Wetter summers can intensify departures from natural variability in a warming climate

Climate change can drive local climates outside the range of their historical year-to-year variability, straining the adaptive capacity of ecological and human communities. We demonstrate that dependencies between climate variables can produce larger and earlier departures from natural variability than is detectable in individual variables. Using the example of summer temperature (Tx) and precipitation (Pr), we show that this departure intensification effect occurs when the bivariate climate change trajectory is misaligned with the dominant mode of joint historical variability. Departure intensification is evident in all six CMIP5 models that we examined: 23% (9–34%) of the global land area of each model exhibits a pronounced increase in 2σ anomalies in the Tx-Pr regime relative to Tx or Pr alone. Observational data suggest that summer Tx-Pr correlations in distinct regions on all continents are sufficient to produce departure intensification. Precipitation can be an important driver of multivariate climate change signals relative to natural variability, despite typically having a much weaker univariate signal than temperature.

: There are interesting differences between the observed and simulated T X-Pr correlations such as equatorial West Africa, as well as areas where the correlations are remarkably similar, like Australia and the US. It would be worth commenting on potential causes of differences between the observed and simulated correlations with respect to West Africa-are there individual models with similar patterns? Do we trust the observations in this region? L55: While I like the multivariate approach here, I suspect that the TX change is dominating over the Pr change in line with the findings of previous studies. Figure 2b: I think the label should read "Historical + RC P4.5 30-yr running mean" L89: Is the Tx change always larger than the Pr change? Figure 3: I'm a bit confused as to exactly what is being shown here -is it the average departure between runs of the same model? Is the average a median or a mean (a mean -average is sensitive to outliers)? It would be useful to have an indication of the level of agreement between land area proportions between runs of the same model and dif ferent models (similar to King et al. 2015;Bador et al. 2016).
The authors show that dependencies in earth system models between multiple variables (here: temperature and precipitation) cannot be neglected when computing the 'time of emergence' or departure from natural variability at each model location. Specifically they show, that many regions on Earth depart faster from natural variability in case one considers the multivariate correlations structure of temperature and precipitation. They provide sufficient evidence for their conclusions.
Technically, they use the Mahalanobis distance to the mean as a measure of multivariate departure from natural variability. The statistical analysis via Mahalanobis distance is sound as such. Although the technique dates back several decades ago and is common in other fields of science, it is not commonly used in this particular field of science to the best of my knowledge. Thus, the technique is novel for this particular application on C MIP5 models. The novel multivariate perspective furthermore offers advance to previous journal articles on this topic. In general, the manuscript allows to reproduce the results. There are only minor issues to improve understandability, which are described in detail below.
The paper is timely and interesting to others in the field as it goes in line with recent activity on multivariate extremes / compound events. I believe, that it sets new standards for future publications on the time of emergence / departure time, as it highlights the imp ortance of the multivariate perspective on this particular topic.
I would recommend to a accept the paper for publication in nature communications after the authors carefully addressed the following questions.
Best regards, Milan Flach _________________________________ *Major C omments to the Authors: * 1.) The definition of summer in the paper seems to be a bit too simplistic to me. Specifically, as already mentioned in the discussion (p.6, l.158), it hinders a straightforward interpretation of yo ur results in the tropics (p.5, l.110). I was wondering, if it would be possible to change the definition of your summer (the warm period) to be the hottest three month of tmax (comparable e.g. to (1)). This rather small change would make your statement much stronger in low latitude regions, which are very much affected by the intensification of departure.
2.) You state in the introduction, that the environment is locally adapted to the climate in which it is living (p.1, paragraph 1/2). You are using runs of the C MIP5 models with historical natural variability to quantify the normal local variability within each gridcell. In case, one uses historical runs, one assumes that no further adaptation is taking place, which is not very plausible to my mind. Nevertheless, your approach is valid and commonly used. However, I was wondering about the time scale of local adaptation to climate. May be you could elaborate on this a bit further in the introduction. Defining a specific time scale for adaptation to the loc al climate would be another option for such kind of studies, which goes behind the scope of this paper, but nevertheless should be mentioned.
