**3. Results**

#### *3.1. Stratiform vs. Convective Precipitation*

Since climate models do not resolve clouds explicitly because of their coarse resolution, model precipitation is classified as "convective" if they are produced by the subgridscale parameterization of deep convection, and as "stratiform" precipitation if they are produced by condensation processes of the large-scale (LS) circulation represented by the cloud microphysics parameterization. In this paper, for convenience, we use the term LS rain fraction (LSRF) in the model as synonymous with stratiform rain fraction. The variations in the LSRF (Figure 2a) as a function of the monthly precipitation from January to December (J2D) show that there was an increasing contribution of LS rain as a function of the precipitation intensity (P) over the entire tropics in the control, P4K, and 4xCO2 simulations, respectively. The LS rain fraction increased faster (steeper rise) in the order of control, P4K, and 4xCO2. For very extreme precipitation (P > 30 mm/day), the LS rain fraction rose to above 50%, reaching a maximum of ~70%, for P > 40 mm/day under P4K and 4xCO2. For convenience, the unit for P is omitted hereafter. In comparing the same plots but separated into ocean and land, it is clear that for P < 30, most of the increase in the LSRF came from the ocean (Figure 2b). This is not surprising because of the much larger area of ocean compared to land in providing precipitable water to the atmosphere. Over the ocean, increases in the LSRF as a function of P were more robust under 4xCO2 compared to P4K, with the former showing a steady increase up to P < 30, and the latter showing a peak in the LSRF at P~20. As explained in later sections, the stronger signal under 4xCO2 was likely due to stronger dynamical feedback under a physically consistent SSTA and additional CO2-induced radiative forcing and response compared to the idealized uniform SSTA-only forcing under P4K. Most interestingly, in comparing the LSRF variation over land (Figure 2c) to those over land and ocean (Figure 2a) and over ocean only (Figure 2b), it is clear that almost all of the very extreme precipitation (P > 30), while occurring rarely, were found only over tropical land regions. Worth noting is that the LSRF seldom reached above 0.7 even over land, indicating that the generation and transport of ice-phase condensate by deep convection to the upper troposphere are essential in order for ice-phase microphysics generating stratiform rain to take place under the extended anvil clouds (see Figure 1a). Anvil clouds will dissipate quickly without the sustained generation of ice-phase condensation from the convective core [65,66].

**Figure 2.** Stratiform rain fraction as a function of precipitation rate (mm day<sup>−</sup>1) over (**a**) entire tropics, (**b**) ocean-only, and (**c**) land-only, for control (black), 4xCO2 (red), and P4K (blue). Gray shading and red vertical bars represent a 1-s standard deviation for control, and 4xCO2, respectively. Standard deviations for P4K are similar to 4xCO2, and are not shown for clarity. J2D stands for monthly data taken from January to December.

A breakdown of the cumulative frequency of occurrence (FOC) of extreme monthly precipitation in terms of the total number of model grid points exceeding a given precipitation threshold (Table 1) shows that there was a rapid drop-off in the FOC with increasingly extreme precipitation. In the control climate, the FOCs of very extreme precipitation (P > 25–35) were indeed rarely (fewer than 1 in 1000) occurring preferentially over land, and rare or absent over the ocean. The FOCs of P > 30 increased by 3–5-fold under P4K and 4xCO2 compared to the control and were stronger for the latter than the former. Analysis of the precipitation intensity threshold as a function of the top-percentile (PCT) rain rates showed similar signals, indicating more extreme heavy rain over land than the ocean (see Table S1). The preference for very extreme precipitation over land compared to the ocean appears to be an intrinsic property of the tropical ocean–land–atmosphere system, which was already present in the control, amplified under P4K, and even more so under 4xCO2.



