Kaya Variations: Decarbonization Math for Nations, Corporations, and Data Centres
Data Centres, AI, Rising Energy and Emissions, Oh My!
Experiment Box
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For those who are aural learners, Google’s NotebookLM was used to auto-generate a podcast from this post. All I submitted is the URL for this post. No additional “human instruction”. Enjoy.
https://notebooklm.google.com/notebook/17a036d2-9c07-46b7-8f97-6dd6be0e5e44/audio
See comments for my notes on this “translation” of post to podcast.
Introduction
The rapid rise of Data Centres has been a recent recurrent theme in technology media through spring/summer 2024. This rise, symbiotic with the commercialization of AI (particularly LLMs, Generative AI, as well as enabling software architecture and AI optimized chips), is leading to an increase in carbon emissions for major Tech Cloud Infrastructure providers even in the face of net-zero emissions goals and coincident with energy usage rises straining electrical grids
How can we gain insight into the interplay of Tech advances, associated Economic Activity, as well as the Total Energy Consumption and Carbon Emissions consequences of our society’s technological and economic activity? How do we evaluate these multiple interdependencies in the context of a rapidly evolving electrical grid infrastructure grounding the current renewable energy transition one of whose core goals is Decarbonization?
(https://www.goldmansachs.com/insights/articles/AI-poised-to-drive-160-increase-in-power-demand)
(https://www.bbc.com/news/articles/cj5ll89dy2mo#)
(https://digitalinfranetwork.com/opinions/net-zero-rlasting-cace-is-on-for-data-centres-as-leaders-capture-value-and-build-lasting-competitive-advantage/#:~:text=A%20study%20estimates%20the%20emissions,of%20meeting%20our%20climate%20goals.)
(https://www.datacenterdynamics.com/en/news/amazon-all-our-operations-now-run-on-renewable-energy/)
(https://www.ft.com/content/2d6fc319-2165-42fb-8de1-0edf1d765be3)
(https://www.irena.org/Energy-Transition/Outlook)
In the early 1990s energy economist Yoichi Kaya introduced The Kaya Identity as a tool that can help us measure the relative effects of Technology, Economic Activity, Energy Usage and Emissions as they affect us (People). It expresses the relative effects of the above factors as a simple mathematical identity and has been used in its original and modified formulations to identify the relative contributions of these factors and act on them to achieve decarbonization of carbon emissions associated with energy usage.
In this note we will review the “Classic Kaya Identity” in the context of an interpretation system developed by Roger Pielke Jr over several publications. We will then extend the Classic Kaya Identity to additional use cases required for applicability to corporations, data centres, even landscapes.
(https://en.wikipedia.org/wiki/Kaya_identity#:~:text=The%20Kaya%20identity%20is%20a,per%20unit%20of%20energy%20consumed)
(https://www.actuaries.org.uk/system/files/field/document/Kaya%20identity_JC%20Final%20050219.pdf)
(https://archive.ipcc.ch/ipccreports/sres/emission/index.php?idp=50)
(https://archive.ipcc.ch/publications_and_data/ar4/wg3/en/ch1s1-3-1-2.html)
(https://ourworldindata.org/grapher/kaya-identity-co2)
(https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7459989/)
(https://www.e3s-conferences.org/articles/e3sconf/pdf/2023/73/e3sconf_iced2023_05001.pdf)
Classic Kaya Identity
In a recent post “Is Global Climate Policy Working” in his blog “The Honest Broker” Roger Pielke Jr introduces the Kaya Identity through a simple mnemonic,
“People engage in economic activity that uses energy from carbon emitting generation”
(
)
This sentence leads to the formulation of the Kaya Identity. (Notation slightly modified from Pielke’s post cited above).
The Kaya Identity requires the following base variables:
Pop = Population (“People”)
GDP = Gross Domestic Product (“Economic Activity”)
TEC = Total Energy Consumption (“Energy)
CE = Carbon Emissions (“Carbon”)
These base variables are then organized into the following ratios.
