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Divvying Up the Warming

By Chip Knappenberger -- December 15, 2010

In a MasterResource article a few months back, I walked everyone through a series of recent scientific findings and described how they cast new light on how the total amount of observed global warming to date could be divvied upon among various causes. I ultimately concluded that the high confidence that the IPCC (and later echoed by the EPA) placed on the statement that “Most of the observed increase in global average temperatures since the mid-20th century is very likely due to the observed increase in anthropogenic greenhouse gas concentrations” was misplaced.

This line of reasoning was recently incorporated into statements made by Dr. Patrick Michaels when testifying before the U.S. House of Representatives, Committee on Science and Technology, Subcommittee on Energy and Environment.

During the questions and answers portion of the hearing, one of the other panelists, Dr. Benjamin Santer, quickly objected and claimed that Pat was “wrong” because he didn’t take into account the cooling influence of aerosols when determining how much observed warming should be assigned to greenhouse gases.

A day or so following the testimony, Judith Curry hosted a discussion on her blog site Climate Etc. to further examine Michaels’ logic. In her remarks introducing the thread, she too suggested that Pat was “obliged” to include sulfates in the calculation. When I stepped in to offer additional explanation, RealClimate’s Gavin Schmidt commented that he hoped I was “kidding,” and John Nielsen-Gammon of Texas A&M commented that my explanation was “nonsense.”

So with all these erudite folks claiming that Pat Michaels and I are wrong, I figured I ought to take another look into the logic behind our conclusions.

Our Logic

First let’s get a couple of things out of the way up front. The argument about whether or not the inclusion of sulfates is required to arrive at a logically correct conclusion has nothing whatsoever to do with the veracity and/or applicability of the scientific papers from which I’ve drawn some numbers (see my earlier post for details about these findings). I am not suggesting that there isn’t plenty of room to argue that aspect of things, just that such a discussion does not impinge on the discussion of our logic. So I’ll set aside discussion of those issues in order to focus on the topic at hand.

I’ll state the following things simply as given (if it helps I’ll add this disclaimer “The following are for illustrative purposes only”):

1) The observed warming from 1950-2009 is 0.7°C
2) 0.2°C of that is due to a warm bias in the measurements
3) This leaves 0.5°C of actual warming
4) The anthropogenic increase in well-mixed greenhouse gases is responsible for +3.0 W/m2 of extra climate forcing (positive climate forcing imparts a warming pressure on global temperatures)
5) Sulfate aerosols are responsible for -1.5W/m2 of climate forcing (note this is a negative forcing which imparts a cooling pressure)
6) Black carbon (a.k.a. “soot”) aerosols are responsible for 1 W/m2 of added forcing (warming)
7) Stratospheric water vapor changes are responsible for 0.5W/m2 of added forcing (warming)

I’ll stress again, I use these numbers to make the math cleaner. They are in the ball park, but not intended to represent the exact or even best-guess values. So please set aside any heartburn about them (also note that natural variability is not considered here, but most definitely should be in a more formal evaluation).

Also, the IPCC was unaware of numbers 2, 6, and 7 at the time it made its “most of the observed warming” statement quoted above.

In my MasterResource article and in Pat’s testimony, the logic as to how to assign various amounts of observed warming to various factors is as follows:

The 0.5°C of actual warming [in (3)] was caused by three factors, GHGs, black carbon, and stratospheric H2O. In percentage terms, GHG contributed 67%, black carbon contributed 22% and stratospheric H2O contributed 11 percent. This is calculated by taking the positive forcing from each factor and dividing it by the sum of the positive forcings. Thus for GHG, you get 3.0/(3.0+1.0+0.5)=0.67, or 67%. To determine how much of the actual temperature change that GHGs were responsible for, we multiply 0.5°C by 67% and get 0.34°C—which, we pointed out was about 50% of the “observed” warming of 0.7°C (listed in (1)). Thus, the IPCC statement rests on thin ice.

To this, Santer/Schmidt/Nielsen-Gammon/Curry cried “foul!” claiming that we have committed a sin of omission by not factoring in the negative climate forcing contributed by sulfate aerosols.

