Thongchai Thailand

The Mathematics of AGW

Posted on: January 9, 2020

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bandicam 2020-01-09 17-50-28-333

  1. Earth System Models (ESM) are used by the IPC and climate scientists project what will happen if we emit carbon dioxide. These are simply global climate models with carbon cycles and other geochemical cycles added to them and remarkably, they project that if emissions ceased, the temperature would stay elevated at that level for hundreds of years. That’s because the slowly falling airborne carbon dioxide levels would be counteracted by the move from the transient climate response to the equilibrium climate response and some carbon cycle feedbacks as well.
  2. The implication of this is that in Earth System Models, warming is proportional to the cumulative amount of carbon dioxide emissions. You emit so much carbon dioxide, the temperature goes up so much. You emit another amount, you get … , the temperature goes up in proportion to the amount emitted.
  3. This why people talk about carbon budgets. The carbon budget is simply cumulative emissions to meet some particular {political?} target, so take not more than two degrees warming. And I’m sure these Earth System Model derived carbon budgets are what’s driving policy so {in nevins?} you’ve got this 95% reduction in emissions proposed. I am sure that is driven by a desire to meet a … some kind of carbon budget. I don’t think you will actually achieve that but I think that’s what driving {post?}. bandicam 2020-01-09 18-19-29-611
  4. So these are the socio-economic scenarios that’s produced projected in emissions is with the representative concentration pathways with actually emission based … this one we used in the last IPC report to drive these Earth System Models the top one the IPC 8.5 is often referred to as business as usual in the press, it’s actually a very pessimistic worst case scenario. I don’t think it’s realistic even if there is no further mitigation. I will focus on RCP6, the next one down, which I think is more in line if one didn’t {foo?} further mitigation. And there’s a couple of other scenarios.  bandicam 2020-01-09 18-21-54-097
  5. So in the IPC 5, a report, 5 years ago, 6 years ago, they produced projections by the Earth System Models of a warming, that line, in relation to cumulative emissions, from {dog side?} this is both since about 1870 so they got the {sicklish?} historical projections – these are all simulations not observations. Up to there and then these different scenarios separate off so you – what you can see is that the warming is very similar in all scenarios. It’s slightly higher in relation to cumulative emissions on the RCP8.5 scenario – that’s because that scenario has extremely high methane emissions – {had a long scenario?}. But otherwise they’re going up pretty well the same. And I am {dawning?} here on green this 1.5 degrees target they’re pushing these days and that corresponds to cumulative emissions of about 625 gigatons of carbon. A gigaton is a thousand million tons – and – this is just measuring the carbon content. You can also measure it in terms of the total carbon dioxide weight which will give you a higher figure so you they use both measures. What’s remarkable here is, as of today, we got {tumitive?} to come to 25 gigatons of carbon, slightly more. So warming is not 1.5 degrees, it is actually about 1 degree. So these models have already been falsified.  bandicam 2020-01-09 18-53-28-427
  6. So clearly the carbon budgets that came from these models are ridiculously low. They’ve already been proven wrong. There is a simpler way to project future warming in relation to emissions and this is to use something called the Transient Climate Response to Cumulative Emissions (TCRE). This is the warming for every thousand gigatons of carbon emissions that you put out how much warming will result. This is {sipply?} measured over a period of about 70 years but it’s not critical and indeed in these Earth System Models it doesn’t matter what the period is. And you can measure this easily enough in models you can also measure it from observations, which is my interest. bandicam 2020-01-09 19-45-04-330
  7. So, in these Earth System Models, the Transient Climate Response to Cumulative Emissions averages out to about 1.65 degrees for every thousand gigatons. It’s got a wide range, and in the last IPC report they fixed the range to 0.8 to 2.5 degrees. And again, the models, this only came from models in the very bottom end with inference {bio-projection}. I’ve made an estimate of the Transient Climate Response to Cumulative Emissions from observations, I haven’t got this material in a paper yet but it’s calculated on completely consistent properly probabilistic basis, this I am quite happy with it and that comes out to 1.05 degrees so you can see it’s a long way below the models. And also the range is quite narrow and the top end is only 1.6 degrees rather than 2.5 degrees. That has a big influence on what’s gonna happen in terms of climate damages. bandicam 2020-01-09 20-12-24-320