The spatial distributions of the frequency of occurrence (FOC) of extreme precipitation based on the rain rate for the top 1 percentile (PCT01) and top 5 percentile (PCT05) rainfall were computed. To facilitate comparison, the thresholds for the control for ocean + land were used to compute the FOC geographical distributions for P4K and 4xCO2. The PCT01 (P > 13) rains (Figure 3a) occurred over limited areas within the climatological rainy regions of the Asian monsoon, the maritime continent/Pacific warm pool (SST > 302K), and the equatorial East Pacific ITCZ, with isolated signals over land regions in equatorial South America and Africa. Under P4K (Figure 3b), the warm pool areas expanded substantially, covering much of the tropics. The PCT01 rain areas also expanded, but were still anchored to the climatological wet regions within the much warmer SST (SST > 304K). The increased PCT01 precipitation over the equatorial land region was more prominent compared to the control. Worth noting is that under P4K, except for the expansion of wetter areas, there were no fundamental changes in the spatial structure of tropical rainfall distribution compared to the control, suggesting a strong wet-getting-wetter (WeGW) scenario [10,11]. Under 4xCO2 (Figure 3c), the areal extent of the Pacific warm pool was further expanded compared to P4K, covering the entire tropical ocean (25◦ S–25◦ N). Over the aforementioned WeGW regions, PCT01 rain FOCs were further enhanced and expanded compared to P4K. Additionally, prominent centers of action for PCT01 precipitation were found over the equatorial Indian Ocean, and over the equatorial Atlantic Ocean under 4xCO2. that is, the expanded PCT01 rain areas exhibited not only WeGW but also a warmer-getting-wetter (WaGW) pattern [12]. Overall, the tropical SST was warmer by 1.85 K under 4xCO2 compared to P4K.

**Figure 3.** Spatial distribution of SST and frequency of occurrence (FOC) for top 1% precipitation (PCT01) in fractional units, based on monthly rainfall data from January through December (J2D), for (**a**) control, (**b**) P4K, and (**c**) 4xCO2, with warm pool SST (302K) outlined in red. Corresponding distributions for stratiform (large-scale) rain in fractional units are shown in (**d**–**f**), respectively.

Under the control climate, close matches between the areas of PCT01 rain (Figure 3a) and regions of an enhanced LSRF were discernable over the Asian monsoon land, the maritime continent, and the eastern Pacific ITCZ (Figure 3d). The sparse spatial extent of the PCT01 LSRF signals the rarity of such events in the control. Under P4K, the regions of enhanced FOC (Figure 3b) were well co-located with those with a large LSRF (>45–50%) over the Asian monsoon region, the maritime continent, the SPCZ, and the northern edge of the ITCZ over the eastern Pacific (Figure 3e). Under 4xCO2, the co-location of high FOCs of PCT01 rain (Figure 3c) with an increased LSRF (Figure 3f) could be seen over the aforementioned regions, as well as the land regions of equatorial Africa and the Amazon, consistent with the WeGW and WaGW patterns. Similar patterns of the FOC for PCT05 (P > 10) and an enhanced LS rain fraction were computed, indicating increasing contributions from LS (stratiform) rain types in more expansive regions of a high FOC compared to PCT01 (see Figure S1).

#### *3.2. Precipitation Efficiency and MCS Organization*

Recent model simulations and observations have shown that increased precipitation intensity is highly correlated with enhanced precipitation efficiency (PE), that is, an enhanced rate of microphysical auto-conversion of cloud water (liquid and ice phase), as the surface temperature rises [4,66,69–71], and it is a key driver of the large-scale circulation sustaining tropical heavy precipitation under global warming [72,73]. Here, we define the PE as the ratio of precipitation to the column integration of the total cloud water (TCW), including liquid and ice, as simulated by the microphysics parameterization of clouds and precipitation used in the E3SM (see discussion in Section 2).

$$\text{PE} = \text{P} / \text{TCW (in units of s}^{-1}\text{)}.\tag{1}$$

Physically, the inverse of PE (τ = PE<sup>−</sup>1) represents a characteristic residence time scale for the total condensed cloud water in an atmospheric column undergoing precipitation for a given precipitation rate. A high value of PE (low value of t) reflects vigorous water recycling within the atmosphere, converting cloud liquid and ice water into precipitation, while maintaining an abundant stock of the TCW in the atmosphere through enhanced surface moisture flux and low-level moisture convergence [66,74].

