The thermodynamic environment supporting convection can determine whether a convective system will initiate, the intensity of the storm once initiated, storm characteristics, and much more. Many thermodynamic indices have been developed in the operational and research severe weather community to predict the occurrence of severe storms and to understand why different types of convective systems occur (Doswell 1985; Craven et al. 2002). Results from this study show that the convective population is expected to have fewer weak to moderate storms and more strong convection in a warmer climate (Figs. 7, 8, 9; Sect. 4). In the context of the high-resolution regional climate simulations used in this study, the convective elements were allowed to develop naturally in the larger-scale synoptic and thermodynamic environments provided by the CTRL and PGW-perturbed simulations. Given that the development of convective systems was directly influenced by differences in the thermodynamic environments in the CTRL vs. PGW-perturbed simulations, this section will examine changes in the bulk thermodynamic conditions to provide insights into the physical mechanisms responsible for the corresponding changes in the convective population. As was described in Sect. 2.3 above, mixed-layer convective available potential energy (MLCAPE; J kg−1) and CIN (CIN; J kg−1) are used to look at overall changes in the thermodynamic environment in the following sections.
Bulk thermodynamic environmental changes
Figure 10 presents the monthly average MLCAPE and CIN from the CTRL and PGW simulations and their differences in MJ. In the CTRL simulation, moderate values of MLCAPE and CIN are located east of the Rocky Mountains in the active convective region of the US (Fig. 10a, d). The effect of the low-level jet bringing warm and moist air into the US continent from the Gulf of Mexico is apparent in these figures and has been well documented in the current climate (Carlson et al. 1983; Geerts et al. 2016). A comparison of the meridional moisture flux in the region of the low-level jet and Gulf of Mexico between the ERA-Interim reanalysis and CTRL simulation (not shown) shows that the model is consistent with the moisture and flow characteristics in this region. Immediately east of the Rockies, moderately strong values of CIN are typically generated by dry air flowing over the Rocky Mountains, diurnal heating from the Mexican Plateau, and other sources of midlevel subsidence in the region (Carlson et al. 1983). Moderate CAPE and CIN allow for the gradual build-up of convective energy and is typically released through enhanced lifting along a dryline or a synoptic short wave trough (Carlson et al. 1983). Thus, the region of moderate MLCAPE and CIN downstream of the Rockies provides a favorable environment for moderate to strong convection in the late spring and early summer months in the central Great Plains.
Changes in the thermodynamic environment in the PGW-perturbed simulation are presented in Fig. 10b, c, e, f. Both MLCAPE and CIN increase in magnitude east of the Rocky Mountains, with a clear preference for increases directly east of the mountains. This result indicates that there is more energy available for convection and more energy inhibiting convection, which is complementary to the results from Sect. 5 showing that the occurrence of weaker reflectivity echoes decreases and the occurrence of higher reflectivity echoes increases in a warmer climate. Even with more MLCAPE in the thermodynamic environment, corresponding increases in CIN results in a shift of the convective population spectrum because weak to moderate convection may be suppressed, which modifies the spatial and temporal occurrence of precipitating systems across the US.
As was previously shown, the air above the Gulf of Mexico is expected to have significantly more moisture in the future compared to the current climate (Fig. 5), thus the low-level jet will likely provide greater moisture flux convergence over the central US downstream of the Rockies. The penetration of relatively high values of precipitable water (≥ 50 mm) into the US continent was shown in Fig. 5 and likely contributes to the tongue of stronger CAPE values (between 50 and 500 J kg−1) immediately downstream of the Rockies in the central Great Plains (Fig. 10b, c). A corresponding increase in the magnitude of CIN is observed downstream of the Rockies as well (Fig. 10e, f). Over the Gulf of Mexico, higher moisture also results in more MLCAPE over that region, but increasing CIN results in decreases in weaker reflectivity echoes typically associated with maritime precipitating systems (Fig. 7a–c).
The thermodynamic environment for the current and future simulations in JA is presented in Fig. 11. Similar to Fig. 10a, d, the MLCAPE and CIN in the US in JA is mostly concentrated east of the Rocky Mountains, with generally weaker MLCAPE and CIN shifted to the north and extending into Canada (Fig. 11a, d). During the summer, the low-level jet reaches much farther north compared to the spring and brings warm and moist air into the US and Canada east of the Rockies (Geerts et al. 2016). Frequent intense convective systems occur in a broad geographical region from Texas through the Dakotas and east during the later summer, as was shown by the geographical variability in observed MCSs during the Plains Elevated Convection at Night (PECAN) field campaign in summer 2015 (Geerts et al. 2016).
