Bimodality in Simulated Precipitation Frequency Distributions and Its Relationship with Convective Parameterizations

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Ullrich, Jiwoo Lee, Peter J. Gleckler, Hsi-Yen Ma, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2874349/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 15 Jun, 2024 Read the published version in npj Climate and Atmospheric Science → Version 1 posted 11 You are reading this latest preprint version Abstract Bimodality in precipitation frequency distributions is often evident in atmospheric models, but rarely in observations. This study i) proposes a metric to objectively quantify the bimodality in precipitation distributions, ii) evaluates model simulations contributed to the Coupled Model Intercomparison Project (CMIP) phase 5 (CMIP5), phase 6 (CMIP6), and the DYnamics of the Atmospheric general circulation Modeled On Non-hydrostatic Domains (DYAMOND) project by comparing them to satellite-based and reanalysis precipitation products, and iii) investigates the origin of bimodal precipitation distributions. Our results reveal that about 83% of CMIP5 and 70% of CMIP6 models used in this study exhibit bimodal distributions. The few DYAMOND models that use a deep convective parameterization also show bimodal distributions, while most DYAMOND models do not. Predictably, the bimodality mainly originates from the separation of precipitation process between resolved grid-scale and parameterized subgrid-scale. However, in some models bimodality arises from the parameterized subgrid-scale convective precipitation alone. Earth and environmental sciences/Climate sciences/Atmospheric science Earth and environmental sciences/Hydrology Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Introduction Bimodality in a precipitation frequency distribution, defined as the presence of two distinct peaks in the probability density function (PDF) of precipitation data, has been a long-standing model behavior that is not evident in observations (e.g., Ma et al. 2022 ; Ahn et al. 2023 ). A light precipitation peak in bimodal distributions is associated with exaggerated drizzling ( < ~ 1mm/day), which has been apparent in many climate models (e.g., Dai 2006 ; Chen et al. 2021 ). Although drizzle represents a small portion of the total precipitation amount, frequent and light precipitation plays an important role in modulating soil aridity, wildfire outbreaks, vegetation growth, and freshwater resources (e.g., Trenberth et al., 2003 ; Trenberth 2011 ). In persistent dry conditions, soil hardening makes it difficult for water to soak into the soil, thus increasing the probability of flooding when heavy rain falls. Realistic simulation of extreme events and their impacts may also be further limited in models with a bimodal precipitation distribution. The origin of bimodal distributions in simulated precipitation has been proposed to be a result of separate precipitation processes – parameterized convective precipitation and resolved large-scale precipitation. Many convective parameterizations produce too frequent light precipitation, which is associated with drizzling and bimodality bias (e.g., Lin et al. 2013 ; Kooperman et al. 2018 ; Chen et al. 2021 ). Some models, on the contrary, show that heavy precipitation results more from convective precipitation than from large-scale precipitation (Martinez-Villalobos et al. 2022 ). Model resolution appears to play little role in the bimodal frequency distribution. In a recent study (Ma et al. 2022 ), the bimodality is exhibited in a variety of model simulations with resolutions from a hundred to a few kilometers that participated in various model intercomparison projects, including the Coupled Model Intercomparison Project phase 6/Atmospheric Model Intercomparison Project (CMIP6/AMIP, ~ 150km, Eyring et al., 2016 ), the High Resolution Model Intercomparison Project/AMIP (HighResMIP/AMIP, ~ 50km, Haarsma et al., 2016,), and DYnamics of the Atmospheric general circulation Modeled On Non-hydrostatic Domains (DYAMOND, ~5km, Stevens et al. 2019). To better understand the bimodal distribution characteristics and investigate its relationship with other processes, objective quantification of the bimodality is required. Many previous studies propose metrics to quantify how well models capture a variety of different characteristics associated with observed precipitation distributions (e.g., Dai 2006 ; Perkins et al. 2007 ; Pendergrass and Deser 2017 ; Pendergrass and Knutti 2018 ; Martinez-Villalobos et al. 2022 ; Ahn et al. 2023 ). However, a metric to quantify bimodality in precipitation distributions has yet to be established. On the other hand, efforts to quantify bimodality in probability distributions have been relatively intensive in medical research as bimodality often results from the contributions of dual causal processes underlying the observed data (e.g., Freeman and Dale 2013 ; Pfister et al. 2013 ). Several bimodality measures have been developed as reviewed by Freeman and Dale ( 2013 ), such as the bimodality coefficient (SAS Institute Inc 1990 ; Pfister et al. 2013 ), Hartigan’s dip statics (Hartigan and Hartigan 1985 ), and Akaike’s information criterion difference (Akaike 1974 ). However, these measures are based on statistics best suited for data with a Gaussian distribution, thus their applicability to precipitation data that has a Gamma distribution may be limited. In this study, we propose a new metric that quantifies bimodality in precipitation distributions. As our metric is based on the simple ratio between bimodal distribution peaks (Section 2.2), it can be applied to precipitation data with a Gamma distribution as well as data with a Gaussian distribution. We apply our metric to the daily precipitation from satellite-based observations, atmospheric reanalysis datasets, and CMIP 5 and 6 models. Consequently, we investigate the origin of the bimodal distribution by separating total precipitation into parameterized convective and resolved large-scale precipitation. In addition, DYAMOND simulations are analyzed to further investigate the role of convective parameterizations on the formation of the bimodal precipitation distributions. 2. Results 2.1. Characteristics and quantification of bimodality We evaluate the precipitation frequency distribution curves from the total, parameterized convective, and resolved large-scale precipitation in CMIP models. Figure 1 shows the precipitation frequency distributions over the 30°S-30°N ocean region for 43 CMIP 5 and 6 models with 5 satellite-based (IMERG, TRMM, CMORPH, GPCP, and PERSIANN) and 6 reanalysis (ERA5, ERA-Interim, MERRA2, MERRA, CFSR, and JRA-55) products. Note that the tropical ocean region exhibits the most noticeable bimodality in simulated precipitation distributions, which will be discussed in Section 4. All the satellite-based products consistently exhibit unimodal distribution, but their distribution curves show different peaks (Figs. 1 a-e). IMERG, TRMM, and CMORPH show a peak at a rain rate lower than 1 mm/day, whereas GPCP and PERSIANN show a peak at a rain rate near 10 mm/day. Detecting light precipitation by satellite remote sensing is challenging (e.g., Berg et al. 2010 ), and TRMM Multisatellite Precipitation Analysis (TMPA) is reported as capturing light precipitation better than GPCP (Burdanowitz et al. 2015). On the contrary, all the reanalysis products (Figs. 1 f-k) show a bimodal distribution, and in most of them (ERA5, MERRA, MERRA2, and CFSR) the peak is larger at a lighter rain rate near 1 mm/day. The bimodality of reanalysis precipitation likely stems from their atmospheric model component. Compared to old versions of reanalysis products (ERA-Interim and MERRA), newer versions (ERA5 and MERRA2) exhibit stronger unimodality, suggesting improvements have been made in the simulation of precipitation. Higher resolution and updated parameterizations are two possible drivers behind this improvement, though the degree to which they contribute to the overall improvement is difficult to ascertain without detailed testing. Among all the reanalysis datasets analyzed in this study, MERRA2 and JRA-55 show distribution curves most similar to that of satellite-based observations. Most CMIP models exhibit bimodal distributions (Figs. 1 l-bm). Many of them (e.g., ACCESS models, GFDL models, HadGEM models, MIROC models, and CNRM models) show a larger peak at a lighter rain rate, while in other models (e.g., BNU-ESM, INMCM4, BCC-CSM2-MR, and MRI-AGCM3) the larger peak is at a heavier rain rate. The peak of the light rain rate is associated with exaggerated drizzling ( < ~ 1mm/day precipitation) compared to observations in many models. Previous studies (e.g., Kooperman et al. 2018 ; Chen et al. 2021 ) argue that the exaggerated light rain is mainly produced by parameterized convection that is too frequently triggered. Consistent with previous studies, our results reveal that the exaggerated light rain is produced by parameterized convective precipitation (light showers) in some models (e.g., ACCESS1-0, CSIRO-Mk3-6-0, EC-EARTH, GFDL-CM3, CMCC-CM2-SR5, CNRM-CM6-1, and CNRM-ESM2-1), whereas in some models (e.g., ACCESS1-3, IPSL-CM5A, MIROC5, ACCESS-ESM1-5, CanESM5, and MIROC-ES2L) it is mainly produced by resolved grid-scale precipitation (drizzle). Several single-model studies (e.g., Lin et al. 2013 ; Kooperman et al. 2018 ) show that bimodality originates from the separate contributions of parameterized convective precipitation and resolved large-scale precipitation. While some models in our multi-model analysis have a bimodal distribution due to a combination of convective precipitation and large-scale precipitation (e.g., ACCESS1-3, FGOALS-s2, IPSL-CM5A, MIROC5, ACCESS-ESM1-5, CESM2, CanESM5, and MIROC-ES2L), we also see that bimodality can originate from the convective precipitation alone (e.g., ACCESS1-0, BNU-ESM, CCSM4, EC-EARTH, GFDL-CM3, CMCC-CM2, and TaiESM1). Interestingly, large-scale precipitation alone does not produce a bimodal distribution in any model, implying that convective parameterization is the main driver of bimodality. To quantitatively evaluate precipitation bimodality, we have developed a metric objectively gauging the bimodality in precipitation distributions based on the ratio of the peaks in a bimodal distribution (see Section 2.2 and Fig. 2 a). Figure 2 c shows the values of the bimodality metric for satellite-based products (black), reanalysis products (gray), CMIP5 (blue) and CMIP6 (red) models in ascending order. In the results from our dataset, the bimodality metric value varies from 0 (no bimodality) to about 0.3. We partition the magnitude of the