the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 09 Feb 2024
Data-driven discovery of mechanisms underlying present and near-future precipitation changes and variability in Brazil
Abstract. Untangling the complex network of physical processes driving regional precipitation regimes in the present (1979–2014) and near-future climates (2020–2050) is fundamental to support a more robust scientific basis for decision making in the water-energy-food nexus. We propose a data-driven mechanistic approach to: (Goal 1) identify changes and variability of the regional precipitation mechanisms and (Goal 2) reduce the ensemble spread of future projections by weighting and filtering models that satisfactorily represent these drivers in present climate. Goal 1 is achieved by applying the Partial Least Squares (PLS) technique, a two-sided variant of principal component analysis (PCA), on a reanalysis dataset and 30 simulations of the future climate submitted to CMIP6 to discover the links between global sea-surface temperature (SST) and precipitation in Brazil. Goal 2 is achieved by selecting and weighting the future climate simulations from climate models that better represent the dominant modes discovered by the PLS in the present climate; with this subset of climate simulation, we produce precipitation change maps following IPCC’s WG1 methodology. The main mechanistic link discovered by the technique is that the generalised warming of the oceans promotes a suppression of precipitation in Northeast and Southeast Brazil, possibly mediated by the intensification of the Hadley circulation. We show that this pattern of precipitation suppression is stronger in the near-future precipitation change maps produced using our methodology. This demonstrates that a reduction of epistemic uncertainty is achieved after we select models that skillfully represent these mechanisms in the present climate. Therefore, the approach is capable of supporting both a quantitative analysis of regional changes as well as the construction of storylines supported by mechanistic evidence.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-48', Peter Pfleiderer, 21 Feb 2024
The authors present an interesting model constraining application for precipitation changes in Brazil. The analysis is based on Partial Least Squares (PSL) regression. The scope and results of the study are highly relevant on a methodological as well as on a practical level. In the current state, the manuscript lacks some information on the method as well as some details in the results to allow a reasonable interpretation of the results. I would suggest major revisions before publication.
Although the method section is well written there are a few points that were not fully clear or could be misinterpreted due to lacking details:
1) How is the NRMSE calculated? You say that it is obtained by "comparing PLS scores and loadings between each model and those derived from the ERA5". How do you aggregate the comparison of scores and loadings? Do you weight score differences more than loading differences since the loadings have more features?
2) How many iterations of the PLS are done and how much of the variance is explained by the n(?) components? Is there a way to compute the variance explained by n components (similar to PCA)? For instance, is component 1 considerably more important than component 2?
3) Is the first component in climate models always related to ENSO as shown in fig. 1 for ERA5 or are there some models where the first component resembles more a pattern as in fig. 2? If that would be the case and if component 1 and 2 would be similarly important, do you consider this when computing the NRMSE or do you always compare component 1 in the model with component 1 in ERA5? It would be interesting to see figures comparable to fig. 3 and fig. 4 for individual climate models.My main question concerns the way how PLS is used to weight models: Can we assume that comparing individual scores and loadings identified in ERA5 and a climate model tells us how well the climate model reproduces the dynamics? Couldn't there be cases where different aspects/features of the SST forcing on precipitation (e.g. ENSO) are reproduced by the climate model but where the association of these aspects/features to components in PLS ends up to differ from ERA5? It would be helpful if the authors could discuss the assumptions made for the evaluation of model performance using PLS in more detail.
What are components 3 and 4? is there an interpretation for these components?
Table 2: How would you interpret the high weight of GFDL-ESM4? How skillful can a model be if it does not capture the ENSO dynamic (assuming that component 1 always represents some natural variability related to ENSO)? Or put differently, wouldn't we trust EC-Earth3-CC more as it robustly captures the ENSO and the climate change component? These points relate to my questions above concerning the comparability of components between models and ERA5.
Furthermore, I would find it interesting to have the NRMSE listed in the table. I would also find it interesting to see the NRMSE for models that are dropped due to lower skill.l128-129: Is the trend statistically significant? What do you mean by "scores do not show a strong linear trend"? I would agree, that trends in comparison to the trends of component 2, these trends are "weaker" but I still see a trend in fig. 1c.
Fig. 5: Are the maps (a & b) ensemble medians? Or is it a mean considering the weights from table 2?
