General response:

We thank the reviewer for finding our work interesting. We acknowledge the need for improved clarity and have addressed these areas to avoid overstatements. Your comments regarding the need for more detailed explanations (e.g., data preprocessing, seasonal differences), suggestions to improve the clarity of figures, and recommendations to streamline the presentation of results have helped us better communicate the core findings of this work. We have carefully addressed each of your specific comments and made the corresponding revisions to the manuscript.

Comment 1 (Section 2.2 preprocessing):

Thank you for highlighting this. We will revise Section 2.2 to include a detailed explanation of our detrending and anomalization, specifying that the pre-processing includes an initial linear detrending on a grid-cell basis, followed by anomaly calculation using a long-term daily climatology (correcting the original typo regarding monthly means). The anomalies are calculated by subtracting each day's mean and standard deviation. Those steps are essential because, while SLP data is largely stationary even under historical forcing (Nowack et al. 2020), it is necessary to remove any small trends to ensure robust causal discovery. The causal discovery method relies on the assumption of stationarity to accurately identify dependencies, making this pre-processing a prudent step.

Comment 2 (Section 2.2 seasonality):

The motivation for analyzing each season separately (DJF, MAM, JJA, SON) was to examine seasonal variability in causal dependencies. We acknowledge that detrending and anomalizing remove some seasonal trends; however, the seasonal differences in climate dynamics are still substantial. For example, the Principal Component Analysis (PCA) with Varimax rotation reveals that the components shift significantly between seasons (see Fig. A1 and A2). Consequently, the causal networks of the components also change substantially between seasons, further justifying a seasonally separate approach. In the paper, we found consistent results across all seasons in terms of detecting model similarities and performance, which supported the use of annual F1-scores averaged over seasons in the main findings (see for example Fig. 2).

However, to better address this point, we have discussed these results more explicitly in the text. Additionally, we have included supplementary figures (similar to Fig. 2 but for seasonal F1-score) to illustrate the similarity of F1-scores and model rankings across seasons, providing further support for our approach.

Comment 3 (Figure 1):

Thank you for noting the font size in Figure 1. We agree that the small text may be difficult to read. To address this, we have removed all tiny fonts from the figure, focusing solely on its illustrative purpose. This simplification improves clarity while maintaining the figure's intended role.

Comment 4 (Results Sections 3.1 and 3.2):

Thank you for your suggestion. We agree that the result sections for Step 1 and Step 2 could be shortened. We have combined section 3.1 and 3.2 and moved the detailed discussion of the appendix figures (A1, A2, B1, B2, C1 and C2) to the appendix itself, keeping the main text more concise and focused. Following these changes, the "main results" appear earlier in the main text.

Comment 5 (Figures B1 and B2):

Thank you for your comment. The caption for Fig. B1 incorrectly listed ERA5 instead of NCEP/NCAR, and we have corrected this. However, we could not combine Figures B1 and B2 into a single figure with overlapping arrows because the modes and their positions on the map differ between the two figures. Instead, we have regrouped the figures into a single figure with two subfigures (B1 and B2). Additionally, to better highlight the differences, we have changed the color of the causal dependencies in Figure B2 (ERA5) to red arrows, making it easier to understand that the datasets differ between the subfigures.

Comment 6 (Figure 2):

We agree that consolidating Figure 2 into a single bar chart with distinct colors would improve readability. We have implemented this suggestion.

Comment 7 (Line 298):

The phrase is indeed redundant. We have rephrased it to: "Models with shared developmental features exhibit higher causal network similarity, likely due to their comparable dynamical representations".

Comment 8 (Line 309 and Figure 4):

We agree that the term "strong" may overstate the relationship. We have adjusted the language in the manuscript to reflect the statistical significance without overstating the strength, rephrasing it to indicate "an approximately parabolic relationship over the space of opportunities covered by CMIP6 models."

To improve interpretation, we have included confidence intervals around the parabolic fit in Figure 4 and adjusted the non-significant blue line to a dotted line.

Comment 9 (Line 320):

We have specified in the text that we refer to the x-axis in Figure 4 and use "peak" instead of "distinct peak" (line 322).

Comment 10 (Line 325):

"Previous findings" here refer specifically to results within this study. We have clarified this in the text to prevent misinterpretation.

Kind regards,

The authors.

