Warming Overwhelms the Efficacy of Wet Conditions to Moderate Extreme Heat and Atmospheric Aridity Across the Central Plains

While the relationships between dry land surface conditions, heat, and aridity have been well‐established, few studies have addressed whether global warming will affect the ability of wet conditions to moderate high temperatures and atmospheric aridity. Using Coupled Model Intercomparison Project Phase 6 models, we demonstrate that absolute changes in the monthly maximum temperature distribution during Central North American summers strongly outweigh the historical cooling effect of high precipitation and soil moisture conditions. Although wet conditions nearly always prevent concurrent extreme temperatures in the baseline period, these conditions are 40%–48% and 96%–98% less effective at 1 and 2° of global warming, respectively. However, high precipitation and soil moisture partially retain the ability to constrain concurrent high vapor pressure deficit conditions below historical thresholds at 1–2° of warming. Our results highlight the growing vulnerability of Central North America to warmer temperatures and drier atmospheric conditions, even during periods of high precipitation and soil moisture.

. Under future warming, compound dry-hot and dry-arid events are expected to become more frequent and intense (X. Wu et al., 2021;Zscheischler & Seneviratne, 2017). However, while the historical and future relationships between drought, heat, and aridity have previously been well-studied, there has been considerably less research done on whether rising temperatures driven by anthropogenic climate change will reduce the ability of wet conditions to constrain concurrent extreme temperatures and high VPD conditions.
To address this existing research gap, we analyze how wetter than normal conditions defined by precipitation and soil moisture constrain the occurrence of high temperatures and high VPD conditions during the warm season over Central North America (CNA) across different degrees of global warming. We chose to use precipitation and surface soil moisture for our analysis as both are key variables with strong relationships with atmospheric heat and aridity through various atmospheric and land surface processes (Berg et al., 2015;. We examine surface soil moisture following the approach that previous studies have taken due to difficulties in comparing total column soil moisture across models (Dirmeyer et al., 2013). We focused on the Central North American region as this area has been documented to experience strong land-atmosphere interactions (Koster et al., 2006;Seneviratne et al., 2010) and is highly relevant to agricultural and other climate-sensitive industries (Ben-Ari & Makowski, 2014;USGCRP, 2018). The Central North American region also typically experiences cooler temperatures during wetter than normal summers (Huang & van den Dool, 1993). For these analyses, we sample different warming levels (0-3° K above pre-industrial) from 12 climate model ensembles using the Coupled Model Intercomparison Project Phase 6 (CMIP6) historical and 21st century Shared Socioeconomic Pathway high emissions scenario (SSP5-8.5) simulations (Eyring et al., 2016). Then, we quantify the capacities of specified levels of high precipitation and soil moisture to constrain concurrent high temperatures and VPD conditions under 1-3° of global warming.

Degrees of Warming
For our analysis, we used all CMIP6 models with at least five ensemble members (See Table S1 in Supporting Information S1 for models and ensemble members used). We used monthly average temperature (tas, 2 m near-surface air temperature; K) from each model's historical and SSP5-8.5 simulations from 1850 to 2100 to create a 20-year rolling global (land and ocean) area-weighted average temperature time series for each ensemble member. Then, referring to the global average temperature from 1850 to 1899 (the first 50 years of the available data) from each ensemble member, we found the 20-year periods corresponding to 1, 2, and 3° of warming (IPCC, 2021). We used the SSP5-8.5 simulations as all models warm to at least 3° of warming under this scenario, providing a wider range of warming levels to study.

Climate Variables
For each model and ensemble member, we found the land area-weighted average time series for the Central North American region. We defined the Central North American region ( Figure S1 in Supporting Information S1) as delineated by the Intergovernmental Panel on Climate Change Fifth Assessment Report and other related reports (Field et al., 2012;IPCC, 2013). For each ensemble member, we aggregated monthly precipitation (pr, precipitation rate, all phases; kg m −2 s −1 ) and soil moisture (mrsos, surface top 10 cm soil moisture content, all phases; kg m −2 ) for the June-August warm season for the periods corresponding to the 1850-1899 pre-industrial baseline (hereafter "baseline") and 1-3° of warming. We also averaged monthly maximum temperature (tasmax, 2 m near-surface air temperature; K) and vapor pressure deficit (VPD; mb) for the same 3-month period. We calculated average VPD using average temperature (tas) and relative humidity (hurs, 2 m near-surface relative humidity). First, we approximated saturation vapor pressure with the following equation: where e s is saturation vapor pressure (mb), e 0 = 6.11 mb, L = 2.5 × 10 6 J kg −1 , R v = 461 J K −1 kg −1 , and T is average temperature (K) (Hartmann, 2015). Then, we calculated actual vapor pressure with the following equation: 10.1029/2023GL102939 3 of 10 and calculated VPD with the following equation:

