon that drove the PETM warming was about the same amount as the current 'easily accessible' fossil fuel reserves of about 4,000 billion tons. But the warming that would result from adding such large amounts of carbon to the climate system would be much greater today than during the PETM and could reach up to 10 degrees. This is partly due to the current atmosphere containing much less CO2 -- approximately 400 ppm (parts per million) -- compared to before the PETM, where the concentration was about 1,000 ppm and partly because we emit carbon into the atmosphere at a much faster rate than during the PETM. If we then also take into account the fact that climate sensitivity increases with the temperature, it means that it is all the more urgent to limit global warming as soon as possible by reducing the human-made emissions of greenhouse gases," explains Professor Gary Shaffer, who conducted the study in collaboration with researchers from Purdue University, USA, the University of Chile and the Technical University of Denmark."

Caption for attached image: "Paleo climate sensitivity study reconstructs global warming 56 million years ago and suggests future global warming could be even worse than expected. This graphic shows climate sensitivity at different global temperatures in the atmosphere. The figure shows from the right estimates for the past warm period, the PETM 56 million years ago, the period before the PETM and for the present. On the left the figure shows estimates for the Last Glacial Maximum. Courtesy: Gary Shaffer and Roberto Rondanelli

[AbruptSLR]

The linked RealClimate article discusses the findings of Armour (2017) and Proistosescu & Huybers (2017), that compare CMIP5 findings of ECS vs 'instantaneous' climate sensitivity (ICS) based on observations (see previous posts).  However, I would like to note that since CMIP5 findings were published, numerous references have found that CMIP5 apparently errs on the side of least drama w.r.t. such areas (off the top of my head) as: Paleodata, Model Boundary Conditions/Parameters, Cloud feedback, Aerosol Forcings and Feedbacks, Permafrost Degradation, Methane Hydrates, Ice-Climate Feedback, Tropical Land Degradation & Changes in Land Albedo; Climate Attractors (ENSO, etc), Oceanic CO₂ Venting, Degradation of Oceanic CO₂ Sinks, Degradation of Land CO₂ Sinks, Arctic Amplification and Antarctic Amplification.  Therefore, we should not feel too comfortable that Armour (2017) and Proistosescu & Huybers (2017) represent the final increase in estimated ECS values.

Title: "Sensible Questions on Climate Sensitivity"

http://www.realclimate.org/index.php/archives/2017/08/sensible-questions-on-climate-sensitivity/

Extract: "The recent papers, by Kyle Armour (hereafter A17) and by us (Proistosescu and Huybers, 2017) (hereafter PH17), build on a large literature documenting the time-dependence of climate feedbacks in models. They make quantitative apples-to-apples comparisons between the climate sensitivities simulated by CMIP5 models and those inferred from global energy budget observations.

Because feedbacks may change over time as patterns of warming evolve, observations made today do not necessarily provide estimates of the long-term, equilibrium climate sensitivity (ECS). Rather, they constrain a quantity that we call the inferred (A17), or instantaneous (PH17), climate sensitivity (ICS). The two studies were performed independently using distinct methodologies, and both find that ICS values are systematically lower than ECS values within CMIP5 models. Moreover, they find that model-derived ICS values are consistent with ICS values inferred from observations.
…
What is the magnitude of ECS? (hint:≠ICS)
An important core finding of A17 and PH17 is that values of ICS drawn from the historical record are not sufficient to constrain values of ECS. Indeed, within models, ICS and ECS differ as the strength of radiative feedbacks change over time as patterns of surface temperature evolve with warming. PH17 demonstrated that portions of the climate system that respond over centennial timescales (such as the southern oceans) are important amplifiers of climate sensitivity in the models – a slow-mode response leading to values of ECS that are higher than the values of ICS that reflect more transient warming. Increasing sensitivity over time seems to be associated with a low-cloud feedback excited by warming in the Eastern Equatorial Pacific and Southern Ocean. This slow-mode response (and thus ECS) is essentially unconstrained by global energy budget observations because warming in these regions has been small, possibly held back by upwelling water from the ocean interior.

Key research targets should be improving understanding of (i) how the east-west temperature gradient in the Pacific Ocean will evolve in the future, and (ii) how low-level cloud (and other) feedbacks will respond, in turn. Zhou et al (2017) suggest that feedbacks can vary with the surface warming pattern, at least on decadal timescales."

[sidd]

I think one key warning against using T/CO2 regression is the following argument. Lets say i am god and i have an infinite number of planet earths to play with.

I dial up CO2 (i have an infinite number of CO2 cylinders) in the atmosphere while keeping all else constant. Then T will increase.

Next  i take another planet earth and dial up T keeping all else constant (i have an infinite number of heaters) , then CO2 will increase. 

There are a number of objections to this argument, one is that it is not possible even for god to violate the laws of physics, therefore i could not hold all else constant. That is precisely the problem that vanNes addresses, an attempt to disentangle the major feedbacks and feedforwards.

sidd

[Ned W]

Lets say i am god and i have an infinite number of planet earths to play with.

OK, Sidd Almighty...

I dial up CO2 (i have an infinite number of CO2 cylinders) in the atmosphere while keeping all else constant. Then T will increase.

OK so far.  So CO2 goes up, and temperature goes up.  We divide the temperature increase by the CO2 increase, and calculate climate sensitivity. 

I'm not seeing the problem here.  Actually, this first earth sounds a lot like our own, except the CO2 is coming from Divine CO2 Cylinders rather than coal/oil.

