Observationally constrained projection of Afro-Asian monsoon precipitation

The Afro-Asian summer monsoon (AfroASM) sustains billions of people living in many developing countries covering West Africa and Asia, vulnerable to climate change. Future increase in AfroASM precipitation has been projected by current state-of-the-art climate models, but large inter-model spread exists. Here we show that the projection spread is related to present-day interhemispheric thermal contrast (ITC). Based on 30 models from the Coupled Model Intercomparison Project Phase 6, we find models with a larger ITC trend during 1981–2014 tend to project a greater precipitation increase. Since most models overestimate present-day ITC trends, emergent constraint indicates precipitation increase in constrained projection is reduced to 70% of the raw projection, with the largest reduction in West Africa (49%). The land area experiencing significant increases of precipitation (runoff) is 57% (66%) of the raw projection. Smaller increases of precipitation will likely reduce flooding risk, while posing a challenge to future water resources management.

references here, but there is a whole literature on "pattern scaling" that discusses this in more detail, e.g. [tebaldi_pattern_2014].
Given that, as is standard in analyses of precip change under mean temperature change (I can't think of an example reference here, but there are plenty), the precip changes need to be normalized by the global-mean warming. This removes the direct influence of ECS and results in a clean disentangling of two presumably independent effects: (1) how much warming there is, and (2) given the amount of warming, how the monsoon precip will change. One can then address each factor separately, with constraints on ECS (e.g. very exhaustively addressed by [sherwood_assessment_2020]) and separately constraints such as what the present study attempts on the precip change per unit warming.
In other words, without normalizing by mean warming in each model, the present manuscript's attempt nominally to constrain Afro-Asian monsoon precip change implicitly ends up being a muddied attempt to constrain both ECS and hydrological sensitivity over the Afro-Asian monsoon region.
Most importantly, the "headline" figure is Separately, I'm not sure that the uncertainties are being properly propagated forward into the constraint. Fig. 4 nicely includes measures of uncertainty on both the ITC index (grey shading) and in the regression line (dashed curves). In L149 the quoted "constrained" PC1 value is -0.49 +/-0.63. But these error bounds surely underestimate the uncertainty (also it should be stated more clearly in the main text what specifically the +/-0.63 bounds are and how they were computed). I know this isn't a rigorous way of doing it, but just by eye examine in Fig. 4 the area contained within the two dashed curves and the grey shading as a plausible estimate of the uncertainty in both terms. Within that area, the intersection of the "obs" (vertical dashed line) with the projection (horizontal dashed line) could yield PC1 as low as roughly -1.4 or as high as 0.2, a considerably wider range than -0.49+/-0.63. If I am mistaken and the uncertainty in both the observed ITC index *and* the model PC1-ITC1 regression are in fact both being accounted for, I do apologize, but ask that you clarify the description in the text. If I am not mistaken, then how much does this weaken your constraint?
In addition, L137-139 describe the ITC index used as the constraint as "produced by projecting the present-day trend pattern of surface temperature onto the warming pattern associated with the inter-model PC1 shown in Figure 2c". Why do this projection step and not simply use the present-day trend pattern itself? Your procedure may indeed be the superior one, but it needs to be justified in the manuscript.
Minor comments ============== L2 "less rich" L33-34 An ITCZ-like narrow band is a reasonable description over Africa but certainly not for the Indian and E. Asian monsoons, which are more complicated L38-39 "raising risk on failure in addressing regional climate change" confusing wording; rephrase L53 To me, the definitive citation on emergent constraints and how to do them in the most physically justifiable way is [klein_emergent_2015]. I recommend you cite it and ensure your approach checks all of their requirements for a sound constraint. L69-70 I don't think the reference to the Scenario Model Intercomparison Project is necessary; just referring to CMIP6 is sufficient and has less danger of being confusing L84 The manuscript should briefly note that SSP8.5 is now a highly unlikely scenario given recent trends in decarbonization; e.g. [hausfather_emissions_2020]. L96 systematically -> systematic L102-104 The manuscript should briefly note that, even if the thermal contrast proves to be a useful predictor, modern understanding of the monsoon replaces thermal gradients with moist entropy or moist static energy gradients. The Geen et al review paper cited notes this; see also e.g. [hill_theories_2019]. L110-112 "rooted in" is too vague; please clarify. Also, from Fig. 2c there is much more noise for the historical, such that your claim is not immediately valid by eye from that plot. I recommend adding panels of zonal averages for both the future and historical to make this clearer. L115-116 Should cite one or more papers of the voluminous literature on transient warming, Arctic amplification, etc. L123-125 These are far removed from the E. Asian monsoon sector which you otherwise are including. In addition, similar to the suggestion above for Fig. 2 I recommend adding panels of zonal-mean fields: this is quite noisy to the point that I don't find the claim about clear increases in crossequatorial flow totally convincing. Fig. 4 Omit the "(a)" label since there's only one panel. L250-251 I'm not familiar with these papers, but is this saying that the connection between the Afro-Asian monsoon precip change and the NH-SH thermal contrast has already been well established? If so, that needs to be stated in the main text, not just the methods, and it needs to be clarified specifically what in this study is novel (presumably all the emergent constraint material). L256-259 Why these latitude ranges? Why do they differ between the hemispheres? Without more physical justification, this feels a little fishy. L262 Can you really claim that internal variability influence is weak over a ~3 decade timescale on regional scales? C.f. Clara Deser and Karen McKinnon's work (among others) with large ensembles and internal variability.

