Evaluation of present-day extreme precipitation over the United States: an inter-comparison of convection and dynamic permitting configurations of E3SMv1

Accurate simulation of the present-day characteristics of mean and extreme precipitation at regional scales remains a challenge for Earth system models, which is due in part to deficiencies in model physics such as convective parameterization (CP), and coarse resolution. High horizontal resolution (HR, ∼25 km) and multiscale modeling framework (MMF, i.e. replacing conventional CP with embedded km-scale cloud-resolving models) are two promising directions that could help improve the interaction between subgrid-scale physical processes and large-scale climate. Here, we evaluate simulated extreme precipitation over the United States (US) across three configurations (i.e. low-resolution [LR], HR, and MMF) of the Energy Exascale Earth System Model (E3SMv1) and intercompare them against two gridded observation datasets (climate prediction center daily US precipitation and integrated multi-satellite retrievals for global precipitation measurement). We assess the model’s ability to simulate very heavy seasonal precipitation (illustrated by the difference between the 99th and 90th percentile values) as well as the spatial distributions of several extreme precipitation indices defined by the expert team on climate change detection and indices. Our results show that both the dry (i.e. consecutive dry days (CDD)) and wet (i.e. consecutive wet days, maximum 5 day precipitation, and very wet days) extremes evaluated herein show some improvement as well as degradation with MMF and HR relative to LR. These results vary across seasons and US subregions. For instance, only the very heavy precipitation of winter is improved with MMF and HR. Both configurations alleviate the well-known drizzling bias evident in LR across both winter and summer in many parts of the US, largely due to the overall improvement in intensity and frequency of precipitation. Additionally, our results suggest that while E3SMv1-MMF has higher intensity rates when it does rain, it has too many CDD during the summer, contributing to a low mean precipitation bias.


Introduction
Extreme precipitation events often have significant impacts on many aspects of society, ecosystems, and the economy and are therefore of interest to not only the weather and climate community but also the insurance and financial sector and emergency planners (Franzke and Czupryna 2020, Hu and Franzke 2020).In the overall simulation of precipitation in E3SMv1-HR and E3SMv1-MMF (Kooperman et al 2022), as well as contributions from individual storm types (Reed et al 2023), and this study builds on this to further investigate how the HR and MMF configurations represent commonly used extreme precipitation indices compared to conventionally parameterized LR models (i.e.E3SMv1-LR).We evaluate summer and winter precipitation extremes over the CONUS with a comprehensive set of extreme precipitation indices by intercomparing the three configurations (i.e.LR, HR, and MMF) of E3SMv1 with two gridded observation datasets.The extreme precipitation indices used herein were defined by the expert team on climate change detection and indices (ETCCDI; Klein Tank et al 2009, Zhang et al 2011).The models, observations, and indices are described in the data and methodology section below, followed by results and discussion, and conclusions.

Data and methodology
In this study, we assess three configurations of E3SMv1 (see Kooperman et al 2022 for detailed experimental setup), namely: (a) the standard LR configuration of E3SMv1 (E3SMv1-LR), (b) the high-resolution configuration (E3SMv1-HR), and (c) the MMF (E3SMv1-MMF).E3SMv1 uses the E3SM atmosphere model (EAMv1, Rasch et al 2019), which includes updates to the dynamic grid, vertical resolution, shallow and deep convection, aerosol schemes, and cloud microphysics (details in Zhang and McFarlane 1995, Golaz et al 2002, 2019, Gettelman et al 2015, Liu et al 2016).In the E3SMv1-MMF (also known as superparameterized) version of E3SMv1 (Golaz et al 2019), a CRM (CRM; configured here in two dimensions with 2 km grid spacing and 64 columns oriented in the north-south direction) is embedded within each grid cell of the EAM to replace convective and boundary-layer parameterizations.While E3SM uses 72 vertical levels, the CRM shares only the bottommost 58 vertical levels because anelastic approximation is not valid at very low pressures, and because of computational expedience.The CRM is based on the system for atmospheric modeling (Khairoutdinov and Randall 2003), and more details are available in Hannah et al (2020).We configured the EAM with a spectral element dynamical core at two horizontal resolutions: ∼25 km (i.e.ne120pg2) for E3SMv1-HR and ∼150 km (i.e.ne30pg2) for E3SMv1-LR and E3SMv1-MMF.We used a quasi-equal area lower-resolution physics grid (i.e.pg2) that allows the effective resolution of the simulation to be conserved and alleviates a grid imprinting effect that is particularly evident in the MMF configuration (Herrington et al 2019a, 2019b, Hannah et al 2021).The lower boundary ocean and sea-ice conditions were prescribed as climatological seasonal cycles of sea surface temperatures and sea-ice fractions representing the period of 1990-2010 in the three E3SMv1 configurations (Taylor et al 2000).In addition, E3SMv1-HR and E3SMv1-MMF were configured to use roughly the same computational resources (i.e.number of nodes and wall clock time) when run on the DOE National Energy Research Scientific Computing Center Cori system.Overall, we used a 10 year period from each model configuration for the analysis presented in section 3.
