Why Do Climate Scientists use 15°C for Current GMST?

There's a conspiracy theory floating around the blogosphere and social media that argues (oddly) that climate scientists manufactured global warming by artificially lowering global temperatures. The "thinking" goes like this. Back in 1896, Svante Arrhenius calculated global mean surface temperature (GMST) to be 15°C. Following this, other scientists confirmed this value for later years. For instance, Hansen is reported to have claimed that value in 1981. The first IPCC report is claimed to confirm it again in 1990. In some incarnations of this conspiracy theory use other sources using 15°C, but the concept is the same. Then, after the so-called "pause" began in 1998, scientists needed another way to manufacture global warming, so they lowered GMST to 14°C so that they could increase it again. If that sounds confusing to you, it should. It doesn't make any sense. But let's unpack what's actually going on.

Arrhenius' Calculation in 1896

Svante Arrhenius' calculation[1] comes from his landmark study in which he showed that doubling CO2 would cause a linear increase in GMST, and he estimated that doubling (or halving) CO2 would change GMST by 4°C - 6°C. In order to do these calculations, he needed an estimate for GMST. There was not much data for him to work with here. There of course were many thermometers measuring weather data, but they weren't being collected into a global network of thermometers from which he could make calculations. So he used a recently published report, The Report of Scientific Results of the Voyage of H.M.S. Challenger Curing the Years 1873-76. This report collected temperature data from a single voyage, and there were almost certainly no inland measurements of temperature. His Table VI is below.

From what we learned in Arrhenius' paper, this data was collected and placed in a 10° latitude by 20° longitude grid, and his paper published the mean values by latitude range for Winter, Spring, Summer, Fall and Annual temperatures. He had no data for 70N-90N or for 60S-90S, so about 10% of the surface of the globe is missing. I've reproduced Table VI from his paper below.

The annual temperatures are predictably just the average of the seasonal means. What I wanted to do was figure out how he used this data to arrive at 15°C. I first did a simple average of each column. This would clearly be wrong, since each latitude band covers a different fraction of the surface of the globe. If he used this method, he would have arrived at 14.2°C. Next I weighted this average by the fraction of the surface area of the globe. With no "infilling," GMST would become too high. So in the last column, I "infilled" the 70N-90N columns with the value in 60N-70N, then I infilled the 60S-90S columns with the value in the 50S-60S column. Note that what I'm calling "infilling" here is mathematically identical to simply increasing the weight of the most poleward datapoint to include the entire area poleward from that point (I'm not creating new datapoints). Doing that lead to a calculation of 14.8°C, which I strongly suspect he rounded up to 15°C.

A few things should be obvious here. First, since this data comes from a single ship's data from a four year voyage, this estimate should not be considered as robust an estimate as what we have available to us today. Second, since these are likely only SSTs and coastal measurements, much of the land's surface is missing (including all of Antarctica). Third, since data from polar regions are missing, and since Arrhenius likely just infilled those latitudes with data he had, there is almost certainly a warming bias in his calculations; 10% of the globe is almost certainly colder than the infilled values he used to calculate GMST. So while this truly is a remarkable achievement, this is an estimate that almost certainly has a very high margin of error, and if anything, it's biased warm. But this is where the original figure of 15°C comes from. For Arrhenius' paper, the figure didn't have to be precise; the point was to use an approximate figure to assess the contribution of CO2 to the greenhouse effect.

Due to the Earth's spherical shape, temperatures plotted by latitude follow a roughly sinusoidal curve, and this is observed in recent studies.[6] So I decided to plot Arrhenius' temperatures by latitude with a best fit polynomial curve and chose temperatures for the latitudes missing from Arrhenius' data that are indicated by that curve. I'm taking this to be a best guess absolute GMST indicated by Arrhenius' data. The polynomial curve through Arrhenius' data is consistent with an absolute GMST of ~13.2°C, a full 1.8°C lower than his published value of 15°C.  Arrhenius obviously didn't have access to the tools we have today, so it's perfectly understandable to me that he wouldn't have done this calculation. I obviously can't say for sure that this is the correct curve to use, but I do think it's fair that Arrhenius' estimate is probably at least 1°C too warm.

Improving on Arrhenius' Work

In previous posts, I've shared why it is that scientists usually opt to report temperatures as anomalies. The short answer is that, back in 1987[2], it was discovered that temperature changes appear to be well-correlated over distances up to 1000 km, and so you need fewer datapoints (thermometers) to know how much GMST is changing than you would to determine what absolute GMST actually is. I've gone into more detail on this here and here (and see RealClimate here), so I won't repeat myself except to say that the uncertainties for anomalies are much smaller than for absolute temperatures.

Following Arrhenius' landmark paper, the value of 15°C was frequently used as a more or less traditional approximate baseline for GMST. This value appears in numerous reports, and all of the examples I've seen have to do with either assessing the approximate magnitude of the greenhouse effect or the long-term average temperature in the context of geologic time. However, in 1999 Jones et al[3] published a report that attempted to quantify the absolute value of GMST for a 1961-1990 baseline. Their work arrived at a value of 14°C.

We then provide a globally complete absolute surface air temperature climatology on a 1° × 1° grid. This is primarily based on data for 1961–1990. Extensive interpolation had to be undertaken over both polar regions and in a few other regions where basic data are scarce, but we believe the climatology is the most consistent and reliable of absolute surface air temperature conditions over the world. The climatology indicates that the annual average surface temperature of the world is 14.0°C (14.6°C in the Northern Hemisphere (NH) and 13.4°C for the Southern Hemisphere)

As you can see from the description, Jones' work is far more extensive than Arrhenius' work. Arrhenius was limited to a 10° × 20° grid with only SST and possibly coastal measurements, and without access to polar areas. Jones' work used a 1° × 1° grid (with interpolation for portions of the polar regions) with coverage of land and ocean temperatures. The change in the default value from 15°C to 14°C was due to the fact that in 1999, we had much better access to global data than Arrhenius did in 1896. Still, it's estimated that even in Jones' paper, the 95% confidence interval is about 0.5°C.