Response to reviewers' comments of NCOMMS-21-30260-T "Emergent constraints suggest overestimated future Afro-Asian monsoon precipitation increase"
We hope to express our appreciation to the reviewers for the constructive comments and suggestions, which have greatly helped us to improve the quality of the manuscript. Below, we have provided a point-by-point response to the comments. In the following, the reviewer"s comments are written in black, followed by our response in blue.

Reviewer #1 (Remarks to the Author):
Emergent constraint on future changes of summer precipitation in Afro-Asian monsoon regions finds less rich water resources than previous expectation By Ziming Chen, Tianjun Zhou, Xiaolong Chen, Wenxia, Zhang, Lixia Zhang, Mingna Wu, and Liwei Zou This study investigates the possibility to constraining future changes in precipitation in monsoon regions simulated by CMIP6 models. The models generally predict an increase in precipitation in these regions, yet with significant inter-model spread. This study aims to use the significant correlation between an observable metric (the inter-hemispheric thermal contrast) to constrain precipitation changes. The authors found that, given that since most models overestimate this thermal contrast, the observational constraint suggest a weaker moistening than would be expected from the CMIP model projections.
The article is interesting and the methodology is good and fairly well described. The approach used by the authors follows that of many papers that aim to constrain the uncertainty of different aspects of climate change simulated by CMIP models. That being said, the authors use a metric that has physical meaning, which allows for a physical understanding of the statistical inference. I am less convinced by the part about the social impacts of the constrained projection (e.g. line 73). The authors simplify the issue of precipitation changes in monsoon regions. They defend the idea that a smaller than expected increase in rainfall is a bad thing for the population. This is not necessarily true, considering the possible disasters related to heavy rains, floods.... I would have liked more caution from the authors of the study.
Finally, I find the result relatively weak. While the emergent constraint (EC) constrains a relatively significant part of the PC1, it only constrains a significantly weaker part of the precipitation change. This occurs when your EC indirectly reduces the variable of interest. This reduces the interest of the study, even though the regional constraint part may seem to help improve it. 2 To summarize, the paper has no methodological problems, but I am only slightly convinced by the usefulness of the results.
We would like to express our appreciation to the reviewer for the constructive comments that helped us to improve the manuscript. According to the reviewer"s suggestions, we have thoroughly revised the manuscript. We hope that the new added results on the potential water availability and the regional effects of emergent constraint help to further convince readers of the usefulness of the results.
Major comments: 1. Line 29,168: The authors choose to highlight the increase in precipitation over land areas and extrapolate the impact on the population. However, I think this is a dangerous shortcut as most of the rainfall over monsoon regions is extreme and can cause flooding. Therefore, a smaller increase in monsoon precipitation may be better for the population in these regions than a large increase in extremes.
Thanks for your valuable comment. We agree that the factors affecting water resources include not only the precipitation amount, but also the characteristics of precipitation (Cho et al., 2016;Singh & Kumar, 2013;Li et al., 2016;Kundzewicz er al., 2019). Hence, in the revised manuscript, we have rephrased the statement and discussed the impact of precipitation change on the potential water availability, instead of highlighting the less increase of water resources as you suggested. We also stated that the increase of precipitation may cause negative impact such as flooding. For details, please see L28-L32, L175-L200 and L219-L222 in the revised manuscript. We also list the revision of the text below for your reference: L28-L32: "The land area that will experience a significant increase of precipitation (runoff) is ~57% (66%) of that of the raw projection. A smaller increase of precipitation than raw projection will reduce the risk of extreme precipitation and flooding, while it may also pose a challenge to adaptation and mitigation activities related to water resources management." L175-L200: "Impact on the potential water availability The AfroASM region holds a high density of population. More monsoon precipitation is expected to increase the potential water availability, which is mirrored in the runoff 42,43 , while the associated intense monsoon precipitation will also lead to flood and landslide [44][45][46][47] . The projected increase in monsoon precipitation under global warming is expected to partly offset the drying tendency since the 1950s (Fig. 1a). The less increase of precipitation in the constrained projection will reduce the increased potential water availability as expected from the raw projection, meanwhile the possible disasters related to heavy rainfall and floods will reduce accordingly. Here, we further estimate the impact of emergent constraint on the change in areal extent of precipitation and potential water availability.
To quantify the impact on the areal extent of precipitation, we examine the land area fraction that experiences a significant increase of precipitation ( Fig. 6; see Methods). The fraction with a significant increase of precipitation is 24% in the constrained projection, only 57% of the raw projection. Regionally, in the constrained projection, the land area fraction in East Asian monsoon region is only 37% of the raw projection, while in West African and South Asian monsoon regions, the corresponding results are 50% and 69%, respectively.
Based on the significant positive correlation between precipitation and runoff ( Supplementary Fig. S5), we further quantify the changes of potential water availability in the constrained projection ( Fig. 6; see Methods). About 27% land area in the AfroASM region will witness a significant increase of potential water availability in the constrained projection, which is only 66% of that of the raw projection. Regionally, the constrained land area fraction in West African monsoon region is only 55% of the raw projection, while in South Asia and East Asian monsoon regions, the corresponding result is 71% and 76%, respectively. Hence, less land area in AfroASM will experience a significant increase of precipitation and runoff in the constrained projection. These imply that the characteristics of precipitation change in the future will be milder than the raw projection." L219-L222: "The less increase of potential water availability than the raw projection may pose a challenge to climate change adaptation and mitigation activities related to water management and food security 48,49 , although a smaller than expected increase in rainfall will also reduce the risk of extreme precipitation and flooding." 2. Line 157: The African monsoon region is not in North Africa. It is over the sub-saharian band.
Thanks. We have replaced the "North Africa" with "West Africa" or "West African monsoon region" in the revised manuscript, following the "Annex V: Monsoons" in the IPCC AR6 (2021 calculate the correlation coefficient between and PC1 in each subset, and get correlation coefficients of 0.61 (0.56~0.67 for the 5th-95th range), 0.61 (0.53~0.69), 0.61 (0.51~0.71) and 0.61 (0.49~0.72) by deducting one, two, three and four models, respectively. The emergent constraint in all these subsets is statistically significant, as all the ranges of correlation coefficient exceed the 5% significant level using student t-test.
Hence, the established emergent constraint is independent of the model ensembles, confirming the robustness of the conclusion. Please see L204-L208 in the revised manuscript, and Supplementary Note #1 and Figure S8 in the Supplementary Information. In addition, since the SSP scenarios include regional forcings which are different from the CMIP5 RCPs, and the model response and the main source of the inter-model spread of CMIP6 may be different from that of CMIP5, comparability between CMIP5 and CMIP6 scenarios cannot be established for detailed assessments (Meinshausen et al., 2020;Wyser et al., 2020;Lee et al., 2021). So we only use the 5 CMIP6 model ensemble here.
We also list the revised text below for your reference: L204-L208: "In addition, to examine the robustness of the emergent constraint, we check the inter-model correlation coefficient between and PC1 using different model ensembles, and come to similar conclusion ( Supplementary Fig.  S8). The independence of the results on the model ensemble and the future emission scenarios confirms the robustness of the conclusions." The information added in the Supplementary Information is also listed below:

