Improved Diurnal Cycle of Precipitation in E3SM With a Revised Convective Triggering Function

Abstract

We revise the convective triggering function in Department of Energy's Energy Exascale Earth System Model (E3SM) Atmosphere Model version 1 (EAMv1) by introducing a dynamic constraint on the initiation of convection that emulates the collective dynamical effects to prevent convection from being triggered too frequently and allowing air parcels to launch above the boundary layer to capture nocturnal elevated convection. The former is referred to as the dynamic Convective Available Potential Energy (dCAPE) trigger and the latter as the Unrestricted Launch Level (ULL) trigger. Compared to the original trigger in EAMv1 that initiates convection whenever CAPE is larger than a threshold, the revised trigger substantially improves the simulated diurnal cycle of precipitation over both midlatitude and tropical lands. The nocturnal peak of precipitation and the eastward propagation of convection downstream of the Rockies and over the adjacent Great Plains are much better captured than those in the default model. The overall impact on mean precipitation is minor with some notable improvements over the Indo‐Western Pacific, subtropical Pacific and Atlantic, and South America. In general, the dCAPE trigger helps to better capture late afternoon rainfall peak, while ULL is key to capturing nocturnal elevated convection and the eastward propagation of convection. The dCAPE trigger also primarily contributes to the considerable reduction of convective precipitation over subtropical regions and the frequency of light‐to‐moderate precipitation occurrence. However, no clear improvement is seen in intense convection and the amplitude of diurnal precipitation.

Introduction

Precipitation is one of the most important variables simulated in a climate model. It exhibits pronounced diurnal variability with distinct regional and seasonal features. The diurnal cycle is strong over land during summer with peak occurring in late afternoon or at midnight, mainly resulting from the strong diurnal cycle of solar heating and boundary layer properties that modulate convection activities (e.g., Dai et al., ; Riley et al., ; Wallace, ). In contrast, the diurnal cycle over ocean is relatively weak with the maximum precipitation often observed in the early morning associated with cloud top radiative cooling and propagation of mesoscale convective systems (MCSs; Dai, ; Imaoka & Spencer, ).

The diurnal cycle of precipitation is one fundamental mode of climate variability that climate models need to accurately simulate. It has significant effects on surface energy budget and hydrology and largely controls the surface temperature. The diurnal cycle of precipitation is an excellent measure of how well climate models simulate not only the total amounts of precipitation but also its frequency, intensity, and duration, which all have important climate impact (Trenberth et al., ). It therefore serves as a benchmark for climate models (Covey et al., ). In addition, the diurnal cycle of precipitation is also widely used as a testbed for evaluating model physics and understanding the underlining physical processes.

Current weather and climate models continue having difficulties in modeling the diurnal variation in precipitation (Covey et al., ; Lee et al., ). Over land, most models tend to rain too early after sunrise with a rainfall maximum around the local noon rather than the observed late afternoon peak and fail to capture the observed nocturnal peak (Dai, ; Lee et al., ). Over ocean, the diurnal cycle in most models is weak with peaks around 0200 local solar time (LST) compared to 0400–0600 LST in the observations (Dai, ). In general, models often rain too frequently at reduced intensity (Dai & Trenberth, ; Trenberth et al., ). Increasing model horizontal resolution seems to help slightly improve rainfall intensity, but it has little impact on the phase of the diurnal cycle of precipitation (Bacmeister et al., ; Dirmeyer et al., ; Lee et al., ; Tang et al., ). As indicated in Bacmeister et al. (), the improvement in rainfall intensity may be simply because individual precipitation events become more concentrated in higher‐resolution models. In addition, increasing model resolution leads to more precipitation being resolved as grid‐scale precipitation.

The problems in simulating the diurnal cycle of precipitation are associated with the inappropriate representation of the processes that control subdiurnal phenomenon like convection and phenomena with timescales around the order of several hours to a day, like MCSs. Over land the late afternoon peak is often associated with the transition from shallow to deep convection, which is strongly coupled with the local surface forcing (Zhang & Klein, ). In contrast, the nocturnal peak primarily results from nocturnal elevated convective systems associated with the eastward propagating mesoscale convective systems originating over mountain ranges that promote elevated heating of the troposphere, upslope circulations, and organized convergence, as well as the low‐level jet, a nighttime phenomenon that results from a large‐scale diurnal oscillation in boundary layer circulation centered over the Southern Great Plains (SGP; Carbone & Tuttle, ; Geerts et al., ; Marsham et al., ; Wallace, ). Over ocean the interaction between radiation and convection is believed to be an important factor for the diurnal variation of convection (Ruppert & Hohenegger, ). How to accurately represent these processes in parameterizations of moist convection poses a significant challenge for the climate modeling community.