Intervening Examples

It would be helpful I think to show examples of how ~15°C was used in the hundred years between Arrhenius 1896 and Jones et al 1999.  Some commonly cited examples are:

1.  Hansen et al 1981.[4] Here Hansen calculates the effective radiating temperature of Earth (Te) to be ~255 K and uses ~288 K (or ~15°C) for the current temperature (Ts): "The mean surface temperature is Ts ~ 288 K. The excess, Ts - Te, is the greenhouse effect of gases and clouds, which cause the mean radiating level to be above the surface." The use of  "~288 K" indicates that this value is approximate, and probably he's just using the traditional figure for Ts calculated by Arrhenius, which we can see above has a large margin of error and a warming bias.

2.  A NASA site from 1982 claims, "During most of Earth's history, the climate appears to have been considerably warmer, with average global temperatures about 25 (77°F). The current average global temperature is 15 (59°F)." And yet here it's pretty obvious that NASA is continuing to use the traditional Ts value as an approximate GMST in in the context of the long-term GMST over geologic history, where Ts averaged about 10°C warmer at 25°C.

3. IPCC FAR 1990.[5] There's a chart in the First Assessment Report published in 1990 that reports the observed surface temperature of 15°C and Warming due to the Greenhouse effect to be 33°C.

This is clearly just a rehash of the same traditional values for Ts, Te and the "excess" (Ts - Te) found in Hansen. Interestingly, though, in the text surrounding this table, the IPCC writes, "the mean temperature of the Earth's surface is already 32°C warmer than it would be if the natural greenhouse gases... were not present." Note that if we use Te = 255 K and add 32 K to this, we end up with only 287 K or ~14°C, suggesting that even in 1990 there was some indication to whoever wrote the text that 15°C may be slightly too high, even if that figure didn't make it in the table that used the more traditional values.

4. Sometimes NASA and NOAA reported their annual anomaly values as absolute temperatures. They did this by simply adding the anomaly to the presumed baseline temperature of 15°C, which would maintain a large uncertainty similar to that of Arrhenius' estimate. After Jones' paper, these same anomalies could be reported with reference to a 1961-1990 baseline temperature of 14°C, and this would give the superficial appearance of cooler temperatures when comparing documents from before 1999 to documents published after 1999, but what actually happened is the traditional baseline value was corrected to agree with better available data and analysis. Incidentally, there has been so much warming above the 1961-1990 mean that recent annual temperatures are actually up to ~15°C.

Conclusion

Jones et al 1999's calculations put the 1961-1990 mean at ~14°C. Arrhenius 1896 calculated the 1873-1876 mean to be 14.8°C, which he reported as 15°C. So I decided to have a little fun and calculate the absolute temperature for 1873-1876 assuming that Jones' calculations are correct. Of the three global datasets that include this date range (NOAA, BEST, HadCRUT), the average 1873-1876 anomaly is 0.387°C cooler than the 1961-1990 mean, so that would put Ts during 1873-1876 at 13.6°C. This is a similar value to the 13.2°C value I arrived at above, and it would suggest that Arrhenius' estimate was only off by about 1.2°C to 1.4°C. I find this pretty remarkable, given the amount of data he had to work with. And there has been so much warming since 1961-1990, that 15°C remains the best estimate of current global temperatures.

Clearly this conspiracy theory is built on the premise that 1) Arrhenius' estimate for GMST is accurate and 2) scientists lowered GMST from 15°C to 14°C to hide a presumed pause in GMST (that never actually happened). But clearly and obviously, Arrhenius' calculation was an extremely rough estimate (I would think the uncertainty would have to exceed 2°C), and Jones' estimate a century later is simply a more accurate estimate (still with an uncertainty of ~0.5°C). Afterall, in 1865 Maxwell calculated the speed of light to be 310,740,000 m/s. More recent calculations show it to be 299,792,458 m/s. By the logic of this conspiracy theory, we'd conclude that the speed of light is slowing down. And yet the speed of light is actually constant. Maxwell's calculation in 1865 was a remarkable achievement, but it's far more likely that his estimate was a bit off than that the speed of light is actually changing and all of known physics is wrong.

References

[1] Arrhenius, S.A. (1896) On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground. Philosophical Magazine, 41, 237-276.
https://doi.org/10.1080/14786449608620846 

[2] Hansen, J.E., and S. Lebedeff, 1987: Global trends of measured surface air temperature. J. Geophys. Res., 92, 13345-13372, doi:10.1029/JD092iD11p13345.

[3] Jones, P. D., M. New, D. E. Parker, S. Martin, and I. G. Rigor (1999), Surface air temperature and its changes over the past 150 years, Rev. Geophys., 37(2), 173–199, doi:10.1029/1999RG900002.

[4] Hansen, J., D. Johnson, A. Lacis, S. Lebedeff, P. Lee, D. Rind, and G. Russell, 1981: Climate impact of increasing atmospheric carbon dioxide. Science, 213, 957-966, doi:10.1126/science.213.4511.957.

[5] IPCC First Assessment Report. https://www.ipcc.ch/site/assets/uploads/2018/03/ipcc_far_wg_I_full_report.pdf

[6] Feulner, G., S. Rahmstorf, A. Levermann, and S. Volkwardt, 2013: On the Origin of the Surface Air Temperature Difference between the Hemispheres in Earth's Present-Day Climate. J. Climate, 26, 7136–7150, https://doi.org/10.1175/JCLI-D-12-00636.1.