L73-L88: "Supplementary Information Note #1:
We use different model ensembles to verify the robustness of the emergent constraint. Firstly, we deduct one to four models from the 30 CMIP6 models in sequence, and we get 30 ( To exam whether the addition of outliers would alter the relationship of emergent constraint, we randomly add one to four outliers to the raw 30-model ensemble ("+1" to "+4" of the red bars in the Supplementary Figure S8). The outliers are created randomly in the range of PC1 and , respectively. We repeat the above processes 1000 times to form 1000 synthetic members. The results are shown as the red bars in Supplementary Figure S8.
The robustness is defined as the range of correlation coefficient in different subsets of model ensemble exceeding the thresholds of the 5% significant level under student t-test." 6 Supplementary Figure S8. Robustness test for the emergent constraint using different sets of model ensembles. The relationship is represented by the inter-model correlation coefficient between interhemispheric thermal contrast pattern index ( ) and normalized PC1. The bar charts and the error bars represent the ensemble mean and range of 5th -95th percentile of correlation coefficient across different set of models. The methods on how to create different sets of models is described in Supplementary Information Note #1. The red dash curve shows the thresholds of the 5% significant level under the student t-test. of the raw increase of precipitation increase.

References
Thanks. We have rephrased this statement as "While the constrained projection of the increase in AfroASM precipitation is ~70% of the raw projection in the context of regional average, the effects of emergent constraint on the changes of precipitation and water availability are more pronounced at regional scales." To highlight the effects of emergent constraint, we have clarified the regional impacts in the revised manuscript. Please see L213-L217 in the revised manuscript: L213-L217: "The projection of precipitation constrained by the observation is 49% (70%) of the raw projection in West Africa (East Asia) monsoon region, indicating a reduction exceeding 70% (50%) over a large part of West African (East Asian) monsoon region. The land fraction that will experience a significant increase of precipitation is 50% (37%) of that of the raw projection in West Africa (East Asia) monsoon region." Minor comments: 1. Title: "Find". Emergent constraints do not find results, but suggest. Overall, the title is ambiguous.
Thanks. We have revised the title as "Observationally constrained projection of Afro-Asian monsoon precipitation".
2. Line 59-60: Not relevant, as several papers provide emergent constraints on different aspects of climate change.
3. Line 73-80: Results should not be described in the introduction. This should be removed. 10. Figure 2: Please use the correct distance between latitudes, since the authors weight the ITC1 metric by area (i.e. the north pole is too highlighted).
Thanks. Corrected. Please see Figure 2 in the revised manuscript.
11. Figure 2: Is there any interesting information below 60°S? Why do the authors remove this part of the globe?
Thanks. We have extended the latitude range in Figure 2, and found a significant positive anomaly related to PC1 across models in present day below 60°S. The positive anomaly may be associated with the model biases of mixed-phase cloud (Trenberth & Fasullo, 2010;Lawson & Gettelman, 2014). We have added a statement 9 in the revised manuscript. Please see Figure 2 and L113-L115 in the revised manuscript.
L113-L115: "In addition, a remarkable warming anomaly related to PC1 in the historical period is seen over the Southern Ocean, which may be associated with the model biases of mixed-phase cloud 36,37 ." 13. Figure 3a: ECS should be in the y-axis.
14. Figure 6a: I didn't understand how the figure is built. Is it the relative distribution an average of all model distribution or an aggregate of every point satisfying the conditional sampling for all models?
Thanks. The spatial distribution in Figure 6 is an aggregate of all grid area satisfying the conditional sampling for the multi-model ensemble, following Fischer et al. (2013). To avoid misleading, we have described it with more details in L385-L388 in the revised manuscript. We also list the description below: L385-L388: "According to the latitude-dependent area, the grid points falling in each bin of the PDF have been weighted. Hence, the spatial distribution is an aggregated of all grid area satisfying the conditional sampling. The PDF is derived from the nonparametric assessment of the PDF." References: Fischer EM, Beyerle U, Knutti R. Robust spatially aggregated projections of climate extremes. Nature Climate Change 3, 1033-1038, doi:10.1038/nclimate2051 (2013) 15. Figure S1: Lines are confusing because models are not related. Please use dots for 11 instance.