Previous studies have reported that the ability of ESMs to reproduce present-day extreme precipitation depends somewhat on the choice of reference observations (e.g.Sillmann et al 2013, Akinsanola et al 2020a, Faye 2021), so here the models are evaluated against two gridded precipitation datasets, and we focus on conclusions that are robust for both datasets.The observations include the National Aeronautics and Space Administration global precipitation measurement mission (GPM) Integrated Multi-satellitE Retrievals for GPM (IMERG) final precipitation level 3 at 0.1 • × 0.1 • (longitude × latitude) resolution (see Huffman et al 2019), and the National Oceanic and Atmospheric Administration climate prediction center (CPC) daily US precipitation at 2.5 • × 2.0 • (longitude x latitude) resolution (see Higgins et al 1996Higgins et al , 2000 for details) for details).These datasets have shown reliable performance over the region and have been useful for evaluating climate models (e.g.Beck et al 2019, Kooperman et al 2022).To be consistent with the models, and similar to our previous study (Kooperman et al 2022), ten-year periods (2001-2010and 1988-1997 for IMERG and CPC, respectively) are used to provide estimates for present-day climatological conditions.
In this study, all model outputs and observations are regridded to a common grid of 2.5 • × 2.0 • (i.e. the LR CPC grid) using the first-order conservative regridding method described in Jones (1999).This approach reflects the viewpoint that precipitation output from climate models represents an area average over the grid cell (Chen and Knutson 2008).We focus primarily on the two major seasons that are distinguished by the scale of convective events that contribute to total precipitation (i.e.December-January-February, DJF; and June-July-August, JJA).For the analyses of spatial distributions, we assess where the difference between the model and observations is statistically significant at the 95% level using the student's t-test.In addition to assessing the model's ability to realistically reproduce the frequency and amount distributions of daily precipitation alongside the spatial patterns of the extreme precipitation indices, we also use three descriptive statistics (i.e. percentage bias [BIAS], normalized root mean square error [NRMSE], and pattern correlation coefficient [PCC]) to further evaluate their performance over the seven subregions defined in the National  S11).For the extreme precipitation indices, we adopt a subset of the indices recommended by WMO's (ETCCDI; Zhang et al 2011).One dry and three wet indices, including consecutive dry days (CDD, number of consecutive days with precipitation less than 1 mm), consecutive wet days (CWD, number of consecutive days with precipitation greater than 1 mm), maximum consecutive 5 d precipitation (RX5day), and very wet days (R95pTOT), are selected and used as indicators of dry and wet extreme precipitation (described in table 1 and discussed in detail by Zhang et al 2011).These are non-parametric indices that describe moderate extremes with a recurrence time of at most a year and are calculated from daily precipitation.In addition, we analyze the distribution of the right tail of the seasonal precipitation distribution, defined as the range between the 99th and 90th percentile (Scoccimarro et al 2013(Scoccimarro et al , 2014)), similar to the interquartile range, which is calculated as the 75th to 25th percentile.