GDP/Pop = GDP per capita (“Engage in Economic Activity”)
TEC/GDP = Total Energy Consumption per GDP (“Uses Energy From”)
CE/TEC = Carbon (dioxide) emissions per total energy consumed (“Carbon Emitting Generation”)
Base variables and derived ratios are assembled into the four terms of the Kaya Identity,
CLASSIC KAYA IDENTITY:
CE = Pop x GDP/Pop x TEC/GDP x CE/TEC
Pielke further condenses the Kaya Identity into two component expressions that summarize economic activity (EA; Pielke uses GDP) and technology (TECH)
Let EA = Pop x GDP/Pop
Let TECH = TEC/GDP x CE/TEC
Then, CE = EA x TECH
which can be rearranged as
CE/EA = TECH
Pielke notes of the ratio CE/GDP that:
“a reduction in this ratio is called decarbonization”
Pielke further notes:
“We want emissions to go down but we also want GDP to go up”
Micro Kaya Identity
The rise in Data Centres over the last few years has led to the current technology media focus (circa summer 2024) on Decarbonization within large technology cloud infrastructure companies with respect to sudden rises in both energy usage as well as carbon emissions associated with this growth. The Kaya Identity seems well structured to be a relevant probe in light of corporate Decarbonization goals. To apply the Kaya Identity to use cases such as Data Centre growth we have to find Micro substitutes applicable to corporations for the two Macro Variables applicable to national economies used in Classic Kaya Identity — Population (“People”) and GDP (“Economic Activity”).
For Population — Employee Number is an obvious analogue.
For GDP, Market Capitalization (Share Price x Outstanding Shares) has been suggested as a useful analogue representing the total economic activity within a business; particularly in the comparison of large businesses whose total economic activity rivals that of nations.
(https://fastercapital.com/content/Market-Cap-vs--GDP--A-Comparative-Analysis-of-Valuation-Metrics.html)
(https://www.visualcapitalist.com/the-tech-giants-worth-compared-economies-countries/)
The argument could be made that Enterprise Value could also be used as an analogue of economic activity ; as it includes Market Capitalization but also adds in Debt, and Cash
(https://www.raseedinvest.com/learn/how-enterprise-value-differs-from-market-cap)
(https://www.investopedia.com/terms/e/enterprisevalue.asp)
We’ll stick to using Market capitalization in this post as it is (a) simpler to calculate and (b) less likely to be negative (which can happen with Enterprise Value).
(https://breakingintowallstreet.com/kb/equity-value-enterprise-value/negative-enterprise-value/ )
(https://www.investopedia.com/terms/e/enterprisevalue.asp#:~:text=EV%20tells%20investors%20or%20interested,its%20market%20cap%20and%20debts)
GDP is usually considered to be positive except in Pathological Edge Cases, such as when imports dominate exports by a value that is greater than all other terms in the GDP formulation.
(https://economics.stackexchange.com/questions/57704/can-gdp-ever-be-negative#:~:text=Yes%2C%20theoretically%2C%20GDP%20could%20be,in%20the%20second%20period%20negative)
(https://www.bea.gov/system/files/2020-04/GDP-Education-by-BEA.pdf)
The substitutions required to move from Macro Kaya Identity to Micro Kaya Identity are
Pop —> EMP (“number of employees”)
GDP —> MC (“market capitalization”).
With these substitutions the Micro Kaya Identity is,
MICRO KAYA IDENTITY:
CE =EMP x MC/EMP x TEC/MC x CE/TEC
Let EA = EMP x MC/EMP
Let TECH = TEC/MC x CE/TEC
Then, CE = EA x TECH
which can be rearranged as,
CE/EA = TECH
Again, reduction in this ratio can be called decarbonization; now at a Micro economics level applicable to data centres and other corporate activities that use energy and produce carbon emissions.
Kaya Density Identity
Many corporations, levels of government, and other organizations have operating areas. For example: forests, farms, mines, parks, lakes, municipalities, etc. Similarly buildings, factories, heavy industry zones, data centres can be associated with areas — either the physical structures themselves or the surrounding area they draw inputs from and output emissions to. Even roads and rail lines are associated with areas.