Anyhoo, onwards to earth #2:

Next  i take another planet earth and dial up T keeping all else constant (i have an infinite number of heaters) , then CO2 will increase.

This is slightly trickier, but follow me here.  T rises, and CO2 follows, and then the CO2 adds some additional temperature rise.  Now, if we ascribed ALL of the rise in T to the rise in CO2, that would be a problem.  In fact, that's sort of what happens in the Snyder paper that was discussed in your RealClimate link, and it's why they reported some insane climate sensitivity of 9 C or whatever.

But that's not how I do it!   I scale the initial climate sensitivity by the fraction of the total forcing that comes from CO2.  In the case of our earth, 74% of it is from CO2 but there's a bit more from CH4, N2O, ozone, halocarbons, etc.   So we multiply the initial sensitivity (er, TCR) by 0.74. 

In the case of your earth #2, most of the total forcing is Divine Intervention from Almighty Sidd.  Say that 5% is the result of the CO2 feedback.  Thus, we multiply our initial estimate of TCR by 0.05, because most of the warming is due to Sidd, not CO2.

So, again, it works. 

There are a number of objections to this argument, one is that it is not possible even for god to violate the laws of physics, therefore i could not hold all else constant. That is precisely the problem that vanNes addresses, an attempt to disentangle the major feedbacks and feedforwards.

I think that is a big problem when we don't have enough information, and that's what vanNes is addressing. 

If someone tries to do this over the past 65 million years, or for the PETM, or for the LGM, or for the Azolla Event, or whatever ... they don't know how much of the observed temperature change is due to CO2.  There are lots of arguments about dust forcings at the LGM.  So the derived value for TCR will be highly dependent on the assumptions one makes about other forcings.

But for the past 50 years, we actually have a lot of information!  There isn't 100% agreement, but at least we have a pretty good idea what the forcings are.  At least we have a much better idea than we do about what was happening at the PETM, or the Eemian, or MIS 11, or whatever.

So it's not perfect, but sadly, nothing is perfect.  And it has the following virtues:

(1) It's clear and straightforward.  Anyone can understand it (with a little help).

(2) All the data needed are freely available.

(3) The result is at least plausible.  It is near the middle of the IPCC's range and it demolishes the oft-repeated denialist argument that "there's no correlation between CO2 and temperature", usually accompanied by plots of non-log-transformed CO2 concentration and UAH LT temperature over a short cherry-picked time interval.

In fact, merely writing that last sentence makes me want to post this again:

 

[wehappyfew]

...

OK, that is a good idea.  However, there are some constraints:

...

Tamino's temperature data start in 1950, but the early years are noisy and I'm reluctant to go back much more than 50 years (1967-ish)

...

So let's split the 1967-2018 period in half, and have two non-overlapping, 25-year periods (1967-1992 and 1993-2018).

...

That gives ECS of 2.3 (early) and 2.8 (late).  Not too surprising, since the full period was 2.5.

Now for the million-dollar question: is the increase due to just random noise, or is it the non-stationarity that ASLR alluded to? 

...

This is back-of-the-napkin stuff, here, people.  But that's what napkins are for, right?

Right, my napkins are practically unreadable by now.

Thanks for the new calculation and graph.

Here are my reactions:

A) The period from the late 1930's to the late 1950's is a rather unique, interesting, and potentially valuable time for consideration in this debate about ECS. Total anthro forcing paused and did not increase at all for 20ish years (1937 to 1958 for example).

B) The formal definition of TCS used in modeling climate requires a very fast rate of increase in CO2 forcing - 1% per year for 72 years to achieve a doubling.



Synthesizing these points, while the forcings paused for 20 years we were not at all observing anything related to TCS, but were slowly evolving towards equilibrium (ECS) for few decades. When forcings resumed their increase, the rate of change in CO2 forcing was far less than 1% per year at the beginning, and is still barely above 1/2% per year now.

So the temperature increased more than it would in a strict TCS model at the beginning of your time period - it was able to get slightly closer to equilibrium. For the second half, the forcing increased faster, and therefore closer to the TCS condition.

So the scatter plot graph of CO2 forcing vs temp has a bias towards higher temps at the left side than it would if TCS were calculated at the full rate of CO2 increase. This means your slope shows a bias towards flatter on the left, and steeper on the right.




Prediction:

If we are foolish enough to continue accelerating our CO2 emission, or if natural sinks break down, and thereby we see CO2 forcings increase at a rate close to 1% per year ...
... Then the ECS calculated by your method would be even higher on the next 25 year segment, as the true TCS conditions are felt.




Next calculation discussion:

Tamino's method of removing non-anthro effects is useful for shorter time spans, and a valuable refinement for your calculation, but over much longer time spans the natural forcings are mostly constant.

Therefore I think it would be interesting to repeat your method on longer time spans, and include pre-1950 data to get a longer term view.

The limitation I discussed above still apply... but it still may be useful to see how it has evolved over longer time spans.

[sidd]

Re: "Say that 5% is the result of the CO2 feedback."

Mmm. Glacial-interglacial swing is a lot more than that. But, there are a lot of other things going on, so back to a vanNes type approach, for me, nyhoo.

I think  a lot of the difficulty in is imprecision of definition. We don't have an Earth where CO2 ppm increases by 1%/yr for seventy year. We don't have an Earth where we instantaneously double CO2, hold it there and see what happens in a thousand. So everything is in terms of hypothetical, modelled Earths. TCR, ECS and even ESS are what happens on these modelled Earths.

Meta: not on topic

In a larger view indicators like global mean surface temperature or climate sensitivities are of peripheral interest to me.

