Joe Romm’s Fuzzy Math

April 23rd, 2008

Posted by: Roger Pielke, Jr.

[UPDATE: Joe Romm replies in the comments: "Roger -- Thanks for catching my C vs CO2 error.those are very hard to avoid. And thank you for this post. I probably should have elaborated on this issue already -- so I'll just do it in a new post, which will take me a few hours to put together. As you'll see, there actually isn't a gap in my math -- there is a gap in Socolow's and Pacala's math that most people (you included) miss. I'll leave it at that, for now, and Post the link when I am finished."]

Readers here will know that Joe Romm has been extremely critical of the idea that we need any new technological advances to achieve stabilization of atmospheric carbon dioxide concentrations at a level such as 450 ppm. Now Joe helpfully lays out his plan for how stabilization at such a low level might be achieved. It turns out that there is a significant gap in Joe’s math. Even the remarkably ambitious (some would say impossibly fantastic) range of implementation activities that he proposes cannot even meet his own stated goals for success. The only way for him to close the mathematical gap that he has is to rely on – get this — assumptions of spontaneous decarbonization of the global economy (and by this I mean specifically reductions in energy per economic growth and reductions in carbon per unit energy). In fact, the emissions reductions that he needs to occur automatically (i.e., assumed) for his math to work out are larger than those he proposes through implementation.

Joe relies on a useful concept from Pacala and Socolow (2004, PDF) called the “stabilization wedge” defined as follows:

A wedge represents an activity that reduces emissions to the atmosphere that starts at zero today and increases linearly until it accounts for 1 GtC/year of reduced carbon emissions in 50 years.

Each wedge thus equates to a reduction of 25 GtC over 50 years.

Joe starts out by observing that we are at about 8.4 GtC (“30 billion tons of carbon dioxide emissions a year”) and “rising 3.3% per year” (for consistency I am expressing all units in GtC, though do note that Joe switches back and forth with carbon dioxide). He says that “We need to peak around 2015 to 2020 at the latest, then drop at least 60% by 2050 (to 4 billion tons a year or less).” Here I think that Joe actually means 4 GtC and not carbon dioxide, which we’ll adopt as Joe’s chosen mid-century target value. Joe presents 14 proposed wedges worth of implementation: 4 are focused on efficiency, 4 on sequestration, and 6 on carbon-free energy totaling about 12.5 terawatts (compare).

OK, let’s look at the math that Joe provides and how his proposed actions square with his goal. Let’s set aside political realism and all that, and just focus on the simple arithmetic of mitigation. If emissions continue to rise at 3.3% per year then by 2058 total global emissions will be about 42 GtC. With Joe’s 14 wedges all successfully implemented that would equate to an emissions reduction of 33% to 28 GtC per year, falling 24 GtC (i.e., 24 wedges)short of his goal of 4 GtC.

Well, you might say that emissions rising at 3.3% per year is unrealistic; after all, in the last two decades of the last century the global economy became more efficient and the world relied on less carbon intensive sources of fuel. The rate of this decline from 1980-2000 was about 1.0% per year, so maybe it’ll happen again at this rate from 2008-2058. Why not? Increasing emissions at the lower rate of 2.3% per year would indeed make a huge difference, meaning that total emissions in 2058 would be about 26 GtC – representing a reduction equal to the contribution of 16 wedges!! Yet even with this generous assumption of 16 free wedges, after we subtract Joe’s 14 wedges we’d still be left with an annual emissions gap of 12 GtC.

But wait, the careful reader might object, and report to us that Joe already assumes vast improvements in efficiencies — in fact 4 total of his 14 wedges. Is it reasonable to assume that we can get 20 (16 free + 4 from Joe) wedges of improved energy efficiency and decarbonization of the energy supply? Maybe, maybe not, but the assumption sure helps the math. And yet it still doesn’t get us all of the way to Joe’s goal.

What about if we shorten the time frame? Joe did suggest that we need to implement each wedge over four decades and not five: “If we could do the 14 wedges in four decades, we should be able to keep CO2 concentrations to under 450 ppm.” Of course, one wedge over four decades is equal to 20 GtC not 25 GtC, so we’ll call this a “short wedge.”

A 3.3% growth in emissions to 2048 would result in annual emissions totaling about 31 GtC. Subtracting 14 of Joe’s short wedges would still leave us 13 GtC short of his goal of 4 GtC. OK, I guess that it’s probably time to invoke those assumptions again. With a return to the 1980-2000 rate of decarbonization of the global economy and a 2.3% rate of emissions increase, the 2048 emissions would be about 21 GtC. If we subtract out Joe’s 14 short wedges that still has Joe missing his target by 3 “short wedges,” which we could probably erase by upping the assumed decarboniztion of the global economy to about 1.5% per year.

