The Precipitation Response to Warming and CO2 Increase: A Comparison of a Global Storm Resolving Model and CMIP6 Models

Global storm‐resolving models (GSRMs) that can explicitly resolve some of deep convection are now being integrated for climate timescales. GSRMs are able to simulate more realistic precipitation distributions relative to traditional Coupled Model Intercomparison Project 6 (CMIP6) models. In this study, we present results from two‐year‐long integrations of a GSRM developed at Geophysical Fluid Dynamics Laboratory, eXperimental System for High‐resolution prediction on Earth‐to‐Local Domains (X‐SHiELD), for the response of precipitation to sea surface temperature warming and an isolated increase in CO2 and compare it to CMIP6 models. At leading order, X‐SHiELD's response is within the range of the CMIP6 models. However, a close examination of the precipitation distribution response reveals that X‐SHiELD has a different response at lower percentiles and the response of the extreme events are at the lower end of the range of CMIP6 models. A regional decomposition reveals that the difference is most pronounced for midlatitude land, where X‐SHiELD shows a lower increase at intermediate percentiles and drying at lower percentiles.

Most previous studies of the precipitation response to warming have used general circulation models (GCMs, e.g., Chadwick et al., 2022;Pendergrass & Hartmann, 2014b;Sugiyama et al., 2010), limited-domain idealized convection-resolving models (e.g., Abbott et al., 2020;Muller et al., 2011;Romps, 2011), or high-resolution regional models (e.g., Lenderink et al., 2021;Prein et al., 2017).Traditional GCMs are limited by their coarse resolution (∼100 km) and therefore need parameterizations for subgrid processes such as deep convection, which are known to affect the precipitation distribution (e.g., Kuo et al., 2017).The coarse resolution in these models results in biased distributions of daily and sub-daily precipitation (e.g., Norris et al., 2021).Limited-domain convection-resolving models do not simulate large-scale climate and lack the interaction between small and large scales.In recent years, technological and computational advances have allowed for relatively long integrations of global storm resolution models (GSRMs) with kilometer-scale resolution, where deep convection is explicitly resolved (Satoh et al., 2019;Stevens et al., 2019;Tomita & Satoh, 2004).These models produce more realistic daily and sub-daily precipitation distributions, especially for organized and intense precipitation (Ma et al., 2022;O'Gorman et al., 2021), while still having biases (Feng et al., 2023;Ma et al., 2022).This makes the examination of precipitation and its response to warming in GSRMs an exciting new opportunity that we pursue here.
In this study, we present results from 2-year long integrations of the eXperimental System for High-resolution prediction on Earth-to-Local Domains (X-SHiELD) model, a GSRM developed at the Geophysical Fluid Dynamics Laboratory (GFDL) and performed on the Cooperative Institute for Modeling the Earth System (CIMES) HPC at Princeton University.The GSRM-simulated precipitation changes are compared with results from the corresponding Coupled Model Intercomparison Project 6 (CMIP6) GCM simulations.We focus mainly on the daily precipitation response to both uniform warming and the isolated effect of CO 2 increase (with unchanged sea surface temperature).We begin by describing the methods and data used in this study in Section 2. In Section 3, we compare the changes in the daily precipitation in response to warming and the isolated response to CO 2 increase in X-SHiELD and CMIP6 models.We end with discussion and conclusions in Section 4.