Similar to the results from Fig. 10, both MLCAPE and CIN increase in magnitude in the PGW simulation in late summer (Fig. 11b, c, e, f). However, although the increases directly downstream of the Rockies in JA are not as apparent as in MJ, the influence of the low-level jet advecting very moist air from the Gulf of Mexico into the continental US downstream of the Rockies is clear. In addition, large increases in magnitude in both MLCAPE and CIN over the Gulf of Mexico leads to decreases in the occurrence of reflectivity echoes between 0 and 50 dBZ since lifting mechanisms to break through the stronger cap are not typically present over the ocean. An exception to this pattern is the increase in convective activity across all reflectivity ranges along the Gulf Coast from Louisiana through Florida that may be related to increased tropical convection or a potential enhancement in land-sea breezes, but is beyond the scope of the present study and will be examined in future research.
Focusing on the US Great Plains region, Fig. 12 shows a comparison of the thermodynamic environments supporting convection in the CTRL and PGW simulations for both MJ and JA. In each panel of Fig. 12, the thermodynamic environment is represented by the relationship between MLCAPE and CIN and how frequently the environment occurs. In the CTRL simulation in MJ (Fig. 12a), low values of CIN and MLCAPE are the most frequent, with an extension to approximately − 100 J kg−1 of CIN and 400 J kg−1 of MLCAPE representing a relatively narrow range. In the CTRL simulation in JA (Fig. 12c), a higher frequency of environments with moderate CIN and MLCAPE are observed compared to MJ (Fig. 12a). In addition, a protrusion to higher MLCAPE values in the environmental characteristics is seen between − 20 and − 50 J kg−1 of CIN and represents a different mode of the thermodynamic environment during JA associated with a different spectrum of convective systems that have higher values of MLCAPE but weaker CIN to overcome.
In a future climate, the thermodynamic environments supporting convection represent a broader distribution of MLCAPE and CIN values in both MJ and JA (Fig. 12b, d). Compared to the CTRL simulation in MJ, the PGW distribution shows a significant expansion to almost double the MLCAPE values and 1.5 times the CIN values in Fig. 12b. This expansion represents a modulation in the thermodynamic environments supporting convection in the US Great Plains and helps explain the shift in the convective population shown in Figs. 7 and 9. While the environment can support more vigorous convective storms, the capping inversion is stronger and requires more energy to break through. Thus, the convective population changes in MJ shown in Figs. 7 and 9 are consistent with these simultaneous changes in the thermodynamic environment, with fewer weak to moderate storms and more intense storms. The thermodynamic environment in the PGW simulation in JA shows a similar, but less pronounced expansion to higher CAPE and CIN values (Fig. 12d). However, the most notable difference in the PGW JA distribution (Fig. 12d) is the lateral expansion of the aforementioned bulge in moderate CIN values to higher MLCAPE values, indicating a shift in the thermodynamic environment supporting convection in the late summer.
These results are consistent with state-of-the-art climate model simulations that suggest future increases in hazardous convective weather due to an increase in CAPE (Trapp et al. 2007, 2009; Diffenbaugh et al. 2013; Brooks 2013; Lackmann 2013; Gensini and Mote 2014; Trapp and Hoogewind 2016). Other studies have demonstrated that CAPE is expected to increase in a warming climate using an idealized Radiative Convective Equilibrium (RCE) perspective appropriate for tropical environments (Muller et al. 2011; Igel et al. 2013; Singh and O’Gorman 2013; Romps 2016; and many others). However, the results of this study suggest that the amount of energy inhibiting convection (CIN) is critical to understanding changes in the convective population in the US and surrounding maritime environments. Increases in the amount of both MLCAPE and CIN over the Gulf of Mexico also result in a decrease in the weak to moderate precipitating systems south of the coastal region (Figs. 5a–c, 7a–c), indicating a strong response in tropical maritime environments as well. Thus, a more comprehensive understanding of the changes in the convective population in a future climate likely requires a full diagnosis of changes in the thermodynamic environment in all climate regimes around the world.
Specific changes in thermodynamic profiles in a future climate
A typical method to examine the thermodynamic conditions of the atmosphere is to use atmospheric sounding data collected from rawinsondes. The examination of bulk thermodynamic metrics in Sect. 5.1 demonstrated the geographic variability of future changes in the thermodynamic environment across the US and how those changes resulted in a shifting convective population. In this section, sounding observations at various sites across the US are compared to both the CTRL and PGW simulations to provide greater confidence in both the model representation of thermodynamic environments and future changes in those environments. The methodology for the sounding analysis is described in Sect. 2.4 and all sounding comparisons are at 0 UTC to capture the environment most relevant to convective storms across the US.