Reviewer #2 (Remarks to the Author):
The authors show that the intermodel spread in future Afro-Asian monsoon precipitation has a dominant mode of increased precipitation over land to the north, and reduced precipitation over the Equator to the south. They show this mode is related to the difference in inter-hemispheric temperature contrast between models.
As the modelled present-day and future inter-hemispheric thermal contrast are correlated, they argue that present-day inter-hemispheric thermal contrast can be used to constrain the future change in precipitation over the Afro-Asian monsoon region. They show that constraining projections in this way suggests less change in precipitation by the end of the century than the raw simulation data indicates.
Identifying sources of dynamical uncertainty in future monsoon precipitation is an ongoing challenge. Previous work, which the authors cite, has identified that interhemispheric and land-sea thermal contrast link to the spread in CMIP6 simulations ) but did not propose a constraint as is done here. This study identifies a physically grounded emergent constraint on intermodel spread in projected rainfall, and so marks a valuable contribution to understanding future tropical rainfall changes. I am pleased to recommend this study for publication once some concerns with the methodology and framing are addressed.
We would like to express our appreciation to the reviewer for the constructive comments that helped us to improve the manuscript. According to the reviewer"s suggestions, we have thoroughly revised the manuscript. We hope the results from the scaling EOF analysis and significant relationship of emergent constraint help to further demonstrate the robustness of the conclusion.

EOF analysis:
The physical arguments relating the increase Afro-Asian monsoon precipitation seen in Fig. 2a to the ITC seem sound, but I am concerned that a similar pattern might result simply from some models precipitating more strongly than others due to differences in their convection schemes. This would undermine the causality you base your emergent constrain on.
Did you explore whether scaling individual models to account for this prior to taking the EOF affected the results? e.g., by removing a mean (over the tropics or globally) for each model and normalize by the corresponding spatial standard deviation?
Thanks for your comments and suggestions. As suggested, to assess whether the projected uncertainty results from some models, we scale each model before taking the inter-model EOF analysis. To scale each model, we remove the mean precipitation over tropics and global from the projected changes of precipitation, respectively, and 13 then normalize the projected changes by the corresponding spatial standard deviation. The results are shown in Figure R1 below. We found that the patterns of projected changes of precipitation and low-level circulation regressed onto the scaled PC1 across models closely resemble the pattern in Figure 2a in the revised manuscript. Both of two PC1-related patterns exhibit a spatially consistent increase of precipitation over the AfroASM domain. In addition, the scaled PC1 accounts for 24% of inter-model variance (Fig. R1), which is close to that in the unscaled EOF analysis (Fig. 2a in the revised manuscript). Hence, the synchronized precipitation changes in the model spread are dominated by the inter-model uncertainty of ITC.
Based on your comments, we have added the following statements to clarify that the projected uncertainty does not result from some individual models (Please also see L94-L97 and L289-L296 in the revised manuscript) L94-L97: "To exclude that the above pattern may be dominated by strong diversity in mean precipitation and spatial variability across model, we scale each model prior to taking the inter-model EOF analysis (see Methods), and obtain similar patterns compared with that in Figure 2a."

L289-L296: "Scaling individual models
To scale each model, the mean precipitation changes over tropics and global for each model have been removed from the original precipitation changes, respectively, and then the precipitation changes have been normalized by the corresponding spatial standard deviation. We take the inter-model EOF analysis for the scaled precipitation changes. The results show that the patterns of projected changes of precipitation and low-level circulation regressed onto the scaled PC1 across models closely resemble that in Figure 2a. Thus, we only present the results without scaling." Figure R1. Same as the Figure 2a in the revised manuscript, but the precipitation changes in the projection is scaled before taking the inter-model empirical orthogonal function (EOF) analysis. To scale the precipitation changes in each model, the mean precipitation changes over tropics (a, 30S~30N) and global (b, 90S~90N) have been removed from the original precipitation changes, and then the precipitation changes have been normalized by the corresponding spatial standard deviation.

Robustness of constraint:
How sensitive is your relationship between PC1 and ITC1 to individual model datapoints? From Fig. 4 it seems the particularly high-PC1/high-ITC1 CanESM2 datapoints are key in giving a positive correlation. If you remove these datapoints, or remove some other randomized selection of models, are your constrained projections altered? Would the addition of an outlier considerably alter your results?
Thanks. To demonstrate the robustness of the emergent constraint, we select different model ensembles from 30 CMIP6 models, and then re-examine the relationship of the emergent constraint (blue bars in Supplementary Fig. S8). The results show that the relationship of the emergent constraint in all of members are statistically significant at 5% level under student t-test ( Supplementary Fig. S8). In addition, as suggested, we have tested adding one to four additional outliers to 30 CMIP6 models" ensemble, and then check the relationship of the emergent constraint (red bars in Supplementary Fig.  S8). We repeat these processes over 1000 times. The relationship of the emergent constraint is statistically significant at 5% level under student t-test. Hence, the relationship between PC1 and is not sensitive to individual model datapoints.
Please see Supplementary Figure S8 and L204-L208 in the revised manuscript.

