What's your Carbon Footprint?

Much has been made of the question of how we can reduce our individual impact on climate change. We all of us want to make a difference. If we individually consume less, surely we're doing our part to save the planet.

But I really think the premise is wrong, because in an interconnected world, none of us can be meaningfully separated from the whole. 

Consider the number of degrees of separation between you and anyone else on the planet. This might seem like a pretty hard thing to assess given how many of us there are and in some pretty far-flung places. I don’t know personally anyone in the Papua New Guinea Highlands (to mention some arbitrarily remote location), but I can be pretty sure that it’s not too much of a stretch to suppose my Australian friend has a friend who has been to the PNG capital Port Moresby where he ran across a guy whose cousin occasionally makes trips to the capital to work for “luxury” items to take back to his remote mountain jungle dwelling where he presents them to his wife. 

That would be just five degrees of separation. Certainly, the relationships are pretty far-flung, but it’s like the line from the TV series Breaking Bad,  “I know a guy who knows a guy.” None of us is truly independent of anyone else.

The same principle can apply to all of history. Suppose that an estimated 100 billion people have walked the earth in the last 50,000 years. With each successive generation, each of us is related to two others to the power of the number of generations. Exponentials lead to big numbers quickly: 100 billion people equates to just 37 successive generations. So, it shouldn’t take too great a number of generations before the number of your number ancestors is similar to the number of people living at that time. As evidence, all humans look and act pretty much the same. One way or another, there was sufficient intermingling for us all to have ancestors in common.

So, as a first approximation, we are linked through our social and economic connections to everyone currently alive, and moreover we can be linked by blood and tradition to everyone who has ever been alive.

It seems then that the question should be not what is your carbon footprint but what instead is our carbon footprint, that for humanity as a whole. We are a collective “super-organism” that has evolved over time by burning carbon based fuels to sustain ourselves and to grow. Individually, we may profoundly feel that we can behave as isolated entities; our personal economic choices, in however limited a way, can reduce the collective rate of CO2 exhalation. 

The evidence is against this argument, however.  If we term our collective wealth as the accumulation of all past economic production, summing over all of humanity over all of history, then the data reveal a remarkable fact: independent of the year that is considered, collective wealth has had a fixed relationship to added atmospheric CO2 concentrations. Expressed quantitatively,  2.42 +/- 0.02 ppmv CO2 is added every year for every one thousand trillion inflation-adjusted 1990 US dollars of current global wealth.   

A useful analogy here is to a growing child, who consumes food and oxygen and exhales carbon dioxide. The rate of CO2 exhalation by the child is determined by the sum of all cellular activity in the child. All the child’s current living cells require energy, and all produce CO2 as a waste product. But there are two key things: first, no set of cells can be magically dissociated from any set of others, e.g. the heart from the brain, as they are all interdependent; and second, the total number of current cells in the child is not determined by what the child does today, but rather by child’s past. Over time, the child grew from infancy to its current size, accumulating cells such that prior growth determined the child's current capacity to exhale CO2.

For humanity, it is the same. We currently “exhale” CO2 as a total civilization, but our current rate of exhalation is a collective enterprise by its intertwined parts as they have emerged from past civilization growth. 

So, if emissions are so tightly linked to the collective whole, and all past growth of civilization’s consumptive needs has already happened, entirely beyond our current control, what individually can we do right now?

To further illustrate the problem, let’s look at CO2 concentrations in the atmosphere. To calculate the actual increase in atmospheric CO2 concentrations, one has to consider that the land and oceans absorb a fraction of what is emitted. Estimating carbon sinks is possible but can get pretty tricky. Nonetheless, we can look at the observed relationship between economic activity and atmospheric chemistry to get a sense of what is going on. 

Looking above at the past 2000 years of atmospheric carbon dioxide concentrations, obtained from Mauna Loa in Hawaii and from ice cores in Antarctica, and measured as a perturbation from a baseline “pre-industrial” concentration of 275 ppmv, there is a surprisingly tight power-law relationship with global GDP. For the entire dataset :

log[CO2(ppmv perturbation)] ~ 0.6 x log[GDP(2005 USD)]

Amazingly, for over 2000 years, the relationship between CO2 and economic activity has been pretty much a mathematical constant.

In fact, if we look just at the past 60 years in the above, the relationship is linear and even tighter: since 1950, for every trillion inflation-adjusted year 2005 USD of global economy, the atmospheric concentration of CO2 has been 1.7 ppmv higher.

