Category: Commentary

The thermodynamic efficiency of materials production averages 20%, within an interquartile range of 5% to 50%. In other words, if the thermodynamic minimum energy needed to make a typical material is 1,500 kWh/ton, then the most likely case is that a typical industrial process for that material today consumes 7,500 kWh/ton of energy.

This note explores the numbers and implications. Calculations are linked here. The work makes us more optimistic on the potential for efficiency gains as part of the energy transition, especially in complex value chains, forms of CO2 capture, and using AI.

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Definitions: what is thermodynamic minimum energy for materials?

ΔHf° denotes the Standard Enthalpy of Formation. This is the change of enthalpy (i.e., heat), when 1 mole of a substance forms from its constituent elements in their reference state.

For example, the chemical element silicon will slowly oxidize when exposed to air, yielding pure white sand (Si + O2 -> SiO2). Now for some numbers. This reaction involves a release of enthalpy, of -910 kJ/mol. The molar mass of silicon is 28.1 grams/mol. Hence by division, the energy released per mol of silicon is 32kJ/gram, which, by juggling the energy units, equates to 9,000 kWh/ton. If you walked along the most pristine beach in the world, with some kind of “magic ray gun” that decomposed SiO2 back into Si and O2, then the thermodynamic minimum energy needed is going to be the same number, around 9,000 kWh/ton, to overcome the enthalpy of formation of SiO2. In reality, there actually is a broad landscape of silica producers, who mine high-purity silica, and sell this product on, into value chains that yield glass, solar panels and semiconductors. For the latter two applications, silica might be reduced into silicon ‘metal’ in an electric arc furnace. And overall, we think this industrial process requires around 13,500 kWh/ton of input energy. Or in other words, producing low-purity silicon metal is about 67% efficient.

Hence in our analysis, we can compare the Standard Enthalpy of Formation with the actual industrial energy consumption of producing different materials.

If you want to calculate some of these standard enthalpies of formation yourselves, there are excellent free reference sources online, such as Engineering Toolbox.

Methodology: getting the right baseline?

Other examples are more complex than our silicon study above, and require some careful consideration of the appropriate baseline.

We don’t want to ‘cheat’ in our numbers by starting from some unrealistic baseline (“if I have a working iPhone, right here in my hand, then the energy costs of making an iPhone are zero”).

Ammonia makes a nice example. The standard enthalpy of formation of ammonia (NH3) is -46 kJ/mol. This is an exothermic reaction, releasing 750 kWh/ton of energy. But clearly the global ammonia industry is a net energy consumer, not a net energy producer!!

Remember, the standard enthalpy of formation assumes you are forming ammonia from its constituent elements, i.e., gaseous hydrogen and gaseous nitrogen.

Pure hydrogen does not occur naturally, but itself needs to be produced, most likely by steam methane reforming.

And pure nitrogen does not occur naturally: it needs to be separated out of air, overcoming the entropy of mixing, using air separation technology.

So in our analysis, our thermodynamic minimum (i) adds the minimum thermodynamic work to separate pure nitrogen from air (ii) adds the minimum thermodynamic work to decompose a 50/50 mixture of CH4 and H2O into pure hydrogen (iii) subtracts the energy that could theoretically be harnessed as the nitrogen and hydrogen react together again.

The result is that we think the minimum thermodynamic efficiency for producing ammonia is something around 1,200 kWh/ton. Compared to this baseline, the real-world ammonia industry is typically around 12% efficient.

The point here is that in each case, in our data-file, we need to make some ballpark estimates about what is a fair starting point, and it is from this baseline that the minimum thermodynamic work is calculated.

Conclusion #1: high thermodynamic efficiencies are challenging to achieve in the real world?

The average material in our screen has a c20% thermodynamic efficiency. In other words, real world industrial processes tend to consume around 4-5x more energy than the thermodynamic minimum (chart below), even after 100-200 years of incremental efficiency gains by industrial civilization.

Conclusion #2. Complex value chains tend to be less efficient?

For the bottom quartile of processes in our data-file, the thermodynamic efficiency is below 5%. In other words, real world industrial processes tend to consume over 20x more energy than the thermodynamic minimum. Generally, these appear to be more complex value chains, starting with less concentrated input materials, and demanding more sophisticated output materials.

Another illustration of this point is that the very simple ‘silicon metal’ example, which we discussed above, yields one of the highest efficiencies. So too does thermally decomposing CaCO3 in cement production, or thermally reducing Fe2O3 in iron ore reduction for steel. On the other hand, the industrial processes needed to produce battery materials, lithium, nickel, PGMs are an order of magnitude more complex.

Conclusion #3. Efficiency Opportunities?

There are enormous opportunities in industrial efficiency. If we had run the charts above and found that most materials value chains were already in the mid-90s efficiency levels, then there would not be much opportunity for future improvement. But half of all the materials value chains in the world are around 20% efficient and one-quarter are less than 5% efficient.

This matters as energy efficiency is one of the most important controversies in the future of global energy demand and in the energy transition (notes below). Especially given that human civilization produces over 60 bn tons per year of ‘stuff’ across 40 different material categories, accounting for 40% of all global energy use and 35% of all global emissions.

Energy efficiency: a riddle, in a mystery, in an enigma?

EROEI: energy return on energy invested?

Omniscience: how will AI reshape the energy transition?

Conclusion #4: beware hydrogen hubris?

One of the more surprising bars in our charts is over green hydrogen, where many forecasters are hoping that future value chains will be around two-thirds efficient (build-up here). It is simply interesting to note that this assumption would make hydrogen an outlier on our thermodynamic efficiency chart.

To re-iterate, if it were possible to convert two-thirds of ratable incoming electricity into useful recoverable hydrogen energy, then this would be one of the most efficient materials value chains in all of global industry.