In short, the only way that Joe Romm’s ambitious solution even comes close to the mark is by assuming a significant spontaneous decarbonization of the global economy (i.e., reductions in energy and carbon intensities). Because Joe does not tell us how these spontaneous reductions will occur, his math is, at best, fuzzy. It seems quite odd that Joe, who has said that the fate of the planet is at stake, is willing to bet our future on baseline carbon dioxide emissions increasing at a rate of less than 2.0% per year, plus some fantastically delusional expectations of the possibilities of policy implementation (and the political realism of Joe’s solution will have to wait for another post). It may be unwelcome and uncomfortable for some, but Joe’s fuzzy math explains exactly why innovation must be at the core of any approach to mitigation that has a chance of succeeding.

Is it possible that assumed decarbonization of the global economy carries the weight of future emissions reductions? Sure, its possible. Is this something you want to bet on? Maybe some do, but I’d be much more confident with an approach that can succeed even if carbon dioxide growth rates exceed 2.0% per year.

13 Responses to “Joe Romm’s Fuzzy Math”

  1. Sylvain Says:

    Strangely the most effective solution to reducing co2 production is happening without the interference of any government, or taxes.

    The rising price of gas (and food) is the best way to force people to switch to more fuel efficient car and travel less.

    Of course, a recession wouldn’t do a bad job either.

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  3. jromm Says:

    Roger — Thanks for catching my C vs CO2 error.those are very hard to avoid.

    And thank you for this post. I probably should have elaborated on this issue already — so I’ll just do it in a new post, which will take me a few hours to put together.

    As you’ll see, there actually isn’t a gap in my math — there is a gap in Socolow’s and Pacala’s math that most people (you included) miss. I’ll leave it at that, for now, and Post the link when I am finished.

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  5. Tom C Says:

    Mr. Pielke -

    Why are you wasting so much time arguing with a guy who thinks the bridge collapse in Minnesota was caused by global warming?

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  7. jromm Says:

    As I explain here
    my math isn’t fuzzy. But I can see how it might look that way. Princeton’s math is fuzzy.

    Anyway, this post should just about explain everything.

    BTW — for the record, I don’t think “the bridge collapse in Minnesota was caused by global warming.” I merely said it was legitimate to ask whether extreme heat events contributed to it, based on what many other people wrote at the time and since.

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  9. Roger Pielke, Jr. Says:

    Wedge inflation?

    Keep trying, Joe, you are getting closer, here is what I posted over at Climate Progress:


    Thanks for the exchange. You appear to have identified another case where assumed efficiency gains contribute to the emisisons reductions challenge. If we can find just a few more of these assumptions then there may be no problem left to solve ;-) Seriously, here are a few comments:

    1. Of your proposed 14 mid-century wedges, only 6 involve the production of energy. Given that the world will need more energy under all scenarios your displacement of coal is therefore limited to 6 wedges, and cannot reach 14 unless you come up with 14 involving the production of energy.

    2. According to the EIA currently coal is responsible for about 3.0 GtC of global emissions, or about 36% of the current total global emissions. In 2050 using your data, of the 28 GtC, only 10 GtC would come from coal (using current technologies). So you can’t get 14 wedges from 10, so even if you came up with 14 on the production side you can’t get more than 10. Of course we could assume a faster rate of growth for coal, and then replace all of that (another creative use of assumptions!)

    3. If Pacala and Socolow are counting the increasing efficiency of coal plants BOTH as a contribution to the 1.5% per year increase in emissions (rather than a higher rate) and ALSO as a wedge, then they are engaged in double counting. You cannot have both! If this is true then they lose a wedge.

    4. You shaved 0.3% off the growth rate from your earlier post. That was worth 4 wedges. Also, you use a 42-year short wedge, rather than 50 as do P&S, that is worth another 7 wedges.

    We can play the assumption game all day long. I will grant you that there are indeed a combination of assumptions that you can put together to get your math to work out. You haven’t yet done so, but I’m sure you can.

    But playing the assumptions game is why the “emissions reduction” framing is a little bit like balancing future gov’t budgets — it encourages the creative use of rosy assumptions. A more useful strategy would be to talk about how to meet the worlds future power needs using carbon free energy. You’ve proposed 12.5 TW for 2050. This won’t be nearly enough.