(https://www.streamdatacenters.com/wp-content/uploads/2024/01/SDC-Brief-Landowners-240112.pdf)
(https://www.forthjunction.ca/c-and-e-railway.htm)
(https://www.cbc.ca/news/canada/british-columbia/cp-rail-sues-for-mineral-timber-rights-on-b-c-lands-1.1384714)
Identifying decarbonization efforts relative to an operating area allows us to both compare decarbonization in differently sized areas as well as to aggregate decarbonization efforts across organizations operating on a common land base.
Macro: Let PEOPLE = Pop
Macro: Let EA = PEOPLE x GDP/PEOPLE
Micro: Let PEOPLE = EMP
Micro: Let EA = PEOPLE x MC/PEOPLE
Let TECH = TEC/EA x CE/TEC
So that, CE = EA x TECH
Normalize by area so that ,
KAYA DENSITY IDENTITY:
CE /AREA = (PEOPLE x EA/PEOPLE x TEC/EA x CE/TEC)/AREA
Then ,
(CE/AREA)/(EA/AREA) = TECH/ AREA
Simplifying to
CE/EA = TECH/ AREA
Again, reduction in the ratio CE/EA indicates Decarbonization.
To normalize by area, all base variables in the equation have to be referrable to the same areas via spatial operations on polygons (or rasters), and to a specific organization There are a number of standard ways to achieve this in vector and raster based GIS systems via a small set of spatial operations, which we will detail in a future post. Each polygon (or raster cell) has Kaya Density Identity calculated separately by organization. Spatial and Organizational aggregation then allows roll ups across land bases.
Kaya Power Density Identity
David JC MacKay notes in his excellent primer on sustainable energy that
“People use the two terms energy and power interchangeably in ordinary speech, but in this book we must stick rigorously to their scientific definitions. Power is the rate at which something uses energy.”
(https://www.withouthotair.com/download.html ; pg 24)
POWER = ENERGY/TIME
MacKay provides an apt visual/physical analogy on the same page: “Energy is like water volume, power is like water flow”.
The Power Industry expresses Demand and Generation most often in terms of Power, so it is useful to express the Kaya Identity in those terms.
POWER = TEC/Time
Within the notation we have developed for Kaya Density Identity,
Macro: Let EA = PEOPLE x GDP/PEOPLE
Micro: Let EA = PEOPLE x MC/PEOPLE
Let TECH = POWER/EA x CE/POWER
So,
KAYA POWER DENSITY IDENTITY:
CE /AREA = (PEOPLE x EA/PEOPLE x POWER/EA x CE/POWER)/AREA
Then,
(CE/AREA)/(EA/AREA) = TECH/ AREA
Simplifying to,
CE/EA = TECH/ AREA
Decrease of this ratio being coincident with decarbonization, now expressed in terms of Power Density (Power/Area ~ Watts/ m**2)
The Kaya Power Density Identity allows the Kaya Identity to be re-expressed in terms of Power and then via normalizing by Area allows the ratios involving power to be expressed as flux variables, similar to other flux variables used in meteorology.
It also allows incorporation of grid demand and generation information in the power units they are commonly expressed inq, such as MW.
(http://ets.aeso.ca/Market/Reports/Manual/AiesGraphs/24_month_supply_and_demand.html)
(http://ets.aeso.ca/ets_web/ip/Market/Reports/CSDReportServlet)
Further Kaya Identity Variations And Use Cases
This post develops variations of the Kaya Identity that extend its application to tracking decarbonization efforts in a wider set of use cases while maintaining a time tested interpretation system. We will follow up with empirical worked examples of how to apply the Kaya Identity to Data Centers to track decarbonation efforts of cloud/AI infrastructure companies and other organizations building out, managing, and monitoring Data Center contributions to power demand and carbon emissions. We plan to further extend the Kaya Identity approach so it can track decarbonization across supply chains (directed networks). Consider the supply chain required for data centers, including: the manufacturing plants that build the chips, the mining operations that source raw materials for the chips, the supply chain of materials required for the physical buildings and cooling and control systems. Decarbonization does not happen in isolation but in the context of procurement supply chains.
Another use case is application of the Kaya Identity approach to landscape level carbon emissions measurement and mitigation efforts. Landscape level efforts across multiple organizations can have a common accounting framework via the Kaya Density Identity; when applied to grid scale decarbonization efforts, via Kaya Power Density Identity.
