Parameterization of the Elevated Convection With a Unified Convection Scheme (UNICON) and Its Impacts on the Diurnal Cycle of Precipitation

To improve the simulation of nocturnal precipitation, we develop a parameterization for the elevated convection that is launched from the level of maximum grid‐mean moist static energy, when grid‐mean vertical flow is upward at the launching interface. The parameterized elevated convection is forced by both cold pool‐driven and partially resolved external mesoscale organized flows. Properties of the external mesoscale flow are estimated from grid‐mean vertical velocity and three dimensional advection tendencies of temperature and moisture. The new parameterization is implemented into a unified convection scheme (UNICON) and tested for both the single‐column case at the Southern Great Plain (SGP) site in US and in global simulations. At the SGP site, the parameterized elevated convection strengthens nocturnal convection, increases nocturnal precipitation, and better simulates the observed diurnal cycle of precipitation. It appears that the elevated and surface‐based convections interact with each other by stabilizing the atmospheric column, which affects subsequent convection. Global simulation shows that the elevated convection mostly occurs over the continents during the night, and also over the oceanic mid‐latitude warm air advection and storm track regions during summer. Without degrading global mean climate, the elevated convection improves the simulation of nocturnal precipitation in the mid‐US but simulates somewhat strong nocturnal precipitation in northeastern Asia. It seems that a key to simulate observed nocturnal precipitation is to appropriately parameterize the impacts of external organized flow on the elevated convection.


Introduction
Precipitation, one of the key meteorological variables, has a strong diurnal cycle as a result of complex and rapidly varying interactions between the atmosphere and the surface through moist convection.The diurnal cycle of precipitation is strong over land during summer with the peak occurring in the late afternoon or the night, partly due to the strong diurnal cycle of solar heating and boundary layer properties that modulate convective activities (e.g., Dai et al., 1999;Riley et al., 1987;Wallace, 1975).In contrast, the diurnal cycle of precipitation over the ocean is relatively weak with the maximum precipitation often observed in the early morning in association with cloud top radiative cooling and propagation of mesoscale convective systems (Dai, 2001;Imaoka & Spencer, 2000).
Compared to seasonal and interannual variation, the diurnal cycle of precipitation is strongly tied to the changes in surface temperature and boundary-layer structure on a much smaller timescale, which greatly challenges the equilibrium assumption that has been commonly used in convection parameterizations (Davies et al., 2013;Yano & Plant, 2012).Thus, the diurnal cycle of precipitation can be used as a metric that measures how well a general circulation model (GCM) represents the response of moist convection to large-scale and surface forcing.
Unfortunately, many GCMs fail to reproduce the observed diurnal cycle.Most GCMs simulate the rainfall peak around noon instead of late afternoon over land, and also simulate the rainfall peak too early over the ocean, both with a weaker variance than observation (Dai, 2006).Several recently developed convection schemes succeeded in simulating the gross features of the observed diurnal cycle of precipitation (e.g., Baba, 2020;Bechtold et al., 2014;Park, 2014aPark, , 2014b;;Rio et al., 2013;Stratton & Stirling, 2012;Xie et al., 2019), which showed that the performance of the convection scheme in simulating the observed diurnal cycle of precipitation is affected by convective triggering, convective closure, and entrainment parameterization.However, most GCMs still fail to capture the nocturnal precipitation peaks which are observed in several regions including the central US, northern Amazon, and central China.Tang et al. (2021) and Tao et al. (2023) reported that most CMIP6 (phase 6 of the Coupled Model Intercomparison Project, Eyring et al. (2016)) models cannot simulate the nocturnal precipitation in association with elevated convection and the propagating mesoscale convective system.Summertime nocturnal precipitation over the Southern Great Plain (SGP) in the central US has received special attention.In this region, the low-level jet from the Gulf of Mexico induces diurnally varying moisture convergence that peaks during the night due to large-scale circulation generated by the thermal contrast between the Rockies and the SGP.In addition to this large-scale circulation, the mesoscale convective system formed near the slopes of the Rockies can propagate eastward and cause a heavy rainfall over the SGP during the night (Carbone & Tuttle, 2008;Jiang et al., 2006;Maddox, 1980).In these cases, convection can be initiated from the elevated levels above the stable boundary layer, where the moist static energy is high due to moisture convergence.Recent observational studies including the Plains Elevated Convection At Night (PECAN) field campaign (Geerts et al., 2017) provide a deeper understanding of the initiation of the elevated convection.These studies have shown that the uplift forcing of convection from its initiation level to the level of free convection (LFC) is supplied by various mechanisms, such as the low-level jet, advection of mesoscale convective system, synoptic front, bore, density current, and gravity waves (Weckwerth et al., 2019).
Different methods have been tested to improve simulation of the diurnal cycle of precipitation.Increasing the horizontal resolution of a model appears to have a limited impact on the diurnal phase of precipitation, unless the grid size decreases to a convection-permitting resolution (Sato et al., 2009;Sun et al., 2016).The failure to capture the diurnal cycle of precipitation in climate models stems partly from errors in the convection initiation processes that determine the launching level of convection, updraft source air properties, the impacts of large-scale forcing including mesoscale organization, and the sensitivity of convection to tropospheric humidity via entrainment.In many models, the simulated convection is too strongly coupled with surface heating, which degrades simulation of nocturnal precipitation that is decoupled from the surface (Geerts et al., 2017;Marsham et al., 2011;Xie et al., 2014).Several convection schemes parameterize the initiation level of the elevated convection as the level of maximum moist energy (Han & Pan, 2011;Pan & Wu, 1995;Wang et al., 2015).
In addition to the launching level of the elevated convection, mesoscale convective organization and large-scale forcing should be appropriately included into the parameterization of convection initiation processes.Large-scale forcing has a substantial impact on the diurnal cycle of precipitation.Bechtold et al. (2008) modified the European Center for Medium-Range Weather Forecasts model (ECMWF) to be more sensitive to environment moisture, which improved simulation of atmospheric variabilities including the diurnal cycle of precipitation.Extending the previous study, Bechtold et al. (2014) showed that the implementation of non-equilibrium convective closure improved the phase error of the diurnal cycle of precipitation.However, they also noted that simulating the nocturnal convection over land is still an issue, pointing a need to represent the effects of the spreading cold pools at the surface and upper-level mesoscale lifting during the night.G. J. Zhang (2003) found that modifying the convection scheme to respond to tropospheric forcing could significantly improve the diurnal cycle of precipitation.Xie et al. (2019) and Cui et al. (2021) showed that a combined parameterization of elevated initiation level with a dynamic convective available potential energy (CAPE) trigger (Xie & Zhang, 2000) successfully reproduces the observed nocturnal precipitation over the central US.Xie et al. (2019) also noted many issues with GCM simulated diurnal cycle of precipitation that include unrealistic coupling of convection with surface fluxes in current cumulus parameterization, importance in capturing elevated convection for improving simulation of nocturnal precipitation and diurnal cycle, and interaction between daytime convection and nocturnal convection.Recent multi-model intercomparison studies on the diurnal cycle of precipitation in the SGP region and over the globe show that many state-of-the-art models still lack of the diurnal variability of convection (i.e., the shallow to deep convection transition) and associated precipitation (Tang et al., 2021(Tang et al., , 2022)).
The Unified Convection Scheme (UNICON) developed by Park (2014aPark ( , 2014b) ) is one of few convection schemes that parameterizes the life cycle of mesoscale organized flow (including advection) driven by subgrid cold pools and its interactions with convective updraft and downdraft plumes using a prognostic cold pool model.The cold pool parameterization in UNICON is conceptually similar to that of Grandpeix and Lafore (2010).It was shown that a GCM with UNICON produces a realistic diurnal cycle of precipitation in most regions (Park et al., 2019).The success of UNICON is due to its ability to simulate complex feedback interactions between convective updrafts, convective downdrafts, and mesoscale organized flows driven by subgrid cold pools.In UNICON, the degree of subgrid mesoscale organization (Ω) is estimated by using the fractional area of subgrid cold pool within the planetary boundary layer (PBL).UNICON computes the temporal evolution of Ω and associated perturbations of thermodynamic scalars in both convective updraft plumes and the environment.During the daytime over land, Ω increases due to evaporation of convective precipitation and associated convective downdraft, and reaches its maximum strength in the late afternoon when simulated rainfall is also maximum.However, UNICON substantially underestimates the amount of nocturnal precipitation in several regions such as the central US and central China in June-July-August (JJA), and the Himalayas and the Andes.We speculate that this problem happens because UNICON launches all convective updraft plumes from the surface, regardless of whether PBL is stable or convective, as noted in Park (2014aPark ( , 2014b)).
This study aims at relaxing the surface-based plume assumption and allowing UNICON to launch the elevated convection.We will examine how the elevated convection affects the diurnal cycle of precipitation, in particular, the nocturnal precipitation.The structure of this paper is as follows.Section 2 explains a conceptual framework and the mathematical formulation of the elevated convection parameterization that computes the launching level, initial thermodynamic properties, and vertical evolution of elevated convective updraft plumes.Section 3 describes the setting for single-column model (SCM) and global simulations; the results are shown in Sections 4a and 4b, respectively, including sensitivity tests in Section 4c.A summary and discussion is provided in Section 5.