Figure 4a shows a nearly linear increase in the PE as a function of P over the entire tropics, with a faster rate (steeper gradient) of increase in the PE for extreme precipitation from the control to P4K to 4xCO2. The typical range of values of PE (0.02–0.2) is from τ = 50 to 5 minutes, that is, there is a 10-fold reduction in the residence time scale of the TCW in the atmosphere, from light to the most extreme precipitation in the tropics. These values of τ can be considered a crude estimate of increasingly fast cloud–water–precipitation recycling time scales in MCS-like organization systems, contributing to the extreme precipitation in the E3SM model. Compared to the ocean-only plot (Figure 4b), it can be seen that most of the PE increase for P < 30 represents contributions mainly from oceanic precipitation, with a faster increase in the order of control, P4K, and 4xCO2. However, very extreme precipitation (P > 30) with high PE (PE > 0.1) was not found over the ocean. In contrast, the rate of increase in the PE as a function of P (Figure 4c) was faster over land than over the ocean for all precipitation rates. For extreme precipitation (P > 30) over land, the rate of increase in the PE was clearly accelerated compared to lower rain rates (Figure 4c). Comparing Figure 4a–c, it can be seen that almost all of the very extreme tropical precipitation (P > 30) and high PE (>0.1) events came from the land.

**Figure 4.** Precipitation efficiency (minute−1) as a function of the precipitation rate (mm day−1) for January through December, for (**a**) land + ocean, (**b**) ocean-only, and (**c**) land only, based on monthly data from January through December (J2D). Gray shading and red vertical bars represent 1 s standard deviation for control and 4xCO2, respectively. Standard deviations for P4K are similar to 4xCO2, but are not shown for clarity.

The geographic distributions of the PE of PCT01 rainfall for the control, P4K, and 4xCO2 (Figure 5a–c) show strong similarities to the pattern of outgoing longwave radiation (OLR), indicating an abundance of cold anvil clouds with low OLR (<190 Wm<sup>−</sup>2) in regions with enhanced PE (Figure 5d–f). Under P4K and 4xCO2, more so in the latter than the former, higher PE with lower OLR (more elevated clouds with colder tops) were found over the Asian monsoon, maritime continent, and equatorial Africa and South America regions. In contrast, over the open oceans of the Pacific ITCZ, the tropical western Pacific, and the South Pacific Convergence Zone (SPCZ), extreme precipitation was derived mostly from increased PE in regions with OLR >215 Wm<sup>−</sup>2, consistent with an increased abundance of warm rain as a key signal of climate warming [69,75]. For moderately extreme precipitation (PCT05), the areal extent of high PE and low OLR increased substantially in conjunction with the expansion of the tropical SST warm pool (see Figure 3). Overall, the PE and OLR distributions for PCT01 and PCT05 exhibited the WeGW pattern under the control and P4K, and the WeGW + WaGW under 4xCO2, similar to those for the LSRF (see discussion about Figure 3).

**Figure 5.** Spatial distribution of SST and precipitation efficiency (PE) for top 1% precipitation (PCT01) in units of minute<sup>−</sup>1, based on monthly rainfall data from January to December (J2D) for (**a**) control, (**b**) P4K, and (**c**) 4xCO2, with respective warm pool SST outlined in red. Corresponding distributions for outgoing longwave radiation (OLR) in units of Watt m−<sup>2</sup> are shown in (**d**), (**e**), and (**f**) respectively.

