1. Introduction
Continental clouds and convection are closely coupled with the underlying land surface. The heterogeneous characteristics of the land surface result from the spatial variation of land cover and land use across a spectrum of length scales (Avissar and Chen 1993). Both modeling and observational studies support the notion that differential heating of the atmosphere by a heterogeneous land surface may induce a secondary circulation that influences the turbulent transport in the planetary boundary layer (PBL) and the development of clouds (Chen and Avissar 1994; Avissar and Liu 1996; Taylor et al. 2007; Kang et al. 2007; Lothon et al. 2011). Therefore, it is important to understand the different processes governing the interactions of the PBL and clouds with a heterogeneous land surface.
There are a number of large-eddy simulation (LES) studies that investigate the influence of idealized surface heterogeneity on the PBL characteristics and clouds. Representations of surface heterogeneity are diverse but fall into two main categories: static and dynamic heterogeneity. In the static heterogeneity, the land surface is represented by prescribed surface properties, such as the heterogeneity size and pattern and the surface heat flux contrast (Kang and Bryan 2011; Huang and Margulis 2013; Rieck et al. 2014; Rochetin et al. 2017). In the dynamic heterogeneity, the cloud itself generates the discontinuity on the surface temperature through either cloud radiative effects or the effects of cold pools induced by precipitation evaporation (Lohou and Patton 2014; Rieck et al. 2015; Gronemeier et al. 2017). Regardless of the surface specification, a main subject of these studies is the influence of surface heterogeneity on the development of secondary mesoscale circulations and clouds.
For instance, the optimal length scale to induce a secondary circulation is commonly suggested to be mesoscale but varies considerably. Avissar and Schmidt (1998) and Baidya Roy and Avissar (2000) suggested the heterogeneity wavelength to be larger than 5–10 km, and Patton et al. (2005) found the scale to be 2–4.5 times the boundary layer height from their dynamically coupled LES–land model. Apart from the heterogeneity length scale, heterogeneity amplitude can modify the secondary circulation, which in turn triggers an earlier onset of convection (Kang and Bryan 2011) and even a transition from shallow to deep convection (Kang and Ryu 2016).
The distribution of clouds itself can impact heterogeneity on the surface via cloud radiative effects. Lohou and Patton (2014) found that an organized circulation may result from the surface heating difference generated by overpassing shallow cumuli. Gronemeier et al. (2017) found a dramatic change on the development of mesoscale circulation and clouds following a shift in the direction of shadows relative to the heterogeneity orientation. For instance, Gronemeier et al. (2017) presented that the existence of clouds can reduce the effect of surface heterogeneity by surface shading. However, Rieck et al. (2015) suggested that cold pools can strengthen any existing secondary circulation and overwhelm the cloud-shading effect. Additionally, a heterogeneous distribution of shallow cumuli can induce the net surface warming by increasing the diffusive component of solar radiation (Berg et al. 2011), adding additional complexity in the land–atmosphere interaction (Xiao et al. 2018).
At the same time, the atmospheric background wind is a well-known factor that dampens the secondary circulation through rapid mixing in the PBL. Avissar and Schmidt (1998) found that a wind speed of 2.5 m s−1 is effective enough to reduce the impact of surface heterogeneities when their length scale is in the range of 2–40 km. Furthermore, a moderate wind speed of 5 m s−1 virtually eliminates the heterogeneity impact in their study. Avissar and Schmidt (1998), however, do not discuss the impact of background wind speed on the potential development of clouds over heterogeneous land surfaces.
Characteristics of the surface heterogeneity and the background wind speed exert an opposite impact on the development of the secondary circulation. But only a few studies have investigated the combined influence of surface heterogeneity and the background wind speed on the PBL characteristics only but not on the convective clouds development (Hadfield et al. 1991; Raasch and Harbusch 2001; Maronga and Raasch 2013; van Heerwaarden et al. 2014). Recently, Rochetin et al. (2017) investigated the combined influence of the large-scale wind and the heterogeneity of surface heat flux on the triggering of deep convection over a semiarid Sahelian environment. Their finding suggests that the surface heterogeneity not only expedites the initiation of deep convection, it also affects the spatial distribution of deep convection where clouds mostly form over the dry surface by the induced mesoscale breeze circulation.
In this study, we examine the combined influence of heterogeneity size and the background wind speed on the development of secondary circulation, PBL turbulence, and boundary layer clouds. Our LESs are based on the Continental Active Surface-Forced Shallow Cumulus (CASS) case based on the summertime observation at midlatitude grassland/cropland from Zhang et al. (2017) but over a chessboard-patterned heterogeneous surface. Some of the clouds are shown to grow deeper than shallow cumulus and produce precipitation in the afternoon under the influence of surface heterogeneity in surface heat fluxes and background winds. Our goal is to determine and understand the range of the patch sizes and the wind speeds that trigger a convection transition over the heterogeneous land surface. This transition results from a secondary circulation that includes large moisture variability across the PBL.
In section 2, the LES model and case setup are described. The general influence of patch size and the background wind on the development of clouds and their related processes are documented in section 3. Section 4 presents the vertical transport of moisture in the PBL through the secondary circulation and its scalability with patch size. Section 5 documents the structural change of the secondary circulation under the nonzero background wind and discusses why the background wind is effective in mitigating the heterogeneity that the surface is trying to impose. In section 6, we present a criterion that determines the likelihood of the convection transition for a given patch size and background wind speed. This paper ends with the summary in section 7.
2. Methodology
a. SAM
The widely applied System for Atmospheric Modeling, version 6.10.10 (SAM 6.10.10; Khairoutdinov and Randall 2003), is used to run LESs to explicitly resolve cloud and precipitation processes over the heterogeneous land surface. SAM adopts the anelastic approximation for the equation of air motion. Along with the wind velocities, SAM predicts the liquid water/ice moist static energy, total nonprecipitating water (vapor, cloud water, and cloud ice), and total precipitating water (rain, snow, and graupel). The computation of longwave and shortwave radiation follows the scheme used in the National Center for Atmospheric Research (NCAR) Community Climate Model, version 3 (CCM3; Kiehl et al. 1998). We use a double-moment bulk microphysics scheme (Morrison et al. 2005) as it includes more comprehensive ice microphysics, but our simulation results are not particularly sensitive to the choice of single- or double-moment scheme. The mixing ratio and the number concentration are predicted for each of the four hydrometeor species (cloud droplets, cloud ice, rain, and snow) by considering the balance among the advection, sedimentation, turbulent diffusion, and microphysical processes. A damping layer is applied near the domain top to reduce the reflection and buildup of gravity waves.
b. Simulation setup
Our case setup closely follows the new composite case study of CASS (Zhang et al. 2017), which is based on long-term observations at the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) site. This case represents a typical daytime evolution from sunrise to sunset on the days observed to have fair weather nonprecipitating surface-forced shallow cumulus at the SGP site. The detailed case setup with the initial sounding, surface heat fluxes, and large-scale forcing are available at the CASS website (http://portal.nersc.gov/project/capt/CASS). The surface roughness length is set to 0.035 m following the CASS setup. To the CASS setup, we add heterogeneity in the prescribed surface heat fluxes and modify the background wind. Cloud droplet number concentration is prescribed to be 100 cm−3 in the microphysics scheme.
The horizontal domain size of our LES is 28.8 km × 28.8 km with periodic boundary conditions. The horizontal resolution is 50 m in both the x and y directions. Beneath 4 km, the vertical resolution is 20 m with stretching grids up to 16 km. A 1-s time step is used.
The land surface heat fluxes are prescribed with a chessboard pattern (Fig. 1). We refer to the patches with greater latent heat flux (LHF) as “WET” and the other patch type with lesser latent heat flux as “DRY.” All other properties of the surface including surface albedo and roughness length are homogeneous throughout the domain and do not vary with the patch type. The wet and cool patches alternate with dry and warm patches, but the sum of latent plus sensible heat fluxes (SHFs) at every grid point is constant throughout the domain. Simulations are performed with patch sizes of 1.2 (HET1), 2.4 (HET2), 4.8 (HET5), 7.2 (HET7), and 14.4 km (HET14).