3.) On p.4, l 95, you are stating that large departure correlation goes in line with orthogonality to the natural mode of interannual variability. Would it be possible to provide further (quantitative) evidence for this finding as supplementary material? Probably, the second component of a principal component analysis (PC A) could serve as a measure of orthogonality to natural variability. PC A is technically very much related to / the same as the Mahalanobis distance to the mean. 4.) On p. 7, ll. 224-225 your are defining the univariate 2 sigma proportion as the maximum of the 2 sigma proportions of temperature and precipitation for computing the departure difference. May be it would improve understanding, if you add a (pseudo) formula here, like max(prop(Tx), prop(Pr)), in case I understood it correctly. It would also be nice if you elaborate further on the reason for this specific choice. Furthermore other choices would be thinkable, like computing the 2 sigma proportion as sigma exceedances of either precipitation or temperature (prop(Tx or Pr)), or computing the 2 sigma proportion of the marginal distributions of temperature or precipitation separately (prop(Tx) or prop(Pr)). The latter choice would probably be very helpful to disentangle / attribute high departure differences to the univariate drivers. Thus, I would highly appreciate if you could provide some supplementary material on e.g. the latter alternative choice. *Minor C omments to the Authors:* p.1, l. 3.: 'interactions between climate variables'. The meaning of the word 'interactions' goes much further, than what you are actually looking at. I would favour a more neutral wording like 'correlations' or 'dependencies'. (similar: p.4, l. 48; p. 5, l. 146; p.6, l. 173, 182, 184, 187) p.4, l. 87: 'sigma dissimilarity, a novel method.' The technique of 'sigma dissimilarity' translates anomaly scores of the multivariate Mahalanobis distance into percentiles of the theoretically received chi-squared distribution. Although I am in favour of the 'sigma dissimilarity' technique, calling this method 'novel' without a detailed literature review seems a bit exaggerated to me. The Mahalanobis distance is used since 1936 (2) and used for novelty / anomaly detec tion as Hotelling's T^2 control chart since 1947 (3). The reviewer would be wondering, if nobody used percentiles of the chi-squared distribution in these decades. The reviewer would like to ask the authors to remove 'novel' from the sentence or to reword and clarify: what is particularly novel on the sigma dissimilarity technique? p. 5, ll.132-134: This finding is particularly interesting for estimating departure intensification in (methodologically more simplistic) impact focussed studies on novel clima tes. However, wether higher correlations lead to a higher 'risk' in therms of impact on humans or biological systems is questionable / not a direct result of this study. It would require further research or might be better moved to the discussion part. p. 6, l. 175: Did you actually try to detect the multivariate events by SPEI? p. 6, ll. 178-179 and 184: Misleading for my understanding is the 'mechanism by which compound events to occur', which you refer to. As far as I understood the study, it is focu ssed on statistical correlations between precipitation and temperature and not on 'mechanisms' which would induce those kind of departures. C ould you please elaborate further on what they specifically mean or rephrase the statement. p. 6, ll. 182-183: 'We have demonstrated that variable interactions can accelerate the rate at which locally unfamiliar climates develop, which is a critical limitation on the ability of organisms and societies to adapt to climate change.' The second part of this statement is not a direct finding of this study and requires a citation as such.
p. 6, l.190: Mentioning the reference period immediately rises the question: which reference period? It would probably helpful for better understanding to include a reference to the late r section on this topic. p.7, l. 204: Please add a citation for the Mahalanobis distance ,e.g. (2) or (3) below, and/or reference number 31 from your manuscript (as more recent one).  General C omments: This is a very nice paper that clearly and thoroughly makes the case for considering pertinent variables in concert rather than in isolation when looking at changes in climate extremes. The authors focus on the relationship between summertime mean daily maximum temp erature (Tx) and total precipitation (Pr), demonstrating that in many regions of the globe these variables are negatively correlated, with wet summers tending to be cool and dry summers tending to be hot. A warming climate, however, is pushing some regions towards warmer and wetter conditions. At these locations, the authors demonstrate that future conditions are likely to move beyond the historically-covered regions of the Tx-Pr parameter space more quickly than a climate change signal would emerge when considering either variable by itself. The authors made a good case for why these changes could have important consequences for many ecosystems. I believe this is a very strong paper and that Nature C ommunications is an excellent outlet for the material. I h ave listed a few minor suggestions for improvements below.