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  11. Roger Pielke, Jr. Says:


    To summarize:

    At 8.4 GtC in 2008 (which is too low, but OK), at 3% growth to 2050 this results in 29 GtC. If we allow your new and improved super-sized wedges of 1.8 GtC, you get 6 of these, or about 11 GtC. You have 8 remaining regular-sized wedges for another 8 GtC. Thus you are 29 minus 19, or 6 GtC short of your 4 GtC target in 2050.

    If you had stuck with your original 3.3% emissions increase that would add 4 GtC, and if we went out th full 50 years add another 7 GtC. This results in another 11 regular sized wedges.

    So I count you as still being either 6 or 17 wedges short, depending on assumptions, and granting you these super-sized wedges that you have come up with.

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  13. jromm Says:

    Roger — I reply to all these on my website, but I’ll repeat it here, starting with your “summary”:

    First, you don’t have to “grant” me supersize wedges. That’s just the way the numbers work out. But I’m glad you accept them.

    Second — Your phrase “the full 50 years” is a complete non sequitur. How many times do I have to repeat this point? I’m not defending Princeton’s flawed approach. Quite the reverse. I’m proposing my own approach using their framework. There never was anything magic in their 50 years. I have repeatedly said we need to do this faster than 50 years. You can keep attacking Princeton’s approach all you want if it makes you happy, but it is quite irrelevant to my proposed solution.

    Third, let’s not claim we know the carbon emission from 2000 to 2006 so precisely. I think 3% is a pretty damn conservative assumption, given that it is double the rate from 1970 to 2000.

    Fourth, finally, I don’t “get” 6 super-sized wedges. I get more than 10. Your assumptions are off. In your 3% growth scenario, probably all of the extra tons (above the 1.5% scenario) are coal.

    To elaborate, You can’t take EIA’s fraction of coal today and use it in 2050 — the whole point is that the re-carbonization is occurring because the world is building a disproportionate amount of coal. Thus I would say probably 100% of the extra tons in 2050 are coal. By extra tons, I mean the ones beyond the 15 GtC that we would otherwise have if we stayed at the 1.5% carbon growth of the previous three decades that Socolow had assumed in their BAU. So in the heavily carbonized scenario you are positing, probably some 18 GtC are coal.

    And 10 of my wedges are zero-carbon power generation (or generation avoidance), so that works out fine.

    As for the double counting claim — This comment is a real non sequitur. Who cares if Pacala’s and Socolow’s more efficient coal plants wedge is double counting? I don’t use that wedge. I only use a few of their wedges. I thought it was clear that I’m only using the framework of their otherwise flawed analysis.

    I haven’t made any rosy assumptions. One would have to say that assuming emissions growth of 3.3% per year for the next 42 years is pretty unrosy, though. In any case, you assert “I’ve proposed 12.5 TW for 2050″ but you haven’t shown any analysis to support the 12.5 claim, nor have you shown any analysis why it wouldn’t be adequate.

    I didn’t realize this was a game to you. For me, avoiding catastrophic global warming is the most serious thing we could possibly be doing. My math clearly works out. I guess it was overly optimistic of me to assume you would concede my math is right, but at least my readers know that my 14 to 16 wedges are the solution I promised.

    You have NEVER proposed your own specific solution , however, so I think people should take your comments with a large grain of salt. If you won’t do that, I’m not sure why I should keep responding to these largely irrelevant potshots at my solution.

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  15. docpine Says:

    “1 of cellulosic biofuels — using one-sixth of the world’s cropland [or less land if yields significantly increase or algae-to-biofuels proves commercial at large scale]. ”

    Hmmm. I thought the point of cellulosic biofuels would be to not use cropland, but rather to use land that is not suited to crop production, or to use extra woody and non woody biomass from forests, crop residues, yard waste, etc. In fact, I thought there were technologies being discussed to make biofuels from garbage. this seems like the second post this week that leaves out non-crop plants. What’s up with that?

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  17. Roger Pielke, Jr. Says:


    You promised a list of technologies that if deployed in the coming decades would lead to net global emissions of 4 GtC. When it was pointed out that your math did not add up you played with your assumptions as follows:

    1) Increased the size of your wedge from 1.0 GtC 50 years from now to 1.8 GtC 42 years from now. The shorter time frame means that you need less wedges.

    2) Decreased the baseline growth rate that you had first proposed by about 10%. (Recall that you suggested 3.3%, not me.)