Maximum Temperature or VPD Probability Distributions Given High Precipitation or Soil Moisture Conditions
Following this, we conducted a copula-based assessment of the conditional distribution of maximum temperature at specified percentiles of precipitation for each degree of warming. For each model, we pooled the data from all ensemble members for the baseline period and the periods associated with each degree of warming.
For each period, we then selected the best-fit copula family with the VineCopula R package with the lowest Bayesian information criterion and passing the White's information matrix equality goodness-of-fit test with an alpha of 0.05 (Nagler et al., 2019;White, 1982). We selected from Gaussian, Clayton, Gumbel, Frank, and Joe copulas, which have been used to represent hydrometeorological multivariate dependencies in the literature (Li et al., 2021;Sadegh et al., 2017;Zscheischler & Seneviratne, 2017). The joint probability distribution of each pair of variables is as follows: where C represents the copula cumulative distribution function and X is maximum temperature and Y is negative precipitation (Sklar, 1959). We use negative precipitation, calculated by multiplying precipitation values by −1, in order to more easily find the best-fit copula families.
We then found the probability density function (PDF) of temperature conditioned on a specified high precipitation value: where c represents the copula PDF and f X (x) is the marginal temperature PDF Parker et al., 2022). The resulting PDF represents the conditional distribution of temperature at the high precipitation value. For our analysis, we chose to define high precipitation as the 75th percentile of the 1850-1899 baseline period. We then repeated this analysis for maximum temperature conditioned on high soil moisture (75th percentile of the baseline), VPD conditioned on high precipitation, and VPD conditioned on high soil moisture. We chose to use the 75th percentile instead of alternative thresholds (e.g., 80th, 90th) since the higher percentiles would not be present in many of the models at 2 and especially 3° of warming.
In our analysis, we excluded the PDFs conditioned on high soil moisture generated with MIROC-ES2L at 2° of warming and with MIROC-ES2L, MPI-ESM1-2-LR, and UKESM1-0-LL at 3 degrees of warming. These models lacked adequate data at the specified degrees of warming corresponding to the 75th percentile of the baseline period, inhibiting an accurate estimate of their conditional PDFs (see Supporting Information S1).

Conditional Non-Exceedance Probability
Using the conditional PDFs generated for each degree of warming, we found the probability that maximum temperature or VPD stays below the 75th percentile of the baseline period, which we refer to as non-exceedance probabilities. We used the 75th percentile to represent high temperature or VPD events and to evaluate the changing probability of constraining these high-impact events across increasing degrees of warming. We also examined the non-exceedance probabilities associated with the 80th and 90th percentiles of maximum temperature or VPD in the Supporting Information S1 to evaluate the sensitivity of our results to varying thresholds.

Signal-To-Noise Ratio
Finally, we examined the signal-to-noise ratio of each model for each pair of variables. We defined the signal-to-noise ratio as the ratio of the mean difference between 2° of warming and the baseline marginal distributions to the standard deviation of the baseline marginal. Lower signal-to-noise ratios represent smaller changes in the location of the marginal distribution relative to the variance of the original baseline distribution. We used the signal-to-noise ratio values to better understand the intermodel variability of the non-exceedance probabilities from the above analysis.