It should be noted, we think, that the Gibbs Free Energy of hydrogen is 237 kJ/mol, while the Enthalpy of Formation is 286kJ/mol, and so there is always going to be a 13% energy loss in trying to recover useful energy back out of hydrogen as an energy carrier.

We would be wary of some studies that quote efficiency relative to the Gibbs Free Energy baseline, rather than the enthalpy baseline. This will tend to overstate efficiency. Being 100% efficient relative to the Gibbs Free Energy baseline still connotes a 13% loss relative to the enthalpy baseline.

Another very interesting point is that in thermodynamic terms, it is materially easier to make hydrogen from reforming methane than from electrolysing water. Methane is 25% hydrogen by mass, while water is 11% hydrogen. While the enthalpy of formation of methane from C and H is -75kJ/mol, the enthalpy of formation of water from H and O is -286kJ/mol. In other words, it takes 3.8x more energy to decompose H2O than CH4, and the decomposition of H2O yields 50% less H2 than the decomposition of CH4. Some might see this as an argument for making hydrogen out of CH4 rather than out of H2O, for example, in blue hydrogen or turquoise hydrogen value chains (more below).

Hydrogen: overview and conclusions?

Conclusion #5: still looking for magic bullets in CCS and DAC?

If you are starting from a baseline of air, with 400ppm CO2 concentration (i.e., 0.04%), then the minimum thermodynamic energy needed to separate out CO2 can be calculated via the Entropy of Mixing, and comes out at 134kWh/ton (calculation here). If energy costs 10c/kWh, this is $13/ton. This is not a high energy use or a high energy cost.

The challenge today is that technically ready DAC processes are only around 5% efficient (model here), and even many technically ready CCS applications absorb 10-50% of the energy that was harnessed when emitting that CO2 in the first place (note here).

There is going to be potential for CCS and DAC in the future of materials science. We have screened some of these opportunities, and will continue screening them in our CCS research, but for now, the two notes below capture what we are looking for, to get excited by next-gen membranes and adsorbents.

Membranes for carbon capture: separation anxiety?

Industrial gas separation: swing producers?

Many questions that matter in the energy transition are engineering questions, which flow through to energy economics: which technologies work, what do they cost, what energy penalties they have, and which materials do they use? We see an increasing intersection for economics and engineering in our energy transition research.

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Behold thermodynamics!! Read the notes below, and you will no longer be tempted to commit exergetic harakiri by converting ratable electricity into some fuel that you can then run through a heat engine.

Thermodynamics: Carnot, Rankine, Brayton & beyond?

How does that work? Frankly, some of the statements we hear about decarbonization are akin to a totally untrained person, casually walking in off the street to a neurosurgery, and deciding to grab a scalpel. Sometimes it is helpful to understand how energy units work, how electricity works, how power grids work, how magnetism works, how metals work, how gas compression works, how cryogenics works, how semiconductors work or how the internet works.

Metals and materials: strength and temperature resistance?

What does it cost? Some commentators seem to think decarbonizing the planet is going to be simple. If you think the solution is simple, the most likely reason is that you do not understand the complexity of the problem. We have built over 160 economic models, of different technologies in the energy transition, or different materials and manufacturing value chains that will themselves need to be decarbonized. One of our strongest held views is that decarbonization will be easier using low-cost technologies, and a good cut-off for “too expensive” is decarbonization technologies costing well over $100/ton.

What energy penalties? Net energy return on energy invested (EROEI) has risen by 5x over the past 200-years, to 28x in today’s global energy system. Strangely, even our own roadmap to net zero sees this mega-trend reversing to 2050 (note below). But hopefully EROEI declines will not be overly severe or maybe they can even be ameliorated. Yes, you guessed it, engineering equations govern the energy efficiencies of power plants, energy penalties of CCS, energy penalties of hydrogen or energy losses in inverters and power electronics.

EROEI: energy return on energy invested?

How much metal or material? The average metal and material sees demand grow 3-30x in the energy transition, due to the growth of wind, solar, electric vehicles and batteries, and the current use factors in those spaces. But often, it takes some energy economics to determine how much material you can thrift.

Solar surface: silver thrifting?

Power cables: how much aluminium and copper?

Does that company’s technology work? We like to answer this question by reviewing the company’s patents, and scrutinizing the engineering details. All of our patent reviews are linked here, ranging from true breakthroughs with a moat around them, to other companies that seem to have the engineering equivalent of a flat tyre. A recent observation is that many technologies progress more slowly, and are harder to de-risk, than we naively hoped, based on a former career covering large-cap equities. We really like the 5-point framework at the back of this note for assessing the road to maturation.

TSE Patent Assessments: a summary?

Humility moment. After five years running a research firm focused on the energy transition, we are still working hard to correct our historical misconceptions, and educate ourselves into how the world’s energy-industrial complex works. If we can help you, field requests, or dig into any topics that are swirling around in your minds, then please do contact us.

Investing involves being paid to take risk. And we think energy transition investing involves being paid to take ten distinct risks, which determine justified returns. This note argues that investors should consider these risk premia, which ones they will seek out, and which ones they will avoid.

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Investment strategies for a fast-evolving energy transition?

Thunder Said Energy is a research firm focused on energy technologies and energy transition. Over the past 4-years, we have published over 1,000 research notes, data-files and models, to help our clients appraise different opportunities in the energy transition, across new energies, hydrocarbons and industrial decarbonization.

Energy transition is evolving very quickly. This means that many investors are continually iterating their investment strategies, stepping into new themes/sectors as they emerge, and candidly, it also means that many risks are mis-priced.

