This study examines the roles of the tropospheric large-scale forcing, surface sensible and latent heat fluxes and convective inhibition in the diurnal variation of convection in the U.S. Southern Great Plains using data from the Atmospheric Radiation Measurement program. It is shown that the diurnal variation of the tropospheric large-scale forcing has a strong in-phase relationship with convection, whereas the diurnal variations of surface sensible and latent heat fluxes as well as the thermodynamic properties of the near-surface air are nearly out of phase with that of convection. Both the single column version and the full global model of the NCAR CCM3 are used to test the roles of the tropospheric and boundary layer forcing in the observed diurnal variation of convection. When convection is parameterized based on the tropospheric large-scale forcing, the diurnal variation of convection is in good agreement with the observations.
 Atmospheric convection undergoes strong diurnal variation over both land and oceans [Gray and Jocobson, 1977; Dai, 2001]. Because of the nature of the diurnal variation of solar radiation, the phasing of convection with solar radiation has a significant impact on the atmospheric radiation budget and cloud radiative forcing. The diurnal variation of convection has been investigated in a number of studies [Gray and Jocobson, 1977; Randall et al., 1991; Dai et al., 1999; Dai, 2001]. Yet, in regional and global climate models it remains poorly simulated, particularly over land [Dai et al., 1999; Betts et al., 1999; Betts and Jacob, 2002]. For example, over the U.S. Southern Great Plains (SGP) and the Mississippi River basin, convection simulated by the NCAR Community Climate Model (CCM3) peaks in early afternoon [Dai et al., 1999], whereas observations indicate that convection reaches maximum at night. Similar errors in the diurnal phase of convection are found in the ECMWF global forecast model [Betts et al., 1999].
 In this paper, we investigate the diurnal variations of convection at the SGP site of the Atmospheric Radiation Measurement (ARM) program. The objective is to understand what controls such variations in this continental environment. A single-column model and a fully 3D global climate model are used to understand the observational results.
2. Observations and Models
 The 3-hourly sounding data from the summer 1997 Intensive Observation Period (IOP) at the SGP site of the ARM program are used in this study. The observations cover 29 days from June 19 to July 18, 1997 and they are processed by the variational analysis of Zhang and Lin . The dataset has a vertical resolution of 50 hPa, starting from 965 hPa and ending at 115 hPa. It has been used extensively for evaluating single-column and cloud-resolving model simulations of convection [Xie et al., 2002; Xu et al., 2002]. During the 29-day IOP, a wide range of convective systems were observed, varying from scattered showers to organized mesoscale convective systems [Xie et al., 2002]. Most of these convective systems are associated with the large-scale upper-level troughs and surface frontal systems [Zhang, 2003]. For this study, the data is stratified into convective and non-convective periods based on observed precipitation rate. A composite diurnal variation for each variable is constructed by averaging it separately over convective and non-convective periods at each hour of the day. The models used in this study are the NCAR CCM3 global climate model and its single column version. Convection in the model is parameterized using the Zhang and McFarlane  scheme.
 We use CAPE (convective available potential energy) to measure convective instability in the atmosphere. It is defined by:
where pb is the level in the boundary layer at which convective air parcels originate, pt is the level at which the parcel loses its buoyancy. Tv is virtual temperature, subscript p denotes the parcel's property following an undilute adiabat and overbar denotes the property of the parcel's large-scale environment. In this study, the parcel's originating level is set to the second lowest level at 915 hPa, where the air is often the most unstable.
 From equation (1), the temporal variation of CAPE is given by:
Clearly, CAPE can change when either the parcel's virtual temperature or that of its environment changes. For instance, large-scale processes in the free troposphere (hereafter referred to as tropospheric forcing) can change CAPE by modifying the ambient virtual temperature of the air parcel, v, whereas surface sensible and latent heat fluxes (hereafter referred to as boundary layer forcing) can change CAPE by modifying Tvp since the parcel originates from the boundary layer.