Their Logic

When calculating the percentage contribution from each climate forcing agent, they maintain that we should have divided each element’s contribution not by the sum of the positive forcing, but by the sum of all forcings (including negative ones). So instead of dividing by (3.0+1.0+0.5)=4.5 like we did, we should have used (3.0+1.0+0.5-1.5)=3.0.

And, they argue, that had we done that, we would have found out that GHGs contribute 100% of the warming, black carbon 33%, stratospheric H2O 17% and sulfates -50%. Therefore, even taking into account measurement errors (listed in (2) above) GHGs still contribute more than half of the observed warming. And the IPCC is right and Michaels and I are wrong (see John Nielsen-Gammon’s explanation at Climate Etc. for further evidence of this line of reasoning).

It is now my turn to reply, “Nonsense!”

Pieces Greater than the Whole?

You can’t divide a physical quantity into pieces that together are greater than the whole. Which is precisely where the latter logic leads you.

The flaw in the Santer/Schmidt/Nielsen-Gammon/Curry logic is in confusing “potential” warming with “observed” or “actual” warming.

I completely agree that using the numbers above, GHGs contribute 0.5°C*100%=0.5°C of potential warming, black carbon contributes 0.5*33%=0.17°C of potential warming, and stratospheric H2O contributes 0.5*17%=0.08°C of potential warming and that of this 0.75°C of potential warming, sulfates offset 0.25°C of it, leaving 0.5°C of observed warming.

But, in employing potential warming to divvy up observed warming is mixing apples and oranges, and leads to results that don’t make practical sense.

Take for instance this hypothetical situation:

GHG = 2 W/m2
Black Carbon = 2 W/m2
Stratospheric H2O = 2 W/m2
Sulfates = -4 W/m2
Observed Warming = 0.5°C

If this were the situation, you would arrive at the answer that GHGs are responsible for 100% of the warming AND black carbon is responsible for 100% of the warming AND stratospheric H2O is responsible for 100% of the warming. This result allows you to assign any and all warming to whatever your favorite postive forcing element is. Certainly this is creative, but it is not practical.

Doing things my way, you get the logical result that each positive forcing element contributes 33.3% to the warming and is equally responsible for what has been observed.

So there you have it, two different ways of describing the observed warming.

I’ll leave it up to you all to decide which one is the more reasonable.

The IPCC’s Take

But before I go, I’ll leave with one additional thing to consider.

Here are two successive statements in the IPCC’s Summary for Policymakers of its Fourth Assessment Report (p. 10).

The first you will recognize:

“Most of the observed increase in global average temperatures since the mid-20th century is very likely due to the observed increase in anthropogenic greenhouse gas concentrations.”

And here is the separate bulleted statement that comes next:

“It is likely that increases in greenhouse gas concentrations alone would have caused more warming than observed because volcanic and anthropogenic aerosols have offset some warming that would have otherwise taken place.”

Clearly the IPCC recognizes the difference between observed warming (as reflected in the first statement) and potential warming (as reflected in the second statement).

Bottom Line

The latter IPCC statement will remain true so long as the value of the net climate forcing remains less than that of the GHG forcing (which would take a significant scientific finding to overturn). I think this is the gist of what Santer/Schmidt/Nielsen-Gammon/Curry are saying, and that such a major development has not occurred.

The former statement, however, and the one whose veracity is being assessed by Pat Michaels and I (and the one highlighted by the IPCC and the EPA), is more readily falsifiable through even relatively minor tweaks to our understanding of the various influences on the climate system. And Pat and I are claiming that such minor tweaks have occurred and have led to a falsification of the IPCC statement—or at the very least, demonstration that it is undeserving of the level of confidence placed upon it by the IPCC.

I welcome on-topic comments.


  1. cknappenberger  

    Maybe this more practical analogy will make things clearer:

    Three apple growers deliver apples to an apple seller. Grower A delivers 300 lbs of apples, Grower B delivers 100 lbs of apples and Grower C delivers 50 lbs of apples. On the way to market, the apple sellers cart overturns, and of the 450 lbs of apples that he is taking to sell, 150 lbs are lost. He is able to sell the remaining 300 lbs for $1.67/lb taking in a total of $500.

