We employ the CESM2-LE to study hot and dry compound events in preindustrial, present, and future climates (Rodgers et al., 2021; Danabasoglu et al., 2020). CESM2-LE follows protocols provided by the Coupled Model Intercomparison Project Phase 6 (CMIP6), with historical forcings for 1850-2014 and SSP3-7.0 forcings for 2014-2100 (Eyring et al., 2016). Monthly data for precipitation rate (PRECT), 2m temperature (TREFHT), surface temperature (TS), and surface-level pressure (PSL) are used to define and analyze compound events on a 0.94° by 1.25° horizontal grid. The ensemble mean over all 100 members is computed monthly and subtracted from each member to remove the forced response and the seasonal cycle. Temperature and precipitation anomalies are then analyzed for each month of every year from 1850 to 2100.

Monthly El Niño Southern Oscillation (ENSO), Indian Ocean Dipole (IOD), and Pacific Decadal Oscillation (PDO) indices from the CESM Climate Variability Diagnostics Package (Maher et al., 2024; Phillips et al., 2014) are used to explore the connection between modes of internal climate variability and hot and dry compound events (calculations of these indices are defined in the Supplementary material). Monthly North Atlantic Oscillation (NAO) indices are calculated in each member from the difference of normalized sea level pressure between Ponta Delgada, Azores (38.17 N, 25 W) and Stykkisholmur/Reykjavik, Iceland (63.61 N, 22.5 W) (Hurrell and Deser, 2009). Although climate change could impact the spatial patterns of the modes of internal variability, there is no consensus on how potential shifts may be manifested. We therefore have chosen to compute the large-scale climate mode indices in a consistent manner over time (e.g., Maher et al., 2023; McKenna and Maycock, 2022). The positive phase of each of these four modes is defined as the anomalies in the indices (standard deviation) that are ≥0.5, the negative phase as ≤ –0.5, and the neutral phase as the anomalies between these two bounds.

All climate models, including CESM2, exhibit biases in their simulation of internal climate modes and their teleconnections relative to observations. For instance, during El Niño, CESM2 tends to exhibit a dry bias over the Maritime Continent in June-November and a wet bias the rest of the year (Maher et al., 2024; Phillips et al., 2020a). There is also a dry bias in the majority of Australia in all seasons, but a regional wet bias does occur in some members (Maher et al., 2024; Phillips et al., 2020a). For highly variable metrics—such as those associated with modes of internal variability—the extent to which CESM2 aligns with the single realization that the observations represent is highly dependent on the CESM2 ensemble member chosen for comparison (Maher et al., 2024), which is not surprising as it is a free-running simulation. Despite these biases and challenges in comparing with observations, the simulation of climate modes and their teleconnections in CESM2 are improved over earlier versions of the model and many aspects are consistent with the observational record (e.g., Chen et al., 2021; Capotondi et al., 2020; Danabasoglu et al., 2020; Phillips et al., 2020b; Simpson et al., 2020; Meehl et al., 2020; Lawrence et al., 2019). Existing research further demonstrates CESM2's ability to simulate extremes (e.g., Chen et al., 2023; Gessner et al., 2023; McKinnon and Simpson, 2022). Here, our primary purpose is to leverage the 100 member CESM2-LE to calculate robust statistics of simulated compound events and explore the influence of both internal climate variability and anthropogenic climate change on them.

To compare our compound event results from the CESM2-LE to observational estimates, we use the ECMWF Reanalysis V5 data (ERA5; Hersbach et al., 2020). Monthly 2m temperature (t2m), precipitation (tp; converted to a monthly rate), and surface temperature (skt) from ERA5 is analyzed from January 1940 through December 2023 after regridding to the CESM2-LE spatial grid using bilinear interpolation via the Climate Data Operators package (Schulzweida, 2023). We also use a 3rd order polynomial fit (e.g., Gordon and Diffenbaugh, 2025; Mayer et al., 2025) for each month and at every grid point to estimate and remove climate forcing and deseasonalize the ERA5 data to produce monthly anomalies. We note that although ERA5 does have biases, the reanalysis data compares well to other observational products when used for compound event research (Mukherjee et al., 2020).