Initialization of the Surface-Based Convection at the Surface
As detailed in Park (2014a), all convective updraft plumes in the original UNICON are launched from the surface.Properties of the updraft plume at the surface (i.e., the radius R, where the caret denotes updraft plume properties; relative vertical velocity ŵ with respect to the grid-mean vertical velocity; condensate potential temperature θc ≡ θ (L v / C p /π) ⋅ ql (L s / C p /π) ⋅ qi , where L v and L s are the latent heats of vapourization and sublimation, respectively, C p is the specific heat of the air at constant pressure, and π is an Exner function; total specific humidity qt ≡ qv + ql + qi ; zonal and meridional velocities, û and v, respectively; the mass and number concentrations of aerosols and chemical species ξ) are parameterized from given surface fluxes and subgrid mesoscale perturbations induced by subgrid cold pools without using triggering functions or quasi-equilibrium assumptions.The vertical velocity and thermodynamic scalars of a single convective updraft plume at the surface, ŵs = ŵ(z = 0) and φs = φ(z = 0), are computed as where k w = 0.4 is an anisotropic factor of nonorganized turbulent eddies; e PBL is the mean turbulent kinetic energy (TKE) within the PBL; ϕ s is the grid-mean thermodynamic scalar ϕ (=θ c , q t , u, v, ξ) at the surface; w′ϕ′) s is the turbulent flux of ϕ at the surface given from a separate surface flux computation routine; and Δw Ω and Δϕ Ω are the perturbations induced by subgrid mesoscale organized flow within the PBL, which are the functions of subgrid cold pool properties, as defined in Equations 73 and 74 of Park (2014a).The updraft plume radius at the surface, Rs = R(z = 0), is parameterized as where R o | Ω = 0 and R o | Ω = 1 are the externally specified intercept plume radius at minimally (Ω = 0) and maximally (Ω = 1) organized states, respectively, which are set to ,500 over the ocean, and R o | Ω = 1 = 9,000 over land.The updraft fractional area at the surface, Âs = Â(z = 0), is parameterized in a similar way as where Âs | Ω=0 and Âs | Ω=1 are the externally specified updraft fractional areas at the surface at minimally and maximally organized states, respectively; the second equality comes from the assumption of Âs | Ω=1 = 0.1 ⋅ Âs | Ω=0 ; and Âs | Ω=0 = 0.04 over the ocean and Âs | Ω=0 = 0.025 over land, respectively.Finally, the updraft mass flux of a single convective updraft plume at the surface is computed as where ρ s is the grid-mean air density at the surface.Using a set of given inputs of ϕ s , w′ϕ′) s , and e PBL with the internally prognosed Ω, Δw Ω , and Δϕ Ω for ϕ = θ c , q t , u, v and ξ, UNICON finishes the initialization of convective updraft plumes originated at the surface, that is, surface-based convection.As noted by Park (2014b), the values of several tuning parameters in the above Equations 1-4 (e.g., k w , R o | Ω = 0 , R o | Ω = 1 , 50 in Equation 3, and Âs | Ω=0 ) are obtained from extensive trial-and-error tuning exercises.

Parameterization of the Elevated Convection
In addition to the aforementioned surface-based convection, we added a new parameterization for the elevated convection originated above the surface.To save computation time, UNICON launches only one of the surfacebased convection or the elevated convection, instead of launching both simultaneously.To parameterize the elevated convection, we compute the launching level, source air properties (i.e., ŵe , φe , Re , Âe , and Me ), and vertical evolution of the elevated convection.The following sections explain how these processes are parameterized.The default values of various tuning parameters are summarized in Table 1.

The Launching Level of the Elevated Convection
We define the launching level of the elevated convection as the top interface of the grid layer with maximum gridmean moist static energy (MSE = C p ⋅ T + g ⋅ z + L v ⋅ q v ) below the 600 hPa level.A similar approach using the maximum MSE has been used in other convection schemes [e.g., a Simplified Arakawa-Schubert (SAS) scheme (Han & Pan, 2011;Pan & Wu, 1995) and a revised ZM scheme (Wang et al., 2015)].The midlevel convection parameterization in the Tiedtke scheme (Tiedtke, 1989), designed to simulate convective cells originated from above the boundary layer, is analogous to the elevated convection parameterized in our scheme.Our initialization strategy with the maximum grid-mean MSE is based on a simple conceptual argument: when an unsaturated stable atmospheric layer-with the MSE profile decreasing with height-rises and is saturated, it becomes statically unstable due to the release of latent heat (i.e., so called convective instability, Yau and Rogers (1996)).Thus, the parameterized elevated convection is launched only when the grid-mean vertical velocity at the launching interface is upward.The cases with grid-mean subsidence at the launching interface or maximum grid- mean MSE in the lowest grid layer are treated as the surface-based convection.We also tested more strict triggering criteria for the elevated convection (e.g., the grid-mean vertical velocity at the launching interface should be larger than 0.2 [m/s]; the launching level should be located above the PBL; and etc.), which, however, produced similar results.