Results and discussion
The ability of the E3SMv1 configurations used herein to capture the general precipitation climatology, including the frequency and amount distributions of precipitation, has been assessed in detail in our previous study (see Kooperman et al 2022), and we found that E3SMv1-HR and E3SMv1-MMF can simulate more intense and less frequent precipitation than E3SMv1-LR.Additionally, both E3SMv1-HR and E3SMv1-MMF reduce the high bias observed in the western US.E3SMv1-HR better captures the higher magnitude in the eastern US compared to E3SMv1-LR during winter (also shown herein in figures 1, S1 and tables S1, S2).During summer, both E3SMv1-HR and E3SMv1-MMF effectively alleviate the bias along the Rocky Mountains observed in E3SMv1-LR, and E3SMv1-HR has a lower bias in the eastern US relative to E3SMv1-LR.Furthermore, E3SMv1-MMF exhibits improved performance in many parts of the US during the summer, yet none of the model configurations accurately reproduces the higher magnitude of mean precipitation in the central US seen in the observations (figures 1, S1 and tables S1, S2).
Before assessing the ability of the three E3SMv1 configurations to realistically represent the spatial characteristics of the extreme precipitation indices, we first investigate the shape of the right tails in the seasonal precipitation probability density function, illustrated by the differences between the 99th and 90th percentile values (figures 2 and S2), and the results of the summary statistics are presented in tables S1 and S2.Across both seasons, CPC exhibits heavy rain events mostly over the eastern half of the US and more evident over the Southeast in winter and the central US in summer, with differences exceeding 24 mm d −1 .Compared to CPC, E3SMv1-LR grossly underestimates the intense precipitation over the eastern half of the US in both seasons.This bias is slightly reduced in E3SMv1-HR and E3SMv1-MMF in the winter but persists Grid points with statistically significant differences at the 95% level are marked with stippling.
in the summer.The summer bias in E3SMv1-HR and E3SMv1-MMF is opposite in sign; the differences between the 99th and 90th percentile displayed in the former are considerably less (although the bias is less than that of E3SMv1-LR), and the latter significantly overestimates the heavy precipitation events.These biases are also evident when compared with IMERG observations (supplementary information, figure S2) and are largely due to the alternating dry and wet biases evident in both the 99th (figure S3) and 90th (figure S4) percentiles of precipitation.Nevertheless, the overall frequency and amount distributions of the precipitation are considerably improved in both E3SMv1-HR and E3SMv1-MMF across the two seasons (figure S5).
We further assess and compare the ability  differences between the observations and models are statistically significant at the 95% level are identified with stippling.Because of the large spatial heterogeneity of precipitation characteristics over the study area, we further assess the performance of the models over the seven subregions defined in the National Climate Assessment Report (see figure S11) using three descriptive statistics.Previous studies have shown that the statistics of precipitation can vary significantly between observations (e.g.Sun et al 2017, Akinsanola et al 2020a), so we computed the statistics using CPC and IMERG separately, and results are presented in tables 2 and S3-S4 in the supplementary information.