Minor comments:
l56: does the "t" in "XtY" stand for transpose?
equation 1: why is it max||u|| = ||v|| ?
l63-64: Check sentence. Is there something missing?
l162-163: Is this strong linear trend seen in most models or could it be that the trend is mostly due to a subset of climate models (relating to question 3).
l222-223: Do you have a reference supporting this hypothesis?Citation: https://doi.org/10.5194/egusphere-2024-48-RC1 -
AC1: 'Reply on RC1', Maria Kovalski, 01 Jul 2024
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॥=1Cov(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.
Citation: https://doi.org/10.5194/egusphere-2024-48-AC1
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AC1: 'Reply on RC1', Maria Kovalski, 01 Jul 2024
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RC2: 'Comment on egusphere-2024-48', Elena Saggioro, 22 Apr 2024
General comments
This paper applies an interesting technique, the Partial Least Squares (PLS) technique - a variation of the Principal Component Analysis to two temporally varying fields, to: 1) detect relationships between global SSTs and local precipitation over Brazil in the past observed record and 2) select and weight CMIP6 models based on their representation of this relationship to investigate its change in the next 30 years and via this constraint the spread of precipitation projections in the region.
This analysis provides interesting insights in the local character of precipitation change in Brazil. It also applies a novel technique for selection of regionally skilful climate models based on physical mechanisms, which is an area of research where new ideas are much needed to provide information that can be useful from a climate adaptation point of view. The paper is overall well written and provides conclusions that are of interest to the WCD community.
However, in the current form, there are several methodological aspects and elements of the interpretation that needs clarification before publication. I therefore suggest major revision before publication.
Specific comments
Introduction:
There is a lack of reference to previous analysis of the link between SST and precipitation in the region (only mentioned in L45). Can you please provide a brief overview, to better locate the contribution of this study?
Method:
I would appreciate a more detailed introduction to the PLS method:
- Can you rephrase in physical terms what “maximize the information present in XtY” mean? (Is it the correlation in time between SST and Precip at two different locations?)
- Could the authors expand on how the modes are identified (e.g. Where can we see the “modes” from Eq 1? )
- Can you give, as example, how the reader should interpret two “loading patterns” in relation to each other (e.g. for mode 1 in Fig1.a and Fig1.b)?
- I would find helpful if the authors could clearly define each term (e.g. mode, loading, scores), associate with a mathematical symbol and show their formula where relevant. Please then repeat the symbol each time it is mentioned in the Methods section, to help the reader connect the terms/formula more easily. Also, as noted in the technical corrections, the use of this terminology is at times inconsistent in the text/figures captions.
How do you combine the NRMSE from the scores and loads into one value (for each mode)? (L93)
Present climate results:
To increase the readers’ trust of the selected models, it would be good to see the 1 and 2 components of the models to get a feeling of how well they perform compared to “observation” beyond the NRMSE. A selection could appear in the Supplementary Material and only referenced in the text.
What do components 3 and 4 represent? Why using them, in case they are not linked to any physical mechanisms?
Future climate results:
What is the implication of models that do not represent well some of the first 4 components selected? (see Table 2; some models do not represent component 1 even which seems to be crucial). Does considering all 4 of them regardless not result in possibly selecting models that actually behave very differently?
To allow for clearer link between components and decrease in uncertainty in Fig 5.b, it would be interesting to see what changes to Fig5.b if:
- Only the models that match ERA for at least Component 1 are included (e.g. no GFDL-ESM4 as seen from Table 2): will the Component 1 of the precipitation signal dominates the overall projected change from the models?
- Only the models that match ERA for at least Component 1 and 2 are included (e.g. no CNRM-ESM2-1 as seen from Table 2
These tests are suggested because it seems that most of the drying in the north/wetting in the south is due to Components 1 and 2. Hence, I would imagine the models that represent them will be the ones that reduce the uncertainty and reveal that pattern.
Further, it would be interesting to see what happens to Fig5.b if no weighting is applied to the selected models (but just a simple average is taken): is the weighting very important, or does the PLS method identified models are already “better” without the need for weighting?
Discussion:
While I do not think the following is the case, it still would be good for the authors to comment on how the reduction in the uncertainty in precipitation changes for the PLS ensemble versus the full one is not an “automatic” result deriving from the construction of the procedure itself. I think this is not the case, because the selection is done on the past climate, not on the future. But it would be good to elaborate on this as it is a question that often arises for filtering methods like this one.