Schematic representation of the prescribed heterogeneous domain surface with various patch sizes of (left to right) 14.4, 7.2, 4.8, 2.4, and 1.2 km.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Schematic representation of the prescribed heterogeneous domain surface with various patch sizes of (left to right) 14.4, 7.2, 4.8, 2.4, and 1.2 km.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Schematic representation of the prescribed heterogeneous domain surface with various patch sizes of (left to right) 14.4, 7.2, 4.8, 2.4, and 1.2 km.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
The contrast of surface heat fluxes between patches is maintained at 60% of domain-averaged sensible heat flux at any time (Fig. 2). For WET (DRY) patch, 30% of domain-mean sensible heat flux is subtracted from the sensible (latent) heat flux and is added to the latent (sensible) heat flux. This prescribed patch contrast roughly represents the difference in the surface heat fluxes between grassland and crop fields measured by energy balance Bowen ratio (EBBR) stations and eddy correlation (ECOR) flux measurement sites at SGP, respectively (Zhang et al. 2017). The evaporative fraction for DRY and WET patch at noon local standard time (LST) is about 0.75 and 0.45, respectively, in comparison to 0.6 for the CASS case (Fig. 2c). The diurnal cycle of the domain-averaged surface sensible and latent heat fluxes is the same as in CASS. In comparison to the HET cases, an additional case with a homogeneous surface (HOM) is simulated using the domain-mean values for the surface heat forcing. To separate the local surface buoyancy forcing on the vertical velocity in the PBL, we provide separate additional simulations where we prescribed a homogeneous land surface with the same surface sensible and latent heat fluxes that were used for the DRY and WET patches, denoted as HOMU0_DRY and HOMU0_WET.
The daytime variation of the prescribed surface (left) SHF, (center) LHF, and (right) evaporative fraction for dry (red) and wet (blue) patches and the domain mean (black).
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
The daytime variation of the prescribed surface (left) SHF, (center) LHF, and (right) evaporative fraction for dry (red) and wet (blue) patches and the domain mean (black).
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
The daytime variation of the prescribed surface (left) SHF, (center) LHF, and (right) evaporative fraction for dry (red) and wet (blue) patches and the domain mean (black).
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
To examine the impact of the background wind speed, we set the initial horizontal winds Ub (0 m s−1) to be purely zonal and vertically constant. Simulations are performed with Ub of 0, 1, 2, 3, to 10 m s−1 (U0, U1, U2, U3, and U10). The wind field is relaxed to its initial state with a 1-h time-scale at all levels.
3. General influence of surface heterogeneity in development of clouds and related processes
Figure 3 illustrates the spatial organization of clouds and precipitation at midday in different patch sizes and background wind speeds. Under zero background wind speed, large patch sizes (>5 km) generate clouds that form primarily over DRY patches with cloud tops reaching well above 6 km and produce significant precipitation, while uniformly scattered shallow cumulus clouds prevail over smaller patch sizes (<5 km). Relative to the case with zero background wind, clouds in HET14 are shown to shift downwind with 1 m s−1 zonal background wind, but the convection transition and precipitation are still mostly over DRY patches. As the wind speed increases further, clouds remain shallow cumulus and do not transition into cumulus congestus/deep convection. In the HOMU0 case, all clouds remain shallow and are distributed uniformly across the domain, and the same is observed when the surface heat fluxes are prescribed following that of DRY patch (HOMU0_DRY).
Spatial distribution of clouds and precipitation at midday for (top) HET14U0, HET5U0, and HET2U0 and for (left) HET14U0, HET14U1, and HET14U2. Grid points with clouds (anywhere in the vertical column) are shaded gray, and white–green color scale represents surface precipitation rate. DRY (WET) patches are the red (blue) squares. Arrows in the HET14U1 and HET14U2 panels represent the direction and relative speed of the background wind. HOMU0 and HOMU0_DRY cases are also shown as a reference.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Spatial distribution of clouds and precipitation at midday for (top) HET14U0, HET5U0, and HET2U0 and for (left) HET14U0, HET14U1, and HET14U2. Grid points with clouds (anywhere in the vertical column) are shaded gray, and white–green color scale represents surface precipitation rate. DRY (WET) patches are the red (blue) squares. Arrows in the HET14U1 and HET14U2 panels represent the direction and relative speed of the background wind. HOMU0 and HOMU0_DRY cases are also shown as a reference.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Spatial distribution of clouds and precipitation at midday for (top) HET14U0, HET5U0, and HET2U0 and for (left) HET14U0, HET14U1, and HET14U2. Grid points with clouds (anywhere in the vertical column) are shaded gray, and white–green color scale represents surface precipitation rate. DRY (WET) patches are the red (blue) squares. Arrows in the HET14U1 and HET14U2 panels represent the direction and relative speed of the background wind. HOMU0 and HOMU0_DRY cases are also shown as a reference.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Figure 4 shows all of the simulations performed as a function of patch size and wind speed. Note that we define the convection transition as occurring when any simulated cloud top reaches the 6-km-height level following the definition of triggering of congestus clouds in Rochetin et al. (2017). Throughout this study, the convection transition case is characterized with the transition of shallow cumulus to congestus cumulus or deep convection. By this definition, HET14U0, HET14U1, HET7U0, and HET5U0 are the transition cases with a transition time all around 1200–1300 LST and surface precipitation exceeding 1 mm day−1 at any time of day. All other simulated clouds remain as shallow cumulus with no precipitation reaching to surface, thus the so-called nontransition cases.
Diagram of all simulations performed as a function of patch size and background wind speed. Different markers represent the occurrence of congestus cumulus/deep convection (DC) and hence the precipitation. For DC cases, color indicates the time (LST) when the convection transition occurs.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Diagram of all simulations performed as a function of patch size and background wind speed. Different markers represent the occurrence of congestus cumulus/deep convection (DC) and hence the precipitation. For DC cases, color indicates the time (LST) when the convection transition occurs.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Diagram of all simulations performed as a function of patch size and background wind speed. Different markers represent the occurrence of congestus cumulus/deep convection (DC) and hence the precipitation. For DC cases, color indicates the time (LST) when the convection transition occurs.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
In the following, all time-averaged analyses represent the shallow cumulus stage before the convection transition, unless specified otherwise. Transition cases are averaged for 30 min right before the convection transition, which is around 1200 LST with small variations among the transition cases. The nontransition cases including the homogeneous cases are averaged between 1130 and 1200 LST. In this way, we ensure the impact of changing the patch size and the background wind is represented for the same stage of the PBL and cloud development, when the subcloud-layer turbulence strength is the strongest but not yet affected by significant precipitation.
a. Daytime evolution of cloud properties and cloud radiative forcing
Figure 5 presents the daytime variation in cloud macrophysical properties and cloud radiative forcing at the surface. All the simulated cloud properties show the peak around noon coinciding with the maximum time of the surface heat fluxes. The shallow cumulus clouds simulated over the homogenous land surface fluxes fall generally within the range of the nontransition case over the heterogeneous land surface. Before 1200 LST when all cases are still in the shallow cumulus stage, transition cases are marked with the lower cloud fraction but with higher domain-mean cloud water (liquid plus ice) path compared to the nontransition cases. It is consistent that the clouds in the transition cases grow deeper while convection aggregates into a narrower region. It is worth noting that the cases that produce precipitation already have deeper clouds from cloud onset. The sharp reduction in the cloud water path in the afternoon in the transition cases represents the reduction of cloud water content by precipitation. The reduction is the largest in the HET14U0 corresponding to the strong precipitation. Figures 5d and 5e show that before noon, the net surface shortwave radiative cooling remains similar because the effects from the lower cloud fraction and the higher liquid water path in transition cases cancel out each other; however, the net surface longwave warming is reduced in transition cases because of the decrease in cloud fraction. In the afternoon, all the transition cases produce the surface precipitation with multiple peaks as shown in Fig. 5f. The peaks that follow the first precipitation maximum reflect the convection developing over the cold pools that spread from the first precipitation event. The precipitation rate tends to increase with the patch size for zero-background-wind cases similar to Rieck et al. (2014). The time evolution of cloud-base height is about the same in all cases, while the cloud tops show the clear separation between the transition and nontransition cases (Figs. 5g,h). In the afternoon, all transition cases have cloud tops reaching 6 km and above, while all nontransition cases reach up to 4–5 km. Cloud depth tends to gradually increase with the patch size but not in a linear way. However, as seen in HET14U1, even 1 m s−1 background wind strongly influences the intensity of precipitation and cloud depth.