During the winter (figure 3(a)), CDD, an indicator of extended dry conditions, exhibits minimum (maximum) values over NW, NE, and SE (MW, NGP, SGP, and SW) with a maximum length of ∼12 d yr −1 (∼30 d yr −1 ).Both CPC and IMERG are spatially consistent, but the maximum length of CDD is slightly higher in CPC than in IMERG (figure S6(a), tables 2 and S4).Relative to CPC, E3SMv1-LR and E3SMv1-HR are able to capture the minimum CDD center over SE, resulting in lower bias (figures 3(c) and (e)), but fail to reproduce the maximum CDD center that is evident over the MW, NGP, SGP, and southern SW subregions and is reflected in the descriptive statistics (tables 2 and S4).The winter CDD is better captured in E3SMv1-MMF over the northern US (figure 3(g)), and the statistics are largely consistent with the two  observation datasets, although considerable differences still exist, particularly in the south.For instance, CDD is slightly overestimated (underestimated) in the southern SGP and SE (the northern NGP).Similar biases are also evident when compared to IMERG (supplementary information, figure S6), but the underestimation in the cases of E3SMv1-LR and E3SMv1-HR is generally confined to NGP.The summer CDD distribution exhibits a zonal pattern, with CDD transitioning from the lowest values in NE and SE to the highest values in NW and SW (figure 3(b)).Relative to both observation datasets, E3SMv1-LR and E3SMv1-HR (figures 3(d), (f) and S6(d), (f)) reasonably reproduce the observed spatial distribution of summer present-day CDD with considerably lower biases, particularly in the east.The performance of E3SMv1-MMF, however, is relatively poor (figures 3(h) and S6(h)), as is evident in the statistically significant positive bias over most of the US (tables 2 and S4), and it is statistically different from the two observations over most of the MW, NGP, SGP, and SW subregions owing to its higher values when compared to the two observational products.Improving the limitations of the model configurations reported herein in future model development and updates would improve the accuracy of the information available for drought assessment and irrigation water needs.Another metric of heavy precipitation amount is maximum consecutive 5 d precipitation, which is presented in figures 5 and S8, and the results of the statistics are in tables 2 and S4.The CPC's highest values for RX5day occur over SE, SGP, coastal NW, and SW in winter and over the eastern half of the US in summer, with maximum values exceeding 40 mm yr −1 (figures 5(a), (b) and S8(a), (b)).Again, E3SMv1-LR shows biases in the magnitude of RX5day across all seasons, exhibiting statistically significant underestimation (overestimation) over SE and parts of SGP (NW and SW) in winter (figure 5(c)).Similarly, widespread underestimation is also evident in summer, especially over the eastern half of the US (figure 5(d)).But the overall performance of E3SMv1-LR is remarkable over the western half of the US in summer, and over MW and NGP in winter.Both E3SMv1-HR and E3SMv1-MMF show a slight increase in RX5day magnitude relative to E3SMv1-LR, which leads to improvements in some regions but not in others (figures 5(e)-(h)), as is also evident in the regional statistics (tables 2 and S4).For example, while E3SMv1-HR and E3SMv1-MMF lower the bias in SE and SGP relative to E3SMv1-LR during winter, E3SMv1-HR (E3SMv1-MMF) underestimates (overestimates) RX5day over the eastern US during summer.
The spatial distribution of R95pTOT, another heavy precipitation measure, is presented in figures S9 and S10, alongside the results of the statistics in tables S3 and S4.R95pTOT is an important precipitation extreme index because a high value can favor flood conditions.The spatial distributions of R95pTOT are very similar to those of RX5day; both have relatively the same locations of maximum values but differ in magnitude.Overall, E3SMv1-MMF exhibits better performance than E3SMv1-HR or E3SMv1-LR, which have very weak summer values, particularly over the eastern half of the US.Meanwhile, both E3SMv1-MMF and E3SMv1-HR are an improvement over E3SMv1-LR in the winter in most parts of the US, which is more evident in SE.

Summary and conclusion
Realistically representing precipitation characteristics has been a challenge for conventional ESMs, such as those used in the Coupled Model Intercomparison Project Phases 3, 5, and 6, which tend to simulate precipitation that is too frequent and weak compared to observations (Sun et al 2015, Srivastava et al 2020, Akinsanola et al 2020aAkinsanola et al , 2021)).These biases, which persist in different phases of the models, remain larger for many aspects of precipitation characteristics, including extremes (Akinsanola et al 2020a(Akinsanola et al , 2021)), intensity (Norris et al 2021), and diurnal timing (Christopoulos andSchneider 2021, Tang et al 2021).Overall, these biases limit confidence in future climate projections and highlight a need for alternative methods of representing convection and precipitation (Fiedler et al 2020).In order to improve the interaction between subgrid-scale physical processes and large-scale climate, one possible approach is to simply run models at a finer spatial resolution (i.e.high-resolution modeling).Another approach is to replace the conventional CPs with a high-resolution cloud-system resolving model (i.e. a MMF).
