development of the convective boundary layer capping with a thick neutral layer in badanjilin:...

ADVANCES IN ATMOSPHERIC SCIENCES, VOL. 29, NO. 1, 2012, 177–192

Development of the Convective Boundary Layer Capping

with a Thick Neutral Layer in Badanjilin:

Observations and Simulations

HAN Bo∗(� �), LU Shihua (��), and AO Yinhuan (��)

Cold and Arid Regions Environmental and Engineering Research Institute,

Chinese Academy of Sciences, No. 320, Donggang West Road, Lanzhou 730000

(Received 6 December 2010; revised 27 May 2011)

ABSTRACT

In this study, the development of a convective boundary layer (CBL) in the Badanjilin region wasinvestigated by comparing the observation data of two cases. A deep neutral layer capped a CBL thatoccurred on 30 August 2009. This case was divided into five sublayers from the surface to higher atmosphericelevations: surface layer, mixed layer, inversion layer, neutral layer, and sub-inversion layer. The developmentprocess of the CBL was divided into three stages: S1, S2, and S3. This case was quite different from thedevelopment of the three-layer CBL observed on 31 August 2009 because the mixed layer of the five-layerCBL (CBL5) eroded the neutral layer during S2. The specific initial structure of the CBL5 was correlatedto the synoptic background of atmosphere during nighttime. The three-stage development process of theCBL5 was confirmed by six simulations using National Center for Atmospheric Research (USA) large-eddysimulation (NCAR-LES), and some of its characteristics are presented in detail.

Key words: convective boundary layer, neutral layer, large-scale circulation, large-eddy simulation

Citation: Han, B., S. H. Lu, and Y. H. Ao, 2012: Development of the convective boundary layer cappingwith a thick neutral layer in Badanjilin: Observations and simulations. Adv. Atmos. Sci., 29(1), 177–192,doi: 10.1007/s00376-011-0207-4.

1. Introduction

The convective boundary layer (CBL) is the mainmanifestation of the atmospheric boundary layer dur-ing daytime. Its development and maintenance havea direct influence on many atmospheric phenomena,such as cloud formation (Kuo, 1974; Chen and Cotton,1983; Wyngaard, 1985; Lock et al., 2000) and pollu-tant distribution (Trainer et al., 1995; Hourdin et al.,2002). Many meteorologists have pointed out that thedevelopment of a CBL is mainly correlated with twofactors: first, buoyancy from the underlying heating,and second, wind shear in the vertical direction (Mo-eng and Sullivan, 1994; Conzemius and Fedorovich,2006).

Based on a large number of observations, a typi-cal and well-developed CBL on a clear day generallyconsists of three sublayers (Fig.1a; Conzemius and Fe-dorovich, 2006): the surface layer, the mixed layer, and

the inversion layer (also called the interfacial layer).Above the inversion layer, there is usually a free at-mospheric layer that is fairly stable. With regard tothe potential temperature (PT) distribution in the in-version layer, we defined the first PT jump from thesurface to the mid-level of the atmosphere as the topof the CBL. Although equipment and techniques formonitoring a CBL have greatly advanced in recentdecades (see Wilczak et al., 1996 for a review), thismethod of determining the height of a CBL is stillwidely accepted (Driedonks, 1982; Pul et al., 1994;Piringer et al., 1998).

In a well-developed CBL, the PT is usually approx-imately uniform in the mixed layer when averaged overa horizontal plane (Garratt, 1992). This facilitatesCBL modeling because only the properties inside thesurface layer and the inversion layer need to be inves-tigated in detail. General structure models (GSM) ofCBLs have been established based on this approach

∗Corresponding author: HAN Bo, [email protected]

© China National Committee for International Association of Meteorology and Atmospheric Sciences (IAMAS), Institute of AtmosphericPhysics (IAP) and Science Press and Springer-Verlag Berlin Heidelberg 2012

178 CONVECTIVE BOUNDARY LAYER CAPPING WITH A THICK NEUTRAL LAYER VOL. 29

Fig. 1. (a) Conceptual model of a typical CBL3 and (b) a particular CBL5.The solid line and dashed line are profiles of potential temperature (PT) andkinematic heat flux (Hθ), respectively. The dotted line shows the bound ofeach sublayer: surface layer, mixed layer, inversion layer, neutral layer, subin-version layer, and free atmosphere layer.

since the work of Lilly in 1968. Historically, in the1970s the inversion layers of GSMs were treated as azero-order jump of PT (Tennekes, 1973; Zeman andLumley, 1976; Zeman and Tennekes, 1977). Subse-quently the inversion layers of GSMs were extendedto the first order (Deardorff, 1979; Fedorovich andMironov, 1995) and to higher-order expressions (Fe-dorovich et al., 2004), depending on the results of ob-servations.