Daytime evolution of (a) projected cloud fraction at the surface, (b) fraction of clouds with depth deeper than 300 m, (c) in-cloud condensate water path, (d) shortwave cloud radiative forcing at surface, (e) longwave cloud radiative forcing at surface, (f) surface precipitation, (g) cloud-base height, and (h) maximum cloud-top height. In-cloud condensate water path is defined as the domain-averaged cloud condensate water path divided by the cloud fraction. The cloud radiative forcing is defined as the net whole-sky radiation minus the net clear-sky radiation at the surface. Thus, negative (positive) radiation forcing means the net surface cooling (warming) under the presence of clouds. In (a)–(e), all the transition cases (DC) are enclosed in the red-shaded area, and all nontransition cases (no DC) are represented in the green-shaded area. The HOMU0 case is marked with a black solid line. In (f), each line color corresponds to transition cases that produces significant rainfall during the day. In (g) and (h), colored lines represent the transition cases denoted in (f), while the black line and green-shaded area represent HOMU0 and no DC, respectively. Except for (c) and (h), all fields are domain averaged.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Daytime evolution of (a) projected cloud fraction at the surface, (b) fraction of clouds with depth deeper than 300 m, (c) in-cloud condensate water path, (d) shortwave cloud radiative forcing at surface, (e) longwave cloud radiative forcing at surface, (f) surface precipitation, (g) cloud-base height, and (h) maximum cloud-top height. In-cloud condensate water path is defined as the domain-averaged cloud condensate water path divided by the cloud fraction. The cloud radiative forcing is defined as the net whole-sky radiation minus the net clear-sky radiation at the surface. Thus, negative (positive) radiation forcing means the net surface cooling (warming) under the presence of clouds. In (a)–(e), all the transition cases (DC) are enclosed in the red-shaded area, and all nontransition cases (no DC) are represented in the green-shaded area. The HOMU0 case is marked with a black solid line. In (f), each line color corresponds to transition cases that produces significant rainfall during the day. In (g) and (h), colored lines represent the transition cases denoted in (f), while the black line and green-shaded area represent HOMU0 and no DC, respectively. Except for (c) and (h), all fields are domain averaged.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Daytime evolution of (a) projected cloud fraction at the surface, (b) fraction of clouds with depth deeper than 300 m, (c) in-cloud condensate water path, (d) shortwave cloud radiative forcing at surface, (e) longwave cloud radiative forcing at surface, (f) surface precipitation, (g) cloud-base height, and (h) maximum cloud-top height. In-cloud condensate water path is defined as the domain-averaged cloud condensate water path divided by the cloud fraction. The cloud radiative forcing is defined as the net whole-sky radiation minus the net clear-sky radiation at the surface. Thus, negative (positive) radiation forcing means the net surface cooling (warming) under the presence of clouds. In (a)–(e), all the transition cases (DC) are enclosed in the red-shaded area, and all nontransition cases (no DC) are represented in the green-shaded area. The HOMU0 case is marked with a black solid line. In (f), each line color corresponds to transition cases that produces significant rainfall during the day. In (g) and (h), colored lines represent the transition cases denoted in (f), while the black line and green-shaded area represent HOMU0 and no DC, respectively. Except for (c) and (h), all fields are domain averaged.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
As an aside, we note that cloud properties in Fig. 5 show an early morning peak around 0930 LST. The residual layer is responsible for the early peak in cloud fraction but does not change whether a convection transition occurs.
b. Size distribution of clouds and subcloud thermals
Figure 6 presents the horizontal size distribution of clouds, cloud cores, subcloud-layer thermals, and thermal cores. Cloud size is determined from the average length of connected cloudy points in both the x and y directions. Similarly, the cloud-core size is based on the connected cloudy points that are positively buoyant with upward motion. The transects of the cloudy area and cloud-core areas are examined at the cloud base and cloud-core base, respectively. Here, the cloud base is defined as the height of maximum cloud fraction below 3 km from the domain-mean profile. The subcloud-layer thermal is defined as the connected area of updrafts, and the subcloud-layer thermal core is the connected area of the buoyant updraft points. Thermal and thermal-core lengths are examined at the same height that is the 20 m below the base of the lowest cloud to avoid including any cloudy grid point in the thermal diagnostics. The height difference between the aforementioned cloud base and the lowest cloud base is around 200 m on average in our simulations.
Time-averaged horizontal size distribution of (a) clouds, (b) cloud cores, (c) subcloud thermals, and (d) thermal cores. The x axis is the size (km), and the y axis is the probability for the given size. Colors for the shaded area and solid line follow Figs. 5a–e. (e)–(h) Scalability of the cloud and thermal size with the heterogeneity length scale for the cases with the zero background wind speed. The x axis represents the patch size including the homogeneous case denoted as “HOM.” The yellow line corresponds to the size for a given probability [yellow horizontal line that transects across the size in the corresponding figure in (a)–(c)], and the purple line represents the probability for a given size [the size corresponds to the purple line that vertically transects in (a)–(c)].
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Time-averaged horizontal size distribution of (a) clouds, (b) cloud cores, (c) subcloud thermals, and (d) thermal cores. The x axis is the size (km), and the y axis is the probability for the given size. Colors for the shaded area and solid line follow Figs. 5a–e. (e)–(h) Scalability of the cloud and thermal size with the heterogeneity length scale for the cases with the zero background wind speed. The x axis represents the patch size including the homogeneous case denoted as “HOM.” The yellow line corresponds to the size for a given probability [yellow horizontal line that transects across the size in the corresponding figure in (a)–(c)], and the purple line represents the probability for a given size [the size corresponds to the purple line that vertically transects in (a)–(c)].
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Time-averaged horizontal size distribution of (a) clouds, (b) cloud cores, (c) subcloud thermals, and (d) thermal cores. The x axis is the size (km), and the y axis is the probability for the given size. Colors for the shaded area and solid line follow Figs. 5a–e. (e)–(h) Scalability of the cloud and thermal size with the heterogeneity length scale for the cases with the zero background wind speed. The x axis represents the patch size including the homogeneous case denoted as “HOM.” The yellow line corresponds to the size for a given probability [yellow horizontal line that transects across the size in the corresponding figure in (a)–(c)], and the purple line represents the probability for a given size [the size corresponds to the purple line that vertically transects in (a)–(c)].
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Figure 6 shows the clear separation in the size distribution of clouds and thermals between transition and nontransition cases. The transition cases are characterized with the larger-sized clouds and the broader cloud cores, and the same applies to the subcloud thermal and thermal cores. The size of the shallow clouds and the connected thermals linearly scales with the patch size from HET1 to HET5, and then it plateaus for the transition cases. This suggests during the formation of clouds over 5-km patch size, small clouds start to cluster into large ones. While for cases with patch size less than 5 km, shallow cumuli remain as smaller convective cells that are located close but disconnected from each other. These findings are consistent with the size distribution of instantaneous cloud field near the time of convection transition over various patch sizes shown in Rieck et al. (2014).