We investigate multivariate extremes, or two hazards that occur in the same place at the same time (Zscheischler et al., 2020a). The 90th percentile of monthly 2m temperature anomalies across the 100 members in the CESM2-LE is used to define extreme high temperatures. The 10th percentile of monthly precipitation rate anomalies across the 100 members is used to define extreme low precipitation. Concurrent hot and dry events (T90/P10) at a grid point thus occur when the monthly temperature anomaly exceeds the 90th percentile and the concurrent precipitation anomaly is below the 10th percentile. We use different baselines to calculate percentiles for hot and dry compound events. For the results shown in Figures 1–4, temperature and precipitation percentiles are calculated over 1940–2024. We use this baseline for consistency between CESM2-LE and ERA5. For Figure 5, we use a 1850–1950 baseline for compound event analysis for that same period, and a 2000–2100 baseline for the later period as our aim is to extract any variance or distribution changes even when external forcing is removed. Compound event frequencies for both 1850–1950 and 1940–2024 are very similar when external forcing is removed (Supplementary Figures S1, S2), facilitating comparison between results. For results in Section 3.2, we use the 1850–1900 period to establish a pre-industrial baseline for evaluating anthropogenic changes in hot and dry compound events. We investigate what drives compound events regardless of time of year; therefore, percentiles for each variable are computed for each month after combining the ensemble members. In this way, anomalies from internal variability in specific seasons can be isolated and investigated (e.g., warm and dry extremes can occur in winter months and in wet seasons). A value of 1 is assigned to a gridpoint to signify a compound event in a given month, and a value of 0 is assigned if there is not a compound event. Analysis is then performed based on this binary classification. The global distribution of T90/P10 compound event frequencies are computed by averaging across all ensemble members over the 1940–2024 period. We then display the results as a percentage relative to this reference period.

We compare our T90/P10 frequencies to independent frequencies, where temperature and precipitation variables are uncorrelated, to determine the extent to which internal variability is influencing the frequency of compound events. Independent frequencies are calculated via bootstrapping, where T90/P10 events are computed across scrambled ensemble members. Namely, the ensemble members for temperature are kept fixed and the ensemble members for precipitation are shifted down by one member (e.g., pairing temperature of member 1 with precipitation of member 2, temperature of member 2 with precipitation of member 3, etc.). The ensemble-mean frequencies across the 100 member pairings are then computed. We then proceed to shift the precipitation members again and run the same calculation. This is continued through the last possible combination. The result is 99 ensemble-mean frequencies under the null hypothesis of independent, uncorrelated variables. From here, we compute the 1st and 99th percentiles to define the bounds of independent chance. If the unscrambled frequencies fall outside of these bounds, we suggest that there may be evidence that internal climate variability drives correlations between T90 and P10 events, leading to more (or less) frequent extremes.

We also recognize the impact of climate change on T90/P10 compound events and thus analyze results when the forced response is retained. In this case, 1850–1900 is used as the baseline period for percentile calculation and compound events are determined using the same methods as before with the exception that the ensemble mean is not removed.

We then investigate the year of emergence of T90/P10 compound events from internal variability to demonstrate when climate change has or will become a significant influence on the occurrence of T90/P10 compound events under historical and SSP 3-7.0 forcing. As defined here, compound events emerge from internal variability when the median number of events in the 100-member ensemble exceeds and remains above the 90th percentile of compound events from all members over the 1850–1900 period. Time series of compound events in different locations are visualized by taking a five-year forward moving sum of the events (Supplementary Figure S3).

In the first part of our results, we quantify the influence of internal climate variability on the occurrence of T90/P10 compound events (henceforth referred to as compound events or CEs). We begin by computing frequencies in CESM2-LE and ERA5 from 1940–2024 (Figures 1a, b). Our results demonstrate the ability and need for a large ensemble to analyze compound events due to the large sample size and its ability to capture similar historical patterns of CE frequency to ERA5 data (Figures 1a, b). Particular locations, including northern South America, eastern Africa, the Indian subcontinent, and the Indonesian archipelago, depict the highest frequencies of compound events in both the CESM2-LE and ERA5 (Figures 1a, b). While ERA5 generally shows higher compound event frequencies than CESM2-LE, the two datasets exhibit largely similar spatial patterns (Figures 1a, b, Supplementary Figures S1). Despite this frequency bias, we leverage the large ensemble size of CESM2-LE to calculate robust statistics for the drivers of hot and dry CEs.

