Sensitivity of Tropical Extreme Precipitation to Surface Warming in Aquaplanet Experiments Using a Global Nonhydrostatic Model

Increases of atmospheric water vapor holding capacity with temperature (7% K−1–8% K−1, CC‐rate) can lead to increasing extreme precipitation (EP). Observations show that tropical EP has increased during the last five decades with a rate higher than in the extratropics. Global climate models (GCM's) diverge in the magnitude of increase in the tropics, and cloud‐resolving models (CRM's) indicate correlations between changes in tropical EP and organization of deep convection. We conducted global‐scale aquaplanet experiments at a wide range of resolutions with explicit and parameterized convection to bridge the gap between GCM's and CRM's. We found increases of tropical EP beyond the CC rate, with similar magnitudes when using explicit convection and parametrized convection at the resolution it is tuned for. Those super‐CC rates are produced due to strengthening updrafts where extreme precipitation occurs, and they do not exhibit relations with changes in convective organization.

General Circulation Model (GCM) simulations also produce a general increase of extremes, the strength of which depends on latitude (O'Gorman, 2012;O'Gorman & Schneider, 2009b). In models from the Coupled Model Intercomparison Project (CMIP) Phase 3, for example, extratropical sensitivities consistently predict that precipitation extremes increase more slowly with surface air temperature than atmospheric water vapor content; however, tropical changes are not consistent among models, with sensitivities ranging from 1.3% K −1 to 30% K −1 (O'Gorman & Schneider, 2009a). These studies suggest that the discrepancy in the tropics may arise from inaccurate simulation of upward velocity during convection. Bhattacharya et al. (2017) suggested that to improve modeled tropical precipitation extremes, it is essential to better represent the upward velocity associated with those extremes. Increasing horizontal resolution may be a way to improve the simulation of convection in GCM's where precipitation is not resolved by the coarse grid and has to be parametrized. However, those convective parametrization schemes are sensitive to horizontal model resolution and time-step length (Benedict et al., 2017;Li, Collins, Wehner, Williamson, Olson, & Algieri, 2011;Lu et al., 2014;Williamson, 2013;Yang et al., 2014) and thus the sensitivity of extreme precipitation to warming varies not just among individual models, but also across horizontal resolutions with a single model.
Given the long-standing structural uncertainties among CGM's, Cloud Resolving Models in idealized setups of Radiative-Convective Equilibrium (RCE) (Manabe & Strickler, 1964;Nakajima & Matsuno, 1988;Tompkins & Craig, 1998) have been used to study tropical convection and sensitivities of extreme precipitation to warming. On such setups and under certain conditions, RCE can become unstable (Nilsson & Emanuel, 1999) and lead to spontaneous spatial organization of convection. In RCE simulations, it has been shown that extreme precipitation increases close to the CC rate if self-aggregation is absent (Muller et al., 2011;Romps, 2011) or if the degree of organization does not change (Bao et al., 2017); whereas super-CC behavior has been found when self-aggregation increases with warming (Bao & Sherwood, 2019;Bao et al., 2017;Pendergrass et al., 2016;Singleton & Toumi, 2013).
Here, we use a less idealized set of aquaplanet simulations to study the uncertainties of changes in tropical extreme precipitation by using a nonhydrostatic atmospheric GCM in rotating configuration with a meridional gradient of temperature (Medeiros et al., 2015;Neale & Hoskins, 2000). Model description and methods are presented in Section 2. In Section 3, we compare the sensitivity of tropical extreme precipitation to warming between simulations with parametrized and explicit convection and its resolution dependency, study contributors to those sensitivities, and look for relationships between the change of convective organization and the change of precipitation extremes. Finally, we present the conclusions in Section 4.