Earlier studies highlighted that deficiencies in representing moist convection processes, in particular convection initiation, could account largely for the failure in capturing the diurnal cycle of precipitation in climate models (Dai & Trenberth, ; Lee et al., ). The model errors over land are thought to be associated with unrealistically strong coupling of convection to the surface heating, which is largely controlled by solar insolation in summer (Lee et al., ; Xie et al., ; Xie & Zhang, ; Zhang, , ). As a result, model convection is triggered too often and too early over land during the day particularly in the summer. The strong coupling of convection to surface heating is also partially responsible for the failure to capture nocturnal convection since nocturnal convection is often elevated and decoupled from the surface (Geerts et al., ; Marsham et al., ; Xie et al., ). It is also highly likely that certain biases in the diurnal cycle arise from errors in how convection initiation depends on lower free tropospheric water vapor and mesoscale organization. It has been suggested that the interaction between water vapor in the lower free troposphere and moisture convection, mainly by way of entrainment processes (Holloway & Neelin, ), is a primary control on the onset of deep convection.

Significant efforts have been made to improve the simulation of diurnal cycle of precipitation over different climate regimes through improvements to convective triggers in convection schemes for weather and climate models. The too frequent, too weak problem in model precipitation suggests that model convection responds too quickly to the diurnal cycle of surface heating, preventing the convective potential available energy (CAPE) from accumulating and intense rainfall from occurring at a later time. To reduce the strong surface control on model convection initiation and prevent CAPE from being released spontaneously, many studies attempted to link convective trigger to the large‐scale dynamic processes (e.g., low‐level convergence) since these processes play a key role in destabilizing the atmospheric structure and initiating moist convection. For instance, the Kain‐Fritsch scheme described in Kain and Fritsch () and Kain () linked convective trigger to the large‐scale low‐level convergence to help prevent excessive convection in areas where the low‐level upward motion is weak. Explicitly linking the convective triggering to the large‐scale vertical velocity was made in convection schemes used in an earlier version of the European Centre for Medium‐Range Weather Forecasts model (Bechtold et al., ) and the National Centers for Environmental Prediction (NCEP) Global Forecast System model (Han & Pan, ) to improve the time of peak precipitation. Xie and Zhang () and Xie et al. () introduced an empirical dynamic constraint, the dynamic CAPE generation rate (dCAPE) determined by the large‐scale advective tendencies of both temperature and moisture to control the onset of moist convection. The dCAPE trigger can be considered as an empirical large‐scale parameterization of the dynamical triggering processes, including large‐scale upward motion and warm and moist advection in the low levels. Bechtold et al. () made the European Centre for Medium‐Range Weather Forecasts model more sensitive to environment moisture to improve the simulation of model variability including the diurnal cycle of precipitation. Zhang () found that making model convection directly respond to the tropospheric forcing could significantly improve the diurnal cycle of precipitation in a single‐column framework. Lee et al. (), Han and Pan (), and Wang et al. () suggested that allowing the air parcel launch level above the boundary layer is a key for weather and climate models to capture nocturnal elevated convection over the central Great Plains. Recently, Suhas and Zhang () and Song and Zhang () tested several commonly used convective triggering mechanisms (including some mentioned here) against data collected from the U.S. Department of Energy (DOE)'s Atmospheric Radiation Measurement (ARM) program and found that the dCAPE trigger as originally introduced in Xie and Zhang () has the overall best performance in capturing convection initiation for the metrics used in their studies. Sakaguchi et al. () applied the dCAPE trigger to CAM5 that resulted in an improvement in both nocturnal and late afternoon precipitation amount over the Amazon region.

Based on these earlier studies, this study proposes a new convective triggering function by combining the dCAPE trigger developed in Xie and Zhang () and the Unrestricted air parcel Launch Level (ULL) trigger described in Wang et al. () to improve convection initiation in climate models. Particularly, this new trigger is aimed to address two key issues with current modeling of the diurnal cycle of precipitation: (1) model convection is often triggered too often and too quickly with largely reduced intensity and (2) most models fail to capture nocturnal elevated convection. For the first, the dCAPE trigger provides a dynamic constraint for preconditioning of convection‐favoring environment to establish and prevent CAPE from being released spontaneously. Therefore, it relaxes the strong coupling of convection to surface heating and allows CAPE to be accumulated for later and stronger convection. For the second, the ULL trigger removes the constraint that convection always has its root within the boundary layer as often assumed in deep convection schemes, such as the Zhang‐McFarlane scheme (Zhang & Mcfarlane, ), and allows atmospheric instability above the boundary layer to be detected for capturing nocturnal elevated convection systems, which often occur from moist conditionally unstable layers located above the stable boundary layer (Marsham et al., ). A separate study showed that the revised trigger agreed well with observations collected from ARM at its midlatitude and tropical sites. It was able to capture the nocturnal elevated convection systems observed over the ARM SGP site in a single‐column model test with the U.S. DOE's Energy Exascale Earth System Model (E3SM; Golaz et al., ).