Atmospheric sounding observations from three stations (Corpus Christi, TX; Norman, OK; and Topeka, KS) are compared to model-derived thermodynamic profiles from the closest grid point to these stations from the CTRL and PGW simulations in Figs. 13, 14 and 15. The median temperature and dewpoint observations are notably similar to the profiles derived from the CTRL simulation at all three stations (Figs. 13, 14, 15), providing confidence in the ability of the CTRL simulation to capture atmospheric thermodynamic properties. As Liu et al. (2016) showed, the addition of the PGW perturbations resulted in a general warming and increase in moisture throughout the troposphere. A result of the warmer and moister troposphere is the higher frequency of large MLCAPE values, as demonstrated by the probability density function figures showing the range of MLCAPE in all derived profiles in the 13-year dataset (Figs. 13b, 14b, 15b). Mean MLCAPE values increase in a warmer climate by an average of 783 J kg−1 at Corpus Christi, TX, 391 J kg−1 at Norman, OK, and 314 J kg−1 at Topeka, KS with all of these differences being statistically significant according to the non-parametric Mann–Whitney U test at the 0.05 level. While the increase in MLCAPE is most notable at the Corpus Christi location (Fig. 13b), all 23 stations analyzed in the central US showed increasing mean MLCAPE in the PGW simulation (Tables 1, 2), which supports the results from Figs. 10, 11 and 12 and Sect. 5.1.
A similar analysis was conducted for CIN in each observational and model-derived sounding profile and the results are presented in Figs. 13c, 14c, and 15c for the three stations and for all stations in Tables 1 and 2. Overall, probability density functions show that in the PGW simulation, CIN values are expected to increase in magnitude and provide a stronger capping inversion or more energy inhibiting convection. Mean CIN values increased in magnitude by 47 J kg−1 at Corpus Christi, TX, 44 J kg−1 at Norman, OK, and 41 J kg−1 at Topeka, KS with all of these differences being statistically significant according to the non-parametric Mann–Whitney U test at the 0.05 level (Figs. 13c, 14c, 15c). Similar to the increases in MLCAPE at all stations, CIN also increased in magnitude at all stations examined in this analysis (Tables 1, 2). The sounding locations represent different environment conditions since Norman, OK and Topeka, KS are located at a continental region, while Corpus Christi, TX is located at a coastal region. Regardless of the region, these stations show the same sign of the changes in MLCAPE and CIN. Thus, these results are consistent with the analysis from Figs. 10, 11 and 12 and Sect. 5.1 and demonstrate a robust response in the thermodynamic environment supporting convection in a warmer and moister climate.
In convective storm development and organization, the amount of vertical wind shear is important in determining the mode of convection as shown by Rotunno et al. (1988) and many other studies. Thus, an analysis of the magnitude of the 0–6 km vertical wind shear in each sounding profile was calculated and the probability density functions are presented in Figs. 13d, 14d, and 15d for the three stations. The wind shear at all three stations decreases in the PGW simulation and thus is likely not responsible for the differences in the convective population presented in Figs. 7, 8 and 9. However, the use of spectral nudging at the large scales in these simulations limits full shear changes from being realized, as noted in Trapp et al. (2007). While a detailed investigation of the three-dimensional structure of the precipitating systems is beyond the scope of this study, future research on this topic would provide more information on the three-dimensional characteristics of storms in a changing climate.
Idealized thermodynamic response in a future climate
From the results presented in Sects. 5.1 and 5.2, the thermodynamic environment in a future climate will provide more energy available for convection and more energy inhibiting convection. The fact that all stations showed statistically significant increases in magnitude in these parameters in the PGW simulation (Table 2) is particularly notable, especially given the complex response of precipitation, convective storm frequency, and many other phenomena to a changing climate (Prein et al. 2015, 2016; Romps et al. 2014). Given the robust response in the thermodynamic environment to a warmer and moister climate, a question arises about the fundamental behavior of MLCAPE and CIN parameters in a cooler vs. warmer climate state. In the context of convective storm dynamics and thermodynamics, the atmospheric sounding profile from Weisman and Klemp (1982), hereafter referred to as WK, is a canonical and standard profile that has been used for decades to test the response of convection to wind shear and many other processes important for convective dynamics (Weisman and Klemp 1982; Rotunno et al. 1988). As described in Sect. 2.4, this study uses the WK sounding and modifies the temperature profile (keeping relative humidity constant) to represent idealized atmospheric conditions for ± 5 °C. Using this approach, the fundamental behavior of both MLCAPE and CIN will be examined for varying environments and the results will provide a greater understanding of how the thermodynamic environments supporting convection vary with changes in temperature.
