**4. Concluding Remarks**

Based on the AMIP-type model simulations using the Exascale Energy Earth System Model (E3SM), we investigated the changing characteristics of climate-scale (monthly) tropical extreme precipitation in a warming climate. Three ten-year-long AMIP-type model simulations were carried out: (1) a control, with the present-day SST, and CO2 atmospheric concentration, (2) P4K, the same as the control but with a forced idealized uniform 4K increase in the SST globally, and (3) 4xCO2, the same as the control but with SSTA derived from coupled model simulations under a four-times-higher atmospheric CO2 concentration, including the corresponding 4xCO2 radiative heating of the atmosphere. The key results of this study include the following:


to increased CIN, delaying the triggering of deep convection, while building up the convective available energy in the lower atmosphere associated with the warming climate. When deep convection is triggered eventually through moisture advection from episodic small-scale atmospheric eddy processes associated with land–sea breeze, thunderstorms, and orography, an explosive growth of MCS-like organization occurs preferentially over land, releasing extra amounts of convective available potential energy (CAPE) stored during CIN, and resulting in very extreme "record-breaking" precipitation over land, as global climate warming continues unabated.

The similarities in MCS extreme precipitation development over ocean and land and between 4xCO2 and P4K underscore the importance of SST warming as the primary forcing in the development of MCS-like organization, leading to extreme precipitation. However, non-uniform SSTA based on ensemble coupled models together with dynamically consistent CO2 radiative forcing of the atmosphere is needed to produce stronger and presumably more realistic regional characteristics of extreme precipitation in the warming climate of a future world through dynamical adjustments and feedback processes in the coupled atmosphere–ocean–land system. For a better understanding of the effects of CIN in staging very extreme "record-breaking" regional precipitation events over land, intrinsic land–atmosphere feedback processes and impacts by concomitant changes in the tropical large-scale circulation, land–sea contrast, and under P4K and 4xCO2, comparisons with CMIP6 model outputs, and multiple sources of precipitation and cloud observations are being investigated in our ongoing research.

Finally, we note that high-resolution MCS resolving meso-scale (10–20 km) and cloudscale (<5–10 km) models are required to conduct studies of extreme precipitation events on hourly/daily time scales over limited spatial/time domains. Cloud-scale GCM and coupled GCMs are certainly desirable for better simulations of MCS over the global domain. However, such GCM simulations are highly labor-intensive and expensive for climate-scale long-term integrations. That is why most long-term GCM climate experiments, such as in CMIP6, are still expected to run at moderate-to-low resolution (>50–100 km) in the foreseeable future. Here, we show important results indicating that improved cumulus parameterization in a state-of-the-art GCM with moderate resolution can show MCS-like organization features for extreme tropical precipitation, on monthly time scales. Such an approach allows for the physics of extreme precipitation, such as MCS-like organization, to be explored and evaluated by precipitation and cloud observations on a global climatic scale, bridging the gap between meso-scale and low-resolution climate models.

**Supplementary Materials:** The following supporting information can be downloaded at: https://www. mdpi.com/article/10.3390/atmos14060995/s1, Figure S1. Spatial distribution of SST, Frequency of Occurrence (FOC), and the fraction of stratiform (large-scale) rain for top 5% monthly precipiptation; Figure S2. Spatial distribution of SST, precipitation efficiency (PE), outgoing longwave radiation (OLR) for top 5% monthly precipitation; Table S1. Extreme tropical monthly precipitation intensity threshold (mm/day) as a function of top-percentile rain rate for the entire tropics (30◦ S–30◦ N).

**Author Contributions:** Conceptualization, W.K.M.L. and L.R.L.; methodology, W.K.M.L., B.H. and K.-M.K.; software, B.H. and K.-M.K.; validation, W.K.M.L., B.H. and K.-M.K.; formal analysis, K.-M.K.; investigation, W.K.M.L. and K.-M.K.; resources, L.R.L., B.H. and K.-M.K.; data curation, B.H. and K.-M.K.; writing—original draft preparation, W.K.M.L.; writing—review and editing, L.R.L., B.H. and K.-M.K.; visualization, K.-M.K. and W.K.M.L.; supervision, W.K.M.L.; funding acquisition, W.K.M.L. and L.R.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the U.S. Department of Energy (DOE), the Office of Science, Biological, and Environmental Research as part of the Regional and Global Model Analysis Program Area under Grant Award #300426-00001, awarded to the University of Maryland from the Pacific Northwest National Laboratory (PNNL). The PNNL is operated for the DOE by the Battelle Memorial Institute under contract DE-AC05-76RL01830. Partial support was also provided by the NASA Modeling and Analysis Program, Federal Award Identification # 80NSSC21K1800, awarded to the University of Maryland and to the NASA Goddard Space Flight Center.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data used in this research were based on model outputs of the DOE/PNNL, available at https://portal.nersc.gov/archive/home/b/beharrop/www/e3sm\_v1\_pd\_ and\_warming\_experiments/e3sm\_v1\_control\_simulations.tar (assessed on 1 June 2023).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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