The current study emphasizes the testing of the dCAPE&ULL trigger in the full E3SM Atmosphere Model version 1 (EAMv1), which, like other climate models, also fails to properly capture the diurnal cycle of the precipitation (Rasch et al., ; Tang et al., ). The goal of the paper is to examine the impact of the new trigger on the characteristics of precipitation simulated in EAMv1 with a particular focus on its diurnal variability.

The paper is organized as the follows. Section provides detailed information about EAMv1 and the sensitivity experiments conducted in this study. The simulated characteristics of the mean precipitation and its global and regional features are briefly discussed in section . The impact of the revised trigger on the diurnal cycle of precipitation over different climate regimes is discussed in section . Conclusion and future work are given in section .

EAMv1 and Experiment Design

EAMv1

EAMv1 is the atmospheric component of the DOE's E3SM. The model was developed from the Community Atmosphere Model version 5.3 (CAM5.3; Neale et al., ) with notable changes to its physical parameterizations and using a much higher vertical resolution, which was increased from 30 layers (used in CAM5) to 72 layers and the model top extended to 60 km. The updated physics package includes a simplified third‐order turbulence closure parameterization (Cloud Layers Unified By Binormals) (Golaz et al., ; Larson, ; Larson & Golaz, ) that unifies the treatment of planetary boundary layer turbulence, shallow convection, and cloud macrophysics to remove the unrealistic separation among these physical processes, which is characteristic of most climate models. Cloud Layers Unified By Binormals are paired with the same deep convection scheme used in CAM5, which was developed by Zhang and McFarlane (; ZM hereafter) with a dilute CAPE modification by Neale et al. (), and an updated microphysics scheme, version 2 of Morrison and Gettelman (; MG2008; Gettelman & Morrison, ; Gettelman et al., ; MG2). Other major updates include improved cloud and aerosol physics. More details about EAMv1 are referred to Rasch et al. (), which provided an overview of the model. Given these changes, several tunable parameters used in CAM5.3 were retuned in EAMv1 to make the global radiative energy budget balance and produce a reasonable climate. Xie et al. () provided more detailed information about the model tuning. Sensitivity of EAMv1 to a number of its adjustable parameters is explored in Qian et al. (). EAMv1 simulated cloud and convective characteristics can be found in Xie et al. () and Zhang et al. ().

Experiment Design

The 1° resolution configuration of EAMv1 is used in this study. Table  lists the sensitivity experiments performed to investigate the impact of the revised trigger, as well as the individual contributions from dCAPE and ULL, on the simulated characteristics of precipitation and its diurnal cycle. Below we provide more details about the convective triggers tested in this study.

Summary of Model Experiments

Model ID	Description	Convective trigger	Reference
CNTL	Default low‐resolution (1°, 72 L) EAMv1	(1) CAPE >70 J/kg	Xie et al. ()
(2) The air parcel launch level is chosen within the boundary layer
dCAPE&ULL	CNTL with the dCAPE&ULL trigger	(1) CAPE >0	Xie and Zhang () and Wang et al. ()
(2) dCAPE >0
(3) The air parcel launch level is chosen between the surface and 600 hPa
dCAPE	CNTL with the dCAPE trigger only	(1) CAPE >0	Xie and Zhang ()
(2) dCAPE >0
(3) The air parcel launch level is chosen within the boundary layer
ULL	CNTL with the ULL trigger only	(1) CAPE >70 J/kg	Wang et al. ()
(2) The air parcel launch level is chosen between the surface and 600 hPa

The Default Trigger

A CAPE‐based trigger is used in current EAMv1 deep convection scheme (i.e., the ZM scheme), in which CAPE is determined with a dilute plume approximation (dilute CAPE) described in Neale et al. (). This method considers mixing of the reference parcel with the free troposphere through mixing of entropy properties in a proportion depending on an assumed the entrainment rate (0.7 × 10⁻³ m⁻¹) in CAPE calculation. In addition, the ZM scheme assumes that the launch level for the air parcel used for calculating the cloud top and associated CAPE is from the maximum moist static energy (MSE) level within the boundary layer, which is diagnosed based on bulk Richardson number following Holtslag and Boville (). A threshold value of 70 J/kg is used to control model convection initiation. That is, model deep convection occurs whenever the dilute CAPE is larger than 70 J/kg in EAMv1. In the implementation of ZM in EAMv1, whether deep convection finally occurs in the model is also dependent on the cloud function and closure. It should be noted that the increase of vertical resolution in EAMv1 also accompanies some adjustments to capeten, the number of negative buoyancy layers that deep convection can penetrate, and the lowest possible air parcel launch level above the model's bottom level liftlevel. capeten is used in the calculation of CAPE and determining the depth of deep convection. Since there is no quantitative information about the vertical extent or strength of stable regions (e.g., convective inhibition), this calculation is extremely resolution dependent. EAMv1 reduced this dependency by terminating the CAPE calculation when the parcel encounters a single negatively buoyant layer in the plume buoyancy calculation; that is, capeten is changed from its default setting 5 in CAM5 to 1 in EAMv1. In addition, liftlevel in ZM is lifted from the default setting 0 (the bottom model level, whose midpoint altitude is about 50 m) to 2 (two levels above the bottom, whose midpoint altitude is about 100 m). The additional model layers allow more variation in layer stability, relative humidity, and buoyancy to avoid water vapor being confined to the boundary layer due to the increase of vertical resolution. These adjustments have a large impact on tropical convection, resulting in substantially suppressed convection over the Tropical Western Pacific and the Eastern Pacific warm pool off the central American coast and enhanced precipitation over most tropical lands (including Amazon) and adjacent oceans as discussed in Xie et al. (). In the sensitivity tests conducted by this study we keep the setting for these two parameters the same as that used in the default EAMv1.

