A ban on solar-geoengineering research?

A colleague asked me about whether I would sign on to an effort that would effectively ban most research on solar geoengineering. Here is a lightly edited response.

A few points:

1. The main problem with this letter is that it is an assault on freedom of research that is in-itself benign. 

I don’t see that banning outdoor research on solar geoengineering is different in kind from the Catholic Church banning Galileo from dropping balls off the leaning tower of Pisa.

There should be a presumption that if an experiment is expected to lead to negligible direct harm, that the experiment can go forward unless it would lead to an expectation of imminent harm that could not easily be averted by other means.

2. I am increasing critical about people signing onto policy positions where it is not entirely clear whether the person has special expertise related to the issues contained therein.

If I sign a letter saying Trump should be prosecuted for his crimes, nobody will think that I have special insights into Trump’s crimes or appropriate legal processes.

But if I sign onto a letter like this, a reader might reasonably assume that I have special expertise on policy measures that would lead to international risk reduction. In fact, I have no such expertise.

I try to avoid signing anything that is in this grey zone, where it would not be clear to readers whether I was signing as a domain-area expert or merely as a concerned citizen with no special expertise.

3. As a matter of public policy, a no first use ban may or may not be effective at banning first use. I am not expert in the efficacy of such bans.

We can see how successful various international constraints were at stopping Russia from taking Crimea. Maybe having countries declare that they won’t do bad things helps to prevent bad things from happening, but maybe not. 

Were it clear that I was signing as a citizen, and not as someone with special expertise, I would sign onto a “no first use” ban.

4. As a practical matter, defining what is or is not solar geoengineering research will be very difficult as the definitions are based on establishing intent. 

Bad actors can still go ahead and study stratospheric chemistry, aerosol distribution techniques, effects of changes in diffuse radiation on ecosystems, climate effects of stratospheric aerosol loading, etc. They just need to do this without the intent of producing a system that would geoengineer the planet.

These sorts of bans will stop good actors and force bad actors to be less forthcoming about intent.

I recall with the iron fertilization experiments, many of the scientists could care less about iron fertilization as a climate mitigation tool, but they just saw the experiments as a chance to learn more about how marine ecosystems respond to nutrient additions. I think we can assume there are stratospheric chemists who might feel the same way about stratospheric aerosol release experiments.  

Politicians can fund these programs thinking of solar-geo as the use case with the scientists engaged in the study as pure science.

How are such cases to be adjudicated?  What are the proposed procedures if you do an experiment and I think your intent is really to learn about solar geoengineering? Do I take my charges to some sort of inquisition so that they can determine what is truly in your heart of hearts?


Thought, action and social-system models

I was asked by a journalist to comment on a paper. Here is an edited form of part of my response.

Thought evolved over evolutionary time to mediate between sensory perception and muscular action. Models are tools for thought, and help us to mediate between our perceptions and our actions.

Models are like crutches that allow our thinking to advance where it might otherwise be hobbled.

It would seem that recommendations of what sorts of modeling should be done should start with a discussion of what actions we are considering and what tools might be most helpful for informing decisions related to those actions, and then proceed to a discussion of the feasibility and resources needed to construct a model that could usefully inform decisions.

This question is particularly problematic when it comes to models involving social systems.

Clearly, there is some predictability to social systems: We can reliably predict that if political leaders engage in racially or religiously discriminatory speech that there will be an uptick in racial or religious violence within the society.

On the other hand, our primary goal is to inform decisions, not predict those decisions. We do not necessarily want to predict whether political leaders will engage in racially or religiously discriminatory speech, but rather inform the political leaders of the likely outcomes of their actions.

Further, while there is some predictive skill in predicting that increased prices will have a negative influence on demand, for example, the evidence of predictive skill for what we might call “future history” is limited at best.

There remains a major challenge in thinking through what sorts of models of social systems at global scale can usefully improve understanding and decision making at a cost that is commensurate with the value of generated information.


Consumption value and asset value

Much of my work gets done by way of “productive procrastination”, that is, working on things other than what I “should” be working on. This in an example.

There have been differences of opinion about how best to address the question of temporal discounting, especially with respect to intergenerational equity and the climate problem. In its simplest form, this question is often framed:

How should we be valuing the future?