It is also seen in Fig. 6 that the nontransition cases over heterogeneous domain show a similarity in the cloud characteristics with HOMU0, while those cases produce slightly larger subcloud-layer thermals when compared to the HOMU0 case.
c. Scale-dependent contributions to PBL turbulence
We have shown that the simulations can be divided into those that transition into cumulus congestus or deep convection and those that remain with shallow cumulus depending on the surface heterogeneity length scale and background wind speed (Fig. 4). The influence of the surface heterogeneity on the PBL flow dynamics has been reported in several LES studies (Hadfield et al. 1991; Avissar and Schmidt 1998; Patton et al. 2005). The common finding is that the turbulence structure differs greatly from the commonly known mixed-layer scaling with an additional secondary circulation triggered by variations in surface heating. Increased horizontal wind variance near the surface and the top of the PBL develops corresponding to the convergence (divergence) at the bottom (top) branch of the triggered secondary circulation. This phenomenon is most pronounced when the heterogeneity length scale lies within the mesoscale range. In this section, we examine the influence of the heterogeneous land surface and background wind on the dynamics and thermodynamics of the turbulent flow in the PBL with an emphasis on the horizontal scale of the involved processes.
Figure 7 shows the time-averaged vertical profiles of zonal wind variance, vertical wind variance, vertical moisture flux, and buoyancy flux along with their scale-dependent contributions during the shallow cumulus stage. We apply the scale decomposition method following Kang and Ryu (2016) to verify if the given surface heterogeneity condition develops any mesoscale processes strong enough to influence the PBL characteristics. By adopting a cutoff wavelength of 4 km, any signals larger than the cutoff are labeled mesoscale, while any signals shorter than the cutoff are labeled turbulent scale (Mahrt and Gibson 1992; Kang et al. 2007; LeMone et al. 2007; Kang 2009; Moeng et al. 2010; Kang and Ryu 2016).
Time-averaged vertical profiles of (a) zonal wind variance, (b) vertical moisture (water vapor) flux, (c) buoyancy flux, and (d) vertical wind variance. (top) The total variance and covariance profiles are then scale separated into (middle) mesoscale and (bottom) turbulence-scale contributions with the scale cutoff wavelength at 4 km. All the transition cases (DC) are enclosed in the red-shaded area, and all nontransition cases (no DC) are represented in the green-shaded area. The HOMU0 case is marked with a black solid line.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Time-averaged vertical profiles of (a) zonal wind variance, (b) vertical moisture (water vapor) flux, (c) buoyancy flux, and (d) vertical wind variance. (top) The total variance and covariance profiles are then scale separated into (middle) mesoscale and (bottom) turbulence-scale contributions with the scale cutoff wavelength at 4 km. All the transition cases (DC) are enclosed in the red-shaded area, and all nontransition cases (no DC) are represented in the green-shaded area. The HOMU0 case is marked with a black solid line.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Time-averaged vertical profiles of (a) zonal wind variance, (b) vertical moisture (water vapor) flux, (c) buoyancy flux, and (d) vertical wind variance. (top) The total variance and covariance profiles are then scale separated into (middle) mesoscale and (bottom) turbulence-scale contributions with the scale cutoff wavelength at 4 km. All the transition cases (DC) are enclosed in the red-shaded area, and all nontransition cases (no DC) are represented in the green-shaded area. The HOMU0 case is marked with a black solid line.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Most of the heterogeneous land surface cases show increased variability in the zonal wind throughout the PBL, which is attributable to the increased mesoscale component (Fig. 7a). HET14U0 and HET14U1 (both are transition cases) show the largest zonal wind variability near the surface and the top of the PBL, indicating the strengthening of the mesoscale secondary circulation.
The domain-averaged vertical flux of water vapor does not differ much in the PBL between transition and nontransition cases (Fig. 7b). However, the vertical transport for transition cases is mainly through mesoscale processes, while in nontransition cases, there are larger contributions from turbulent scale processes (Patton et al. 2005; van Heerwaarden and Guerau de Arellano 2008; Huang and Margulis 2009; Maronga and Raasch 2013; Kang and Ryu 2016). Thus, the domain-average vertical moisture flux is inadequate to measure the influence of surface heterogeneity on the PBL unless its scale dependency is considered.
Similarly, the area-averaged buoyancy flux shows much less distinction between transition and nontransition cases in the PBL (Fig. 7c). Heat transport in all cases is mostly dominated by turbulence-scale motions. However, transition cases have enhanced contribution from mesoscale process that compensates a slightly reduced turbulence-scale heat transport.
Transition cases have a weaker vertical wind variance in the PBL as compared to the nontransition cases (Fig. 7d). This characteristic is specific to the transition cases and is attributable to the effect of a well-defined secondary circulation on the distribution of vertical velocity in the PBL. When the horizontal thermal contrast in the PBL triggers the secondary circulation, the strong and narrow updraft branch is located primarily over DRY patches, while weak and broad downdrafts are prevalent over WET patches. Figure 8 presents the probability distribution function (PDF) of vertical velocity at 500-m height separately for the WET and DRY patches and also for the whole domain for HET14U0, HET5U0, HET1U0, and HOMU0. HET14U0 and HET5U0 represent transition cases, and HET1U0 and HOMU0 cases represent nontransition cases. The difference in the distribution of vertical velocity between transition and nontransition cases are most pronounced over WET patches with the marked weakening but larger coverage of downdrafts (Fig. 8). When the updraft branch of the secondary circulation entrains free tropospheric air, the entrained air mass is horizontally advected toward WET patches near the PBL top where it eventually converges and moves downward. This subsidence branch of the secondary circulation suppresses thermals from rising over WET patches.
PDF of vertical velocity at 500-m height at 1130 LST for (left) WET patches, (center) DRY patches, and (right) the entire horizontal domain. Vertical velocity is binned with a bin size of 0.2 m s−1. Cases presented are divided into transition cases [HET14U0 (red) and HET5U0 (green)] and nontransition cases [HET1U0 (purple) and HOMU0 (black)]. For the patch comparisons, HOMU0 cases for WET and DRY patches are from the additional simulations where the surface SHFs and LHFs are prescribed with the ones used for WET and DRY patches in heterogeneous cases (HOMU0_WET and HOMU0_DRY, respectively).
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
PDF of vertical velocity at 500-m height at 1130 LST for (left) WET patches, (center) DRY patches, and (right) the entire horizontal domain. Vertical velocity is binned with a bin size of 0.2 m s−1. Cases presented are divided into transition cases [HET14U0 (red) and HET5U0 (green)] and nontransition cases [HET1U0 (purple) and HOMU0 (black)]. For the patch comparisons, HOMU0 cases for WET and DRY patches are from the additional simulations where the surface SHFs and LHFs are prescribed with the ones used for WET and DRY patches in heterogeneous cases (HOMU0_WET and HOMU0_DRY, respectively).
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
PDF of vertical velocity at 500-m height at 1130 LST for (left) WET patches, (center) DRY patches, and (right) the entire horizontal domain. Vertical velocity is binned with a bin size of 0.2 m s−1. Cases presented are divided into transition cases [HET14U0 (red) and HET5U0 (green)] and nontransition cases [HET1U0 (purple) and HOMU0 (black)]. For the patch comparisons, HOMU0 cases for WET and DRY patches are from the additional simulations where the surface SHFs and LHFs are prescribed with the ones used for WET and DRY patches in heterogeneous cases (HOMU0_WET and HOMU0_DRY, respectively).
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
In Fig. 8, the PDF of vertical velocity over DRY and WET patches over heterogeneous cases is compared with HOMU0_DRY and HOMU0_WET, respectively. Suppression of turbulence intensity over WET patches in transition cases is not explained by the reduced surface buoyancy. This suggests that the decrease of vertical velocity variance in the PBL for transition cases is attributable to the mesoscale secondary circulation.
Figure 9 shows the time-averaged vertical profiles of the domain-averaged second- and third-moment fields during the shallow cumulus stage. Significant differences among cases are shown in the cloud layer (z > 1.5 km) but not so much in the PBL below 1 km. In transition cases, the cloud layer is characterized by large variability in moisture, temperature, and vertical velocity, while in nontransition cases, the profiles in the cloud layer do not differ much and are rather close to the homogeneous case.