The dCAPE&ULL Trigger

The revised trigger contains two parts. The dCAPE trigger introduces an empirical dynamic constraint, the dynamic CAPE generation rate determined by the large‐scale advective tendencies of both the temperature and moisture, to control the onset of deep convection (Xie & Zhang, ). It assumes that deep convection occurs only when the large‐scale advection makes a positive contribution to the existing positive CAPE. This large‐scale dynamic constraint allows CAPE to be accumulated before convection occurs, and it also links model deep convection closely to the large‐scale dynamical processes, including large‐scale upward motion and low‐level moisture convergence. The dCAPE trigger can be considered as an empirical large‐scale parameterization of the dynamical triggering processes, including large‐scale upward motion, and warm and moist advection in the low levels. In addition, it emphasizes the continuation of convection after initiation; that is, convection can only be sustained when/if there is positive large‐scale forcing at a given time (i.e., under disturbed large‐scale conditions). As described in Xie and Zhang () and Suhas and Zhang (), the dCAPE is defined as [Image Omitted. See PDF]where (T, q) are the temperature and specific humidity of current environmental profile and (T^*, q^*) are (T, q) plus the changes due to the total large‐scale dynamical advection over a time interval Δt, which is equal to the time step used in numerical models. In the implementation to EAMv1, CAPE is calculated under the same dilute plume approximation as described in Neale et al. ().

The ULL trigger identifies the source layer for launching air parcel used in the calculation of cloud properties and rainfall based the maximum MSE intensity (Wang et al., ). In contrast to the default ZM assumption that the maximum MSE layer has to be in the boundary layer in ZM, the ULL trigger searches for the source layer from the surface to 600 hPa. This allows for both surface‐driven convection, as the default ZM scheme does, and elevated convection that is initially decoupled from the surface.

Eleven‐year AMIP‐style climatology runs with present‐day forcing from the Intergovernmental Panel on Climate Change (IPCC) AR5 emission data set (Lamarque et al., ) for year 2000 are conducted using present‐day emissions along with climatological sea surface temperature and sea ice prescribed from the observations (repeating seasonal cycle without interannual variability). The last 10 years from each run are analyzed and evaluated using various observational data sets as summarized in Table . Overall, the impact of the revised trigger on simulated mean climate is small. Without tuning, the residual of the radiative energy budget at the Top of Model (RESTOM) is 0.96 W/m² for the default model (CNTL), 1.3 W/m² for EAMv1 with the revised trigger (dCAPE&ULL), 1.67 W/m² for EAMv1 with the dCAPE trigger only (dCAPE), and 0.38 W/m² for EAMv1 with the ULL trigger only (ULL). This indicates that only a minor model retuning might be needed with the new triggers. To isolate the effect of the triggering mechanisms on model simulations, no model retuning is performed in this study.

Summary of Observations

Observation	Source	Geophysical quantity used in the analysis	Period	Reference
GPCP	Global Precipitation Climatology Project (GPCP) version 2.3	Monthly total precipitation rates	1981 to 2010	Adler et al. ()
GPCP1DD	Global Precipitation Climatology Project (GPCP) 1° daily data (GPCP1DD)	Daily total precipitation rates	1997–2013	Huffman et al. ()
TRMM	The Tropical Rainfall Measuring Mission (TRMM)	3‐hourly total precipitation rates	2000–2012	Huffman et al. ()

