the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Impulse response functions as a framework for quantifying ocean-based carbon dioxide removal
Abstract. Limiting global warming to 2 °C by the end of the century requires dramatically reducing CO2 emissions, and also implementing carbon dioxide removal (CDR) technologies. A promising avenue is marine CDR through ocean alkalinity enhancement (OAE). However, quantifying carbon removal achieved by OAE deployments is challenging because it requires determining air-to-sea CO2 transfer over large spatiotemporal scales–and there is the possibility that ocean circulation will remove alkalinity from the surface ocean before complete equilibration. This challenge makes it difficult to establish robust accounting frameworks suitable for an effective carbon market. Here, we propose using impulse response functions (IRFs) to address such challenges. We perform model simulations of a short-duration alkalinity release (the “impulse”), compute the resultant air-sea CO2 flux as a function of time, and generate a characteristic carbon uptake curve for the given location (the IRF). Applying the IRF method requires a linear and time-invariant system. We attempt to meet these conditions by using small alkalinity forcing values and creating an IRF ensemble accounting for seasonal variability. The IRF ensemble is then used to predict carbon uptake for an arbitrary-duration alkalinity release at the same location. We test whether the IRF approach provides a reasonable approximation by performing OAE simulations in a global ocean model at locations that span a variety of dynamical and biogeochemical regimes. We find that the IRF prediction can typically reconstruct the carbon uptake in continuous-release simulations within several percent error. Our simulations elucidate the influences of oceanic variability and deployment duration on carbon uptake efficiency. We discuss the strengths and possible shortcomings of the IRF approach as a basis for quantification and uncertainty assessment of OAE, facilitating its potential for adoption as a component of the carbon removal market’s standard approach to Monitoring, Reporting, and Verification (MRV).
- Preprint
(5706 KB) - Metadata XML
- BibTeX
- EndNote
Status: open (until 23 Oct 2024)
-
CC1: 'Comment on egusphere-2024-2697', Benoit Pasquier, 16 Sep 2024
reply
I just stumbled on this article and noticed a few issues with the maths that I thought I should point out to the authors in case it is useful:
- Eq. (1) misdefines the Dirac delta function δ, of which the value at 0 is not 1. The Dirac δ does not have a finite value at 0 and is not technically a function. The Dirac δ is instead a "generalised" function, or more specifically a "distribution". It cannot be defined the way Eq. (1) is written. While the first line of Eq. (1) is correct (the Dirac δ is 0 everywhere except at 0), the second line is incorrect and should be replaced with its integral over the entire real line being equal to 1: ∫ δ(t) dt = 1.
- Eq. (2) uses the discrete summation symbol ∑, which seems to suggest that t is an integer, which does not seem correct to me. Why not use the integral notation, x(t) = ∫ δ(t') x(t') dt', instead?
- Eq. (3) could work without the intermediate equality (the one with the summation symbol ∑)
- Eq, (3) and throughout the paper, parentheses must be placed around the functions being convoluted, as in (x ∗ h)(t) instead of x(t) ∗ h(t), the latter being easily confused for simple multiplication otherwise.
This looks like a timely and worthy article otherwise!
Benoît PasquierCitation: https://doi.org/10.5194/egusphere-2024-2697-CC1 -
AC1: 'Reply on CC1', Elizabeth Yankovsky, 16 Sep 2024
reply
Hello Benoît, thank you very much for your comments. We will make these corrections to the manuscript.
Citation: https://doi.org/10.5194/egusphere-2024-2697-AC1 -
CC2: 'Reply on AC1', Benoit Pasquier, 18 Sep 2024
reply
No worries!
Apologies, there is a typo in my comment for Eq. (2): it should be x(t) = ∫ δ(t - t') x(t') dt' instead of x(t) = ∫ δ(t') x(t') dt'.
Good luck with the review!
Citation: https://doi.org/10.5194/egusphere-2024-2697-CC2
-
CC2: 'Reply on AC1', Benoit Pasquier, 18 Sep 2024
reply
-
AC1: 'Reply on CC1', Elizabeth Yankovsky, 16 Sep 2024
reply
Viewed
HTML | XML | Total | BibTeX | EndNote | |
---|---|---|---|---|---|
493 | 79 | 14 | 586 | 2 | 1 |
- HTML: 493
- PDF: 79
- XML: 14
- Total: 586
- BibTeX: 2
- EndNote: 1
Viewed (geographical distribution)
Country | # | Views | % |
---|
Total: | 0 |
HTML: | 0 |
PDF: | 0 |
XML: | 0 |
- 1