Initialization of Thermodynamic Properties of the Elevated Convection
For the parameterization of the elevated convection, we treat grid-mean vertical flow as one kind of mesoscale organized flow under special situations (i.e., external mesoscale organization, hereinafter), similar to the cold pool-driven mesoscale organized flow that has already been parameterized in UNICON.Previous studies have used grid-mean vertical velocity to parameterize various processes in the convection scheme [e.g., Han and Pan (2011)].The impacts of external mesoscale organization on convective updrafts are parameterized in a way similar to those of cold pool-driven mesoscale organization, Ω.The subgrid vertical velocity of external mesoscale flow, Δw ext (z), is estimated as where w(z) is a given grid-mean vertical velocity in units of [m s 1 ] and f is a grid factor defined as where G is the horizontal area of the model grid (G ≡ Δx ⋅Δy, where Δx and Δy are the zonal and meridional width of the model grid, respectively) and G o is the assumed horizontal area of external mesoscale upflow that is set to . We note that Δw ext (z) can be either positive or negative.If G → G o , Δw ext → 0, indicating that external mesoscale flow becomes a fully resolved phenomena.As G increases, f increases; however, the magnitude of w(z) is also likely to decrease, expecting a resolution-insensitive Δw ext (z), as it should be.A similar grid size dependency has been used in Kain (2004) and Bechtold et al. (2001).Associated perturbations of thermodynamic scalars driven by external mesoscale flow are parameterized as where adv ϕ)(z) is the three dimensional advection tendency of the grid-mean ϕ = θ c , q t , u, v that changes with height, and τ is the forcing time scale that is set to τ = 200 [s].Our parameterization of Δϕ ext (z) is different from the approaches of Kain (2004) and Bechtold et al. (2001) who added temperature perturbation as a function of grid-mean vertical velocity when defining the updraft source property, in order to make the updraft plume more buoyant in large-scale uplifting.We use Equation 8 since we are trying to mimic external mesoscale flow embedded in grid-mean flow with a subgrid convection scheme.
The upward vertical velocity of the elevated convection at the launching level, ŵe ≡ ŵ(z e ) , where z e is the launching height of the elevated convection, is parameterized as and where Δw sym (z e ) ≥ 0 is vertical velocity perturbation driven by symmetric turbulent eddies parameterized in a separate PBL scheme with e(z e ) denoting TKE at z e and k w = 0.4; Δw Ω ≥ 0 is cold pool-driven, mesoscale vertical velocity perturbation that exists only within the PBL [Equation 74in Park (2014a)]; and Δw ext (z e ) is from Equation 6.To be consistent with the geometric structure, we define ŵe without Δw Ω if the elevated convection is launched from above the PBL.It has been observed that the mesoscale convective system propagating eastward into the region with a stable nocturnal PBL can cause heavy rainfall in the SGP region during the night (Carbone & Tuttle, 2008;Jiang et al., 2006;Maddox, 1980).Weckwerth et al. (2019) also showed that about 35% of nocturnal convection initiation cases during the PECAN field campaign are associated with the pre-existing mesoscale convective system (or cold pool) and about 25% are associated with the bore/density current.Our approach to parameterize ŵe with a cold pool-driven component (Δw Ω ) (and also for temperature and moisture perturbations, as will be shown) is in line with these observational studies.
The thermodynamic properties of the elevated convection at the launching level, φe ≡ φ(z e ), for ϕ = θ c , q t , u, v are parameterized as and where w′ϕ′(z e ) is non-organized subgrid turbulent flux at z e by symmetric turbulent eddies obtained from a separate PBL scheme; Δϕ Ω is cold pool-driven mesoscale perturbation [Equation 73in Park (2014a)]; and Δϕ ext (z e ) is from Equation 8at z e .To be consistent with the geometric structure, we define φe without Δϕ Ω if the elevated convection is launched from above the PBL.
We define the following non-dimensional external mesoscale organization, Ω ext , with a scaling vertical velocity, w o that is set to 1 [m s 1 ].Previous observational studies indicate that the elevated convection generally appears in the form of a mesoscale convective system (MCS) with a large horizontal scale and mesoscale ascent (e.g., Colman (1990)).Through a series of test simulations, we found that a large updraft radius and small entrainment rate for the parameterized elevated convection is important to produce a realistic nocturnal precipitation.Thus, similar to the surface-based convection, we assume that the updraft plume radius of the elevated convection at the launching level increases with Ω ext .We parameterize the intercept plume radius for the elevated convection, R o,elevated | Ω=0 , as an increasing function of , we compute the updraft plume radius of the elevated convection at the launching interface, Re ≡ R(z e ) , as and Re increases with Ω ext .If Ω ext = 0, then Re = Rs , whereas if Ω ext = 1, the elevated convection is launched with its maximum plume radius Re = R o | Ω=1 + 50.We assume that if the elevated convection is launched within the PBL, the updraft fractional area of the elevated convection at the launching interface, Âe ≡ Â(z e ) , is identical to that of the surface-based convection, Âs , as defined in Equation 4.However, if z e is located above the PBL, Âe is parameterized as an increasing function of Ω ext , where we set c A = 5.This equation comes from a simple conceptual argument that as mesoscale external flow becomes strong, associated convective updraft mass flux of the elevated convection increases.Both Re and Âe increase as Ω ext increases.However, as Ω increases, Âe decreases, although Re increases (Equation 14).This is because Âs (Ω) in Equation 15is parameterized as a decreasing function of Ω (Equation 75in Park (2014a)).
Finally, the updraft mass flux of a single elevated updraft plume at the launching interface, Me ≡ M(z e ) , is computed as where ρ e is the grid-mean air density at the launching level of the elevated convection.Note that all these equations are necessary to define the initial properties of the elevated convective plume within UNICON: updraft vertical velocity [Equations 6, 7, 9 and 10], updraft thermodynamic scalars [Equations 8,11 and 12], updraft radius [Equations 13 and 14], updraft fractional area [Equation 15], and updraft mass flux [Equation 16].As will be shown from the sensitivity simulations in Section 4.3, the simulation results are rather insensitive to the choice of several tuning parameters for the elevated convection.This completes the initialization of the elevated convection.

Vertical Evolution of the Elevated Convection
In many cases, nocturnal convection is driven by the upward lifting of the low-level jet along the frontal slope (i.e., isentropic upglide) (Trier et al., 2020;M. Zhang & Meng, 2019).With this dynamic uplifting, the updraft plume can reach its level of free convection (LFC) more easily and grow deeper.Thus, to simulate nocturnal convection, we need to appropriately parameterize the impacts of dynamic uplifting on the plume vertical velocity.We slightly modified the steady-state vertical velocity equation for a convective updraft plume [Equation 27in Park (2014a)] by including relaxation forcing and accounting for non-zero environmental vertical velocity, as where a R) is the buoyancy coefficient, b is the entrainment drag coefficient, c is the detrainment thrust coefficient, L r is the relaxation length scale of the elevated convection that is set to L r = 350 [m], and Δw mix,env is the anomalous vertical velocity of mixing environmental air [i.e., the environmental air that is mixed with the convective updraft plume, Equation 78in Park (2014a)] with respect to grid-mean vertical velocity.To be consistent with the geometric structure, in the case of the surface-based convection, we set Δw mix,env = Δw Ω within the PBL and Δw mix,env = 0 above the PBL and then use Δw mix,env for both updraft buoyancy sorting and entrainment mixing without the relaxation forcing term [that is, set L r = ∞ in Equation 17].In the case of the elevated convection, we set Δw mix,env = Δw Ω + Δw ext (z) within the PBL but Δw mix,env = Δw ext (z) above the PBL; these are used for both updraft buoyancy sorting and entrainment mixing.However, for the elevated convection, if ŵ(z)< Δw mix,env (z), we apply relaxation forcing: from the launching interface to the saturated LFC, or up to 150 hPa above the launching interface-whichever comes first.In this way, an updraft plume can sustain more positive vertical velocity, reach its saturated LFC, and grow deeper, even when it is negatively buoyant at the launching interface.Finally, similar to Δw mix,env , thermodynamic properties of the mixing environmental air (ϕ mix,env for ϕ = θ c , q t , u, v) are defined by adding Δϕ Ω + Δϕ ext (z) within the PBL and Δϕ r (z) + Δϕ ext (z) above the PBL, where Δϕ r (z) is the anomalous detrained air property at the previous time step [Equation 78 Park (2014a)].
Other than the usage of relaxation forcing and different definitions of the mixing environmental airs, vertical evolution of the elevated convection is treated in the same way as that of the surface-based convection.Regarding updraft vertical velocity, dynamic uplifting drives the parameterized elevated convection by enhancing both the initial vertical velocity of the elevated convective updraft (Equation 9) and the vertical velocity of the mixing environmental air that is entrained into convective updraft (Equation 17) and exerts the relaxation forcing on convective updraft.