Hence we think it is helpful to consider risk premia. Which risk premia are you getting paid to take? Are you getting paid enough? Or worse, are you exposed to risk for which you are not getting paid at all?

Decarbonizing global energy: the route to net zero?

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Energy Transition: ten risk premia?

We think there are ten risk factors, or risk premia, that determine the justified returns for energy transition investing. Sweeping statements about the global energy system are almost always over-generalizations that turn out to be wrong. Nevertheless, we will make some observations, as we define each risk factor below.

(1) Risk free rate. The risk free rate is a baseline. It is the return available with almost no risk, when investing in cash deposits and medium-term Treasuries. Our perspective is that many technologies in the energy transition will be inflationary. They will stoke inflationary feedback loops. And in turn inflation puts upwards pressure on the risk free rate. Thus rising rates should raise the bar on allocating capital across the board and investors should consider how they are being compensated. Our favorite note on this topic is here.

(2) Credit/equity risk. This risk premium compensates decision makers for the risk of capital loss inherent in owning the debt and equity of companies. It might vary from sub-1% in the senior secured credit of highly creditworthy companies, through to a c3-5% equity risk premium, and c5-10% for smaller/private companies? Our perspective is that there is great enthusiasm to invest in the energy transition. This means credit/equity risk premia for some of the most obvious energy transition stocks may be compressed. But energy transition is also going to pull on many adjacent value chains, which have non-obvious exposure to the energy transition, while their risk premia have not yet compressed. So we think it is a legitimate investment strategy to target “non-obvious” exposure to the energy transition. Our favorite note on this topic is here.

(3) Project risk. Energy transition is the world’s greatest building project. But over 90% of all construction projects take longer than expected, or cost more than expected, and the average over-run is 60%. Opportunities with more of their future value exposed to delivering large projects have higher project risk. Infrastructure investors can happily stomach 5-10% total returns as they accept project risk. This might include building out power grids, pipelines, fiber-optic cables, and PPA-backstopped wind and solar. And thus another legitimate strategy in the energy transition investing is to get paid for appraising and defraying project risks; get paid for the ability to execute projects well.

(4) Liquidity risk. This premium compensates investors against the possible inability to withdraw capital in a liquidity crunch. It is clearly higher for small private companies than publicly listed large-caps. Energy transition sub-sectors that might debatably warrant higher liquidity premia are CCS projects (50-year monitoring requirements after disposal), reforestation projects (40-100 year rotations for CO2 credit issuance) and infrastructure with very long construction times. A legitimate strategy for endowments and pension funds in the energy transition hinges on their large size and longevity, which allows them to withstand greater liquidity risk than other groups of investors. Another legitimate strategy is to earn higher returns by taking higher liquidity risk, building up a portfolio of privately owned companies with exposure to the energy transition, rather than investing in public companies that will tend to have lower liquidity risk premia.

(5) Country risk. This premium compensates investors against deteriorating economic conditions, tax-rises, regulatory penalties or cash flow losses in specific countries. This is becoming relevant for wind and solar, as many investors are increasingly willing to take country risk to achieve higher hurdle rates, and given the vast spread in different countries’ power prices and grid CO2 intensities (chart below). It is no good if only a few countries globally decarbonize. Net zero is a global ambition. And so another very legitimate strategy in the energy transition is to specialize in particular countries, where those country risks can be managed and defrayed, while driving energy transition there.

Global electricity prices vs. CO2 intensities?

(6) Technology risk. This risk premium compensates investors for early stage technologies not working as intended, or suffering delays in commercialization, which derail the delivery of future cash flows. One observation in our research has been that some technologies at first glance seem to be mature, but on closer inspection still have material technology risks (such as green hydrogen electrolysers, post-combustion CCS). But technology risk is interesting for two reasons. First, we think that investors can command some of the highest risk premia (i.e., highest expected returns) for taking technology risk, compared to other risk premia on our list. Second, appraising technology risk is a genuine skill, possessed by some investors, a font at the wellspring of “alpha”. We enjoy appraising technology risk by reviewing patents (see below).

TSE Patent Assessments: a summary?

(7) New market risk. This risk premium compensates investors for immature markets. For example, if you produce clean ammonia, then you can sell it into existing ammonia fertilizer markets which does not carry any new market risk; or you can sell it as a clean fuel to decarbonize the shipping industry, which involves persuading the shipping industry to iron out ammonia engines, despite challenging combustion properties, prevent NOx emissions, and retrofit existing bulk carriers and container ships, which clearly does carry new market risk. Another interesting example is that in geographies with high renewables penetration, there may be some hidden market risk in reaching ever-higher renewables penetration? Our personal perspective is that new market risk is the most ‘uncompensated’ risk in the energy transition. It is pervasive across many new energies categories, many investors are exposed to this risk, and yet they are not paid for it. Although maybe another legitimate strategy in the energy transition is to collect new market risk premia while helping to create new markets?

(8) Competition risk. This risk premium compensates against unexpected losses of market share and cash generation due to new and emerging competition. It also includes the risk of your technology “getting disrupted” by a new entrant. Across our research, the area that most comes to mind is in batteries. There is always a headline swirling somewhere about a disruptive battery breakthrough that will crater demand for some incumbent material. Arguably, competition risk goes hand in hand with technology risk and new market risk. It is not enough to develop a technology that is 20% better than the incumbent if someone else develops a technology that is 40% better. Again, we think investors may not get compensated fairly for taking competition risk, while excess returns may accrue to investors that can appraise this risk well.