bimodality into weak (0 < bimodality < 0.1), moderate (0.1 < = bimodality < 0.2), and strong (0.2 < = bimodality). Also, the metric values of individual realizations of the CMIP models are shown as markers in Fig. 2 c, where we found that in most cases the inter-realization spread is negligible compared to the inter-model spread. This suggests that our metric is not very sensitive to internal variability across multiple realizations, building confidence in the robustness of our findings. All satellite-based products show unimodal distributions with bimodality of 0, and most reanalysis products show only weak bimodality compared to most models. Two exceptions in the reanalysis results are ERA-Interim and MERRA, which are early iterations of ERA5 and MERRA2 and show the 3rd and 6th strongest bimodality among our dataset, even including CMIP models. Among reanalysis products and CMIP models showing bimodality, most of them (4 out of 6 reanalysis products, 16 out of 20 CMIP5, 15 out of 21 CMIP6) have the larger peak at a lighter rain rate. The performance of CMIP 5 and 6 multi-modal ensembles is visualized in Fig. 2 b as a percentage of models falling in each bimodality range. About 17% of CMIP5 and 30% of CMIP6 models fall into the bimodality 0 category, indicating about 83% of CMIP5 and 70% of CMIP6 models produce a bimodal precipitation distribution. Among all bimodality categories, the weak bimodality range (0 < bimodality < 0.1) includes the largest number of models (about 50% of CMIP5 and 60% of CMIP6 models). In the moderate bimodality range (0.1 < = bimodality < 0.2), about 25% of CMIP5 and 7% of CMIP6 models are found. Fewer than 10% of CMIP5 and 6 models fall into the strong bimodality range (0.2 < = bimodality), suggesting these models are anomalous among CMIP-class models. The CMIP6 models show better performance than the CMIP5 models, but nonetheless more than half of the models still show bimodal distribution. To mitigate bimodality in precipitation frequency distributions, the origin of the bimodality itself needs to be better understood. 2.2. Relationship between bimodality and convective parameterization Convective parameterizations have been speculated to be the origin of bimodal precipitation distributions (e.g., Lin et al. 2013 ; Kooperman et al. 2018 ). To examine the relationship between bimodality and various convective parameterizations in CMIP models, we categorize convective parameterizations of CMIP models by their provenance (Table S1 ), following Chen et al. ( 2021 ). The AS collection includes the convective parameterizations of Arakawa and Schubert ( 1974 ), Chikira and Sugiyama ( 2010 ), and Yoshimura et al. ( 2015 ); the Emanuel collection includes the convective parameterizations of Emanuel ( 1991 ), Grandpeix and Lafore ( 2010 ), Betts ( 1986 ), and Piriou et al. ( 2018 ); the GFDL collection includes the convective parameterizations of Donner (1993), Bretherton et al. ( 2004 ), and Zhao et al. (2018); the Tiedtke collection includes the convective parameterizations based on Tiedtke ( 1989 ); the UK collection includes the convective parameterizations based on Gregory and Rowntree ( 1990 ); the UNICON collection currently has one convective parameterization of Park ( 2014 ); the ZM collection includes the convective parameterizations based on Zhang and McFarlane ( 1995 ). Figure 3 shows the relationship between the convective parameterizations and the quantitative bimodality of the precipitation frequency distributions. Here the negative or positive bimodality value represents a bimodal distribution with a large peak on lighter or heavier rain rate, respectively. The ZM collection shows the largest spread in bimodality features, while the UK and Tiedtke collections show the least variation. In the ZM collection, there are many models from diverse modeling institutes (BCC, BNU, CCCma, CMCC, DOE, IAP-CAS/THU, NCAR, NCC, and AS-RCEC), which may explain the larger spread in bimodality than other convection collections. The UK collection shows weak bimodality (i.e., |bimodality| is less than 0.1), and the Tiedtke collection exhibits weak-to-moderate bimodality (0-0.15) with a larger peak at lighter rain rates. The UNICON collection does not show bimodality, but this only contains one model (SAM0-UNICON), requiring different model simulations with a unified convection scheme for a robust evaluation. CMIP5 models in the GFDL collection show moderate bimodality (0.1–0.2) with a larger left peak, while a CMIP6 model (GFDL-CM4) does not show bimodality. GFDL-CM4 updated the convective parameterization from Donner (1993) to Zhao et al. (2018), in which deep convection occurs only when the ambient environment is sufficiently moist, which may help reduce the exaggerated light convective precipitation shown in GFDL-CM3 and consequently mitigate the bimodality. GFDL-HIRAM simulations turned off the deep convection scheme and replaced it with a shallow convection scheme based on Bretherton (2004), but this produced bimodality that was even larger than in GFDL-CM3. For CMIP5 models in the AS collection, MRI-AGCM3-2H and MRI-AGCM3-2S show weak to moderate bimodality (~ 0.1) with a larger peak on a heavier rain rate, while MRI-CGCM3 shows nearly zero bimodality. MRI-CGCM3 uses the same deep convection scheme as MRI-AGCM3-2S but uses a new cloud scheme that is a two-moment bulk cloud scheme coupled to an aerosol model (Yukimoto et al. 2012), the likely driver behind the simulation of more realistic precipitation. For CMIP6 models in AS collection, only the MRI-ESM2-0 model shows bimodality with a larger peak at a lighter rain rate, while others (MIROC-ES2L, MIROC6, and IITM-ESM) do not show bimodal distributions. All MIROC models that participated in CMIP5 and CMIP6 (MIROC5, MIROC6, and MIROC-ES2L) consistently do not exhibit bimodality. In the Emanuel collection, CMIP6 models (CNRM-CM6, CNRM-ESM, and IPSL-CM6A-LR) show weak or nearly zero bimodality while some CMIP5 models have larger bimodality. IPSL-CM5A-LR and IPSL-CM5A-MR show the largest bimodality among all CMIP 5 and 6 models analyzed here, while IPSL-CM5B-LR and IPSL-CM6A-LR show a weak bimodality (< 0.1). IPSL-CM5B-LR couples Emanuel’s convection scheme used in IPSL-CM5A-LR with a density current parameterization representing a population of cold pools with vertical frontiers. Implementing the coupling between convection and cold pools yields a more realistic simulation of moist convective processes (Grandpeix and Lafore 2010 ). It is also supported by the fact that the convection-cold pool coupling process is also a key feature in UNICON (Park 2014 ), which exhibits zero bimodality. Our results suggest that the bimodality characteristics are not solely determined by the default convection scheme; that is, the bimodality can vary substantially from one model to the next by tuning parameters or adding processes. We will discuss a key parameter in convective parameterizations that controls bimodality in Section 4. 2.3. Bimodality in global storm-resolving model simulations We analyze GSRMs that participated in DYAMOND to further investigate the effect of convective parameterizations on bimodal precipitation distributions by comparing GSRM simulations with or without convective parameterization. While the GSRMs aim to resolve convective storms explicitly on a grid scale of several kilometers so as to remove the need for deep convective parameterizations, some DYAMOND models nonetheless provide simulations with a convective parameterization, as there is a lack of consensus on the necessity of convective parameterization when grid spacing is only a few kilometers. Figure 4 shows the precipitation frequency distributions from the DYAMOND simulations separated into no convective parameterization (no CP), shallow convective parameterization (shallow CP), and full (i.e., shallow and deep) convective parameterization (full CP) collections. All models in the full CP collection show a bimodality with weak-to-moderate magnitude (0-0.2 bimodality), whereas most models in no CP and shallow CP collections do not show bimodality. The one exception is NICAM simulations, which do not use a convective parameterization but exhibit weak bimodality. Curiously, the magnitude of bimodality in NICAM actually increases as grid spacing is reduced from 7km to 3.5km. We do not have an adequate explanation for this anomalous behavior. Compared to observations, the full CP collection underestimates precipitation frequencies with very light ( 30mm/day) rain rates and overestimates the other frequencies on light to moderate (0.2-30mm/day) rain rates. This is a common property of many CMIP models that use a deep convective parameterization (Fig. 1 ). In the shallow CP collection, the models are improved in simulating the very light and heavy precipitation frequencies but still overestimate precipitation frequencies at light (0.2-5mm/day) rain rates. The models in the no CP collection exhibit more improvement across all precipitation frequencies from very light to heavy. The overestimated light precipitation (or exaggerated drizzling) frequencies are especially improved. More specific implications can be obtained by comparing simulations using a different configuration of the same model. The IFS modeling group provides two simulations – 4-km with shallow CP (orange solid curve) and 9-km with full CP (orange dashed curve). The 9-km IFS simulation with full CP shows moderate bimodality of 0.15, while bimodality is zero in the 4-km shallow CP simulation. This implies that simulations using kilometer-scale model configuration without deep convective parameterization help simulate more realistic precipitation distributions. The MPAS modeling group provides two different horizontal resolution simulations at 3.75-km (green solid curve) and 7.5-km (green dashed curve) grid spacing with full CP. While the 7.5-km simulation shows moderate bimodality of 0.17, in the 3.75-km simulation the bimodality is almost mitigated to 0.005. The MPAS model simulations use a scale-aware convective parameterization based on Tiedtke scheme (Wang 2022 ), where the convective adjustment time scale and mass flux are scaled by the grid spacing, thus the mitigated bimodality in the higher resolution simulation is likely due to a decrease in parameterized convective precipitation and increase in resolved grid-scale precipitation. 