Differing from GSMs, which only concern the prop-erties of the CBL averaged over a horizontal plane,large-eddy simulations (LES) can describe the three-dimensional (3D) structure of a CBL. With fine gridspacing and shorter time intervals, the structure oflarge-scale eddies, which dominate the exchange ofmass, momentum, and energy in the mixed layer, canbe detailed in an LES. The first application of the LESapproach was made by Deardorff (1972, 1974). Sincethen, extensive and detailed simulations have beenconducted by Moeng (1984), Mason (1989), Schmidtand Schhumann (1989), Moeng and Sullivan (1994),and Moeng et al. (2007). Because of the difficulties inobserving the atmospheric motions in the mixed layersand the inversion layers, knowledge about the develop-ment and structure of CBLs has been mainly obtainedfrom LES experiments (Sorbjan, 2004).

The vertical gradient of PT in the free atmosphericlayer affects the entrainment process in the inversionlayer (Deardorff et al., 1969; Deardorff, 1979; Fe-

dorovich and Mironov, 1995). This phenomenon wasdiscussed by Stull (1976) with regard to a Wangara ex-periment in which a neutral layer above the inversionlayer was observed. The neutral layer has also beencalled the residual layer in many studies (Stull, 1988),but the neutral layer was chosen as a better definitionin this study for two reasons: first, the residual layer isalways associated with a nocturnal boundary layer (orstable boundary layer; Stensrud, 1993; Fochesatto etal., 2001; Tjernstrom et al., 2009), rather than a CBL;and second, the residual layer originates from the CBLon the previous day. In this paper, another cause ofthe neutral layer is presented in section 4.

Although the importance of the neutral layer forthe development of the CBL has been noted previ-ously (Stensrud, 1993; Fochesatto et al., 2001), it hasnot yet been studied intently. For example, most sim-ulations of CBLs have assumed a positive gradient ofPT above the inversion layer, as shown in Fig. 1a(Driedonks, 1982; Fedorovich et al., 2004). This ap-proximation is acceptable in many cases, because theneutral layer is usually shallow and is seldom observed.However, if a CBL is accompanied by a deep neutralor near-neutral layer capping the inversion layer (Fig.1b), the development of the CBL may carry importantimplications for the study of the atmospheric bound-ary layer. The CBL discussed in this study is distinctfrom that shown in Fig. 1a due to its deep neutrallayer and its additional inversion layer that caps the

NO. 1 HAN ET AL. 179

neutral layer (Fig. 1b). This inversion layer is calledthe subinversion layer to distinguish it from the lowerinversion layer. For convenience, we have named theCBL with three sublayers as CBL3 and the CBL withfive sublayers as CBL5.

2. Data and methods

2.1 The Badanjilin experiment

Observation data was obtained from the Badanjilinexperiment (BDEX hereafter), which was performedfrom 16 July 2009 to 16 September 2009. The experi-mental site was located at 39◦28.124′N, 102◦22.365′E,with an elevation ∼1400 m above sea level. The re-gion is a typical desert in Northwest China, where aCBL with a height >3000 m was reported by Zhanget al. (2006). The ground has very sparse shrub cov-erage near BDEX site, comprising an approximatelyhomogeneous underlying surface.

An eddy covariance (EC) system and a net ra-diometer (CNR1, Campbell Scientific Inc., USA) wereset at the camp. The EC system and radiometerwere mounted at heights of 3.0 m and 1.5 m, respec-tively. The EC system included a 3D sonic anemome-ter (CSAT3, Campbell Scientific Inc., USA) and aCO2/HO2 open-path gas analyzer (LI7500, LI-CORInc., USA). The sampling rate of the EC system was10 Hz. After the Webb–Pearman–Leuning correctionsWebb et al. (1980) as well as other quality controlmethods being performed on the data, sensible (Hs)and latent heat flux density were calculated every 30minutes. The radiation flux was recorded at the sametime interval.