Time-averaged vertical profiles of (a) variance of total water, (b) variance of liquid water potential temperature, and (c) third moment of vertical velocity. All the transition cases (DC) are enclosed in the red-shaded area, and all nontransition cases (no DC) are represented in the green-shaded area . The HOMU0 case is marked with a black solid line. The HET2U0 and HET1U0 cases are marked with blue and yellow lines, respectively, in (c).
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Time-averaged vertical profiles of (a) variance of total water, (b) variance of liquid water potential temperature, and (c) third moment of vertical velocity. All the transition cases (DC) are enclosed in the red-shaded area, and all nontransition cases (no DC) are represented in the green-shaded area . The HOMU0 case is marked with a black solid line. The HET2U0 and HET1U0 cases are marked with blue and yellow lines, respectively, in (c).
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Time-averaged vertical profiles of (a) variance of total water, (b) variance of liquid water potential temperature, and (c) third moment of vertical velocity. All the transition cases (DC) are enclosed in the red-shaded area, and all nontransition cases (no DC) are represented in the green-shaded area . The HOMU0 case is marked with a black solid line. The HET2U0 and HET1U0 cases are marked with blue and yellow lines, respectively, in (c).
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Interestingly, HET1U0 and HET2U0 show stronger updrafts in the PBL as compared to the homogeneous case (Fig. 9c). This suggests that a heterogeneous land surface with length scales smaller than mesoscale (<5 km) can influence PBL dynamics under zero-background-wind condition. In this case, secondary circulations are triggered at a smaller spatial scale and intensify PBL thermals; however, they are not strong enough to trigger the convection transition.
Our results suggest that the convection transition happens when the spatial distribution of surface heating over the heterogeneous land triggers a secondary mesoscale circulation promoting large moisture variability at the PBL top. In sections 4 and 5, we will discuss in more detail the independent influence of patch size and wind speed on triggering the secondary circulation.
4. Moisture and the secondary circulation
Figure 10 shows the horizontal contrast of water vapor specific humidity at 1.2 km just beneath the cloud base for the WET versus DRY patches and under clear versus cloudy skies. The anomaly of the water vapor specific humidity is computed by removing the horizontal mean at the same vertical level. Then the anomaly field is averaged separately over the particular areas (e.g., WET, DRY, CLOUDY, and CLEAR) just before the transition.
Water vapor specific humidity anomaly at 1.2 km near the PBL top as a function of patch size Lpatch in the late morning prior to transition to deep convection (if occurring). Moisture perturbation is computed by subtracting horizontal average at the same vertical level and then horizontally averaged separately for (a) WET and (b) DRY patches and for (c) clear and (d) cloudy skies. Note that “cloudy” skies are those grid points with clouds at any vertical level; usually, the clouds are at levels higher than 1.2 km. The numbers within the panels correspond to the background wind speed enforced for each case study except that U10 cases are marked with an asterisk. A red symbol indicates a transition case.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Water vapor specific humidity anomaly at 1.2 km near the PBL top as a function of patch size Lpatch in the late morning prior to transition to deep convection (if occurring). Moisture perturbation is computed by subtracting horizontal average at the same vertical level and then horizontally averaged separately for (a) WET and (b) DRY patches and for (c) clear and (d) cloudy skies. Note that “cloudy” skies are those grid points with clouds at any vertical level; usually, the clouds are at levels higher than 1.2 km. The numbers within the panels correspond to the background wind speed enforced for each case study except that U10 cases are marked with an asterisk. A red symbol indicates a transition case.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Water vapor specific humidity anomaly at 1.2 km near the PBL top as a function of patch size Lpatch in the late morning prior to transition to deep convection (if occurring). Moisture perturbation is computed by subtracting horizontal average at the same vertical level and then horizontally averaged separately for (a) WET and (b) DRY patches and for (c) clear and (d) cloudy skies. Note that “cloudy” skies are those grid points with clouds at any vertical level; usually, the clouds are at levels higher than 1.2 km. The numbers within the panels correspond to the background wind speed enforced for each case study except that U10 cases are marked with an asterisk. A red symbol indicates a transition case.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Consistent with Fig. 9a, there is a clear distinction between transition cases and nontransition cases. The transition cases are characterized by a large positive moisture anomaly over the DRY patches and a large negative moisture anomaly over the WET patches, while the PBL is relatively well mixed for nonzero background wind speeds. The amplitude of the perturbation increases as the patch size increases under zero wind. One exception is the transition HET14U1 case, which does not show any appreciable moisture contrast between patches similar to all nontransition cases. It is due to a shifting position of the mesoscale circulation and the clouds’ position relative to the WET–DRY patch boundaries. When the moisture anomaly near the PBL top is compared between clear and cloudy skies, all the transition cases including HET14U1 are characterized with a strongly positive moisture anomaly below cloud base, and the anomaly increases linearly with patch size. On the other hand, the nontransition cases have a positive moisture anomaly of 0.5 g kg−1 below cloud base regardless of the patch size or background wind speed (Figs. 10c,d).
HET2U0 shows the similar moisture contrast pattern between patches when compared to HET5U0 but still does not trigger cumulus congestus/deep convection (Fig. 10). For the rest of this section, we focus on HET5U0 and HET2U0 to explain what determines the convection transition and what the role of the patch size is. Figure 11 shows a structure of a secondary circulation, organization of moisture anomaly and moist static energy (MSE), and clouds across the WET–DRY boundary over HET5U0 (a transition case) and HET2U0 (a nontransition case) at 1200 LST. A secondary circulation develops even for the HET2 case under zero background wind. The structure and strength of the triggered circulation are similar over 2.4- (HET2) and 4.8-km patches (HET5) with near-surface convergence located over DRY patches. The spatial pattern of moisture distribution of HET2U0 is analogous to the pattern of HET5U0 with moisture surplus (deficit) over DRY (WET). Clouds in both cases develop mostly over DRY coupled to deeper and moister PBL with high MSE. Despite all these similarities, only HET5U0 triggers the convection transition. The only visible difference between HET5U0 and HET2U0 seems to be the magnitude of the moisture contrast between DRY and WET patches. Therefore, we assume that we can understand what drive the triggering of secondary circulation, moisture pool below cloud base, and convection transition by comparing HET5U0 and HET2U0.
(a) The x–z plane view of meridionally averaged by patch type of wind (vectors), water vapor specific humidity anomalies (color contours), and cloud condensates (gray lines at 0.001, 0.1, and 0.2 g kg−1) for (top) HET5U0 transition case and (bottom) HET2U0 nontransition case across the DRY–WET boundary. The x axis is the relative distance from the patch boundary, with negative distances corresponding to DRY patches and positive distances corresponding to WET patches. (b) As in (a), but for MSE (shaded). The vertical profiles are taken from a snapshot of the simulation at 1200 LST, just before the transition to deep convection of HET5U0.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
(a) The x–z plane view of meridionally averaged by patch type of wind (vectors), water vapor specific humidity anomalies (color contours), and cloud condensates (gray lines at 0.001, 0.1, and 0.2 g kg−1) for (top) HET5U0 transition case and (bottom) HET2U0 nontransition case across the DRY–WET boundary. The x axis is the relative distance from the patch boundary, with negative distances corresponding to DRY patches and positive distances corresponding to WET patches. (b) As in (a), but for MSE (shaded). The vertical profiles are taken from a snapshot of the simulation at 1200 LST, just before the transition to deep convection of HET5U0.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
(a) The x–z plane view of meridionally averaged by patch type of wind (vectors), water vapor specific humidity anomalies (color contours), and cloud condensates (gray lines at 0.001, 0.1, and 0.2 g kg−1) for (top) HET5U0 transition case and (bottom) HET2U0 nontransition case across the DRY–WET boundary. The x axis is the relative distance from the patch boundary, with negative distances corresponding to DRY patches and positive distances corresponding to WET patches. (b) As in (a), but for MSE (shaded). The vertical profiles are taken from a snapshot of the simulation at 1200 LST, just before the transition to deep convection of HET5U0.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
In Fig. 12, we compare vertical profiles of vertical moisture flux and its components in HET5U0 and HET2U0 averaged only over DRY patches, as most clouds are located over DRY patches in both cases. After removing the horizontal mean from the whole domain, the profiles in Fig. 12 are averaged separately for clear-sky column and cloudy-sky column only over DRY patches and also time averaged during the shallow cumulus stage. Consistent with Fig. 11, vertical wind anomaly profiles show the presence of the general upward motion under the clouds, which strengthens over the heterogeneous land surface compared to the homogeneous case. Under the clear sky, the vertical wind anomaly profiles over the homogeneous cases are marked with the general downward motion, while the “S” shape—positive peak around 500 m and negative peak around 1.5 km—exists in the vertical wind profile over the heterogeneous cases. Caution needs to be taken when interpreting the profiles under clear sky in Fig. 12. For heterogeneous cases, the average is taken across DRY patch only, and therefore, the weak updraft below 1 km corresponds to the enhanced surface buoyancy of the DRY patch, while the downdraft above 1 km represents the divergence of flow near the PBL top (Fig. 12a).