3. Discussion In this study, we investigate the bimodality evident in many simulated precipitation frequency distributions, focusing on the tropical (30°S-30°N) ocean region where the bimodality bias is particularly egregious. Figure S1 shows the precipitation frequency distributions over the Northern Hemisphere extratropics (NHEX, 30°N-50°N) and Southern Hemisphere extratropics (SHEX, 50°S-30°S) as well as the tropics after separating ocean and land regions. Among all the regions, the bimodality in the simulated precipitation distributions is the most distinctive over the tropical ocean region, which includes a large portion of deep convective precipitation regions (e.g., Indo-Pacific Warm Pool and ITCZ) as well as large-scale precipitation regions (e.g., Subtropical eastern Pacific and Atlantic). This supports the notion that bimodal precipitation distributions are mainly caused by parameterized convective precipitation being generated separately from resolved grid-scale precipitation. To explore the possibility that the bimodality results from a sampling issue, we test the sensitivity of the bimodality to the temporal and spatial resolution of the analysis data. Figure S2 shows the frequency distributions of 1-day, 5-day, and 1-month averaged total precipitation. As the temporal resolution is lowered from 1-day to 1-month, very light and heavy precipitation rates tend to become less frequent, while moderate precipitation rates become more common. These changes, especially the increased moderate precipitation frequency, mitigate the bimodality in some models (e.g. CMCC-CM and EC-EARTH models). However, bimodality still persists in most models and is even amplified as the distribution becomes concentrated into a narrower range in some models (e.g, IPSL-CM5A models, MIROC5, CNRM-CM6-1 models, CNRM-ESM2-1, GFDL-CM4, MIROC-ES2L, and MIROC6). In the satellite-based observations, the shapes of the distribution curves become more consistent with each other, with a unimodal peak near 7 mm/day (i.e., the long-term mean precipitation rate) as the temporal resolution is lowered. On the other hand, the precipitation frequency distribution is not sensitive to the spatial resolution of analysis data (Fig. S3). The results of our sensitivity tests indicate that the bimodality is not due to spatial or temporal sampling issues, but rather is due to the way precipitation processes are modeled. In convective parameterizations, the convective adjustment timescale is a key parameter to control the intensity of parameterized convection by regulating the timescale for the consumption rate of convective available potential energy. Kooperman et al. ( 2018 ) tested the effects of convective adjustment timescale on precipitation distributions using CCSM4 with the ZM convection scheme. They showed that a bimodal distribution appears in a simulation with a longer (~ 100 minutes) convective adjustment timescale, but is mitigated when the timescale is shortened (~ 30 minutes). In the longer convective timescale simulation, the bimodality originates from the combination of the convective precipitation on lighter frequencies and the large-scale precipitation on heavier frequencies. On the other hand, shortening the convective adjustment timescale has an effect on shifting the convective precipitation distribution to the right (heavier side) and the large-scale precipitation distribution to the left (lighter side), which increases moderate precipitation frequency – that is, where the trough in the distribution normally exists. This result suggests that the convective adjustment timescale in convective parameterizations could be an effective controlling factor to mitigate bimodality in simulated precipitation distributions, but could also result in unwanted trade-offs between precipitation distribution and mean state. 4. Conclusions We introduce a metric to objectively quantify bimodality in precipitation distributions and apply it to daily precipitation from multiple satellite-based products, reanalysis products, CMIP 5 and 6 models. While all satellite-based products used in this study do not exhibit bimodality in precipitation distributions, we find that all reanalysis products and approximately 83% of CMIP5 and 70% of CMIP6 models show bimodal distributions. The bimodal distribution generally originates in two different ways – first, from the combination between parameterized subgrid-scale convective precipitation and resolved grid-scale precipitation, and second, from parameterized subgrid-scale convective precipitation alone. The first one supports the findings from previous studies that identify bimodality in a single model (e.g., Lin et al. 2013 ; Kooperman et al. 2018 ), and the second one is newly revealed in our study with multi-model analysis. The magnitude and sign of bimodality in CMIP models do not appear to be related to the provenance of convective parameterizations, which indicates that bimodality is likely sensitive to the retuning or modification of the parameterization. The ZM collection shows the largest spread in bimodality among all convective parameterization collections we analyzed. This is likely a consequence of the ZM convection scheme being widely used, and subsequently modified or retuned in different ways across many modeling centers. Intercomparison of GSRMs with or without a convective parameterization indicates that a deep convective parameterization is the main cause of bimodal precipitation distributions and implies that reducing the portion of parameterized convection could help mitigate the bimodal precipitation distribution. The bimodal distribution in simulated precipitation is primarily associated with an exaggerated drizzling bias. Drizzling can modulate soil aridness, which is an important factor in the Earth system influencing wildfire outbreaks, vegetation growth, freshwater resources, etc. To improve model simulations, it is fundamental to objectively quantify model biases and identify the origins of the biases. The current study is the first to propose a bimodality metric for precipitation distributions and investigate the origin of bimodality in a multi-model dataset. Our multi-model analysis results provide insights that the bimodality could be mitigated as follows; i) reducing the portion of convective parameterization with a horizontal resolution of several kilometers (insight from the comparison of DYAMOND simulations with or without a convective parameterization, IFS_4km vs IFS_9km, and MPAS_3.75km vs MPAS_7.5km), ii) implementing more realistic processes into convective parameterization, such as including cold pool processes (insight from the comparison of IPSL-CM5A-LR vs IPSL-CM5B-LR) and coupling between convection and ambient environmental moisture (insight from the comparison of GFDL-CM3 vs GFDL-CM4), and iii) tuning a parameter controlling convective adjustment time scale in convective parameterization (insight from the result of Kooperman et al. 2018 ). Although it is hard to rule out the possibility that these changes could drive unwanted trade-offs, we would propose that these will be good directions of investigation to possibly mitigate bimodal distributions or drizzling bias in simulated precipitation for next-generation models. 5. Data and Methods 5.1. Data We analyze daily total precipitation and convective precipitation from all available realizations of AMIP contributed to CMIP5 (Taylor et al. 2012 ) and CMIP6 (Eyring et al. 2016 ). Table S1 lists the CMIP models providing both total and convective precipitation and their default deep convective parameterization schemes. Note that many CMIP models may use different tuning parameters and formulations for certain processes, even though they use the same default scheme (e.g. ZM scheme). We evaluate the most recent 20 years (1985–2004) that both CMIP5 and CMIP6 models have in common. To investigate the role of convective parameterizations on bimodal precipitation distributions, we use global storm-resolving models (GSRMs) with and without a convective parameterization, made available via the DYAMOND summer protocol (Stevens et al., 2019). The DYAMOND model simulations and their convective parameterizations are listed in Table S2. The simulation period is 40 days (1 August − 10 September 2016); we analyze the last 38 days to avoid the initial shock of the simulation following Ma et al. ( 2022 ). As reference data for model evaluation, we use daily precipitation from 5 satellite-based products (IMERG, TRMM, CMORPH, GPCP, and PERSIANN) and 6 atmospheric reanalyses (ERA5, ERA-Interim, MERRA2, MERRA, CFSR, and JRA-55). The information on the 5 satellite-based and 6 reanalysis precipitation products is summarized in Table S3. We analyze data periods available via obs4MIPs and CREATE-IP as follows: 2001–2020 for IMERG, 1998–2018 for TRMM, 1998–2012 for CMORPH, 1997–2020 for GPCP, 1984–2018 for PERSIANN, 1979–2018 for ERA5, 1979–2017 for ERA-Interim, 1980–2018 for MERRA2, 1979–2015 for MERRA, 1979–2018 for CFSR, and 1979–2018 for JRA-55. As in previous studies evaluating simulated precipitation in CMIP 5 and 6 models (e.g., Fiedler et al. 2020; Tang et al. 2021 ; Ahn et al. 2022 , 2023 ), all CMIP models and observational data are regridded to 2x2 degrees with a conservative method for a fair comparison. In analyzing DYAMOND model simulations, the DYAMOND model and observational data are regridded to 1x1 degrees as in Ma et al. ( 2022 ). 