Hansen's 1988 prediction scenarios - numbers and details.

There has been a great deal of blog posting on the thirtieth anniversary of James Hansen's famous Senate testimony on global warming, and the accompanying 1988 prediction paper. I reviewed a lot of this in my previous post and I have since been in a lot of blog arguments. I suppose this has run its course for the moment, but there may be another round in 2020, since Hansen's prediction actually went to 2019.

Anyway, for the record, I would like to set down some clarification of what the scenarios for the predictions actually were, and what to make of them. Some trouble has been caused by Hansen's descriptions, which were not always clear. This is exacerbated by readers who interpret in terms of modern much discussed knowledge of tonnage emissions of CO₂. This is an outgrowth of the UNFCC in early 1990's getting governments to agree to collect data on that. Although there were estimates made before 1988, they were without benefit of this data collection, and Hansen did not use them at all. I don't know if he was aware of them, but he in any case preferred the much more reliable CO₂ concentration figures.

Sources

I discussed the sources and their origins in a 2016 post here. For this, let me start with a list of sources:

• Hansen's 1988 prediction paper and a 1989 paper with more details, particularly concerning CFCs
• Some discussions from 10 years ago: Real Climate and Steve McIntyre (later here). SM's post on scenario data here. See also Skeptical Science
• A 2006 paper by Hansen, which reviews the predictions
• From that 2007 RC post, a link to data files - scenarios and predicted temperature. The scenarios are from the above 1989 paper. I'll call this data Scen_1
• A RealClimate page on comparisons of past projections and outcomes
• A directory of a slightly different data set from Steve McIntyre here, described here. I'll call that Scen_2. The post has an associated set of graphs. It seems that SM calculated these from Hansen's description.
• A recent Real Climate post with graphs of scenarios and outcomes, and also forcings.
• I have collected numerical ascii data in a zipfile online here. H88_scenarios.csv etc are Scen_1; hansenscenario_A.dat etc are Scen_2, and scen_ABC_temp.data.txt is the actual projection.

Hansen's descriptive language

The actual arithmetic of the scenarios is clear, as I shall show below. It is confirmed by the numbers, which we have. But it is true that he speaks of things differently to what we would now. Steve McIntyre noted one aspect when Hansen speaks of emissions increasing by 1.5%:

"One idiosyncrasy that you have to watch in Hansen's descriptions is that he typically talks about growth rates forthe increment , rather than growth rates expressed in terms of the quantity. Thus a 1.5% growth rate in the CO₂ increment yields a much lower growth rate than a 1.5% growth rate (as an unwary reader might interpret)."

Hansen is consistent though. His conventions are

• Emissions of CO₂ are always spoken of in terms of % increase. Presumably this is because he uses tonnages for CFCs, where production data is better than air measurements, and % works for both. Perhaps he anticipated having CO2 tonnages some time in the future.
• So emissions, except for CFCs, are actually quantified as annual increments in ppm. He does not make this link very explicitly, but there is nothing else it could be, and talk of a % increase in emissions translates directly into a % increase in annual ppm increment in the numbers.
• As SM said, you have to note that is is % of increment, not % of ppm. The latter would in any case make no sense. In Appendix B, the description is in terms of increments
• Another usage is forcings. This gets confusing, because he reports it as ΔT, where we would think of it in W m^-2. He gives in Appendix B for CO₂ as the increment from x₀=315 ppm of a log polynomial function the current ppm value. This is not far from proportional to the difference in ppm from 315. Other gases are also given by such formulae.
• An exception to the use of concentrations is the case of CFCs. Here he does cite emissions in tons, relying on manufacturing data. Presumably that is more reliable than air measurement.

Note that each scenario also includes an aerosol calculation, which is where volcanoes come in.

Arguments

Update. Eli notes in comments that he went through a lot of this in 2006, here, and continued here. I'll show his forcing graph below.  

I'll just briefly summarise some of the misconceptions I battle in blogs:

• Ignoring scenarios
  Many people want to say that Hansen made a prediction, and ignore scenarios altogether. So naturally they go for the highest, scenario A, and say that he failed. An example Noted by SkS was Pat Michaels, testifying to Congress in 1998, in which he showed only Scenario A. Michaels, of course, was brought on again to review Hansen after 30 years, in WSJ. This misuse of scen A was later taken up by Michael Crichton in "State of Fear", in which he said that measured temperature rise was only a third of Hansen's prediction. That was of course based, though he doesn't say so, on scenario A, which wasn't the one being followed.
  