Other Modifications
We modified the parameterization of the fractional mixing rate εo for convective updraft plumes.In the original UNICON, the term representing evaporative enhancement of mixing rate was parameterized as an inverse function of the updraft plume radius (Park, 2014a).In nature, the entrainment of environmental air that drives the evaporative enhancement of fractional mixing rate is likely to occur on the head portion of cumulus plume with a cross-sectional area of R2 (z).Since this cross-sectional area is linearly proportional to the volume of the updraft air column ( h ⋅ R2 , where h is the depth of the updraft plume), it is more reasonable to assume that the evaporative enhancement of the fractional mixing rate is independent of R (note that fractional mixing rate is defined as the ratio of the air mass involved in the mixing to the existing air mass in the updraft plume).Based on this consideration, we reformulate εo as follows: Journal of Advances in Modeling Earth Systems where a 1 = 0.2 is a dry mixing coefficient, a 2 is a tunable moist mixing coefficient in units of [m 1 ] and E is the non-dimensional evaporative enhancement factor parameterized as: where ql and qi are the in-cumulus liquid and ice condensates, respectively, and Ũ is the relative humidity of the mixing environment air.The above formulae slightly differ from the original εo √ [see Equations 31 and 32 in Park (2014a)].
Compared to the original E, Equation 19 has slightly different sensitivity to Ũ, but are qualitatively similar.From a series of tuning exercises, we choose a smaller a 2 = 1/1,800 for the elevated convection than the surface-based convection, a 2 = 1/400.The use of a smaller a 2 for the elevated convection than the surface-based convection was helpful in simulating a strong nocturnal precipitation peak (see Section 4.3).

Simulation Setting
We used a single-column model (SCM) to test the performance of the newly developed parameterization for the elevated convection at the SGP site (36.61°N,262.51°E) in US.The SCM used in our study is the same as the one used by Park and Bretherton (2009) but with modified physics parameterizations that include the unified convection scheme (Park, 2014a(Park, , 2014b) ) and the refined treatment of detrained cumulus (Park et al., 2017).The GCM with these updated physics parameterizations will be referred to as the Seoul National University Atmospheric model Version 0 with a Unified Convection Scheme (SAM0-UNICON, Park et al. ( 2019)), which is one of the GCMs participating in the CMIP6 project.We ran the SCM with a model integration time step Δt = 1,200 [s] at the vertical resolution of 30 vertical layers.Our parameterization of the elevated convection requires information on the domain size, G [Equation 7], which is not given in most SCM test cases.To use the SCM as a direct tuning tool for global simulations, we assume G = 100 × 100 [km 2 ], which is roughly similar to the size of the horizontal grid (1-degree) employed in the subsequent global simulations.The observed long-term hourly forcing data at the SGP site is derived from operational analyses using the Atmospheric Radiation Measurement (ARM; Ackerman & Stokes, 2003;Stokes & Schwartz, 1994) Climate Research Facility and NOAA GOES-8 satellite observations from 2004 to 2015 (Xie et al. (2004)).The forcing data provides information on basic atmospheric state, surface and top-of-atmosphere fluxes, and horizontal and vertical advective forcing.To run the SCM, we used the observed (rather than internally computed) horizontal wind profile at each time step (we also found that the simulation with the internally computed horizontally wind combined with interactive surface fluxes of heat and moisture produced similar results as the simulation with the observed horizontal wind, but with a slightly improved RMSE error); vertical advective forcings for temperature (T ) and water vapor specific humidity (q v ) computed from observed mean vertical velocity and simulated vertical profiles of T and q v at each time step; internally computed radiation; and externally specified upward latent and sensible heat fluxes at the surface.We found that the SCM simulation results are sensitive to how surface heat and moisture fluxes are computed.Thus, as a sensitivity test, we also ran the same SCM simulation forced by the internally computed surface fluxes with an interactive land model.
A set of hindcast SCM simulations are conducted for 5 days starting from 00UTC of each days during April 28-August 30 in the calendar years, 2004-2015.The 24-48 hr forecast simulations of individual hindcast runs are analyzed.Following Y. Zhang and Klein (2010), we grouped the days into the nocturnal, afternoon, and clearlight precipitation regimes based on timing and magnitude of observed precipitation peaks, with a slight modification of the original criterion to better represent the diurnal cycle of precipitation at the SGP site (Tang et al., 2022): nocturnal deep convection days (NOC) are defined as days when peak rainfall larger than 1 mm/day occurred between 0000 and 0700 LST; late-afternoon deep convection days (AFT) are defined as days when peak rainfall larger than 1 mm/day occurred between 1300 and 2000 LST; and clear/light-precipitation days (CLR) are defined as the remaining days.The number of days used for the compositing of NOC, AFT, and CLR cases are 355, 223, and 922, respectively.
In addition to SCM simulations, we also ran global simulations in atmospheric standalone mode for 10 years.These simulations are forced by observed climatological sea surface temperature (SST) and sea-ice fraction with their annual cycles at a horizontal resolution of 0.98°latitude × 1.258°longitude (nominally, 1-degree simulation), vertical resolution of 30 vertical layers, and a model integration time step of Δt = 30 [min].The land model is fully interactive with the atmosphere.The simulation with the default SAM0-UNICON will be referred to as SAM0, whereas the simulation with the parameterization of the elevated convection will be referred to as SAM0-ELE.Furthermore, we conducted a series of sensitivity simulations by changing several tuning parameters for the elevated convection, as listed in Table 1, and also by turning off contributions of external and cold pool-driven mesoscale flows on the elevated convection.