Next, we explored the capability of the E3SM in simulating MCS-like extreme precipitation organization, with regard to an increased contribution from stratiform (anvil) rain, enhanced PE in the production by freezing, and the removal of cloud ice by melting and precipitation fallout. Specifically, we computed composite change patterns of P4K and 4XCO2 relative to the control and that of 4xCO2 relative to P4K in the vertical profiles of key MCS quantities, i.e., cloud ice concentration, condensation heating, and large-scale vertical velocity, as a function of the precipitation intensity of the entire tropics, separately for land and ocean. Over the ocean, the level of maximum cloud ice can be seen to shift upward relative to the control as precipitation increases under P4K (Figure 6a), starting at P~10 and continuing up to P > 25–30. The negative (positive) values of cloud ice signals accelerated the removal (accretion) of cloud ice below (above) 300 hPa by enhanced precipitation (condensation) relative to the control. Given the co-location of the regions of enhanced precipitation (PCT01) and the increased LSRF (Figure 3), as well as the increased PE and low OLR values (Figure 5), the cloud ice features are consistent with the enhanced model of MCS-like organization compared to the control and analogous to those shown in Figure 1a. Under 4xCO2 (Figure 6b), the cloud ice anomaly pattern is similar to that under P4K, indicating the primary importance of ocean warming in initiating the MCS organization. However, the MCS structure appears to be more robust under 4xCO2 compared

to under P4K. The stronger organized MCS development under 4xCO2 can also be seen in the difference plot of 4xCO2-minus-P4K (Figure 6c), indicating a stronger removal of cloud ice by precipitation near 400–250 hPa, and increased melting due to the warming of the middle and lower troposphere, coupled with enhanced cloud ice formation near 250–150 hPa. These likely reflect the effect of increased CO2 radiative heating in the lower troposphere, enhancing convective instability in the upper troposphere [76]. Over land (Figure 6d,e), the changes in the cloud ice in the upper troposphere reflecting the increasing MCS organization under P4K and 4xCO2 are similar to those in the ocean, as is evident by the strong removal of cloud ice near 500–350 hPa and the accumulation of cloud ice above (250–150 hPa) associated with anvil cloud development. Under P4K and 4xCO2 (Figure 6d,e), the MCS organization over land shows less cloud ice loading (solid contours) but a more vertically confined region of negative anomalies, indicating stronger cloud ice removal compared to over the ocean. However, very extreme precipitation P ≥ 30–35 occurred only over land in 4xCO2, but not over the ocean (solid contours in Figure 6b,e). The additional radiative heating effect due 4xCO2 further enhanced the MCS precipitation organization over land compared to P4K (Figure 6f).

**Figure 6.** Vertical profiles of anomalous cloud ice contents (10−<sup>6</sup> kg/kg, ice mass per kilogram of air mass) as a function of precipitation intensity (mm day<sup>−</sup>1) over ocean for (**a**) P4K-minus-control, (**b**) 4xCO2-minus-control, and (**c**) 4xCO2-minus-P4K, from January to December (J2D). Panels (**d**), (**e**), and (**f**) are the same as (**a**), (**b**), and (**c**), respectively, but over land. Contours show the mean profiles of condensation heating for the minuend (first term of the subtraction) indicated in the respective subpanel labels. Regions with statistical significance exceeding 95% confidence are highlighted by green dots.

Over the ocean, the condensation heating profiles as a function of P for P4K and 4xCO2 (Figure 7a,b) reveal an essential feature of MCS organization, that is, the elevation of the level of condensation heating is characterized by positive (negative) anomalies above (below) 300 hPa as the precipitation intensifies (cf. Figure 1b). This is consistent with the increase in the LSRF (see Figure 2) and PE (see Figure 4), as discussed previously. Strong cooling found near the freezing level at 500 hPa and regions slightly above signals enhanced melting and evaporation of falling rain. The MCS organization appears to be stronger under 4xCO2 relative to P4K, with more condensation heating above (below) 250hPa (Figure 7c). Over land, the condensation heating profiles (Figure 7d,e) exhibit similar features to their ocean counterparts, but with more robust MCS-like features, that

is, elevated condensation heating, strong cooling at the mid-troposphere freezing level and regions below (Figure 7d,e), and a stronger response in 4xCO2 compared to P4K (Figure 7f) due to the additional radiative heating of the atmospheric CO2.