Reference:

Nowack, P., Runge, J., Eyring, V., & Haigh, J. D. (2020). Causal Networks for Climate Model Evaluation and Constrained Projections. Nature Communications, 11, 1415. https://doi.org/10.1038/s41467-020-15195-y .

General response:

We thank the reviewer for their thoughtful and constructive comments, which have helped us evaluate and enhance the robustness and clarity of our study. Your feedback, particularly regarding the robustness of our weighting method, the role of internal variability, and the role of additional variables to constrain precipitation, has led to significant improvements in the manuscript. Below, we respond to each of your individual comments.

Comment 1 (Section 2.2 preprocessing):

We have extended the explanation of the pre-processing section to clarify the detrending and anomalizing approach. We have revised Section 2.2 to clarify that the pre-processing includes an initial linear detrending on a grid-cell basis, followed by anomaly calculation using a long-term daily climatology (correcting the original typo regarding monthly means). The anomalies are calculated by subtracting each day's mean and dividing by the standard deviation. Those steps are essential because, while SLP data is largely stationary even under historical forcing (e.g., Nowack et al. 2020), it is necessary to remove any small trends to ensure robust causal discovery. The causal discovery method relies on the assumption of stationarity to accurately identify dependencies, making this preprocessing a prudent step.

Comment 2 (Section 3.5):

We are not entirely certain if we fully understood the reviewer’s suggestion. Do you mean a leave-one-model-out approach to test whether the incorporation of an additional variable in the weighting could lead to an improvement? Alternatively, could the suggestion involve evaluating the causal networks against networks derived from one of the other models treated as a "ground truth," and assessing whether constrained projections move closer to that model?

In our study, to avoid overconfidence in weighting, a “perfect model” calibration approach was used, specifically tuning the performance shape parameter. This method evaluates robustness by treating each model iteratively as “truth,” ensuring weighted projections are not overconfident.

We acknowledge the limitation of using only SLP for the causal weighting scheme and mention future research plans to incorporate additional diagnostics such as temperature, following precedents in emergent constraints on global precipitation (e.g., Dai et al., Shiogama et al.). This multi-diagnostic approach could improve precipitation projections further by addressing model differences more comprehensively. In addition, we acknowledge that the dynamical aspects covered by the causal networks constrain only part of the drivers of precipitation. However, this focus on a dynamical quantity such as SLP was intentional, as incorporating thermodynamic quantities like surface temperature would make the causal networks far less stationary. Building multivariate causal networks that include thermodynamic variables would require significant methodological adjustments and is beyond the scope of this study. We recognize this as an important direction for future research.

Comment 3 (Internal variability):

We appreciate the reviewer highlighting the critical role of internal variability in our analysis. We recognize that both the observational data and the climate model simulations contain internal variability, which can introduce noise and potentially bias the comparison between models and observations. To mitigate its influence, multiple ensemble members for each model were processed, with causal networks derived independently for each. The final F1-scores represent an ensemble average, which reduces the variability effects by smoothing out member-specific results. Recognizing that reanalysis datasets themselves are subject to internal variability and measurement uncertainties, we have analyzed multiple reanalysis products (ERA5 and NCEP/NCAR). Although not eliminating internal variability completely, this approach provides a more robust comparison by reducing noise from individual ensemble members. We have added this clarification on how we account for internal variability in the main text of the paper.

Additionally, we note that internal variability itself offers opportunities to learn about the robustness of our method. Specifically, we have found differences between the causal networks of the models, which were shown to be larger than the differences between the causal networks across ensemble members of individual models. This supports the idea that the differences we capture are meaningful and not purely due to internal variability. This finding aligns with results from previous work (Nowack et al., 2020), where this was demonstrated clearly.

Kind regards,

The authors.

Reference:

Dai, P., Nie, J., Yu, Y., & Wu, R. (2024). Constraints on Regional Projections of Mean and Extreme Precipitation under Warming. Proceedings of the National Academy of Sciences, 121, e2312400121. https://doi.org/10.1073/pnas.2312400121

Nowack, P., Runge, J., Eyring, V., & Haigh, J. D. (2020). Causal Networks for Climate Model Evaluation and Constrained Projections. Nature Communications, 11, 1415. https://doi.org/10.1038/s41467-020-15195-y .

Shiogama, H., Watanabe, M., Kim, H., & Hirota, N. (2022). Emergent Constraints on Future Precipitation Changes. Nature, 602, 612–616. https://doi.org/10.1038/s41586-021-04310-8