Internal climate modes influence the dependency between precipitation and temperature anomalies (e.g., Feng and Hao, 2021, Supplementary Figures S4, S5) which then impacts the occurrence of compound events (Zscheischler and Seneviratne, 2017). However, even if the temperature and precipitation values are treated as independent variables, random sampling of their distributions would still result in CEs. We use a bootstrapping technique (see Methods) to calculate 99 ensemble-mean frequencies under the null hypothesis of independent, uncorrelated variables. We compare our unscrambled frequencies with the 99 ensemble-mean frequencies under this null hypothesis to analyze where frequencies are greater or less than independent chance (Figure 1c). Most of the land areas in the world exhibit frequencies of CEs that are distinguishable from independent chance (Figure 1c), and regions with CEs that are not distinguishable from independent chance are often found in transition regions. Dry regions, such as some high-latitude areas (including the ice sheet regions) and the Saharan and Arabian deserts, have compound event frequencies that are below independent chance because precipitation and precipitation variance is low.

To investigate the connection between internal climate modes and compound events, we first examine the mean sea surface temperature (SST) conditions during months containing compound events at twenty different locations (Figure 2, Supplementary Figures S7–S10). This is done to obtain a qualitative understanding of SST relationships to compound event occurrence and identify large-scale climate modes to investigate in this study. Specific grid points are selected to build on previous studies investigating internal climate drivers of compound events (e.g., Mukherjee et al., 2020; Hao et al., 2020, 2018). We also pick locations that are underrepresented in the current literature, including South America, Africa, and Southeast Asia (Brett et al., 2025) (Figure 2, Supplementary Figures S7–S10). Furthermore, the grid points are representative of regional averages (Supplementary Figure S11).

For many regions, the SST patterns during CEs in CESM2-LE and ERA5 resemble combinations of multiple large-scale climate modes that are known to influence local weather patterns (Supplementary Figure S4, S5). For example, CEs for locations in northern Brazil, northeast Nigeria, and southeast and southwest Australia are accompanied by SST patterns that resemble El Niño-like conditions and a positive PDO (Figure 2, Supplementary Figure S10). Additionally, SST anomalies during events for locations in southwest and southeast Australia and northern Brazil show conditions resembling a positive IOD (Figure 2, Supplementary Figure S10). Thus, we include ENSO, the PDO, and the IOD in the following analysis. Furthermore, despite previous studies (e.g., Hurrell and Van Loon, 1997) documenting the effects of the NAO on temperature and precipitation patterns in Europe, we find that neither CESM2-LE nor ERA5 show SST patterns typically associated with NAO during CE occurrence in Europe (Figures 2e, f, Supplementary Figures S7, S9, S10). We then analyze sea level pressure patterns during CEs in CESM2-LE for further investigation (Supplementary Figure S12), finding NAO-like conditions during CEs in multiple locations, and include NAO in our analysis.

The SST patterns that occur during CEs qualitatively indicate how internal climate modes may influence the presence of compound events. We quantify the possible influence of ENSO, PDO, IOD, and the NAO on compound events in CESM2-LE and ERA5 by calculating conditional frequencies of CEs during each phase of each climate mode (Figures 3, 4). As ENSO is known to drive temperature and precipitation anomalies globally (Lenssen et al., 2020; Latif and Keenlyside, 2009), the analysis for PDO, IOD, and the NAO is conditioned on ENSO being in its neutral phase. Conditional frequencies without the neutral ENSO condition are also calculated for comparison and show minor differences except in regions with known strong ENSO teleconnections (Supplementary Figures S13, S14, S15). For the calculation of conditional frequencies, we pool all members and sum the number of compound events that occur concurrently with the two phases of the climate modes (e.g., positive PDO and neutral ENSO). We then divide this sum by the total number of months where the two phases of the climate modes are present to determine the conditional frequencies (Figure 3). A chi-square test for independence is used to determine if the conditional frequencies are significant relative to our null hypothesis of independent, uncorrelated variables. Grid points where we do not reject the null hypothesis at 98% are represented through the gray shading (Figures 3, 4). We use this shading to demonstrate the spatial characteristics of the conditional frequencies. We note that significance is likely much more difficult to obtain using ERA5 due to the low sample size in the reanalysis data (1,008 months) and is particularly true for the conditional frequencies with the PDO, IOD, and NAO (Figure 4). Sample sizes for CESM2-LE are more than 100 times larger than the ERA5 sample sizes, allowing for more confidence in our assessments of where climate modes significantly influence compound events (Figures 3, 4).