Model Setup and Methods
Simulations were performed using the ICOsahedral Nonhydrostatic Atmospheric general circulation model (ICON-A). ICON-A is built using the Max Planck Institute physical parametrization package, which originates from the ECHAM6.3 general circulation model  and with adaptations to account for the change in the dynamical core and a new turbulence parametrization. A full description is given in Giorgetta et al. (2018).
The experiments were conducted using the aquaplanet configuration, which uses the Qobs zonally symmetric sea surface temperatures (SST) as surface boundary conditions (Neale & Hoskins, 2000). Owing to its simplicity (e.g., no topography, land-sea contrasts, surface heterogeneities), this configuration helps to understand the physical atmospheric processes driving the changes of extremes in response to global warming . Moreover, because diurnal insolation and the radiatively active species are held at equinoctial and hemispherically symmetric geometry, the model statistics are zonally and hemispherically symmetric, which helps to identify significant signals using relatively short integrations.
A range of simulations at different horizontal resolutions were performed with parametrization of convection on and off (explicit convection) for the control and uniformly increased SST of 4K (Table 1). We used explicit convection at resolutions lower than 10 km since even at coarse resolutions without parametrization of convection, models are able to produce large scale features related to convection (Retsch et al., 2019;Webb et al., 2015). The simulations were initialized analytically and used time-invariant boundary conditions for SST, spectral solar irradiation, well mixed greenhouse gases CO 2 , CH 4 , N 2 O, CFCs, and O 3 concentration. All experiments were run for four years and we treated the first year as spinup, except for R2B8 where the simulation length was limited to six months with one month of spinup.
Daily zonal mean precipitation for explicit and parametrized experiments are shown in supporting information Figure S1. As is to be expected, the global mean precipitation increases with warming, whereas the meridional distribution of precipitation follows a double Intertropical Convergence Zone (ITCZ) structure for explicit convection simulations. When resolution is increased, precipitation tends to be more meridionally distributed with a displacement of the ITCZ away from the equator and an increase of midlatitude precipitation at the expense of tropical precipitation, particularly for R2B6 and R2B8. In general, however, the meridional distribution of precipitation in the parametrized convection experiments is somewhat erratic across resolutions, and the ITCZ behaviors in our experiments differ from those of Retsch et al. (2019), who used an earlier version of ICON-A and found a single ITCZ structure for explicit convection simulations at resolutions R2B4, R2B5, and R2B6, while a double ITCZ prevailed for parametrized convection. Since extremes in the tropics are more likely to occur within the ITCZ, simulated shifts in the large-scale tropical circulation might obscure our results and so in the following we shall discuss precipitation extremes in the entire tropics from 30°S and 30°N.
To study changes in tropical Extreme Precipitation (EP) with warming, we define EP as the cases of grid points between 30°S and 30°N over the entire period exceeding the ith percentile of daily precipitation: where i varied from 99.9 to 99.99, Pr is daily precipitation and Pr i is the ith percentile of daily precipitation. The selection of this metric allows us to capture the behavior of the precipitation distribution tail instead of focusing on one particular percentile. With it, we calculate the sensitivity of tropical extreme precipitation to warming (SEP) as the fractional change in EP (δEP(i)/EP(i)) normalized by change in temperature (δT): where the subscripts CTL and 4K denote control and 4K experiments, respectively.

Sensitivity of Tropical Extreme Precipitation to Warming
Sensitivities of tropical extreme precipitation to warming are displayed as solid lines in Figure 1. Extremes from both explicit and parametrized convection experiments increase with warming. For explicit convection simulations, sensitivities vary from 9% K −1 to 15% K −1 with a tendency to converge for the strongest extremes. This tendency is not clear for the experiments with parametrized convection, where at low resolution (R2B4) we observe a nearly constant sensitivity value, then at R2B5, it ranges from 14% K −1 to 24% K −1 and finally for the highest resolution (R2B6) it drops for the strongest extremes.
Fractional changes of lower tropospheric saturation specific humidity with warming in the tropics fall close to the CC rate (dots in Figure 1). In all simulations, extreme increases are higher than those changes in lower tropospheric saturation specific humidity (super-CC, compare solid lines and dots). This suggests that not just increases in the capacity of the atmosphere to hold water vapor have an impact on extremes, but other processes contribute too. However, we note that for parametrized convection the amplitude of this difference varies with resolution more than it does for explicit convection. When aggregating the simulations to the coarsest resolution (R2B4), similar tendencies are observed for explicit convection, whereas results URIBE ET AL.  Figure S7). Since the convective parametrization implemented in ICON-A has been tuned for a grid resolution of R2B4, spurious behaviors at resolutions R2B5 and R2B6 resolutions might occur. This is mainly because the convective scheme is tuned to remove convective instability on a certain timescale. When resolution is increased from R2B4, the model dynamics may produce finer scale instabilities more rapidly than the parametrization can remove these, resulting in explicitly resolved updrafts or so-called grid-point storms (Williamson, 2013). We speculate that the erratic behavior of the higher resolution simulations is caused by the inadvertent competition between parameterized convection and partially resolved convective clouds. Increases of extreme precipitation from parametrized convection at the resolution it is tuned for (R2B4) are similar to the increases with explicit convection, particularly to that at R2B4 and one might think that the model shows a low sensitivity of extreme precipitation changes with warming to the activation of convective parametrization for this resolution; however, the different large scale circulation between explicit and parameterized convection observed in Figure S1 suggest this may be coincidental.

Contributors to Increases of Tropical Extreme Precipitation
Next, we will use a scaling derived by Muller et al. (2011) that, as explained in Supporting Information S1, is valid for explicit convection simulations. The scaling separates changes in extremes in terms of changes in dynamics, through vertical motion (here pressure velocity, ω), in thermodynamics, through the vertical gradient of saturation specific humidity, and in precipitation efficiency: From the components of the scaling, and since increases of vertical gradient of saturation specific humidity with warming are expected to follow the CC rate due to the strongest vertical gradients of saturation specific URIBE ET AL. humidity locate in the lower troposphere, we can identify that increases of tropical extreme precipitation beyond the CC-scaling are caused by positive net contributions from dynamics and precipitation efficiency, here calculated as the residual.
Results of the scaling (Equation 3) are displayed in Figure 2. We note a similar behavior across resolutions with explicit convection, in that increases of extreme precipitation result from both positive dynamics and thermodynamics contributions. In all simulations, the dynamic contribution is positive and larger in magnitude than that from precipitation efficiency, which in all cases is negative. Thus, the combined effect of dynamics and precipitation efficiency changes contributes to the super-CC behavior of the model, whereas the thermodynamic contribution alone is close to the CC rate. Similar results are obtained for coarse grained resolutions to R2B4, see Figure S8.