Finally, I would suggest adding a comment on the assumptions of this method. If I understand correctly, this approach rests of the assumption that the features detected in the past for the CMIP6 models (via the PLS procedure) are going to identify models that will also behave closer to reality in the future. More specifically, it seems that:
- the physical assumptions are
- in the future, some of the dominant features relevant to Brazil precipitation will be linked to SSTs (and more specifically to ENSO and generalised warming of the oceans)
- that the models that better represent these connection in the past will continue to be the most able to represent it under increasing forcing in the future
- while the methodological assumption is that the PLS method can reliably detect the models with the correct mechanisms representing the physical connection between SST/ENSO and precipitation.
These are justifiable assumptions, but I think a discussion of them and their limitations are missing.
Technical corrections
Data: are anomalies or full field used?
l45: is this a separate question (then better to phrase with question mark for consistency with the style of the first question) or a comment to the first question above?
L49: this question is phrased rather oddly, a rewrite would be useful. ( adding also a question mark at the end for consistency with the style of the first question)
L54: introduce lat-lon as “latitude – longitude (lat-lon)”
L56: Xt means transpose?
L56: seems there is an extra “and”? in “The PLS method identifies pairs of latent variable vectors and that maximises….”
L59-62: Please explain in simple terms why you get the modes from this equation. Does “Xu” stands for matrix-vector product between X and u? What is the dimension of u?.
L79: can you comment briefly on why was ERA5 chosen instead of GPCP directly for precipitation?
L85: can you comment briefly on why SST used from COBE and not ERA5?
L108-109: Why does the ratio between 2020-2050 and historical ensemble mean climatology is interpreted as “uncertainty?” Is this not the climate change signal, instead? And do you maybe mean a change (future-past) is at the numerator?
L119: is the Amazon region removed before or after the PLS analysis?
L120: can you comment on why “the precipitation in the Amazon region presents significantly higher variability” : is this because of the precipitation induced by transpiration from the trees? Is this choice of cropping out the Amazon forest something done in other papers too?
L139: was it not between 1979 and 2014? (see L85)
L140: what is the anomaly? I have noticed a somewhat inconsistent (or unclear) use of the terms “saliences – correlation” (figure title), “anomaly” and “loading matrices” (caption) : please clarify.
L199: is the map showing a ratio between the CHANGE in precipitation and the past [Precip(future)- Precip(Past)]/ Precip(Past), or a ratio between the values Precip(future)/Precip(Past)? It is not clear from the text or the caption.
Fig 1.c: There is a negative trend in Figs 1.c (not commented on, only for Fig 1.d): could you elaborate on it? Is this linked to any observed trends in variability in the region? How does this relate to the interpretation of Lines 66-69?
Fig 5,6 : I would find more intuitive and consistent to use the brown-green colorscale here since we talk about precipitation change? Why not cropping the Amazon are from here too?
Citation: https://doi.org/10.5194/egusphere-2024-48-RC2 -
AC2: 'Reply on RC2', Maria Kovalski, 01 Jul 2024
-- 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॥=1Cov(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 XtY. ‘.
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 ω1.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.
Citation: https://doi.org/10.5194/egusphere-2024-48-AC2
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-48', Peter Pfleiderer, 21 Feb 2024
The authors present an interesting model constraining application for precipitation changes in Brazil. The analysis is based on Partial Least Squares (PSL) regression. The scope and results of the study are highly relevant on a methodological as well as on a practical level. In the current state, the manuscript lacks some information on the method as well as some details in the results to allow a reasonable interpretation of the results. I would suggest major revisions before publication.
Although the method section is well written there are a few points that were not fully clear or could be misinterpreted due to lacking details:
1) How is the NRMSE calculated? You say that it is obtained by "comparing PLS scores and loadings between each model and those derived from the ERA5". How do you aggregate the comparison of scores and loadings? Do you weight score differences more than loading differences since the loadings have more features?
2) How many iterations of the PLS are done and how much of the variance is explained by the n(?) components? Is there a way to compute the variance explained by n components (similar to PCA)? For instance, is component 1 considerably more important than component 2?
3) Is the first component in climate models always related to ENSO as shown in fig. 1 for ERA5 or are there some models where the first component resembles more a pattern as in fig. 2? If that would be the case and if component 1 and 2 would be similarly important, do you consider this when computing the NRMSE or do you always compare component 1 in the model with component 1 in ERA5? It would be interesting to see figures comparable to fig. 3 and fig. 4 for individual climate models.My main question concerns the way how PLS is used to weight models: Can we assume that comparing individual scores and loadings identified in ERA5 and a climate model tells us how well the climate model reproduces the dynamics? Couldn't there be cases where different aspects/features of the SST forcing on precipitation (e.g. ENSO) are reproduced by the climate model but where the association of these aspects/features to components in PLS ends up to differ from ERA5? It would be helpful if the authors could discuss the assumptions made for the evaluation of model performance using PLS in more detail.