Since, here in the sidd Unalmighty world, we subject Gaia to multiple stressors, CO2 being just one. We use around a third of NPP, we hugely increase runoff impermeable surface, we establish monoculture and GMO crop to exclusion of else, we suck underground aquifers dry and mighty rivers, and poison both and kill oceans to boot. And many more stressors will occur to you.
 
Doom looms nigh. The threat that will overtake us first is not direct temperature increase but habitat collapse. Our habitat.

There's probably a thread for that discussion, but it is not here, so i'll shutup.

sidd

[sidd]

Re: There's probably a thread

i began one

https://forum.arctic-sea-ice.net/index.php/topic,2428.msg177592/topicseen.html#msg177592

sidd

[Archimid]

Has anyone done an estimate for ECS based on hemisphere, not the globe? What is the ECS of the Northern Hemisphere?

It seems to me that because the SH is mostly covered with water with the south pole covered with land, and the NH has much larger land surface area with a north pole covered in water, their ECS might be significantly different. 

[Ned W]

Therefore I think it would be interesting to repeat your method on longer time spans, and include pre-1950 data to get a longer term view.

Has anyone done an estimate for ECS based on hemisphere, not the globe? What is the ECS of the Northern Hemisphere?

It seems to me that because the SH is mostly covered with water with the south pole covered with land, and the NH has much larger land surface area with a north pole covered in water, their ECS might be significantly different. 

You all don't ask much, do you?     Actually, I love all the suggestions -- these are great.  Let me tackle the first one first.

Here's the same method, applied to (a) Cowtan & Way, and (b) Berkeley Earth, for the entire length of their data (1850-2017):

Over that time period, the CO2 forcing was 1.914 W/m2 and the total (including solar & volcanic) was 2.036 W/m2, for a ratio of 0.940.  Multiplying the two slopes by 0.94 and dividing by 0.74 (our assumed TCR/ECS ratio) gives ECS of 2.7 (Cowtan and Way) or 3.0 (Berkeley Earth).

Next, for Archimid's truly excellent question about differing values of ECS for different hemispheres:

We can do even better than that.  NASA GISTEMP provides land/ocean temperature records from 1880-present by zone (Arctic, tropics, N vs S hemispheres, etc.) for 14 latitudinal zones.  I applied the same methodology:

* All zones have their own temperatures, but use the same CO2 data (obviously).

* Likewise, all zones use the same CO2/Total_RF ratio (which for 1880-2017 is 0.883).

* Likewise, all zones use the same TCR/ECS ratio (the same 0.74 we've been using all along).  This could well be a problem, in fact I think it almost certainly is, but for consistency let's run with it for now, while I try to figure out how to do this better.

Anyway, here are the results:

ASIF readers will be astounded (NOT!  ) to learn that ECS for the Arctic is much higher than for the rest of the globe. 

Note that I'm rather dubious about the overall validity of this as an estimate of ECS -- the numbers are very much plausible, but as we move from doing this for the whole globe to doing it for latitudinal zones, I am increasingly uncomfortable with the assumed (and fixed) TCR/ECS ratio, plus the assumption that the slopes are actually representative of TCR over this long time period.

With that caveat, here is a table with the CO2 vs temperature slopes, and the final ECS estimates:

Zone	T/CO2 slope	ECS estimate
Glob	2.37	2.83
NHem	2.71	3.24
SHem	2.03	2.43
24N-90N	3.14	3.75
24S-24N	2.09	2.5
90S-24S	1.96	2.34
64N-90N	5.67	6.77
44N-64N	3.38	4.03
24N-44N	2.31	2.76
EQU-24N	2.06	2.46
24S-EQU	2.13	2.54
44S-24S	2.13	2.54
64S-44S	1.56	1.86
90S-64S	2.12	2.54

Thanks to wehappyfew and Archimid for the suggestions.

[FishOutofWater]

One thing you all should consider it that the fraction of CO2 that dissolves in sea water goes down over time as the oceans warm because CO2 is more soluble in cold water than warm water. The fraction of CO2 emissions that stays in the atmosphere increases over time as the oceans warm.

Fifty years is not a long time in geologic terms. It's not a long time in terms of processes in the oceans. I suspect that the cancelling out of terms is an accident of the way you analyzed the problem, not something that will be borne out by detailed scientific investigation. I think the papers which ASLR cites are onto a big problem. As the world warms beyond key tipping points things that helped keep down temperatures in the past, such as CO2 dissolution in the oceans, stop working.

Even if the value of 2.5 is correct, we will be in trouble when Siberian permafrost the Amazon becomes major emissions sources of CO2 and the coastal seas and ocean margins become increasingly anoxic. There is evidence if temperatures rise to 1.5C, Siberian permafrost CO2 emissions will take us up another .5C or more. And then there's methane....

So it's important to remember that the curve you display represents the ECS for atmospheric CO2, not anthropogenic CO2 emissions.

[Ned W]

One thing you all should consider it that the fraction of CO2 that dissolves in sea water goes down over time as the oceans warm because CO2 is more soluble in cold water than warm water. The fraction of CO2 emissions that stays in the atmosphere increases over time as the oceans warm.

Yes, I'm extremely aware of that.  A long time ago I actually wrote code to describe that process in an air/sea gas exchange model, along with all the related carbonate chemistry processes in seawater. It was rather more complicated than anything we're doing here.

I suspect that the cancelling out of terms is an accident of the way you analyzed the problem, not something that will be borne out by detailed scientific investigation.