Lately, I have been taking a different tack on addressing this question, asking :

Why do we value the future as much as we do, and not more and not less?

One way of thinking about the discounting question is to ask: What is the relative value of consuming a thing versus owning a thing? How do we compare the consumption value of a thing versus asset value of a thing?

I have been working on a simple mathematical model to explore these issues, as a kind of “fiction science” – a make-believe world that I hope shares properties with the real world, to function as a mathematical metaphor.

From working with this model, I have convinced myself that we value the future as we do because organisms that valued the future (or at least, valued having an asset more than they valued consuming it) increased their evolutionary fitness.

The squirrel that buried the acorn was more likely to survive and successfully reproduce than the squirrel that didn’t bury the acorn.

The psychology of valuing the future is a product of an evolutionary process that tends to increase reproductive success and evolutionary fitness.

Paul Cezanne, Bridge across the Marne at Creteil, 1894

In an earlier version of my model, the agents hoarded assets until they had sufficient assets to achieve reproductive success. This led me to ask a question that I had never thought of before:

Why do we value current consumption as much as we do, and not more and not less?

If we are comparing consumption value versus asset value of a thing, we need to ask not only why we value the asset as much as we do, but also why we value consumption as much as we do.

And I think the understanding of consumption value largely parallels the understanding of asset value. We value consumption because consumption increases our evolutionary fitness.

If that squirrel did not eat acorns today, the squirrel will die and fail to reproduce. Note that the squirrel doesn’t die right now if it does not eat the acorn right now. Eating the acorn right now is another form of investing in the future.

Camille Pissarro, Autumn morning at Eragny, 1897

Consumption value and asset value are two forms of investing in the future, and the balance between consumption value and asset value is the balance that tends to increase reproductive success and evolutionary fitness.

Humans are not squirrels. I doubt squirrels explicitly think very far into the future.

Evolution gives us psychological properties that manifest in unpredictable ways. Evolution, for example, did not select for the ability to play chess, but the ability to play chess is nevertheless a product of our evolutionary past.

One of the properties of human psychology is, when given the opportunity, we tend to consume far in excess of what might be thought to be optimal for maximizing fitness.

Diseases related to obesity and over-eating are rampant in wealthy societies.

Further, people who have enough money, often consume expensive clothing, automobiles, live in large and expensive homes, and so on. They display their consumptive behavior.

What is the explanation for the human tendency to want to consume far in excess of what might be thought sufficient to maximize fitness?

One possible contributing factor is that humans evolved in a resource limited environment, so that we evolved to consume as much as we possibly could, because in most of our evolutionary history, consuming as much as you possibly could directly maximized fitness.

However, one might also imagine that earlier in our past, consuming beyond what was needed to sustain life signaled to potential mates that a potential partner would have the resources to feed and care for offspring – and thus increase reproductive success.

Our drive to consume beyond what is needed to sustain our lives may be in part a consequence of a psychology that improved our evolutionary fitness by signaling our desirability as mates.

Observations indicate that financially successful people tend to be more sought after as mates than people who are living at a subsistence level.

The potential mate that is able to give valuable gifts is likely to be the potential mate that can provide for offspring, increasing reproductive success and evolutionary fitness.

People’s happiness tends to be associated with their amount of consumption relative to their peers, and less so to absolute levels of consumption. This is consistent with the drive to consume being closely tied to social signaling functions that increase evolutionary fitness.

Our drive to excessive consumption might be a bit like the peacock’s tail – something that, absent the signaling value, would decrease our evolutionary fitness; something that is maintained through sexual selection.

One might imagine that, in evolutionary equilibrium in a simple system with perfect information, the marginal benefit to fitness from consumption would equal the marginal benefit to fitness from savings. This, I think, is the conceptual underpinning of determination of the optimal savings rate from the perspective of evolutionary fitness.

Paul Baum, Willows on the brook, 1900

Of course, we are not slaves to evolution.

We have a neo-cortex that not only allows us to play chess, but also allows us to be thoughtful about how we might increase our evolutionary fitness.

If our drive to excessive consumption is damaging the planet, we can use reason to develop ways to meet our psychological needs while lessening this damage. (An alternative is to deny our psychological desires, but this seems to be a much more difficult path both psychologically and politically.)