Framing:
You discuss "Societal impacts of less increase in precipitation" from line 162 and refer to this point again on lines 193-194. You suggest that your findings are concerning because a smaller increase in precipitation will be a problem for agriculture in the Afro-Asian monsoon region.
Is it actually desirable to have a greater increase in precipitation, and specifically, would it be problematic to have a smaller increase than the raw projections predict? You cite Schewe et al. 2014 in the conclusions to support the water scarcity issue, but that study looks at precipitation change globally. While their Fig. 1 indicates reduced annual discharge at 2 degrees warming across the Americas and Europe, it is not clear from their figures or discussion that the Afro-Asian monsoon region overall is expected to suffer water scarcity, besides perhaps China.
While decreased precipitation can reduce water available for agriculture, increased precipitation can itself connect to flooding, loss of crops, increased occurrence of gastrointestinal and vector borne diseases. The raw projection in Fig. 1a suggests that by the end of the 21st Century we might on average see a 0.75mm/day increase in precipitation compared to 1950. If this is reduced in your constrained projection, might that not be a good thing? I don"t think the reduction you predict is so great as to maintain precipitation below 1950s levels?
I suggest that if you want to contextualize your results in this way, you should: Support your discussion on line 162 onwards with references to recent literature. Add a line to Fig. 1a to show the constrained precipitation projection.
Thanks. Reviewer #1 is also concerned about the implications of less increase in precipitation. We agree that the factors affecting water resources include not only the precipitation amount, but also the characteristics of precipitation (Singh & Kumar, 2013;Li et al., 2016a;Kundzewicz et al., 2019). As suggested, we have revised the discussion of the societal impact of the constrained precipitation and added the time series of the constrained precipitation in Figure 1a in the revised manuscript. We stated that the risk of extreme precipitation, flood and landslide will change consequently according to the recent studies (Kundzewicz et al., 2019;Cho et al., 2016;Ranasinghe et al., 2021). Given that the regional precipitation change is mirrored in runoff, affecting the risk of flood, we quantify the impact of constrained projection by examining the fraction of land area that experiences a significant increase of precipitation and runoff. The results show that the land area that will experience a significant increase of precipitation and runoff in the constrained projection is only ~57% and ~66% of that of the original expectation. These imply that the characteristics of precipitation in the future will be milder than the raw projection. Please see L175-L200 and L219-L222 and Figure 1a in the revised manuscript. We also list the revised statements below for your reference: L175-L200: "Impacts on the potential water availability The AfroASM region holds a high density of population. More monsoon precipitation is expected to increase the potential water availability, which is mirrored in the runoff 42,43 , while the associated intense monsoon precipitation will also lead to flood and landslide [44][45][46][47] . The projected increase in monsoon precipitation under global warming is expected to partly offset the drying tendency since the 1950s (Fig. 1a). The less increase of precipitation in the constrained projection will reduce the increased potential water availability as expected from the raw projection, meanwhile the possible disasters related to heavy rainfall and floods will reduce accordingly. Here, we further estimate the impact of emergent constraint on the change in areal extent of precipitation and potential water availability.
To quantify the impact on the areal extent of precipitation, we examine the land area fraction that experiences a significant increase of precipitation ( Fig. 6; see Methods). The fraction with a significant increase of precipitation is 24% in the constrained projection, only 57% of the raw projection. Regionally, in the constrained projection, the land area fraction in East Asian monsoon region is only 37% of the raw projection, while in West African and South Asian monsoon regions, the corresponding results are 50% and 69%, respectively.
Based on the significant positive correlation between precipitation and runoff ( Supplementary Fig. S5), we further quantify the changes of potential water availability in the constrained projection ( Fig. 6; see Methods). About 27% land area in the AfroASM region will witness a significant increase of potential water availability in the constrained projection, which is only 66% of that of the raw projection. Regionally, the constrained land area fraction in West African monsoon region is only 55% of the raw projection, while in South Asia and East Asian monsoon regions, the corresponding result is 71% and 76%, respectively. Hence, less land area in AfroASM will experience a significant increase of precipitation and runoff in the constrained projection. These imply that the characteristics of precipitation change in the future will be milder than the raw projection." L219-L222: "The less increase of potential water availability than the raw projection may pose a challenge to climate change adaptation and mitigation activities related to water management and food security 48,49 , although a smaller than expected increase in rainfall will also reduce the risk of extreme precipitation and flooding." Changes in precipitation (units: mm day -1 ) under SSP5-8.5 scenario (2050SSP5-8.5 scenario ( -2099 relative to historical simulation . The region surrounded by the contour is the Afro-Asian monsoon region (see Methods). (c) The inter-model standard deviation of projected precipitation changes. Hatched regions denote signal-to-noise ratio between the absolute value of projected changes and the standard deviation less than 1.5. The regions where precipitation changes are lower than 0.1 mm day -1 or over ocean is omitted. Minor comments: 1. Use of percentages: I found phrasing such as "26% less increase" (line 77) confusing. Does this mean the precipitation increase of the constrained projection is 74% of that of the raw projections? It would help to be explicit how you are comparing the constrained and raw precipitation somewhere in the main text.
Thanks. Yes. To avoid misleading, we have rephrased relevant statement of percentages throughout the revised manuscript. Please see L25-L27 and L164 in the revised manuscript.
2. Line 65: You discuss coherent rainfall variability "on various timescales" across North Africa and Asia. Although this is true on millennial timescales, on shorter timescales the picture is less clear, and your phrasing does not specify what timescales you refer to. I suggest adjusting this line to separately cite the work looking at 19 millennial and decadal timescales.
Thanks. We have separately cited the work looking at different timescales. Please see L63-L66 in the revised manuscript. We also list the revised statement below: L63-L66: "Given the fact that the monsoon precipitation in West Africa and Asia shows in-phase changes due to the modulation of interhemispheric thermal contrast (ITC) and sea surface temperature (SST) variation of North Atlantic on millennial 1,27 , centurial 4,12,26 , and decadal timescales 3,28, , …" 3. Line 84: SSP5-8.5 -acronym should probably be expanded? And perhaps it"s worth stating this is a severe scenario for anyone not familiar with the CMIP6 experimental design.
Thanks. We have expanded the SSP5-8.5 acronym, and added a brief introduction of  in the revised manuscript. Please see L77-L81 in the revised manuscript.
4. Line 88-89: Clarify that "ensemble mean and inter-model standard deviation" refer to the projected change.
Thanks. Clarified. Please see L83-L85 in the revised manuscript.
5. Line 149: You could discuss here which models/model families particularly overestimate ITC1.
Thanks. We have shown the of each model and discussed the models which overestimate the . Please see L154-L156 and Supplementary Table S3 in the revised manuscript. We also list this added information below.
L154-L156: "The models with a larger ECS, such as CanESM5 and CanESM5-CanOE, simulate a stronger ( Fig. 3a and Supplementary Tab. S3)."  6. Line 164-165: "a remarkable drying tendency is seen in the observations in the latter half of the 20th century" -perhaps specifically guide the reader to compare rainfall in the 1950s with 1980s. Because of where the 0mm/day line sits, at first glance the weakening of precipitation in the 1980s did not look large to me.

