Learning curves and clean-energy R&D: Follow the curve or try to leap?

For most energy technologies, cost decreases with as the cumulative amount of deployment increases. Often, the cost is seen to decrease approximately the same amount with each doubling of the amount deployed. Straight line curve fits to cost data are commonly known as ‘learning curves’ and look like this:

1-s2.0-S0301421517303130-gr1Fig. 1. (from Shayegh et al., 2017) Learning curves for clean and conventional energy technologies. The horizontal axis represents cumulative quantity of electricity generation and the vertical axis represents the unit cost of electricity generation. Both scales are logarithmic. Learning rates (R) are shown in parentheses. Q0 indicates starting quantity and C0 is starting cost. With this axis scaling, straight lines represent power laws (Eq. (1)). We use data from this figure for subsequent analysis of the impact of different types of R&D (EIA, 2015, Wene, 2000 ; Rubin et al., 2015).

The idea is that as more of a technology gets deployed, people learn how to make the technology more cheaply, although economies of scale and other factors also play roles in bringing down costs.

I had the good fortune to be in a discussion with venture capitalists who were investing in companies doing research and development (R&D) on energy technologies. They mentioned that they didn’t want their R&D investment to just push them down the learning curve — they didn’t want to just learn things that they would have learned as production scaled up.

They said they want to shift the learning curve downward. They wanted to invest in innovations that would decrease cost as a result of innovations that would not come about simply by scaling up manufacture. (For example, maybe by shifting solar photovoltaic cells to a new kind of substrate.) This raises the question: If an R&D investment could reduce cost by the same amount by shifting the cost-starting-point of the learning curve downward (“curve-shifting R&D”) instead of effectively following the learning curve to that cost (“curve-following R&D”), which one would be better and how much better would it be?

To address this question, I got the help of Soheil Shayegh, a specialist in optimization and other mathematical and technical arts, and talked him into leading this project.

The “learning subsidy” is the total amount subsidy that would be needed to make a new more-expensive technology competitive with an incumbent technology. The needed subsidy to make a more expensive technology competitive in the marketplace starts out high but decreases as learning brings down the costs of the new technology (Fig 2a).

Figure 1 above shows cumulative quantity on the horizontal axis on a logarithmic scale, but such a figure can be redrawn with a linear axis, which turns the straight lines into curves. Figure 2 shows such curves for an idealized case:


Fig. 2. (from Shayegh et al., 2017) Illustration of two stylized types of R&D for solar PV, a clean energy technology. (a) Learning-by-doing reduces the cost of the clean energy technology as the cumulative quantity of electricity generation increases. (b) Curve-following R&D reduces cost by producing the same knowledge as learning-by-doing, with an effect equivalent to increased cumulative quantity. (c) Curve-shifting R&D reduces cost by producing knowledge that would not have been gained by learning-by-doing, scaling the learning curve downward by a fixed percentage. The learning investment is the total subsidy necessary to reach cost parity with fossil fuels. For the same initial reduction in cost, curve-shifting R&D reduces the learning investment more than curve-following R&D. Note that horizontal and vertical scales are linear. The learning curves would be straight lines if both scales were logarithmic as in Fig. 1.

We found was that cost reductions brought about by breakthrough curve-shifting innovations were much more effective and bringing technologies closer to market competitiveness than were the same cost reductions brought about by incremental curve-following innovations. For example, that cost reductions in wind and bioenergy that come from curve-shifting research are more than 10 times more valuable than cost reductions that come about from curve-following research.

Further, we found in this idealized framework that the relative benefit of breakthrough innovations depended on only two things: (1) the initial cost of the new technology relative to the incumbent technology, and (2) the slope of the learning curve. The more expensive the new technology and the shallower the learning curve, the higher the value of breakthrough curve-shifting R&D.

I am principally a physical scientist, and Soheil Shayagh is principally some sort of mathematically-oriented engineer. To make a successful study, we needed to make some contact with the real world, or at least the academic literature on learning and technological innovation. To this end, we brought Dan Sanchez into the project. Dan thinks a lot about how public policy can help promote innovation and the deployment of new, cleaner energy technologies.

The result of our work was a study titled “Evaluating relative benefits of different types of R&D for clean energy technologies“, published in the journal Energy Policy. (Unfortunately, due to an oversight, our study ended up behind a paywall but you can email me at kcaldeira@carnegiescience.edu to request a copy.)

Our results indicate that, even if steady curve-following research produces results more reliably, when successful, step-wise curve-shifting research produces much greater benefits.

Our simple calculations are highly idealized and schematic and are designed only to illustrate basic principles.

I infer from our study that, other things equal (and other things are never equal), government funded R&D should focus on trying to achieve step-wise curve-shifting breakthroughs.