And, we could turn this around. With an extremely high degree of accuracy, we could estimate the global GDP simply with a CO2 probe at Mauna Loa. In units of trillion year 2005 USD and ppmv CO2:

   

GDP  = 0.58 x CO2 - 174

An atmospheric chemist could easily obtain the size of the global economy within a 95% uncertainty bound of just 1.5%! No need for economists!

Of course, we have to be careful with correlation and causation. And even if the above relationship has worked extraordinarily well for the past 65 years, the underlying basis for a relationship between GDP and CO2 concentrations is in fact rather more complicated. Nonetheless, these data clearly support an argument that what matters for determining the concentrations of this key greenhouse gas are collective human activities. 

The relationship between CO2 and world economic activity has been extremely tight and invariant over a very long time period during which the configuration of humanity has changed extraordinarily. There have been periodic wars,  famines, and global economic crises. We do not consume the same raw materials with the same efficiencies to the same extent now as we did in the past. The mix of wind, solar, nuclear and fossil fuels has been consumed in widely varying mixtures using an extraordinary range of different technologies. 

Yet this tie remains. What is going on? Speculating, perhaps one way to look at it is to consider individually the impact of buying that fuel efficient Prius, or turning down the thermostat. A car or house that consumes less fuel allows for an instantaneously incremental reduction in the demand for fuel. Sounds great. Except, the resources for producing the fuel are still available. If demand drops incrementally, then oil producers reduce prices to increase demand. Cheaper gas is more desirable, and so the collective response of all consumers is to consume more. Ultimately, the net effect on the collective rate of fossil fuel consumption of buying a fuel efficient Prius is zero (or even an increase). 

“No man is an island entire of itself...” We have no individual carbon footprint. We are only “... a part of the main”. We'd like to think our individual actions matter but it is only collectively will they reduce our impact on climate. And this will be very, very hard. As unpalatable as it may be, the only successful climate action will be to dramatically and collectively deflate the global economy.  Unfortunately, this may be a bit like asking that growing child, once it has reached a healthy adulthood, to voluntarily suffocate or shrink back to infancy. 

Is there an alternative perspective that allows for change but is still consistent with the observations? It would be nice to think that our individual or collective actions can meaningfully decouple the economy from changes in atmospheric composition. But how? 

Determinism and the human machine

I've been called a "dangerous nihilist" for trying to show how humanity can be treated usefully as a simple physical object. And a paper by D. Cullenward et al. strongly critical of my work - albeit by totally getting it wrong - referenced this rather funny cartoon, concluding that "Perhaps in the future a particularly brilliant scientist will discover a robust and verifiable means for deterministically predicting energy system dynamics. Until that time, however, the evidence suggests we should err of the side of humility and uncertainty in making projections about the future."

I get it. Treating the collective behavior of humans as simple by-products of the 2nd Law of Thermodynamics, something reducible to one line equations in physics, would hardly be the stuff of Keats or Shakespeare sonnets. Obviously, interpersonal dynamics can feel strong, and those feelings lead to decisions that seem at times to be utterly unpredictable, certainly a far, far cry from the elegant simplicity of an equation in physics.

But I don't see that poor predictability of the human condition is inconsistent with it being strictly deterministic, something that could be, at least in principle, reduced to a mathematical representation. 

The father of chaos theory, MIT atmospheric scientist Ed Lorenz was perhaps the pioneer of this idea. In his seminal paper Deterministic Nonperiodic Flow  he devised a simplified set of equations that represented some key processes in the atmosphere. The details don't really matter, but for edification here's the set up:

Aside from the rather extraordinary genius of representing the atmosphere in such a compact manner, what was so enormously influential was that Lorenz showed how purely deterministic equations - X, Y, and Z at any given time is uniquely determined by where X, Y, and Z start out - are nonetheless unstable and inherently unpredictable. This did not mean the solutions aren't well bounded. That is to say, on Earth, X, Y, and Z couldn't become just anything. It's just that the precise solution of X, Y, and Z  at any point in time could not be predicted very far ahead because even very small differences in the precision of the initial state translated to large differences in some not-so-distant future state. 

Sensitivity to initial conditions means the final outcome can be deterministic but nonetheless unpredictable. Determinism does not mean knowability. 

Of course, this does not mean we give up in despair. Well-bounded solutions do nonetheless exist. Not everything is possible, although we must accept a certain loss of resolution in our results the further out we look. 

Due to the approximate length of the water cycle, we know we can't peer beyond about 10-days in our weather forecasts, but we will accept a 1-week forecast for our weekend planning - albeit with a larger grain of salt than the 1-day forecast for the kids' soccer game. And we can still make climate forecasts that are averaged over space and time: it's not idiocy to claim that summer will arrive in the Northern Hemisphere around May, 2026 even if there's no prayer of saying it will rain in New York City on July 15.