A tethersonde (TTS-111, Vaisala Inc., USA) anda radiosonde (RS-92, Vaisala Inc., USA) system wereused to obtain the vertical profiles of atmospheric vari-ables, such as pressure, temperature, specific humidity,wind, etc., during the experiment. Details about thetethersonde and radiosonde can be found in Day et al.(2010) and Vomel et al. (2007) respectively. We used10 radiosondes during BDEX, and two sets of themwere selected for the two cases presented here. Thefirst day chosen was 30 August 2009 (D1 hereafter),and the second day chosen was 31 August 2009 (D2hereafter).

Notably, without specification, the time for all thedata used in this study was local standard time (LST),which is 8 hours earlier than Coordinated UniversalTime (UTC).

2.2 NCAR-LES

National Center for Atmospheric Research (USA)large eddy simulation (NCAR-LES) was selected for

numerical simulation of the CBL in this study. It wasdeveloped by Moeng (1984), and it has been used toinvestigate the spectrum properties (Moeng and Wyn-gaard, 1988) and the mechanisms of buoyancy andwind shear (Moeng and Sullivan, 1994) in a CBL. Sul-livan et al. (1994) improved the parameterization ofsub-grid-scale process and added a grid-nesting sub-routine (Sullivan et al., 1996). McWilliams et al.(1997) used it to simulate the mixed layer in ocean.By coupling it with a land surface model, Patton etal. (2005) extended this model to simulate a CBL overa heterogeneous surface. Having been extensively usedin CBL simulations (Nieuwstadt et al., 1993; Ayotteet al., 1996; Huang et al., 2008), NCAR-LES has be-come a useful tool for reproducing the developmentof a real CBL. Details of the governing equations andthe parameterizations of the sub–grid scale in NCAR-LES can be found in Moeng (1984) and Sullivan et al.(1994, 1996).

3. Observation results

3.1 Observations on D1

Vertical profiles of PT on D1 are shown in Fig. 2a.The profiles at 0800 LST and 1200 LST were obtained

Fig. 2. Observed vertical profiles of (a) PT and (b)mixed ratio on 30 August 2009. The observation time(LST) of each profile is showed in the legend.


by using tethersonde and others using radiosonde. At0800 LST, the atmospheric boundary layer exhibitedthe features of a nocturnal boundary layer in whichthe atmosphere was intensely stable below a height of500 m. We defined the top of the CBL (Ht) as thefirst PT jump from the surface to the top of atmo-sphere (Driedonks, 1982; Pul et al., 1994; Piringer etal., 1998). At 1000 LST, Ht was ∼200 m, and a deepneutral layer with the thickness of >2000 m was cap-ping the inversion layer. The structure of the CBL wasquite similar to that in Fig. 1b, so it can be defined asa CBL5. At 1200 LST, the Ht was ∼400 m, and PTsin the mixed layer and the neutral layers were ∼314 Kand ∼319 K, respectively. If the PT in the mixed layerincreased to 319 K as a result of underlying heating,the inversion layer might vanish, and the mixed layerwould merge with the neutral layer. This appeared tooccur at 1400 LST when the Ht was ∼3000 m. ThePT profile at 1600 LST was similar to that at 1400LST, indicating that the structure of the CBL duringthis period might have been quasi-steady.

The vertical profiles of mixing ratio on D1 areshown in Fig. 2b. The CBL featured by mixing-ratioprofiles was similar to that defined by PT (Grimsdellet al., 1998). Notably, both the inversion layer andthe subinversion layer featured a sharp decrease of themixing ratio at 1000 LST.

The vertical profiles of the mixing ratio and PTshow a three-stage process in the development of theCBL5. In the first stage (S1 hereafter), Ht slowly in-creased, and the deep neutral layer was capping theinversion layer, like a CBL5. In the second stage (S2hereafter), the former CBL5 quickly modified into aCBL3, and Ht increased sharply from 400 m to ∼3000m. In the third stage (S3 hereafter), the CBL becamequasi-steady again.