Method and Data
X-SHiELD is a configuration of the System for High-resolution prediction on Earth-to-Local Domains (SHiELD, Harris et al., 2020).The model runs at a horizontal resolution of ≈3.25 km globally with 79 vertical layers.The model uses a simplified parameterization for shallow convection, while deep convection is explicitly simulated (more details on the model configuration can be found in Cheng et al., 2022).In the control run, the lower boundary consists of a mixed layer ocean that is nudged toward analyzed ECMWF sea surface temperature (SST) for the years 2020 and 2021.The control run of X-SHiELD was validated against observations, and no signs of model drift were detected during the length of the integration.Figures S1-S3 in Supporting Information S1 show how the control precipitation, net top of the atmosphere radiation, and near surface (2-m) temperature compare with observations (IMERG, CERES, and ERA5, respectively Cucchi et al., 2022;Huffman et al., 2023; NASA/ LARC/SD/ASDC, 2017) together with a time series for all experiments.The local biases of X-SHiELD in these key variables are within the range of CMIP6 models (e.g., Huang & Huang, 2023); however, the estimation of X-SHiELD bias is limited by its short integration.X-SHiELD was previously used to study convective updrafts in the current (Harris et al., 2023) and warm climate (Cheng et al., 2022) and their connection to ice clouds (Bolot et al., 2023).Furthermore, X-SHiELD simulations were used as a reference for corrective machine learning algorithms to improve coarser climate models (Bretherton et al., 2022;Kwa et al., 2023).
In addition to the control experiment, we perform two additional experiments, a uniform increase in SST of 4K (hereafter, warming or +4K), a simulation with a CO 2 concentration of 1270 ppmv with unchanged SST (hereafter, CO 2 increase, with X-SHiELD's control simulation runs with a present day concentration of 407 ppmv).Each two-year simulation used about 15 million core hours on Princeton University's Stellar cluster.
For an appropriate comparison, we used the daily precipitation output of CMIP6 with AMIP configuration models (Eyring et al., 2016) that, in addition to a control run, have experiments with a uniform increase of 4K (amip-p4K, warming, +4K) and a CO 2 quadrupling (amip-4xCO 2 , CO 2 increase).Note that the CO 2 increase experiment considers the isolated radiative effect of CO 2 as the SST remains unchanged: that is, the SST is that of the control.The following 9 models have the daily precipitation output for these experiments: TaiESM1, CanESM5, CNRM-CM6-1, GFDL-CM4 (gr1), MIROC6, HadGEM3-GC31-LL, MRI-ESM2-0, CESM2, NorESM2-LM.
We use The Integrated Multi-satellitE Retrievals for GPM (IMERG) product V07 (Huffman et al., 2020) as an observational estimate for the precipitation to assess the models' control precipitation distribution.We note that IMERG's calibration process results in it being more reliable for the mean, and it tends to underestimate light precipitation and overestimate heavy precipitation (Pradhan et al., 2022).

Results
The precipitation distribution and its changes can be presented in several ways.One example is the use of frequency and amount by Pendergrass and Hartmann (2014b);alternatively, Sugiyama et al. (2010) used percentiles to analyze changes in the precipitation distribution and this is a common way that precipitation extremes are defined (e.g., O'Gorman & Schneider, 2009).Here, we use percentiles of precipitation rate intensity and their changes to compare the response between the different models.The percentiles are calculated for the entire data; that is, no threshold is imposed (zeros are included).Given that each model has its own distribution and we are interested in the response of the entire daily precipitation distribution and not only extreme events, we present the results in terms of the control run's precipitation percentile values, P c (in mm day 1 , abscissa in Figures 1-4).In this way, we compare similar precipitation intensity in a way that gives a more physical sense when discussing changes under warming and CO 2 increase.For example, examination of Figure 1c shows that precipitation events with an intensity of 100 mm day 1 in the control climate will intensify in a warmer climate by ∼6% K 1 .In other words, in the +4K simulation, precipitation events with an intensity of 124 mm day 1 will occur at a rate similar to precipitation events of 100 mm day 1 in the control simulation.The percentage change for an intensity also has relevance for hazards that occur when precipitation rates exceed a certain threshold.
We focus on values greater than 0.01 mm day 1 and up to the maximum value of the 99.999 percentile.For a fair comparison, we present each year of the X-SHiELD run separately and consider the spread of CMIP6 models by calculating the standard deviation (SD) among all individual years of the models.We also assess the 95% range of individual years for regional averages in Table 1.Therefore, this measure of the CMIP6 spread includes both that arising from interannual variability and differences in model formulation (inter-model spread).Changes in precipitation are presented as changes relative to the control distribution and normalized by the imposed SST warming (4K) for the warming case and by the fractional CO 2 increase for the CO 2 case (expressed per doubling of CO 2 by dividing by the respective changes imposed: 4 in the CMIP6 models and ≈3.12 times for X-SHiELD).
Following Ma et al. (2022), Figure 1a shows a comparison of the tropical (20°S -20°N) precipitation distributions of X-SHiELD (black lines) and CMIP6 models (solid red for the multi-model mean, with individual models shown in dotted red lines) with observations (IMERG, blue), where X-SHiELD and IMERG are coarsened (area averaged) to ≈100 km.Note that this is different from Ma et al. (2022) who interpolated, rather than coarse-grained, all data to a grid of similar resolution to the 100 km that we show here.After coarsening, X-SHiELD is indistinguishable from other CMIP6 models (Figure 1b).Similar to the CMIP6 models, X-SHiELD produces a relatively high amount of drizzle and light rain (≲10 mm day 1 , Figures 1a and 1b). Figure 1b compares the control precipitation distribution for X-SHiELD and IMERG at their native resolution, coarsened to 25 km, and coarsened to 100 km.At native resolution, X-SHiELD and IMERG show a similar distribution for intermediate precipitation rates (10 100 mm day 1 ), the rain rate for which IMERG is more reliable (Pradhan et al., 2022;Figure 1b).
Coarsening influences the control precipitation distribution (Figure 1b, and Na et al., 2020).Additionally, Na et al. (2020) have found that the precipitation response can also be sensitive to coarsening; however, in X-SHiELD the response to warming is significantly less sensitive to coarsening (Figure 1c).Interestingly, coarsened (c) Comparison of the response to SST warming (+4K) for X-SHiELD's native (solid), coarsening to ≈25 km (dashed), and coarsening to ≈100 km (dotted).Open circles represent the 99.9 percentile.Green and yellow lines shows the 7%/K and 0%/K lines, respectively.X-SHiELD output and IMERG data set are shown for the year 2020, and CMIP6 output are shown for 1979-2011.