For the CESM2-LE, regions with high conditional frequencies during El Niño (Figure 3a), such as northern South America, the Indonesian Archipelago, and the Indian subcontinent, can be partially explained by the warmer temperature anomalies and drier conditions that occur during an El Niño month (Supplementary Figures S4, S5). Despite the precipitation biases in CESM2-LE, including dry biases over Australia in most members during El Niño events (see Data), we do see overlap in significant conditional frequencies between the CESM2-LE and ERA5 analyses (Figures 3a, 4a). Further, our ERA5 results for the conditional frequencies for ENSO (Figures 4a, b) are largely consistent with previous studies (Zhang et al., 2023; Hao et al., 2020).

When investigating the conditional frequencies during the PDO, there are higher frequencies of CEs in India and southeast Asia during the positive PDO and neutral ENSO phases that correspond well with the known lower precipitation and warmer temperature anomalies associated with the PDO in these regions (Figure 3c, Supplementary Figures S4, S5). Although this assists in demonstrating that temperature and precipitation are largely correlated, we show the need to investigate both these variables in compound event analysis with the example of Alaska and western Canada. Although there are warmer temperature anomalies in Alaska and western Canada during a positive PDO event (Supplementary Figure S4), the region does not experience drier conditions (Supplementary Figure S5). This leads to a low frequency of CEs despite the PDO's influence on temperature (Figure 3c). In an univariate analysis, it would be possible to misinterpret the number of compound events in this region (i.e., warmer temperatures equating to more hot and dry compound events), further demonstrating the need for multivariate analyses.

In the conditional frequencies for the IOD and NAO, we find that the positive phase of the IOD leads to higher frequencies of compound events in India and the conditional frequencies for the negative phase of the IOD has the highest number of compound events in eastern Africa (Figures 3e, f). Figures 3g, h depict the NAO's influence on compound events in Europe and lack of influence in the majority of the Southern Hemisphere (Figures 3g, h), consistent with known NAO teleconnections (Hurrell and Van Loon, 1997).

The variability of climate modes may change over the 21^st century (Cai et al., 2021; Geng et al., 2019). With the forced trend still removed, we investigate how the statistics (i.e., conditional frequencies) of CEs change in the future using CESM2-LE and how this may be related, in part, to changes in internal variability. We take the difference in conditional frequencies for the four climate modes between 2000–2100 and 1850–1950 to depict future changes of CE occurrence. We note that the earlier period (1850–1950) strongly resembles the 1940–2024 results shown in Figures 1, 3 (Supplementary Figures S2, S16). A z-test comparison of two proportions is used to determine if our difference in conditional frequencies between the two periods is significant relative to our null hypothesis of equal conditional frequencies.

Overall, conditional frequencies show signs of change under future climate conditions that largely align with each mode's teleconnection pattern of temperature and precipitation. These responses are mostly of the opposing sign between positive and negative phases of the climate mode. Specifically for ENSO, future changes in the conditional frequency with El Niño are largest in South America, Africa (south of the Sahara), and the Maritime Continent (Figure 5a). As these regions are most impacted by ENSO teleconnections (Lenssen et al., 2020, Supplementary Figures S4, S5), a change in ENSO, which includes intensification until around 2050 and then weakening through the end of the century (e.g., Maher et al., 2023; Cai et al., 2022), may more strongly impact CEs in these regions compared to other locations.

Likewise, the variability and amplitude of the PDO, IOD, and NAO may change throughout the 21^st century (e.g., Rezaei et al., 2023; Deser et al., 2017; Cai et al., 2014). We find that the conditional frequency changes under the PDO are largest in South America (Figures 5c, d), throughout central Africa (Figures 5c, d), and in Indonesia in the CESM2-LE (Figure 5d). The conditional frequencies under the positive IOD phase increase across the Indonesian archipelago and decrease across the sub-Sahara and India in the future (Figure 5e). Although existing literature predicts a decrease in future precipitation over southern Europe under the positive NAO phase (McKenna and Maycock, 2022), the change in conditional frequencies in most of this region does not reject the null hypothesis of equal frequencies (Figure 5g). However, under the negative NAO phase we find an increase of compound events over the United Kingdom and Ireland, Iceland, and northern Europe, while there is a decrease in regions surrounding the Mediterranean (Figure 5h). We would also like to note that in southern South America, accounting for the PDO's influence lowers the magnitude of change in conditional NAO frequencies relative to ENSO alone (Figure 5g, Supplementary Figure S17).