 Recent studies find that CAPE changes due to the free tropospheric large-scale advection correlate well with convection at the ARM SGP site [Xie and Zhang, 2000; Zhang, 2002]. Xie and Zhang  used this observed correlation as a triggering function for convective parameterization, while Zhang  used it as a closure to determine the amount of convection. To understand its role together with the role of the boundary layer properties in the diurnal variation of convection, we show in Figure 1 the composite diurnal variation of CAPE, CIN (convective inhibition, the negative part of CAPE in the lower troposphere), CAPE generation rate from the large-scale processes, and the boundary layer properties for convective and non-convective periods, respectively. The method to calculate CAPE generation rate due to large-scale forcing is detailed in Zhang . At diurnal timescale, CAPE and CIN are out of phase for both convective and non-convective periods (Figure 1a). CAPE reaches maximum in mid-afternoon and minimum at night, while CIN is the smallest in mid-afternoon and the largest in early morning. CIN is considerably larger in non-convective periods than in convective periods. The CAPE generation rate from the tropospheric large-scale forcing (second term on the rhs of equation (2) due to large-scale advection) shows the most dramatic difference between convective and non-convective periods (Figure 1b). During non-convective periods it is small throughout the day, while during convective periods it is large and its diurnal variation is in excellent agreement with the phase of precipitation. In contrast, there is no significant difference between convective and non-convective periods in the diurnal variations of the large-scale CAPE generation rate by the surface fluxes (first term on the rhs of equation 2) or the sensible and latent heat fluxes themselves, both reaching maximum near 1400 LST and minimum near 0200 LST (Figures 1c and 1d). Furthermore, they are largely out of phase with convection.
 The thermodynamic properties of the near-surface air can be important for convection. The lifting condensation level (LCL) and level of free convection (LFC) of the near-surface air (at 915 hPa) undergo significant diurnal variation (Figure 1e). During convective periods, the LFC is lowest in early to mid-afternoon, and the LCL is also close to being the lowest. These, together with the low value of CIN may help to initiate convection. At night, although LCL and LFC are high, strong upward motion of the air below the LCL (averaged over the layer from 815 to 965 hPa, Figure 1f) seems to help the near surface air parcels to break the CIN barrier. This together with the free tropospheric large-scale generation of CAPE makes convection reach maximum near midnight. During non-convective periods, the LCL and LFC are higher, indicating the air is drier and has deeper stable layer barrier. The low level vertical velocity is rather weak throughout the day, with subsidence most of the time. All of these conditions make convection unfavorable.
 The above results suggest that the free tropospheric forcing plays a dominant role in the observed diurnal variation of convection, and surface fluxes of sensible and latent heat are not directly related to it. To test this observational deduction, the NCAR CCM3 single-column model is run, forced with the advective tendency and surface fluxes derived from the observations using the variational analysis of Zhang and Lin . Two closures are used for convection. In the standard setup, the Zhang and McFarlane  scheme is used, which determines convection by the amount of CAPE in the atmosphere. Since CAPE strongly depends on the boundary layer equivalent potential temperature, which in turn is largely governed by surface heat and moisture fluxes, this closure ties convection closely to boundary layer forcing. In the second simulation, a revised closure proposed by Zhang  is used, where convection is determined by the CAPE generation rate from the free tropospheric large-scale forcing. Figure 2 shows the diurnal variation of the observed and simulated precipitation, as well as the vertical velocity from the forcing data for the 29-day IOP. When CAPE is used to parameterize convection, precipitation is excessive, with large amplitude in diurnal variation, and reaches maximum around 1500 LST, roughly at the same time when CAPE peaks. When the revised closure is used, both the amplitude and phase of the diurnal variation are close to the observed values, with maximum precipitation at night. The vertical velocity from the observed forcing field shows a maximum upward motion at night and a minimum near noon, with substantial downward motion in the lower troposphere from early morning to mid-afternoon. Clearly, in spite of the same forcing field to the single column model simulations, convection produced by CAPE-based closure reflects more on the boundary layer forcing, whereas convection produced by the revised closure reflects more on the tropospheric vertical velocity. These results differ from those of Betts and Jacob . In their single column model investigation, Betts and Jacob  noted that the diurnal variation of convection is insensitive to changes in convective parameterization schemes.
