1)  We thank the reviewer for this comment. The NRMSE was calculated between the loadings and scores from the models and the ERA5. For example, the X score of model A had its correlation calculated with the X score of ERA5, and so on. That means, we calculated scores and loadings separately and after that, we used RMSE normalisation. 

It is not the case that loadings have more features, because the lat-lon points were interpreted as samples, so correlation here is a metric of similarity between the loadings maps; it is important to recall that loadings do not have the time dimension. Scores, on the other hand, only have the time dimension, so correlation measures the similarity of the time series between pairs of scores.

We realise that this may cause confusion, so we expanded the explanation in the revised manuscript.

2)  Only the first four modes of the PLS were performed, but additional iterations could have been applied. It is possible to compute the explained variance by reconstructing the full dataset based on the scores and comparing it to the original dataset. Although we appreciate the question, this is without the scope of analysis of this work because the goal of the PLS is to retain the maximum co-variance between the two datasets rather than  explaining the variance of only one dataset.

3)  In most models, the first component corresponds to the ENSO pattern. Due to the PLS method, it was decided to use the same component for each comparison, not mixing patterns from component 1 and component 2. We thank the reviewer for the suggestion and will be including an Annex with the individual figures for the first two components of each climate model. 



4)  Thanks for raising that question, we have improved the discussion in the revised manuscript of the underlying assumptions and its possible shortcomings. We believe that it is true that models with dynamics more similar to reality will result in PLS scores and loadings closer to the reanalysis. This belief is based on the fact that the PLS seeks for relationships between SST patterns and precipitation patterns and that these relationships are physically mediated by the atmospheric dynamics; therefore, models with a more accurate representation of atmospheric dynamics should yield PLS components closer to the reanalysis.

However, as with any data driven methodology, there could be instances where there are confounding factors influencing our interpretation. To mitigate that, we will provide a clearer and more complete discussion of these pitfalls.

5) Thank you for pointing this out. We decided not to discuss these components for conciseness. We have included in the Annex components 3 and 4 for ERA5.

6)  Table 2:  We thank the reviewer for raising this point. Firstly, it is useful to remind that the goal of the method is not to select models that better represent the climate system as a whole, but rather the ones that perform better at the task of simulating the impacts on Brazilian rainfall. 

The high weight of GFDL-ESM4 indicates that this model performs well in representing the overall components more accurately when compared to other models. While it is true that component 1 relates to the ENSO dynamics, the overall evaluation takes into components that represent other important forcings of the Brazilian precipitation regime. For example, the Atlantic SST variability drives the Brazilian precipitation variability in the Amazon (Yoon and Zeng, 2010), Northeast Brazil (Hastenrath and Greischar, 1992) and subtropical regions (Perez et al., 2022). 

Furthermore, by including multiple components in the analysis, we acknowledge that climate dynamics are multifaceted, and a comprehensive evaluation should account for more than just the primary modes of variability like ENSO. Thus, GFDL-ESM4's performance signifies its robustness in capturing these diverse aspects effectively. This approach rests on the importance of a holistic evaluation of model performance across various components, rather than focusing solely on the primary modes.

Yoon, Jin-Ho, and Ning Zeng. "An Atlantic influence on Amazon rainfall." Climate dynamics 34 (2010): 249-264.

Perez, Gabriel MP, et al. "Using a synoptic-scale mixing diagnostic to explain global precipitation variability from weekly to interannual time scales." Journal of Climate 35.24 (2022): 8225-8243.

Hastenrath, Stefan, and Lawrence Greischar. "Circulation mechanisms related to northeast Brazil rainfall anomalies." Journal of Geophysical Research: Atmospheres 98.D3 (1993): 5093-5102.

7)  This is a very interesting suggestion, we will include a table in the Annex with the requested information.

8) l128-129:  In the revised manuscript, we have included a p-value testing the significance of the trends in the caption of each figure. We used the word 'strong' to highlight the difference with the second component. In the revised manuscript we reformulated this phrase to be clearer.