I suppose my group’s research should also focus on trying to achieve step-wise breakthroughs, but that’s a tough challenge.



Will using a carbon tax for revenue generation create an incentive to continue CO2 emissions?

Most economists think a tax on carbon dioxide emissions is the simplest and most efficient way to get us to stop using the sky for disposal of our waste CO2. This tax could be applied when fossil fuels are extracted from the ground or imported, and credits could be given if someone could show that they permanently buried the waste CO2 underground.

This carbon tax would make fossil fuels more expensive. If the tax level continued to increase, eventually using fossil fuels (without underground CO2 disposal) would become more expensive than every other energy technology, and economics would squeeze carbon dioxide emissions our of our economy.

A tax is an anathema to most politicians. One proposal to make such a tax more palatable would be to distribute the revenue evenly on a per capita basis. Due to inequalities in income distribution, this would result in most people receiving a direct net economic benefit. This could make it politically popular. In terms of net transfer, money would be transferred from the rich and given to the poor and middle classes. Thus, a revenue-neutral carbon tax would both help eliminate carbon dioxide emissions and help reduce economic inequality. Sounds like a good thing. (Why aren’t we doing it?)

Another idea would be to institute a carbon tax to generate tax revenue that could then be used to help provide essential services such as health care, education, income subsidies, and so on. Some of the carbon tax could potentially be used to help pay down the national debt, which in the United States now stands at $165,000 per taxpayer.

Today, we have a carbon tax rate of zero and get no carbon tax revenue. When the carbon tax rate is so high that there are no longer any carbon emissions from our energy system, the carbon tax revenue will again be zero. There is some tax level in-between that would maximize revenue generation from the carbon tax. An increase in tax rate beyond this level would reduce carbon dioxide emissions so much that carbon tax revenues would start to diminish.

Whether the proceeds of the tax are distributed on a per capita basis, or used to provide essential services, people will not be happy to see tax rates rise while direct and immediate benefits from the tax decrease. These tax increases could be a tough sell for politicians. Politicians could be motivated to avoid raising the carbon tax rate, so that they can continue providing the benefits of the revenue generation to their constituents. This would result in continued CO2 emissions.

This issue had been nagging me for over a decade, and I have long tried to interest someone in taking the lead on addressing this question. (Avoiding work is one of my key objectives, so my usual strategy is to try to talk people into doing the work that I am trying to avoid doing myself.) Luckily, I was able to talk Rong Wang into addressing this problem. Because Rong is a physical scientist and not an economist, we were fortunate to be able to lure the economist Juan Moreno-Cruz into helping us.

Together, we produced a study titled “Will the use of a carbon tax for revenue generation produce an incentive to continue carbon emissions?“, and published it in Environmental Research Letters, where it is available for free download.

The key conclusion is represented in this figure:

Wang_fig 1b_170523

Figure 1b. Projected emissions under a set of standard assumptions for three scenarios: Zero carbon tax, welfare-maximizing carbon tax, and revenue-maximizing carbon tax. Under the revenue maximizing assumption, CO2 emissions continue long into the future but at a level that is lower than would occur if there were no carbon tax at all.

Our main conclusions are: For the next decades, the incentive to generate revenue would provide motivation to increase carbon tax rates and thus achieve even lower emissions than would occur at an economically optimal ‘welfare-maximizing’ tax rate. However, by the end of this century, the incentive to generate revenue could result in too low a tax rate — a tax rate that would allow CO2 emissions to persist far into the future.

Overall, I see our result as rather encouraging. Right now, the problem is that we don’t have enough disincentives on carbon emission and politicians are having trouble motivating themselves to provide this disincentive. If revenue generation provides an additional incentive (beyond the incentive of generating climate benefits) to institute a carbon tax, that is all well and good. As mentioned above, these revenues could be distributed on a per capita basis to help combat inequality, or they could be used to provide essential services.

By the end of the century, the incentive to generate revenue could become a perverse incentive to keep carbon taxes low so that CO2 emissions might continue. However, for now, the incentive to generate revenue would motivate increased carbon tax rates, which would cause carbon emissions to decrease.

Given that today’s carbon tax rate is zero, which is clearly too low, the incentive to generate revenue can help motivate politicians to do the right thing for the climate system. That is a good thing.


Climate of Risk and Uncertainty

ClimateFeedback.org contacted me asking what I thought about Bret Stephens’ first column in the New York Times. Here, is a slightly edited version of my response.

Bret Stephens’ opinion piece, titled “Climate of Complete Certainty”, is attacking a straw man. No working scientist claims 100% certainty about anything.