Our previous work using these approaches has shown that both the MMF and HR methods implemented in E3SMv1 can improve some general characteristics of precipitation (Kooperman et al 2022).Here we assess whether these general improvements lead to corresponding improvements in the representation of important extreme precipitation indices.In this study, we quantitatively evaluate the ability of three configurations of E3SMv1 (i.e.LR, HR, and MMF) to accurately reproduce several extreme precipitation indices over the US through an intercomparison against two gridded observation datasets.We assess the model's ability to reproduce very heavy precipitation events (illustrated by the differences between the 99th and 90th percentile values in the seasonal precipitation probability density function) alongside the spatial distributions of precipitation extreme indices (i.e.CDD, CWD, RX5day, and R95pTOT) during the present-day period.We further use three descriptive statistics to investigate the model's subregional performance across the seven subregions defined in the National Climate Assessment Report.Our results show that both E3SMv1-HR and E3SMv1-MMF improve the winter heavy precipitation events over the US relative to the conventional model (E3SMv1-LR).Summer biases are the opposite across the E3SMv1 configurations: E3SMv1-LR and E3SMv1-HR underestimate the very heavy summer precipitation over the eastern half of the US, and E3SMv1-MMF overestimates the event.While E3SMv1-MMF has more intense rates when it does rain, it has too many CDDs during the summer, indicating trade-offs across statistics of model performance.Interestingly, E3SMv1-MMF exhibits a slight improvement over the other two configurations in the representation of winter CDD, while also improving other winter statistics.The well-known drizzling bias of conventional models (i.e. they simulate precipitation that is too frequent) explored herein with CWD analysis is evident in both seasons in E3SMv1-LR.Both the E3SMv1-MMF and E3SMv1-HR configurations are an improvement over E3SMv1-LR across both seasons by lowering the spatial overestimations as a result of improved frequency in the case of E3SMv1-HR and intensity in the case of E3SMv1-MMF.Furthermore, the maximum consecutive 5 d precipitation is more intense (weak) during summer (winter) in E3SMv1-MMF (E3SMv1-HR), and R95pTOT is slightly better represented in E3SMv1-MMF in both seasons.Overall, compared to the conventional model, our results suggest that both high-resolution and MMFs better represent several aspects of precipitation extreme statistics (including dry and wet extremes) in many subregions of the US across the two seasons.It is important to note that the overall improvements in E3SMv1-HR and E3SMv1-MMF depend not only on the region and season but also on the type of extreme under consideration, as both dry and wet extremes exhibit some improvements as well as degradation.The combination of both E3SM-HR and E3SM-MMF, which can also be somewhat achieved through a regionally refined mesh, could be beneficial for the improved representation of extreme precipitation across all seasons in the United States.The findings presented herein highlight the strengths and weaknesses of two development configurations of E3SM with potential to improve the simulation of extreme precipitation, which should prove useful in guiding model development as well as configuration choices for targeted experiment design.Further investigation into the reasons for the observed differences between the model configurations is beyond the scope of this study and should be addressed in future research.
of the three E3SMv1 configurations to reproduce the present-day extreme precipitation indices (defined by ETCCDI) by comparing their results to CPC and IMERG observations, and the results are presented for winter (a,c,e,g) and summer (b,d,f,h) in figures 3-5 and S6-S10.The spatial distribution of the CPC observations is presented in (a,b) and the bias relative to CPC in (c-h), while the spatial distribution of the IMERG observations is presented in figures S6-S8, S10(a), (b), and the bias relative to IMERG in figures S6-S8 and S10(c)-(h).Grid points where the

Table 1 .
List of precipitation extreme indices used in this study.
mmClimate Assessment Report (i.e.NW-Northwest, SW-Southwest, NGP-Northern Great Plains, SGP-Southern Great Plains, MW-Midwest, SE-Southeast, NE-Northeast, US-all of US; see supplementary information figure