Are Sensitivities Related to Changes in Convective Organization?
We showed that tropical extreme precipitation increases with warming at rates higher than the CC rate and that strengthening of convective circulations when extremes occur leads to those super-CC tendencies in our experiments with explicit convection. As mentioned in Section 1, the amplitude of the sensitivity of tropical extreme precipitation to warming might be related to changes of convective organization, whereby super-CC changes in extremes are correlated with increases of convective organization, and so we investigate if this is also the case in our simulations, including R2B4 with parametrized convection. To this end, we quantify the degree of convective organization in the tropics and its change with warming in a variety of ways: using subsiding fraction prime (SF´, Noda et al., 2019) in the entire tropical band, as well as in smaller subdomains of varying sizes centered at the extreme event, and solely in the tropical band using organization index with eight-point connectivity for resolutions R2B6 and R2B8 (Iorg, Tompkins & Semie, 2017) and an organization index with zero connectivity to include coarse resolutions (Iorg_ 0 , Becker & Wing, 2020). A detailed description of the metrics is given in Supporting Information S2.
URIBE ET AL.
10.1029/2020GL091371 5 of 8 Figure 2. Sensitivity of tropical extreme precipitation to warming (black) and contributions to sensitivities from dynamics (yellow), thermodynamics (red), and precipitation efficiency (blue). Values are calculated by averaging the extremes interval (99.9-99.99). The precipitation efficiency contribution is estimated as the residual between the first two terms in the right side of Equation 3, and the actual sensitivity. The dashed gray line indicates the mean fractional change of lower tropospheric saturation specific humidity across simulations.
We found both increased and decreased tendencies of convective organization with warming ( Figure 3). At high resolution (R2B5-8), all indices show a reduction in convective organization, whereas at coarse resolution (R2B4) convection tends to self-organize with warming in the areas where extremes occurs, while disorganize at large scale (we obtained similar results for coarse grained resolutions to R2B4, see Figure S9). Those results are opposite to Bao et al. (2017), Singleton and Toumi (2013), and Pendergrass et al. (2016) where increases of extremes correlate with self-organization. This discrepancy across resolutions suggests that changes in tropical convective organization have a negligible impact on changes of tropical extreme precipitation with warming in our simulations.

Conclusions
Aquaplanet simulations with the ICON-A model are performed to explore the sensitivity of tropical extreme precipitation to warming across a wide-range spatial resolutions with and without parametrization of convection. We find positive sensitivities with amplitudes larger than the increase of lower tropospheric saturation specific humidity, or CC rate, at all resolutions. Results from explicit convection simulations converge for the strongest precipitation extremes, whereas for parameterized convection simulations, the sensitivities strongly vary with horizontal resolution, although results from R2B4 are similar to those from the explicit convection simulations. We suggest this occurs since the parametrization scheme used in ICON-A was tuned for that particular resolution.
We next investigate whether dynamical changes can explain the super-CC behavior of tropical extreme precipitation in our explicit convection simulations, using a diagnostic framework. In all simulations, we URIBE ET AL.
10.1029/2020GL091371 6 of 8 . The vertical line separates explicit convection experiments from parametrized convection at R2B4. Note that given the resolution of R2B4, a subdomain of 2° × 2° will contain a unique grid point and the fractional change of SF´ will be zero; and subdomains from 6° × 6°, and 8° × 8° will contain the same amount of grid points, producing equal fractional changes.
find positive contributions from dynamics, resulting in stronger updrafts where extreme precipitation occurs. Nevertheless, thermodynamical changes resulting from changes in the vertical gradient of saturation specific humidity also contributes relative to the simple CC-scaling in the higher resolution simulations, but not in the coarse resolution simulations (R2B4). Furthermore, for all simulations, reductions in precipitation efficiency with warming counteract the increases produced by dynamics and thermodynamics, but its magnitude is not enough to prevent the super-CC tendencies.
Finally, we explore whether convective organization could be involved using an array of indices that in various ways characterize the degree of organization. We find somewhat surprisingly in most cases organization decreases with warming: in the explicit convection simulations with 10-80 km resolution (R2B5-8) it decreases by about 1% K −1 . In the two simulations with 160 km (R2B4) convection disorganizes at large scale; but self organizes in the areas where extremes occur. We suggest more investigation is needed to better understand the processes controlling the change of organization of convection in simulations like those here presented. It is concluded that convective organization played either no or a negligible role in causing the model's super-CC behavior of tropical extreme precipitation.

Data Availability Statement
The primary data for this study, that is, the ICON-A model is described in Giorgetta et al. (2018) and its source code and components are available on https://mpimet.mpg.de/en/science/modeling-with-icon/ code-availability. The configuration scripts to run the model, the data and scripts to reproduce the figures can be found in Uribe et al. (2020).