We analyze subdaily continental convective precipitation data relative to the Southeastern U.S. from gridded rain gauge measurements, conventional global climate models (GCMs) from the Coupled Model Intercomparison Project Phase 5 (CMIP5) archive, and a multiscale GCM. GCMs react too quickly to local convective instability and, therefore, overestimate the incidence of middle rainfall events and underestimate the incidence of no, little, and heavy rainfall events. Moreover, GCMs overestimate the persistence of heavy precipitation and underestimate the persistence of no and light precipitation. In general, GCMs with suppression mechanisms in the treatments of convective precipitation compare best with rain gauge derived data and should be trusted more than the others when assessing the risk from extreme precipitation events. The multiscale GCM has the best estimate of the diurnal cycle and a good estimate of heavy rainfall persistence.
 It is difficult to quantify the cost of extreme climatic event impacts on human population [IPCC, 2012, section 4.5.4], but it is certain that extreme events result in severe damage to property, destruction of environment, and loss of life. We have studied the characteristics of extreme rainfall that causes floods and landslides. Its occurrence is underestimated in Global Climate Models (GCM) [Stephens et al., 2010], and this bias can affect decisions at both the individual and the community level.
 Rainfall estimates in GCMs depend on the theoretical treatment of several atmospheric and surface physical processes. Though many processes contribute to rainfall, heavy rainfall is mainly due to cloud cumulus convection (CC). This physical process has been approached in different ways to make it operationally affordable [Arakawa, 2004]. Our goal is to investigate which approaches best estimate the observed frequency distribution of heavy rainfall by analyzing data from conventional GCMs that have different CC parameterizations and from a multiscale GCM which resolves cloud processes explicitly and has been shown to compare better to observations [Li et al., 2012].
 Our case study is the well-populated and highly convective [Higgins et al., 2011] Southeastern U.S. between the latitudes 30 and 40°N and longitudes 265 and 280°E. We analyze the months from May to August for the years 1996–2001 of the Climate Prediction Center (CPC) spatially gridded hourly rainfall rate estimates from rain gauges [Higgins et al., 2000] of Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations [Taylor et al., 2012] and of a conventional and a multiscale GCM [Rosa et al., 2012] forced with meteorological National Centers for Environmental Prediction (NCEP) reanalysis [Kalnay et al., 1996]. Nomenclature and descriptions are in Table 1.
Table 1. Observational and Simulated Data Sources and Descriptionsa
aThe suffixes CTM, A, and H for the simulation Name stand for chemical transport mode (forced with NCEP), AMIP (forced sea ice and surface temperature), and historical (prescribed realistic atmospheric composition), respectively. CAPE and RH stand for convective available potential energy and relative humidity, respectively. Mass flux refers to the vertical component. As we have not been able to find the details of the mass flux closure for ACCESS1-3_A, we will include this GCM in the analysis without discussing its behavior.
Climate Prediction Center of National Oceanic and Atmospheric Administration (USA). Gridded rain gauge data. [Higgins et al., 2000]
Center for Multiscale Modeling of Atmospheric Processes (USA). Explicit simulation of cloud processes on a two-dimensional Cloud Resolving Model. Mass flux from buoyancy. [Rosa et al., 2012]
National Center for Atmospheric Research (USA). CAPE from undiluted plume. Mass flux from quasi-equilibrium assumption and fixed time scale for CAPE consumption. No inhibition/suppression. [Rosa et al., 2012]
Commonwealth Scientific and Industrial Research Organization and Bureau of Meteorology (Australia). Described as “CAPE closure scheme based on relative humidity” from a personal communication with Hirst, T. (CSIRO, Australia).