What are components 3 and 4? is there an interpretation for these components?
Table 2: How would you interpret the high weight of GFDL-ESM4? How skillful can a model be if it does not capture the ENSO dynamic (assuming that component 1 always represents some natural variability related to ENSO)? Or put differently, wouldn't we trust EC-Earth3-CC more as it robustly captures the ENSO and the climate change component? These points relate to my questions above concerning the comparability of components between models and ERA5.
Furthermore, I would find it interesting to have the NRMSE listed in the table. I would also find it interesting to see the NRMSE for models that are dropped due to lower skill.l128-129: Is the trend statistically significant? What do you mean by "scores do not show a strong linear trend"? I would agree, that trends in comparison to the trends of component 2, these trends are "weaker" but I still see a trend in fig. 1c.
Fig. 5: Are the maps (a & b) ensemble medians? Or is it a mean considering the weights from table 2?
Minor comments:
l56: does the "t" in "XtY" stand for transpose?
equation 1: why is it max||u|| = ||v|| ?
l63-64: Check sentence. Is there something missing?
l162-163: Is this strong linear trend seen in most models or could it be that the trend is mostly due to a subset of climate models (relating to question 3).
l222-223: Do you have a reference supporting this hypothesis?Citation: https://doi.org/10.5194/egusphere-2024-48-RC1 -
AC1: 'Reply on RC1', Maria Kovalski, 01 Jul 2024
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॥=1Cov(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.
Citation: https://doi.org/10.5194/egusphere-2024-48-AC1
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AC1: 'Reply on RC1', Maria Kovalski, 01 Jul 2024
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RC2: 'Comment on egusphere-2024-48', Elena Saggioro, 22 Apr 2024
General comments
This paper applies an interesting technique, the Partial Least Squares (PLS) technique - a variation of the Principal Component Analysis to two temporally varying fields, to: 1) detect relationships between global SSTs and local precipitation over Brazil in the past observed record and 2) select and weight CMIP6 models based on their representation of this relationship to investigate its change in the next 30 years and via this constraint the spread of precipitation projections in the region.
This analysis provides interesting insights in the local character of precipitation change in Brazil. It also applies a novel technique for selection of regionally skilful climate models based on physical mechanisms, which is an area of research where new ideas are much needed to provide information that can be useful from a climate adaptation point of view. The paper is overall well written and provides conclusions that are of interest to the WCD community.
However, in the current form, there are several methodological aspects and elements of the interpretation that needs clarification before publication. I therefore suggest major revision before publication.
Specific comments
Introduction:
There is a lack of reference to previous analysis of the link between SST and precipitation in the region (only mentioned in L45). Can you please provide a brief overview, to better locate the contribution of this study?
Method:
I would appreciate a more detailed introduction to the PLS method:
- Can you rephrase in physical terms what “maximize the information present in XtY” mean? (Is it the correlation in time between SST and Precip at two different locations?)
- Could the authors expand on how the modes are identified (e.g. Where can we see the “modes” from Eq 1? )
- Can you give, as example, how the reader should interpret two “loading patterns” in relation to each other (e.g. for mode 1 in Fig1.a and Fig1.b)?
- I would find helpful if the authors could clearly define each term (e.g. mode, loading, scores), associate with a mathematical symbol and show their formula where relevant. Please then repeat the symbol each time it is mentioned in the Methods section, to help the reader connect the terms/formula more easily. Also, as noted in the technical corrections, the use of this terminology is at times inconsistent in the text/figures captions.
How do you combine the NRMSE from the scores and loads into one value (for each mode)? (L93)
Present climate results:
To increase the readers’ trust of the selected models, it would be good to see the 1 and 2 components of the models to get a feeling of how well they perform compared to “observation” beyond the NRMSE. A selection could appear in the Supplementary Material and only referenced in the text.
What do components 3 and 4 represent? Why using them, in case they are not linked to any physical mechanisms?
Future climate results:
What is the implication of models that do not represent well some of the first 4 components selected? (see Table 2; some models do not represent component 1 even which seems to be crucial). Does considering all 4 of them regardless not result in possibly selecting models that actually behave very differently?
