[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 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.