(9) Commodity risk. This risk premium compensates investors for the inherent volatility of commodity markets, which can have deleterious effects on valuations, liquidity, solvency, sanity (!). Consider that within the past five years, oil prices started at $80/bbl, collapsed into negative territory in Apr-2020, then recovered above $120/bbl in mid-2022. Our work has progressively gone deeper into cleaner hydrocarbons, metals, materials. Our energy transition roadmap contains bottlenecks where total global demand must rise by 3-30x. Yet our perspective is that many investors are reluctant to take commodity risk. Stated another way, commodity risk can be well-compensated. If you have the mental resiliency to ride this roller-coaster.

(10) Environmental risk. This risk premium compensates investors against tightening environmental standards, deteriorating environmental acceptance or regulations that lower future cash generation, especially in CO2 emitting value chains. It is sometimes called “stranded asset risk”. The most obvious example is investing in coal, where investors can get paid c10% dividend yields to own some of these incumbents. Our perspective is that environmental risk premia blew out to very high levels in 2019-2021, and they still remain high, especially if you believe that an era of energy shortages lies ahead (note below). Another perspective is that it feels “easier” to get paid a 5-10% environment risk in an insurance policy against future energy shortages, than to earn a 5-10% risk premium by doing the due diligence on a new and emerging technology? And finally, it is a legitimate strategy in the energy transition to own higher-carbon businesses, then improve their environmental performance, so that the market will reward these companies with lower environmental risk premia.

Energy macro: our top ten charts?

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Economic models: moving beyond 10% hurdle rates?

We have constructed over 160 economic models of specific value chains, in new energies and in decarbonizing industries. Usually, we levy a 10% hurdle rate in these models, for comparability. But the justified hurdle rate should strictly depend upon energy transition risk premia discussed above.

Please contact us if we can help you appraise any particular ideas or opportunities, to discuss their justified hurdle rates, or to discuss how these risk premia align with your own energy transition investing strategy.

The very simple spreadsheet behind today’s title chart is available here, in case you want to tweak the numbers.

How does methane increase global temperature? This article outlines the theory. We also review the best equations, linking atmospheric methane concentrations to radiative forcing, and in turn to global temperatures. These formulae suggest 0.7 W/m2 of radiative forcing and 0.35ºC of warming has already occurred due to methane, as atmospheric methane has risen from 720 ppb in 1750 to 1,900 ppb in 2021. This is 20-30% of all warming to-date. There are controversies over mathematical scalars. But on reviewing the evidence, we still strongly believe that decarbonizing the global energy system requires replacing coal and ramping natural gas alongside low-carbon energies.

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On the Importance of Reaching Net Zero?

There is a danger that writing anything at all about climate science evokes the unbridled wrath of substantially everyone reading. Hence let us start this article by re-iterating something important: Thunder Said Energy is a research firm focused on the best, most practical and most economical opportunities that can deliver an energy transition. This means supplying over 100,000 TWH of useful human energy by 2050, while removing all of the CO2, and avoiding turning our planet into some kind of Waste Land.

Our roadmap to net zero (note below) is the result of iterating between over 1,000 thematic notes, data-files and models in our research. We absolutely want to see the world achieve important energy transition goals and environmental goals. And part of this roadmap includes a greatly stepped up focus on mitigating methane leaks (our best, most comprehensive note on the topic is also linked below).

However, it is also helpful to understand how methane causes warming. As objectively as possible. This helps to ensure that climate action is effective.

It is also useful to construct simple models, linking atmospheric methane concentrations to global temperature. They will not be perfect models. But an imperfect model is often better than no model.

Decarbonizing global energy: the route to net zero?

Global gas: catch methane if you can?

Methane is a powerful greenhouse gas

An overview of the greenhouse effect is written up in a similar post, quantifying how CO2 increases global temperature (note below). We are not going to repeat all of the theory here. But it may be worth reading this prior article for an overview of the key ideas.

Greenhouse gases absorb and then rapidly re-radiate infra-red radiation. This creates a less direct pathway for solar radiation to be reflected back into space. The ability of different gas molecules to absorb and re-radiate infra-red radiation depends on the energy bands of electrons in those molecules, especially the shared electrons in covalent bonds between non-identical molecules with “dipole moments” (this is why H2O, CO2, CH4 and N2O are all greenhouse gases, while N2, O2 and Ar are not).

There are two reasons that methane is up to 200x more effective than CO2 as a greenhouse gas. The first reason is geometry. CH4 molecules are tetrahedral. CO2 molecules are linear. A tetrahedral molecule can generally absorb energy across a greater range of frequencies than a linear molecule.

The second reason is that methane is 200x less concentrated in the atmosphere, at 1,900 parts per billion, versus CO2 at 416 parts per million. We saw in the post below that radiative forcing is a log function of greenhouse gases. In other words, the first 20ppm of CO2 in the atmosphere explains around one-third of all the warming currently being caused by CO2. Each 1ppm increase in atmospheric CO2 has a ‘diminishing impact’, because it is going to absorb incremental radiation in a band that is already depleted by the pre-existing CO2. Thus small increases in methane cause more warming, as methane is currently present in very low concentrations, and thus at a much steeper part of the radiative forcing curve.

The most commonly quoted value we have seen for the instantaneous global warming potential of methane (instantaneous GWP, or GWP0) is 120x. In other words 1 gram of methane has a warming impact of 120 grams of CO2-equivalent. Although the 20, 50 and 100-year warming impacts are lower (see below).

How does CO2 increase global temperature?

What formula links methane to radiative forcing?

Our energy-climate model is linked below. It contains the maths and the workings linking methane to radiative forcing. It is based on a formula suggested in the past by the IPCC:

Radiative Forcing from Methane (in W/m2) = Alpha x Methane Concentration (in ppb) ^ 0.5 – Small Adjustment Factor for Methane-N2O interaction. Alpha is suggested at 0.036 in the IPCC’s AR5 models, and the adjustment factor for methane-N2O interactions can be ignored if you are seeking an approximation.