One particular use case of interest to myself (originally trained as a forester) is the carbon release due to wildfires and carbon capture through healthy forest stand growth and sustainable harvest strategies.
Other applications include empirical methods to evaluate carbon credit systems.
Finally, the motivation behind our current transformation to a renewable energy grid is decarbonization to mitigate climate change and to reduce our dependency on fossil fuels. The Kaya Identity approach provides a mathematical framework from which to develop practical methodology to evaluate if our efforts to evolve our energy grids are having their intended effects on decarbonization; and to course correct if not. Of course, there is much work to do to go from Math to Methodology to Decision Process. We make moon shots not in a single arc, but through many mid course corrections. Evolving the complex system that is our electrical grid infrastructure is likely more difficult than steering a projectile through space; but moon shot remains an apt label reflecting a challenge that requires keeping our eye on the destination in the face of many obstacles .
And we will need a bit of care to avoid tripping over Goodhard’s law.
(https://en.wikipedia.org/wiki/Goodhart%27s_law)
(https://www.ribbonfarm.com/2016/06/09/goodharts-law-and-why-measurement-is-hard/)
Ultimately, the Kaya Identity approach is effective because it mathematizes some core physical, economic, and demographic factors that must be balanced to achieve a trifecta of economic, environmental, and technological progress. Its core ideas can be stated simply as a sentence. Repeating Pielke’s mnemonic from the beginning of this post,
“People engage in economic activity that uses energy from carbon emitting generation”
The Kaya Identity approach to Decarbonization is the mathematization of common sense.
From Math to Methodology
We have now gone through several Kaya variations -- introducing ways to extend the classic Kaya Identity so it can be applied to a wider variety of use cases. Just as the Classic Kaya equation had to be incorporated into measurement, prediction, and decision methodologies to be effective as a pragmatic tool(s) leveraged by the IPCC, and other organizations -- the same effort will be required to extend the Kaya Variants from mathematics to pragmatic methodology tracking Decarbonization in Data Centres and to other use cases, to identify when we are making progress on Decarbonization, when we are not, and how to weigh alternate options via the Kaya Identities quartet of tools/options (see annotated Deeper Dive).
Stay Tuned.
If you would like to help work out methodology based on the Kaya Identity Variations -- feel free to drop us a line directly or in comments/notes in Bits and Bytes of Climate Science and start a conversation.
Annotated Bibliography
For Those Interested in a Deeper Dive into Kaya Identity, Decarbonization, and Climate Change.
The Climate Fix. 2010. By Roger Pielke Jr.
See “Decarbonization Math” section in Chapter 3, “Decarbonization of the Global Economy”. This chapter introduces the Kaya identity and then uses it (in the current and following chapters) as a probe of how global economies are making progress (or not) on Decarbonization. On page 70, Pielke likens the Kaya Identity as pointing towards tools for Decarbonization. Paraphrasing slightly, the four tools are:
reducing population,
reducing economic activity per capita,
increasing efficiency,
switching to energy sources with lower carbon density.
Craftsmanship comes into how societies, and organizations orchestrate these tools through advocacy, policy, technology and business practices.
The Rightful Place of Science: Disasters and Climate Change. 2nd Edn. 2018. By Roger Pielke Jr.
The Kaya Identity is introduced in Chapter 6, “What About Climate Policy and Politics” as “The Only Equation You Need to Know”. This chapter introduces “the iron law of climate policy” which is that (paraphrasing) people have limited price tolerance towards achieving environmental objectives. From this iron law, Pielke draws — via the Kaya Identity — a surprisingly simple threshold for the environmental objective of Decarbonization: “To achieve a stabilization of carbon dioxide in the atmosphere requires that more than 90 % of the energy that we consume comes from carbon-free sources, such as nuclear, wind, or solar, or even coal or gas with carbon capture and storage”. Perhaps a good initial threshold for Tech companies scaling out Data Centres with an eye towards self imposed rather than regulated thresholds. As an aside, the subtitle of this post is a riff on Chapter 5’s title, “Heat, Rain, Hurricanes, Floods, Tornadoes, Drought, Oh My”
The Honest Broker. Making Sense of Science in Policy and Politics. 2007. Roger Pielke Jr.