SCM Simulation
Figure 1 shows observed diurnal-averaged variations of surface precipitation (P s ), surface buoyancy flux (B s ), pressure vertical velocity (ω), and horizontal [hadv(T ), hadv(q v )] and three-dimensional advections [adv(T ), adv (q v )] of temperature and water vapor during the nocturnal precipitation (NOC), late-afternoon precipitation (AFT), clear/light-precipitation (CLR), and all day (ALL) regimes at the SGP site.The peak B s at around noon gets stronger from NOC through AFT to CLR.Other than this, the diurnal variations of B s in various regimes are quite small, with consistently negative B s during the night in all regimes.In contrast, P s shows substantial interregime variations with a peak at 0300 LST in NOC, 1800 LST in AFT, and 2400 LST in CLR.In the AFT regime, P s lags B s , whereas P s leads B s in NOC.On average, P s peaks at 0300 LST and reaches its minimum at 1200 LST, which is almost exactly out-of-phase with the diurnal cycle of B s (Figure 1d).These results indicate that the observed diurnal cycle of precipitation at the surface in the SGP region is controlled by some other processes occurring above the surface.
The composite time-height plot of ω indicates that the diurnal cycle of the surface precipitation is strongly influenced by the variation of ω in the troposphere above the PBL, with greater P s when ω is negative (i.e., upward motion) and vice versa.This association between ω and P s is particularly strong in the NOC regime during the night (Figure 1e).Even the precipitation maximum in the late afternoon during AFT is associated with strong upward motion (Figure 1f).Previous studies have suggested that these ascending motions are related to the eastward propagating, organized convection system that originated from the Rockies (Y.Zhang & Klein, 2010).After sunrise, weak subsidence motion develops in the lower troposphere and is sustained throughout the afternoon (i.e., 09-17 LST in Figure 1e), which may be driven by the thermally direct circulation between the Rockies and the SGP (Carbone & Tuttle, 2008).As expected, the diurnal composites patterns of adv(T ) and adv(q v ) are somewhat similar to that of ω because potential temperature (water vapor) increases (decreases) with height in the typical troposphere.In contrast to our expectation, however, the nocturnal precipitation maximum during NOC does not seem to have a clear association with hadv(q v ).At around 02 LST, there exists a maximum hadv(T ), which is a common feature in all four regimes.These observations indicate that in order to simulate the observed nocturnal precipitation maximum in a GCM, it may be necessary to use the grid-mean ω and three dimensional (not horizontal) advection tendencies of temperature and moisture.
Figure 2 shows diurnal variations of SCM-simulated surface precipitation rates compared to the observed precipitation rate.As reported by Park (2014aPark ( , 2014b)), SAM0 does a good job in reproducing the observed precipitation maximum in the late afternoon during AFT (Figure 2b).However, in the NOC and CLR regimes, SAM0 simulates too much afternoon precipitation and too little nocturnal precipitation.Consequently, the overall diurnal cycle of simulated surface precipitation rate is almost out-of-phase with that of the observation (Figure 2d).Our new parameterization for the elevated convection (SAM0-ELE) substantially improves the simulated diurnal cycle of surface precipitation.In all four regimes, too-strong afternoon precipitation in SAM0 is substantially suppressed, whereas too-weak nocturnal precipitation in SAM0 during NOC and CLR is amplified, resulting in a more realistic overall diurnal cycle of precipitation.
One notable feature that needs to be further improved is stronger precipitation than observation during 12-20 LST (the red line in Figure 1d).We speculate that some of these biases are related to the simulation setting.As explained in the previous section, our SCM simulations are forced by prescribed observed surface heat and moisture fluxes rather than by internally computed surface fluxes obtained from an interactive land model.In nature, upward surface heat flux decreases as temperature of near-surface air increases.Since our SCM simulations do not have this self-regulating negative feedback, near-surface air temperature in the late afternoon and associated convective activity are likely to be over-amplified.To assess this effect, we ran an additional SCM simulation with an interactive land model and the results are shown in Figure 2 (SAM0_isflx and SAM0-ELE_isflx).Compared to simulations with prescribed surface fluxes, the simulation with internally computed surface fluxes produces less precipitation during the late afternoon and, interestingly, more precipitation during the night, particularly in SAM0.This is presumably due to reduced convective stabilization of the grid-mean atmosphere in the afternoon, which strengthens nocturnal convection.Thus, some of the biases in SAM0 and SAM0-ELE stem from the use of observed surface fluxes that do not interact with simulated near-surface air.However, the SCM simulation with interactive surface fluxes also has an important caveat, since the enhancement of surface heat flux by surface wind gustiness driven by subgrid cold pools and associated mesoscale organized flow, has not been parameterized yet.(In contrast to the simulation, the observed surface heat and moisture fluxes already contain this gustiness effect.)Thus, the simulated surface fluxes of heat and moisture may be smaller than observation (we checked that the simulated surface heat flux is smaller than the observation at all times, and except in the afternoon, the simulated moisture flux is also smaller than the observation).A missing gust parameterization may explain the negative biases of surface precipitation in SAM0-ELE_isflx during the late afternoon in AFT when cold pool-driven mesoscale organization is strong.
Another important limitation of our SCM simulation is its inability to handle the horizontal advection of subgrid cold pools and associated mesoscale organized flow (i.e., the fractional area of subgrid cold pools and associated perturbations of temperature, moisture, horizontal and vertical velocities within subgrid cold pools with respect to the grid-mean values within the boundary layer).As noted by previous studies, observed nocturnal precipitation in this SGP region is influenced by the eastward propagating, organized convection system that originated from the Rockies [e.g., Y. Zhang and Klein (2010)].Consequently, our SCM may not produce enough nocturnal precipitation.Other than the lack of a gust parameterization (which is a future research subject), these limitations in our SCM simulations (i.e., a missing interaction between the atmosphere and land, and the absence of horizontal advection of subgrid cold pools) can be adequately handled in the global simulation.In spite of these limitations, our SCM test indicates that the parameterized elevated convection improves the simulation of nocturnal precipitation: regardless of whether observed or internally computed surface fluxes are used, SAM0-ELE simulates a better diurnal cycle of surface precipitation than SAM0, as shown by the substantial reduction of the Root-Mean-Squared-Errors (RMSE) against observation from SAM0 to SAM0-ELE (see Figure 2d).Another important aspect shown in Figure 2 is that more (less) nocturnal precipitation tends to be associated with less (more) afternoon precipitation.Through a series of tuning exercises, we found that without suppressing afternoon convection, it was difficult to enhance nocturnal precipitation even with a strong grid-mean upward flow during the night.This is presumably because strong afternoon convection stabilizes the atmospheric column, which suppresses subsequent nocturnal convection.This indicates that afternoon and nocturnal convections interact with each other, and an appropriate simulation of the relative strengths of the surface-based and elevated convection is one of the key factors necessary for a successful simulation of the diurnal cycle of precipitation in this region.Similar interaction between daytime convection and nocturnal convection has been found and discussed in Xie et al. (2019).They also showed that the suppression of daytime convection helps strengthen nocturnal convection.
Figure 3 shows the time-height cross-sections of the launching interface frequency of the elevated convection [FQ e (z)] and updraft mass flux.In SAM0-ELE, FQ e (z) is computed as the frequency of maximum MSE below the 600 hPa level above the second lowest grid layer with a positive grid-mean vertical velocity at the launching interface.In SAM0, however, FQ e (z) = 0, since SAM0 does not handle the elevated convection.In all regimes, SAM0 is dominated by afternoon convection that rises up to the tropical upper troposphere and nocturnal convection during the night is very weak M < 0.01) .On the other hand, SAM0-ELE simulates stronger nocturnal convection than SAM0, particularly, in the NOC regime M > 0.01) , and afternoon convection gets weaker from SAM0 to SAM0-ELE.In all regimes, SAM0-ELE frequently launches the elevated convection below 700 hPa during the night with a relatively smaller FQ e (z) in CLR than in NOC and AFT.These diurnal variations of FQ e (z) is similar to those derived from the observed MSE profile (not shown).
To obtain further insight, we plotted in Figure 4 diurnal variations of the mesoscale convective organization driven by subgrid cold pools (Ω), external mesoscale organization (Ω ext ), buoyancy Δ θv ) , vertical velocity ( ŵ) , and radius R) of convective updraft plumes at the launching interface (including both the surface-based and elevated convections) simulated by SAM0 and SAM0-ELE.In SAM0, Ω ext = 0.Both models simulate maximum Ω just before midnight and minimum Ω at around noon.In SAM0-ELE, Ω controls the strength of the elevated convection as well as the surface-based convection.In the afternoon, SAM0-ELE simulates a smaller Ω than SAM0, indicating that weaker afternoon convection may enhance nocturnal convection.In NOC, from 00 to 09 LST, SAM0-ELE simulates a higher Ω than SAM0.The external mesoscale organization, Ω ext , is strongest during the night in all regimes.If the horizontal advection of Ω and associated perturbations of thermodynamic scalars were properly included, simulated nocturnal precipitation in SAM0-ELE might have been larger.Consistent with the changes in Ω, during the afternoon, both Δ θv (z o ) and ŵ(z o ) decrease from SAM0 to SAM0-ELE.However, during the night, Δ θv (z o ) decreases from SAM0 to SAM0-ELE even though Ω increases, which is partly due to enhanced three-dimensional cold advection in association with a strong Ω ext in SAM0-ELE (see Figure 5g).In SAM0-ELE, as formulated in Equations 11 and 9, Δ θv (z o ) and ŵ(z o ) are influenced by external organized flow (Δϕ ext , Δw ext ) as well as cold pool-driven organized flow (Δϕ Ω , Δw Ω ).The most pronounced change from SAM0 to SAM0-ELE is a substantial increase of R during the night due to Ω ext > 0 [Equation 14].With a larger plume radius and stronger vertical velocity, the elevated convection can grow deeper and generate more nocturnal precipitation in SAM0-ELE.At least in our SCM simulation, higher updraft buoyancy at the launching interface does not seem to be a necessary factor required for simulating strong nocturnal precipitation (see Figures 4d  and 2a).
Figure 5 shows the relative contributions of cold pool-driven mesoscale flow and external mesoscale flow to thermodynamic properties of the convective updraft plumes at the launching interface.The diurnal variations of the PBL top height (z PBL ) and the plume launching height (ẑ o ; ẑo = 0 for the surface-based convection and ẑo = z e for the elevated convection) are also plotted.In all regimes, z PBL is maximized during the mid-afternoon with the deepest PBL in the CLR regime.During the night, ẑo is higher than z PBL , indicating that the elevated convection is initiated.Both subgrid cold pools and external organized flow contribute to enhancing the updraft vertical velocity at all times, although the frequency of occurrence of the elevated convection is low during the daytime (see Figure 3).During the late afternoon and night, subgrid cold pools generate highly positive Δθ c,Ω but negative Δq t,Ω .During the night, external mesoscale flow increases the relative humidity of the updraft plume by decreasing updraft temperature (Δθ c,ext < 0) and increasing updraft moisture (Δq t,ext > 0) that partially compensates for the negative Δq t,Ω .With a higher relative humidity, the elevated convection can readily reach its LCL and grow deeper.Furthermore, from the launching interface to the LFC, the elevated convection receives a dynamic uplift forcing from external organized upflow through the parameterized relaxation forcing, entrainment mixing, and updraft buoyancy sorting, all of which are a function of external mesoscale upflow [Equation 17].At the launching interface, both updraft vertical velocity and plume radius increase with Ω ext and Ω [Equations 9 and 14], but updraft fractional area increases as Ω ext increases and as Ω decreases [Equation 15].As a result, the updraft mass flux of the elevated convection at the launching interface may increase or decrease depending on the relative variations of Ω ext and Ω.
In summary, our analysis of SCM simulations indicates that in contrast to the surface-based convection in the afternoon, the elevated convection in the night is driven by external mesoscale organized flow that forces the convective updraft plume to readily reach its LFC by increasing the plume's relative humidity and providing it dynamic uplift forcing; decreases entrainment dilution by increasing updraft plume radius; and increases updraft fractional area and updraft mass flux.Subgrid cold pools-a major driver of the surface-based convection during the late afternoon-also contribute to enhancing the elevated nocturnal convection.Although parameterized in an exclusive and separated way, it appears that the surface-based and elevated convections interact with each other through the stabilization of the grid-mean atmospheric column that affects subsequent convection.