  8. So the way you project future warming is very simple. You take your future emissions, multiply them by the Transient Climate Response to Cumulative Emissions and you add in an estimate of warming from human non-CO2 emissions because that’s a {paid sloong fee?} you can just use a model for that without any real accuracy. Remarkably, this is exactly what the IPC did. The first time they didn’t use their 3D complex models for their projections. In the special report on 1.5 degrees last year, it used exactly this method. However, they use of course the IPCC range from AR5 of TCRE=[0.8 to 2.5] and its midpoint is exactly the average for their Earth System models. So the result is that their result reflect the models. The link is now indirect. So I thought well what’s the … This is what the corresponding graph – the key graph in SR1.5 report so this is once again relates warming to cumulative emissions since about 1870 or 1875 but there are differences from the corresponding graphs in AR5. So we got the AR-5, the ones up there, the simulations 2005 and then on up the {aucity?} 8.5 line, this has got the actual observed warming, you can see that it’s up to 1 degree up to the star, that’s 2017 there, it’s only 1 degree not 1.5 degrees where it would be in the IPCC AR5 projections and then they project on from there. So, the green line is using their original model for non-carbon-dioxide-warming. And that original model simply mimics the earth system models, they’re using the Earth System Model range of Transient Climate Response to Emissions and therefore unsurprisingly the green line goes up parallel to the red line but it’s lower because effectively they corrected their over-estimates, their historic over-estimates, but they kept the same sensitivity going forward which may seem a bit stupid since it didn’t work in the past. They’ve also got another model on this yellow line, you can see that, for the non-CO2 warming which is less than even their main projection average. bandicam 2020-01-09 20-27-55-335
  9. So that’s the key graph on the SR15 report and that now is projecting about on RCP6 level about 2.6 degrees warming rather than by decades or centuries rather than 3.2 on the AR5 estimates. I found the same thing in the SR1.5 report, but I a using now my observationally based estimates of the Transient Climate Response to Cumulative Emissions and the simple model for the non-CO2 emissions using my observational estimates of the Transient Climate Response and the Equilibrium Climate Sensitivity. I’ve got he old IPCC AR5 ones there; and these are mine, are the solid lines, So, black is observed and you can see the point where the IPCC was projecting we get to in 52,000 {nunkeys?} on RCP6 it’s just going to get frequent  warming. If you go down to the same level of cumulative emissions on my estimates, it’s only 2 degrees warming. So this is quite significant. This is warming from the 1870s so this is the same base as essentially the 2 degrees Celsius composite. And this makes quite a lot of difference. bandicam 2020-01-09 22-21-13-725
  10. If I didn’t use Transient Climate Response to Cumulative Emissions and used my own carbon climate model I’d actually get it slightly lower still but about 1.8 degrees but this one I can do a very solid probabilistic uh it would  be publishable. It’s much more difficult if you are using carbon climate models you get many answer.  Finally, I move on to forced invitations as I see it of these {cynics?}. On the IPCC, I think the IPCC AR5 Earth System Models projections linking warming to cumulative emissions are still driving climate policies even though they’ve been shown to be wrong so far and these are driving carbon budgets so I, the policies the cheapest carbon budgets. And these imply rapid reductions in carbon dioxide emissions in order to meet these carbon budget targets, certainly, 2 degrees and 1.5 degrees, probably rapid reduction. Whereas if you use the observation based projection then the implications are that you’ve got a much longer so you can have a slower reductions in emissions and still meet these targets. I would say that if we are post 2100, then if we really want to stick to this 2 degrees target then emissions even on even on minus would have to be pretty low by then but you certainty don’t have to be low by 2050.
  11. And finally some depressing thoughts. Many climate policies are stupid and wasteful and they’re not going to achieve much. It’s not Europe that’s going to drive emissions in the future. It’s the Chinas the Indias the Indonesia, whatever. And some of them are harmful … things like biofuels is crazy, Also, it is unclear that a warming of 2C or 3C is a serious problem – if we go above the 2 degrees or maybe it’s foolish and certainly in climate models everything is incredibly linear. It doesn’t fall apart if you get to 3 degrees of 4 degrees or even 5 degrees, it just gets warmer. AGW is a long term problem. We should adjust policy adaptively we should look at the adaptation measures.  bandicam 2020-01-09 22-57-02-935