While not about the Kaya Identity per se, this book has great coverage of methodology, policy, and political issues behind science informed decision processes. That is the gap between equations and measurements on the science side and how they can guide decisions that have to navigate through business, policy, and political terrain. It has also inspired a blog of the same name, “The Honest Broker”.
The Honest Broker Blog has a good series of recent (2022 - 2024) posts on the Kaya Identity that updates the book length works cited above, carrying forward, and refining many of the themes and methodologies in the books, while also bringing in recent cases and data. Relevant recent posts include:
20220808:
20220829:
20240304:
20240404:
20240513:
20240801:
20240809:
20240812:
Power Density. A Key to Understanding Energy Sources and Uses. 2015. Vaclav Smil.
A book length exposition of Smil’s approach to Power Density (W/m**2) to evaluate a wide range of energy sources from nuclear to fossil fuels to renewables with an emphasis on how to construct power density calculations for specific use cases and how to compare power density values across use cases, and in the context of energy transitions.
Sustainable Energy - Without the Hot Air. 2009. David JC MacKay.
An introduction to the fundamental calculations in energy, costs, and emissions that allow comparison of various sources of sustainable energy to each other and to fossil fuels. I tend to use Sustainable Energy and Power Density in tandem. Overlapping concerns, but differing perspectives. Sustainable Energy has a clear focus on accurate measurements and calculations, identification of assumptions, and worked out empirical cases. Similar concerns also drive Pielke’s work, and is the methodological theme of “The Honest Broker” book and blog. Sustainable Energy is available online at : https://www.withouthotair.com/download.html
The Whole Story of Climate. What Science Reveals About the Nature of Endless Change. 2019. E. Kirsten Peters.
Excellent background on the deep history of earth’s climate, and climate processes (aka climate science) that introduces the discovery of, and early mitigation attempts for global warming. Chapter 11, “Global Warming Discovered” introduces the several lines of evidence of rising carbon : increases in airborne carbon from the 1960s forward, ice core studies that show coincident rises and falls in temperature and carbon dioxide and carbon monoxide over 420,000 years with a rapid rise of temperature and carbon levels in modern times. Chapter 12, “Leaving the Garden” describes the early interplay of climate science, energy policy, and politics up to 2012. The “Epilogue for the Paperback Edition” updates the state of current affairs to 2019, right before COVID, and takes us to the cusp of rapid rise of Data Centres both during and post-COVID which happened soon after The Whole Story of Climate was published.
Environment, Energy, and the Economy. Strategies for Sustainability. 1997. Edited by Y. Kaya and K Yokobori.
Proceedings of a 1993 conference that introduces the Kaya Identity to a larger audience. If you wish to see the origin of themes that currently reverberate through the renewable energy transition that electrical grids worldwide are currently evolving through, this is as good a starting point as any. Chapter 4, “Environment, Economy, Energy and Sustainable Development” introduce the main themes. Chapter 13, “Decarbonization as a Long Term Energy Strategy” introduces the Kaya Identity:
“In general, the instrumental determinants of future energy-related CO2 emissions can be described by the Kaya identity. The Kaya identity establishes a relationship between population growth, per capita value added, energy per unit value added and CO2 emissions per unit of energy on one side of the equation, and total carbon dioxide emissions on the other.”
This book is out of print, but often available for under $30 CAN at used book sellers.
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SOURCE POST & GENERATED PODCAST
The content of this “Kaya Variations” post is a bit more arithmetic oriented, and there are (to my ear) some infecilities to the interpretation in the podcast. But I am the author, so may either know too much or be subject to bias towards analogies summarizing the math that differ from the ones I chose to use.
Listen to the podcast and read the post. Or read the post then listen to the podcast. Please let me know what you think directly, or share in the comments.
Is the podcast “translating” the post with veracity.
Or is it “riffing” off the post like a jazz AI?
This issue of what is brought from a source to a translation is one that has long been considered by translators of poetry and prose. Perhaps it now needs to be considered in the context of generated text where an automaton rather than a human is the translator.
https://russianlife.com/the-russia-file/pasternak-a-great-translator-reflects-on-translation/