For temperature and precipitation, we use the Parameter elevation Regression on Independent Slopes Model (PRISM; PRISM Climate Group, 2023), which uses observed daily temperature and precipitation for a 20-year period, January 1981–December 2000, to diagnose behavior of contemporary climate. We neglected more recent PRISM data as the data set began to include radar-based estimates of precipitation starting in 2002 (PRISM Climate Group, 2023). In diagnostics that included precipitation data from 2002 onward, we observed a shift in results starting at 2002, suggesting an inhomogeneity from adding the radar estimates. We have therefore restricted our PRISM analysis to a prior period that uses only station-based observations. PRISM data are provided on a 4 km × 4 km grid. We aggregate the precipitation data to a 25-km grid to match our simulations’ grid spacing, using a mass-conserving aggregation scheme (Jones, 1999). For temperature, we aggregated the PRISM data to a 25-km grid box using a patch-based aggregation scheme.

Our model output for daily temperature and precipitation comes from two combinations of global climate models (GCMs) driving a regional climate model (RCM) that produced simulations for the North America portion (Bukovsky and Mearns, 2020; McGinnis and Mearns, 2021) of the Coordinated Regional Downscaling Experiment (CORDEX; Giorgi and Gutowski, 2015; Gutowski and Giorgi, 2020). The RCM driving came from GCM simulations by the Geophysical Fluid Dynamics Laboratory (GFDL) and the Max Planck Institute for Meteorology (MPI) under the CMIP5 program (Dunne et al., 2012, 2013; Taylor et al., 2012; Jungclaus et al., 2013; Stevens et al., 2013). The output from both GCMs drove the Regional Climate Model, Version 4 (RegCM4; Giorgi and Anyah, 2012). RegCM4 used 25-km grid spacing to simulate the period 1950–2100. The simulation period 2006–2100 used the RCP8.5 scenario (Moss et al., 2010). We used the bias-corrected model output produced by the North America CORDEX program (Bukovsky and Mearns, 2020; McGinnis and Mearns, 2021) using the multivariate quantile method developed by Cannon (2018).

Our research goal was to identify short-term-drought and heat-stress events, as defined below. To this end, we used the object-oriented analysis program Tempest Extremes (TE; Ullrich and Zarzycki, 2017). As implied by its name, TE was developed to track features such as tropical and extratropical cyclones, as well as tropical easterly waves. We adapted TE to identify spatially and temporally continuous features in climate data that exceed a prescribed threshold (e.g., Fisel et al., 2023). We consider these features to be events. Here, the relevant thresholds are precipitation below a threshold, identified as drought, and daily maximum temperature above the threshold for agricultural heat stress; we discuss these thresholds in detail below. TE is sufficiently efficient (Zarzycki and Ullrich, 2017) that we can extract a large collection of events from data sets covering multiple decades in a sizeable region, thereby allowing us to develop a climatology of the targeted events. Details of TE’s formulation and coding appear in Ullrich and Zarzycki (2017). An advantage of the approach is that it allows one to diagnose events based on regional climate characteristics that potentially can be defined by stakeholder-relevant impactful events (Sillmann et al., 2021; Fisel et al., 2023) rather than more standard hydroclimate metrics, such as return periods for extreme events or percentile exceedances.

To ensure that an object has some degree of space–time continuity that the models can resolve, we required an object to have at least four adjacent grid points in the space–time domain of the data. Points exceeding the threshold that are not adjacent in the space–time domain cannot be part of the same event. Each event of a given type (heat stress or short-term drought) thus has its own set of points in the space–time domain so that two distinct events can occur in different parts of the domain at the same time. We assumed that all diagnosed objects were events produced by the same climate dynamics in the region. We identified several event characteristics: location, duration, areal extent, and intensity relative to the prescribed thresholds. We arrived at event climatologies by examining the collection of all events for their frequency of occurrence and distribution of properties, as well as possible overlap of short-term drought and heat-stress events that would be compound events. Overlap occurs if a short-term drought event and a heat-stress event have at least one space–time point in common, although, typically, the object overlap involved many more than just one point. The compound events we diagnose, where two types of hazards interact, would be considered multivariate compound events in the typology presented by Zscheischler et al. (2020).