Specific C omments: 1. The introduction does a nice job of establishing the motivation for this study. You could draw further support by referring to examples of studies of future climate extreme s that used variables depending on both temperature and humidity, e.g. wet-bulb temperature (Pal and Eltahir, 2016;Im, Pal and Eltahir, 2017) or wet-bulb globe temperature (Knutson and Ploshay, 2016 2. Figure 1: "historicalNat" hasn't been defined yet. I think it is only defined in the methods. You should mention that Figure S7 shows results from the individual models. 3. Figure 2: The specific examples of different possibilities (low Tx -Pr correlation, etc) are great, and the text describing Figure 2 very clearly explains the three relevant factors for departure intensification. The caption should mention the time period captured by the map in plot a. What does negative number of years for the red lines mean? According to the y-axis label they are a number of years (out of 30) divided by 30. If this is not correct, please clarify. In the methods you describe how the departure difference can be negative, but not how the 2σ proportion can be negative. 4. Line 164: Your results only show variability correlations stronger than -0.5, not +/-0.5. I understand that you are leading into talking about other variable pairs, but perhaps you can rephrase this sentence so it is cleaner. 5. Line 219: I think you should more explicitly indicate how you compute that a 3σ exceedance is a 1-in-370-year event.
The supplementary materials provide details that may be of interest to certain readers and enhance the rigor and thoroughness of the study. I believe they are corr ectly placed in the supplement.

Response to reviews
We would like to thank the reviewers for providing thorough reviews with helpful suggestions. We have described the changes we have made and any responses to comments below in blue font.
With the exception of some minor edits, the only change we have made that is unrelated to the reviewer comments is the deletion of the last two sentences of the abstract, to conform to the 150word limit in the Nature Communications formatting standard.

Reviewers' comments:
Reviewer #1 (Remarks to the Author): Review of "Wetter summers can intensify departures from natural variability in a warming climate." by Mahony and Cannon.
This study applies a signal-to-noise approach to maximum temperature and precipitation in combination, and identify where this approach finds earlier climate change influences compared with a univariate methodology.
The results are interesting and the paper is very well-written and will make an excellent contribution to the literature. I only have a few minor comments. We have added a discussion paragraph that raises this issue. The CESM-CAM5 ensemble produces a similar but weaker pattern of positive correlations in western equatorial Africa ( Figure S9). Given the scope and focus of the study, we cannot comment on the reasons for this difference or on the credibility of the observations in this region. However, Berg et al.
(2015) speculate on physical processes responsible for model differences in simulated temperatureprecipitation correlations. In the context of negative correlations, they found that an analysis of "five climate models, which were integrated with prescribed (noninteractive) and with interactive soil moisture over the period 1950-2100.
[…] confirm the interpretation that negative correlations between seasonal temperature and precipitation arise through the direct control of soil moisture on surface heat flux partitioning, the presence of widespread negative correlations when soil moisture-atmosphere interactions are artificially removed in at least two out of five models suggests that atmospheric processes, in addition to land surface processes, contribute to the observed negative temperature-precipitation correlation." Differences in the relative contributions of these processes may explain some of the differences between the models. L55: While I like the multivariate approach here, I suspect that the TX change is dominating over the Pr change in line with the findings of previous studies.
We have added a new section S8 that confirms the reviewer's assertion: the Tx S/N is greater that the Pr S/N in almost all grid cells. We have added some clarifying text to the Results section "Factors contributing to departure intensification": "The strength of the projected climate change signal is larger in temperature than in precipitation in almost all grid cells (Supp. Info. S8). However, the precipitation trend determines the alignment of climate change with interannual variability." Figure 2b: I think the label should read "Historical + RCP4.5 30-yr running mean" We originally excluded a reference to the "historical" run for brevity, but agree with this suggestion and have now included it in both Figure 1 and Figure 2.
L89: Is the Tx change always larger than the Pr change?
We have added a new section S8 "Relative departures of temperature and precipitation" to the supporting information to answer this question. We have provided an assessment of the difference in 2σ proportions of Tx and Pr in the 2021-2050 period ( Figure S11). There are only a few locations where Pr departures are greater than Tx departures, and these occurences are not consistent between models. Some of these occurrences persist into the 2071-2100 period. Important question. We have reworded the Figure 3 caption and added a supp info section S9 to clarify the calculation of the values being mapped. The calculation of maximum departure difference from the ensemble of runs for each model is illustrated in Figure 2b. First, we calculate the mean time series of univariate and bivariate 2-sigma proportion from the time series of each run; then we find the maximum departure difference between these mean time series. The alternate approach would be to take the mean of the maximum departure differences of each model run. We used the former approach and not the latter because 2-sigma proportion is quite noisy (due to calculation from a binary criterion); the maximum difference between noisier time series is greater, and hence the latter approach produces a biased (overestimated) maximum departure difference. A Figure 3 calculated from the latter approach is shown below: compared to Figure 3 in the manuscript, it clearly demonstrates the bias induced by taking the mean of the maximum departure differences of individual runs. The drawback of our approach is that it synthesizes all model runs into a single value, and therefore precludes the calculation of within-model variation in departure intensification (though see shaded regions of the 2-sigma proportion time series in Figures 2b-g for a sense of intramodel variation in a few grid cells of the CanESM2 model). We agree that this opening statement to this paragraph was misleading because it was overly generic and have changed it to read:  Figure 3b), and found that the emergences detected with the KS test were entirely undetected with S/N>1. In addition to the S/N method being less sensitive, the 2-sigma proportion has lower sensitivity to small (<0.5 sigma) climate shifts because increases in the frequency of 2-sigma anomalies on one tail of the distribution are partially balanced by decreases on the other tail (indicated by the sigmoidal shape of the response curves in Figure S7a). This is a useful, conservative, feature of the 2-sigma proportion but it does reduce the potential to detect departures and departure intensification in the early stages of emergence of the climate signal.