It's not even something that would be borne out by superficial scientific investigation  .  In fact, the cancellation of terms in the first post was a highly improbable coincidence associated with the particular time window I happened to pick (1967-2017) for which one particular definition of forcings happened to exactly match one particular estimate of the TCR/ECS ratio.  As soon as we moved on to other time ranges, the ratios no longer matched.  (But that's OK, nothing here depended on the two ratios being the same). 

I should probably edit the first post to clarify this, and other things as well.  This thread is very much a work in progress.

Even if the value of 2.5 is correct, we will be in trouble when Siberian permafrost the Amazon becomes major emissions sources of CO2

That might speed up the warming,  but it doesn't necessarily affect the calculation of ECS.  ECS tells us that when CO2 reaches X ppmv, temperature will reach Y degrees.  Adding in CO2 feedbacks just means that both X and Y will be reached faster (or slower, for a negative feedback). 

But nothing in the calculations here says anything about time.  Indeed, the whole point of this thread is to show the value of looking at global temperature as a function of CO2 concentration instead of as a function of time. 

The 1850-2017 graph I posted above shows that there has been a highly linear relationship between temperature and the base-2 logarithm of CO2 concentration, lasting for more than 150 years.  By contrast, a graph of temperature versus time (as is usually shown) is extremely nonlinear over that time period.

And I'll emphasize again that I don't actually claim that this thread proves that ECS is 2.5.  The specificity of that was something of a joke.  I do think it's likely to be somewhere in the 2.5 to 3.0 range.  It could be slightly lower than 2.5, but probably not much.  It could be higher than 3.0, but probably not a lot higher.  In particular, a lot here is riding on the assumptions that the slope of these lines is close to TCR, and that the TCR/ECS ratio can be specified as 0.74 (or some other value).  I have ideas about how to test those, I just need time.

FWIW, looking back through this thread, using different combinations of time period and temperature data set, the estimates for ECS (global, not zonal) under different circumstances have been 2.3, 2.5, 2.7, 2.8, and 3.0.  That's without even getting into the issues mentioned in the previous paragraph.

[Sebastian Jones]

Witnessing the science being developed on this thread is the reason I was initially attracted to the Forum .
Fascinating stuff, thank you very much Ned W - and to Sidd, FooW et al.who contributed.

[Ned W]

Witnessing the science being developed on this thread is the reason I was initially attracted to the Forum .
Fascinating stuff, thank you very much Ned W - and to Sidd, FooW et al.who contributed.

Thanks!

I am not a graphic designer, and someone else could do a much better job with this ... but it was fun putting it together:

Suggestions are welcome.

Also, I made a bunch of updates to the top post.

Edited to add:  I should add some notes/credits at the bottom of that.  The temperature data are from Berkeley Earth (founded by skeptics! funded by the Kochs!).  Other data sets are from various places -- I can provide links if anyone wants to replicate.  For each graph, I used the entire length of the data set in question, or from 1850, since the temperature data start in 1850.  All of them are over 100 years of data, except the cosmic ray measurements (from 1964).

[oren]

Something is still bothering me here and I apologize in advance for presenting it in layman's terms. CO2 in the atmosphere contributes to warming for as long as it is not absorbed, and for as long as there remains an energy imbalance. Should CO2 concentration stabilize at current levels, or even slowly drop, warming would still continue for many years (am I wrong here?).
In other words, a linear relationship between CO2 and global temperatures is IMHO not expected, and is more of a coincidence of the relatively linear rising trend in CO2 over the past decades.
So if I am right and such a relationship is not expected, how can it so easily lead to a great calculation of ECS?
As a thought experiment, should humans drive up CO2 to 500 ppm and then over a few decades it would drop to 400, while temps still continued to warm due to the high energy imbalance, would the same calculation give us a negative ECS?
My guess is this has to do with the assumed fixed relationship between TCR and ECS.

[sidd]

Re: "(am I wrong here?)."

No. warming will continue until fossil emissions reach zero.

" a linear relationship between CO2 and global temperatures is IMHO not expected"

Nor is it found. The x axis in Mr NedW graph is logarithmic.

sidd

[Richard Rathbone]

In other words, a linear relationship between CO2 and global temperatures is IMHO not expected, and is more of a coincidence of the relatively linear rising trend in CO2 over the past decades.
So if I am right and such a relationship is not expected, how can it so easily lead to a great calculation of ECS?
As a thought experiment, should humans drive up CO2 to 500 ppm and then over a few decades it would drop to 400, while temps still continued to warm due to the high energy imbalance, would the same calculation give us a negative ECS?
My guess is this has to do with the assumed fixed relationship between TCR and ECS.

The lag is relatively short compared to the data length, and the increase in logCO2 is pretty constant. Under these conditions a straight line is expected and Ned's analysis is valid.

If you want to predict what happens on shorter timescales when CO2 change ceases to be exponential, you do need knowledge of the dynamics of the lag, but because atmospheric CO2 has been forced with a simple function, the simple analysis here works.

[Archimid]

Thanks for the answers Ned W.
 

ASIF readers will be astounded (NOT!  ) to learn that ECS for the Arctic is much higher than for the rest of the globe.

I was expecting it, but seeing it in your visualization was still shocking and sad. I wish it wasn't that way.  If the ECS was even throughout the planet climate change wouldn't be so bad. Arctic amplification makes climate change worse. Much worse.

The lowest ECS belongs to 44S-24S. I'm under the impression that is because 44S-24S has the least land surface area and the most sea surface area. Also Antarctic sea ice may be playing a huge role in that low ECS.