**Figure 7.** Vertical profiles of anomalous condensational heating (K day−1) as a function of precipitation intensity (mm day−1) over ocean for (**a**) P4K-minus-control, (**b**) 4xCO2-minus-control, and (**c**) 4xCO2-minus-P4K, from January to December (J2D). Panels (**d**), (**e**), and (**f**) are the same as (**a**), (**b**), and (**c**), respectively, but over land. Contours show the profiles of condensation of the minuend (first term of the subtraction) indicated in the respective subpanel labels. Regions with statistical significance exceeding 95% confidence are highlighted by green dots.

For the large-scale vertical velocity over the ocean under P4K and 4xCO2 (Figure 8a,b), increased upward (downward) motions in the upper (middle-and-lower) troposphere are evident and consistent with the condensation heating (cooling) changes (see Figure 7). The decrease in the upward vertical motion in the mid-troposphere is indicative of the MCS organization, pertaining to an increased melting of cloud ice at the distinctive freezing level near 500 hPa and increased downdraft associated with evaporative cooling in the regions of falling rain (cf. Figure 1a). Again, the effects are stronger under 4xCO2 compared to P4K (Figure 8c). Over land (Figure 8d,e), the changes in the large-scale vertical motions are similar to those in the ocean, except they appear more muted under both P4K and 4xCO2, with the latter only slightly stronger than the former (Figure 8f). The stronger MCS-like signals over the ocean, especially the strong, distinctive cooling at the freezing level compared to over land, reflect the direct effects of stronger forcing over the ocean from the SSTA, as well as positive feedback from changes in the large-scale circulation. Importantly, the anomalous large-scale vertical motions over land shown here are likely attributable to not only the MCS organization but also changes in the large-scale Walker Circulation, driven by an east–west SST gradient and the land–sea thermal contrast, further modulating changes in the MCS convective updraft over land [77,78].

**Figure 8.** Vertical profiles of anomalous upward vertical velocity (Pa/s) as a function of precipitation intensity (mm day<sup>−</sup>1) over ocean for (**a**) P4K-minus-control, (**b**) 4xCO2-minus-control, and (**c**) 4xCO2 minus-P4K, from January to December (J2D). Panels (**d**), (**e**), and (**f**) are the same as (**a**), (**b**), and (**c**), respectively, but over land. Contours show the profiles of condensation of the minuend (first term of the subtraction) shown in the respective subpanel labels. Regions with statistical significance exceeding 95% confidence are highlighted by green dots.

#### *3.3. Convective Inhibition (CIN) and Extreme Precipitation*

In this subsection, we explore further the fundamental reason why very extreme but rare (record-breaking) precipitation tends to occur over land rather than the ocean. Under GHG warming, the convective available potential energy (CAPE) is expected to increase due to the relative fast rate (~7% K−1) of increase in the atmospheric saturated moisture with higher temperature. However, convective inhibition (CIN), that is, near-surface negative buoyancy, is known to be enhanced under global warming over land, resulting in increased drying (sub-saturation) of the near-surface air due to a lack of moisture supply relative to the fast land warming [79,80]. CIN drying is reflected in reduced low-level relative humidity, a higher lifting condensation level (LCL), and an elevated level of free convection (LFC), inhibiting deep convection [81].

To illustrate the effect of CIN under P4K and 4xCO2 and its relationship with extreme precipitation, an analysis of the surface moist energy budget follows. The convective instability of the atmosphere is controlled by the vertical gradient of the moist static energy (MSE), with

$$\text{MSE} = \mathbf{C}\_{\text{D}} \mathbf{T} + \mathbf{L} \mathbf{q} + \mathbf{g} \mathbf{z}, \tag{2}$$

where Cp is the thermal capacity at a constant pressure, T is the surface air temperature, L is the latent heat of condensation, q is the specific humidity, g is the gravitation constant, and z is the geopotential height. A negative MSE vertical gradient (high—below, low—above) implies convective instability and vice versa for stability. For CIN, we focused on the first two terms (1) near the surface, that is, the lowest model level, where gz is negligibly small.