RESPONSE#1: Climate Sensitivity:

    1. Nic Lewis proposes that the IPCC estimates of climate sensitivity and therefore of future warming are too high because his estimates from observational data are lower. As seen above under “Conclusions”, Nic computes climate sensitivity values of λ=1.7 for long time scales and λ=1.35 for multi-decadal time scales from observational data and finds that these values are 25% to 45% lower than those derived from climate models (2.27 & 2.45). He uses these findings to challenge IPCC assessments about future warming.
    2. Listed below are a large number of estimates of climate sensitivity both short term sensitivity (multi-decadal) and long term ECS. They do not show that climate science is homing in on the correct value of sensitivity nor that there is a correct value of sensitivity. Instead, what we see in these estimates of climate sensitivity is a failure of climate science to estimate the sensitivity value. The large uncertainty implied by these findings do not show that therefore the values of λ=1.7 and λ=1.35 presented above are low and therefore correct and that therefore the IPCC is incorrect. They show instead that the new values of λ=1.7 and λ=1.35 are yet more numbers to be added to a mountain of disparate numbers that have not led to a a useful conclusion about climate sensitivity. The mountain of disparate values already contains similar estimates. This new estimate does not tell us that now we know what the climate sensitivity is. When considered along with all the other values presented here, it tells us that we don’t know what the climate sensitivity is and whether it is a relevant or useful concept in understanding AGW.
    3. The uncertainty problem in climate sensitivity has driven many climate scientists to abandon the sensitivity idea and move to the TCRE as seen for example in Knutti 2017  “Beyond Climate Sensitivity” where Reto Knutti and co-authors Rugenstein and Hegerl acknowledge that the search for sensitivity has failed. They propose that the sensitivity idea should be abandoned and that we should move on to the TCRE metric offers the only reliable relationship between emissions and warming.
    4. As a historical note, in Callendar (1938) [LINK] used observational data for the period 1900-1938 to estimate a multi-decadal climate sensitivity of λ=2. More recently, James Hansen and NASA GISS, have claimed that AGW as a measurable phenomenon began in 1950 with Hansen making the further claim that data for the 30-year period 1950 to 1980 provides clear evidence of human caused global warming and climate change by way of the heat trapping effect of carbon dioxide [LINK] . As of this writing, the Hansen hypothesis can be extended to 2019 but it still remains in the multi-decadal category at time span of 70 years. A similar claim is made by climate scientist Peter Cox for the period “1970s” to 2018 (a 44-year period if “1970s” is interpreted as 1975). He uses an observationally constrained climate model to show a strong proportionality between surface temperature and Ln(CO2).
    5. Using Mauna Loa CO2 data and HadCRU and UAH global mean temperatures 1959-2019, some  estimates of multi-decadal climate sensitivity can be made at these time spans. The multi-decadal sensitivities found are tabulated in the chart below. Their time spans range from 30 to 70 years . sensitivity
    6. The chart shows multidecadal sensitivities from a low of λ=1.3 to a high of λ=3.2 for the full span and sub-spans of the HadCRU dataset 1959-2019 and a consistent value of λ=1.8 for the full span and sub-spans of the UAH satelllite data for mid tropospheric temperature 1979-2019. These sensitivities are supported by strong correlations and statistically significant detrended correlations between temperature and Ln(CO2) as seen in the chart below. correlations


  1.  In a recent post Dr. Frank Bosse, Senior Scientist of Molecular Neurobiology, Heinrich-Heine-University, Duesseldorf uses Earth Energy Imbalance data to estimate that the multidecadal climate sensitivity is  λ=1.72 for the period 1999-2018. [LINK] It is noted that the Bosse estimate closely matches the UAH 1979-2019 estimates of multidecadal sensitivity at 31-year and 41-year time spans. 
  2. In a related post, climate sensitivity estimates in the literature up to the year 2012, both from observational data and  climate models, are summarized in charts  provided by the Late Stephen Schneider [LINK] . The relevant charts are reproduced below. They show a number of sensitivity estimates of λ<2.
  3. A history of sensitivity estimates compiled more recently is also presented [LINK] . It shows estimates from observations, from climate models, from observations constrained by climate models, and from climate models constrained by observations as follows:
  4. Observations: Callendar 1938 λ=2, Johansson, 2015 with corrections for the ‘pause’ in 2000-2014. λ=3.25 90%CI = [2.0 – 4.5]. Aldrin, 2012 90%CI=[1.2 – 7.7]
  5. Climate Models: Charney:  λ=[2.0-3.5], λ=[2.6-4.1], and λ=[1.5-4.5], [λ=3]. Hansen 1981: λ=[2.0-3.5], Knutti 2002: λ=5.7 with 90%CI λ=[2.7-8.7], Murphy 2004: 90%CI=[2.4–5.4],  Stainforth, 2005) very large ensemble model study λ=6.7  90%CI = [1.9 – 11.5].
  6.  Observations Constrained by Climate Models: Andronova 2000: λ=[0.94-2.35],  Gregory 2002: 1860-2000: λ=6 with long tailed distribution skewed right. 90% CI λ= [1.1 – infinity] but with certain assumptions, Gregory is able to reduce the 90% CI to λ=[1.7 – 2.3]. , Frame 2005: λ= 2.4 with 90%CI = [1.4-4.1],  Kummer, 2017 λ=2.3, 90%CI=[1.6-4.1].  Aldrin 2012:  90%CI= [1.0 – 2.7], [1.0 – 3.5], [1.0 – 4.2], [1.3 – 4.9], [1.5 – 7.8], [1.5 – 7.3], and [1.0 – 7.0],  Lewis and Curry 2018 90%CI=[1.05-4.05]. Paleo Data Constrained by Models: Hegerl 2006: 700-year paleo data indicate 90% CI=[1.5-6.2] although values as high as λ=7 to 9 were observed .
  7.  Climate Models Constrained by Observations: Gregory 2002 & Forest 2002: λ=4.2 Symmetrical distribution with 90%CI of λ=[1.4 – 7.7].




