the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Emulating chemistry-climate dynamics with a linear inverse model
Abstract. Coupled chemistry–climate models (CCMs) are powerful tools for investigating chemical variability in the climate system, but high computational cost limits their use for hypothesis testing and adequately sampling variability on long timescales. Here, we present the first application of a linear inverse model (LIM) to emulate a CCM. A LIM is a lowdimensional empirical model that reproduces the CCM’s statistics and dynamics at low computational cost. By linearizing the CCM’s dynamics, the LIM captures coherent modes of variability, such as the El Niño Southern Oscillation (ENSO), that describe the coupled evolution of physical and chemical fields. Deterministic seasonal forecasts of the LIM result in skillful predictions of physical and chemical variables at lead times up to a year, outperforming damped persistence models. We show that the LIM’s skill in chemical fields depends on its coupled chemistry–climate modes: forecasts without the ENSO dynamical mode show a substantial loss of skill, suggesting the importance of ENSO in driving predictable chemical variability. These results demonstrate that the LIM can efficiently emulate CCM dynamics. It offers a practical tool for testing hypotheses about the drivers of chemistry-climate interactions and may enable efficient chemical data assimilation in the future.
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- RC1: 'Comment on egusphere-2025-3258', Anonymous Referee #1, 28 Aug 2025
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RC2: 'Comment on egusphere-2025-3258', Anonymous Referee #2, 28 Aug 2025
In “Emulating chemistry-climate dynamics with a linear inverse model” the authors use 3000 years of a GFDL-CM3 simulation to train a linear inverse model (LIM). The resultant model is capable of reproducing internal modes of climate variability (e.g., ENSO) and accurately representing the relationship between these climate modes and ozone and the hydroxyl radical. The value of this empirical model lies with its computational efficiency, which should allow for potential studies that are unfeasible with traditional, physics-based climate models, and as such, this is a valuable contribution to the effort to understand drivers of variability in the hydroxyl radical. The article is well-reasoned and well-written and is suitable for publication in its current state. One minor comment is listed below.
Line 180: Why does LIM performance fall off at the extreme ends of the frequency range? Is there a way to improve this? What are the implications of this for OH? Would this limit applicability of this methodology to trying to understand impacts of something like the Madden Julian Oscillation?
Citation: https://doi.org/10.5194/egusphere-2025-3258-RC2 -
AC1: 'Response to reviewer comments', Eric Mei, 23 Sep 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-3258/egusphere-2025-3258-AC1-supplement.pdf
Status: closed
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RC1: 'Comment on egusphere-2025-3258', Anonymous Referee #1, 28 Aug 2025
General Comment:
This manuscript presents an innovative application of the Linear Inverse Model (LIM) to a coupled chemistry–climate model for predicting variations in atmospheric composition in response to climate variability. The approach is novel, the manuscript is clearly written and well structured, and the method provides a computationally efficient framework for diagnosing variability in atmospheric composition. Overall, I find this work to be a valuable contribution to the field and recommend it for publication in ACP after the authors consider the following minor comments.Specific Comments:
- LIM has been widely and successfully used to predict internal climate variability, such as ENSO. However, its applicability becomes more limited when dealing with rapidly evolving external forcing. For atmospheric composition, external drivers such as anthropogenic and biomass burning emissions can undergo substantial short-term variations, which may challenge LIM’s predictive skill. I suggest that the authors explicitly discuss LIM’s strengths (e.g., robust performance for processes dominated by linear dynamics like ENSO) and limitations (e.g., reduced reliability under strongly time-varying external forcing) in the introduction and discussion sections. Such a discussion would provide a clearer perspective on the contexts in which LIM is most suitable for predicting atmospheric composition changes
- Figure 2a: It is not entirely clear whether the OH anomalies predicted by LIM and those simulated by GFDL-CM3 exhibit synchronous temporal variability or if they only match in terms of amplitude. Including a quantitative measure of agreement, such as the correlation coefficient between the two, would significantly enhance the evaluation of LIM’s predictive capability.
- Line 211-224: The authors show that LIM captures the variations of OH and ozone associated with the ENSO mode phase. It would strengthen this analysis to also present the corresponding ENSO-related OH and ozone responses simulated by GFDL-CM3. Such a comparison would allow a more direct assessment of LIM’s ability to reproduce the underlying relationships captured by the full chemistry–climate model.
- Line 249: The manuscript uses the CE metric to evaluate LIM’s forecast skill. Are there commonly accepted thresholds for interpreting CE values? For example, a 3-month OH forecast skill of 0.17(figure 5), does this indicate a reasonably skillful forecast, or does it suggest limited predictive capability? Providing a brief explanation or reference regarding commonly accepted benchmarks for CE would help readers better assess the significance of the reported forecast skill values.
Citation: https://doi.org/10.5194/egusphere-2025-3258-RC1 -
RC2: 'Comment on egusphere-2025-3258', Anonymous Referee #2, 28 Aug 2025
In “Emulating chemistry-climate dynamics with a linear inverse model” the authors use 3000 years of a GFDL-CM3 simulation to train a linear inverse model (LIM). The resultant model is capable of reproducing internal modes of climate variability (e.g., ENSO) and accurately representing the relationship between these climate modes and ozone and the hydroxyl radical. The value of this empirical model lies with its computational efficiency, which should allow for potential studies that are unfeasible with traditional, physics-based climate models, and as such, this is a valuable contribution to the effort to understand drivers of variability in the hydroxyl radical. The article is well-reasoned and well-written and is suitable for publication in its current state. One minor comment is listed below.
Line 180: Why does LIM performance fall off at the extreme ends of the frequency range? Is there a way to improve this? What are the implications of this for OH? Would this limit applicability of this methodology to trying to understand impacts of something like the Madden Julian Oscillation?
Citation: https://doi.org/10.5194/egusphere-2025-3258-RC2 -
AC1: 'Response to reviewer comments', Eric Mei, 23 Sep 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-3258/egusphere-2025-3258-AC1-supplement.pdf
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General Comment:
This manuscript presents an innovative application of the Linear Inverse Model (LIM) to a coupled chemistry–climate model for predicting variations in atmospheric composition in response to climate variability. The approach is novel, the manuscript is clearly written and well structured, and the method provides a computationally efficient framework for diagnosing variability in atmospheric composition. Overall, I find this work to be a valuable contribution to the field and recommend it for publication in ACP after the authors consider the following minor comments.
Specific Comments: