This exercise in data analysis pins down a value of 1.8C for ECS.
Guest essay by Jeff L.
If the global climate debate between skeptics and alarmists were cooked down to one topic, it would be Equilibrium Climate Sensitivity to CO2 (ECS) , or how much will the atmosphere warm for a given increase in CO2 .
Temperature change as a function of CO2 concentration is a logarithmic function, so ECS is commonly expressed as X ° C per doubling of CO2. Estimates vary widely , from less than 1 ° C/ doubling to over 5 ° C / doubling. Alarmists would suggest sensitivity is on the high end and that catastrophic effects are inevitable. Skeptics would say sensitivity is on the low end and any changes will be non-catastrophic and easily adapted to.
All potential “catastrophic” consequences are based on one key assumption : High ECS ( generally > 3.0 ° C/ doubling of CO2). Without high sensitivity , there will not be large temperature changes and there will not be catastrophic consequences. As such, this is essentially the crux of the argument : if sensitivity is not high, all the “catastrophic” and destructive effects hypothesized will not happen. One could argue this makes ECS the most fundamental quantity to be understood.
In general, those who are supportive of the catastrophic hypothesis reach their conclusion based on global climate model output. As has been observed by many interested in the climate debate, over the last 15 + years, there has been a “pause” in global warming, illustrating that there are significant uncertainties in the validity of global climate models and the ECS associated with them.
There is a better alternative to using models to test the hypothesis of high ECS. We have temperature and CO2 data from pre-industrial times to present day. According to the catastrophic theory, the driver of all longer trends in modern temperature changes is CO2. As such, the catastrophic hypothesis is easily tested with the available data. We can use the CO2 record to calculate a series of synthetic temperature records using different assumed sensitivities and see what sensitivity best matches the observed temperature record.
The rest of this paper will explore testing the hypothesis of high ECS based on the observed data. I want to re-iterate the assumption of this hypothesis, which is also the assumption of the catastrophists position, that all longer term temperature change is driven by changes in CO2. I do not want to imply that I necessarily endorse this assumption, but I do want to illustrate the implications of this assumption. This is important to keep in mind as I will attribute all longer term temperature changes to CO2 in this analysis. I will comment at the end of this paper on the implications if this assumption is violated.
There are several potential datasets that could be used for the global temperature record. One of the longer and more commonly referenced datasets is HADCRUT4, which I have used for this study (plotted in fig. 1) The data may be found at the following weblink :
I have used the annualized Global Average Annual Temperature anomaly from this data set. This data record starts in 1850 and goes to present, so we have 163 years of data. For the purposes on this analysis, the various adjustments that have been made to the data over the years will make very little difference to the best fit ECS. I will calculate what ECS best fits this temperature record, given the CO2 record.
Figure 1 : HADCRUT4 Global Average Annual Temperature Anomaly
The CO2 data set is from 2 sources. From 1959 to present, the Mauna Loa annual mean CO2 concentration is used. The data may be found at the following weblink :
For pre-1959, ice core data from Law Dome is used. The data may be found at the following weblink :
The Law Dome data record runs from 1832 to 1978. This is important for 2 reasons. First, and most importantly, it overlaps Mauna Loa data set. It can easily be seen in figure 2 that it is internally consistent with the Mauna Loa data set, thus providing higher confidence in the pre-Mauna Loa portion of the record. Second, the start of the data record pre-dates the start of the HADCRUT4 temperature record, allowing estimates of ECS to be tested against the entire HADCRUT4 temperature record. For the calculations that follow, a simple splice of the pre-1959 Law Dome data onto the Mauna Loa data was made , as the two data sets tie with little offset.
Figure 2 : Modern CO2 concentration record from Mauna Loa and Law Dome Ice Core.
From the above CO2 record, a set of synthetic temperature records can be constructed with various assumed ECS values. The synthetic records can then be compared to the observed data (HADCRUT4) and a determination of the best fit ECS can be made.
The equation needed for the calculation of the synthetic temperature record is as follows :
∆T = ECS* ln(C2/C1)) / ln(2)
∆T = Change in temperature, ° C
ECS = Equilibrium Climate Sensitivity , ° C /doubling
C1 = CO2 concentration (PPM) at time 1
C2 = CO2 concentration (PPM) at time 2
For the purposes of this test of sensitivity, I set time 1 to 1850, the start of the HADCRUT4 temperature dataset. C1 at the same time from the Law Dome data set is 284.7 PPM. For each year from 1850 to 2013, I use the appropriate C2 value for that time and calculate ∆T with the formula above. To tie back to the HADCRUT4 data set, I use the HADCRUT4 temperature anomaly in 1850 ( -0.374 ° C) and add on the calculated ∆T value to create a synthetic temperature record.
ECS values ranging from 0.0 to 5.0 ° C /doubling were used to create a series of synthetic temperature records. Figure 3 shows the calculated synthetic records, labeled by their input ECS, as well as the observed HADCRUT4 data.