Supplementary Table
Thanks. We have replaced the baseline period of 1965-2014 with the period of 1950-1980 in the Figure 1a in the revised manuscript, to highlight the drying tendency in the observation in the latter half of the 20 th century. Please see the Figure 1a in the revised manuscript.

Summary
The authors analyze 21st century changes in precipitation over land across the African and Asian monsoon sectors in CMIP6 models under a high-emissions scenario and attempt to develop an emergent constraint thereof based on the interhemispheric thermal contrast. They argue that this constraint narrows uncertainty and results in a mean projection of increased precipitation over these regions, but less of an increase than without the emergent constraint.
There are several interesting results here, but the manuscript has two critical problems that would need to be fixed before being a plausible candidate for publication: (1) its lack of disentangling the effect of ECS on the precip changes of interest, and (2) confusing and potentially problematic methods employed to generate the emergent constraint. These and more minor comments are detailed below.
We would like to express our appreciation to the reviewer for the constructive comments that helped us to improve the manuscript. According to the reviewer"s suggestions, we have thoroughly revised the manuscript. We believe that the new results from constraining the hydrological sensitivity and global mean warming separately and clarifying the procedures on the emergent constraint help to further convince readers of our conclusions.

Role of ECS
The manuscript notes that the projected summer rainfall changes of interest are well correlated with model equilibrium climate sensitivity (ECS). This is not entirely surprising, as it is well established that more generally hydrological cycle changes to first order scale with the global-mean warming. Held and Soden 2006 and Allen and Ingram 2002 are early and canonical references here, but there is a whole literature on "pattern scaling" that discusses this in more detail, e.g. [tebaldi_pattern_2014].
Given that, as is standard in analyses of precip change under mean temperature change (I can't think of an example reference here, but there are plenty), the precip changes need to be normalized by the global-mean warming. This removes the direct influence of ECS and results in a clean disentangling of two presumably independent effects: (1) how much warming there is, and (2) given the amount of warming, how the monsoon precip will change. One can then address each factor separately, with constraints on ECS (e.g. very exhaustively addressed by [sherwood_assessment_2020]) and separately constraints such as what the present study attempts on the precip change per unit warming.
In other words, without normalizing by mean warming in each model, the present 24 manuscript's attempt nominally to constrain Afro-Asian monsoon precip change implicitly ends up being a muddied attempt to constrain both ECS and hydrological sensitivity over the Afro-Asian monsoon region.
Thanks for your valuable comments. As you suggested, we have normalized the precipitation changes using the global-mean warming, viz. hydrological sensitivity. The dominant pattern of projected uncertainty in hydrological sensitivity is shown below as Figure R2, which is similar to that in Figure 2, with a spatially consistent increase in precipitation over AfroASM ( Figure R2a) and a "NH warmer than SH" pattern ( Figure R2b and R2c). The intermodel spread of hydrological sensitivity are significantly correlated with the projected increase of ITC ( Figure R3a). Based on the relationship between present-day and the projected hydrological sensitivity, we constrain the projected hydrological sensitivity ( Figure R4). The result shows that the constrained response of hydrological sensitivity is only 87% of that of the raw projection.
While global mean surface air temperature (GMSAT) warming in the constrained projection will be weaker than that in the raw projection Liang et al., 2020;Ribes et al., 2021;Lee et al., 2021), our results show that the observational constraint leads to a weaker response of hydrological sensitivity.
We quantify the constrained projection of precipitation increase based on the constrained hydrological sensitivity and constrained GMSAT (Fig. R5). The spatial pattern of constrained projection shown in Figure R5 is like that of constraining precipitation changes directly in Figure 5 in the revised manuscript.
To quantify the relative contribution of constrained hydrological sensitivity and GMSAT to the total constrained effect, we decompose the precipitation changes as follow: where ∆ is the projected fractional change of precipitation (%), is the hydrological sensitivity (% K -1 ), and ∆ is the projected GMSAT changes (K). ∆ denote the projected changes in 2050-2099 relative to 1965-2014. and denote constrained and raw projection, respectively. Since the constrained projection consists of raw projection ( ) and constrained effect ( ′ ), the Eq. (1) can be further divided as follow: where the • ∆ denotes precipitation increase in the raw projection (∆ ). The difference between constrained and raw projection is as follow: The difference of precipitation increases and hydrological sensitivity between 25 constrained and raw projection (viz, is -30% and -13%.
of the ∆ . So the constrained effects contributed from hydrological sensitivity and GMSAT reduce the raw projection by 13% and 21%, respectively.
Based on above analyses, the conclusion based on constraining hydrological sensitivity and GMSAT separately is consistent with that based on constraining the precipitation changes directly.
In addition, both the GMSAT warming and the hydrological sensitivity are closely related to the increase of ITC ( Figure R3). Given that the large-scale monsoon circulation is generally driven by the ITC caused by the seasonal swing of solar incidence via diabatic fluxes of moist static energy (Trenberth et al., 2000;Geen et al., 2020;, we constrain the projection of AfroASM precipitation by correcting the model biases of ITC, since a pronounced overestimation of ITC is seen in the raw projection.
In summary, since the results based on your suggestion are like our original results, instead of re-organizing the logic of the manuscript, we have added a discussion on the constraint of hydrological sensitivity and GMSAT in L223-L235 of the revised manuscript while keeping the method unchanged in the text. If you think the new analysis shown here is more convincing, we are happy to replace the original results with the new results shown above. Your recommendation is appreciated in advance. In addition, the recommended references have been cited.
We also list the discussion on the constraint of hydrological sensitivity and GMSAT below for your reference: L223-L235: "Given that the inter-model uncertainty of global mean warming is closely associated with the inter-model spread of ECS 50,51 , with normalizing by the global mean warming, the precipitation response (viz, hydrological sensitivity) still shows a remarkable spread across models 10,12,52 . Recent study indicated that the projected uncertainty of hydrological sensitivity over the AfroASM regions is related to the projected uncertainty of ITC and land-sea thermal contrast 12 . Since the inter-model uncertainties of both hydrological sensitivity and global mean surface air temperature (GMSAT) are significantly correlated with the ITC (Supplementary Fig. S9), we further constrain the hydrological sensitivity and GMSAT separately based on the relationship between projected uncertainty and present-day biases (see Methods). The results based on constraining hydrological sensitivity and GMSAT separately are consistent with that based on constraining the precipitation changes directly. The constrained effects contributed from hydrological sensitivity and GMSAT reduce the raw projection by 13% and 21%, respectively."