Paul Signac, The port at sunset (opus 236, Saint Tropez)

The increase in value from the service sector relative to the manufacturing sector (for example, the value we get from books, movies, music, and so on) points to ways that we can satisfy desires to consume with relatively little impact in the material world.

Rather than asking people to consume less, we can work on dematerialization of value generation. This can be done by expanding the service sector, for example by increasing the value of information and social relationships.

The internet is be a major step forward in human history. We are interacting with each other, often in real time, without the need for transportation. We are consuming music and videos and video games that can be replicated at very low marginal cost.

We may be entering a new era of increasingly dematerialized consumption may allow us to reconcile our evolutionary past with a future that places fewer material demands on our environment.

I thank Harry Saunders and Juan Moreno Cruz for contributing to some of the ideas expressed here.


Aphorisms and over-simplifications


Twitter is interesting because if forces you to try to say things in 280 characters. This tends to lead one to speak in Yoda-like aphorisms or make gross over-simplifications. (And on Twitter, there is no shortage of people to remind you of the myriad ways in which you are over simplifying.)

Also, for those insufficiently disciplined to compose offline and tweet only carefully edited tweets, Twitter is all about rough first drafts, preserved forever, warts and all.

Twitter is odd because it is both ephemeral and eternal — ephemeral in the sense that thoughtful tweets tend to get lost in the sands of time; eternal in the sense that some thoughtless boneheaded comment is there to pursue you for the rest of your life.

That all said, this blog post, which I expect to evolve over time, will be my place to dust the sand off of some old tweets so that they might live on a bit longer.

By the way, my “not-so-professional” Twitter account is @KenCaldeira.

(I meant to write “After decades of R&D and subsidies …”.) https://twitter.com/KenCaldeira/status/1471511631892914189

(above should have read “CO2 (and N2O somewhat)” https://twitter.com/KenCaldeira/status/1453832941419876355

On prescriptive and normative statements in academic research papers

Andrey Lyssenko, pensive artist

A postdoc asked a question about being prescriptive and/or normative in academic papers, noting that some of the people with the most successful scientific careers were scientist/activists who did not shy away from saying in their technical work what we should do or what is good and what is bad.

My response:

It is fine to say “I think we should do XYZ” or “XYZ is good [or bad]” in an opinion piece in academic or informal settings.

But is it OK to make those kinds of statements in regular academic research papers?

A starting point is that there are multiple paths and strategies to success and you have to do something that fits your personal style and also takes account the reality of the job market.

I was trained on Hume’s distinction between empirical and prescriptive/normative statements.

My feeling has always been that we as scientists are trained to generate and disseminate information and our opining on public issues was just our hobby, not our profession.

That said, I am not above language of the sort: “Policy makers should consider doing XYZ” rather than coming right out and saying “Do XYZ”. 

This may seem rhetorical artifice, but there is implicit acknowledgement in that construct that I may be wrong in my recommendation when a broader range of facts is considered.

I am probably near one end of the spectrum of wanting to keep recommendations to a minimum in academic papers (research suggestions, factors for policy consideration).

Others say that the distinction between opinion/informal pieces and scientific/technical reports is artificial and all that is required is transparency.

What should we do? Good or bad?

When something is written in an academic paper, it should be true and you should stand behind it for all time.

Usually the errors are not in what you did, but errors in interpreting the implications of what you did. Often the error is believing your result applies more generally than it does.

When I look back since graduate school, my policy prescriptions have evolved, but I stand by all of the basic findings I have published over the years.

Enough responsibility to go around


To attribute damage to climate change, in principle we would like to fully understand the state of the system with climate change and then subtract out a counterfactual without climate change.

If we wanted to estimate the impact of current climate change on flood damage we could seek to understand current flood damage and then subtract off our best estimate of what would have happened in the absence of climate change.

Obviously, the stochastic nature of weather makes attribution challenging, but here I am after another conceptual issue.

We could have said, “The flood damage would not have been so bad had we not built valuable infrastructure in harm’s way.”

How could we attribute damage to building in harm’s way?

We could adopt a procedure that is similar to climate attribution: We could ascertain the observed damage under current conditions and subtract off what the damages would have been had we not built in harm’s way.

If we assume that damage would occur if and only if there were both climate change and a history of building in harm’s way, then this procedure would attribute the full cost of the damage to each of climate change and building in harm’s way.