[AbruptSLR]

In other words, a linear relationship between CO2 and global temperatures is IMHO not expected, and is more of a coincidence of the relatively linear rising trend in CO2 over the past decades.
So if I am right and such a relationship is not expected, how can it so easily lead to a great calculation of ECS?
As a thought experiment, should humans drive up CO2 to 500 ppm and then over a few decades it would drop to 400, while temps still continued to warm due to the high energy imbalance, would the same calculation give us a negative ECS?
My guess is this has to do with the assumed fixed relationship between TCR and ECS.

The lag is relatively short compared to the data length, and the increase in logCO2 is pretty constant. Under these conditions a straight line is expected and Ned's analysis is valid.

If you want to predict what happens on shorter timescales when CO2 change ceases to be exponential, you do need knowledge of the dynamics of the lag, but because atmospheric CO2 has been forced with a simple function, the simple analysis here works.

As I noted in my Reply #3, Andrew Dessler calculates/estimates that the range for ECS "… is likely 2.4‐4.6 K (17‐83% confidence interval), with a mode and median value of 2.9 and 3.3 K, respectively."  Thus, if Ned W wants to convince real climate scientists that ECS is 2.5C, he might want to follow Dessler's advice in the linked Twitter thread:

Title: "To the whack jobs out there who think they have a better theory of climate, here's what you have to do to convince scientists: 1/"

https://twitter.com/AndrewDessler/status/919321354104475648

Extract: " step 1: you have to show the governing equations; i.e., temperature as a function of the key variables; T = XXX or dT/dt = XXX 2/

step 2: then you must show this reproduces key observations. Mainstream theory explains just about everything, so ur theory should too 3/

step 3: if you want to superced mainstream climate theory, you must show your theory explains something that mainstream theory doesn't 4/

…"

[Ned W]

Thus, if Ned W wants to convince real climate scientists that ECS is 2.5C, he might want to follow Dessler's advice in the linked Twitter thread:

Title: "To the whack jobs out there who think they have a better theory of climate, here's what you have to do to convince scientists:

This kind of obnoxious, passive-aggressive shit is exactly why so many people who want to talk about science here end up leaving. 

[sidd]

Re: "obnoxious, passive-aggressive shit "

Perhaps take that to "forum decorum" thread. Else, or and, hit the ignore button and move on ?

sidd

[Rod]

This kind of obnoxious, passive-aggressive shit is exactly why so many people who want to talk about science here end up leaving.

I agree. 

[AbruptSLR]

This kind of obnoxious, passive-aggressive shit is exactly why so many people who want to talk about science here end up leaving.

I agree.

All models are wrong, but some models are useful and others are not.  At the very minimum the title of this thread should be changed to cite a defensible range of values for ECS.  Furthermore, I note that since the AR5 range was published, numerous studies have demonstrated that the AR5 range errs on the low side.

[AbruptSLR]

As a follow-on to my last post, I note that USGCRP (2017) Chapter 15: Potential Surprises provides the following supporting evidence for their medium confidence assertion that consensus climate models underestimate paleo reconstructions of climate sensitivity:

USGCRP, 2017: Climate Science Special Report: Fourth National Climate Assessment, Volume I [Wuebbles, D.J., D.W. Fahey, K.A. Hibbard, D.J. Dokken, B.C. Stewart, and T.K. Maycock (eds.)]. U.S. Global Change Research Program, Washington, DC, USA, 470 pp.

Title: "Chapter 15: Potential Surprises: Compound Extremes and Tipping Elements"

https://science2017.globalchange.gov/chapter/15/

Extract: "While climate models incorporate important climate processes that can be well quantified, they do not include all of the processes that can contribute to feedbacks, compound extreme events, and abrupt and/or irreversible changes. For this reason, future changes outside the range projected by climate models cannot be ruled out (very high confidence). Moreover, the systematic tendency of climate models to underestimate temperature change during warm paleoclimates suggests that climate models are more likely to underestimate than to overestimate the amount of long-term future change (medium confidence).
…
The second half of this key finding is based upon the tendency of global climate models to underestimate, relative to geological reconstructions, the magnitude of both long-term global mean warming and the amplification of warming at high latitudes in past warm climates (e.g., Salzmann et al. 2013; Goldner et al. 2014; Caballeo and Huber 2013; Lunt et al. 2012)."

Note USGCRP (2017) classifies Medium Confidence as: "Suggestive evidence (a few sources, limited consistency, models incomplete, methods emerging, etc.), competing schools of thought"

Furthermore, the guide to USGCRP (2017) classifies these "Potential Surprises" as 'potential low probability/high consequence "surprises" resulting from climate change' and as 'high-risk tails and bounding scenarios'; and acknowledge that 'knowledge gaps' exist that limit their ability to precisely define the probability/risks associated with these "surprises".

https://science2017.globalchange.gov/chapter/front-matter-guide/

Extract: "Complementing this use of risk-focused language and presentation around specific scientific findings in the report, Chapter 15: Potential Surprises provides an overview of potential low probability/high consequence “surprises” resulting from climate change. This includes its analyses of thresholds, also called tipping points, in the climate system and the compounding effects of multiple, interacting climate change impacts whose consequences may be much greater than the sum of the individual impacts. Chapter 15 also highlights critical knowledge gaps that determine the degree to which such high-risk tails and bounding scenarios can be precisely defined, including missing processes and feedbacks."

This USGCRP (2017) characterization of "Potential Surprises", reinforces my belief that consensus climate scientists are acting as co-dependents who cleverly facilitate the fossil fuel addiction of the decision makers that have put us all at risk of climate catastrophe this century, as illustrated by the cascading tipping points cited by the DominoES project.