I don't see it as being entirely dehumanizing to treat humanity in a similar fashion. We are wonderfully unpredictable and predictable at the same time. We don't know what exactly the day or year will bring even if we have a pretty good idea. Like the popular quote in the financial world "History doesn't repeat itself but it often rhymes". 

So it is with the approach I've taken to the evolution of civilization. There is no pretense at being able to explain the details at any given time or place, but there is predictability, predictability that can be tested with hindcasts, provided we step back and look at humanity as a whole. Stepping back, we can see farther into the future. Sensitivity to initial conditions yields to bounded solutions that are constrained by the laws of thermodynamics. For example, whatever a Nobel prize winning economist might imagine, we will not decouple the economy from energy consumption and carbon dioxide emissions. It's as physically possible as a perpetual motion machine.

Maybe we are a bit like Don Draper in the opening credits of the Mad Men series, falling deterministically through a series of life events, lacking any real internal control. Watching the series we already know the story: Don is irretrievably trapped by his mysterious past, and will inevitably succumb to women and booze. However, because we never know exactly how, we nonetheless derive the very human joy of watching his agonies as we binge-watch the next episode. Is this Nihilism? Voyeurism? I don't know. But I feel a bit the same about watching the progression of civilization through its own coming struggles with resource depletion and environmental decline.

EIA energy forecasts also spell economic doom?

The last post looked at the Energy Information Administration (EIA) energy forecasts to conclude that the 1% per year global energy consumption growth rate implied that over the course of the next 40 years we will consume as much energy total as the total we consumed in the past 100 years. Of course, we will consume even more if the growth rate continues at 2% per year, as it has in the past decade. If the past century of environmental destruction is any guide, destruction powered by our energy consumption, then the planet will be rather worse for wear in most of our lifetimes.

But what does it imply economically? Agencies like the World Bank and the International Monetary Fund forecast between 3% and 4% global GDP growth in the coming years. Can this be reconciled with EIA forecasts of just 1% for the fuel that power the economy?


A direct implication of the constant relating energy consumption and historically accumulated wealth that I have described is

GDP growth rate = Energy consumption growth rate  + Growth rate of energy consumption growth rate

So just to show that this isn't totally out to lunch, the respective mean growth rates for the 40 year period between 1970 and 2010 are

3.1%/year = 2.0%/year + 1.4%/year

3.1%/year = 3.4%/year. So not perfect, but pretty close, about 10% error. What we see globally is that GDP has been growing faster than energy consumption, but the difference can be accounted for by the second term on the right hand side above, the growth rate of the growth rate, a term I have been calling innovation since it can be related to improvements in energy efficiency.

So, let's now take a look at what the EIA forecasts imply for the future. If energy consumption has been growing at 2.0%/year, and the EIA projects instead a steady 1%/year, then the equation above for GDP growth would read:

1.0%/year = 1.0%/year + 0% per year

1.0%/year. Isn't that something close to a permanent recession? Keep in mind that 1.0%/year is an average value for the world, and that there will be competition among countries for this global constraint. Developed economies tend to grow more slowly than average, so this doesn't sound particularly rosy for those of us who live there. Really, I'm in no position to say what such an anemic growth rate actually looks like on the global economic stage, but it would seem to be well below what most economists would consider desirable. The last time growth stagnated like this over a long period of time was the 1930s. We know what followed.

And meanwhile, even at 1% per year energy consumption growth, we would still consume enough energy to bring about roughly a doubling of pre-industrial CO2 concentrations in the atmosphere, sufficient to blow well beyond the 2 degrees Celsius cap proposed by the Paris Climate Accords.

It seems we can't win!

The EIA forecasts environmental doom?

The United States Energy Information Administration provides projections for how much energy the world can be expected to use over the next few decades. Predicting the future is hard, but I think one has to give them credit for trying. The low, medium, and high economic growth projections shown above are largely just extrapolations of existing trends. Even if there is a curious inflection point around 2030, assuming persistence in trends is not a bad way of going for something as highly aggregated as the global economy.

The simulations use an everything but the kitchen sink philosophy for approaching the problem, representing to the greatest extent possible the myriad forces that drive energy consumption, such as political agreements and national and sectoral competition for a range of energy sources. Just the US macroeconomic module alone has well over one thousand equations.