The damage would not have occurred had we not changed climate and the damage would not have occurred had we not built in harm’s way.

Is there a truth to the matter in this case what fraction of the flood damage should be attributed to climate change and what fraction to building in harm’s way?

“Responsibility” is a social construct. Bad outcomes are often the consequence of a confluence of a series of unfortunate events, and there is no unique way of partitioning responsibility across the range of events that are jointly sufficient to produce the bad outcome.

We can agree on the empirical facts but disagree on how much responsibility for damage should (or should not) be attributed to climate change.


As a practical matter, as a climate modeler, if I wanted to estimate climate damage I would subtract results from a simulation without climate change from results of a simulation with climate damage, and I would attribute that full difference to climate change.

Also as a practical matter, if I were a coastal hazards investigator and I wanted to estimate the damage caused by inappropriate coastal development, I might compare cases with the same weather but with and without coastal development, and attribute the full difference to coastal development.

If a large number of studies examined damage with and without various factors (e.g., damage from failure to build adequate flood control systems), the sum of all of the attributed amounts could greatly exceed total damage.

There is value in these “all other things equal” studies, but in the real world other things are seldom equal.

Income Inequality and climate damage: Relative impact on utility


Dog deriving utility by watching a dog on television.

Nordhaus’s DICE model represents utility as population times per capita utility, and it represents per capita utility as increasing with per-capita consumption to the 0.45 power.


A lot of attention has been paid to the issue of temporal discounting in quantifying current value of future costs and benefits. That is, a lot of attention has been paid to assessing how we should value future generations relative to our own, but relatively less attention has been paid to addressing how we should value others living today relative to ourselves.

To address this issue, I thought I would look at the increase in total utility that would be predicted by the DICE utility functions under an assumption of income equality and compare that with the change in utility expected to come from addressing the climate change problem.

That is, what would the predicted change in utility be if everyone were brought to the mean income. (Before people start complaining, I too have read Kahneman and Ariely and understand that real utility is far more complicated than represented in the DICE model.)


Another view of this data is:


Unfortunately, I did not find a location to download this data easily. (I’ll fix up this blog post when I find it.) Therefore, I will just do a very rough-and ready analysis. Since they give us the median and the mean, let’s just assume this is a log-normal distribution with that median and mean.

Luckily, trusty Wikipedia gives us the appropriate formulas for the median and mean of a lognormal distribution:


For a mean income of $5375/year and a median income of $2010/year, this yields mu = 7.6 and sigma = 1.4. (We will forgo pretense to greater accuracy.) Density of people making X $/yr can be estimated by plugging in these numbers into the lognormal function above.

If we now assume that utility goes with income to the 0.45 power, we can calculate that global utility is 78% of what it would be were income distributed evenly. That is, this analysis suggests we are taking a 22% hit on global utility due to income inequality.

This 22% reduction in global utility is of the same order of magnitude as some of the more high-end climate damage estimates and an order of magnitude larger than many climate damage estimates.

This suggests that if we are interested in human welfare, addressing income inequality may be as important as addressing climate challenges.

I know this is just a back-of-envelope calculation and human psychology is a lot more complicated than income raised to the 0.45 power and climate damage is a lot more complicated than temperature squared. No doubt there are complicated relationships between income distributions, capital accumulation, and economic growth. Nevertheless, this analysis suggests that income inequality may be regarded as a challenge to human welfare that is on a scale comparable to that of the climate problem.

Lastly, I would just like to point out that there are two ways of decreasing income inequality: increasing incomes at the lower end of the spectrum and decreasing incomes at the upper end of the spectrum. While some of both strategies may prove useful, it is only by increasing incomes at the lower end of the spectrum that we can increase aggregate utility without decreasing anyone’s individual utility. Thus, while income redistribution may have important roles to play, this suggests that economic development will be the leading player in increasing global aggregate utility.



I am a geoscientist who thinks about energy systems and climate policy, and while I have some general knowledge of energy systems, I do not claim any policy expertise, so this is just me thinking out loud and in public …

WARNING: This blog post is more prescriptive than most things I write.


There are many people who put a lot of faith in the operation of markets who like to see governments do as little as possible.

Often, these people are OK with government action if someone can demonstrate that there is a market failure that government can address.

