State-of-the-art decomposition tools to help integrated assessment modelers better understand and assess their results

TLDR: Below you can download a new open-source python package for calculating and comparing key drivers of emissions using outputs from Integrated Assessment Models.

In 2004-2006 I served on the dissertation committee of Holmes Hummel at Stanford University. Holmes's thesis showed how a commonly used identity (called the Kaya Identity) could enable deeper understanding of the energy-sector outputs from Integrated Assessment Models (IAMs). These models help analysts assess key drivers affecting energy use and emissions in long term greenhouse gas emissions scenarios.

The most common version of the Kaya Identity is the four factor version, which reads as follows:

Four factor Kaya identity, showing how energy-sector CO2 emissions relate to population, wealth per person, primary energy use per dollar, and carbon intensity of primary energy, respectively.

As Holmes showed, the four factor Kaya identity masks complex system dynamics in energy scenarios, so she created a more comprehensive version, which in its fully developed form looks like this (see Koomey et al. 2019, below):

Expanded Kaya identity, showing how energy-sector CO2 emissions relate to population, wealth per person, final energy use per dollar, energy supply loss factor, the fraction of primary energy supplied by fossil, fuels, the carbon intensity of fossil fuels supplied, and the net emissions of CO2 from energy sector after sequestration, respectively.

Holmes finished and defended her dissertation in December of 2006. I and a few others used her tools and it soon became clear that some additional tweaking was needed. Over many years, Holmes, John Weyant, my colleague Zachary Schmidt, and I developed the analytical tools more fully, which culminated in our 2019 refereed journal article laying out the theory and methods supporting this work:

Koomey, Jonathan, Zachary Schmidt, Holmes Hummel, and John Weyant. 2019. "Inside the Black Box:  Understanding Key Drivers of Global Emission Scenarios." Environmental Modeling and Software. vol. 111, no. 1. January. pp. 268-281. [https://www.sciencedirect.com/science/article/pii/S1364815218300793]

One of the key additions was summarizing emissions for all sectors, including the energy sector (as characterized in the expanded Kaya identity), land use, industrial process CO2 emissions, biomass carbon capture and storage (CCS), and emissions of other gases than CO2 (like CH4, N2O, and F-gases). This fully expanded decomposition, which characterizes total carbon equivalent emissions is summarized in this equation:

C for fossil fuels comes from the equation above. The negative term for CS is carbon sequestration from biomass combustion. For scenarios including direct air capture, an additional negative term for that option would also need to be added.

We applied these tools to two scenarios in our 2022 refereed journal article:

Koomey, Jonathan, Zachary Schmidt, Karl Hausker, and Dan Lashof. 2022. "Exploring the black box: Applying macro decomposition tools for scenario comparisons." Environmental Modeling and Software. vol. 155, September. [https://doi.org/10.1016/j.envsoft.2022.105426]

Holmes built her initial tools in Excel workbooks, and these served well for years, but it proved hard to convince modelers to integrate spreadsheets into their workflows, which were largely automated using Python and other more modern tools. With that reality in mind (and with funding from World Resources Institute) we set out to recreate our tools as a Python package that modelers could just grab and use.

Today we are releasing that Python package for general use.

Virtually all IAMs generate the required data to use our tools, and we stuck closely to the terminology and definitions embodied in IIASA's PYAM tools.

To download the Python package directly from PyPI, click here.

To view the Github project page, where you can also download the package, click here.

To view an example notebook in Github showing how to use the tools, click here.

The Python package is licensed under Apache 2.0, which is an open-source license that allows free use, modification, and distribution for commercial or private use. Any contributors automatically grant a royalty-free license to any patented algorithms they add to the software.

To view example dashboards generated by these tools, go here.

We are confident that these tools will facilitate analysis of IAM-based scenarios, assist in troubleshooting those scenarios, and increase understanding of key drivers affecting greenhouse gas emissions

Please do email us if you have questions or suggestions.

Jonathan Koomey

Zachary Schmidt


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Koomey researches, writes, and lectures about climate solutions, critical thinking skills, and the environmental effects of information technology.

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