The route to net zero: an energy-climate model for 2-degrees

This is the formula that we have used in our chart below (more or less). As usual, we can multiply the radiative forcing by a ‘gamma factor’ which calculates global temperature changes from radiative forcing changes. We have seen the IPCC discuss a gamma factor of 0.5, i.e., 1 W/m2 of incremental radiative forcing x 0.5ºC/[W/m2] gamma factor yields 0.5ºC of temperature increases. However, there are controversies over the correct values of alpha and gamma.

Interaction Effects: Controversies over Alpha Factors?

The alpha factor linking methane to radiative forcing is suggested at 0.036 in the IPCC’s AR3 – AR5 reports. Plugging 0.036 into our formula above would suggest that increasing methane from 720 ppb in pre-industrial times to 1,900 ppb today would have caused 0.52 W/m2 of incremental radiative forcing. In turn, this would be likely to raise global temperatures by 0.27ºC.

Helpfully, this tallies with the values you might see in other well-known sources, such as the Wikipedia page on Radiative Forcing.

However, many technical papers, and even the IPCC’s AR5 report, have argued that alpha should be ‘scaled up’ to account for indirect effects and interaction effects.

Tropospheric Ozone. In the troposphere (up to 15km altitude), ozone is a ridiculously powerful greenhouse gas, quantified at around 1,000x more potent than CO2. It is postulated that the breakdown of atmospheric methane produces peroxyl radicals (ROO*, where R is a carbon-based molecule). In turn, these peroxyl radicals react with oxygen atoms in NOx pollutants, yielding O3. And thus methane is assumed to increase tropospheric ozone. Several authors, including the IPCC, have proposed to scale up alpha values by 20% – 80%, to reflect the warming impacts of this additional ozone.

Stratospheric Water Vapor. Water is a greenhouse gas, but it is usually present at relatively low concentrations in the stratosphere (12-50 km altitude). Water vapor prefers to remain in the troposphere, where it is warmer. However, when methane in the stratosphere decomposes, each CH4 molecule yields 2 H2O molecules, which may remain in the stratosphere. Several authors, including the IPCC, have proposed to scale up alpha values by around 15% to reflect the warming impacts of this additional water vapor in the stratosphere.

Short-wave radiation. Visible light has a wavelength of 400-700nm. Infra-red radiation has a wavelength of 700nm – 1mm and is the band that is mainly considered in radiative forcing calculations. However, recent research also notes that methane can absorb short-wave radiation, with wavelengths extended down to as little as 100-200nm. Some authors have suggested that the radiative forcing of methane could be around 25% higher than is stated in the IPCC (2013) assessment when short-wave radiation is considered. This impact is not currently in IPCC numbers.

Aerosol interactions. Recent research has also alleged that methane lowers the prevalence of climate-cooling aerosols in the atmosphere, and this may increase the warming impacts of CH4 by as much as 40%. This impact is not currently in IPCC numbers.

Hydrogen interactions. Even more recent research has drawn a link between methane and hydrogen GWPs, suggesting an effective GWP of 11x for H2, which is moderated by methane (note below).

Hydrogen: what GWP and climate impacts?

N2O interactions. The IPCC formula for radiative forcing of methane suggests a small negative adjustment due to interaction effects with N2O, another greenhouse gas, which has been rising in atmospheric concentration (from 285ppb in 1765 to 320ppb today). The reason is that both N2O and CH4 seem to share an absorption peak at 7-8 microns. Hence it is necessary to avoid double-counting the increased absorption at this wavelength. The downwards adjustment due to this interaction effect is currently around 0.08 W/m2.

The overall impact of these interaction effects could be argued to at least double the instantaneous climate impacts of methane. On this more strict vilification of the methane molecule, rising atmospheric methane would already have caused at least a 1.0 W/m2 increase in radiative forcing, equivalent to 0.5ºC of total temperature increases since 1750 due to methane alone.

Uncertainty is high which softens methane alarmism?

Our sense from reviewing technical papers is that uncertainty is much higher when trying to quantify the climate impacts of methane than when trying to quantify the climate impacts of CO2.

The first justification for this claim is a direct one. When discussing its alpha factors, the IPCC has itself acknowledged an “uncertainty level” of 10% for the scalars used in assessing the warming impacts of CO2. By contrast, it notes 14% uncertainty around the direct impacts of methane, 55% on the interaction with tropospheric ozone, 71% on the interaction with stratospheric water vapor. These are quite high uncertainty levels.

A second point is that methane degrades in the atmosphere, with an average estimated life of 11.2 years, as methane molecules react with hydroxyl radicals. This is why the IPCC has stated that methane has a 10-year GWP of 104.2x CO2, 20-year GWP of 84x CO2, 50-year GWP of 48x CO2 and a 100-year GWP of 28.5x CO2.

There is further uncertainty around the numbers, as methane that enters the atmosphere may not stay in the atmosphere. The lifetime of methane in additional sinks is estimated at 120 years for bacterial uptake in soils, 150-years for stratospheric loss and 200 years for chlorine loss mechanisms. And these sources and sinks are continuously exchanging methane with the atmosphere.

Next, you might have shared our sense, when reading about the interaction effects above, that the mechanisms were complex and vaguely specified. This is because they are. I am not saying this to be some kind of climate sceptic. I am simply observing that if you search google scholar for “methane, ozone, interaction, warming”, and then read the first 3-5 papers that come up, you will find yourself painfully aware of climate complexity. It would be helpful if the mechanisms could be spelled out more clearly. And without moralistic overtures about natural gas being inherently evil, which sometimes simply makes it sound as though a research paper has strayed away from the scientific ideal of objectivity.