For the climate challenge, the most well-known market failure is the failure of markets to reflect future costs of climate damage in current prices. Where there is no price signal from future climate damage, markets continue to operate as if the operation of markets will not cause any climate damage — and this is driving us to dangerous climate change.

Economists often conclude that the most efficient way to represent this “unpriced externality” — an external cost that is not represented in market prices — is to have a carbon tax (or fee, if you prefer). A problem with this approach is that taxes are politically unpopular. A basket of policy approaches have been tried instead: carbon-trading markets, subsidies, regulations, etc.

These policies that drive technology deployment are addressing the “cost pricing failure” — the failure to represent costs of future climate damage.

“Unpriced future climate damage” is a market failure that is impeding deployment of clean energy technologies, but there is another market failure that is impeding development and improvement of energy technologies.

Horseshoe crab

Think of all the benefits of technology that we have today. Right now, you are using a computer and staring at a monitor screen. You have a cell phone. You’ve ridden in cars and flown in airplanes.

When these technologies were developed, some proprietary knowledge was generated and patented and this is a mechanism by which investors got rewarded for investing in innovation.

However, such innovative efforts also produced a lot of knowledge of a sort that is not patentable and where the benefits were not privatizable.

People watch each other.

When people see someone try to do something and fail, that gives people ideas on what they could do differently to succeed.

When people see someone try to do something and succeed, that gives people ideas on what they could do even better to out-compete them in the market.

Look around yourself right now: Can you find a single product in your field of view that was not informed by non-privatizable knowledge generated by private investment?

One of the things in my field of view is my DSLR camera.

This is a Canon camera, but the camera looks very similar to a Nikon or a number of other brands. Camera makers have converged on similar designs because there is non-privatizable knowledge about what works, what can be manufactured cost effectively and what can be sold into a market at what price.

Billboard in Wyoming, 2010

Economies and societies benefit from the non-privatizable benefits of private investment.

In most areas, we just accept that investment will be motivated only by privatizable benefits of an investment, and the entirety of non-privatizable benefits will go to other individuals or society-at-large. But the urgency and scale of the climate challenges warrant addressing this market failure specifically in climate tech innovation.

We can accelerate development and deployment of energy technologies that can help us attain net-zero emissions as soon as is practicable.

It is of course important to publicly fund the basic research that is the seed corn for long-term economic growth. But it takes risk-accepting investors to provide resources to develop the best ideas of scientists and engineers to the point where there is a product that can compete in the marketplace.

If the main reason we want private investors to invest in clean energy technologies is to benefit society, wouldn’t it make sense for society to provide incentives to generate that societal benefit?

The failure to adequately incentivize people to rapidly generate shared knowledge about better energy systems is a “benefit pricing failure” — a failure to provide a price signal to investors that reflects non-privatizable benefits of energy innovation.

Nearly everyone will benefit from cheaper clean energy technologies, especially-when those technologies can be nearly as cheap or cheaper than their CO2-emitting alternatives .

Ochopee, FL

In addressing climate challenges, one important market failure is the failure of markets to price social costs of future climate damage. Another important market failure is the failure of markets to price the social benefits of future cheaper clean energy technologies.

Policies that address the failure to price widely-shared benefits of energy innovation can be complement policies that address the failure to price widely-shared costs of climate damage. These policies address different market failures but are aimed at achieving the same goal.

And these two sorts of policies are complementary. Whatever the policy is that is aimed at driving deployment, having cheaper technologies will make that deployment-driving policy even more effective. With cheaper technologies, more clean energy technologies can get deployed faster and at lower cost — enabling earlier and deeper reductions in emissions.

We are not in an “either/or world”. The climate challenge is daunting enough that we need to live in an “and/and world”. We need policy drivers that promote deployment of clean energy technologies and we need policy drivers that promote development of better and cheaper technologies that are ready to be deployed.


We do not have to choose between policies that drive deployment of existing technologies and policies that drive development of better technologies.

We can do both and we should do both.

Hydrogen production from curtailed generation


There has been a lot of talk about making electrolytic “Green Hydrogen” using electricity from wind and solar power that would otherwise be curtailed. Less climatically helpful, there is also potential to use electricity from natural gas generators that would otherwise be idled.

Tyler Ruggles set out to answer the questions:

1. How much additional flexible load could we put on electricity systems before we would need to add more generating capacity?
2. In an economically efficient system, how would the fixed generation costs be allocated across fixed and flexible loads?