Results
We first examine the marginal and conditional distributions of maximum temperature ( Figure 1) and VPD ( Figure 2) under the baseline period of 1850-1899 and the periods associated with each degree of warming. In the Supporting Information S1, we also provide the marginal distributions for precipitation and soil moisture ( Figures S2 and S3 in Supporting Information S1) and percentiles for each degree of warming equivalent to the 75th percentile of the baseline period (Tables S2 and S3 in Supporting Information S1), which we use to determine which models and degrees of warming to present for the conditional PDFs. Figure 1a shows how the marginal distributions of maximum temperature have consistently shifted to the right across increasing degrees of warming while retaining a similar distributional shape. There are minor differences in the magnitudes of the changes, but shifts in the distributions toward warmer conditions are universal across all the models. Figures 1b and 1c show the conditional distributions of maximum temperature based on high precipitation and high soil moisture conditions, respectively. In the baseline period, all models show that high precipitation and high soil moisture are consistently coupled with maximum temperature conditions that fall below the 75th percentile of the baseline. However, even at 1° of warming, the attenuating effects of high precipitation and soil moisture are partially outweighed by the absolute changes in the marginal maximum temperature distributions, resulting in lower probabilities of non-extreme temperatures. At 2° of warming, the vast majority of maximum temperatures concurring with high moisture conditions are higher than the 75th percentile of the baseline.
In Figure 2a, we see that the marginal distributions of VPD have also shifted to the right across the warming levels. However, in many of the models, the range of the VPD distribution widens over time, including much higher VPD values while still retaining values from the baseline period. Relative to maximum temperature, we see greater increases in the right tail of the marginal distribution due to the non-linear dependence of saturated vapor pressure on temperature (Seager et al., 2015). Meanwhile, in Figures 2b and 2c, high precipitation and soil moisture produce substantially larger constraining effects on the locations and ranges of VPD distributions that persists to 2° of warming relative to maximum temperature. These conditional differences between maximum temperature and VPD originate from how the locations and shapes of the marginal distributions of maximum temperature and VPD have evolved over increasing degrees of warming. Differences in the strength of the dependencies between maximum temperature and precipitation (or soil moisture) and between VPD and precipitation (or soil moisture) conditions also contribute to the ranges of the conditional distributions. In the Supporting Information S1, we include an additional analysis of maximum temperature and VPD conditioned on high precipitation during 1950-1969 and 2000-2019 using the Ensemble Meteorological Data set for Planet Earth (EM-Earth) data set to provide an observational benchmark for our model-based results ( Figure S4 in Supporting Information S1). We also present an equivalent time period analysis with the CMIP6 models ( Figure  S5 in Supporting Information S1).
Using the conditional distributions from Figures 1 and 2, Figure 3 presents the maximum temperature and VPD non-exceedance probabilities. At baseline 1850-1899 conditions, maximum temperature and VPD almost always fall below the 75th percentile threshold. At the baseline, the multi-model ensemble mean non-exceedance probability for maximum temperature conditioned on high precipitation is 96.82%, while the ensemble mean non-exceedance probability for maximum temperature conditioned on high soil moisture is 97.95%. For VPD, the corresponding mean non-exceedance probabilities conditioned on high precipitation and high soil moisture are 99.01% and 99.78%, respectively. At 1° of warming, large differences appear between the non-exceedance probabilities for maximum temperature and VPD. Maximum temperature non-exceedance probabilities decrease substantially (to 50.09% and 58.43% for precipitation and soil moisture), while VPD non-exceedance probabilities are more stable (at 81.04% and 90.85%). At 2° of warming, there is very little probability of constraining maximum temperature below the baseline threshold. On the other hand, a group of models (ACCESS-ESM1-5, CanESM5, CNRM-CM6-1, CNRM-ESM2-1, and to some extent, UKESM1-0-LL) continue to constrain the probability of high VPD conditions under high precipitation and high soil moisture conditions. Overall, Figure 3 highlights the strong differences between maximum temperature and VPD conditioned on high precipitation and high soil moisture conditions.
In the Supporting Information S1, we include tables of correlations for each pair of variables (Tables S4-S7 in Supporting Information S1). For most models, soil moisture possesses stronger relationships with both maximum temperature and VPD, which allow soil moisture to constrain maximum temperature and VPD to a greater extent 10.1029/2023GL102939 6 of 10 relative to precipitation. Across the degrees of warming, we also see that there are no systematic changes in the dependence between the variables. In the Supporting Information S1, we also show that individual changes in actual or saturated vapor pressure do not influence the magnitudes of the non-exceedance percentiles ( Figure  S6 in Supporting Information S1). Therefore, the conditional PDF changes observed here are mainly driven by changes in the marginal maximum temperature and VPD distributions. We additionally show that the results are consistent across different non-exceedance thresholds ( Figures S7 and S8 in Supporting Information S1).
Finally, to further investigate the differences in model representations of VPD responses to high moisture conditions, we examine the impact of the "signal-to-noise" on the non-exceedance probabilities. In Figure 4, we compare signal-to-noise against the non-exceedance probabilities at 2° of global warming to better understand the  emerging divergence in non-exceedance values amongst the models at 2°. In general, lower signal-to-noise ratios correlate with higher non-exceedance probabilities as expected, with Kendall tau correlation values of −0.697 under high precipitation and −0.418 under high soil moisture. We see moderate deviations from this general trend due to concurrent changes in the conditional VPD distributions relative to the marginals that stem from how precipitation and particularly soil moisture are projected to change across the warming levels. For example, the GISS-E2-1-G and GISS-E2-1-H models experience relatively wetter soil moisture conditions under the 2° warming level (see Table S3 in Supporting Information S1), which push the conditional VPD distribution to be sampled closer to the center of the marginal, and effectively decrease the non-exceedance probabilities due to the stability of the relationship between soil moisture and VPD across the warming levels. This is likely due to the inclusion of irrigation in the GISS models, which is not accounted for in the other models (Cook et al., 2020).
In the Supporting Information S1, we provide additional signal-to-noise results at 1° of global warming for both maximum temperature and VPD ( Figure S9 in Supporting Information S1). Overall, these results highlight the need to better characterize present and future relative changes in marginal distributions in the climate models in order to better understand conditional risks under future degrees of global warming.