    3) Assumed that the proportion of future primary energy consumption from coal will more than double (!) over the next 4 decades, representing a 6-fold increase in coal consumption.

    I may have missed a few new assumptions. So what you have shown is that a list of practically impossible steps (I know we didn’t discuss this) can be shown to be sufficient to the task of reducing emissions if and only if we accept a wide range of assumptions put in place/modified after the analysis was challenged.

    Look, I understand that you believe that it would be feasible for each of your proposed wedges to be implemented with 100% success on the time scale that you propose, and that you further believe that the assumptions required to make your math work out will pan out. But I’d ask that you respect that I doubt your optimism on wedge feasibility and also on the rosy scenarios. On this reasonable people can disagree. So lets agree to disagree.

    But I hope that you will understand that my view of the importance of innovation 9as a complement, not replacement) lies in exactly these doubts of the likelihood of success of your proposed strategy. You have said that if we don’t get started by 2012 we’re in deep trouble. Well, that isn’t too far away, and when global emissions are around 10 GtC near 2012, I’d expect that you’ll find an innovation-based approach a lot more appealing. We shall see.

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  19. jromm Says:

    Roger — you keep misstating what I’ve done, so this is getting tiresome. You didn’t like the fact that my analysis was correct, so you’re trying to say it wasn’t correct — but you haven’t disproved what I wrote.

    I didn’t change the size of the wedge — I explained why a larger wedge falls out of the analysis logically. I ALWAYS assumed a 4-decade wedge — read my original post.

    I never “proposed” a baseline rate of 3.3% for the next four decades! I just noted that was what some people have reported has happened to date.

    I haven’t “Assumed that the proportion of future primary energy consumption from coal will more than double” (!) over the next 4 decades. I merely pointed out that this is an inevitable consequence of YOUR assumption that CO2 emissions will continue at their anomalously high rate of 3% per year (or 3.3%) per decade, compared to the rate of the last 3 decades, 1.5% per year.

    What I don’t understand is why you don’t realize that if my wedges are delusional, your innovation strategy is doubly so. That seems so obvious. But I’ll deal with it in my next post to spell it out.

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  21. Roger Pielke, Jr. Says:

    Joe- We’ve showed our work, and our assumptions, I’m happy to let readers decide on their own. And as I said, I respect that you have a different view that I do, c’est la vie.

    Readers should have a look at Ted Nordhaus’s comment, which is a great summary of the debate:

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  23. Roger Pielke, Jr. Says:


    Just so that you can be completely accurate in the future, we are in 2008 at an estimated 9 GtC emissions from fossil fuels (i.e., not including land use). See the ppt here: activities/ AcceleratingAtmosphericCO2.htm

    Starting at 9 GtC rather than 8 GtC means instead of BAU being 28 GtC in 2050 (as you have written) then this value is 31 GtC (using your 3.0% rate of increase per year, at 3.3% it is 35 GtC). So you should probably correct this error in the post above and then also tell us where these 3 extra wedges will come from.

    My suggestion is to reduce the future baseline to 2.8%, and this will get you 3 free wedges in 2050 under your other various assumptions.

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  25. Roger Pielke, Jr. Says:

    A reader writes in to observe:

    “Roger: Thought you would appreciate this.. Joe Romm’s guest blogger, Elizabeth Grossman, writes (without a word of protest from Joe):

    “The underestimation of greenhouse emissions occurred, Field said, because the IPCC failed to include in its scenarios the rapid increase in carbon dioxide from Asia’s coal-reliant industrial expansion between 2000 and 2007.
    “‘We were too optimistic,’ Field said. ‘There was no decrease in emissions from developed countries and the sharpest increases and overall intensity came from China and India that rely heavily on coal.’
    “‘It was assumed that coal would become less important,’ says Ken Caldeira, also of the Carnegie Institution. What happened, however, is that China and India developed rapidly while rising oil prices pushed wealthy nations to use more coal, which is more CO2 intensive in its emissions. Scientists at NASA’s Goddard Space Science Institute concur that the past five years’ sharp increase in atmospheric CO2 is attributable to the steep rise in global coal use, pushed upward by accelerated Asian economic and industrial development.
    “‘IPCC scenarios assume an increase in energy efficiency during this period,’ Caldeira says. But that didn’t happen. ‘Efficiency flattened out,’ he says.”

    Can it be? That sounds suspiciously like an endorsement of your Nature paper on assumptions about spontaneous decarbonization!”