5.2. Methods We calculate precipitation frequency distribution for total precipitation, and where possible parameterized convective-scale and resolved large-scale precipitation. Following Pendergrass and Hartmann ( 2014 ), Pendergrass and Deser ( 2017 ), and Ahn et al. ( 2023 ), we set logarithmically-spaced bins with each successive bin 7% wider than the adjacent previous bin. We then obtain the total precipitation frequency distribution that corresponds to the number of days in each bin normalized by the total number of days. To obtain frequency distributions for convective and large-scale precipitation, we use the following analysis procedure: i) calculate amount distributions, the sum of precipitation amount in each bin normalized by the total number of days, for total precipitation and convective precipitation, respectively, as a function of total precipitation bins; ii) save the ratio of convective precipitation amount to total precipitation amount in each precipitation bin; iii) obtain frequency distribution for convective precipitation by multiplying the ratio of convective precipitation to total precipitation amount in each precipitation bin; iv) obtain frequency distribution for large-scale precipitation by subtracting the convective precipitation from total precipitation in frequency distributions. With this process, each bin of total precipitation distribution can be exactly separated by the ratio of the convective or the large-scale precipitation to the total precipitation. The bimodality metric is formulated based on the two bimodal peaks and an intermodal minimum in the frequency distribution or PDF of daily total precipitation (Fig. 2 a): $$Bimodality=\frac{PDF\left(lower peak\right) - PDF\left(intermodal minimum\right)}{PDF\left(taller peak\right)}$$ The peaks are identified by finding where the gradient of the distribution curve is zero after smoothing the distribution curve by a Savitzky-Golay smoothing filter (Savitzky and Golay 1964 ). The metric is based on the ratio of the lower peak to the taller peak, with the lower peak set to the difference from the intermodal minimum. If there are more than two peaks, the calculation algorithm first identifies the deepest intermodal minimum, and then finds the tallest peak on the left and right side from the deepest intermodal minimum. Given the formulation, the metric values can vary from 0 (no bimodality) to 1 (maximum bimodality). The metric is designed to be able to identify the taller peak between two peaks – the sign of the metric value is positive or negative if the right or left peak is taller. Therefore, this metric can be used in both its absolute value form and in the left/right peak distinguishing form; The absolute value gives us a sense of the bimodality magnitude and the sign of the bimodality tells us whether the taller peak is at a lighter or heavier precipitation rate. Declarations Data availability All of the data used in this study are publicly available. The satellite-based precipitation products used in this study (IMERG, TRMM, CMORPH, GPCP, and PERSIANN) and ERA5 precipitation product are available on the Obs4MIPs at https://esgf-node.llnl.gov/projects/obs4mips/. The other reanalysis precipitation products (ERA-Interim, MERRA2, MERRA, CFSR, and JRA-55) are available on the Collaborative REAnalysis Technical Environment (CREATE-IP) at https://esgf-node.llnl.gov/projects/create-ip/. The CMIP data is available on the ESGF at https://esgf-node.llnl.gov/projects/esgf-llnl. The DYAMOND data is archived by the DKRZ and available through the ESiWACE at https://www.esiwace.eu/services/dyamond. Code availability The bimodality metic code is available via the collection of precipitation distribution metrics in the PCMDI Metrics Package (PMP, https://github.com/PCMDI/pcmdi_metrics, DOI: 10.5281/zenodo.7231033). Acknowledgments This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. The efforts of the authors were supported by the Regional and Global Model Analysis (RGMA) program of the United States Department of Energy's Office of Science. We acknowledge the World Climate Research Programme’s Working Group on Coupled Modeling, which is responsible for CMIP, and we thank the climate modeling groups for producing and making available their model output, the Earth System Grid Federation (ESGF) for archiving the output and providing access, and the multiple funding agencies who support CMIP and ESGF. The U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison (PCMDI) provides coordinating support and led the development of software infrastructure for CMIP. Author contributions M.A., P.U., J.L., P.G. conceived the idea and M.A. and H.M. performed the analysis. M.A., P.U., J.L., P.G., H.M., C.T., P.B., A.O contributed to the discussion and wrote the manuscript. M.A., J.L., A.O implemented the code to the PCMDI Metrics Package. Competing interest The authors declare no competing interests. References Ahn, M.-S., P. A. Ullrich, P. J. Gleckler, J. Lee, A. C. Ordonez, and A. G. 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Ordonez","email":"","orcid":"","institution":"Lawrence Livermore National Laboratory, Livermore, CA, USA","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Ana","middleName":"C.","lastName":"Ordonez","suffix":""}],"badges":[],"createdAt":"2023-04-28 19:31:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2874349/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2874349/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41612-024-00685-3","type":"published","date":"2024-06-15T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":37851025,"identity":"99e24805-1fb0-4728-b8c7-d679d1cd3e7a","added_by":"auto","created_at":"2023-06-01 14:53:22","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":903893,"visible":true,"origin":"","legend":"\u003cp\u003eFrequency distributions of total (black), convective (orange), and large-scale (green) precipitation over 30°S-30°N ocean region for satellite-based products, reanalysis products, CMIP5, and CMIP6 models. Each subplot title is color-coded by black: satellite-based products, gray: reanalysis products, blue: CMIP5 models, and red: CMIP6 models.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-2874349/v1/a6a5a6999e3dc787012e6f1b.png"},{"id":37851024,"identity":"5b13d70f-b2a2-42b0-8bab-9c12f8f3fc7e","added_by":"auto","created_at":"2023-06-01 14:53:22","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":370685,"visible":true,"origin":"","legend":"\u003cp\u003ea) Schematic for the formulation of bimodality metric, b) Probability distribution of model performance, c) Bar graph of bimodality metric for satellite-based observations (black), reanalysis products (gray), CMIP5 (blue), and CMIP6 (red) models. Circle marks over each bar represent individual ensemble members. Plus or minus marks under each bar respectively indicate that the maximum peak is on a lighter or heavier rain rate.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-2874349/v1/613696cd6927954b147c2753.png"},{"id":37851023,"identity":"17185402-33bc-4a32-9c6a-80c7695eb542","added_by":"auto","created_at":"2023-06-01 14:53:22","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":129833,"visible":true,"origin":"","legend":"\u003cp\u003eRelationship between convective parameterizations and bimodality in precipitation frequency distributions for CMIP5 (blue) and CMIP6 (red) models. Negative or positive bimodality value represents a bimodal distribution with a large peak on a lighter or heavier rain rate.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-2874349/v1/722854c305c870528f158541.png"},{"id":37852712,"identity":"b4491a4b-cdc8-4bb9-9d4a-a4cae5e4ccd8","added_by":"auto","created_at":"2023-06-01 15:01:22","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":184958,"visible":true,"origin":"","legend":"\u003cp\u003eFrequency distributions of total precipitation from DYAMOND simulations separated into a) no Convective Parameterization (CP), b) shallow CP, and c) full CP simulations.\u003c/p\u003e\n\u003cp\u003eThe calculation for this figure is in accordance with Ma et al. (2022); the analyzed domain and period are 20°S-20°N and 3 August-9 September 2016. IMERG and CMORPH are also calculated accordingly. The number next to each model label indicates the bimodality.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-2874349/v1/2dccb7f9d368f7725f683c1c.png"},{"id":58435257,"identity":"45ad0935-0f90-4ae6-85fc-8a4c0cdd4b50","added_by":"auto","created_at":"2024-06-16 07:07:06","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1767048,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2874349/v1/8c114288-4356-4c5c-82e9-d9650b8e2122.pdf"},{"id":37851027,"identity":"fb33dfdc-e179-4c9f-833b-7f5690585263","added_by":"auto","created_at":"2023-06-01 14:53:22","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":3015902,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"supplementalmaterialsubmitted.docx","url":"https://assets-eu.researchsquare.com/files/rs-2874349/v1/ddf2113010407508eb383e4d.docx"}],"financialInterests":"(Not answered)","formattedTitle":"Bimodality in Simulated Precipitation Frequency Distributions and Its Relationship with Convective Parameterizations","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eBimodality in a precipitation frequency distribution, defined as the presence of two distinct peaks in the probability density function (PDF) of precipitation data, has been a long-standing model behavior that is not evident in observations (e.g., Ma et al. \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Ahn et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). A light precipitation peak in bimodal distributions is associated with exaggerated drizzling (\u0026thinsp;\u0026lt;\u0026thinsp;~\u0026thinsp;1mm/day), which has been apparent in many climate models (e.g., Dai \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Chen et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Although drizzle represents a small portion of the total precipitation amount, frequent and light precipitation plays an important role in modulating soil aridity, wildfire outbreaks, vegetation growth, and freshwater resources (e.g., Trenberth et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Trenberth \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). In persistent dry conditions, soil hardening makes it difficult for water to soak into the soil, thus increasing the probability of flooding when heavy rain falls. Realistic simulation of extreme events and their impacts may also be further limited in models with a bimodal precipitation distribution.\u003c/p\u003e \u003cp\u003eThe origin of bimodal distributions in simulated precipitation has been proposed to be a result of separate precipitation processes \u0026ndash; parameterized convective precipitation and resolved large-scale precipitation. Many convective parameterizations produce too frequent light precipitation, which is associated with drizzling and bimodality bias (e.g., Lin et al. \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Kooperman et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Chen et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Some models, on the contrary, show that heavy precipitation results more from convective precipitation than from large-scale precipitation (Martinez-Villalobos et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Model resolution appears to play little role in the bimodal frequency distribution. In a recent study (Ma et al. \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), the bimodality is exhibited in a variety of model simulations with resolutions from a hundred to a few kilometers that participated in various model intercomparison projects, including the Coupled Model Intercomparison Project phase 6/Atmospheric Model Intercomparison Project (CMIP6/AMIP, ~\u0026thinsp;150km, Eyring et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), the High Resolution Model Intercomparison Project/AMIP (HighResMIP/AMIP, ~\u0026thinsp;50km, Haarsma et al., 2016,), and DYnamics of the Atmospheric general circulation Modeled On Non-hydrostatic Domains (DYAMOND, ~5km, Stevens et al. 2019). To better understand the bimodal distribution characteristics and investigate its relationship with other processes, objective quantification of the bimodality is required.