Time-averaged vertical profile of (a) vertical velocity anomaly, (b) water vapor specific humidity anomaly, and (c) vertical moisture flux, which are horizontally averaged over clear sky and cloudy sky separately. The average is applied to DRY patches only for HET5U0 and HET2U0, while the average is computed across the entire domain for HOMU0 and HOMU0_DRY. In (c), the percentages in the parenthesis represent the area fractions of cloudy sky over DRY patches for HET5U0 and HET2U0.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Time-averaged vertical profile of (a) vertical velocity anomaly, (b) water vapor specific humidity anomaly, and (c) vertical moisture flux, which are horizontally averaged over clear sky and cloudy sky separately. The average is applied to DRY patches only for HET5U0 and HET2U0, while the average is computed across the entire domain for HOMU0 and HOMU0_DRY. In (c), the percentages in the parenthesis represent the area fractions of cloudy sky over DRY patches for HET5U0 and HET2U0.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Time-averaged vertical profile of (a) vertical velocity anomaly, (b) water vapor specific humidity anomaly, and (c) vertical moisture flux, which are horizontally averaged over clear sky and cloudy sky separately. The average is applied to DRY patches only for HET5U0 and HET2U0, while the average is computed across the entire domain for HOMU0 and HOMU0_DRY. In (c), the percentages in the parenthesis represent the area fractions of cloudy sky over DRY patches for HET5U0 and HET2U0.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
The effect of a stronger sensible heat flux on vertical velocity can be inferred by comparing the HOMU0 to HOMU0_DRY simulations. There is some strengthening, but it is less than the full effect as the HOMU0_DRY shows a weaker vertical velocity w than the one over the DRY patch of the heterogeneous land surface (Fig. 12a). When only updrafts (w > 0 m s−1) are considered, the mean profile of updrafts in the PBL under clouds is indeed similar between the heterogeneous land surface cases and HOMU0_DRY given the same surface heat fluxes (not shown). The main difference is that the area fraction of updraft under clouds is greater over heterogeneous land surface because of the merging of thermals as shown in the thermal size distribution in Figs. 6c and 6d. Therefore, mean vertical velocity in larger thermals becomes stronger. The organization of vertical velocity due to the triggered secondary circulation between the neighboring patches also explains a good portion of the enhanced upward air motion under clouds in simulations with a heterogeneous land surface.
However, even with the similar upward motion in HET2U0 and HET5U0 over DRY patches, the large moisture anomaly and strong vertical moisture transport in cloudy columns are only found in HET5U0. In fact, the moisture anomaly in the cloudy column in HET2U0 does not differ much from that in the homogeneous land surface cases even with the secondary circulation.
Figure 13 shows the patch-averaged vertical profiles of potential temperature and specific humidity for HET5U0, HET2U0, HOMU0_DRY, and HOMU0_WET. To verify the effect of surface buoyancy on the development of local PBL, we use HOMU0_DRY (HOMU0_WET) in the place for the profiles averaged over DRY (WET) patches for the comparisons. The DRY patch has a stronger surface sensible heat flux, which triggers stronger thermals and a deeper and drier PBL than that over the WET patch. However, the local surface buoyancy forcing is not sufficient to account for the development of the PBL over heterogeneous land surface. Over DRY patches, temperature in the PBL is slightly lower and water vapor specific humidity in PBL is higher than what it would have been for the homogeneous case with the DRY patch’s surface fluxes. The opposite holds true for WET patches.
Vertical profiles of (a),(b) potential temperature and (c),(d) water vapor specific humidity for HET5U0 (red), HET3U0 (blue), and HOMU0 (green and yellow) averaged over (a),(c) WET patches and (b),(d) DRY patches separately. For HOMU0, profiles over WET and DRY patches are from the HOMU0 cases where the surface heat fluxes are prescribed for WET and DRY (HOMU0_WET and HOMU0_DRY, respectively). The vertical profiles are taken from a snapshot of the simulation at 1200 LST, just before the transition to deep convection of HET5U0.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Vertical profiles of (a),(b) potential temperature and (c),(d) water vapor specific humidity for HET5U0 (red), HET3U0 (blue), and HOMU0 (green and yellow) averaged over (a),(c) WET patches and (b),(d) DRY patches separately. For HOMU0, profiles over WET and DRY patches are from the HOMU0 cases where the surface heat fluxes are prescribed for WET and DRY (HOMU0_WET and HOMU0_DRY, respectively). The vertical profiles are taken from a snapshot of the simulation at 1200 LST, just before the transition to deep convection of HET5U0.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Vertical profiles of (a),(b) potential temperature and (c),(d) water vapor specific humidity for HET5U0 (red), HET3U0 (blue), and HOMU0 (green and yellow) averaged over (a),(c) WET patches and (b),(d) DRY patches separately. For HOMU0, profiles over WET and DRY patches are from the HOMU0 cases where the surface heat fluxes are prescribed for WET and DRY (HOMU0_WET and HOMU0_DRY, respectively). The vertical profiles are taken from a snapshot of the simulation at 1200 LST, just before the transition to deep convection of HET5U0.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Difference in the PBL growth rate between different patches can be explained by the effect of mesoscale secondary circulation between WET–DRY boundaries on the entrainment at the PBL top. The horizontal advection of entrained air from DRY to WET near the PBL top warms and dries the upper PBL with the secondary circulation, but the strength of those warming and drying effects is stronger in HET5U0.
Difference in the moisture profile in the PBL is also found in the mixed layer over DRY patches (Fig. 13d). The HET5U0 case along with other transition cases (not shown) shows higher qυ in the mixed layer over DRY patches in comparison to the nontransition cases. Analogous to our earlier discussion that the larger thermal has stronger upward motion as it can protect its core better while rising, the moisture also seems to be less vulnerable from mixing if thermals are large.
To summarize, the transition occurs because the secondary circulation transports water vapor from the WET patch to the DRY patch where it accumulates, creating a large moisture anomaly that favors the creation of the clouds. Also, a larger patch size helps to induce the entrainment that is strong enough to modify the upper PBL properties over WET patches and isolate the DRY patch from the WET patch.
5. Impact of the background wind speed and a criterion for convection transition
In this section, we explore how the secondary circulation changes with background wind speed and what impact the changes have on clouds and precipitation.