 To confirm the role of the large-scale tropospheric forcing in the diurnal variation of convection simulated by the single column model, the NCAR CCM3 global model is run for 3 years using the two closures for convection, with observed sea surface temperatures as the lower boundary condition. The model integration starts from September 1 1996 and ends at August 31 1999. Convective precipitation from the three summer seasons (JJA) is used to composite the diurnal cycle of convection. Figure 3 shows the diurnal variation of convective precipitation and vertical velocity from the model simulations averaged over the 4 grid points bounded by the latitude-longitude box (37°N, 41°N), (98°W, 102°W). The area roughly corresponds to the ARM SGP site. When the original CAPE-based closure is used, the diurnal variation of convective precipitation is very similar to its counterpart in the single column model simulation, with maximum near 1600 LST. The upward motion reaches maximum around 2000 LST. The phase lag between the two suggests that the vertical motion is in response to convective heating. When the revised closure (labeled as RZM in the figure) is used, convective precipitation has a much smaller diurnal variation (probably a little too small), and reaches maximum at night and minimum in early to mid-afternoon. The diurnal variation of the vertical velocity shows a maximum upward motion around midnight and early morning, with significant downward motion in the lower troposphere from 0300 to 1200 LST. It is interesting to note the gross similarity between the diurnal patterns of vertical velocity in Figures 2 and 3c, although the former is from a one-month observation whereas the latter is from a three-year simulation averaged over the entire summer season (JJA).
Figure 4 shows the phase dial vector of diurnal cycle of convection across the U.S. following Dai et al. . In the plot, the direction of a vector gives the local time at which the maximum precipitation occurs using the harmonic analysis of Dai et al. , and the vector length gives the amplitude of the diurnal harmonic of convective precipitation, normalized by the seasonal average precipitation amount at each grid point. A vector pointing southward means maximum precipitation at 0000 LST, pointing westward means maximum precipitation at 0600 LST, etc. In the standard CCM3 simulation, maximum convective precipitation occurs in early to mid afternoon across the country, with large amplitude. This is similar to the results from other studies [Dai et al., 1999]. When the revised closure is used, there is a significant change in the diurnal cycle of convection. West of the Rockies, maximum precipitation occurs near 1800 LST, with fairly large amplitude. East of the Rockies across the Great Plains and further eastward, maximum convection occurs from early evening to night. The diurnal amplitude of convective precipitation is much weaker than in the standard CCM3 simulation. All these features are in good agreement with the observations [Dai et al., 1999; Figure 3 of Trenberth et al., 2003]. In the southeast of the U.S., the amplitude of the diurnal variation is somewhat too weak while the phase is in good agreement with the observations.
 In this study, we find that the diurnal variation of the free tropospheric large-scale forcing has a strong in-phase relationship with convection at the ARM SGP site, both reaching maximum near midnight and minimum before local noon. The diurnal variations of CAPE, surface sensible and latent heat fluxes, and the thermodynamic properties of the near-surface air are not directly related to that of convection. Convective inhibition is larger in non-convective periods than in convective periods, and is in opposite diurnal phase to that of CAPE.
 The NCAR CCM3 and its single column model are used to confirm the role of the tropospheric forcing in the observed diurnal variation of convection. When convection is parameterized using CAPE, which is largely linked to the boundary layer forcing, maximum convection occurs in early to mid afternoon in the Southern Great Plains as well as elsewhere across the country. When convection is parameterized based on the tropospheric large-scale forcing, its maximum occurs in early evening west of the Rockies, and from early evening to night east of the Rockies. This diurnal variation of convection is in much better agreement with the observations.
 This research was support by the Environmental Science Division of U.S. Department of Energy under grant DE-FG02-03ER63532, and by NOAA under grant GC03-074. The author thanks Aiguo Dai for helpful discussions on fitting the diurnal harmonics for Figure 4. The reviewers' constructive comments have helped to improve the manuscript.