Beijing Normal University. CAPE from undiluted plume. Mass flux from quasi-equilibrium assumption and fixed time scale for CAPE consumption. No inhibition/suppression. (http://esg.bnu.edu.cn/BNU_ESM_webs/htmls/)
CAM4 National Center for Atmospheric Research (USA). CAPE from entraining plume. Mass flux from quasi-equilibrium assumption and fixed time scale for CAPE consumption. No inhibition/suppression. [Gent et al., 2011]
Centro Euro-Mediterraneo per I Cambiamenti Climatici (Italy). CAPE from undiluted plume. Mass flux from resolution dependent time scale for CAPE consumption. Positive subcloud layer moisture convergence requirement. [Scoccimarro et al., 2011]
Centre National de Recherches Meteorologiques (France). Mass flux from in-cloud minus environment moist static energy and positive subcloud layer moisture convergence requirement. [Voldoire et al., 2013]
Geophysical Fluid Dynamics Laboratory (USA). CAPE from undiluted plume. Mass flux from fixed time scale CAPE consumption. CAPE relaxed to positive value. [Donner et al., 2011]
Met Office Hadley Centre (UK). Mass flux empirical formulation proportional to initial parcel buoyancy in excess of a threshold. [Martin et al., 2011]
Japan Agency for Marine-Earth Science and Technology (Japan). CAPE from undiluted plume. Mass flux from quasi-equilibrium assumption and fixed time scale for CAPE consumption. Suppression if less than RH threshold. [Watanabe et al., 2011]
Beijing Climate Center (China). Free troposphere CAPE from undiluted plume. Mass flux from quasi-equilibrium assumption and fixed time scale for CAPE consumption. Suppression if less than RH threshold. [Wu, 2012]
 Simulated data are 3-hourly or they are linearly interpolated in time from lower frequency values, then they are linearly interpolated in space to the 2°×2.5° CPC grid. CPC is averaged to 3-hourly.
 Although CPC has biases deriving from instrumental errors and analytical methods for gridding unevenly spaced point source measurements [Higgins et al., 2011], we believe it is the best available observational data for the analysis we present here.
 We test the sensitivity of rainfall to atmospheric instability estimated here with Δθv=θvSfc−θv850, where , T is temperature, q is specific humidity, p is pressure, and Ra and cp are gas constant and specific heat of air. Subscripts Sfc and 850 stand for surface and 850 hPa.
 CPC reports only rainfall greater than ∼1 mm/day, hence, we set to zero all rainfall below 1 mm/day in simulations. This produces a deficiency between 1 and 4% in total rainfall.
 For each data set, we use for all the precipitation events (about 370K points) and for the events in the upper 90th percentile of Δθv which we consider the subset with high atmospheric instability to CC.
2.1 Rainfall Diurnal Cycle
 CPC diurnal partitioning of average rainfall differs between the northern and southern regions of our case study area (Figure 1). For the entire area, the diurnal cycle is similar to the cycle in the southern region but weaker. In the southern region (30 to 34°N) rainfall peaks around 18:00 and reaches its minimum, half of its maximum, at 3:00. In the northern region (36 to 40°N), the diurnal cycle is very weak with a maximum at 6:00 being about 10% more than its minimum at noon. Simulations have a stronger diurnal cycle which is similar between the regions, and they have a lead on CPC of 3 to 6 h. Simulations are more synchronous to the development of convective instability and continue to produce an early onset bias [Dai, 2006]. SPC_CTM is overall more similar to CPC but does not differ qualitatively between the regions. The bcc-csm1-1-m_A fails to reproduce the diurnal cycle of rainfall in the southern region but is the model that does best for the northern region. CAM3.5_CTM and BNU-ESM_A differ even though they share the same parameterization for CC. The reanalysis data forced CAM3.5_CTM estimates a weaker diurnal cycle. In this simulation, local surface evaporation and the profiles of temperature and horizontal winds are prescribed, whereas in BNU-ESM_A, CC is free to interact with the large-scale environment.