The vertical profiles of horizontal wind on D1 aredisplayed in Fig. 3. At 1000 LST, there was a maxi-mum wind speed at the height of 100 m. Below the topof the CBL, the wind direction was anticlockwise be-low 100 m height and clockwise above 100 m. At 1400LST, below 1200 m, the wind showed an intensive ro-tation. At 1600 LST, the wind direction changed fromeasterly near the surface to westerly near the top ofthe CBL, and the wind speed increased approximatelylinearly with height.

3.2 Comparison with observations on D2

Observation data on D2 shows a typical CBL3.The vertical profiles of PT and mixing ratio are shownin Fig. 4. At 1130 LST (Fig. 4a), Ht was ∼750m, much higher than that at 1200 LST on D1 (Fig.2). While at 1530 LST and 1830 LST, Ht values were∼1500 m and ∼1700 m, respectively, much lower than

those at the same time on D1.The horizontal wind profiles of D2 are shown in

Fig. 5. Differing from D1, the wind speed and direc-tion on D2 was more uniform inside the mixed layer.

3.3 Comparison of fluxes in the surface layer

Considering that the development of a CBL is de-termined primarily by underlying surface heating (Mo-eng and Sullivan, 1994; Conzemius and Fedorovich,2006), we show the surface energy fluxes from D1 toD2 in Fig. 6. Given that D1 and D2 were two sunnydays, the effects of clouds on the CBL were excluded.Since the Hs overwhelmed latent heat flux during thedaytime, we shall discuss Hs only.

Before noon, both Hs and Ht on D1 were muchsmaller than those on D2. This implies that before1200 LST, the CBL heights on both days were mainlycontrolled by Hs. However, Ht values after 1400 LSTin the two cases were quite different. Although the Hs

on D2 was still greater than that on D1, the Ht on D1was almost twice as large as that on D2 at that time.

Wind shear in surface layer is also important forthe development of a CBL. We also compared the fric-tion velocity (u∗) (Fig. 6a) between D1 and D2. Be-fore 1200 LST, u∗ on D1 was smaller than that on D2,and after 1200 LST, the variability of u∗ on the twodays were similar. This suggests that the wind shearmight have contributed little to the greater Ht after1400 LST on D1.

In our analysis of observation data, we found arapid development process of CBL after 1200 LST onD1, which appeared to be a jump of Ht when the in-version layer vanished. This process seemed to be con-nected to the initial thermal structure of the CBL5, es-pecially the neutral layer. It is not clear whether theneutral layer observed in this field study could be re-garded as a residual layer as discussed by Fochesatto etal. (2001), because the CBL profile before D1 was notavailable. However, given a deep CBL in the late af-ternoon on D1 and no neutral layer (or residual layer)observed on the next day (D2, Fig. 4), the dynamicand thermal process of atmosphere during nighttime(e.g., long-wave radiation, horizontal and vertical ad-vection) might be important to forming or sustaininga deep neutral layer. In the next section, the effect oflarge-scale circulation on the vertical structure of theatmosphere is described.

4. Analysis of the large-scale circulation dur-ing nighttime

The initial stage of a CBL5 might contain signa-tures of energy storage during the night, since the neu-tral layer formed before mixed the layer began to de-


Fig. 3. Profiles of wind speed (solid line) and wind direction (dashed line) on30 August 2009. The observation time is (a) 1000 LST, (b) 1400 LST, and (c)1600 LST. Dotted lines indicate the location of the Ht.

Fig. 4. Observed vertical profiles of PT (solid line) and mixed ratio (dashedline) on 31 August 2009. The observation time is (a) 1130 LST, (b) 1530 LST,and (c) 1830 LST.


Fig. 5. Same as in Fig. 3, but for 31 August 2009.