The authors show that dependencies in earth system models between multiple variables (here: temperature and precipitation) cannot be neglected when computing the 'time of emergence' or departure from natural variability at each model location. Specifically they show, that many regions on Earth depart faster from natural variability in case one considers the multivariate correlations structure of temperature and precipitation. They provide sufficient evidence for their conclusions.
Technically, they use the Mahalanobis distance to the mean as a measure of multivariate departure from natural variability. The statistical analysis via Mahalanobis distance is sound as such. Although the technique dates back several decades ago and is common in other fields of science, it is not commonly used in this particular field of science to the best of my knowledge. Thus, the technique is novel for this particular application on CMIP5 models. The novel multivariate perspective furthermore offers advance to previous journal articles on this topic. In general, the manuscript allows to reproduce the results. There are only minor issues to improve understandability, which are described in detail below.
The paper is timely and interesting to others in the field as it goes in line with recent activity on multivariate extremes / compound events. I believe, that it sets new standards for future publications on the time of emergence / departure time, as it highlights the importance of the multivariate perspective on this particular topic.
I would recommend to a accept the paper for publication in nature communications after the authors carefully addressed the following questions.
Best regards, Milan Flach _________________________________ *Major Comments to the Authors: * 1.) The definition of summer in the paper seems to be a bit too simplistic to me. Specifically, as already mentioned in the discussion (p.6, l.158), it hinders a straightforward interpretation of your results in the tropics (p.5, l.110). I was wondering, if it would be possible to change the definition of your summer (the warm period) to be the hottest three month of tmax (comparable e.g. to (1)). This rather small change would make your statement much stronger in low latitude regions, which are very much affected by the intensification of departure.
We agree with the reviewer that a hottest-3 months analysis can be helpful, and we have provided a parallel set of results using this alternative definition of summer in supporting information section S10. We would prefer to maintain our current definition of summer in the main manuscript to maintain the connection to the many other studies that use a JJA/DJF definition of summer, and also due to the simplicity and transparency of the approach. The overall difference between the two approaches is subtle, though it is regionally important in the tropics as predicted by the reviewer. We believe that providing results for both definitions of summer will be informative for readers.
Thank you for pointing us towards Zscheischler & Seneviratne (2017)., a highly relevant related study which we have added to our references on compound events.
2.) You state in the introduction, that the environment is locally adapted to the climate in which it is living (p.1, paragraph 1/2). You are using runs of the CMIP5 models with historical natural variability to quantify the normal local variability within each gridcell. In case, one uses historical runs, one assumes that no further adaptation is taking place, which is not very plausible to my mind. Nevertheless, your approach is valid and commonly used. However, I was wondering about the time scale of local adaptation to climate. May be you could elaborate on this a bit further in the introduction. Defining a specific time scale for adaptation to the local climate would be another option for such kind of studies, which goes behind the scope of this paper, but nevertheless should be mentioned.
This is an excellent point, and applies more generally to the larger literature on time-of-emergence and climate departures. We have added a paragraph in the discussion to raise this issue. We agree that at any point in time, ecological and social systems will have adapted to some extent to historical climate changes, and that a pre-industrial baseline doesn't account for these adaptations. However, there is a counter-argument that many of these adaptations will have been disruptive and costly, and therefore should be accounted for as impacts of climate change. . The added paragraph reads: "The impacts of climate departures are subject to the timescales over which maladaptation to unfamiliar local conditions is mitigated by gene flow, innovation, and other nondisruptive adaptive processes. In contrast to studies using a recent reference period (Giorgi and Bi 2009, Hawkins and Sutton 2012, Mora et al. 2013, our pre-industrial baseline precedes any local adaptation that has occurred during the industrial period, and may overstate the timing and magnitude of some of the disruptions associated with climate departures. The timescales of local adaptation are an important consideration in the assessment of the specific impacts of climate departures." 3.) On p.4, l 95, you are stating that large departure correlation goes in line with orthogonality to the natural mode of interannual variability. Would it be possible to provide further (quantitative) evidence for this finding as supplementary material? Probably, the second component of a principal component analysis (PCA) could serve as a measure of orthogonality to natural variability. PCA is technically very much related to / the same as the Mahalanobis distance to the mean.