I wish that I had the time and energy to repeat the thousands of posts that I have made that indicate that such "Potential Surprises" this century are much more likely than low probability high-risk tail events; which ignores such consideration as: that CO2e is currently over 530ppm, that recent masking mechanisms and lag time have hidden some of the apparent risk, that none of the CMIP5 modeling include ice-climate feedback mechanism, etc.  Nevertheless, I repost the four attached images, with:

The first image by Friedrich et al. (2016), illustrating that USGRP (2017) ignored numerous recent studies that used dynamical analysis of paleo data to show that ECS has been/is higher than consensus science acknowledge.

The second image by Armour (2016), illustrating that USGRP (2017) ignored consideration of slow response mechanisms that PH17 show have been slowly/progressively activated since 1750 and are now in effect.  When considering these slow response feedbacks the most frequent (mode) value for ECS is about 4C, but due to the right-skew of the PDF the mean value is close to 5C.

The middle panel of the third image from Andrew's 2015 Ringberg presentation shows that the slow response mechanism identified by PH17 is characterized by a warm Tropical Pacific and has an ECS value of about 5C.  Furthermore, I note that the ice-climate feedback mechanism (including freshwater hosing events from the AIS (particularly the WAIS), the GIS, and from a reversal of the Beaufort Gyre) were ignored by consensus models and all contribute to rapid warming of the tropical oceans and particularly the Tropical Pacific.

While all consensus models cited by USGRP (2017) ignored radiative forcing input from permafrost regions, the fourth image illustrates just one such ignored positive feedback mechanism that following RCP 8.5 until about 2050-2060 will result in major pulse emissions of both carbon dioxide and methane from thermokarst lakes in the Arctic permafrost.

There are many other 'dominoes' that I could cite for a scenario of a potential cascade of tipping points leading to abrupt climate change this century; however, as the US DOE is spending hundreds of millions of dollars on the state-of-the-art E3SM climate model (to be completed by 2027).

[Ned W]

Something is still bothering me here and I apologize in advance for presenting it in layman's terms. CO2 in the atmosphere contributes to warming for as long as it is not absorbed, and for as long as there remains an energy imbalance. Should CO2 concentration stabilize at current levels, or even slowly drop, warming would still continue for many years (am I wrong here?).

Yes, I mean no, you're not wrong.  How it plays out depends on how fast or slowly the stabilization occurs.  I've been looking at what climate models (GISS Model E, to be specific) can say about the methodology of this thread (see forthcoming post) so let's look at this using the outputs from some runs of Model E forced with the RCP 8.5 forcings.  First, here are the total and CO2 forcings:

The rate of forcing slows down after 2100 and stabilizes in 2250 (literally, the values are constant after that).  Here are the resulting temperatures, in six model runs:

In most cases, temperature does continue to rise slowly (and slightly) after 2250, even though the forcings are constant.  More detail:

In five of the six model runs, the temperature rises by about a third of a degree during the 50 years after stabilization of forcings.

In other words, a linear relationship between [the log of] CO2 and global temperatures is IMHO not expected, and is more of a coincidence of the relatively linear rising trend in CO2 over the past decades.
So if I am right and such a relationship is not expected, how can it so easily lead to a great calculation of ECS?

Hope you're OK with my emendation there. 
The idea here is that there are fast and slow responses to forcing.  While the forcing is still occurring, we're only seeing the fast response and part of the slow response.  (Call this "transient sensitivity").  But if we assume there is a certain ratio between the "transient sensitivity" and the ultimate, post-stabilization "equilibrium sensitivity", then we can use the thing that we do see (transient S) to estimate the thing that we don't see (equilibrium S). 

Each of the versions of this analysis up-thread involves three steps:

(1) Calculate the slope of the CO2/temp line.

(2) Adjust the slope [downward, usually] to compensate for the percent of forcing that is from CO2 (we don't want to "credit" CO2 with warming that's due to other forcings).

(3) Adjust the slope [upward] to convert from transient S to equilibrium S.

So ... that step 3 is an attempt to deal with what Oren is talking about here.

As a thought experiment, should humans drive up CO2 to 500 ppm and then over a few decades it would drop to 400, while temps still continued to warm due to the high energy imbalance, would the same calculation give us a negative ECS?

This all depends on how fast (& how far) the forcings rose, and how fast (& how far) they fall. If the rise is slow enough, some of the "slow response" manifests during the transient period.  If the rise is very fast, and then it stops suddenly, there's more warming still left in the pipeline.

In your thought experiment there, dropping CO2 from 500 to 400 in "a few decades" is a pretty big and fast drop.  My guess is that the fast response (cooling) would overwhelm the remaining slow response (warming), so temperature would drop.  But it wouldn't drop as fast as expected due to the lagging, residual slow response from the previous warming.

BUT if the changes in forcing and temperature are very small, it's possible for this method to give crazy results, like a negative ECS. 

My guess is this has to do with the assumed fixed relationship between TCR and ECS.

Yes, exactly.  To keep sidd happy, let's de-formalize that slightly and just refer to a "quasi TCR" because we haven't raised CO2 fast enough or far enough to meet the formal definition of TCR.  In theory, if CO2 and temp are rising for a long enough time at a rate that yields a reasonably stable "quasi TCR", and we know how much higher ECS should be compared to "quasi TCR", this method should give a correct answer for ECS.

But quasi TCR is not TCR, and there is uncertainty about the TCR/ECS ratio, and there is uncertainty about the ratio of CO2 to total forcing.  So this method is not perfect.  But there might be ways we can characterize that imperfection, or improve it....