The results from the idealized experiment are presented in Fig. 16a, with example profiles from − 5 °C and + 5 °C included with the original WK sounding profile. When temperature is decreased by 5 °C, both the MLCAPE and CIN decrease in magnitude compared to the original profile (MLCAPE and CIN for the WK profile are shaded in red and blue colors, respectively). In contrast, when the temperature is increased by 5 °C, both the MLCAPE and CIN increase in magnitude, echoing the results from the bulk and atmospheric sounding thermodynamic analysis from Sect. 5.1 and 5.2. Given the strong dependence between temperature and the saturation vapor pressure of the atmosphere from the Clausius–Clapeyron equation, the fundamental behavior of both MLCAPE and CIN in a warmer climate is perhaps not a surprising result. This is especially true because both MLCAPE and CIN are calculated using the virtual temperature, which takes atmospheric moisture into account. Thus, if more atmospheric moisture is present in the atmosphere, the parcel will contain more buoyancy than a similar atmosphere with less moisture as is shown graphically in Fig. 16a, b. Similarly, a warmer and moister environment results in a greater magnitude of CIN (Fig. 16c). This relationship holds true for every degree of warming and cooling as demonstrated by the MLCAPE and CIN values in Fig. 16b, c. The slope of the MLCAPE curve is steeper than the CIN curve, indicating the profound role of temperature in generating atmospheric buoyancy and convective energy (Fig. 16b, c). However, as was described in Sect. 2.3, if the CIN is too strong, convection may be inhibited if a lifting mechanism is not present. In a warmer climate, if a significant lifting mechanism is present, the severity of the convection will likely be greater than in the current climate, given that more energy will be available for convection. This result is consistent with other studies showing extreme convective weather events increasing in frequency and intensity in a future climate (Prein et al. 2015, 2016; Ban et al. 2015; Romps et al. 2014).
Results from Lucarini et al. (2010) suggest that entropy production and the degree of irreversibility of the earth system are linearly proportional to the logarithm of CO2 concentrations. In other words, they propose that the climate system becomes less efficient, more irreversible, and features higher entropy in a warmer climate. From a thermodynamic perspective, higher entropy in the thermodynamic profile for the warmest temperature profile considered in the idealized thermodynamic analysis (Fig. 16) is apparent given the steep slope of the moist adiabatic lines that ultimately determine the amount of MLCAPE in the profile. Since entropy is conserved in a reversible adiabatic process, increases in the irreversibility of the earth system also results in an increase in entropy (Lucarini et al. 2010). Given that potential temperature is a meteorologist’s entropy (Bohren and Albrecht 1998), increased MLCAPE and CIN in the warmest climate (+ 5 °C) are a result from the increasing irreversible processes that span a larger range of potential temperatures (dry adiabatic lines) than cooler temperatures (Fig. 16a). Lucarini et al. (2010) also show that changes in latent heat fluxes are the dominant ingredients for this change, demonstrating the critical importance of representing clouds and precipitation correctly in future climate simulations.
The fundamental relationship between important thermodynamic parameters that are critical to understanding changes in the convective population in a future climate is revealed. Even in the absence of variations in synoptic and mesoscale conditions, a warmer climate will provide greater energy available for convection and also greater energy inhibiting convection. This seesaw effect is critical for understanding potential changes in the convective population across the US and beyond. It explains why the high-resolution convection-permitting simulations show a decrease in weak to moderate precipitating systems and an increase in strong to extreme precipitating systems. The latter result agrees with prior research on this topic, that we can expect more extreme storms and more intense precipitation rates in a warmer climate (Prein et al. 2016). However, when considering convection in general, the detailed thermodynamic conditions are critical to understanding the type and intensity of convection that results. In addition, since the changes of CIN in the idealized profiles are modest relative to the PGW simulation (Figs. 10, 11, 16), the importance of complex interactions with the Earth system, including land–atmosphere interactions that can influence the thermodynamic environment supporting convection should be explored in future research.
By considering both MLCAPE and CIN in this study, we have shown that it is likely that enhanced CIN in a future climate both suppresses weak to moderate convection across the US, and also provides an environment where convective energy can build to extreme levels and result in more frequent violent severe convection compared to the current climate. Although the relationship between increased MLCAPE and CIN is especially important for mid-latitude continental convective storms, as has also been shown in a previous study looking at extreme tornadic cases using the PGW method (Trapp and Hoogewind 2016), these parameters also appear to explain decreases in weak to moderate convection and increases in strong convection over the Gulf of Mexico, which is predominantly characterized by maritime and tropical convection. The uniform increases in temperature and humidity throughout the troposphere provide a conceptual framework to gain understanding of how such changes will impact the thermodynamic environment of future convection. Studies have shown that upper tropospheric temperatures might increase more in a warmer climate leading to a stabilization of the atmosphere (Liu et al. 2016; Kröner et al. 2016). This would limit the increase in MLCAPE but have no significant effect on CIN. In addition, expected decreases in near surface relative humidity over land areas (Seager et al. 2007) might affect MLCAPE and CIN. Thus, the interplay between MLCAPE and CIN may be important for many regions of the Earth where convective processes are present and should be considered in future convection-resolving studies on climate change.