As noted above, we focused on a north-central region of the United States (Figure 1) because of its agricultural importance. The specific domain was based on the climatological regions established by Seneviratne et al. (2012), except that we used only the northern half of their Central North America region, in recognition of the weather and climate differences going from north to south across the regions, which ultimately contributes to agricultural differences, too. Elevation variations are relatively minor in the region, so that topographic effects are not a primary determinant of the region’s climate (USGS, 2024). We analyzed two twenty-year time periods: contemporary (1981–2000), motivated above by the observational considerations above, and future scenario (2041–2060). We chose our future period from a decision-making perspective. Planning horizons for national security and infrastructure often focus 20–50 years into the future (e.g., Schwartz et al., 2008; Department of Defense, 2021; Zeng et al., 2022). Also, some have raised doubts about the viability of an RCP 8.5 scenario through the final decades of the 21st century (Ritchie and Dowlatabadi, 2017; Ho et al., 2019). Further, mid-century global-temperature changes tend to show less sensitivity to RCP scenario compared to changes toward the end of the century (IPCC, 2013, 2021), so the mid-century should be less dependent on the specific scenario used.

Crops generally can tolerate periods of a few days with little, if any, impairment. However, periods of several weeks during the growing season with little to no rainfall can have substantial impact (e.g., Otkin et al., 2018; Licht and Glisan, 2019; Yuan et al., 2023). We diagnose short-term drought that impacts as a 40-day period with total precipitation less than 25 mm, an amount that is roughly 20–25% of long-term summer averages for our analysis region (NOAA National Centers for Environmental Information, 2023). A drought event may last longer than 40 days, so we use a 40-day moving window when summing precipitation. We identify each 40-day period by the first day in the window. The window shifts forward in 1-day increments, so that the month of June in one year, for example, would have 30 successive windows that would be examined for their cumulative precipitation. We identify drought duration as the number of successive windows for which cumulative precipitation is below the 25-mm threshold.

Our analysis period uses windows that start in April, May, June, and July, the prime growing season. The windows toward the end of July thus include August and parts of September in their precipitation summation. Drought occurring later than early September is occurring after all or most of the crop maturation. Dry conditions after maturation can actually be beneficial, rather than detrimental, because they can help prepare the crop for harvest, as it is desirable to have grain lose much of its moisture in preparation for storage.

For heat stress, as noted above, maize and soybeans experience stress at temperatures 30°C and higher. We use daily maximum temperature, Tmax, to identify episodes of stress. We recognize that exceeding the threshold for an isolated day is not as impactful as exceeding the threshold for multiple days in a row. Thus, we compute a running, 5-day average of Tmax and identify when that 5-day average exceeds the threshold, thereby identifying a pentad of persistent heat stress that some have tied to “flash droughts” (Otkin et al., 2018) and that is sufficiently long to impact negatively plant development, especially if it occurs during key reproductive stages (dos Santos et al., 2022). Similar to our short-term drought diagnosis, we use a moving 5-day window to compute the average Tmax, shifting the window forward in 1-day increments and identifying the 5-day period by the first day in the window. Heat-stress duration is then the number of successive windows with average Tmax above 30°C.

Figure 2 shows the spatial distribution of event frequency experienced at each grid point across our domain. The observations and the two contemporary simulations show similar overall features, with low or even zero frequency in eastern locations and higher frequency to the west. Frequencies in all three are higher in the northwest and southwest corners of the analysis domain, although the MPI-driven simulation has frequencies in the west that match the observed frequencies more closely. The overall behavior is consistent with average precipitation in the region, which decreases to the west (NCEI, 2023). In the scenario climates, the models give mixed results. The MPI-driven simulation has frequency increases in the west and a mix of relatively small, perhaps inconsequential, changes in the east. In contrast, the GFDL-driven simulation has decreases over most of the domain, including larger areas with zero events.