[Ned W]

From earlier in this thread, here are the CO2-vs-T curves for observations (Cowtan & Way, and Berkeley Earth) for the entire period of record (1850 to 2017):

For comparison, here is the same thing, for the six runs of GISS Model E from the previous post:

Same time period (1850 to 2017).  The main thing to note is that the general behavior is similar.  Temperature pretty much rises in reasonably linear proportion to the increased forcing from CO2.  I put trendlines on two of the six model runs as examples, but the details don't really matter.  (And any discussion of obs vs models needs this caveat).

FWIW, I vaguely recall that Model E2R has an ECS around 2.4 or so.  Applying the methods from this thread to the 1850-2017 model results gives estimates of ECS from 2.4 to 3.6.    

[Pmt111500]

"ECS is not 2.5" -thread might be in order.

[Ned W]

"ECS is not 2.5" -thread might be in order.

Feel free to start one. 

Aside from that, I'd just reiterate that the point of this thread is more about the method -- and the learning opportunities that go with the method -- rather than the result.  If you're just joining the thread now, there is a lot of interesting discussion in previous posts.

[Ned W]

Here's an example of why I like this.

Let's say that someone asks "What will the global mean temperature be, later in this century when CO2 hits 500 ppm?"

How can one answer this? 

There are a bunch of different ways.  You can go through the literature and try to find an answer.  You could go to the CMIP5 model archives and find an answer (or a bunch of answers).  You could try to come up with a ballpark estimate based on climate sensitivity, but the climate won't be in equilibrium when it first hits 500 ppm.  You could look at how fast temperature has been rising in recent decades, make some assumption about how many years it will take to hit 500 ppm, and extrapolate.

Another way is to plot CO2 vs temperature, like this:

and say "OK, over the past 50 years, temperature has been rising at a rate of about 2.5 C per doubling of CO2.  Going from 408 to 500 ppm is 0.293 doublings, so the temperature will probably be about 0.7 to 0.8 C higher than today."

I think that's a pretty reasonable approach for ordinary purposes.  I'm not suggesting that it's superior to running a climate model.  It's just a nice back-of-the-envelope method, one which doesn't require a supercomputer.

[oren]

Hi Ned. Thank you for taking the time to understand my issue and for your detailed and very clear response. (And yes, I missed that it's log CO2).
As I was reading the second of your posts, I wondered at the shape of the T vs log CO2 chart for 2200 to 2300, or even better for 2250 to 2300. Surely it will best exemplify how the ratio breaks down under certain CO2 trajectories.
Another question which occurs to me and for which my intuition is probably off is how fast is the "fast response". Is this a couple of years or a couple of decades? In other words, for a thought experiment of a big spike in CO2 and then immediate stabilization at the new higher level, what would be the temperature trajectory over time? My intuition tells me fast warming (the initial sharp rise) is a couple of decades, not a couple of years. If that is indeed the case, my famed intuition tells me that the calculation method shown in this thread should have a high uncertainty, as changes in CO2 trajectory will not be recorded quickly in the temperature trajectory, and therefore the ratio could be spread widely.
I apologize for not framing it in more formal terms. If I sit down and quantify the whole method and play with some climate simulations, I believe I could formalize this, but I doubt this will ever happen. Just an armchair scientist unfortunately (and even that title is highly debatable).

[Ned W]

Hi, Oren. I like your comments there.  I am traveling now, so won't have any fancy graphics, but here are some reactions:

1. The shape of the curve for 2250 to 2300 is, as you would imagine, just a straight vertical uptick.  The forcing is zero (no change in CO2 or anything else after 2250) but there is still a change in temperature.  So there is a small dY and zero dX.

My recollection is that as the curve approaches 2250 (ie, as it slowly stabilizes) it flattens out.  This is not what I was expecting, and I haven't yet wrapped my head around it.  It seems like it ought to steepen, not flatten.  I am probably being stupid.

2. I believe that the timescale for the fast response is on the order of a year or two, not decades.  That's how we are able to see the effect of, e.g., Pinatubo or El Nino in the temperature record.  On this point, it's worth noting that the fast response involves warming of the atmosphere, while there are actually a bunch of slow responses, not just a single one.  The ocean, the biosphere, and the cryosphere all contribute to various slow responses at different timescales.

For simple models (like the two-box model that every climate aficionado ends up creating sooner or later) I think one timescale is typically on the order of months or years, and the other is a couple of decades (???) ... which just means that the longer, slower responses are being neglected. 

Another example of a two-box model (Tamino's!) is here. 

Oh, and don't worry too much about the terms.  Your comments are actually very clear and easy to follow. 

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Edited to fix mixup of dX and dY...

[oren]

Thanks again Ned. If the fast response is that fast, this whole thread makes much more sense to me, given CO2 has been rising quite steadily.
And a final thought - if CO2 is rising linearly with time (so its log is rising lesa than linear) and annual temps are slightly accelerating above linear, the T/logCO2 should be non-linear, and later decades should give higher values than earlier decades. My own caveat - as I recall annual CO2 change has been rising as well, and only seems to be stable over shorter periods, so that means CO2 concentration is accelerating as well.

[wdmn]

Exponential function fits the keeling curve pretty very well.

[AbruptSLR]

The lag is relatively short compared to the data length, and the increase in logCO2 is pretty constant. Under these conditions a straight line is expected and Ned's analysis is valid.