\u003c/p\u003e \u003cp\u003eMany previous studies propose metrics to quantify how well models capture a variety of different characteristics associated with observed precipitation distributions (e.g., Dai \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Perkins et al. \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Pendergrass and Deser \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Pendergrass and Knutti \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Martinez-Villalobos et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Ahn et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). However, a metric to quantify bimodality in precipitation distributions has yet to be established. On the other hand, efforts to quantify bimodality in probability distributions have been relatively intensive in medical research as bimodality often results from the contributions of dual causal processes underlying the observed data (e.g., Freeman and Dale \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Pfister et al. \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Several bimodality measures have been developed as reviewed by Freeman and Dale (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), such as the bimodality coefficient (SAS Institute Inc \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e1990\u003c/span\u003e; Pfister et al. \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), Hartigan\u0026rsquo;s dip statics (Hartigan and Hartigan \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e1985\u003c/span\u003e), and Akaike\u0026rsquo;s information criterion difference (Akaike \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1974\u003c/span\u003e). However, these measures are based on statistics best suited for data with a Gaussian distribution, thus their applicability to precipitation data that has a Gamma distribution may be limited.\u003c/p\u003e \u003cp\u003eIn this study, we propose a new metric that quantifies bimodality in precipitation distributions. As our metric is based on the simple ratio between bimodal distribution peaks (Section 2.2), it can be applied to precipitation data with a Gamma distribution as well as data with a Gaussian distribution. We apply our metric to the daily precipitation from satellite-based observations, atmospheric reanalysis datasets, and CMIP 5 and 6 models. Consequently, we investigate the origin of the bimodal distribution by separating total precipitation into parameterized convective and resolved large-scale precipitation. In addition, DYAMOND simulations are analyzed to further investigate the role of convective parameterizations on the formation of the bimodal precipitation distributions.\u003c/p\u003e"},{"header":"2. Results","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Characteristics and quantification of bimodality\u003c/h2\u003e \u003cp\u003eWe evaluate the precipitation frequency distribution curves from the total, parameterized convective, and resolved large-scale precipitation in CMIP models. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the precipitation frequency distributions over the 30\u0026deg;S-30\u0026deg;N ocean region for 43 CMIP 5 and 6 models with 5 satellite-based (IMERG, TRMM, CMORPH, GPCP, and PERSIANN) and 6 reanalysis (ERA5, ERA-Interim, MERRA2, MERRA, CFSR, and JRA-55) products. Note that the tropical ocean region exhibits the most noticeable bimodality in simulated precipitation distributions, which will be discussed in Section 4. All the satellite-based products consistently exhibit unimodal distribution, but their distribution curves show different peaks (Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea-e). IMERG, TRMM, and CMORPH show a peak at a rain rate lower than 1 mm/day, whereas GPCP and PERSIANN show a peak at a rain rate near 10 mm/day. Detecting light precipitation by satellite remote sensing is challenging (e.g., Berg et al. \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2010\u003c/span\u003e), and TRMM Multisatellite Precipitation Analysis (TMPA) is reported as capturing light precipitation better than GPCP (Burdanowitz et al. 2015). On the contrary, all the reanalysis products (Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef-k) show a bimodal distribution, and in most of them (ERA5, MERRA, MERRA2, and CFSR) the peak is larger at a lighter rain rate near 1 mm/day. The bimodality of reanalysis precipitation likely stems from their atmospheric model component. Compared to old versions of reanalysis products (ERA-Interim and MERRA), newer versions (ERA5 and MERRA2) exhibit stronger unimodality, suggesting improvements have been made in the simulation of precipitation. Higher resolution and updated parameterizations are two possible drivers behind this improvement, though the degree to which they contribute to the overall improvement is difficult to ascertain without detailed testing. Among all the reanalysis datasets analyzed in this study, MERRA2 and JRA-55 show distribution curves most similar to that of satellite-based observations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMost CMIP models exhibit bimodal distributions (Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003el-bm). Many of them (e.g., ACCESS models, GFDL models, HadGEM models, MIROC models, and CNRM models) show a larger peak at a lighter rain rate, while in other models (e.g., BNU-ESM, INMCM4, BCC-CSM2-MR, and MRI-AGCM3) the larger peak is at a heavier rain rate. The peak of the light rain rate is associated with exaggerated drizzling (\u0026thinsp;\u0026lt;\u0026thinsp;~\u0026thinsp;1mm/day precipitation) compared to observations in many models. Previous studies (e.g., Kooperman et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Chen et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) argue that the exaggerated light rain is mainly produced by parameterized convection that is too frequently triggered. Consistent with previous studies, our results reveal that the exaggerated light rain is produced by parameterized convective precipitation (light showers) in some models (e.g., ACCESS1-0, CSIRO-Mk3-6-0, EC-EARTH, GFDL-CM3, CMCC-CM2-SR5, CNRM-CM6-1, and CNRM-ESM2-1), whereas in some models (e.g., ACCESS1-3, IPSL-CM5A, MIROC5, ACCESS-ESM1-5, CanESM5, and MIROC-ES2L) it is mainly produced by resolved grid-scale precipitation (drizzle).\u003c/p\u003e \u003cp\u003eSeveral single-model studies (e.g., Lin et al. \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Kooperman et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) show that bimodality originates from the separate contributions of parameterized convective precipitation and resolved large-scale precipitation. While some models in our multi-model analysis have a bimodal distribution due to a combination of convective precipitation and large-scale precipitation (e.g., ACCESS1-3, FGOALS-s2, IPSL-CM5A, MIROC5, ACCESS-ESM1-5, CESM2, CanESM5, and MIROC-ES2L), we also see that bimodality can originate from the convective precipitation alone (e.g., ACCESS1-0, BNU-ESM, CCSM4, EC-EARTH, GFDL-CM3, CMCC-CM2, and TaiESM1). Interestingly, large-scale precipitation alone does not produce a bimodal distribution in any model, implying that convective parameterization is the main driver of bimodality.\u003c/p\u003e \u003cp\u003eTo quantitatively evaluate precipitation bimodality, we have developed a metric objectively gauging the bimodality in precipitation distributions based on the ratio of the peaks in a bimodal distribution (see Section 2.2 and Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea). Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec shows the values of the bimodality metric for satellite-based products (black), reanalysis products (gray), CMIP5 (blue) and CMIP6 (red) models in ascending order. In the results from our dataset, the bimodality metric value varies from 0 (no bimodality) to about 0.3. We partition the magnitude of the bimodality into weak (0\u0026thinsp;\u0026lt;\u0026thinsp;bimodality\u0026thinsp;\u0026lt;\u0026thinsp;0.1), moderate (0.1\u0026thinsp;\u0026lt;\u0026thinsp;=\u0026thinsp;bimodality\u0026thinsp;\u0026lt;\u0026thinsp;0.2), and strong (0.2\u0026thinsp;\u0026lt;\u0026thinsp;=\u0026thinsp;bimodality). Also, the metric values of individual realizations of the CMIP models are shown as markers in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec, where we found that in most cases the inter-realization spread is negligible compared to the inter-model spread. This suggests that our metric is not very sensitive to internal variability across multiple realizations, building confidence in the robustness of our findings. All satellite-based products show unimodal distributions with bimodality of 0, and most reanalysis products show only weak bimodality compared to most models. Two exceptions in the reanalysis results are ERA-Interim and MERRA, which are early iterations of ERA5 and MERRA2 and show the 3rd and 6th strongest bimodality among our dataset, even including CMIP models. Among reanalysis products and CMIP models showing bimodality, most of them (4 out of 6 reanalysis products, 16 out of 20 CMIP5, 15 out of 21 CMIP6) have the larger peak at a lighter rain rate.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe performance of CMIP 5 and 6 multi-modal ensembles is visualized in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb as a percentage of models falling in each bimodality range. About 17% of CMIP5 and 30% of CMIP6 models fall into the bimodality 0 category, indicating about 83% of CMIP5 and 70% of CMIP6 models produce a bimodal precipitation distribution. Among all bimodality categories, the weak bimodality range (0\u0026thinsp;\u0026lt;\u0026thinsp;bimodality\u0026thinsp;\u0026lt;\u0026thinsp;0.1) includes the largest number of models (about 50% of CMIP5 and 60% of CMIP6 models). In the moderate bimodality range (0.1\u0026thinsp;\u0026lt;\u0026thinsp;=\u0026thinsp;bimodality\u0026thinsp;\u0026lt;\u0026thinsp;0.2), about 25% of CMIP5 and 7% of CMIP6 models are found. Fewer than 10% of CMIP5 and 6 models fall into the strong bimodality range (0.2\u0026thinsp;\u0026lt;\u0026thinsp;=\u0026thinsp;bimodality), suggesting these models are anomalous among CMIP-class models. The CMIP6 models show better performance than the CMIP5 models, but nonetheless more than half of the models still show bimodal distribution. To mitigate bimodality in precipitation frequency distributions, the origin of the bimodality itself needs to be better understood.