2.2 Rainfall Intensity
 Simulations estimate higher average rainfall in comparison to CPC (Figure 2, top). In relative terms, the bias is greater for , hence, it increases with atmospheric instability (Figure 2, middle). For , simulated rainfall is primarily from CC rather than stratiform rainfall (Figure 2, bottom). The fraction of convective rainfall decreases for but remains large, between 50 and 80%. Such partitioning is not available for SPC_CTM and CPC but Yang and Smith [2008, Figure 5] estimate a zonal continental value from satellite measurements. The simulations analyzed here capture the increase of the convective component between spring and summer (not shown) but overestimate absolute amounts and differ greatly among each other, especially for .
 For CPC, all rainfall intensities larger(smaller) than 1 mm/day occur more frequently for () than for () (Figure 3). Only a few simulations show this feature. In general, the sensitivity of rainfall intensities to atmospheric instability is higher for simulations than for CPC. There are appreciable biases for to the extent that the frequency of rainfall is overestimated for middle intensity, between 1 and 10 mm/day, and underestimated below(above) 1(50) mm/day of intensity (Figure 3, right). These biases become larger for : the higher the convective instability, the greater the biases from simulations.
 Our findings are consistent with the results for a larger region from Dai . However, the difference is the following: for our case study, it is the frequency of rainfall between 1 and 10 mm/day that is overestimated, whereas the frequency of lighter rainfall is underestimated.
2.3 Rainfall Persistence
 For each atmospheric column, we calculate the ratio between the number of times a 3-hourly rainfall rate greater than or equal to 75 mm/day is repeated multiple times within 1 following day, to the total number of 75 mm/day events. We do similar calculations for the persistence of light rainfall for events smaller than or equal to 1 mm/day repeated multiple times within 5 following days. The threshold values are discretional, hence, these results need to be evaluated in relation to the frequencies of rainfall intensities (Figure 3). We have chosen 1 and 75 mm/day, because the former is the lower limit reported by CPC and the latter is the highest value that allows a nonzero persistence measure for all models. In general, the persistence of heavy(light) rainfall is overestimated(underestimated) by simulations (Figure 4). SPC_CTM heavy rainfall persistence compares better than the other simulations to CPC, whereas light rainfall persistence is estimated accurately in several simulations—bcc-csm1-1-m_A, CMCC-CM_A, CNRM-CM5_A, and HadGEM2-A_A. The greatest differences among GCMs occur for a persistence of little rainfall of 3.5 days.
 Different surface energy balances and moisture convergences for the case study region could partly explain the differences in average rainfall among data sets. However, this will not be discussed and not assumed to have implications for the discussion of the diurnal cycle, intensity distribution, and persistence of rainfall.
 We have shown that the frequency of GCMs subdaily rainfall estimates are not conservative with respect to potentially harmful extreme events. Moreover, these estimates become less reliable in conditions that are, in principle, more conducive to CC. Therefore, despite the fact that many processes contribute to rainfall estimates in GCMs, we discuss our findings in relation to the key assumptions present in the CC parameterizations vertical mass flux closures of the GCMs we surveyed, as rainfall rates ultimately depend on the amount of humidity exceeding saturation in the vertical flux of atmospheric air.