    The next day, the apples growers come to collect their share. Grower A says, since the apples sold for $1.67/lb and I contributed 300 lbs, you owe me $500. Grower B, multiplying $1.67/lb by his 100 lb contribution, asks for $167 and Grower C, using the same math, asks for $84. The apple seller responds that each claim is legitimate, but, that as a result of the losses, that he only has a total of $500 to distribute. Thus, the only equitable way to distribute the proceeds is to do so based upon the percentage contribution that each grower made to the total amount of apples that were originally intended to be sold. In this case, Grower A contributed 67%, Grower B contributed 22% and Grower C contributed 11%. Thus the seller paid out $335, $110, and $55 to Growers A, B, and C, respectively (to the dismay of Grower A, who continued to insist that he should receive the entire amount).

    The percentage pay-out to each Grower is the same no matter how great the losses are, although the actual dollar amount that each receives will change depending on the total sales.

    Thus, in determining the percentage of the pay-out, the size of the loss does not enter into the calculation.

    In the same way, the negative forcing from sulfate aerosols does not enter into the calculation of how to apportion the observed global warming among the positive forcing agents.



  2. John N-G  

    Chip – You’ve noted the strangeness with the IPCC statement, but your formulation is at least as strange. Take, for instance, you hypothetical situation. Black carbon and sulfates are both aerosols. So your hypothetical is equivalent to:

    GHG = 2 W/m2
    Stratospheric H2O = 2 W/m2
    Aerosols = -2 W/m2
    Observed Warming = 0.5°C

    By your accounting, you get the “logical” result that GHG are responsible for 50% of the observed warming, even though your earlier accounting with exactly the same hypothetical forcings (just lumped differently) came up with GHG = 33% of the observed warming.

    So we have two possible interpretations of the IPCC statement. Both interpretations are unsatisfactory. The IPCC statement is arguably wrong if interpreted in one of the two unsatisfactory ways.

    My bottom-line position is not that the IPCC is right and you are wrong. It is that the IPCC statement itself is not a useful way of framing the issue. It simply does not make sense to talk about a proportion of the warming attributable to a particular factor when there are both positive and negative factors.

    I hope that, next time around, the IPCC avoids this confusion by simply providing their estimates of the amount of GHG forcing compared to the total amount of forcing, and their estimates of the net effects of external forcing compared to internal variability. Then we wouldn’t need to have this argument.


  3. John N-G  

    Chip- Actually, I’d expect the seller to compensate the growers for the apples the seller lost while under his care, unless the concept of assumption of risk applies.


  4. Craig Goodrich  

    It should be noted that the various climate models use “aerosols” as the label for a curve-fitting fudge factor thrown in to match the late 20th-century temperature increase while maintaining enough sensitivity to produce the horrific numbers so loved by the IPCC.

    In point of fact, almost nothing is known about the effect of aerosols on climate. These people have been playing with their models so long they have almost come to believe them.


  5. Andrew  

    I saw their argument and immediately thought, also, that this was an absurd line of reasoning. Clearly if you include the negative forcings in “percentage” calculations of warming the numbers that result are total gibberish.

    If the IPPC used this line of reasoning, they would have said that humans are very likely responsible for 300% of the observed warming, which one hopes would get them laughed out of even the most deluded academic circles.


  6. cknappenberger  

    John N-G { 12.15.10 at 11:29 am }:

    Thanks for your comments.

    Taking your suggestion to the extreme, I guess we could just lump everything together under the label “anthropogenic forcing” and then the IPCC could have attached some level of confidence to some statement about how much “observed” warming was from changes to net anthropogenic forcing. In that case, our discussion would mostly be limited to the magnitude of natural contributions and how close the “observed” warming was to the “true” warming. But as the IPCC introduced a breakdown of the anthropogenic forcing agents (i.e. GHGs), then it seems like looking at the roles of the individual forcing elements (as best as we can) is fair game to bring into the discussion. So looking at BC separate from cooling aerosols seems legitimate approach.