We have made several modifications of the manuscript to quantify the orthogonality of the bivariate climate signal as a factor in departure intensification.
• Added Illustration of orthogonality to Figure 2b and quantified orthogonality in figures 2b-g; • modified Figure 4 to include color-theming by orthogonality; • added maps of the orthogonality of climate change to Supp Info Section S7; • Restructuring of results section "Factors contributing to departure intensification" to emphasize correlation and orthogonality as the two key factors in departure intensification; and • Added method for calculating orthogonality to methods section "Bivariate standardized anomalies.
We thank the reviewer for this suggestion, as the quantification of orthogonality is an important improvement to this paper.
4.) On p. 7, ll. 224-225 your are defining the univariate 2 sigma proportion as the maximum of the 2 sigma proportions of temperature and precipitation for computing the departure difference. May be it would improve understanding, if you add a (pseudo) formula here, like max(prop(Tx), prop(Pr)), in case I understood it correctly. It would also be nice if you elaborate further on the reason for this specific choice. Furthermore other choices would be thinkable, like computing the 2 sigma proportion as sigma exceedances of either precipitation or temperature (prop(Tx or Pr)), or computing the 2 sigma proportion of the marginal distributions of temperature or precipitation separately (prop(Tx) or prop(Pr)). The latter choice would probably be very helpful to disentangle / attribute high departure differences to the univariate drivers. Thus, I would highly appreciate if you could provide some supplementary material on e.g. the latter alternative choice.
We have added two sections in the supporting information that address this comment: The first, "S9. Pseudocode for calculation of maximum departure difference," describes and provides a rationale for the approach we took. This pseudocode complements the R code provided in the original package. The second section, "S8. Relative departures of temperature and precipitation," demonstrates that temperature is almost exclusively driving the univariate departure, and therefore that the suggested alternative approach of calculating departure difference from the marginal distributions would likely have very subtle impact on the results. We used the word "novel" in the context of calculating multivariate S/N and standardized anomalies. That said, we see that it can easily be misinterpreted as a more general claim of novelty. We concur with the reviewer that a more conservative wording is appropriate. We removed the word "novel" as suggested and included an explicit reference to Mahalanobis distance: "…sigma dissimilarity (Mahony et al. 2017), a parametric method of calculating multivariate S/N ratios and standardized anomalies using Mahalanobis distance (Mahalanobis 1936)." p. 5, ll.132-134: This finding is particularly interesting for estimating departure intensification in (methodologically more simplistic) impact focussed studies on novel climates. However, wether higher correlations lead to a higher 'risk' in therms of impact on humans or biological systems is questionable / not a direct result of this study. It would require further research or might be better moved to the discussion part.
We changed the wording from "…at risk of…" to "…that are susceptible to…" p. 6, l. 175: Did you actually try to detect the multivariate events by SPEI?
We did not. Moreover, this sentence is not correct, since PC2 is a synthetic univariate index that would indeed capture departure intensification quite well. We have changed the wording: "The case of departure intensification illustrates that some compound events are purely primarily multivariate : they cannot be detectedand can remain undetected in by univariate indices that synthesize temperature and precipitation, such as the standardized precipitation-evapotranspiration index and wet bulb temperature".
p. 6, ll. 178-179 and 184: Misleading for my understanding is the 'mechanism by which compound events to occur', which you refer to. As far as I understood the study, it is focused on statistical correlations between precipitation and temperature and not on 'mechanisms' which would induce those kind of departures. Could you please elaborate further on what they specifically mean or rephrase the statement.
We changed the wording to "Our study demonstrates a form of compound extremes arising from historically unusual combinations of conditions. These compound anomalies can occur both as singleyear events and long-term climatic shifts." p. 6, ll. 182-183: 'We have demonstrated that variable interactions can accelerate the rate at which locally unfamiliar climates develop, which is a critical limitation on the ability of organisms and societies to adapt to climate change.' The second part of this statement is not a direct finding of this study and requires a citation as such.
We softened the wording to "which may be a limitation on the ability of some organisms…" and added references to the literature that suggests this to be the case.