The changes in conditional frequency between phases for ENSO, PDO, IOD, and NAO are not always identical (or opposite). For example, although conditional frequency for compound events with El Niño increases across Australia in the future, conditional frequencies for La Niña stay approximately the same (Figures 5a, b). The future conditional frequencies under the positive IOD phase decrease across the Indian subcontinent but largely stay the same for the negative IOD phase (Figures 5e, f). Therefore, changes in the amplitude and/or variability of these climate modes due to anthropogenic climate change could affect the frequency of compound events in different regions and highlights the continued influence of the modes on CEs under anthropogenic climate change.

Many studies have documented increasing frequencies of hot and dry compound events under historical and future scenarios (e.g., Meng et al., 2022; Wu et al., 2021), but few have examined the time of emergence of CEs from internal climate variability (e.g., Schmutz et al., 2025). Due to the consequential impacts of hot and dry compound events, identifying how they may change over the 21^st century is crucial for adaptation planning. We use 1850–1900 as our baseline period, retain external forcing, and compute the 90th percentile of compound events of the 100 members in CESM2-LE at all grid points. The year of emergence from internal variability is defined to be when the median number of CEs in a 5-year forward moving sum at every grid point exceeds and remains above the 90th percentile of the baseline (Supplementary Figure S3).

We find that compound events emerge from internal variability before 2025 for most land regions under SSP 3-7.0 (60% of land area, excluding Antarctica, Figure 6a). The majority of the Southern Hemisphere emerges prior to 2025 (87% of land area, excluding Antarctica), except for portions of central Africa and southern South America. In contrast, there is far more heterogeneity in emergence timing over the Northern Hemisphere, with only 50% of the land area emerging prior to 2025 (Figure 6c). Later emergence in the Northern Hemisphere is likely due to higher variability in precipitation and 2m temperature over the Northern Hemisphere relative to the Southern Hemisphere (van Loon, 1991; Kang et al., 2015, Supplementary Figure S18).

Regions with the highest frequency of CEs in the early historical period (Figures 1a, c) display a wide range of emergence times. For example, northern Brazil and eastern Africa exhibit similar frequencies of CEs between 1940–2024 (Figure 1a), but northern Brazil emerges around 2003 while eastern Africa still has not emerged by the end of the 21^st century ( Figure 6a). The difference in emergence years likely relies on the mean trends of temperature and precipitation and the correlation between the two variables. Existing literature suggests that, under climate change, mean precipitation trends are more influential than the dependence between temperature and precipitation in determining the frequency of hot and dry compound events (Bevacqua et al., 2022). Although temperature increases may contribute more to the global frequency of compound events due to globally increasing temperatures (Zeng et al., 2024), differing mean precipitation trends throughout the world will impact regional emergence. Our results agree with this, as we find that precipitation trends are likely a major reason for late or no emergence in many regions (Supplementary Figures S19–22). In the northern Brazil and eastern Africa cases, there is a decrease in precipitation over northern Brazil in the 21^st century and an increase in precipitation over eastern Africa, including South Sudan (Supplementary Figure S19), likely leading to differing emergence years.

Time series of compound events for eighteen locations are shown in Figures 6b– g, Supplementary Figures S19, S23, S24. Over northern France, as well as other locations across Europe, a consistently increasing trend of compound events is evident beginning early in the 21^st century (Figure 6c, Supplementary Figures S23, S24). This result is consistent with projections of the global average of hot and dry compound events under SSP 3-7.0 found in previous studies (Zhang et al., 2022; Vogel et al., 2021). For locations exhibiting earlier emergence, including southern Brazil and the Indonesian Archipelago, emergence during the 20^th century is followed by stabilization of CE frequencies. This early emergence could be due to observed decrease in natural vegetation in the mid-twentieth century (Supplementary Figure S25). The consistent and stable frequencies across the 21^st century are likely due to unchanged precipitation patterns when compared to the historical period (Figures 6e, g, Supplementary Figure S20). Other regions with historically low frequencies, including northeast India and northeast Nigeria, show minimal changes under climate change ( Figures 6d, f). Locations including the southeast United States, northeast India, and southern Alaska, United States, that have late or no emergence by the end of the century also have increasing mean precipitation trends, affecting how often compound events would occur (Supplementary Figures S20–S22).