Global Simulation
Global simulation differs from the SCM simulations in several aspects.Global simulation handles advection of subgrid cold pools and associated perturbations of thermodynamic scalars but the SCM cannot.The SCM simulation uses observed surface fluxes but the global simulation internally computes surface fluxes, that is, the atmosphere-land interactions exist in the global simulation.In contrast to the SCM simulation, the global simulation simulates the feedback of the parameterized physical processes on grid-mean advective forcing, that is, grid-mean vertical velocity and three-dimensional advection of thermodynamic scalars are influenced by parameterized convection.Because of these differences, the parameterized elevated convection may have different impacts on the SCM and global simulations.Here, we examine how the elevated convection changes the global climate.Figure 6 shows a Taylor diagram (Taylor, 2001) that summarizes the model's ability to reproduce the observed global mean climate.Observation data used for this diagram are: Interim ECMWF Re-Analysis product (ERAI) for three-dimensional standard atmospheric variables (Simmons et al., 2007), Global Precipitation Climatology Project (GPCP) for surface rainfall (Adler et al., 2003), Clouds and Earth's Radiant Energy Systems Energy Balanced and Filled for shortwave (SWCF) and longave cloud radiative forcing (LWCF) (CERES-EBAF) (Loeb et al., 2009), Willmott-Matsuura near surface air temperature (Willmott) (Willmott & Matsuura, 1995), and European Remote Sensing Satellite Scatterometer (ERS) for surface wind stress (Bentamy et al., 1999).The mean relative RMSE of the SAM0-ELE simulation compared to that of the SAM0 simulation with respect to the observations averaged over the 10 semi-independent climate variables (the RMSE in Figure 6) is 0.978, indicating that the new parameterization for the elevated convection slightly improves the overall mean climate.However, the simulation of the land rainfall is slightly degraded in terms of both correlation and standardized deviation.We can further improve the global performance score by tuning some parameters.For example, with a larger G o = 15 2 [km 2 ], the mean RMSE drops to 0.964, which, however, degrades the simulation of nocturnal precipitation in the mid-US (see Figure 11).
Figure 7 shows the global climatology of precipitation rate at the surface during DJF and JJA obtained from the GPCP observation and the model biases compared to the observations.SAM0-ELE performs slightly better than SAM0 in DJF in terms of both spatial correlation (r) and rmse error but with a similar performance as SAM0 in JJA.Two noticeable improvements are the reduction of strong positive biases over the eastern equatorial Pacific Ocean west of Panama and the reduction of negative bias over the central US in JJA.The latter is likely due to enhanced nocturnal precipitation by the elevated convection, whereas the former is more likely due to nonlocal feedback interactions, since the elevated convection does not occur in this region (see Figures 8a and 8d).Also improved are the biases in South America and Africa in DJF.Not shown but a sensitivity simulation with a larger G o = 15 2 [km 2 ] produces a better precipitation climatology with improved spatial correlation, r = 0.909 (0.904), and rmse = 1.483 (1.631) between simulation and observation in DJF (JJA).
Figure 8 shows global maps for vertically integrated frequency of occurrence (I ≡ ∑ ∞ z=z e FQ e (z) and 0 ≤ I ≤ 1), vertically averaged launching height (z e ), and vertically averaged Δw ext (z e ) [Equation 6] of the elevated convection simulated by SAM0-ELE in JJA and DJF during the late night (02-04 LST) and afternoon (14-16 LST).The parameterized elevated convection is simply diagnosed to occur when the grid-mean maximum MSE exists above the lowest model layer and below the 600 hPa level with an upward grid-mean vertical velocity at z e .In SAM0-ELE, the elevated convection mostly occurs over the continents during the night.In this region, mean z e is Figure 6.A Taylor diagram (Taylor, 2001) measuring the global performance of the model based on the spatiotemporal correlation and standardized deviation (the ratio of simulated-to-observed standard deviation) of 10 semi-independent climate variables with respect to observations.A perfect simulation has correlation 1 and standardized deviation 1.The RMSE and Bias on the top right portion are obtained by first computing the Root-Mean-Squared-Error (RMSE) and absolute percentage difference (bias) of individual climate variables with respect to observation from each SAM0 and SAM0-ELE simulations; taking the ratio of SAM0-ELE's rmse (bias) to SAM0's rmse (bias) for individual variables; and then averaging the ratio of all 10 climate variables.mostly lower than 2000 [m] where the low-level jet can exist, and mean Δw ext (z e ) is lower than 2 [m s 1 ].In large mountain areas, however, Δw ext (z e ) is very strong (>2) with small z e , reflecting a dynamic up-slope lifting of nearsurface air.Due to abundant surface moisture, simulated convection over the ocean is dominated by the surface- based convection.However, the elevated convection also occurs in several oceanic regions with a weak diurnal cycle: the warm air advection region with cold sea surface temperature (SST) in the northwestern Pacific and northwestern Atlantic Oceans and the eastern equatorial Pacific Ocean west of Peru, where z e is relatively low; subtropical marine stratocumulus decks, where z e is high but Δw ext (z e ) is small; mid-latitude storm tracks during boreal summer, where z e is high; and some portions of the South-Pacific Convergence Zone and the South-Atlantic Convergence Zone.It is not clear whether the simulated elevated convection in the warm air advection regions and subtropical stratocumulus decks over the ocean is realistic.However, the parameterized elevated convection in the other regions seems to be consistent with previous observational studies that the elevated convection in nature can be driven by various mechanisms including the low-level jet convergence, synoptic front, mountains, and advection of mesoscale convective system (Geerts et al., 2017;Weckwerth et al., 2019).
Figure 9 shows the diurnal cycle of surface precipitation rate during JJA obtained from SAM0, SAM0-ELE, and 3-hourly TRMM satellite observations (Huffman et al., 2007).We performed a Fourier analysis to compute the phase and amplitude of surface precipitation rate fitted to the first harmonic function with a period of 1 day, following the work of Yang and Slingo (2001).Different colors denote the local hour when the surface precipitation rate is maximum, whereas the shading represents the amplitude of the diurnal cycle, with a darker color denoting a larger amplitude.As reported by Park et al. (2019), SAM0 already reproduces well the observed maximum precipitation rate in the late afternoon over the summer continents and in the early morning over the ocean.However, SAM0 does not reproduce observed nocturnal precipitation maxima in the mid-US during JJA  6] in DJF and JJA during the late night (02-04 LST) and the afternoon (14-16 LST) simulated by SAM0-ELE.Here, z e and Δw ext (z e ) are averages only for cases when the elevated convection was diagnosed to occur.
(Figure 9d).With its new parameterization of the elevated convection, SAM0-ELE improves the simulation of nocturnal precipitation in the mid-US (Figure 9g).In addition, nocturnal precipitation maxima in the vicinity of the Himalaya and central China regions are better simulated.However, SAM0-ELE simulates unrealistically strong nocturnal precipitation over northeastern Asia and northwestern India with degradation of late afternoon precipitation maxima over western Africa.This indicates that our parameterization scheme for the elevated convection is missing some important processes necessary to capture the observed inter-regional variations of nocturnal precipitations-or, simulated grid-mean vertical velocity is not realistic.
The improved simulations of nocturnal precipitation in the mid-US can also be seen in Figure 10 which shows the composite diurnal time series of surface precipitation rate over the three regions in the mid-US (W:western, C:central, and E:eastern) and the southern US.From the western to eastern mid-US, the observed timing of maximum surface precipitation gradually shifts from late afternoon to midnight with increasing mean precipitation amount.SAM0 does a good job in the western mid-US and southern US but fails to reproduce the observed west-to-east delay of maximum precipitation timing in the mid-US: in the eastern mid-US, the SAM0-simulated diurnal cycle of surface precipitation is almost out-of-phase with observation, mainly due to the lack of nocturnal precipitation.With the parameterized elevated convection, SAM0-ELE is better than SAM0 at simulating nocturnal precipitation, particularly in the eastern mid-US.The added parameterization for the elevated convection does not degrade already-good simulations of late afternoon precipitation maxima in the western mid-US, but further improves afternoon precipitation in the southern US.Although the results are encouraging, the improvements are less impressive than the ones in the single-column simulation (see Figure 2d).In the Eastern mid-US box in which the SGP site is located, the global simulation reproduces well the overall pattern of the SCM-simulated diurnal cycle of precipitation; however, it simulates weaker nocturnal precipitation maxima than the SCM simulation and observation.This may indicate that the grid-mean upward vertical velocity during the night in the global simulation is not as strong as observation in this region, which may be indicative of too strong stabilizing feedback of subgrid convection on the grid-mean flow in the global simulation.