Characteristics of Mean Precipitation

Global Distributions

Figure  displays the annual mean Global Precipitation Climatology Project (GPCP) estimated precipitation (Adler et al., ), the biases against the observations from CNTL, and the differences between CNTL and the experiment runs with the revised convective triggers. Only the biases or differences statistically significant at the 95% confidence level are shown in the figure. The spatial correlations (CORR) and root‐mean‐square errors (RMSE) between the models and GPCP are also given in the figure to quantify model biases. In general, the impact of these changes in trigger on the simulated mean precipitation is small. The error pattern shown in Figure b is almost identical across all the models. They all produce excessive precipitation over large portions of the tropics but less precipitation over the central U.S. and South America compared to the GPCP observations. Compared to CNTL, the revised trigger (dCAPE&ULL) has a marginally higher correlation coefficient (CORR) with GPCP (0.91 versus 0.90), but it shows a slightly larger RMSE (1.03 mm/day versus 0.99 mm/day) likely due to the use of the dCAPE trigger. Although the slight degradation is seen in these globally averaged annual mean statistics with dCAPE, it produces some encouraging regional features over a few climate important regions as discussed below. It is interesting to see that ULL yields an overall better simulation compared to CNTL in terms of the global statistics.

Figures c–e more clearly show the impact of these modifications. The differences are statistically insignificant over most of regions. The revised trigger shows improvements over the equatorial and subtropical Pacific and Atlantic, the Indian peninsula and surrounding oceans, tropical eastern Indian Ocean, central U.S., and South America where the sign of the differences in Figure c is generally opposite to that shown in Figure b, suggesting a reduction of the mean precipitation biases in EAMv1. A slight degradation is seen in the northern Intertropical Convergence Zone (ITCZ) in the eastern Pacific and South Africa. These changes are primarily from the use of the dCAPE trigger (Figure d) given the similarity between Figures c and d in terms of both spatial pattern and magnitude. The dCAPE trigger reduces the large wet bias over the Bay of Bengal and the dry bias over the tropical eastern Indian Ocean considerably, but it degrades the model performance in the northern ITCZ in the eastern Pacific and South Africa. Over the Amazon basin where most climate models (including E3SMv1) show a dry bias (e.g., Yin et al., ), the impact of dCAPE is mixed. It reduces the dry bias over the south part of the Amazon, while it makes the dry bias worse over the north of the region. Although the effect of ULL on the mean precipitation is smaller than dCAPE, most changes arising from ULL are toward an improvement of the simulated precipitation, particularly over the Amazon basin (Figure e).

Precipitation Partitioning

Changes in convective and resolved scale precipitation partitioning could have a large implication on the vertical profiles of diabatic heating, which in turn affect the dynamical response of the environment to convection (e.g., Lin et al., ; Wu et al., ). They could also affect the precipitation intensity distributions as the overall too frequent, too weak model precipitation bias is largely caused by convection triggered too often and too quickly. Figure a displays the zonally averaged annual mean total precipitation from GPCP and different model configurations used in the experiment runs. The differences among different model configurations in total precipitation are small, while notable differences are seen in their convective‐to‐total precipitation ratios (Figure b). The convective precipitation fraction is reduced by ~20% to about 55–70% with the revised trigger over the subtropical region in both hemispheres. We note that the Tropical Rainfall Measuring Mission (TRMM) observations (Huffman et al., ) estimate this ratio to be 45–60% over most the low latitudes (Dai, ). It is clear that this is primarily due to the use of the dCAPE trigger that acts to suppress convection. It is interesting to see that ULL has the largest convective precipitation fraction between 30°S and 45°S and between 30°N and 45°N. This is likely due to more nocturnal elevated convective systems captured by using the ULL trigger as discussed in the next section. Although the total precipitation does not change much in these experiments, the shift in the precipitation partitioning with the revised trigger could have a large impact on the vertical diabatic heating profiles and thereby the large‐scale circulation. This would be a subject of future studies to further understand the effect of the revised trigger on the simulated climate.

Precipitation Frequency and Intensity Distribution

In addition to the precipitation rates (P), precipitation frequency and intensity are also important quantities that need to be accurately simulated by climate models given their large societal impact (Dai, ; Trenberth et al., ). In the figures discussed below (Figures ), the precipitation frequency and intensity are computed from 1° daily data for both observations and models. Similar to Chen and Dai (), the frequency is defined as the ratio of the number of precipitation events to the total number of all days with data in percentage, and the intensity is the mean precipitation rate averaged over all precipitation events. A precipitation event is defined as a day with a precipitation rate larger than a threshold value. Before deriving the distribution, model precipitation rates are interpolated to 1° × 1° grids and averaged over daily intervals. The frequency and intensity were computed at each grid box for the whole year for each year and then averaged over all the years.