Figure 14 compares the x–z cross section of the secondary circulation, MSE, and clouds averaged over DRY and WET patches of size 14.4 km for cases of 0, 1, and 2 m s−1 wind speed at 1130 LST before significant precipitation. With Ub = 0 m s−1, the near-surface convergence that initially forms near patch boundaries in the morning strengthens and moves inward toward the center of the DRY patch with time as the surface heterogeneity contrast becomes stronger toward local noon. The enhanced updraft in the center of the patch forms from the collision of fronts approaching from all sides of the DRY patch and supports the organization of the moisture pool and cloud development. When Ub = 1 m s−1, the symmetry of the fronts is destroyed as the background wind enhances eastward motion but deters the westward motion. The end result is a near-surface convergence zone shifted downwind near the eastern edge of the DRY patch (Fig. 14b). With the dislocated convergence zone, the pocket of higher MSE stemming from the higher evaporation over the WET patch feeds the cloud base and returns to the WET patch. This causes the moisture variability beneath 500 m to be even larger in the HET14U1 case as compared with the HET14U0 case (Fig. 14a) as air with higher MSE over the WET patch does not mix with the lower-MSE air over the DRY patch. In this HET14U1 simulation, clouds initially develop over the DRY patch over the updraft branch of the secondary circulation and then move downwind following the high-MSE air located over to the WET patch. With Ub = 2 m s−1, we can still see the effects of the surface heat fluxes as the mean wind transports properties downwind. For example, the deepest boundary layer occurs downwind of the DRY patch, and the highest MSE occurs downwind of the WET patch. However, the imprints of heterogeneous surface flux forcing are much reduced with Ub = 2 m s−1, because of the elimination of the secondary circulation.
The patch-averaged x–z cross section of MSE (color shading), x–z wind (vectors), and cloud (gray lines) for the HET14 case with (top) U0, (middle) U1, and (bottom) U2. The snapshot is taken at 1130 LST before the convection transition of the HET14U0 and HET14U1 cases. Red box marks the strip along the y axis with a cross section of 1 km along x axis by 0.5 km in the vertical to compute an average wind speed that crosses the DRY–WET boundary.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
The patch-averaged x–z cross section of MSE (color shading), x–z wind (vectors), and cloud (gray lines) for the HET14 case with (top) U0, (middle) U1, and (bottom) U2. The snapshot is taken at 1130 LST before the convection transition of the HET14U0 and HET14U1 cases. Red box marks the strip along the y axis with a cross section of 1 km along x axis by 0.5 km in the vertical to compute an average wind speed that crosses the DRY–WET boundary.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
The patch-averaged x–z cross section of MSE (color shading), x–z wind (vectors), and cloud (gray lines) for the HET14 case with (top) U0, (middle) U1, and (bottom) U2. The snapshot is taken at 1130 LST before the convection transition of the HET14U0 and HET14U1 cases. Red box marks the strip along the y axis with a cross section of 1 km along x axis by 0.5 km in the vertical to compute an average wind speed that crosses the DRY–WET boundary.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
We examine the near-surface zonal wind near patch boundaries to better understand the strength of the secondary circulation that can withstand the applied background wind speed. Figure 15 shows the daytime evolution of near-surface zonal wind at patch boundaries (denoted as Uc) averaged over the red-box area marked in Fig. 14. With the negative cross-border wind, the flow is directed from the WET to DRY patches, and the flow is part of the lower branch of the secondary circulation that converges over the DRY patch. We believe that the cross-border wind in U0 cases (denoted as Uc0) represents the potential strength of a secondary circulation for a given patch size and specified heterogeneity amplitude. The speed of this flow is around 1.5 m s−1 in the hour before the transition for the HET14U0 case, and we believe that this is the maximum background wind speed that the triggered secondary circulation can overcome. This is consistent with the fact that the HET14 case with background wind speed of 1 m s−1 still triggers a secondary circulation and the convection transition but the HET14 case with background wind speed of 2 m s−1 fails to produce a secondary circulation or precipitaing convection, and hence, the influence of the surface heterogeneity becomes minimal. A schematic diagram illustrating the dependence of the secondary circulation on background wind speed is shown in Fig. 16. We propose a criterion of |Uc0| > |Ub| to be a necessary condition for the convection transition to occur for a given patch size and heterogeneity amplitude in an atmosphere that favors shallow convection but is also conditionally unstable with respect to deeper moist convection.
Daytime evolution of the cross-boundary zonal wind speed Uc for cases with a patch size of 14.4 km but different wind speeds of 0 (red), 1 (blue), and 2 m s−1 (black). The cross-boundary zonal wind is volume averaged, denoted by the red box in Fig. 14, which is located on the DRY side of the patch boundary. The maximum speed of Uc before the convection transition for the case with 0 m s−1 background wind Uc0 is marked with a red dashed line.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Daytime evolution of the cross-boundary zonal wind speed Uc for cases with a patch size of 14.4 km but different wind speeds of 0 (red), 1 (blue), and 2 m s−1 (black). The cross-boundary zonal wind is volume averaged, denoted by the red box in Fig. 14, which is located on the DRY side of the patch boundary. The maximum speed of Uc before the convection transition for the case with 0 m s−1 background wind Uc0 is marked with a red dashed line.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Daytime evolution of the cross-boundary zonal wind speed Uc for cases with a patch size of 14.4 km but different wind speeds of 0 (red), 1 (blue), and 2 m s−1 (black). The cross-boundary zonal wind is volume averaged, denoted by the red box in Fig. 14, which is located on the DRY side of the patch boundary. The maximum speed of Uc before the convection transition for the case with 0 m s−1 background wind Uc0 is marked with a red dashed line.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Schematic illustration of the influence of the background wind speed Ub on the triggered circulation. Uc0 is the cross-boundary zonal wind for cases with zero background wind speed given a certain patch size and represents the potential maximum speed of the triggered circulation. Uc is the cross-boundary zonal wind for cases with any background wind speed (if secondary circulation is occurring).
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Schematic illustration of the influence of the background wind speed Ub on the triggered circulation. Uc0 is the cross-boundary zonal wind for cases with zero background wind speed given a certain patch size and represents the potential maximum speed of the triggered circulation. Uc is the cross-boundary zonal wind for cases with any background wind speed (if secondary circulation is occurring).
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Schematic illustration of the influence of the background wind speed Ub on the triggered circulation. Uc0 is the cross-boundary zonal wind for cases with zero background wind speed given a certain patch size and represents the potential maximum speed of the triggered circulation. Uc is the cross-boundary zonal wind for cases with any background wind speed (if secondary circulation is occurring).
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
Our proposed criterion proves to be reliable for different patch sizes and even with different heterogeneity amplitudes. For instance, Uc0 in HET7 case is 1 m s−1, and only HET7U0 and HET7U0.5 (an additional case with 0.5 m s−1 background wind; not shown) case triggers the convection transition. In separate additional simulations, we prescribe HET14U0 and HET7U0 cases with the surface heat fluxes with the doubled amplitude (cases denoted as Ax2). In Ax2 cases, the maximum values for sensible and latent heat fluxes are 350 (80) and 200 (450) W m−2 over DRY (WET) patches, respectively. The value of Uc0 in HET14_Ax2 barely reaches 2 m s−1, and hence, the HET14U1_Ax2 case triggers the convection transition, while the HET14U2_Ax2 case does not develop a secondary circulation, and only shallow cumulus clouds are present. Likewise, Uc0 in HET7_Ax2 becomes 1.5 m s−1, and hence, HET7U1_Ax2 becomes the transition case. As a patch size and heterogeneity amplitude increase, the potential strength of a triggered secondary circulation increases but not monotonically. A prediction for Uc0 for a given surface condition becomes imperative to apply the criterion over a broad spectrum of surface conditions.