To allow for clearer link between components and decrease in uncertainty in Fig 5.b, it would be interesting to see what changes to Fig5.b if:
- Only the models that match ERA for at least Component 1 are included (e.g. no GFDL-ESM4 as seen from Table 2): will the Component 1 of the precipitation signal dominates the overall projected change from the models?
- Only the models that match ERA for at least Component 1 and 2 are included (e.g. no CNRM-ESM2-1 as seen from Table 2
These tests are suggested because it seems that most of the drying in the north/wetting in the south is due to Components 1 and 2. Hence, I would imagine the models that represent them will be the ones that reduce the uncertainty and reveal that pattern.
Further, it would be interesting to see what happens to Fig5.b if no weighting is applied to the selected models (but just a simple average is taken): is the weighting very important, or does the PLS method identified models are already “better” without the need for weighting?
Discussion:
While I do not think the following is the case, it still would be good for the authors to comment on how the reduction in the uncertainty in precipitation changes for the PLS ensemble versus the full one is not an “automatic” result deriving from the construction of the procedure itself. I think this is not the case, because the selection is done on the past climate, not on the future. But it would be good to elaborate on this as it is a question that often arises for filtering methods like this one.
Finally, I would suggest adding a comment on the assumptions of this method. If I understand correctly, this approach rests of the assumption that the features detected in the past for the CMIP6 models (via the PLS procedure) are going to identify models that will also behave closer to reality in the future. More specifically, it seems that:
- the physical assumptions are
- in the future, some of the dominant features relevant to Brazil precipitation will be linked to SSTs (and more specifically to ENSO and generalised warming of the oceans)
- that the models that better represent these connection in the past will continue to be the most able to represent it under increasing forcing in the future
- while the methodological assumption is that the PLS method can reliably detect the models with the correct mechanisms representing the physical connection between SST/ENSO and precipitation.
These are justifiable assumptions, but I think a discussion of them and their limitations are missing.
Technical corrections
Data: are anomalies or full field used?
l45: is this a separate question (then better to phrase with question mark for consistency with the style of the first question) or a comment to the first question above?
L49: this question is phrased rather oddly, a rewrite would be useful. ( adding also a question mark at the end for consistency with the style of the first question)
L54: introduce lat-lon as “latitude – longitude (lat-lon)”
L56: Xt means transpose?
L56: seems there is an extra “and”? in “The PLS method identifies pairs of latent variable vectors and that maximises….”
L59-62: Please explain in simple terms why you get the modes from this equation. Does “Xu” stands for matrix-vector product between X and u? What is the dimension of u?.
L79: can you comment briefly on why was ERA5 chosen instead of GPCP directly for precipitation?
L85: can you comment briefly on why SST used from COBE and not ERA5?
L108-109: Why does the ratio between 2020-2050 and historical ensemble mean climatology is interpreted as “uncertainty?” Is this not the climate change signal, instead? And do you maybe mean a change (future-past) is at the numerator?
L119: is the Amazon region removed before or after the PLS analysis?
L120: can you comment on why “the precipitation in the Amazon region presents significantly higher variability” : is this because of the precipitation induced by transpiration from the trees? Is this choice of cropping out the Amazon forest something done in other papers too?
L139: was it not between 1979 and 2014? (see L85)
L140: what is the anomaly? I have noticed a somewhat inconsistent (or unclear) use of the terms “saliences – correlation” (figure title), “anomaly” and “loading matrices” (caption) : please clarify.
L199: is the map showing a ratio between the CHANGE in precipitation and the past [Precip(future)- Precip(Past)]/ Precip(Past), or a ratio between the values Precip(future)/Precip(Past)? It is not clear from the text or the caption.
Fig 1.c: There is a negative trend in Figs 1.c (not commented on, only for Fig 1.d): could you elaborate on it? Is this linked to any observed trends in variability in the region? How does this relate to the interpretation of Lines 66-69?
Fig 5,6 : I would find more intuitive and consistent to use the brown-green colorscale here since we talk about precipitation change? Why not cropping the Amazon are from here too?
Citation: https://doi.org/10.5194/egusphere-2024-48-RC2 -
AC2: 'Reply on RC2', Maria Kovalski, 01 Jul 2024
-- 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॥=1Cov(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 XtY. ‘.
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 ω1.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.
Citation: https://doi.org/10.5194/egusphere-2024-48-AC2
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Márcia Talita A. Marques
Maria Luiza Kovalski
Gabriel M. P. Perez
Thomas C. M. Martin
Edson L. S. Y. Barbosa
Pedro Augusto S. M. Ribeiro
Roilan H. Valdes
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