  In arguing with someone rejecting scenarios at WUWT, I was told that an aircraft designer who used scenarios would be in big trouble. I said no. An aircraft designer will not give an absolute prediction of performance of the plane. He might say that with a load of 500 kg, the performance will be X, and with 1000 kg, it will be Y. Those are scenarios. If you want to test his performance specs, you have to match the load. It is no use saying - well, he thought 500 kg was the most likely load, or any such. You test the performance against the load that is actually there. And you test Hansen against the scenario that actually happened, not some construct of what you think ought to have happened.
• Misrepresenting scenarios
  This is a more subtle one, that I am trying to counter in this post.People want to declare that scenario A was followed (or exceeded) because tonnage emissions increased by more than the 1.5% mentioned in Hansen. There are variants. These are harder to counter because Hansen made mainly qualitative statements in his text, with the details in Appendix B, and not so clear even there.
  
  But there isn't any room for doubt. We have the actual numbers he used (see sources). They make his description explicit. And they are defined in terms of gas concentrations only (except for CFCs). Issues about how tonnage emissions grew, or the role of China, or change in airborne fraction, are irrelevant. He worked on gas concentration scenarios, and as I shall show, the match with scenario B was almost exact (Scen A is close too).

Scenario arithmetic for CO₂

. As mentioned, Hansen defined scenario A as emissions rising by 1.5% per year, compounded. The others differed by a slightly slower rate to year 2000. Scenario B reverted to constant increases after 2010, while scenario C had zero increases in CO₂ ppm thereafter. See the graphs below. With all the special changes in Scenario B, it still didn't get far from Scenario A over the 30 years.

The basic arithmetic for Scenario A is that, if a1, a2, a3 are successive annual averages of CO₂ ppm, then
(a3-a2)/(a2-a1) = 1.015
or the linear recurrence relation a3 = a2 +1.015*(a2 - a1)

There is an explicit solution of this for scen_2, which is the set Steve Mc calculated:

CO₂ ppm = 235 + 117.1552*1.015^n where n is the number of years after 1988. That generates the dataset.

The formula for the actual Hansen set is slightly different. Oddly, the increment ratio is now not 1.015, but 1.0151131. This obviously makes little difference in practice; I think it arises from setting the monthly increment to 0.125% and compounding monthly. However
1.00125^12 = 1.015104 which is close but not exact. Perhaps there was some rounding.
Anyway, with that factor, the revised formula for Scen_1 is

Scen A: CO₂ ppm = 243.8100 + 106.1837*1.0151131^n

Scenario B is much more fiddly from 1988-2000, though a straight line thereafter. Hansen describes it thus
"In scenario B the growth of the annual increment of CO₂ is reduced from 1.5% yr^-1 today to 1% yr^-1 in 1990, 0.5% yr^-1 in 2000, and 0 in 2010; thus after 2010 the annual increment CO₂ is constant, 1.9 ppmvyr^-1".

It isn't much use me trying to write an explicit formula for that. All I can report is that Scen_1 does implement that. I also have to say that this definition is too fiddly; the difference between A and B after all that fussy stuff is only 0.44 ppm at year 2000.

Scenario C is then CO₂ ppm = 349.81 + 1.5*n for n=0:12; then constant at 367.81.

Conclusion

Hansen's descriptions of the scenarios are not always clear. But we have the numbers used, and then it is seen to be consistent, with the scenarios defined entirely in terms of gas concentrations.

Graphs

In the latest RealClimate, Gavin showed plots of the graphs and data for trace gases. Note how the data for CO2 sits right on scenario B. This is the Scen_1 data (click to enlarge):





For comparison, Steve McIntyre showed graphs for his Scen_2, with data to 2008 only. There is no visual difference from scenario plots of Scen_1.



Gavin also gave this plot of forcing, which demonstrates that when put together, the outcome is between scenarios B and C. This was also Steve McIntyre's conclusion back in 2008.




And here is another forcings graph, this time from Eli's posts in 2006 linked above (click to enlarge):