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Relationship between bimodality and convective parameterization\u003c/h2\u003e \u003cp\u003eConvective parameterizations have been speculated to be the origin of bimodal precipitation distributions (e.g., Lin et al. \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Kooperman et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). To examine the relationship between bimodality and various convective parameterizations in CMIP models, we categorize convective parameterizations of CMIP models by their provenance (Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e), following Chen et al. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The \u003cem\u003eAS\u003c/em\u003e collection includes the convective parameterizations of Arakawa and Schubert (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e1974\u003c/span\u003e), Chikira and Sugiyama (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2010\u003c/span\u003e), and Yoshimura et al. (\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2015\u003c/span\u003e); the \u003cem\u003eEmanuel\u003c/em\u003e collection includes the convective parameterizations of Emanuel (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e1991\u003c/span\u003e), Grandpeix and Lafore (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2010\u003c/span\u003e), Betts (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e1986\u003c/span\u003e), and Piriou et al. (\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2018\u003c/span\u003e); the \u003cem\u003eGFDL\u003c/em\u003e collection includes the convective parameterizations of Donner (1993), Bretherton et al. (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2004\u003c/span\u003e), and Zhao et al. (2018); the \u003cem\u003eTiedtke\u003c/em\u003e collection includes the convective parameterizations based on Tiedtke (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e1989\u003c/span\u003e); the \u003cem\u003eUK\u003c/em\u003e collection includes the convective parameterizations based on Gregory and Rowntree (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e1990\u003c/span\u003e); the \u003cem\u003eUNICON\u003c/em\u003e collection currently has one convective parameterization of Park (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2014\u003c/span\u003e); the \u003cem\u003eZM\u003c/em\u003e collection includes the convective parameterizations based on Zhang and McFarlane (\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e1995\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the relationship between the convective parameterizations and the quantitative bimodality of the precipitation frequency distributions. Here the negative or positive bimodality value represents a bimodal distribution with a large peak on lighter or heavier rain rate, respectively. The \u003cem\u003eZM\u003c/em\u003e collection shows the largest spread in bimodality features, while the \u003cem\u003eUK\u003c/em\u003e and \u003cem\u003eTiedtke\u003c/em\u003e collections show the least variation. In the \u003cem\u003eZM\u003c/em\u003e collection, there are many models from diverse modeling institutes (BCC, BNU, CCCma, CMCC, DOE, IAP-CAS/THU, NCAR, NCC, and AS-RCEC), which may explain the larger spread in bimodality than other convection collections. The \u003cem\u003eUK\u003c/em\u003e collection shows weak bimodality (i.e., |bimodality| is less than 0.1), and the \u003cem\u003eTiedtke\u003c/em\u003e collection exhibits weak-to-moderate bimodality (0-0.15) with a larger peak at lighter rain rates. The \u003cem\u003eUNICON\u003c/em\u003e collection does not show bimodality, but this only contains one model (SAM0-UNICON), requiring different model simulations with a unified convection scheme for a robust evaluation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eCMIP5 models in the \u003cem\u003eGFDL\u003c/em\u003e collection show moderate bimodality (0.1\u0026ndash;0.2) with a larger left peak, while a CMIP6 model (GFDL-CM4) does not show bimodality. GFDL-CM4 updated the convective parameterization from Donner (1993) to Zhao et al. (2018), in which deep convection occurs only when the ambient environment is sufficiently moist, which may help reduce the exaggerated light convective precipitation shown in GFDL-CM3 and consequently mitigate the bimodality. GFDL-HIRAM simulations turned off the deep convection scheme and replaced it with a shallow convection scheme based on Bretherton (2004), but this produced bimodality that was even larger than in GFDL-CM3.\u003c/p\u003e \u003cp\u003eFor CMIP5 models in the \u003cem\u003eAS\u003c/em\u003e collection, MRI-AGCM3-2H and MRI-AGCM3-2S show weak to moderate bimodality (~\u0026thinsp;0.1) with a larger peak on a heavier rain rate, while MRI-CGCM3 shows nearly zero bimodality. MRI-CGCM3 uses the same deep convection scheme as MRI-AGCM3-2S but uses a new cloud scheme that is a two-moment bulk cloud scheme coupled to an aerosol model (Yukimoto et al. 2012), the likely driver behind the simulation of more realistic precipitation. For CMIP6 models in \u003cem\u003eAS\u003c/em\u003e collection, only the MRI-ESM2-0 model shows bimodality with a larger peak at a lighter rain rate, while others (MIROC-ES2L, MIROC6, and IITM-ESM) do not show bimodal distributions. All MIROC models that participated in CMIP5 and CMIP6 (MIROC5, MIROC6, and MIROC-ES2L) consistently do not exhibit bimodality.\u003c/p\u003e \u003cp\u003eIn the \u003cem\u003eEmanuel\u003c/em\u003e collection, CMIP6 models (CNRM-CM6, CNRM-ESM, and IPSL-CM6A-LR) show weak or nearly zero bimodality while some CMIP5 models have larger bimodality. IPSL-CM5A-LR and IPSL-CM5A-MR show the largest bimodality among all CMIP 5 and 6 models analyzed here, while IPSL-CM5B-LR and IPSL-CM6A-LR show a weak bimodality (\u0026lt;\u0026thinsp;0.1). IPSL-CM5B-LR couples Emanuel\u0026rsquo;s convection scheme used in IPSL-CM5A-LR with a density current parameterization representing a population of cold pools with vertical frontiers. Implementing the coupling between convection and cold pools yields a more realistic simulation of moist convective processes (Grandpeix and Lafore \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). It is also supported by the fact that the convection-cold pool coupling process is also a key feature in UNICON (Park \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), which exhibits zero bimodality. Our results suggest that the bimodality characteristics are not solely determined by the default convection scheme; that is, the bimodality can vary substantially from one model to the next by tuning parameters or adding processes. We will discuss a key parameter in convective parameterizations that controls bimodality in Section 4.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Bimodality in global storm-resolving model simulations\u003c/h2\u003e \u003cp\u003eWe analyze GSRMs that participated in DYAMOND to further investigate the effect of convective parameterizations on bimodal precipitation distributions by comparing GSRM simulations with or without convective parameterization. While the GSRMs aim to resolve convective storms explicitly on a grid scale of several kilometers so as to remove the need for deep convective parameterizations, some DYAMOND models nonetheless provide simulations with a convective parameterization, as there is a lack of consensus on the necessity of convective parameterization when grid spacing is only a few kilometers. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the precipitation frequency distributions from the DYAMOND simulations separated into no convective parameterization (no CP), shallow convective parameterization (shallow CP), and full (i.e., shallow and deep) convective parameterization (full CP) collections. All models in the full CP collection show a bimodality with weak-to-moderate magnitude (0-0.2 bimodality), whereas most models in no CP and shallow CP collections do not show bimodality. The one exception is NICAM simulations, which do not use a convective parameterization but exhibit weak bimodality. Curiously, the magnitude of bimodality in NICAM actually increases as grid spacing is reduced from 7km to 3.5km. We do not have an adequate explanation for this anomalous behavior.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eCompared to observations, the full CP collection underestimates precipitation frequencies with very light (\u0026lt;\u0026thinsp;0.2mm/day) and heavy (\u0026gt;\u0026thinsp;30mm/day) rain rates and overestimates the other frequencies on light to moderate (0.2-30mm/day) rain rates. This is a common property of many CMIP models that use a deep convective parameterization (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). In the shallow CP collection, the models are improved in simulating the very light and heavy precipitation frequencies but still overestimate precipitation frequencies at light (0.2-5mm/day) rain rates. The models in the no CP collection exhibit more improvement across all precipitation frequencies from very light to heavy. The overestimated light precipitation (or exaggerated drizzling) frequencies are especially improved.\u003c/p\u003e \u003cp\u003eMore specific implications can be obtained by comparing simulations using a different configuration of the same model. The IFS modeling group provides two simulations \u0026ndash; 4-km with shallow CP (orange solid curve) and 9-km with full CP (orange dashed curve). The 9-km IFS simulation with full CP shows moderate bimodality of 0.15, while bimodality is zero in the 4-km shallow CP simulation. This implies that simulations using kilometer-scale model configuration without deep convective parameterization help simulate more realistic precipitation distributions. The MPAS modeling group provides two different horizontal resolution simulations at 3.75-km (green solid curve) and 7.5-km (green dashed curve) grid spacing with full CP. While the 7.5-km simulation shows moderate bimodality of 0.17, in the 3.75-km simulation the bimodality is almost mitigated to 0.005. The MPAS model simulations use a scale-aware convective parameterization based on Tiedtke scheme (Wang \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), where the convective adjustment time scale and mass flux are scaled by the grid spacing, thus the mitigated bimodality in the higher resolution simulation is likely due to a decrease in parameterized convective precipitation and increase in resolved grid-scale precipitation.