Figure  shows the annual mean precipitation frequency (left panel) and intensity (right panel) for P ≥ 1 mm/day computed from the GPCP 1° daily (GPCP1DD) data (Huffman et al., ) over 1997–2013 and the 10‐year model simulations. The EAMv1 generally shares the same too frequent, too weak problem as shown in other climate models (Trenberth et al., ). The default model largely overestimates the observed frequency and significantly underestimates the observed intensity over both ocean and land for P ≥ 1 mm/day (Figures b and g). This problem is noticeably reduced with the dCAPE&ULL trigger, which leads to a clear reduction of the frequency and a noticeable increase of the intensity over most of the regions (Figures c and h). By examining the individual effect from dCAPE and ULL (the lower four panels), the improved frequency and intensity simulation can be mostly attributed to the use of the dCAPE trigger that effectively suppresses the frequency of the light‐to‐moderate precipitation (i.e., 10 mm/day > P > 1 mm/day) as indicated in Figure  and increases the moderate‐to‐heavy precipitation (P ≥ 10 mm/day) in both tropics and subtropics (Figure ). It is interesting to see that all the models capture well the observed frequency for the moderate‐to‐heavy precipitation globally and slightly overestimate the intensity for the light‐to‐moderate precipitation in the tropics while underestimate it elsewhere. In general, the impact of ULL on these two fields is small.

The zonally averaged annual mean precipitation frequency and intensity calculated with the three different thresholds are shown in Figure . Consistent with the discussion earlier, all the models overpredict the observed frequency and underpredict the observed intensity at all latitudes (Figures a and b), primarily due to model problems in simulating the light‐to‐moderate precipitation (Figures c and d). In contrast, the models have done a decent job in capturing the frequency and intensity for the moderate‐to‐heavy precipitation (Figures e and f). The too frequent, too weak bias is noticeably reduced in dCAPE&ULL over the region between −30S and 20 N, which are related to the improved simulation of the frequency of the light‐to‐moderate precipitation and the intensity of the moderate‐to‐heavy precipitation due to the use of dCAPE.

To further examine the regional features, the precipitation intensity distributions over the summer CONUS and the annual mean in the tropics (25°S to 25°N) are also examined in Figures  and , respectively. Similar to Figures , before aggregating the distribution, modeled precipitation rates are interpolated to the same 1° × 1° grids as GPCP1DD data. All data sets are averaged over daily intervals. The frequency distribution is then derived by combining data from all the grid boxes at 1° × 1° resolution without any further averaging. A bin interval of log10 (1.07) is used for the x axis, starting at 0.1 mm/day and ending at 617.3 mm/day. The frequency values are normalized by the x interval. In this way, the frequency functions from data sets at different spatial and temporal resolutions become comparable.

Over the two examined regions, EAMv1 greatly overpredicts the frequency of precipitation occurrence for rainfall rates less than 10 mm/day, while it underestimates it for rainfall rates larger than 10 mm/day over both examined regions (Figures a and a). Over CONUS, the revised trigger slightly reduces the overestimation between 1 and 10 mm/day due to the dCAPE trigger that suppresses the convection as indicated in Figure b. Figure c indicates that the dCAPE leads to an increase of resolved scale precipitation in the light rain range. In the tropics, the role of dCAPE in suppressing convection becomes clearer. The biggest reduction of the frequency of precipitation occurrence is in the bin of [1–10 mm/day] (Figure a), which is primarily due to the reduction of light rain over the ocean areas as shown in Figures b and c. The reduction is clearly because convection is effectively suppressed with the dCAPE trigger, similar to that found in Zhang and Mu () when dCAPE was used as a trigger and a closure in the ZM scheme. For rainfall rates larger than 50 mm/day, however, no clear improvement is seen with the revised trigger.

The Diurnal Cycle of Precipitation

Section indicates that the revised trigger has a small overall impact on the mean precipitation simulation with some encouraging improvements over several climate important regions. Notable impacts are seen in precipitation partition and its frequency and density distributions. In this section we examine the simulated diurnal cycle of precipitation in different climate regimes.

Figure  displays the phase and amplitude of the first diurnal harmonic of total precipitation from the 3‐hourly TRMM observations (Huffman et al., ) and the experiments over CONUS during the summer. We have found similar results for the spring season (not shown). The first diurnal harmonic explains more than 80% (for TRMM) or 90% (for models) of the diurnal variance over most of the region except along the west coast and over SGP where it only explains less than 40% of the variance (Figure ). The observations show late afternoon to early morning peaks (1600–0200 LST) over most of the CONUS. For example, precipitation peaks at late afternoon (1600 LST) in the southeast U.S., while precipitation maximum features an eastward propagation from the eastern edge of the Rocky Mountains at late afternoon to the central Great Plains at midnight over the central U.S. (105°W–90°W).

The default EAMv1 exhibits many common model biases as shown in other climate models (Covey et al., ; Trenberth et al., ). Its precipitation peaks too early during the day and fails to capture the nocturnal peak over the Great Plains. These model biases are dramatically reduced with the revised convective trigger. The nocturnal peak over the Great Plains, which nearly all climate models failed to capture, is well simulated with the revised trigger. The diurnal cycle of precipitation over the eastern U.S. is also much improved. It is clear that allowing elevated convection to be detected above the boundary layer with ULL is key to capturing the nocturnal peak, while the combination of dCAPE and ULL contributes to the improvement in other regions of the U.S.