If you want to predict what happens on shorter timescales when CO2 change ceases to be exponential, you do need knowledge of the dynamics of the lag, but because atmospheric CO2 has been forced with a simple function, the simple analysis here works.

The linked reference proves that "… regression-based feedback estimates reflect contribution from a combination of stochastic forcing and should not be interpreted as providing an estimate of the radiative feedback governing the climate response to greenhouse gas forcing."  For example it is not adequate to talk about atmospheric contributions to GMSTA without considering that the oceans (with a slower response time) have been warming for at least 250 years:

Cristian Proistosescu et al. (14 May 2018), "Radiative Feedbacks From Stochastic Variability in Surface Temperature and Radiative Imbalance", Geophysical Research Letters, https://doi.org/10.1029/2018GL077678

https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2018GL077678

Abstract
Estimates of radiative feedbacks obtained by regressing fluctuations in top‐of‐atmosphere (TOA) energy imbalance and surface temperature depend critically on the sampling interval and on assumptions about the nature of the stochastic forcing driving internal variability. Here we develop an energy balance framework that allows us to model the different impacts of stochastic atmospheric and oceanic forcing on feedback estimates. The contribution of different forcing components is parsed based on their impacts on the covariance structure of near‐surface air temperature and TOA energy fluxes, and the framework is validated in a hierarchy of climate model simulations that span a range of oceanic configurations and reproduce the key features seen in observations. We find that at least three distinct forcing sources, feedbacks, and time scales are needed to explain the full covariance structure. Atmospheric and oceanic forcings drive modes of variability with distinct relationships between temperature and TOA radiation, leading to an effect akin to regression dilution. The net regression‐based feedback estimate is found to be a weighted average of the distinct feedbacks associated with each mode. Moreover, the estimated feedback depends on whether surface temperature and TOA energy fluxes are sampled at monthly or annual time scales. The results suggest that regression‐based feedback estimates reflect contributions from a combination of stochastic forcings and should not be interpreted as providing an estimate of the radiative feedback governing the climate response to greenhouse gas forcing.

Plain Language Summary
Climate sensitivity quantifies the long‐term warming the Earth will experience in response to the additional energy trapped in the system due to greenhouse gases. The physical processes that ultimately determine climate sensitivity—termed climate feedbacks—have been extensively investigated using information from natural variability in Earth's temperature and net energy imbalance. However, a complete physical model for what controls this natural variability has been lacking. We derive such a physical model and calibrate it to a hierarchy of numerical climate simulations of increasing complexity. We are able to answer several outstanding questions about previous estimates of climate feedbacks and sensitivity drawn from natural variability, such as what is the source of this variability, and how the estimates depend on the how the data is analyzed. We find that at least three different mechanisms for natural variability are needed to explain the relationship between temperature and energy imbalance and that none provide direct estimates of climate sensitivity.

[vox_mundi]

Don't Rule Out Severe Global Climate Change Yet

... In the original study, Cox et al. analyzed a set of 16 climate models, relating the models' natural year-to-year fluctuations in global temperature to their overall equilibrium climate sensitivity. They found that models with the most global temperature variability tend to exhibit greater climate sensitivity. On the other hand, models with the least global temperature variability tend to have small values of ECS. Cox et al. found that the real-world variability was somewhere in between these low and high variability extremes. Using a statistical approach, they were able to create an observationally constrained estimate of ECS.

 When Po-Chedley and colleagues consider 11 additional climate models, the constraint on ECS is substantially weaker and encompasses large values of ECS. The expanded analysis also shows that the temperature variability metric that Cox et al. use is sensitive to the combined influence of solar, volcanic and greenhouse gas forcing in the latter half of the 20th century. When alternative analysis time periods are chosen, the risk of the worst-case global warming scenarios increases substantially. These results make it difficult to discount the possibility that the Earth's climate sensitivity is large.

Stephen Po-Chedley et al. Climate constraint reflects forced signal, Nature (2018)

... Using all models and the early historical period (1880–1962) to compute Ψ¯ (as in Fig. 1c), we arrive at a median ECS of 3.4 °C (95% confidence interval of 1.9–4.9 °C). 


Extended Data Figure 1: Test of emergent relationship against models not used in the calibration.

Abstract
Equilibrium climate sensitivity (ECS) remains one of the most important unknowns in climate change science. ECS is defined as the global mean warming that would occur if the atmospheric carbon dioxide (CO2) concentration were instantly doubled and the climate were then brought to equilibrium with that new level of CO2. Despite its rather idealized definition, ECS has continuing relevance for international climate change agreements, which are often framed in terms of stabilization of global warming relative to the pre-industrial climate. However, the ‘likely’ range of ECS as stated by the Intergovernmental Panel on Climate Change (IPCC) has remained at 1.5–4.5 degrees Celsius for more than 25 years1. The possibility of a value of ECS towards the upper end of this range reduces the feasibility of avoiding 2 degrees Celsius of global warming, as required by the Paris Agreement. Here we present a new emergent constraint on ECS that yields a central estimate of 2.8 degrees Celsius with 66 per cent confidence limits (equivalent to the IPCC ‘likely’ range) of 2.2–3.4 degrees Celsius. Our approach is to focus on the variability of temperature about long-term historical warming, rather than on the warming trend itself. We use an ensemble of climate models to define an emergent relationship2 between ECS and a theoretically informed metric of global temperature variability. This metric of variability can also be calculated from observational records of global warming3, which enables tighter constraints to be placed on ECS, reducing the probability of ECS being less than 1.5 degrees Celsius to less than 3 per cent, and the probability of ECS exceeding 4.5 degrees Celsius to less than 1 per cent.