Figure 3: HADCRUT4 Observed data and synthetic temperature records for ECS values between 0.0 and 5.0 ° C / doubling. Where not labeled, synthetic records are at increments of 0.2 ° C / doubling. Warmer colors are warmer synthetic records.
From Figure 3, it is visually apparent that a ECS value somewhere close to 2.0 ° C/ doubling is a reasonable match to the observed data. This can be more specifically quantified by calculating the Mean Squared Error (MSE) of the synthetic records against the observed data. This is a “goodness of fit” measurement, with the minimum MSE representing the best fit ECS value. Figure 4 is a plot of MSE values for each ECS synthetic record.
Figure 4 : Mean Squared Error vs ECS values. A few ECS values of interest are labeled for further discussion
In plotting, the MSE values, a ECS value 1.8 ° C/ doubling is found to have the minimum MSE and thus is determined to be the best estimate of ECS based on the observed data over the last 163 years.
A comparison to various past estimates of ECS is made in figure 5. The base for figure 5 comes from the following weblink :
See link for the original figure.
Figure 5 : Comparison of the results of this study (1.8) to other recent ECS estimates.
The estimate derived from this study agrees very closely with other recent studies. The gray line on figure 5 at a value of 2.0 represents the mean of 14 recent studies. Looking at the MSE curve in figure 4, 2.0 is essentially flat with 1.8 and would have a similar probability. This study further reinforces the conclusions of other recent studies which suggest climate sensitivity to CO2 is low relative to IPCC estimates .
The big difference with this study is that it is strictly based on the observed data. There are no models involved and only one assumption – that the longer period variation in temperature is driven by CO2 only. Given that the conclusion of a most likely sensitivity of 1.8 ° C / doubling is based on 163 years of observed data, the conclusion is likely to be quite robust.
A brief discussion of the assumption will now be made in light of the conclusion. The question to be asked is : If there are other factors affecting the long period trend of the observed temperature trend (there are many other potential factors, none of which will be discussed in this paper), what does that mean in terms of this best fit ECS curve ?
There are 2 options. If the true ECS is higher than 1.8, by definition , to match the observed data, there has to be some sort of negative forcing in the climate system pushing the temperature down from where it would be expected to be. In this scenario, CO2 forcing would be preventing the temperature trend from falling and is providing a net benefit.
The second option is the true ECS is lower than 1.8. In this scenario, also by definition, there has to be another positive forcing in the climate system pushing the temperature up to match the observed data. In this case CO2 forcing is smaller and poses no concern for detrimental effects.
For both of these options, it is hard to paint a picture where CO2 is going to be significantly detrimental to human welfare. The observed temperature and CO2 data over the last 163 years simply doesn’t allow for it.
Based on data sets over the last 163 years, a most likely ECS of 1.8 ° C / doubling has been determined. This is a simple calculation based only on data , with no complicated computer models needed.
An ECS value of 1.8 is not consistent with any catastrophic warming estimates but is consistent with skeptical arguments that warming will be mild and non-catastrophic. At the current rate of increase of atmospheric CO2 (about 2.1 ppm/yr), and an ECS of 1.8, we should expect 1.0 ° C of warming by 2100. By comparison, we have experienced 0.86 ° C warming since the start of the HADCRUT4 data set. This warming is similar to what would be expected over the next ~ 100 years and has not been catastrophic by any measure.
For comparison of how unlikely the catastrophic scenario is, the IPCC AR5 estimate of 3.4 has an MSE error nearly as large as assuming that CO2 has zero effect on atmospheric temperature (see fig. 4).
There had been much discussion lately of how the climate models are diverging from the observed record over the last 15 years , due to “the pause”. All sorts of explanations have been posited by those supporting a high ECS value. The most obvious resolution is that the true ECS is lower, such as concluded in this paper. Note how “the pause” brings the observed temperature curve right to the 1.8 ECS synthetic record (see fig. 3). Given an ECS of 1.8, the global temperature is right where one would predict it should be. No convoluted explanations for “the pause” are needed with a lower ECS.
The high sensitivity values used by the IPCC , with their assumption that long term temperature trends are driven by CO2, are completely unsupportable based on the observed data. Along with that, all conclusions of “climate change” catastrophes are also completely unsupportable because they have the high ECS values the IPCC uses built into them (high ECS to get large temperature changes to get catastrophic effects).
Furthermore and most importantly, any policy changes designed to curb “climate change” are also unsupportable based on the data. It is assumed that the need for these policies is because of potential future catastrophic effects of CO2 but that is predicated on the high ECS values of the IPCC.
I have also attached a spreadsheet with all my raw data and calculations so anyone can easily replicate the work.
ECS Data (xlsx)
I have followed the climate debate since the 90s. I was an early “skeptic” based on my geologic background – having knowledge of how climate had varied over geologic time, the fact that no one was talking about natural variation and natural cycles was an immediate red flag. The further I dug into the subject, the more I realized there were substantial scientific problems. The paper I am submitting is a paper I have wanted to write for years , as I did the basic calculations several years ago & realized there was no support in the observed data for high climate sensitivity.