Despite broad similarities between contemporary simulations and observations in Figure 2, the individual events contributing to the frequency maps differ between simulations and observations. Figure 3 shows box-and-whiskers plots of the short-term droughts’ event areas and durations, along with the number of events, for the observations and for the contemporary and scenario simulations. For each event, the area is the average area over the duration time periods since the area of an event may change as the analysis window shifts forward in time. The interquartile ranges for the areas so computed are broader in the simulations compared to the observations, and the simulated medians are 25–50% greater than the observed (Table 1). All contemporary-climate sources show a skewing of areas toward a few events that have much larger areas than most of the short-term drought events, as evidenced by the averages among the sources’ areas exceeding the 90^th percentile for each source. However, the simulations show a substantially greater skewing than the observations. Perhaps related to these area differences, the simulated events occur 41–44% less often than observed events (Figure 3), although event durations (Figure 3 and Table 1) in contemporary-climate simulations have approximately the same median and average durations as the observed events. There is a long-standing recognition that the effective resolution of climate models is probably somewhat coarser than their grid spacing (Pielke, 1991; Laprise, 1992; Klaver et al., 2020). The combination here of differences in event areas and frequencies, despite similar event durations and spatial distribution of grid-point frequencies, suggests that the effective resolution of the models is coarser than 25 km, with the behavior producing short-term drought events in observations yielding broader but fewer events in the simulations.

In the scenario climates, the most noticeable change from contemporary climate is the frequency of the drought events, with increases of 8–35%, depending on the driving GCM. In contrast, the event areas and durations change relatively little, except for extreme outliers, which tend to decrease. The similar results for event areas and durations in both climates suggests that the processes causing the events, such as circulation patterns, may be essentially the same in the scenario climates as in the contemporary climates.

Figure 4 shows the spatial distribution of heat-stress event frequency at each grid point across our domain. The observations and the two contemporary simulations show similar overall features, with frequency increasing substantially going from grid points in the northeast toward the southwest, although the simulations tend to show somewhat higher frequencies in the west. The pattern of behavior is consistent with average summer temperatures for this region, which also tend to increase from the northeast toward the southwest (NOAA National Centers for Environmental Information, 2023). In the scenario climates, the overall spatial patterns remain similar, but with higher event frequencies across the domain compared to contemporary climate. The highest frequencies continue to be in the southwestern portion of the domain. The behavior is qualitatively consistent with the pattern of changes in annual temperature for this region produced by the two GCM-RCM combinations used here (Bukovsky and Mearns, 2020).

Figure 5 shows box-and-whiskers plots for areas and durations of heat-stress events and the number of occurrences in observations and each simulation. Consistent with the short-term droughts, the simulations’ event areas for contemporary climate have approximately the same medians and interquartile range as the observations. However, the simulations produce more skewing in their area distributions toward larger values compared to the observations, as evidenced by the mean and 90^th percentile areas for each data source. Event durations in the contemporary simulations, similar to event areas, have the same interquartile range as the observations, but with a skewing toward longer-duration events. The greater skewing of areas and durations in the simulations is consistent with the 22–24% fewer events in the contemporary simulations, compared to the observations (Figure 5). The simulations have fewer events that cover larger areas while exposing individual locations to comparable frequencies of heat stress in both the observations and the simulations. As with short-term drought, the results are consistent with the models having an effective resolution that is coarser than their 25-km grid spacing, in line with arguments and analyses by Pielke (1991), Laprise (1992), and Klaver et al. (2020). The coarser effective resolution would yield a degree of smoothing relative to the observations that can blend features such as our events. Features that would be distinct at finer resolution, would be blended into fewer distinct features (events) in the effectively coarser resolution.

In the scenario climates, both GCM-RCM combinations show a decrease in event frequency, but with different degrees of decrease: 21% under GFDL driving and 2% under MPI driving. Both GCM-RCM combinations also show a decrease in median areas (4% under GFDL driving and 11% under MPI driving; Table 1) but roughly 50% increases in mean areas, indicating much greater skewing toward large-area events in the scenario climates. Duration changes, on the other hand are mixed: increased interquartile range with GFDL driving and decreased interquartile range with MPI driving. Despite these differences, again, both simulations show similar changes in the frequency of heat stress events experienced at individual grid points (Figure 4), with heat stress tending to occur more frequently at every grid point in the scenario climate. This would be a consequence of the increase in very large events that can encompass many more grid points, thus allowing individual grid points to experience more frequent heat stress, despite the somewhat fewer numbers of events. This behavior is especially evident in the MPI-R cases, which have very little decrease in the number of events.