L409-L419: "Constrained projection of hydrological sensitivity and GMSAT
The hydrological sensitivity is defined as the precipitation response normalized by the GMSAT warming in 2050GMSAT warming in -2099GMSAT warming in relative to 1965GMSAT warming in -2014 Since the inter-model spread of hydrological sensitivity is closely related to that of ITC ( Supplementary Fig. S9a), which is consistent with recent study 12 , we constrain the projection of hydrological sensitivity over AASM region based on Eq. (5) and Eq. (8). The constrained response of hydrological sensitivity is only 87% of that of the raw projection.
We constrained the projected GMSAT warming using the observed GMSAT trend in 1981-2014, following Tokarska 70 and Lee 40 . The constrained GMSAT warming is 2.62K (2.05K~3.19K, for the range of ±1 standard deviation), weaker than the raw projection [3.30K (2.52K~4.08K)] under SSP5-8.5." Figure R2. Dominant pattern of projected uncertainty of hydrological sensitivity and related historical pattern. The hydrological sensitivity is defined as the precipitation changes normalized by the global-mean warming. (a) The projected response of hydrological sensitivity (shading, mm day -1 K -1 ) and wind at 850 hPa (UV850; vector, m s -1 K -1 ) across 30 CMIP6 models under SSP5-8.5 scenario regress onto the inter-model normalized leading principal components (PC1). The PC1 are derived from the inter-model empirical orthogonal function (EOF) analysis of projected hydrological sensitivity under SSP5-8.5 in 2050SSP5-8.5 in -2099SSP5-8.5 in relative to 1965SSP5-8.5 in -2014 The percentage on the top-right corner is explained inter-model variance. (b) the future increase of surface temperature in 2050~2099 and (c) the trend of surface temperature (K) in 1965-2014 across models regresses onto the inter-model normalized PC1. The right panels in (b) and (c) are the zonal mean of the regression coefficient, and the thin dash vertical lines are the global area mean of the regression coefficient. The stippling, black vectors and hatching represent the regression exceeds 90% confidence level under student t-test. Black dash boxes in (c) are used to define the pattern indices to constrain the PC1.  can explain the PC1 with high corrected correlation coefficient (r) which is shown on the top right corner. Black fitting line is obtained by the least square method, and the red fitting line is an observational correction. Dashed curves denote the 95% confidence range of the linear regression. The black vertical and horizontal dash lines denote the mean of across multiple observation datasets and the constrained projection, respectively. The dark gray shading denotes the range of ±1-time standard deviation across observation datasets. The light gray shading denotes the range contributed from the unforced internal variability. Figure R5. The constrained projection of Afro-Asian summer monsoon precipitation based on constrained hydrological sensitivity and global mean surface air temperature. (a) The constrained precipitation (shading, mm day -1 ) and wind at 850 hPa (UV850; vector, m s -1 ; vectors drawn for larger than 0.1 m s -1 ), and (b) the constrained effect represented by the difference between constrained and unconstrained multi-model ensemble (MME).
about is the actual change in rainfall over the region. But that's never shown if I'm understanding correctly; it's inferred from the constraint on the PC and its relationship to the PC.
Separately, I'm not sure that the uncertainties are being properly propagated forward into the constraint. Fig. 4 nicely includes measures of uncertainty on both the ITC index (grey shading) and in the regression line (dashed curves). In L149 the quoted "constrained" PC1 value is -0.49±0.63. But these error bounds surely underestimate the uncertainty (also it should be stated more clearly in the main text what specifically the +/-0.63 bounds are and how they were computed). I know this isn't a rigorous way of doing it, but just by eye examine in Fig. 4 the area contained within the two dashed curves and the grey shading as a plausible estimate of the uncertainty in both terms. Within that area, the intersection of the "obs" (vertical dashed line) with the projection (horizontal dashed line) could yield PC1 as low as roughly -1.4 or as high as 0.2, a considerably wider range than -0.49±-0.63. If I am mistaken and the uncertainty in both the observed ITC index and the model PC1-ITC1 regression are in fact both being accounted for, I do apologize, but ask that you clarify the description in the text. If I am not mistaken, then how much does this weaken your constraint?
In addition, L137-139 describe the ITC index used as the constraint as "produced by projecting the present-day trend pattern of surface temperature onto the warming pattern associated with the inter-model PC1 shown in Figure 2c". Why do this projection step and not simply use the present-day trend pattern itself? Your procedure may indeed be the superior one, but it needs to be justified in the manuscript.