Sensitivity Simulations
We explore the model's sensitivity to various tuning parameters for the elevated convection (see Table 1) by changing G o from 12 2 to 15 2 [km 2 ]; τ from 200 to 100 [s]; w o from 1 to 2 [m s 1 ]; c A from 5 to 2; L r from 350 to 10 [m]; and a 2 from 1/1,800 to 1/400 [m 1 ] for the elevated convection.Since the default values of tuning parameters in Table 1 are obtained from extensive tuning exercises, it is necessary to document the model sensitivity to these parameters.If no feedback interactions exist, all these changes other than L r are expected to make the elevated convection weaker than the default simulation.
Figure 11 shows the time series of surface precipitation rate obtained from SCM simulations.Interestingly, simulated diurnal cycles of surface precipitation rate are rather insensitive to changes in these tuning parameters.The simulation results in the ALL and NOC regimes show that weaker elevated convection tends to decrease nocturnal precipitation but increase afternoon precipitation, and vice versa, indicating that afternoon and nocturnal convections interact with each other.Too much nocturnal precipitation during AFT in the default simulation is remedied by using a 2 = 1/400 instead of 1/1,800 in Equation 18for the elevated convection, which, however, also weakens the nocturnal precipitation peak during NOC.This indicates that an appropriate parameterization for the entrainment rate is also important to simulate the observed diurnal cycle of precipitation.
Figure 12 shows the resulting time series of surface precipitation rate in the four selected regions obtained from global simulations.Similar to the SCM simulations, simulated diurnal cycles of surface precipitation rate are rather insensitive to changes in these tuning parameters; although mean precipitation amount tends to decrease systematically as the elevated convection becomes weaker, particularly in the southern US.The global performance score (i.e., mean RMSE in the Taylor diagram) of the default SAM0-ELE and its six sensitivity simulations are 0.978 (default), 0.964 (G o = 15 2 ), 0.979 (τ = 100), 0.987 (w o = 2), 0.993 (c A = 2), 0.987 (L r = 10), and 0.996 (a 2 = 1/400).These results indicate that by tuning the parameters alone, increasing nocturnal precipitation in the eastern mid-US while simultaneously decreasing nocturnal precipitation in the southern US during 04-08 LST without degrading the global performance score is challenging.It may be that simulated grid-mean vertical flow and three-dimensional advection forcing are not strong enough to produce sufficient nocturnal precipitation.
Finally, to obtain more insight into the physical processes responsible for the observed nocturnal precipitation maximum, we conducted two sensitivity simulations by Equation 1 turning off the impacts of external mesoscale organization on the elevated convection (i.e., set f = 0 in Equation 7, such that Δw ext (z) = Δϕ ext (z) = Ω ext = 0), which will be referred to as EXT-OFF, and Equation 2 turning off the impacts of cold pool-driven mesoscale organization on the elevated convection [that is, Δw Ω = 0 in Equation 9; Δϕ Ω = 0 in Equation 11; and Ω = 0 in Equations 14 and 15], which will be referred to as SUB-OFF.These simulations are designed to estimate the relative contributions of external and cold pool-driven mesoscale flows to the elevated convection and associated nocturnal precipitation.Figure 13 shows the resulting time series of surface precipitation rate in the US.Without the parameterization for external mesoscale organization (i.e., EXT-OFF), the simulation of nocturnal precipitation is substantially degraded, particularly in the eastern mid-US, and the resulting diurnal cycle becomes similar to that of SAM0.If we turn off the impacts of cold pool-driven mesoscale organized flow on the elevated convection (i.e., SUB-OFF), the precipitation amount decreases slightly at all times without affecting the diurnal cycle.These sensitivity simulations indicate that a key ingredient for simulating observed nocturnal precipitation is to appropriately parameterize the impacts of external organized flow on the elevated convection.The global mean RMSE of the default SAM0-ELE and of its two sensitivity simulations are 0.978 (default), 0.959 (EXT-OFF), and 1.000 (SUB-OFF), implying that more refinements are necessary to further improve the simulation of both global mean climate and diurnal cycle of precipitation.