Under P4K (Figure 9a), the near-surface CpT anomalies (relative to the control) increased nearly uniformly (~4–5 kJ/kg) over the entire tropical ocean, following closely that of the imposed idealized 4K uniform SST warming. The CpT increase over land was stronger (~5–7kJ/Kg) compared to over the ocean because land has a lower thermal capacity than water. As a result, the land temperature rises faster and higher than that of the ocean with the same amount of heat input. In addition, the lack of land moisture sources

results in less evaporative cooling. Hence, under global warming, the land temperature has to rise much higher compared to the ocean temperature to enhance outgoing longwave radiative cooling, which is needed to balance the land heating from the CO2 greenhouse effect and increased downward solar radiation from reduced clouds due to drying. The surface Lq (Figure 9b) followed a similar change pattern to CpT and was clearly the dominant forcing (~8–15kJ/kg), stronger than that of CpT by 2–3 times. This is because of the well-known exponential increase in the atmospheric saturated moisture content as a function of temperature, governed by the Clausius–Clapeyron relationship. Over the ocean, due to the readily available moisture from below, the near-surface relative humidity (RH) remained close to the saturation values. As a result, the anomalous relative humidity under P4K vs. the control was positive but small (<2–4%) over the ocean (Figure 9c). However, over land, because of the larger increase in the CpT, the additional moisture required to reach saturation far exceeded that which could be derived from local moisture sources. As a result, there was a distinctive reduction in the RH (~3–6 %), indicating drying over land under P4K relative to the control (Figure 9c) and signaling increased CIN [81]. However, as the land temperature rises and CIN increases under P4K, the triggering of convection induced by mesoscale convergence, episodic outflow from land–sea breeze, and forced lifting from surface inhomogeneity and/or orographic may lead to an explosive growth of convection, releasing a large amount of stored CAPE during CIN [81]. The delayed onset of deep convection due to increased CIN could facilitate the occurrence of very extreme but rare precipitation in a warming climate, specifically over land. The stronger and longerlasting the CIN, the more CAPE builds up in the lower troposphere, and the more extreme the precipitation when it eventually occurs, releasing a large amount of built-up CAPE during CIN [82–85].

**Figure 9.** Spatial distribution of surface anomalous (**a**) CpT (kJ/kg), (**b**) Lq (kJ/kg), and (**c**) relative humidity (%) for January to December (J2D) under P4K. Panels (**d**), (**e**), and (**f**) are the same as in (**a**), (**b**), and (**c**), respectively, but under 4xCO2. Panels (**g**–**i**) are the same as (**a**–**c**) but for 4xCO2-minus-P4K.

Under 4xCO2 (Figure 9d), the near-surface anomalous CpT warming over land was much larger (>8–15 kJ/kg) than over the ocean (~5–7 kJ/kg). Again, the increase in the surface Lq (Figure 9e) over the tropical oceans followed the corresponding increase in the SST, consistent with 4xCO2 forcing and indicating enhanced warming and moistening of the surface air over the tropical ocean, following the Clausius–Clapeyron relationship. The differential magnitude of the anomalous Lq and CpT resulted in a large contrast in the relative humidity (RH) between the ocean and land, that is, increased RH over the tropical ocean, and decreased RH over land (Figure 9f), further enhancing the land–sea contrast, as noted in P4K (Figure 9c). Judging from the 4xCO2-minus-P4K pattern in CpT (Figure 9g), it can be seen from the near uniform and small values (<3 kJ/kg) over the ocean that the P4K SST warming was a reasonable analog of the SST surface thermal forcing under 4xCO2. However, the surface moisture forcing Lq reveals more regional features with higher values (>6–10 kJ/kg) over oceanic regions near the equator and subtropical monsoon regions adjacent to land in 4xCO2 compared to P4K (Figure 9h). Clearly, enhanced atmospheric warming by 4xCO2 further exacerbated the surface RH reduction over land compared to P4K (Figure 9i). This is likely due to enhanced land–atmosphere feedback arising from 4xCO2, radiative forcing of the atmosphere and facilitated by cloud–convection–circulation interactions [19] under dynamically consistent SSTA forcing, increasing CIN, and the occurrence of very extreme but rare precipitation already operative under the control, but enhanced by P4K, and further amplified under 4xCO2.