The theory is based on the near-surface observation across adjoining grassland steppe (DRY) and irrigated farm (WET) with a length scale of 10 km or more. On one day of the field campaign, the background wind was blowing in a direction perpendicular to the patch border from DRY to WET, and the speed weakened to be 4 m s−1 into late morning and noon. The difference in sensible heat flux between DRY and WET patches was about 240 W m−2. The observation suggested that the PBL-averaged temperature difference was less than 1 K between the patches because the air column heated over the DRY patch was advected over to WET and experienced less or no further surface heating. Doran et al. (1995) adopted a criterion from Segal and Arritt (1992) that the background wind speed had to make a full stop in order for a triggered secondary circulation to survive. Doran et al. (1995) related the PBL column temperature difference mainly arising from the different sensible heat flux between DRY and WET to the consequent horizontal pressure gradient. The physical background is that the horizontal pressure gradient will decelerate the wind to zero if the pressure gradient and WET patch size are large enough. In Eq. (1) L is the estimated distance for the air at the patch boundary with initial speed Ub to travel before the secondary circulation triggered over a given 
Figure 17a shows the diurnal change of Ub solved from Eq. (1) using all other parameters following our simulated results for each patch size. The background wind speed that the simulated secondary circulation should be able to overcome becomes as large as 4 m s−1 over the 14.4-km-patch case following Eq. (1). However, our results suggest that the background wind speed of 1–2 m s−1 is powerful enough to eliminate all impact of the surface heterogeneity over the 1.2–14.4-km patch. Based on our results, Doran’s parameterization may overestimate the background wind speed threshold, as it does not account for the feedback of secondary circulation on the horizontal temperature gradient over the heterogeneous surface. Figure 17b compares the diurnal cycle of the near-surface (below 100 m) temperature contrast over two patches, one with and one without horizontal mixing. For the case of no horizontal mixing by the secondary circulation, we take the difference between the HOMU0_DRY and HOMU0_WET simulations. The temperature contrast with the circulation is computed from the average temperature difference between the WET and DRY patches of the HET7U0 case. As shown in Fig. 17b, the temperature contrast without the circulation reaches about 1.6 K at 1200 LST. The temperature decreases between 0900 and 1000 LST correspond to the different PBL growth rate over the different surface sensible heat flux. On the other hand, over the heterogeneous land with fully active cross-patch circulation, the temperature contrast becomes 0.2 K toward local noon as the horizontal mixing exerted by the secondary circulation tries to minimize the temperature contrast, which is active starting early on. One may modify Doran’s theory to predict Uc0 by including the effect of a secondary circulation on reducing the temperature contrast. Further work is needed to test this criterion and to modify Doran’s theory for Uc0 prediction.
(a) Daytime variation of the background wind threshold Ub for each patch size computed using Doran’s parameterization solving for Ub from Eq. (1). Different colors represent the different patch sizes. (b) Daytime evolution of the simulated near-surface temperature contrast between the WET and DRY patches. Black line represents the temperature difference in HET7U0 where the secondary circulation is present. Gray line denotes the near-surface temperature contrast when the secondary circulation does not exist, namely, the temperature difference between HOMU0_DRY and HOMU0_WET.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
(a) Daytime variation of the background wind threshold Ub for each patch size computed using Doran’s parameterization solving for Ub from Eq. (1). Different colors represent the different patch sizes. (b) Daytime evolution of the simulated near-surface temperature contrast between the WET and DRY patches. Black line represents the temperature difference in HET7U0 where the secondary circulation is present. Gray line denotes the near-surface temperature contrast when the secondary circulation does not exist, namely, the temperature difference between HOMU0_DRY and HOMU0_WET.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
(a) Daytime variation of the background wind threshold Ub for each patch size computed using Doran’s parameterization solving for Ub from Eq. (1). Different colors represent the different patch sizes. (b) Daytime evolution of the simulated near-surface temperature contrast between the WET and DRY patches. Black line represents the temperature difference in HET7U0 where the secondary circulation is present. Gray line denotes the near-surface temperature contrast when the secondary circulation does not exist, namely, the temperature difference between HOMU0_DRY and HOMU0_WET.
Citation: Journal of the Atmospheric Sciences 76, 2; 10.1175/JAS-D-18-0196.1
It is worth bearing in mind that our simulations are idealized with prescribed surface heat fluxes in order to isolate and focus on the impact of heterogeneity size and background wind speed. This setup overlooks the interactive processes, for example, the potential responses of surface heat fluxes to the changes in background wind speeds, the changes of the surface net radiation budget due to cloud shading, and the changes in temperature and moisture in the subcloud layer and at the surface due to cold pools resulting from precipitation evaporation. In our future work, we will use the LES model (SAM) coupled with the land model (Lee and Khairoutdinov 2015) to study the interactive processes between land surface, the PBL, and clouds following CASS and with a more realistic setup of land properties based on ARM data.
6. Summary
We have presented general characteristics of the development of the PBL and shallow cumulus clouds and their subsequent transition into cumulus congestus/deep convection over the heterogeneous land surface with various background wind speeds and the heterogeneity sizes. We study the conditions of different convective cloud types in an atmosphere that favors shallow convection but is also conditionally unstable with respect to deeper convection.
In our idealized LESs, the surface heterogeneity is applied by prescribing surface heat fluxes with a step function change across the WET and DRY patch boundary. The difference in the surface heat fluxes between the neighboring patches roughly represents the observed contrast between the grassland and crop fields at SGP site. The simulations are largely separated into two groups: the nontransition group with only the shallow cumulus clouds and the transition group where the shallow cumulus clouds over the DRY patch deepen to congestus/deep convection around local noon. We contrast the state immediately prior to the convection transition across simulations to distinguish the physical mechanisms behind the convection transition over heterogeneous land surface without interference from the precipitation processes.
Our simulations indicate that the secondary circulation at mesoscale is the main driver to influence the turbulent transport of moisture in the PBL and the convection transition. The transition cases are characterized with a well-defined secondary circulation that promotes the moisture pool near the PBL top over the updraft branch of the circulation, supplying the cloud base with higher-MSE air. The effect of secondary circulation on the spatial distribution of moisture in the PBL is strongest when the surface heterogeneity size is larger than 5 km under zero background wind, which agrees with Patton et al. (2005). Similarly, subcloud thermals and thermal cores are larger when the patch size is larger than 5 km, which promotes a moister mixed layer in the updraft branch of the secondary circulation and larger cluster of clouds. Thus, our results suggest that the clouds that transition into congestus/deep convection require a moisture pool near the PBL top and enhanced vertical velocity in the subcloud layer that forms over a patch size of at least 5 km. For cases with a patch size smaller than 5-km, the driven circulation effectively mixes the entire PBL across the domain, so the organized moisture pool does not appear and the clouds remain shallow. Although the pattern of surface heterogeneity, mean surface heat flux, and heterogeneity amplitudes are different from those used in Avissar and Schmidt (1998) and Patton et al. (2005), our results agree with their conclusions on the range of heterogeneity scales that induce the secondary circulation and the strengthening of circulation as the patch size increases within that range. However, it is not clear to us why 5 km can be the threshold for the strong-enough secondary circulation that can trigger convection transition.
The secondary circulation over the heterogeneous land surface goes through significant structural changes as the background wind speed increases from zero to nonzero. The updraft branch of the circulation is no longer located in the center of the DRY patch when the background wind speed increases to 1 m s−1 over HET14. With a background wind speed stronger than 2 m s−1, the secondary circulation structure is destroyed in all HET cases. Our analysis of the speed of the secondary circulation confirms that the cross-border wind speed embedded as the return flow from WET to DRY rarely exceeds 1–1.5 m s−1, and the circulation cannot withstand a background wind speed Ub stronger than the speed of this circulation Uc0. The speed of the secondary circulation seems proportional to the temperature contrast (i.e., pressure) between patches, which, however, is smaller than it would be in absence of the secondary circulation leading to the “smallness” of Uc0.
Therefore, we propose a criterion of |Ub| < |Uc0| that is necessary to induce a mesoscale circulation for a given patch size and background wind. Our criterion appears to be relevant for the existence of both the secondary circulation and convection transition in our cases. One might argue that there are other factors that contribute to determine the strength of a triggered secondary circulation, such as the heterogeneity amplitude, wind shear, and wind direction relative to the surface heterogeneity. Also, development of deep convection depends on other factors, such as atmospheric humidity and stability. Further work is needed to test this criterion and includes the impact of these additional factors.
Acknowledgments
Data from the U.S. Department of Energy (DOE) as part of the Atmospheric Radiation Measurement (ARM) Climate Research Facility Southern Great Plains site were used. Jungmin Lee and Yunyan Zhang were supported by the Early Career Research Program (ECRP), and Stephen A. Klein was supported by the Atmospheric Systems Research (ASR) program in the Office of Biological and Environmental Research, Office of Science, DOE. Lawrence Livermore National Laboratory is operated for the DOE by Lawrence Livermore National Security, LLC, under Contract DE-AC52-07NA27344.
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