    I agree with you that the wording of the IPCC has led to these discussions, but the IPCC apparently liked it a lot (as it is highlighted in the SPM) and it is widely repeated (for example, by the EPA). As such, it seems that it is worthy of examination (heck, Ben Santer said that it was, in fact, one the “central conclusions” IPCC findings).

    So, here we are!



  7. Frank  

    Your analysis of the IPCC’s statement of attribution discusses only one of many problems with this statement. Everything would have been fine, if the IPCC had limited itself to saying that “the anthropogenic GHGs (AGGs) contributed more than half of the known positive FORCING driving temperature rise in the second half of the 20th century”. However, the IPCC wanted a statement about how much AGG’s contributed to 20th century TEMPERATURE rise, not to overall positive forcing. The only way I know to convert a forcing into a temperature rise is via climate sensitivity; a process that introduces additional uncertainties.

    Unfortunately, AR4 only provides us with forcing change since 1750, not forcing for the period 1950-2000. [Why is the IPCC drawing conclusions about the cause of 1950-2000 temperature rise from 1750-2005 forcing and 1900-2000 climate models runs?] This is a non-trivial problem because: 1) Most of the increase in sulfur emission was in place by 1950. 2) Sulfur emissions didn’t have a large NET increase between 1950 and 2000 (although there was a higher peak in 1970-85). 3) Sulfur emissions fell in the late 20th century. (Figure 1, Stern (2006); http://www.economics.rpi.edu/workingpapers/rpi0504.pdf). So ignoring aerosol cooling for 1950-2000 period was far less of a problem than you critics assume from looking at the aerosol forcing SINCE 1750 in Figure SPM2 of AR4 WG1.

    Using the forcing data from Figure SPM2, we can calculate the expected temperature change for all anthropogenic forcings by multiplying the forcings (1.6 W/m2 with a 90% confidence interval of 0.6-2.4) times the climate sensitivity (3.0 degK/2X CO2 = 0.82 degK/W/m2, with a 90%?confidence interval of 0.4-1.2 W/m^2. I converted the confidence intervals into standard deviations by assuming that each confidence interval represented +/-1.6 standard deviations and used Excel to do 1000 randomly chosen examples of 1.6+/-0.56 (1 Std) times 0.82+/-0.25 (1 std) . The resulting temperature rise was 1.46+/-0.87 (1 Std) and a 90% confidence interval of 0.07-2.32 degK.

    Now we compare these calculated temperature rises to the observed 1906-2005 temperature rise (we can’t go back to 1750 like the forcings do). Page 5 of the SPM of AR4 WG1 says the temperature rise for the past century was 0.76 (0.57-0.95) degK. Only 7.7% of my 1000 multiplications gave a temperature rise 200% of observed warming was caused by anthropogenic forcing. This is obviously absurd. If 20th century temperature rise due to AGGs is predicted to be 0.07-2.32 degK (90% confidence), uncertainty is too great to draw ANY conclusion about the cause of most of an observed temperature rise of 0.57-0.95 degK. Uncertainty in forcings make it impossible use 20th century warming to place any useful constraints on climate sensitivity. Likewise, uncertainty in climate sensitivity and forcings make is impossible to make any meaningful estimate about the causes of 20th century warming.

    The other half of the evidence for the IPCC’s attribution statement comes from Figure SPM4 and climate models. These models provide a much narrower range of predictions for 20th century warming because the IPCC’s “ensemble of opportunity” doesn’t take into account the uncertainty in the input AGG amounts OR the uncertainty in other model parameters. Instead, “convergent evolution” has probably resulted in similar temperature rises for the 20th century. (After all, who would continue funding a climate model that can’t reproduce the historical temperature record? “Survival of the fittest” provides a reasonable explanation for the narrow spread.) If one used Stainforth’s ensemble of models and a range of AGG inputs, the red range of model predictions in Figure SPM4 would be huge and probably would overlap the blue observations.


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