Geophysical Research Letters
10.1029/2023GL107008 output has more sensitivity for fixed precipitation rate, including extremes that have a response of ∼0.5% K 1 higher than native-resolution output.Looking at a fixed percentile (99.9, circles in Figure 1c), the differences are small and nonmonotonic, with the 25 km coarsening having the highest sensitivity; this can be seen both at the 99.9 percentile represented by the circles or by the end of each line representing the 99.999 percentile (Figure 1c).In physical terms, this increased sensitivity of extremes at 25 km suggests an increase in mesoscale organization with warming for precipitation extremes.Based on the similarity of the response across the different coarsening factors, we proceed with our analysis using the 25 km coarsened output and we use CMIP6 models at their original resolution (≳100 km).
In the annual-and global-mean, X-SHiELD exhibits a precipitation sensitivity that is in the lower range of the sensitivity of the CMIP6 models for both uniform warming (+3.1 vs. +3.5% K 1 ) and CO 2 increase ( 1.0 vs. 1.2% per CO 2 doubling, Table 1).These are near the edge of the CMIP6 distributions, as the 95% interval in parentheses indicates.
Figure 2a shows X-SHiELD has an increase of almost all percentiles of precipitation, except for the lowest (P c ≲ 0.1 mm day 1 ), in response to SST warming.The high percentiles show an increase that is close to the CC scaling (black lines in Figure 2a).In response to CO 2 increase (keeping the SST unchanged) all percentiles show a decrease in precipitation, except for the high percentiles in X-SHiELD's first year (black lines in Figure 2b).The precipitation response in X-SHiELD to both warming and CO 2 increase is mostly within one SD of the CMIP6 mean response, with the exception of light precipitation response (Figure 2).In addition to the light precipitation response being below one SD (shading in Figure 2), the extreme events in the uniform warming case in X-SHiELD intensify at a lower rate than most CMIP6 models: while the CMIP6 multimodel mean has ≈10% K 1 increase in the highest percentiles, X-SHiELD has ≈7% K 1 increase (Figure 2a).At the commonly evaluated 99.9 percentile (shown in circles), X-SHiELD has a ≈5% K 1 and CMIP6 models are mostly near ≈7% K 1 .
To analyze the differences between X-SHiELD and CMIP6 models, we compare the response over land and ocean.The response to warming and CO 2 increase over the ocean is similar to the global response (Figures 3a and  3b).The response of land precipitation to warming shows a decrease for all rates ≲10 mm day 1 and an increase for higher rates (Figure 3c).Percentiles that are ≥∼1 mm day 1 over land increase in response to isolated CO 2 increase, while light precipitation decreases (Figure 3d).For intermediate percentiles (i.e., those that are primary contributors to the mean response), this increase may result from energetically direct land-sea circulations, where   the increase in energy to the atmospheric column is balanced by overturning circulations that export energy and import water vapor.Similarly to the global response, the X-SHiELD simulated changes in the distribution over land and ocean to both warming and CO 2 increase, are within one SD of the CMIP6 models spread for most percentiles.However, the agreement in the warming case is much better over the oceans than over land (Figure 3a vs. Figure 3c).In particular, for land, X-SHiELD shows less intensification and drying that is outside the 1 SD of the CMIP6 models for all values less than ≈3 mm day 1 .
To further diagnose the discrepancy over land between X-SHiELD and the CMIP6 models, we compare the response over tropical (30°S-30°N) and midlatitude land (we consider only 30°N-60°N because of the low fraction of land in the southern hemisphere, but the results are not sensitive to this choice).The response of both tropical and midlatitude land to warming in X-SHiELD are qualitatively similar, with high percentiles increasing and lower percentiles decreasing (Figures 4a and 4c).This is not the case for the response to CO 2 increase, where the tropical land responds qualitatively differently from midlatitude land.While precipitation over tropical land increases in response to CO 2 increase, over midlatitude land, precipitation primarily decreases with only extreme precipitation increasing in response to CO 2 increase (Figures 4b and 4d).
In the tropics, there is close agreement between X-SHiELD and the CMIP6 models for the warming case (Figure 4a).This is not the case in the midlatitudes where X-SHiELD departs from the CMIP6 models in most percentiles, except for the extremes, where there is a close agreement between CMIP6 models and X-SHiELD (Figure 4c, and open circle).This discrepancy also translates into the annual mean, where the tropical land response in X-SHiELD is within the range of the CMIP6 models and close to the multimodel mean, and the midlatitude response is outside the 95% of the years in the CMIP6 models (Table 1).Note that while the changes in precipitation on land in the tropics and midlatitudes in response to warming on X-SHiELD show mostly a decrease (or a slight increase), the total land response has an increase in precipitation, as it includes a large relative increase in polar latitudes (Table 1).This discrepancy in the warming response of the midlatitude land between X-SHiELD and CMIP6 models persist through the seasonal cycle (Figure S4 in Supporting Information S1).X-SHiELD also departs in its midlatitude response to CO 2 increase from the CMIP6 models (Figure 4d).