Summary and Conclusion
To improve the simulation of nocturnal precipitation, we developed a parameterization for the elevated convection that is launched from the top interface of the grid layer with a maximum grid-mean MSE above the second lowest model layer, z e .Initial thermodynamic properties of the elevated updraft plume at z e and their vertical  evolutions are computed in a manner similar to those of the surface-based convection, but with the inclusion of additional perturbations driven by external organized flow.The key assumption is that under certain circumstances (i.e., when grid-mean vertical velocity at z e is upward), grid-mean vertical flow in nature is concentrated in a small sub-area within the grid box as a form of external mesoscale vertical flow.Based on this assumption, we estimated the properties of the partially resolved external mesoscale flow from the grid-mean vertical velocity and three-dimensional advection tendencies of thermodynamic scalars, ϕ (i.e., temperature, moisture, and horizontal momentum), and then tried to mimic embedded external mesoscale flow with the parameterized subgrid elevated convection.This was achieved by enhancing the elevated updraft plume's vertical velocity, radius, fractional area, and mass flux at the launching interface; changing the updraft plume's ϕ at the launching interface; and supplying a dynamic uplift forcing to the updraft plume from its launching interface to the LFC, using estimated properties of the external mesoscale flow.With the modified formula for fractional mixing rate of the updraft plume, our parameterization of the elevated convection is implemented into a unified convection scheme (UNICON) and tested for the single-column case at the SGP site in US and in global simulations using SAM0-UNICON as a host GCM.
Observation data at the SGP site indicate that the diurnal cycle of surface precipitation rate is not tied to surface buoyancy flux but is more strongly connected to mean vertical velocity and three-dimensional advection tendencies of temperature and moisture, consistent with the assumptions used in our parameterized elevated convection.In the single-column test, compared to observation, SAM0 simulates too weak (strong) nocturnal (afternoon) precipitation.Although some limitations exist in our setting of the single-column simulation (e.g., no treatment of horizontal advection of subgrid cold pools and absence of a gust parameterization driven by subgrid cold pools), it was clear that the parameterized elevated convection substantially improves the simulation of nocturnal precipitation and the diurnal cycle of precipitation.More specifically, SAM0-ELE simulates stronger (weaker) nocturnal (afternoon) convection than SAM0, due to a larger plume radius and stronger vertical velocity of the elevated updraft plume during the night, as a result of strong external organized flow.During the late afternoon, subgrid cold pools dominantly drive the surface-based convection, whereas during the night and early morning, external organized flow strongly drives the elevated convection.In our single-column simulations, it appears that the nocturnal convection tends to become stronger as the afternoon convection gets weaker, indicating that the nocturnal convection and afternoon convection are not independent; rather, they interact with each other by stabilizing the grid-mean atmospheric column that affects subsequent convection.
Global simulations showed that the parameterized elevated convection in SAM0-ELE improves the overall model performance and better reproduces the observed mean climate over the globe.The elevated convection mostly occurs over the continents during the night in JJA with a distinct diurnal cycle.With a negligible diurnal cycle, the oceanic elevated convection also occurs in several regions, such as mid-latitude storm tracks during boreal summer and warm air advection regions over the northwestern Pacific and northwestern Atlantic Oceans.Analysis of the diurnal cycle of surface precipitation showed that SAM0-ELE noticeably improves the simulation of nocturnal precipitation over the central US but simulates too-strong nocturnal precipitation over northeastern Asia and northwestern India.Sensitivity simulations showed that the simulated diurnal cycle of precipitation in the mid-US is rather insensitive to changes in tuning parameters, and a key ingredient for simulating observed nocturnal precipitation in the mid-US is to appropriately parameterize the impacts of external organized flow on the elevated convection.
Although encouraging results are obtained with the new elevated convection parameterization, more refinements are necessary to further improve both the diurnal cycle of precipitation and global mean climate.The fact that our elevated convection improves the simulation of nocturnal precipitation in the central US but simulates too strong nocturnal precipitation in northeastern Asia indicates that we may need to parameterize the area of external mesoscale upflow, G o , as a function of other physical processes, instead of specifying it as a constant.To save computation time, we launched only one of the surface-based convection or elevated convection; however, in nature, they may occur at the same time.Thus, we may need to launch both the surface-based and elevated convections at the same time.Substantial differences between single-column simulations with externally specified versus internally computed surface fluxes imply the importance of using a good land model.Finally, as explained in Section 2, the elevated convection uses triggering and closure assumptions different from those of the surface-based convection.For example, the elevated convection parameterization uses grid-mean vertical velocity and three dimensional advection of grid-mean thermodynamic scalars, whereas the surface-based convection does not.To impose consistency, it may be more reasonable to unify the treatment of both convections.We will report these improvements in the near future.

Figure 7 .
Figure 7. Global climatology of (top row) total precipitation at the surface obtained from GPCP observation in units of [mm/day] and the model biases with respect to observation simulated by (middle) SAM0 and (bottom) SAM0-ELE during (left) DJF and (right) JJA.Global mean error against observation, spatial correlation with observation, and the RMSE error against observation are shown on the top portion of each simulation plot.

Figure 8 .
Figure 8. Global distributions of vertically integrated frequency of occurrence of the elevated convection (left, 0 ≤ I ≡ ∑ ∞ z=z e FQ e (z)≤ 1), vertically averaged height of the launching level of the elevated convection (center, z e ), and vertically averaged vertical velocity of external mesoscale flow at the launching level [right, Δw ext (z e ), Equation6] in DJF and JJA during the late night (02-04 LST) and the afternoon (14-16 LST) simulated by SAM0-ELE.Here, z e and Δw ext (z e ) are averages only for cases when the elevated convection was diagnosed to occur.

Figure 9 .
Figure 9.Diurnal cycle of precipitation rate at the surface over (left column) USA, (center column) tropical continents, and (right column) Asia regions in JJA obtained from (top) TRMM satellite observation during January 2000-December 2009, (middle) SAM0, and (bottom) SAM0-ELE.The color scale denotes the local hour when the surface precipitation rate fitted to the first Fourier harmonic is maximum, whereas the dark scale denotes the amplitude of the diurnal cycle.The four domains in US used in the following figures are denoted by red boxes.

Figure 13 .
Figure13.Diurnal cycle of precipitation rate at the surface over the four selected regions in the US during JJA obtained from the observation (black), SAM0-ELE (red), EXT-OFF (orange), and SUB-OFF simulations (green).

Table 1 A
List of Tuning Parameter for the Elevated Convection