To further demonstrate the impact of the revised trigger on the diurnal cycle of precipitation over CONUS and the MCS propagation over the central U.S., Figure  shows the diurnal cycle of the June‐July‐August precipitation averaged over five selected regions: mountains, high plains, middle plains, low plains, and southeastern U.S., as outlined by square boxes in Figure a. The first four regions are selected to examine the eastward propagation of MCSs originating from the Rocky Mountain ranges to the central Great Plains, which is a well‐known feature in this region as discussed earlier.

Over the downstream of the Rockies and the adjacent Great Plains, there is a clear eastward propagation of convection exhibited in TRMM with the precipitation peak appearing at 1600 LST over the mountain region, moving eastward to the Great Plains with increased intensity and reaching the high plains, middle plains, and low plains at 1800, 2100, and 2300 LST, respectively (Figure a). It should be noted that the time of maximum precipitation in TRMM is often a few hours later than that in the surface observations over most land and ocean (Dai et al., ). Over most selected regions, TRMM shows the precipitation peak about 1 hr later than the Next Generation Radar Level 2 Base Data (https://data.nodc.noaa.gov/cgi‐bin/iso?id=gov.noaa.ncdc:C00345; not shown). The exception is over the low plains where the time of maximum in TRMM is 1 hr earlier than that in Next Generation Radar. This indicates potential uncertainties in the observational data used in Figure . Nevertheless, the default EAMv1 clearly fails to capture the eastward propagation and misses the nocturnal precipitation peaks. In contrast, the model with the revised trigger clearly shows an eastward propagation signal of convection over this region with almost perfect timing except for the midplains where the timing is 1 hr late. However, the amplitude of the diurnal cycle of precipitation is still much weaker than observed, particularly over the middle and low plains, consistent with the underestimation of precipitation rates there. It is interesting to see that the combined trigger works clearly better than the individual triggers. The dCAPE trigger alone does not help improve the simulation of the eastward propagation of convection and the nocturnal precipitation over this region. In contrast, ULL starts to show some skill to capture nocturnal precipitation over the middle and low plains.

Over the southeastern U.S., the observed precipitation peak from TRMM is at 1600 LST. In contrast, the default model produces a peak around noon due to the unrealistic coupling of convection to the surface heating in its CAPE‐based trigger used in the ZM scheme. With the revised trigger, the peak is shifted to 1400 LST, closer to the observations. The improvement is attributed to both the dCAPE trigger and ULL over this region, but the combined trigger again gives a better result than any of the individual triggers.

The observed and modeled annual mean diurnal cycle of precipitation over the tropics is shown in Figure . The observed diurnal cycle of precipitation typically exhibits a late evening to midnight peak over tropical lands and an early morning peak around 0500–0700 LST over the oceans. Similar to Dai (), all the models produce a similar precipitation maximum near midnight to early morning (0001–0300 LST) over the tropical ocean, a few hours earlier than the observations. In contrast, they show quite significant differences in the peak time over the tropical lands. The default model fails to capture the late evening to midnight peak. Instead, it produces maximum precipitation between 1000 and 1300 LST over most of the land areas. This problem again is largely reduced with the revised trigger, which simulates the timing of the maximum precipitation between late afternoon and late evening over most of the lands, much closer to the observed. Both dCAPE and ULL contribute to the improvement over the tropical Africa and tropical South America, while ULL plays the dominate role in the better timing of diurnal cycle over the Maritime Continent. Overall, the combined trigger clearly shows a better performance than the individual changes. Similar results are seen for different seasons (not shown).

Figure  shows the diurnal cycle of precipitation in selected climate regimes: the tropical North Africa (20°E–30°E; 0°–10°N), North America Plains (95°W–105°W; 34°N–42°N), central Borneo Island (110°E–116°E; 2°S–2°N), western Pacific ITCZ (160°E–180°E; 12°S–6°S), and tropical South America (50°W–65°W; 5°S–20°S). June‐July‐August is used for the diurnal cycle plots for the first four regimes, and December‐January‐February is used for the tropical South America. Similar to earlier discussions, the default model has difficulties to capture the TRMM‐observed diurnal cycle of precipitation over most of the selected regions and tends to have precipitation peaked around noon. The exception is over the western Pacific ITCZ where the observed diurnal cycle is reasonably reproduced. In contrast, the timing of the diurnal cycle of precipitation is much better captured by the revised trigger for all the selected regions compared to the default model. The contribution of each trigger to the improvement varies with locations. In general, dCAPE mainly acts to suppress daytime convection and delay the peak to late afternoon over lands, while ULL acts to increase nocturnal rainfall over all land regimes. For example, the dCAPE trigger shows a better skill in capturing the observed late afternoon peaks over the tropical North Africa and South America due to its role in suppressing convection during the day while the ULL trigger clearly helps shift the peak precipitation from 1600 LST in the default model to around 1900–2200 LST, closer to the observed midnight peak over the central Borneo Island. Both triggers contribute similarly to the improvement over the North American Plains. The amplitude of diurnal cycle is also generally improved slightly with the revised trigger compared to the default model.