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Discussion","content":"\u003cp\u003eIn this study, we investigate the bimodality evident in many simulated precipitation frequency distributions, focusing on the tropical (30\u0026deg;S-30\u0026deg;N) ocean region where the bimodality bias is particularly egregious. Figure \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e shows the precipitation frequency distributions over the Northern Hemisphere extratropics (NHEX, 30\u0026deg;N-50\u0026deg;N) and Southern Hemisphere extratropics (SHEX, 50\u0026deg;S-30\u0026deg;S) as well as the tropics after separating ocean and land regions. Among all the regions, the bimodality in the simulated precipitation distributions is the most distinctive over the tropical ocean region, which includes a large portion of deep convective precipitation regions (e.g., Indo-Pacific Warm Pool and ITCZ) as well as large-scale precipitation regions (e.g., Subtropical eastern Pacific and Atlantic). This supports the notion that bimodal precipitation distributions are mainly caused by parameterized convective precipitation being generated separately from resolved grid-scale precipitation.\u003c/p\u003e \u003cp\u003eTo explore the possibility that the bimodality results from a sampling issue, we test the sensitivity of the bimodality to the temporal and spatial resolution of the analysis data. Figure S2 shows the frequency distributions of 1-day, 5-day, and 1-month averaged total precipitation. As the temporal resolution is lowered from 1-day to 1-month, very light and heavy precipitation rates tend to become less frequent, while moderate precipitation rates become more common. These changes, especially the increased moderate precipitation frequency, mitigate the bimodality in some models (e.g. CMCC-CM and EC-EARTH models). However, bimodality still persists in most models and is even amplified as the distribution becomes concentrated into a narrower range in some models (e.g, IPSL-CM5A models, MIROC5, CNRM-CM6-1 models, CNRM-ESM2-1, GFDL-CM4, MIROC-ES2L, and MIROC6). In the satellite-based observations, the shapes of the distribution curves become more consistent with each other, with a unimodal peak near 7 mm/day (i.e., the long-term mean precipitation rate) as the temporal resolution is lowered. On the other hand, the precipitation frequency distribution is not sensitive to the spatial resolution of analysis data (Fig. S3). The results of our sensitivity tests indicate that the bimodality is not due to spatial or temporal sampling issues, but rather is due to the way precipitation processes are modeled.\u003c/p\u003e \u003cp\u003eIn convective parameterizations, the convective adjustment timescale is a key parameter to control the intensity of parameterized convection by regulating the timescale for the consumption rate of convective available potential energy. Kooperman et al. (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) tested the effects of convective adjustment timescale on precipitation distributions using CCSM4 with the ZM convection scheme. They showed that a bimodal distribution appears in a simulation with a longer (~\u0026thinsp;100 minutes) convective adjustment timescale, but is mitigated when the timescale is shortened (~\u0026thinsp;30 minutes). In the longer convective timescale simulation, the bimodality originates from the combination of the convective precipitation on lighter frequencies and the large-scale precipitation on heavier frequencies. On the other hand, shortening the convective adjustment timescale has an effect on shifting the convective precipitation distribution to the right (heavier side) and the large-scale precipitation distribution to the left (lighter side), which increases moderate precipitation frequency \u0026ndash; that is, where the trough in the distribution normally exists. This result suggests that the convective adjustment timescale in convective parameterizations could be an effective controlling factor to mitigate bimodality in simulated precipitation distributions, but could also result in unwanted trade-offs between precipitation distribution and mean state.\u003c/p\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eWe introduce a metric to objectively quantify bimodality in precipitation distributions and apply it to daily precipitation from multiple satellite-based products, reanalysis products, CMIP 5 and 6 models. While all satellite-based products used in this study do not exhibit bimodality in precipitation distributions, we find that all reanalysis products and approximately 83% of CMIP5 and 70% of CMIP6 models show bimodal distributions. The bimodal distribution generally originates in two different ways \u0026ndash; first, from the combination between parameterized subgrid-scale convective precipitation and resolved grid-scale precipitation, and second, from parameterized subgrid-scale convective precipitation alone. The first one supports the findings from previous studies that identify bimodality in a single model (e.g., Lin et al. \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Kooperman et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), and the second one is newly revealed in our study with multi-model analysis.\u003c/p\u003e \u003cp\u003eThe magnitude and sign of bimodality in CMIP models do not appear to be related to the provenance of convective parameterizations, which indicates that bimodality is likely sensitive to the retuning or modification of the parameterization. The ZM collection shows the largest spread in bimodality among all convective parameterization collections we analyzed. This is likely a consequence of the ZM convection scheme being widely used, and subsequently modified or retuned in different ways across many modeling centers. Intercomparison of GSRMs with or without a convective parameterization indicates that a deep convective parameterization is the main cause of bimodal precipitation distributions and implies that reducing the portion of parameterized convection could help mitigate the bimodal precipitation distribution.\u003c/p\u003e \u003cp\u003eThe bimodal distribution in simulated precipitation is primarily associated with an exaggerated drizzling bias. Drizzling can modulate soil aridness, which is an important factor in the Earth system influencing wildfire outbreaks, vegetation growth, freshwater resources, etc. To improve model simulations, it is fundamental to objectively quantify model biases and identify the origins of the biases. The current study is the first to propose a bimodality metric for precipitation distributions and investigate the origin of bimodality in a multi-model dataset. Our multi-model analysis results provide insights that the bimodality could be mitigated as follows; i) reducing the portion of convective parameterization with a horizontal resolution of several kilometers (insight from the comparison of DYAMOND simulations with or without a convective parameterization, IFS_4km vs IFS_9km, and MPAS_3.75km vs MPAS_7.5km), ii) implementing more realistic processes into convective parameterization, such as including cold pool processes (insight from the comparison of IPSL-CM5A-LR vs IPSL-CM5B-LR) and coupling between convection and ambient environmental moisture (insight from the comparison of GFDL-CM3 vs GFDL-CM4), and iii) tuning a parameter controlling convective adjustment time scale in convective parameterization (insight from the result of Kooperman et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Although it is hard to rule out the possibility that these changes could drive unwanted trade-offs, we would propose that these will be good directions of investigation to possibly mitigate bimodal distributions or drizzling bias in simulated precipitation for next-generation models.\u003c/p\u003e"},{"header":"5. Data and Methods","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e5.1. Data\u003c/h2\u003e \u003cp\u003eWe analyze daily total precipitation and convective precipitation from all available realizations of AMIP contributed to CMIP5 (Taylor et al. \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) and CMIP6 (Eyring et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e lists the CMIP models providing both total and convective precipitation and their default deep convective parameterization schemes. Note that many CMIP models may use different tuning parameters and formulations for certain processes, even though they use the same default scheme (e.g. ZM scheme). We evaluate the most recent 20 years (1985\u0026ndash;2004) that both CMIP5 and CMIP6 models have in common. To investigate the role of convective parameterizations on bimodal precipitation distributions, we use global storm-resolving models (GSRMs) with and without a convective parameterization, made available via the DYAMOND summer protocol (Stevens et al., 2019). The DYAMOND model simulations and their convective parameterizations are listed in Table S2. The simulation period is 40 days (1 August \u0026minus;\u0026thinsp;10 September 2016); we analyze the last 38 days to avoid the initial shock of the simulation following Ma et al. (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAs reference data for model evaluation, we use daily precipitation from 5 satellite-based products (IMERG, TRMM, CMORPH, GPCP, and PERSIANN) and 6 atmospheric reanalyses (ERA5, ERA-Interim, MERRA2, MERRA, CFSR, and JRA-55). The information on the 5 satellite-based and 6 reanalysis precipitation products is summarized in Table S3. We analyze data periods available via obs4MIPs and CREATE-IP as follows: 2001\u0026ndash;2020 for IMERG, 1998\u0026ndash;2018 for TRMM, 1998\u0026ndash;2012 for CMORPH, 1997\u0026ndash;2020 for GPCP, 1984\u0026ndash;2018 for PERSIANN, 1979\u0026ndash;2018 for ERA5, 1979\u0026ndash;2017 for ERA-Interim, 1980\u0026ndash;2018 for MERRA2, 1979\u0026ndash;2015 for MERRA, 1979\u0026ndash;2018 for CFSR, and 1979\u0026ndash;2018 for JRA-55. As in previous studies evaluating simulated precipitation in CMIP 5 and 6 models (e.g., Fiedler et al. 2020; Tang et al. \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Ahn et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), all CMIP models and observational data are regridded to 2x2 degrees with a conservative method for a fair comparison. In analyzing DYAMOND model simulations, the DYAMOND model and observational data are regridded to 1x1 degrees as in Ma et al. (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e5.2. Methods\u003c/h2\u003e \u003cp\u003eWe calculate precipitation frequency distribution for total precipitation, and where possible parameterized convective-scale and resolved large-scale precipitation. Following Pendergrass and Hartmann (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), Pendergrass and Deser (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), and Ahn et al. (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), we set logarithmically-spaced bins with each successive bin 7% wider than the adjacent previous bin. We then obtain the total precipitation frequency distribution that corresponds to the number of days in each bin normalized by the total number of days. To obtain frequency distributions for convective and large-scale precipitation, we use the following analysis procedure: i) calculate amount distributions, the sum of precipitation amount in each bin normalized by the total number of days, for total precipitation and convective precipitation, respectively, as a function of total precipitation bins; ii) save the ratio of convective precipitation amount to total precipitation amount in each precipitation bin; iii) obtain frequency distribution for convective precipitation by multiplying the ratio of convective precipitation to total precipitation amount in each precipitation bin; iv) obtain frequency distribution for large-scale precipitation by subtracting the convective precipitation from total precipitation in frequency distributions. With this process, each bin of total precipitation distribution can be exactly separated by the ratio of the convective or the large-scale precipitation to the total precipitation.