This study was published in Advances in Applied Energy under the title, “Opportunities for flexible electricity loads such as hydrogen production from curtailed generation”.

Tyler H. Ruggles, Jacqueline A. Dowling, Nathan S. Lewis, Ken Caldeira, Opportunities for flexible electricity loads such as hydrogen production from curtailed generation, Advances in Applied Energy 3, 100051, 2021.

The system considered by Tyler is represented by the following figure:

The system considers several generators, a fixed (i.e. specified and unchangeable) electricity load, and a flexible electricity load, here represented as electrolytic production of hydrogen gas. The dispatchable generator can be thought of as something akin to natural gas, but is left unspecified.

The basic results are summarized in this figure:

The last column (Renew+Storage) is perhaps the most relevant to ongoing discussions of “Green Hydrogen”. In this case, all electricity is produced with wind and solar power. Because of the high cost of storage, with low amounts of flexible load, it is economically efficient to build extra wind and solar generation and then discard some of this potential generation much of the time (curtailment).

However, if we have a lot of excess wind and solar capacity, that means there should be times when there is some excess generation capacity that is going unused. Tyler showed that, with a system sized to meet peak demands, there is some underutilized capacity nearly all the time. Because this underutilized wind and solar capacity has effectively zero variable cost, this excess electricity generation can be offered for free.

Because systems are sized to meet peak demand and there is almost always some underutilized generating capacity, a small amount of flexible load can be added to the system at effectively zero electricity cost and operate at high capacity factors.

The problem is, as additional flexible load is added, there is less and less unclaimed free electricity to go around, and so additional flexible loads need to operate at lower capacity factor, or additional generating capacity would need to be added to the system.

Both of these things cost money.

As can be seen from the above figure, flexible loads can be added to the system with effectively zero additional generating capacity to the point where the flexible load is about 20% of total load.

In other words, if a system is built to satisfy firm loads, it is likely that an additional 25% of that fixed load can be used to satisfy flexible loads with out any additional capacity expansion.

Between about 0.2 and 0.8 (20% and 80% of total load) in the above figures, there is a transition zone, where adding more flexible load would motivate building additional generating capacity, and so the flexible load would need to contribute to this capacity expansion.

When the flexible load is already representing over 80% of the total load, additional flexible load basically requires 1-for-1 expansion of generating capacity and so the flexible load bears the full cost of capacity expansion.

The figure above illustrates this transition. Below a flexible fraction of total load equal to 0.30 in this example, the flexible load draws primarily on capacity that was built to help meet peak electricity demands. Thus the flexible load can largely be a free rider.

But at a flexible fraction of total load equal to 0.40, additional capacity must be added to meet this flexible load. In this case, the flexible load would need to pay for that capacity expansion.

Tyler created this graphical abstract in an attempt to summarize the findings of this study.

As an aside, Tyler has training as a high energy physicist and was working at CERN when I hired him as a postdoctoral research scientist in our group. His most highly cited paper is about Higgs bosons.

My experience is that the most valuable qualities in a scientist include things like creativity, intelligence, work ethic, ability to complete projects, ability to work well with others, writing skills, math skills, etc. These are qualities that Tyler has in abundance.

Our goal is to do simple analyses to highlight fundamental principles. Smart people can learn domain knowledge quickly. This is the kind of analysis for which physicists are well suited.

This study has come to conclusions that are likely to stand the test of time:

  1. In systems designed to meet variable fixed loads, there is almost always some excess generating capacity and so almost always some electricity available to power flexible loads at the variable cost of the generator.
  2. As this excess capacity is increasing utilized, typically when flexible loads exceed 20% of total demand, additional flexible loads will require some additional generating capacity, and in an economically efficient system this cost will be shared between fixed and flexible loads.
  3. When flexible loads exceed about 80% of total demand, nearly every increase in flexible load requires a corresponding increase in generating capacity and so the flexible load would bear the full cost of this capacity expansion.

Replenishing the wind


People sometimes presume that when scientists set out to test a hypothesis, they are engaged in motivated reasoning and want to show that the hypothesis is correct.

While there might be some merit in that presumption, it is also the case that there are few things more pleasurable to the working scientist than being presented with evidence that your beliefs are false.