Finally, the biggest reason to question the upper estimates of methane’s climate impact is that they do not match the data. There is little doubt that the Earth is warming. The latest data suggest 1.2-1.3C of total warming since pre-industrial times (chart below). Our best guesses, based on our very simple models point to 1.0ºC of warming caused by CO2, 0.35ºC caused by CH4 and around <0.2ºC caused by other greenhouse gases. If you are a mathematical genius, you may have noticed that 1.0 + 0.35 + <0.2 adds up to 1.5C, which is more warming than has been observed. And this is not including any attribution for other factors, such as changing solar intensity or ocean currents. So this may all suggest that our alpha and gamma factors are, if anything, too high. In turn, this may mute the most alarmist fears over the stated alpha factors for methane being materially too low.

Global average temperatures: are the data robust and reliable?

Conclusions for gas in the energy transition

How does methane increase global temperature? Of course we need to mitigate methane leaks as part of the energy transition, across agriculture, energy and landfills; using practical and economical methods to decarbonize the entire global energy system. Methane is causing around 20-30% of all the incremental radiative forcing, on the models that we have considered here. If atmospheric methane doubles again to 3,800 ppb, it will cause another 0.2-0.4ºC of warming, as can be stress-tested in our model here.

However, we still believe that natural gas should grow, indeed it should grow 2.5x, as part of the world’s lowest cost roadmap to net zero. The reason is that while we are ramping renewables by over 5x, this is still not enough to offset all demand for fossil energy. And thus where fossil energy remains, pragmatically, over 15GTpa of global CO2 abatement can be achieved by displacing unchecked future coal consumption with gas instead.

Combusting natural gas emits 40-60% less CO2 than combusting coal, for the same amount of energy, which is the primary motivation for coal-to-gas switching (note below). But moreover, methane leaks into the atmosphere from the coal industry are actually higher than methane leaks from the gas industry, both on an absolute basis and per unit of energy, and this is based on objective data from the IEA (note below).

Coal versus gas: explaining the CO2 intensity?

CH4 context: the largest methane leaks of all time?

How does atmospheric CO2 increase global temperature? The purpose of this article is to outline the best formulae we have found linking global temperature to the concentration of CO2 in the atmosphere. In other words, our goal is a simple equation, explaining how CO2 causes warming, which we can use in our models. In turn, this is why our ‘roadmap to net zero’ aims to reach net zero by 2050, stabilize atmospheric CO2 at 450ppm, and we believe this scenario is compatible with 2ºC of warming.

Disclaimer: can a simple equation explain global warming?

Please allow us to start this short note with a disclaimer. We understand that writing anything at all about climate science is apt to incur the unbridled wrath of substantively everyone. We also understand that the world’s climate is complex, and cannot be perfectly captured by simple formulas, any more than ‘world history’ can be.

Nevertheless, the over-arching goal of all of our research is that we are trying to model the best roadmap to decarbonize the global energy system (note below), and the best resultant opportunities in the energy transition.

Hence we think it is useful to have an approximate formula, even if it is only “about 80% right”, rather than a conceptual black hole. So that is the purpose of today’s short note.

Decarbonizing global energy: the route to net zero?

(1) Thermal theory: inflows and outflows?

The Earth’s temperature will be in balance and remain constant if energy inflows match energy outflows. Energy inflows come from the sun, and are approximated by the ‘solar constant’, at 1,361 W/m2. Energy outflows are radiated back into space, and are approximated by the Stefan-Boltzmann law.

One of the terms in the Stefan-Boltzmann equation is Temperature^4. That is temperature raised to the power of four. In other words, if for some reason, the Earth is not quite radiating/reflecting 1,361 W/m2-equivalent back into space, then its average temperature needs to become a little bit warmer, until it is once again radiating 1,361 W/m2-equivalent back into space. Let’s unpack this bit further…

Physics dictates that any physical body with a temperature above absolute zero will radiate energy from its surface, usually small amounts of energy. The wavelength depends on the body’s chemical properties, and more importantly, its temperature, i.e., its thermal energy.

Energy is the inverse of wavelength. Some electromagnetic radiation has a wavelength of 380-700 nm, in which case we call this radiation ‘visible light’. Some has lower energy, and thus higher wavelength. For example, radiation with a wavelength of 700-1,000 nm is often referred to as ‘infra-red’.

So in conclusion, energy is constantly being radiated back “upwards” towards outer space by the Earth’s surface, i.e., its land and its seas. These wavelengths are generally in the infra-red range. They span from 600 – 20,000 nm. But how much of that energy actually escapes into space?

(2) Greenhouse Gases: CO2, CH4, N2O, et al.

CO2 is a greenhouse gas. This means that as thermal energy is radiated upwards from the Earth’s surface — land and sea — it can excite the electrons in CO2 molecules, into a higher energy state, for a few nano-seconds. These electrons quickly relax back into a lower-energy state. As they do this, they re-radiate energy.

In other words, CO2 molecules absorb energy that is “meant to be” radiating upwards from the Earth’s surface back into space, and instead they scatter it in various other directions, so some of it will be re-absorbed (e.g., back in the world’s oceans).

In passing, this is why some scientists object to CO2 being described as ‘a blanket’. It is not trapping heat. Or storing any heat itself. It is simply re-radiating and re-scattering heat that would otherwise be travelling in a more direct path back into space.

This effect of CO2, and other greenhouse gases, can be described as ‘radiative forcing’ and measured in W/m2. In 2021, with 416ppm of CO2 in the atmosphere, the radiative forcing of atmospheric CO2 is said to be 2.1 W/m2 higher than it was in 1750, back when there was 280 ppm of CO2 in the atmosphere.