 GCMs with mass flux closures based on CAPE consumption at fixed time scales with no suppression mechanisms—CAM3.5_CTM, BNU-ESM_A, CCSM4_A, GFDL-CM3_H (Table 1)—have the largest bias in that they greatly overestimate middle intensity rainfall and underestimate light and heavy rainfall (Figure 3). Among these GCMs, CCSM4_A and GFDL-CM3_H have smaller biases. This may be due to using an entraining plume formulation for CAPE for CCSM4_A and to setting a CAPE relaxation target of 1000 j/Kg (10 to 20% of the severe to most severe weather events) for GFDL-CM3_H. Both approaches should, on average, favor accumulation of convective instability, hence reducing the incidence of middle rainfall events and increasing the incidence of no, little, and heavy rainfall events. GCMs with mass flux closures based on CAPE consumption at fixed time scales and suppression mechanisms based on relative humidity (RH) thresholds—MIROC-ESM_H and bcc-csm1-1-m_A—or with a resolution dependent CAPE consumption time scale and a suppression mechanism allowing CC only in case of positive low level moisture convergence—CMCC-CM_A—have overall smaller biases. Similarly, CNRM-CM5_A, which utilizes a mass flux closure based on the difference between in-cloud and environmental moist static energy and requires positive environmental low level moisture convergence, has a smaller bias compared to GCMs with no suppression mechanism. HadGEM2-A_A's mass flux closure is calculated from an empirical formula for the excess buoyancy of the cloud against the environment and includes a threshold value. This model also has a smaller bias than CAPE based GCMs with no suppression mechanisms. Our general conclusion is that subdaily rainfall frequency intensity is better estimated by GCMs with suppression mechanisms or threshold values that prevent CC from responding too rapidly to atmospheric instability.
 The GCM with explicit cloud treatment—SPC_CTM—can simulate the diurnal cycle of average rainfall better that the other GCMs (Figure 1, top). This has already been shown in a similar case study and attributed to its ability to simulate the energy transfer from the surface to CC at a slower, more realistic, rate [Demott et al., 2007]. Nonetheless, SPC_CTM does not capture the weakening of the diurnal cycle observed for CPC from moving from the southern to the northern region of our case study. Instead, SPC_CTM is qualitatively similar to the other GCMs, though to a smaller degree, that is, SPC_CTM is too responsive to local instability (Figure 1, bottom). This is also supported by the fact that SPC_CTM overestimates middle intensity rainfall and underestimates little and heavy rainfall (Figure 3). From the reanalysis data, we estimate a difference of about 1 m/s for the 850 hPa horizontal wind, from 7 m/s for the southern region to 8 m/s for the northern region. Surface level and 850 hPa relative humidities look similar between regions. Vertical wind shear is thought to have an effect on the organization of CC, hence, the difference we estimate could be a reason for the different diurnal cycles. Nonetheless, SPC_CTM, which in principle should allow a more realistic simulation of cloud organization, fails to replicate a flatter diurnal cycle in the northern region. One possible cause of this bias may be related to the two-dimensional character of the cloud resolving model (CRM) embedded in SPC_CTM. Two-dimensional CMRs entrain less environmental air than three-dimensional CRMs, and they are more likely to develop convective updrafts [Petch et al., 2008], which might override possible inhibiting factors including vertical wind shear.
 From the analysis of the heavy rainfall persistence, we have not found a particular clustering of model behaviors that can be attributed to their CC closures. In general, the GCMs analyzed here overestimate the persistence of heavy rainfall (Figure 4, top). Recalling that rainfall heavier than the heavy rainfall persistence threshold (75 mm/day) occurs less frequently in GCMs (Figure 3) suggests the following speculation: locally, GCM CC does not consume atmospheric instability as fast as the real atmosphere does and GCMs create the conditions for heavy but not extreme rainfall too often. The implications for regional landslide and flood risk estimates may be important, because in some locations, the surge in rainfall water that impinges on the ground may be underestimated, and in others, the total amount of rainfall water within, for instance, a day may be overestimated.
 The persistence of little rainfall is best estimated by GCMs with suppression mechanisms; however, in general, GCMs underestimate the persistence of light rainfall (Figure 4, bottom). For some regions, this could mean underestimating the risk of drought for farming and natural ecosystems and should be a reason for concern.
 From satellite remote sensing data, it is possible to estimate instantaneous values of rainfall and some related atmospheric field including the partitioning between convective and stratiform rainfall. We hope that public GCM archives will provide corresponding simulated data and diagnostics emulating satellite retrievals at high time resolution.
 This material is also supported by the National Science Foundation Science and Technology Center for Multiscale Modeling of Atmospheric Processes CMMAP, managed by Colorado State University under cooperative agreement ATM-0425247.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.