A sizeable number of short-term drought events overlap heat-stress events, thus creating compound events (Table 2), although the percent experiencing overlap varies substantially with data source. For short-term drought, the GFDL-driven and MPI-driven simulations in contemporary climate have roughly similar numbers of events, area distributions and duration distributions. The difference in their overlap percentages might be due to heat-stress events with MPI driving having somewhat larger median and average event areas and longer median durations, thus allowing MPI-driven heat-stress events to encompass more short-term drought events. In addition, not only do more short-term drought events occur in the scenario climates, but a larger fraction is part of compound events in the scenario climates. In contrast, the fraction of heat-stress events overlapping short-term drought events is substantially smaller and the fraction involved in compound events changes little with the climate change.

For the observations and for all simulations, the overwhelming majority of compound events start with a heat-stress event (Table 2). The review of “flash droughts” by Lisonbee et al. (2021) notes several authors referring to the simultaneity of such droughts and heat waves as part of behavior appearing with some of the different characterizations of “flash drought.” However, there do not appear to be any clear statements about heat or rainfall deficit preceding the other.

The character of heat-stress and short-term-drought events differs between compound and non-compound events, especially for heat-stress events (Figures 6, 7). Heat-stress events that overlap with short-term drought events cover much larger areas and persist much longer than heat-stress events that do not overlap with any drought event. The larger areas and longer durations can be viewed as providing more opportunity for any drought event to overlap a heat-stress event. Short-term drought events show some differences between events that overlap heat-stress events and those that do not, but the differences are relatively small compared to those for the compounding versus non-compounding heat-stress events.

An important factor is how the intensity of both types of events changes when compound events start. Table 3 shows that both short-term drought and heat-stress events tend to become more intense on the first day of a compound event compared to the day before. For the contemporary climates, the median values for short-term drought events drop down from roughly the 50^th-percentile among all short-term-drought intensities just before becoming part of a compound event to roughly the 33^rd-percentile on the first day of a compound event. (Note that lower percentiles refer to lower precipitation amounts and thus drier conditions.) For the two scenario climates, many of the drought events engage in overlap on the day they form, so the median intensities the day before compounding, in most cases, are average values over the region where the drought event starts the next day. Thus, for the scenario climates, the median intensities are above the threshold for a drought object. This behavior is consistent with the substantial tendency for heat-stress events to precede drought events when compounding occurs.

Similarly, the median intensities for heat-stress events shift to higher (warmer) values in nearly all cases. Compounding appears to reenforce the intensity of both types of events. Drier conditions during a drought imply less evaporative cooling of the surface, promoting warmer surface temperature and thus temperature of the air just above the surface. However, for the heat-stress events, the percentile shift is generally smaller between the day before and the first day of compounding, typically just a few percentiles. This behavior is also consistent with the substantial tendency for heat-stress events to precede drought events when compounding occurs.

The event analysis presented here provides a foundation for constructing climate storylines of climate change using as building blocks the short-term drought and heat-stress events separately and for their compound events. For the individual types of events, the foundation for storylines appears to be straightforward. One can use the set of event characteristics presented here (area, duration, intensity, frequency, and spatial distribution across the region) to explore which conditional factors may govern the occurrence of the event [e.g., Shepherd (2019) and Box 10.2 in Doblas-Reyes et al. (2023)]. For compound events, heat-stress events can be viewed as a conditional factor for the most intense short-term drought events, with those drought events in turn prompting yet more intense heat stress. In this context, a message for agricultural concerns would be to watch especially for heat-stress events as precursors to short-term drought. The heat-stress events may be a warning for both more intense heat and, especially, drought, because when compounding starts, the heat and drought intensities both become stronger: temperatures increase in a region with compounding events and dry conditions become yet drier.