So what equations relate atmospheric CO2 concentrations into radiative forcing effects and ultimately into temperatures?

(3) Absorbing equations: how does CO2 impact temperature?

Let us start with an analogy. You are reading a complicated text (maybe this one). On the first reading, you absorb and retain about 50% of the content. One the second reading, you absorb and retain another 25% of the content. On the third reading, you absorb another 13% of the content. And so on. By the tenth reading, you have absorbed 99.9% of the content. But the general idea is that the more you have absorbed on previous readings, the less is left to be absorbed on future readings.

The absorption profile of CO2 is similar. One way to think about this is that even a very small amount of a particular greenhouse gas is going to start absorbing and re-radiating energy at its particular absorption wavelengths. This dilutes the amount of energy with this particular wavelength that remains. This means that there will be less energy with this particular wavelength left to absorb by adding more of molecules of this greenhouse gas into the atmosphere. By definition, the additional gas is ‘trying to’ absorb radiation at a wavelength that is already depleted.

Hence, without any CO2 in the atmosphere, the Earth would be about 6C cooler. The first 20ppm of CO2 explains perhaps 2ºC of all the warming exerted by CO2. The next 20ppm explains 0.8ºC. The next 20ppm explains around 0.6ºC. And so on. There are diminishing returns to adding more and more CO2.

Systems like this are described with logarithmic equations. Thus in the past, the IPCC has suggested various log equations that can relate radiative forcing to atmospheric CO2. The most famous and widely cited formula is below:

Increase in Radiative Forcing (W/m2) = 5.35 x ln (C/C0) … where C is the present concentration of atmospheric CO2 in ppm; and C0 was the concentration of atmospheric CO2 in 1750, which was 280 ppm.

The scalar value of 5.35, in turn, is derived from “radiative transfer calculations with three-dimensional climatological meteorological input data” (source: Myhre, G., E. J. Highwood, K. P. Shine, and F. Stordal, (1998). New estimates of radiative forcing due to well mixed greenhouse gases. Geophys. Res. Lett., 25, 2715–2718). Note these formulae are quite long-standing and go back to 1998-2001.

Thus in the chart below, we have averaged three log formulas, suggested in the past by the IPCC, to calculate radiative forcing from atmospheric CO2. Next, to translate from radiative forcing into temperature we have used a “gamma factor” of 0.5ºC per W/m2 of radiative forcing, which is also a number suggested in the past by the IPCC.

(4) Temperature versus CO2: mathematical implications?

Let us interpret this chart above from left to right. This is intended to be an objective, mathematical exercise, assessing the implications of simple climate formulae proposed long ago by the IPCC.

(a) Much of the greenhouse effect has “already happened“, due to the log relationship in the chart. The chart implies that the total greenhouse effect occurring today from atmospheric CO2 is around 7-8ºC, of which c6-7ºC was already occurring back in 1750.

(b) Raising atmospheric CO2 to 415ppm should have increased global temperatures by around 1ºC since pre-industrial times, just due to CO2, and holding everything else equal, again just taking the IPCC’s formulae at face value.

(c) Raising atmospheric CO2 by another 35ppm to 450ppm would, according to the simple formula, would result in 1.3ºC of warming due to CO2 alone, and 2ºC of total warming, using the simple relationship that two-thirds of all greenhouse warming since 1750 is down to CO2, and the remainder is due to CH4, N2O and other trace gases.

(d) Diminishing impacts? Just reading off the chart, a further 50ppm rise to 500ppm raises temperature by 0.3ºC; a further 50ppm rise to 550ppm raises temperature by 0.27ºC; a further 50ppm rise to 600ppm raises temperature by 0.25ºC; and a further 50ppm rise to 650ppm raises temperature by 0.23ºC. The point is that rising atmospheric CO2 also raises global temperature along with it. While it is true that each incremental 50ppm has less impact than the prior 50ppm, the pace of the slowdown is itself quite slow, and not enough to dispel our ultimate need to decarbonize.

(e) There is a theoretical levelling off point due to the log relationship, where incremental CO2 makes effectively no difference to global temperatures, but from the equations above, it is so far in the future as to be irrelevant to practical discussions about decarbonization: it is probably somewhere after atmospheric CO2 has surpassed 4,000 ppm and CO2 has directly induced about 8C of warming.

In conclusion, the simple formulae that we have reviewed suggest that the ‘budget’ for 2ºC of total global warming is reached at a total atmospheric CO2 concentration of 450ppm. Of the budget, about two-thirds is eaten up by CO2, and the remaining one-third is from other anthropogenic greenhouse gases, mainly methane and N2O. This is what goes into our climate modelling, and why we think it is also important to mitigate methane emissions and N2O emissions from activities such as crop production.

The route to net zero: an energy-climate model for 2-degrees

(5) Controversies: challenges for simple CO2-warming equations?

Welcome to the section of this short note that is probably going to get controversial. Our intention is not to inflame or enrage anybody here. But we are simply trying to weigh the evidence objectively.

(a) Gamma uncertainty. Our simple climate formula above used a gamma value of 0.5ºC per W/m2 of radiative forcing. The IPCC has said in the past that this is a good average estimate, and that its gamma value has an uncertainty range of +/- 20%. Even this would be quite uncertain. For example, it means that the CO2 budget for 2ºC of total warming would be anywhere between 420-510ppm of atmospheric CO2, using the formulae above.

(b) More gamma uncertainty. Worse, some sources that have crossed our screens have suggested gamma values as low as 0.31ºC per W/m2 of radiative forcing, and others as high as 0.9ºC per W/m2 of radiative forcing. One of the key uncertainties seems to be around interaction effects and feedback loops. For example, a warmer atmosphere can store more water vapor. And water vapor is itself a greenhouse gas.