RESPONSE#2: Transient Climate Response to Cumulative Emissions


bandicam 2020-01-09 20-12-24-320


  1. The TCRE is a regression coefficient derived not from a theoretical relationship but an observational one. It is derived from the observation of a near perfect proportionality between temperature and cumulative emissions in any given time interval t-1 to t-2. It should be noted that the temperature at any given time from t-1 is cumulative annual warming from t-1. Therefore the near perfect proportionality between cumulative annual warming and cumulative emissions is a correlation between cumulative values – between cumulative warming and cumulative emissions.
  2. In a related posts we show that a time series of the cumulative values of another time series contains neither time scale nor degrees of freedom. Therefore a time series of the cumulative values of another time series does not contain information. Therefore, neither the correlation between cumulative warming and cumulative emissions nor the regression coefficient of cumulative warming as a linear function of cumulative emissions has any interpretation in the real world in terms of phenomena that they apparently represent. [LINK] [LINK] .
  3. As it turns out the proportionality between cumulative warming and cumulative emissions derives from a fortuitous sign pattern in these variables. The sign pattern is that emissions are always positive and , during a time of warming, annual warming values are mostly positive. The information contained in the TCRE is this sign pattern and nothing more.
  4. Specifically, the TCRE contains no information about the responsiveness of temperature to emissions. Yet, this erroneous interpretation of the TCRE guides its use and function in climate science as well as in this Nic Lewis video. The TCRE is a spurious correlation and the relationship between warming and emissions it implies is illusory.
  5. This is why the use of TCRE based carbon budgets suffer from the Remaining Carbon Budget (RCB) problem as explained in a related post [LINK] . The remaining carbon budget anomaly is the creation of a spurious correlation and an illusory carbon budget but is interpreted in climate science as an Earth System Model issue and additional variables are sought and found that will resolve the RCB issue. That a spurious correlation and an illusory TCRE statistic play such important roles in the science of climate science discredits the science and the work of the scientists.

Thus apparently scientific analyses of climate using the TCRE, such as “I’ve made an estimate of the Transient Climate Response to Cumulative Emissions from observations, it’s calculated on completely consistent properly probabilistic basis, this I am quite happy with it and that comes out to 1.05 degrees so you can see it’s a long way below the models. And also the range is quite narrow and the top end is only 1.6 degrees rather than 2.5 degrees. That has a big influence on what’s gonna happen in terms of climate damages” contain no actual information about AGW and its claimed relationship between emissions and warming.




RESPONSE#3: Responsiveness of Atmospheric Composition to Emissions

  1. The essence of AGW is that humans burning fossil fuels emit carbon dioxide much of which (40% to 50%, the so called Airborne Fraction) is thought to remain in the atmosphere and cause accumulation thereby increasing atmospheric CO2 concentration.
  2. This relationship is the critically necessary foundation of AGW because without it none of the other steps of AGW is possible. Yet, no evidence exists for this relationship [LINK] .  The carbon cycle mass balance equations used in this attribution suffers from circular reasoning because it assumes the airborne fraction and overlooks uncertainties in carbon cycle flows to carry out the mass balance [LINK]In the same post it is shown that when the uncertainties in carbon cycle flows declared by the IPCC are included in the mass balance, fossil fuel emissions cannot be detected because the system balances with and without fossil fuel emissions [LINK] .



3 Responses to "The Mathematics of AGW"

Your posts are always interesting.

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