Working with Enrico Antonini, I recently had just such a pleasurable experience.

Like many other energy system researchers, I thought kinetic energy removed by wind turbines in large wind farms was replenished primarily by downward transport of kinetic energy from the overlying free troposphere.

For the first row of wind turbines, most of the kinetic energy transport is horizontal with the winds. However, each wind turbine can remove more than half the kinetic energy that passes through the disk swept by its rotors. The wind does not have to pass through many wind turbines before horizontal transport of kinetic energy is largely depleted. A source of kinetic energy is therefore needed to explain why wind turbines can still generate energy even when they are not in the first several rows of wind turbines.

Many energy researchers, including me, thought the wind energy was maintained by downward transport of kinetic energy from the overlying free troposphere. For example, in a 2017 paper published in PNAS, with Anna Possner as lead author, we wrote:

However, it remains unclear whether these open ocean wind speeds are higher because of lack of surface drag or whether a greater downward transport of kinetic energy may be sustained in open ocean environments.”

I believe many people held this view. For example, a paper was published in Geoscientific Model Development with a nice illustration of this mental model, showing a downward flux of kinetic energy


Enrico Antonini did some nice work in a paper published in PNAS this week that expands on a paper published in Applied Energy earlier this year. The Applied Energy paper showed how maximum power densities in regional scale wind farms are limited to a few watts per square meter, and are related to the Coriolis parameter times the pressure gradient.

In these papers, Enrico provides compelling evidence that the kinetic energy removed by wind turbines is replenished primarily by acceleration of air masses within the boundary layer by large-scale pressure forces (which are no longer balanced by apparent Coriolis forces due to the slowing of winds caused by the wind turbines).

Below is a schematic diagram of how things seem to work. Normally, large-scale pressure forces are balanced by apparent Coriolis forces resulting in what is known as “geostrophic flow”. However, as wind turbines remove kinetic energy from the winds, the apparent Coriolis forces weaken, and the unbalanced pressure gradient forces accelerate the air within the boundary layer.

Very little of the replenishment of wind energy is associated with downward transport of kinetic energy from the overlying free troposphere. The dichotomy we presented in our 2017 paper was a false dichotomy. Open ocean wind speeds are higher, but not primarily because there is less drag and not because there is substantially more downward transport of kinetic energy. The explanation for higher wind speeds over the ocean has to do with higher horizontal pressure gradients.

In the supporting material to the 2017 paper, Anna and I showed how wind power potential was closely related to heat fluxes at the planetary surface (blue are ocean areas, green is land; top to bottom is northern latitudes, tropics, and southern latitudes).

We presented this result without firm theoretical foundation. But now it seems that wind speeds over the ocean are high largely because ocean heat fluxes are high, and they can produce large temperature gradients, and these large temperature gradients can produce large pressure gradients, and large pressure gradients can drive strong winds.

Additionally, the theoretical understanding that Enrico developed predicts a length scale for recovery of winds downstream from a regional-scale wind farm. This length scale is the product of a time scale related to the Coriolis parameter times the geostrophic wind speed. The theoretical prediction of a length scale of several tens of kilometers is nicely supported by a recent study of wind speeds near large wind farms in the North Sea that which found a similar length scale in detailed simulations.

It is a real pleasure to be able to work with nice, smart, and productive people like Enrico Antonini. It is a privilege to be able to hire a bright early-career scientist who can show me my beliefs were wrong. And it is really nice to be working in a community where there is no great stigma to being wrong, if you are willing to adjust your beliefs in the light of new evidence.

On a final note, Enrico is on the job market. For his Master’s work, he worked at the scale of the turbine blade. For his PhD work, he worked at the scale of optimizing wind turbine positions within a wind farm. For the first part of his postdoc work, he worked at the transition between wind farm scale and what we might call the mesoscale. Now, he is engaged with a study on placement of wind farms in the context of continental-scale optimization.

Very few postdocs develop a fundamental theoretical understanding that makes testable predictions and has real world implications for energy system transition. (Enrico’s understanding can help people make a quick estimate of how closely wind farms can be spaced without them interfering with each other too much.)

If your department is would benefit from hiring somebody who understands scale-transition issues related with wind power development, you need look no further than Enrico.

Environmental science of climate, carbon, and energy