(c) What percentage of CO2 emitted by human activities remains in the atmosphere and what percent is absorbed by the oceans? We have assumed almost no incremental CO2 emitted by human activities is absorbed in the oceans, and almost all remains in the atmosphere, in our simple climate model.

(d) Other variables. Our model does not factor in the impacts of other variables that have an impact on climate, such as Milankovitch cycles, solar cycles, ocean currents, massive volcanic eruptions or mysterious Dansgaard-Oeschger events. (And no doubt there are some super-nerdy details of climate science that are not yet fully understood. But surely that does not invalidate the basics. While I may not fully grasp the Higgs-Boson, I still try to avoid cycling into large and immovable obstacles).

(e) We have over-simplified radiative forcing. There is no single formula that perfectly sums up the impact of CO2 on climate, because the Earth is not a single, homogenous disc, pointed directly at the sun. Some of these over-simplifications are obvious. Others are more nuanced. Clouds reduce the mean radiative forcing due to CO2 by about 15%. And the impacts of different gases can be different across vertical profiles through the atmosphere, for example, stratospheric adjustments reduce the impact of CO2 by 15%, compared to a perfectly mixed and homogenous atmosphere.

(f) Warming to-date. Perhaps most controversially, our simple formulae discussed above suggest that with atmospheric CO2 at 415 ppm and a gamma value of 0.5ºC, the world should already be 1.1ºC warmer than pre-industrial times due to CO2 alone, and this equates to being around 1.6ºC warmer than pre-industrial times due to a combination of all greenhouse gases. In contrast, the world currently appears to be around 1.1ºC warmer, in total, than it was in pre-industrial times according to the data below. This may mean that our gamma value is too high, or that our formulas are too conservative. Or conversely, it could simply mean that there are time lags between CO2 rising and temperature following. We do not know the answer here, which is unsatisfying.

Global average temperatures: are the data robust and reliable?

Conclusions: what is the relationship between CO2 and warming?

How does CO2 increase global temperature? The advantages of simple formulae are that they are simple and can be used to inform our models. The disadvantages are that the global energy-climate system is complex, and will never be captured entirely by simple formulae.

Our aim in this short note is to explain the formulas that we are using in our energy-climate models and in our roadmap to net zero. We think it is possible to stabilize atmospheric CO2 at 450ppm, by reaching ‘net zero’ around 2050, in an integrated roadmap that costs $40/ton of CO2 abated; and reaches an important re-balancing between human activities and the natural world.

450ppm of atmospheric CO2 is possibly a conservative budget. There may be reasons to hope that true ‘gamma’ values for global warming, or forcing co-efficients, are lower than we have modelled. But it makes sense to ‘plan for the worst, hope for the best’. And regardless of specific climate-modelling parameters, it makes sense for a research firm to look for the best combination of economics, practicality, morality and opportunity in the energy transition.

“It provokes the desire, but it takes away the performance.” That is the porter’s view of alcohol in Act II Scene III of Macbeth, it is also our view of 2022’s impact on the energy transition. The resultant outlook is captured in six concise pages, published in the Walter Scott Journal in Summer-2022.

Further research. Our overview into energy technologies and energy transition for the route to ‘net zero’ is linked here.

Download (free)

This video covers our top five reflections after 3.5 years, running a research firm focused on energy transition, and since Thunder Said Energy was founded in early 2019.

(1) Inter-connectedness. Value chains are so inter-connected that ultimately costs will determine the winning transition technologies.

(2) Humility. The complexity is so high that the more we have learned, the stupider we feel.

(3) Value in nuances. As a result, there is value in the nuances, which are increasingly interesting to draw out.

(4) ‘Will not should’. Bottlenecks need to be de-bottlenecked as some policy-makers have inadvertently adopted the “worst negotiating strategy in the world”.

(5) Bottom-up opportunities. And finally, we think energy transition and value will be driven by looking for bottom-up opportunities in a consistent framework.

For more perspectives on live, the universe, and everything, please see this video on our top perspectives on the energy transition from the first 2-years since setting up TSE.

Chinese coal provides 15% of the world’s energy, equivalent to 4 Saudi Arabia’s worth of oil. Global energy markets may become 10% under-supplied if this output plateaus per our ‘net zero’ scenario. Alternatively, might China ramp its coal to cure energy shortages, especially as Europe bids harder for renewables and LNG post-Russia? Today’s note presents our ‘top ten’ charts on China’s opaque coal industry.

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China’s coal industry provides 15% of the world’s energy and c22% of its CO2 emissions. These numbers are placed in context on page 2.

China’s coal production policies will sway global energy balances. Key numbers, and their impacts on global energy supply-demand, are laid out on page 3.

China’s coal mines are a constellation of c4,000 assets. Some useful rules of thumb are given on the breakdown on page 4.

China’s coal demand is bridged on page 5, including the share of demands for power, industrial heat, residential/commercial heat and coking.

Coal prices are contextualized on page 6-7, comparing Chinese coal with gas, renewables, hydro and nuclear in c/kWh terms.

Coal costs are calculated on page 6-8. We model what price is needed for China to maintain flat-slightly growing output, while earning double-digit returns on investment.

Accelerating Chinese coal depends on policies, however, especially around a tail of smaller and higher cost mines. The skew and implications are explored on page 7-8.

China’s decarbonization is clearly linked to its coal output. We see decarbonization ambitions being thwarted in the 2020s, per page 8.

Methane leaks from China’s coal industry may actually be higher than methane leaks from the West’s gas industry (page 9).

Chinese coal companies are profiled, and compared with Western companies, on pages 10-11.

For an outlook on global coal production, please see our article here.