Conclusion and Future Work

A revised convective trigger is proposed and tested in the DOE E3SM EAMv1. The new trigger consists of two triggering mechanisms: (1) The dCAPE trigger is used to relax the unrealistic coupling of convection to surface heating by providing a simple dynamic constraint on the initiation of convection that emulates the collective effects of the large‐scale advective forcing to prevent convection from being triggered too frequently and (2) the ULL trigger is used to remove the unrealistic constraint that limits convection with its root within the boundary layer in the ZM scheme and allow convective instability above the boundary layer to be detected for elevated convection, which often occurs at night above a very stable boundary layer in the central Great Plains. Four 11‐year AMIP‐type simulations with EAMv1 were conducted to examine the impact of the revised trigger and the role of dCAPE and ULL in the simulated precipitation. Major conclusions are highlighted below:

1. The revised trigger had a small overall impact on the global mean precipitation simulation with some notable improvements seen over the Indo‐Western Pacific, subtropical Pacific and Atlantic, and South America, while slight degradations were found in the ITCZ in the eastern Pacific and South Africa. In general, the dCAPE trigger played a dominant role in these changes. The dCAPE trigger also primarily contributed to the considerable reduction of convective precipitation fraction over the subtropical regions in both hemispheres and the frequency of light‐to‐moderate precipitation occurrence. It also helps to increase the intensity of moderate‐to‐heavy precipitation; however, no clear improvement was seen in rainfall rates larger than 50 mm/day.
2. Compared to the minimal impact on the mean state, the diurnal cycle of precipitation was substantially improved nearly globally with the revised trigger. The long‐standing climate model errors, such as the difficulty in capturing the late afternoon peak and nocturnal elevated convection, were substantially reduced. The model starts to show the eastward propagation signal of MCSs from the eastern edge of the Rockies to the central Great Plains. However, the amplitude of the diurnal cycle of precipitation is still too weak compared to the observations. The dCAPE and ULL triggers generally play a different role in the large improvement of the diurnal cycle of precipitation. The former helps to better capture the late afternoon peak by preventing CAPE from being released too quickly during the day, while the latter is key to capturing the nocturnal elevated convection and the propagation of convection.

The above encouraging results demonstrate the importance of improving the coupling of convection to the large‐scale environment in cumulus parameterizations, including its triggering function. The robustness of the results needs to be further tested in coupled simulations and at different model resolutions. It is expected that the dCAPE trigger should be able to feel the resolution change since the strength of the large‐scale advective forcing varies with model resolution. However, a recent study by Song and Zhang () using coarse graining of cloud‐resolving model simulation to various equivalent GCM resolutions finds that the dCAPE trigger function is scale dependent. Its performance deteriorates quickly as model resolution increases to the gray‐zone scale. Their analysis further suggests that the scale dependence can be mitigated by increasing the dCAPE threshold for convection as GCM resolution increases and by considering the history of convection. More work is needed on this. In addition, the physical mechanisms behind these changes require a better understanding. An ongoing work that uses the short‐term weather hindcast approach (Ma et al., ; Phillips et al., ) is being conducted to further understand the behaviors of the revised convective trigger at process level. Earlier studies (Ma et al., ; Xie et al., ) indicated that many features in the climate simulation of clouds and precipitation can be examined in a few days' hindcasts. The problem with intense precipitation (>50 mm/day) and the amplitude of the diurnal cycle of precipitation also needs to be addressed in future studies.

Acknowledgments

This research was primarily supported as part of the Energy Exascale Earth System Model (E3SM) project and partially supported by the Climate Model Development and Validation (CMDV) activity, funded by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research. The model data used in this study can be downloaded at http://portal.nersc.gov/project/m2136/E3SMv1/Xie‐dcape. Work at LLNL was performed under the auspices of the U.S. DOE by Lawrence Livermore National Laboratory under contract DE‐AC52‐07NA27344. Y. C. W. is also supported by Ministry of Science and Technology, Taiwan, R. O. C. under Grant MOST 105‐2119‐M‐001‐018 and MOST 107‐2111‐M‐001‐010. G. J. Z. was supported by DOE's ESM program under DE‐SC0019373. M. Z. was supported by the CMDV program of DOE. This research used high‐performance computing resources from the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under contract DE‐AC02‐05CH11231.