Discussion and Conclusions
Here we demonstrate the effect of global warming on the ability of high precipitation or soil moisture conditions to constrain high maximum temperatures and VPD below historical thresholds. In Central North America, absolute changes in the maximum temperature distribution outweigh the historical cooling effect of concurrent high precipitation or soil moisture conditions under higher degrees of warming. Even at just 1° of warming, we observe a substantial decline in the cooling effect of wet conditions on maximum temperature and at 2° of warming, this cooling effect no longer has any meaningful impact on the occurrence of non-extreme temperatures. Due to the nature of changes in the VPD distribution, however, wet conditions partially retain the ability to moderate concurrent VPD conditions under similar degrees of warming. However, we also see diverging VPD responses to wet conditions under warming conditions across the models, which relate to variations in the baseline distributions and projected VPD shifts. Due to this, we highlight the need for individual model communities to better understand the factors contributing to model-specific variations in maximum temperature and VPD marginal distributions as well as precipitation and soil moisture distributions, which contribute to differences in non-exceedance probabilities. Additionally, in light of the variability of conditional VPD distributions and non-exceedances, especially at 2° of warming, additional studies on the factors contributing to projected changes in conditional VPD distributions would provide valuable insights into projected risks of high aridity events.
These conditional changes stem primarily from shifts in the marginal maximum temperature and VPD distributions. The directional response of these distributions in the model projections is consistent with observed trends. Maximum temperature distributions have responded strongly to historical global warming, and are expected to continue increasing with future warming USGCRP, 2018). Although there has been less research on changes in VPD, a recent study by Ficklin and Novick (2017) found moderate historical increases in VPD across much of the US in summer months and additional future increases in VPD throughout the 21st century (Ficklin & Novick, 2017). In the Central United States, the historical changes in summer VPD resulted from increases in saturated vapor pressure, with little to no change in actual vapor pressure (Ficklin & Novick, 2017). Projected changes in summer VPD between the late 20th and 21st centuries also stem from larger increases in saturated vapor pressure relative to actual vapor pressure (Ficklin & Novick, 2017). We also observe this in our evaluation of how the individual components of VPD evolve across the degrees of warming ( Figure  S4 in Supporting Information S1).
We found no significant change in the functional relationships between the different variables across the degrees of warming, indicating this is not contributing to the conditional changes mentioned above. Previously, Zscheischler and Seneviratne (2017) showed that the northern CNA region experienced a distinct increase in the dependence between warm season precipitation and temperature from the late 19th to the 21st century in CMIP5 models (Zscheischler & Seneviratne, 2017). Meanwhile, in their results, the southern CNA region experienced little to no change in dependence (Zscheischler & Seneviratne, 2017). In contrast, we do not find notable changes in the dependence between maximum temperature and precipitation in the region in CMIP6. However, our results generally agree with , which found that the dependence between soil moisture and VPD was comparable between historical and future periods across the globe (Zhou, Williams, 10.1029/2023GL102939 9 of 10 et al., 2019). Overall, our results may also be sensitive to the accuracy of individual climate models' representations of the dependence between atmospheric heat, atmospheric dryness, and wet conditions (Hao et al., 2019;R. Wu et al., 2013). We acknowledge that changes (or the lack of) in the relationships between the four major variables of interest may need to be further explored in other regions, as differences may arise across climate regimes. We also recognize that underestimations of evapotranspiration in CMIP6 models may impact temperature and VPD (Dong et al., 2022;Zhao et al., 2022), and further study of model representations of land surface fluxes are critical in refining future projections of atmospheric heat and aridity.
This study shows that in Central North America, underlying changes in the marginal distributions of maximum temperature and VPD reduce the historical ability of wet conditions to constrain high temperature and high VPD conditions under global warming. As temperatures warm to 2-3° of warming, although high precipitation and high soil moisture conditions will continue to reduce high temperatures and extreme aridity in a relative sense, these wet conditions will be unable to prevent temperatures and VPD conditions from exceeding what would historically be considered extreme thresholds. Overall, Central North America is rapidly moving toward warmer temperatures that can no longer be constrained by wet conditions and also moving toward drier atmospheric conditions even during periods of high precipitation and high soil moisture. These projected increases in heat and aridity will seriously impact the region's public health and climate-vulnerable industries (Kovats & Hajat, 2008;Teixeira et al., 2013). Finally, although our study was focused on Central North America, conditional heat and aridity extremes are relevant across the globe and conducting similar studies in different climate regimes may provide better insights on regional global warming impacts.

Data Availability Statement
The CMIP data used in this study is available through ESGF at https://esgf-node.llnl.gov/projects/esgf-llnl/. The CMIP6 models used can be found in Table S1 in Supporting Information S1.