But, as always, there's more than one way to skin a cat. For my part, I have developed a model for global energy consumption that is almost absurdly simple. It has only a few equations. Nonetheless it manages to produce accurate hindcasts for energy consumption and GDP growth rates with skill scores >90% for a 50 year period between 1960 and 2010 using only conditions in the 1950s to initialize the model.

The key ingredients of the model are only that global energy consumption and wealth can be linked through a constant; that inflation-adjusted global GDP grows global wealth; that the coefficient relating wealth to GDP is a function of past innovation; and, that innovation can be related through thermodynamics to resource availability and rates of decay.

Claiming that civilization can be reduced so simply is admittedly a bit unorthodox. What the model does have going for it is that each of these things is testable and based on physical reasoning.

Of course, the tremendous trade-off with this more holistic view is it offers little to nothing about the details, like how national consumption will change over the coming decades. Understandably, some think it's important to distinguish the U.S. from the rest of the world.

Still, we do still talk about the global economy. And, for an atmospheric scientist trying to link economic growth to climate change, it doesn't matter whether a molecule of carbon dioxide comes from Timbuktu or Trump Tower since CO2 is a long-lived well-mixed gas.

But let's assume that those thousands of equations the EIA uses does get things plausibly right, at least in the big picture. On average, EIA projections see the global demand for energy growing by about 50% over the next 40 years, 0.9% per year on the low end and 1.4% per year on the high end.

Using the aforementioned constant, what is being referred to by others as the Garrett Relation, a trivial prediction of the model I mentioned is that inflation-adjusted global Wealth will also grow by 50% over the same time period.

Some of us might feel a bit disappointed by a real growth rate for our collective assets of just 1% per year, but effectively this is what the EIA projections imply.

I am a bit skeptical they are correct partly because the physically-based economic model also forecasts that there is substantial inertia to existing trends. Between 2000 and 2010, the average growth rate for global energy consumption and real wealth was about 2% per year (although GDP grew faster, closer to 3% per year). A sudden revision downward in growth to 1% would require something fairly dramatic in terms of a reduction to resource availability. If we were to assume for the sake of argument a continuation of the 2% growth rate instead of the EIA's 1%, that would mean that global Wealth would increase by 60% in 40 years.

But whether the increase is 50%, as implied by the EIA, or 60%, as implied by persistence in trends, the future still looks good. Right?

Well, maybe not, at least not for the environment. Even maintaining 1% per year growth will require something that might seem pretty extraordinary: over the course of the next 40 years we will consume as much energy total as the total we consumed in the past 100 years. At 2% growth, that number is more like 140 years.

Energy does stuff. In thermodynamics we call it Work. A lot of stuff has happened in the past century. Consuming the same amount of energy in 40 Years will mean, very roughly, we will do the same amount of Work all over again.

A more advanced concept in thermodynamics is that there is a coupling of energy dissipation with material flows. What this means is that energy is consumed not just to sustain civilization's internal circulations, but to take raw materials from the environment like fish, minerals, and wood. These are used to repair and grow civilization (including by making more of us as people) while leaving behind a big pile of garbage in solid, liquid, and gaseous forms.

We've certainly packed on the pounds over the past century, largely at the sacrifice of the critters and plants on land and the fish in the oceans, while leaving behind an added 100 ppm to the atmospheric concentration of CO2.

What will the world look like when we manage to do the same all over again?

What's in a name?

Professor Richard Nolthenius of Cabrillo College has been referring to the constant relationship between power and wealth in talks and podcasts as the Garrett Relation, or GR for short. Of course, its a bit embarrassing to have one's own name attached to a phenomenon. In my view, the really interesting thing about any phenomenon is what it tells us, and not the much more incidental matter of whomever happened to stumble upon it first. But as Richard has pointed out, it needs a name. Is there better wording? The Power Theory of Value (PTV) Relation seems a bit dry but workable. Or is the Garrett Relation as good as any?

A Power Theory of Value?

Economic wealth or capital is not a static quantity that simply exists. Rather it requires continual energy consumption for its sustenance. Civilization is like a living organism, or as Nate Hagens puts it, a super-organism. Energy is required not just to grow civilization but also to maintain its current size.

Sure, civilization is complicated. Valuing any given component of civilization is something all of us try really hard to do with varying degrees of success (myself, I'm a terrible investor). But, as philosophers have recognized for hundreds of years, all components of civilization, whether human or physical, have no innate value in and of themselves; value can only be acquired through connections and the judgement of others, nothing intrinsic to the item or person in question.