9) Fig. 5:  The Figure 5a shows an ensemble median, meanwhile the Figure 5b shows the mean between the models considering the weights from Table 2. Thanks for pointing this out, we have clarified in the revised manuscript.

10) l56: Yes, you are correct! We had an issue with file formatting regarding texts that were subscripted or superscripted. 

11) equation 1: Maybe there is a misunderstanding because of the formatting. In l61 we have:

Cov(ξ₁,ω₁) = max_{॥u॥=॥v॥=1}Cov(Xu, Yv) 

12)  l63-64: The correct is “the first pair of loading matrices is the one in which the corresponding latent vectors ξ and ω are  the most correlated.” Thanks for pointing this out.

13) 162-163: Although the linear trend was observed in most models, it becomes clearer and more robust in the model subset; this directly reflects how sifting models in a mechanistic approach helps reducing the epistemic uncertainties. 

14) l222-223: A number of studies point the intensification and poleward expansion of the Hadley circulation caused by Global Warming (e.g., Hu and Fu (2007)). The South Atlantic Subtropical High is the descending branch of the Hadley Circulation, therefore, its poleward movement and intensification affects precipitation in South America (Carvalho et al., 2011). 

Hu, Y., and Qinjun Fu. "Observed poleward expansion of the Hadley circulation since 1979." Atmospheric Chemistry and Physics 7.19 (2007): 5229-5236.

Carvalho LMV, Jones C, Silva AE, Liebmann B, Silva Dias PL. 2011. The South American Monsoon System and the 1970s climate transition. Int. J. Climatol. 31: 1248–1256, doi: 10.1002/joc.2147.

-- Introduction:

Thanks for the suggestion. We have included more references discussing the links between SST and precipitation in the region, such as Grimm et al. (2000) and Coelho et al. (2002). 

Grimm, Alice M., Vicente R. Barros, and Moira E. Doyle. "Climate variability in southern South America associated with El Niño and La Niña events." Journal of climate 13.1 (2000): 35-58.

Coelho, Caio A. dos S., Cintia Bertacchi Uvo, and Tércio Ambrizzi. "Exploring the impacts of the tropical Pacific SST on the precipitation patterns over South America during ENSO periods." Theoretical and applied climatology 71 (2002): 185-197.

-- Method:

1) We used the expression "maximize the information" as a concise way to convey that the PLS method finds latent variables that represent the maximum covariance between the SST and precipitation. This is done considering all the locations at the same time, rather than the correlation between SST and precip at two different locations as suggested by the reviewer. We have clarified this in the revised manuscript.

2)  In Eq 1, the modes can be seen as the pairs of scores and and pairs of loadings X and Y. In the originally submitted manuscript, there was a formatting problem, the equation was meant to be as follows:

Cov(ξ₁,ω₁) = max_{॥u॥=॥v॥=1}Cov(Xu, Yv).

3) The loading patterns are connected via the scores timeseries. For example, if the SST sign is negative at a certain location and the score sign is positive, it means that it is negatively associated with the corresponding map of precipitation loadings. We have included this expanded explanation in the revised manuscript. 

4) We encountered an issue with file formatting regarding subscripted or superscripted texts, and some mathematical symbols were deleted during the article formatting, which has already been promptly corrected in the revised manuscript. We have also corrected the inconsistencies and included the mathematical symbols where relevant.

5) l93: 

The RMSE is initially calculated for each pair of loadings (models versus ERA5) and scores (models versus ERA5). Then, we normalise the RMSE between 0 and 1 to obtain the NRMSE. Finally, we multiply (1-NRMSE) by the weights in order to obtain a single rank value where higher values are better. 

The weights reflect the importance of each mode through the coefficient of determination in order to reflect how well does a single score represents the original precipitation data, thus favouring “more relevant” modes in the ranking procedure.

This has been described in more detail in the revised manuscript.

-- Present climate results:

1)  Although components 1 and 2 (ENSO and global warming) are crucial, other modes of variability may drive precipitation in Brazil even more directly, such as the Atlantic SST variability mentioned in the previous answer. By including multiple components and weighting them by importance, we acknowledge the complexity and multifaceted nature of the climate system. 