\u003c/p\u003e \u003cp\u003eThe bimodality metric is formulated based on the two bimodal peaks and an intermodal minimum in the frequency distribution or PDF of daily total precipitation (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea):\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$Bimodality=\\frac{PDF\\left(lower peak\\right) - PDF\\left(intermodal minimum\\right)}{PDF\\left(taller peak\\right)}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe peaks are identified by finding where the gradient of the distribution curve is zero after smoothing the distribution curve by a Savitzky-Golay smoothing filter (Savitzky and Golay \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1964\u003c/span\u003e). The metric is based on the ratio of the lower peak to the taller peak, with the lower peak set to the difference from the intermodal minimum. If there are more than two peaks, the calculation algorithm first identifies the deepest intermodal minimum, and then finds the tallest peak on the left and right side from the deepest intermodal minimum. Given the formulation, the metric values can vary from 0 (no bimodality) to 1 (maximum bimodality). The metric is designed to be able to identify the taller peak between two peaks \u0026ndash; the sign of the metric value is positive or negative if the right or left peak is taller. Therefore, this metric can be used in both its absolute value form and in the left/right peak distinguishing form; The absolute value gives us a sense of the bimodality magnitude and the sign of the bimodality tells us whether the taller peak is at a lighter or heavier precipitation rate.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003ch2\u003eData availability\u003c/h2\u003e\n\u003cp\u003eAll of the data used in this study are publicly available. The satellite-based precipitation products used in this study (IMERG, TRMM, CMORPH, GPCP, and PERSIANN) and ERA5 precipitation product are available on the Obs4MIPs at https://esgf-node.llnl.gov/projects/obs4mips/. The other reanalysis precipitation products (ERA-Interim, MERRA2, MERRA, CFSR, and JRA-55) are available on the Collaborative REAnalysis Technical Environment (CREATE-IP) at https://esgf-node.llnl.gov/projects/create-ip/. The CMIP data is available on the ESGF at https://esgf-node.llnl.gov/projects/esgf-llnl. The DYAMOND data is archived by the DKRZ and available through the ESiWACE at https://www.esiwace.eu/services/dyamond.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003eCode availability\u003c/h2\u003e\n\u003cp\u003eThe bimodality metic code is available via the collection of precipitation distribution metrics in the PCMDI Metrics Package (PMP, https://github.com/PCMDI/pcmdi_metrics, DOI: 10.5281/zenodo.7231033).\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003eAcknowledgments\u003c/h2\u003e\n\u003cp\u003eThis work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. The efforts of the authors were supported by the Regional and Global Model Analysis (RGMA) program of the United States Department of Energy\u0026apos;s Office of Science. We acknowledge the World Climate Research Programme\u0026rsquo;s Working Group on Coupled Modeling, which is responsible for CMIP, and we thank the climate modeling groups for producing and making available their model output, the Earth System Grid Federation (ESGF) for archiving the output and providing access, and the multiple funding agencies who support CMIP and ESGF. The U.S. Department of Energy\u0026rsquo;s Program for Climate Model Diagnosis and Intercomparison (PCMDI) provides coordinating support and led the development of software infrastructure for CMIP.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003eAuthor contributions\u003c/h2\u003e\n\u003cp\u003eM.A., P.U., J.L., P.G. conceived the idea and M.A. and H.M. performed the analysis. M.A., P.U., J.L., P.G., H.M., C.T., P.B., A.O contributed to the discussion and wrote the manuscript. M.A., J.L., A.O implemented the code to the PCMDI Metrics Package.\u003c/p\u003e\n\u003ch2\u003eCompeting interest\u003c/h2\u003e\n\u003cp\u003eThe authors declare no competing interests.\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAhn, M.-S., P. A. Ullrich, P. J. Gleckler, J. Lee, A. C. Ordonez, and A. G. Pendergrass, 2023: Evaluating Precipitation Distributions at Regional Scales: A Benchmarking Framework and Application to CMIP 5 and 6 Models, EGUsphere [preprint], \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.5194/egusphere-2022-1106\u003c/span\u003e\u003cspan address=\"10.5194/egusphere-2022-1106\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, 2022.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAhn, M.-S., P. J. Gleckler, J. Lee, A. G. Pendergrass, and C. 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Model Description, Sensitivity Studies, and Tuning Strategies. J. Adv. Model. Earth Syst., 10, 735\u0026ndash;769, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/2017MS001209\u003c/span\u003e\u003cspan address=\"10.1002/2017MS001209\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-climate-and-atmospheric-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npjclimatsci","sideBox":"Learn more about [npj Climate and Atmospheric Science](http://www.nature.com/npjclimatsci/)","snPcode":"41612","submissionUrl":"https://submission.springernature.com/new-submission/41612/3","title":"npj Climate and Atmospheric Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-2874349/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2874349/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBimodality in precipitation frequency distributions is often evident in atmospheric models, but rarely in observations. This study i) proposes a metric to objectively quantify the bimodality in precipitation distributions, ii) evaluates model simulations contributed to the Coupled Model Intercomparison Project (CMIP) phase 5 (CMIP5), phase 6 (CMIP6), and the DYnamics of the Atmospheric general circulation Modeled On Non-hydrostatic Domains (DYAMOND) project by comparing them to satellite-based and reanalysis precipitation products, and iii) investigates the origin of bimodal precipitation distributions. Our results reveal that about 83% of CMIP5 and 70% of CMIP6 models used in this study exhibit bimodal distributions. The few DYAMOND models that use a deep convective parameterization also show bimodal distributions, while most DYAMOND models do not. Predictably, the bimodality mainly originates from the separation of precipitation process between resolved grid-scale and parameterized subgrid-scale. However, in some models bimodality arises from the parameterized subgrid-scale convective precipitation alone.\u003c/p\u003e","manuscriptTitle":"Bimodality in Simulated Precipitation Frequency Distributions and Its Relationship with Convective Parameterizations","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-06-01 14:53:17","doi":"10.21203/rs.3.rs-2874349/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"revise","date":"2023-07-25T05:21:52+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"This content is not available.","date":"2023-07-12T11:47:26+00:00","index":2,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2023-06-28T14:35:07+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2023-06-27T16:43:55+00:00","index":3,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2023-06-13T13:03:29+00:00","index":2,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2023-05-31T08:24:04+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewersInvited","content":"","date":"2023-05-30T15:28:24+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2023-05-05T12:06:12+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2023-05-05T03:04:16+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Climate and Atmospheric Science","date":"2023-05-04T22:50:56+00:00","index":"","fulltext":""},{"type":"checksFailed","content":"","date":"2023-05-04T10:59:43+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-climate-and-atmospheric-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npjclimatsci","sideBox":"Learn more about [npj Climate and Atmospheric Science](http://www.nature.com/npjclimatsci/)","snPcode":"41612","submissionUrl":"https://submission.springernature.com/new-submission/41612/3","title":"npj Climate and Atmospheric Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"eebb122e-44bc-4d14-a31a-b70b77f858c9","owner":[],"postedDate":"June 1st, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":21954763,"name":"Earth and environmental sciences/Climate sciences/Atmospheric science"},{"id":21954764,"name":"Earth and environmental sciences/Hydrology"}],"tags":[],"updatedAt":"2024-06-16T07:06:57+00:00","versionOfRecord":{"articleIdentity":"rs-2874349","link":"https://doi.org/10.1038/s41612-024-00685-3","journal":{"identity":"npj-climate-and-atmospheric-science","isVorOnly":false,"title":"npj Climate and Atmospheric Science"},"publishedOn":"2024-06-15 04:00:00","publishedOnDateReadable":"June 15th, 2024"},"versionCreatedAt":"2023-06-01 14:53:17","video":"","vorDoi":"10.1038/s41612-024-00685-3","vorDoiUrl":"https://doi.org/10.1038/s41612-024-00685-3","workflowStages":[]},"version":"v1","identity":"rs-2874349","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2874349","identity":"rs-2874349","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}