Discussion and Conclusions
In this study, we compare the daily precipitation changes in response to uniform warming and isolated increase in CO 2 with unchanged SST between the commonly used CMIP6 models and X-SHiELD, a state-of-the-art GSRM.
The precipitation changes in X-SHiELD, a GSRM that can resolve deep convection, are within the spread of the CMIP6 models for both the warming and isolated CO 2 increase with unperturbed SST.This statement is particularly true for the intermediate precipitation values that contribute the most to the mean.The response of precipitation extremes to warming in X-SHiELD are in the lower range of the CMIP6 models (Figure 2).This result, together with similar results from previous studies that have used convection resolving models (Abbott et al., 2020;Fildier et al., 2017;Muller et al., 2011;Romps, 2011), suggests that a more realistic representation of convection tends to reduce the response of extremes to warming and is constrained by the CC scaling.Moreover, when comparing the response between the native and coarse resolution, we find that coarsening the output results in a non-monotonic dependence of the precipitation extreme response on the grid size (Figure 1c).This result is not trivial and suggests that convective organization within a traditional GCM scale (∼100 km) can be important for the changes under warming and the fact that traditional models do not resolve it might be the source for the large model spread in the precipitation extremes response.That said, future studies should examine whether this result holds for other GSRMs.
In the global response, X-SHiELD is within the spread of the CMIP6 models for most percentiles, except for the lower percentiles (Figure 2).This departure is more significant in the warming case and is larger over land than over the ocean (Figure 3).Analysis of different regions reveals that this departure is mostly the result of disagreement between X-SHiELD and the CMIP6 models over midlatitude land, where X-SHiELD shows lower intensification in the intermediate percentiles and drying in the low percentiles compared to the CMIP6 models (Figure 4c).This result is surprising, as one expects the added value of a GSRM that resolves deep convection to be more important in tropical regions.Considering the moisture balance, the discrepancy in X-SHiELD midlatitude land precipitation can be balanced by a discrepancy in either evaporation or moisture convergence.Table S1 in Supporting Information S1 shows that the changes in midlatitude land surface fluxes have significant differences compared to those of CMIP6 models.An intriguing possibility is that the discrepancy in X-SHiELD may be a result of the highly resolved interaction with topography and land; however, more detailed research is needed to fully understand the source of the difference between the X-SHiELD and CMIP6 models, and more importantly, determine if other GSRMs show a similar response to X-SHiELD.
We note that the two distinct years of X-SHiELD may differ from both internal atmospheric variability, dependence of the precipitation response on the basic state (e.g., phase of ENSO), and because of transient adjustments (e.g., from land model or land-atmosphere adjustments that have longer timescales than those of the atmosphere).There are no systematic differences between the two simulated years of X-SHiELD.We take this to be a tentative indication that our conclusions concerning the extent to which the GSRM is within versus outside of the range of CMIP6 models is not the result of the factors we enumerated above.
In addition to the comparison between the two model classes, this study provides a detailed description of how precipitation in different models respond to warming and the isolated effect of CO 2 increase with unchanged SST.Consistent with previous studies, we show an increase in precipitation in response to warming (e.g., Allan & Soden, 2008;Allen & Ingram, 2002;Held & Soden, 2006;Pendergrass, 2020;Pendergrass & Hartmann, 2014b) and a decrease in response to CO 2 increase (e.g., Bony et al., 2013;Chadwick et al., 2019;Richardson et al., 2016).Although the extreme response to warming is close to CC scaling or higher (e.g., O'Gorman, 2015), lower percentiles show a decrease.This is especially significant over tropical land (similar results were described in Giorgi et al. (2019)), where the annual mean decreases in both X-SHiELD and most of the CMIP6 models (Table 1).
Land and ocean show a qualitatively different response to CO 2 increase, with ocean precipitation strictly decreasing, while on land, the high and intermediate percentiles show an increase, which indicate a shift of convection to over land, consistent with findings from previous studies (e.g., Richardson et al., 2016).A similar difference occurs between tropical and midlatitude land.While over tropical land the precipitation increases in all percentiles, in the midlatitudes most percentiles experience drying in response to CO 2 increase.Interestingly, the response to the increase in CO 2 over land shows a large spread.This should also be taken into account when analyzing this response together with the possibility that this spread among models will remain in GSRMs.
GSRMs are one frontier for improving our understanding of the climate system and its response to anthropogenic forcing.This study provides a comparison between a GSRM and traditional climate models with parameterized moist convection.Computer resources still limit the use of GSRMs, as these two-year-long integrations indicate.As a result, analysis of these models should be performed with care.Hence, our focus on large regions and inclusion of the spread between individual CMIP6 years that we performed here.The comparison between GSRMs and traditional climate models can point to areas of strengths and weaknesses in both model classes and highlight areas that require future investigation.

