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:

1. 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
2. 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.
3. 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.
4. 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.

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?