As John Donne put it: "No man is an island, Entire of itself. Each is a piece of the continent, A part of the main...” An ounce of gold has no intrinsic worth, but only acquires value by acting as a useful part of society, through banking system networks maintained by the accumulated knowledge capital of bankers, all of which require primary energy to be sustained, either by feeding the bankers or by powering electronic transactions. An ounce of gold left abandoned and forgotten in the middle of the desert is worthless until it is found.

Looking at civilization as a whole we might surmise that, like a living organism, the internal transportation, communication, and human physiological networks that define what we think of as humanity require a continual consumption of energy. Otherwise they wither and die, becoming totally valueless. We're not much use at work if we stop eating. A road never traveled serves little purpose. We can hypothesize that economic value and energy consumption are linked.

This suggests a "Power Theory of Value", that energy consumption and economic wealth are tied by a constant. Importantly, this is a falsifiable hypothesis. And, as shown above, it seems to be borne out by the data. Summing wealth over all the world’s nations, 7.1 Watts is required to maintain every one thousand inflation-adjusted 2005 dollars of historically accumulated economic production.

A lot of people get confused about this relationship though: to be clear, it is not about energy and yearly economic output or GDP. Plenty of people find a correlation there, but the ratio between the two has been increasing with time. The intercept is not zero.

Nor does the relationship refer to the more restrictive view of wealth as physical capital that can be found in traditional economic models. Instead, the constant relates current energy consumption to the summation of production, not just over one year -- the quantity called GDP -- but over all of time, what I refer to as Global Wealth.

Adjusting for inflation is key, in these calculations. Then, as shown in the figure above, this highly aggregated Wealth has a fixed relationship to current energy consumption, independent of the year that is considered. As of 2010, civilization was powered by about 17 trillion Watts of power. This energy consumption supported about 2352 trillion dollars of collective global wealth. In 1970,  civilization was younger and smaller. Both quantities were less than half as large (in fact, GDP was less than a third current values). In the interim, energy consumption and wealth grew in tandem, even at variable rates that increased slowly from 1.4% per year to 2.2% per year. At all times, the constant of proportionality stayed effectively the same, with a standard deviation of only 3%.

If one really wants to relate energy to GDP, then from the perspective above, the correct relationship is to consider year-to-year changes, that is the relationship between global GDP and the annual increase in global power capacity. Then, on average, adding every extra exajoule of global consumption capacity in a year enables 89 billion of year 2005 trillion USD of GDP. Variability is higher, but nonetheless the relationship is more or less fixed.

Why does this matter? Constants of proportionality are what provide a foundation for linking what initially seem to be two independent quantities (e.g. energy and frequency in quantum mechanics or energy and rest mass in relativity). Constants form the basis for all that follows. All other physical results are just math.

The constant of proportionality λ that relates civilization’s economic wealth to its rate of energy consumption has the potential to tell us not just where we are today but to dramatically simplify and constrain long-term estimates of where the global economy is headed. The constant ties economics to physics, so with physics, more robust economic forecasts become possible.

About this blog

I am a professor at the University of Utah interested in the interplay between economics, energy, and climate. Most of my funded research focuses on the complex interplay between aerosols, clouds, precipitation, radiation and climate, another complex problem. My interest in economic questions grew from a ordinary inquiry into possible solutions for some of the most pressing issues of our time. I am fairly naive about economics as a field, yet it has always seemed inescapable that human activities must be governed by the same universal thermodynamic laws as the rest of the climate system. 

In 2006, I started to put together a little model for the physics governing the growth of the global economy and its carbon emissions. The basis of the model was a hypothesis that global rates of energy consumption should be tied through a constant value to the accumulation throughout history of a very general representation of global wealth. It was an exciting time to find out that this does indeed turn out be supported by the data. This constant has a value of 7.1 Watts of primary energy consumption for every one thousand year 2005 dollars of historically accumulated global civilization wealth, independent of the year that is considered.

I expected the result to have been simply "re-discovered" and probably rather standard to the field of Economics. It turned out it wasn't. What I found was that economists approach economic growth and environmental impacts by focusing on the macro and micro-economic parts, using techniques that are mathematically complex but dimensionally inconsistent, full of untestable opinion, and with little to no reference to energy and raw material resource constraints.

This blog takes a different tack by examining physical constraints on the evolution of globally and historically aggregated wealth. The intent is to step back, overlooking internal details of the complexity of the coupled human-climate system, to see their interactions as whole.

Almost all detail is lost from this viewpoint. However, it offers the tremendous advantage of simplifying long-term predictions for where we might be headed by offering the robustness of physics as a guiding tool.  There are some pretty pressing global problems we face this century. It's hard to see how we survive them by pretending we can beat the laws of thermodynamics.