Figure 1 .
Figure 1.(a) Comparison of the daily precipitation intensity percentile distribution for 20°S-20°N between X-SHiELD (black), IMERG (blue), both coarsened to ≈100 km, and CMIP6 models (solid red for the multimodel mean and dotted red for the individual models).(b) Coarsening's effect on the precipitation distribution in X-SHiELD and IMERG.(c)Comparison of the response to SST warming (+4K) for X-SHiELD's native (solid), coarsening to ≈25 km (dashed), and coarsening to ≈100 km (dotted).Open circles represent the 99.9 percentile.Green and yellow lines shows the 7%/K and 0%/K lines, respectively.X-SHiELD output and IMERG data set are shown for the year 2020, and CMIP6 output are shown for1979-2011.

Figure 2 .
Figure 2. Changes in the global precipitation distribution, expressed as a percent change relative to the control simulation normalized by the (a) imposed warming (4K) or (b) CO 2 fractional increase (4 for CMIP6 models and ≈3.12 for X-SHiELD).Black solid (dashed) line is for the first (second) year of X-SHiELD (using the 25-km coarsened output).Red solid line is for the CMIP6 multi-model mean and red dotted lines are for the individual models' long-term mean response.Shading represent one standard deviation from the multi-model mean, accounting for both interannual variability and inter-model spread.Green and yellow dotted lines show the 7%/K and 0%/K, respectively.Open circles represent the 99.9 percentile of the individual CMIP6 models (red) and different X-SHiELD years (black).

Figure 3 .
Figure 3. Changes in the precipitation distribution as in Figure 2, but for (a, b) global ocean and (c, d) global land regions.

Table 1
Annual-Mean Response to (Top) SST Warming and (Bottom) CO 2 Increase for Different Regions Note.The numbers in parentheses in the CMIP6 column represent the interval that includes 95% of individual years for the different models.