Yes, considering all 4 of them might result in selecting models that behave differently, but this is a desired feature of the analyses because we aim to represent the epistemic uncertainty associated with how different models represent reality. 

2) Thank you for your insightful suggestion. I believe that selecting only models that perform well for Component 1 and Component 2 could underestimate the epistemic uncertainty among the models, and perhaps seem like cherry-picking. However, we appreciate the suggestion and have decided to test running the figures like the reviewer suggested. If it leads to substantial changes in Fig 5b, we will include it in the Supplementary Material. 

3) This question is very interesting! Although not by a large amount, weighting the selected models lead to noticeably less uncertainty hatchings and improving the results overall.

-- Discussion:

1) Thanks for the comment. We also believe that this is not the case, since the procedure was “trained” on past climate data. We will expand on that in the revised manuscript.

2) We thank the reviewer for this suggestion. This was also suggested by Reviewer 1. An expanded discussion of the assumptions and potential limitations will be included in the revised manuscript.

-- Technical corrections: 

Data: We employed anomalies in order to filter out the seasonal variability.

l45: It was a comment to the first question. Thanks for noticing.

L49: We have rephrased this question as ‘’What are the predictions for precipitation in Brazil over the next 30 years based on a mechanistic filtering and weighting procedure?’’

L54: Thanks for your point. We have included this.

L56: Yes. Thanks for noticing, we have clarified in the text. We had an issue with file formatting regarding texts that were subscripted or superscripted. 

L56: Yes, we have corrected in the revised version as ‘The PLS method identifies pairs of latent variable vectors ξ and ω that maximises the information present in X^tY. ‘.

L59-62:  Due to malformatting, the equation was displayed incorrectly in the original manuscript. Eq 1 should be read as: 

Cov(ξ₁,ω₁) =  max_{॥u॥=॥v॥=1} Cov(Xu, Yv)

Where X represents the SST, u represents the SST loadings, Y represents precip and v the precip loadings. The matrix-vector product between X and U yields the scores vector ξ₁ and the product between Y and v yields ω_1. 

L79:  GPCP data have a shorter time period (from 1979) when compared to ERA5 data, which is available since 1950. Since we aimed to investigate interannual/interdecadal variability and climate change, we chose the longer dataset.

L85: Because COBE SST also presents a long temporal availability and is observations-based.

L108-109: Yes, the word uncertainty was misplaced there. The intent was to explain how the mean change is computed. This has been fixed now.

L119: The Amazon region was removed before the PLS analysis so that the magnitude of precip variability there would not dominate the subsequent analyses. We have made this clearer in the revised manuscript.

L120: Precipitation in the Amazon is much higher in magnitude than other regions in the country; it varies almost directly depending on ENSO, tropical Atlantic SSTs and evapotranspiration from trees. Many studies using PCA showed patterns where the Amazon region dominated the analyses. Since this paper was focused on regions more socioeconomially active, we decided to crop out the region to have clearer results in the area of interest.

L139: Thanks for noticing that. It was between 1979-2014, not 1979-2015. We corrected that. 

L140: We have fixed the manuscript for consistency. The maps show the loading matrices, which correspond to the saliences of PLS analyses computed as correlations. So the terms are somewhat interchangeable.

L199: The ratio is between the values Precip(future)/Precip(Past). We reformulated this point to be clearer.

Fig 1.c: There is a negative trend in Fig. 1c scores, indicating a change of sign in the patterns of Fig. 1a. This suggests that, in the first half of the timeseries, El Niño conditions were dominant, while in the second half of the time series, La Niña conditions were dominant. This relates to the explanation of lines 66-69, that describes how the relationship between loadings and scores should be interpreted.

Fig 5,6 : Thanks for your suggestion. We decided to use the red-blue colorbar as it is universally used to represent positive-negative dichotomies. Moreover, the suggested colorbar has already been employed in Figures 1-4, so we believe a different colorbar could enhance reader comprehension. The Amazon was excluded from the PLS analyses as to not dominate the signal. Once the selecting and weighting is performed, there is no reason to crop out the Amazon.