Science is the process of falsification. Hypotheses that have withstood a large number of attempts at falsification, and that are consistent with a large body of established theory that has also resisted falsification, are widely regarded as true (e.g., the Earth is approximately spherical). Many hypotheses of modern climate science fall into this category.

It is also true that some ‘environmentalists’ go far beyond the science in making claims, but that is not cause to denigrate the science.

Bret Stephens writes of ‘sophisticated but fallible models’ as if ‘sophisticated but fallible’ gives one license to ignore their predictions. A wide array of models of different types and levels of complexity predict substantial warming to be a consequence of continued dependence on using the sky as a waste dump for our CO2 pollution. It doesn’t take much scientific knowledge to understand that the end consequence of this process involves approximately 200 feet of sea-level rise. We already see the coral reefs disappearinga predicted consequence of our CO2 emissions. How much more do we need to lose before recognizing that our ‘sophisticated but fallible models’ are the best basis for policy that we have?

Yes, we should take uncertainty into account when developing policy, but we should recognize that those ‘sophisticated but fallible models’ are as likely to underpredict as overpredict the potential consequences of our greenhouse gas emissions.

Stephens would have been on more solid ground if he would have confined his comments to uncertainty in the ability of human systems to adapt to the relatively more certain projections of changes in the physical climate system. Will we be able to give up low-lying countries and the major coastal cities of the world (New York, London, Tokyo) without much of a transition cost? Will people in India and the Sahel be able to migrate or air-condition their way out of the harsh conditions projected for those areas? These are open questions about which well-informed people can disagree.

It is dangerous to act as if uncertainty in climate model projects justifies inaction. Uncertainty equals risk. One way to reduce uncertainty is to increase the amount and quality of climate science being conducted. Another and more important way of reducing uncertainty is to reduce human influence on the climate system. This requires a major transformation of our energy system to one that does not rely on the atmosphere as a waste dump for our CO2 pollution.

Climate science does not offer complete certainty about the future. Instead, it points to substantial risks and ways to avoid that risk.

Straw-man attacks on climate scientists do not productively advance the discussion.

For reference: My first reaction to the announcement of the The New York Times decision to hire Bret Stephens.


Scientific reproducibility, communication of uncertainty, and the US House of Representatives

Bobby Magill of Climate Central sent me an email asking me to comment on several bills recently passed by the US House of Representatives. Specifically, he asked me to comment on bills rescentely
– H.Res.229. … would require EPA actions to be based on science that is “transparent” and “reproducible.”
– HR 1431, …would prevent the EPA Science Advisory Board from communicating uncertainties.
My email comments to Bobby are below: His story is here:

All of the climate science, and related environmental science, that I read in the peer-reviewed literature is in-principle reproducible. The reason it is not in fact reproducible is that the Federal funding agencies rarely provide resources to redo work that someone else has already done.

If our Congressional and Senate representatives really want to see us do science that is reproducible in a practical sense, they should double or triple research budgets so that scientists can afford to do the same thing two or three times.

In practice, once someone has done something to the satisfaction of thee peer-review system and the broader scientific community, people move on to try to make new discoveries.

You can be sure that scientists love nothing more than showing that our colleagues are wrong. If something gets published that smells fishy, that’s when scientists are motivated to redo the study and show that they are wrong. This, for example, famously happened with the cold fusion studies that were published some years ago.

Why would a working scientist with limited funds want to allocate scarce resources to testing something the scientific community already thinks it knows rather than exploring something new? To have enough resources to want to spend it treading over old ground would require a substantial increase in science funding.

Science is all about communicating uncertainty. Science doesn’t prove things. Science works by trying to disprove things. The harder people work to disprove a statement, and the more they fail at disproving it, the more people come to believe the statement is true. Science is about expanding the range of what we know to be false. Truth lies in the range of what we don’t know to be false — that is the uncertainty range.

People who don’t want scientists to communicate the uncertainty range are people who don’t understand what science is all about.

Image from Climate Central story: Credit: C.L.Baker/flickr

Dark ages: Do you know what to do?

A friend and colleague wrote me saying “The US is clearly entering the dark ages in terms of climate, environment, etc. This requires action. … I’m not sure what to do. Do you?”

My response (lightly edited) is below:

A few thoughts:

— It is important to focus on the Congressional and Senate Republicans. It is they who are enabled by and who are enabling Trump. They can get rid of Trump if he becomes too much of a liability. We should not focus on a single man, but on the whole corrupt apparatus behind him.

— We all need to get more politically engaged, and in particular get more people out to vote and vote the right way. If more people had just gone out to vote, Trump would not be President today.