Thanks. The reason for using PC1 in Figure 4 is that we want to constrain the spatial pattern of AfroASM precipitation projection instead of a regional average. In the PC1, different model has different values, rightly representing the inter-model uncertainty. The corresponding EOF1 pattern, showing the spatial structure of uncertainty, is model independent. So constraining the PC1 is equivalent to constraining the precipitation itself. Constrained precipitation can be reconstructed by the constrained PC1 and the EOF1 (see Methods). Based on your suggestion, we have shown the constrained AfroASM precipitation directly in Figure 4a of the revised manuscript. Since the regional patterns are informative for policymakers, we not only constrain the regional mean of AfroASM precipitation but also its spatial patterns (Fig. 5a). This explains why we constrain the PC1 in Figure 4b in the revised manuscript. Please see L143-L147, L156-L158 and Figure 4 in the revised manuscript.
The spread of constrained PC1 is estimated by the intermodel variance of constrained PC1, which is compared with the variance of unconstrained PC1. We correct the PC1 of individual model using the observation of , based on the relationship of emergent constraint. Since the PC1 have been standardized before emergent constraint, the standard deviations of constrained and unconstrained PC1 are 0.80 and 1, respectively. Hence, the variance of constrained PC1 is about 37% less than that of unconstrained PC1. On the other hand, the dark and light gray shading denotes the range contributed from the spread across multiple observation datasets and the unforced internal variability. Similarly, the inter-model standard deviations of constrained and unconstrained AfroASM precipitation are 6.13% and 7.70%, respectively. So the constrained variance is also 37% less than the unconstrained one. As you suggested, we have described the method with more details in the revised manuscript. Please see L366-L371 in the revised manuscript.
To clearly reflect the present-day warming pattern and reduce the effect of random noise, we project the historical warming trend of surface temperature onto the PC1-related warming trend using the scalar product in Northern Hemisphere (NH; 20°N~50°N, 0~360°) and Southern Hemisphere (SH; 20°S~50°S, 0~360°), respectively, rather than use the present-day trend pattern directly, following Chen et al. (2020). In addition, we have used the present-day trend of surface temperature directly to calculate the ITC between NH-and SH-longitudinal range of the Eurasian continent (20°W~150°E), and also obtain a significant relationship between the PC1 and the trend of ITC (r = 0.45, p < 0.02).
We have justified the procedure of calculating the . Please see L309-L316 in the revised manuscript. can explain the PC1 with high corrected correlation coefficient (r) which is shown on the top right corner. Black fitting line is obtained by the least square method, and the red fitting line is an observational correction based on Equation (5) (Eq. (5); see Methods). Dashed curves denote the 95% confidence range of the linear regression. The black vertical and horizontal dash lines denote the mean of across multiple observation datasets and the constrained projection, respectively. The dark gray shading denotes the range of ±1-time standard deviation across observation datasets. The light gray shading denotes the range contributed from the unforced internal variability (see Methods) We thank the reviewer for recommending the relevant paper. We have read and cited it carefully in the revised manuscript, and have rephrased the statement. Please see L101-L103 in the revised manuscript. 9. L110-112: "rooted in" is too vague; please clarify. Also, from Fig. 2c there is much more noise for the historical, such that your claim is not immediately valid by eye from that plot. I recommend adding panels of zonal averages for both the future and historical to make this clearer.
Thanks. We have rephrased the "is rooted in" with "resulted from". In addition, we have added the panels of zonal averages for Figure 2b and 11. L123-125: These are far removed from the E. Asian monsoon sector which you otherwise are including. In addition, similar to the suggestion above for Fig. 2 I recommend adding panels of zonal-mean fields: this is quite noisy to the point that I don't find the claim about clear increases in cross-equatorial flow totally convincing.
Thanks. Both of a larger increase of ITC and a larger PC1 will induce a stronger enhancement of low-level cross-equatorial flow over South China Sea (around 105°E), which is closely linked to East Asian Summer monsoon ( Supplementary Fig. S3). We have added a statement in the revised manuscript and added panels of zonal-mean fields in the Supplementary Figure S3. Please see L125-L127 and Supplementary Figure S3 in the revised manuscript. Figure R3. Same as Figure 3 but the is defined as the difference between (0~60°N, 0~360°) and (0~40°S, 0~360°).
15. L262: Can you really claim that internal variability influence is weak over a ~3 decades timescale on regional scales? C.f. Clara Deser and Karen McKinnon's work (among others) with large ensembles and internal variability.
Thanks. The contribution from the internal variability accounts for about 20% based on the variance ratio between the internal variability and intermodel spread. Please see L316-L326 in the revised manuscript.
To avoid misleading, we have rephrased our expression. Please see L306-L308 in the revised manuscript.