— The Democrats needs to have real plans. In the next 10 to 15 years, 3.5 million Americans who work as drivers may lose jobs to automation. What do the Democrats believe someone in their 50’s should do if they have been a driver all their lives and now lose their job to automation? The Democrats need to come out for guaranteed basic health care, a guaranteed basic job or income, access to free or low-cost high-quality education, etc, etc. They need to stand for things that are meaningful to the average person who is not a policy wonk.

— We need to get better at telling stories with happy endings. People respond to narratives. People have be able to envision a better future. Trying to sell the double negative of the bad that will happen if we don’t do something just isn’t going to work.

We go through our days acting as if we are in normal times, when the times are clearly not normal. The level of corruption and destruction and malevolence and incompetence is mind-boggling.

— We need to be vigilant and aware, and help others be vigilant and aware. Already, things that would have seemed crazy in the past are being considered normal behavior. We cannot act like doing terrible things is normal.

I am shocked at how unprincipled the Republican Party is. I thought they stood for things like free trade, containment of Russian expansionism, etc. It turns out all they stand for is power and wealth. I thought they were children of Adam Smith, when they are really just children of Machiavelli.

Part of the problem the Republicans are having now is that they were all about negativism, about being against things. So, now when they are in power, they cannot get consensus on what positive actions to take.

It will ultimately take responding to the negativism of the Republicans with a positive vision. Focusing on being anti-Trump and anti-Republican is ultimately not a winning strategy. It needs to be there, but we need the yin along with the yang.

IMG_1936-IMG_1940_arty2_1920x1080 (1)Colorized photo I took of the Michelson Building at the Potsdam Institute of Climate Impact Assessment, where I am visiting now.

Where do the winds come from?


Eva Ahbe and I wanted to know where the energy came from to make winds.

This is infeasible to directly observe in the global atmosphere. Therefore, we used a model of the atmosphere to study where the energy comes from to drive winds.

The potential energy available to generate winds is created most strongly high above the tropical western Pacific Ocean where the condensation of water in convective systems heats up already warm air, and also in the high polar night where heat radiates to space, cooling already cold air.

These heat fluxes create density contrasts that tend to make the tropical air rise and the polar air sink, and this is a primary driver of global winds.



2016 is Earth’s hottest year on record: A glimpse behind the Washington Post story

Jason Samenow of the Washington Post wrote to me asking for some comments for a story he was doing on the announcement of year 2016 as the hottest year on record.

Here is what he used:


Reaction: 2016 ‘should tip the balance’ for those unconvinced about human-caused warming

If there are still any people out there who remain unpersuaded by past science and data of climate change, the record high temperatures of 2016 should tip the balance.

With the high temperatures of 2016, the evidence for human-induced global warming is now so strong that no sensible person can deny a human role in these temperature increases.

We can argue about what we should or should not do with this knowledge, but the argument is over: Greenhouse gas emissions cause our climate to get hotter.

Ken Caldeira, climate scientist, Carnegie Institution for Science

Here is the full text of what I provided him:


I don’t have time to say anything long and thoughtful but here it is …


Weather naturally varies over time periods ranging from minutes and hours to days and centuries and longer.  Climate is the statistical properties of this weather. As the saying goes: “Climate is what you expect, weather is what you get.”

Because weather is naturally variable, it is not easy to know whether weird weather is just a product of natural variability, or whether it is a consequence of human interference in the climate system.

Scientists try to estimate the amount of ‘weather noise’ to see whether a climate signal remains in temperature data. I remember when I was a graduate student in the late 1980’s, discussing that the human imprint on the climate system would become statistically significant sometime in the 1990’s. Indeed, in 1995, the Intergovernmental Panel on Climate Change suggested there was a ‘discernible influence human influence on global climate’ and by 2001 they stated that most of the warming of the past 50 years was likely due to the increase in greenhouse gas concentrations.

Then, in the early 2000’s, global warming seemed to pause in its increase. To most climate scientists, this was an indicator that decade-scale trends could be strongly influenced by natural variability. To others (pseudo-scientists and so-called ‘climate skeptics’), this hottest (at that time) decade on record was interpreted as evidence that human-induced climate change was a fiction.

If there are still any people out there who remain unpersuaded by past science and data of climate change, the record high temperatures of 2016 should tip the balance.

With the high temperatures of 2016, the evidence for human-induced global warming is now so strong that no sensible person can deny a human role in these temperature increases.

We can argue about what we should or should not do with this knowledge, but the argument is over: greenhouse gas emissions cause our climate to get hotter.

Happy for you to edit or copy-edit etc. If you think you may be changing meaning, please ask.


I thought he did a good job of editing for the pithy parts.

Full story is here: https://www.washingtonpost.com/news/capital-weather-gang/wp/2017/01/18/scientists-react-to-earths-warmest-year-we-are-heading-into-a-new-unknown