Fig. 6. (a) Observed friction velocity (u∗, solid line), sen-sible (Hs, �) and latent (LE, ◦) heat flux density and (b)radiant flux density. In panel b, Rsd and Rsu representdownward and upward shortwave radiation, and Rld andRlu represent downward and upward long-wave radiation,respectively.

velop on D1 (Fig. 2). Therefore, in this section wecompare the atmospheric motions during the night-time. For convenience, hereafter, the night before D1is called N1, and the night before D2 is called N2. No-tably, the long-wave radiation between N1 and N2 is abit different around 0400 LST (Fig. 6b). However, theradiation process could not have contributed markedlyto the different stratification during the mornings ofD1 and D2. Instead, the advection of PT by large-scale circulation might have played a crucial role inthe formation of neutral layer in N1.

To illustrate the large-scale circulation around theBDEX site, we used NCEP–NCAR reanalysis data (6-h intervals; Kalnay et al., 1996). The data were ex-tracted at the pressure levels of 850 hPa, 700 hPa, 600hPa, 500 hPa, and 400 hPa. The atmospheric heightsof these pressure levels were about 50 m, 1500 m, 3000m, 4500 m, and 6000 m, respectively. In this study,the data at 0200 LST (1800 UTC) were assumed torepresent typical nighttime conditions for N1 and N2,respectively.

The synoptic backgrounds in N1 and N2 are shownin Fig. 7. An intensive warm advection in N1 at 500hPa dominated over the BDEX. The temperature ad-vection was not identified in N2. Hence, the heatingrate caused by large-scale circulation was significantlydifferent between the two nights. The profiles of PTnear the BDEX site (40◦N, 102.5◦E) on N1 and N2 ob-tained from the reanalysis data are shown in Fig. 7c.From 700 hPa to 600 hPa, the atmosphere exhibitedstronger neutral stratification during N1 than duringN2.


Fig. 7. The temperature field (thick solid lines, units:K), geopotential height field (thin dashed lines, units: m)and wind vector (arrows, units: m s−1) near the BDEXsite on (a) N1 and (b) N2 at 500 hPa. The vertical profilesof PT near the BDEX site on the two nights are shownin (c). In panels (a) and (b), intervals for temperatureand geopotential height are 2 and 30, respectively, andthe center of crosses indicates the BDEX site. In panel(c), heights for each data point on profiles were derivedby subtracting local elevation from the heights of eachpressure levels, which consist of 850 hPa, 700 hPa, 600hPa, 500 hPa, and 400 hPa.

To further illustrate the heating rate caused by ad-vection of large-scale circulation, we defined the diver-gence of large-scale PT flux as:

Df = ∇p · (Upθ) , (1)

where

∇p =(

∂

∂x,

∂

∂y,

∂

∂p

),

is a 3D gradient operator, and Up = (u, v, ω) is thewind field in the isobaric coordinate, θ is the potentialtemperature, noting that ω = dp/dt. A negative Df

indicates a heating process caused by advection, andvice versa.

In N1, Df was small and positive over the site ofBDEX at 700 hPa and 600 hPa, and Df was negativeat 500 hPa (Fig. 8). This indicated a weak cooling pro-cess below 3000 m height and a considerable heatingprocess above this height. The former helped to main-tain the stratification status in the neutral layer, andthe latter favored the formation of a strong stable layer(subinversion layer). In N2, on the other hand, Df wasnegative at 700 hPa and positive at 600 hPa over thesite of BDEX (Figs. 8e, f), which would increase thestability of atmosphere, preventing the neutral layerfrom being sustained.

Based on this discussion, we suggest that the CBL5was likely initialized during the nighttime when theneutral layer and the subinversion layer were formedand maintained by the warm advection caused by thelarge-scale circulation. During this period, availablepotential energy was stored at the mid-atmosphere, asreported by Stensrud (1993).

5. Large-eddy simulations

Because the observation data was limited, in or-der to gain sufficient information for this CBL5 event,the NCAR-LES model was used to simulate the de-velopment of the CBL5. The model simulations weredesignated to address following questions:

(1) How does a typical CBL5 vary during its threedifferent stages of development?

(2) What is the relationship between the growthrate of a CBL5 and the vertical gradient of PT insideneutral layer (γn)?

(3) How does the wind shear affect the developmentof a CBL5?

These questions are discussed in subsections 5.2.2,5.2.3, and 5.2.4, respectively.

5.1 Initial and boundary conditions

The model domain contained 60×60×150 gridpoints with grid spacing of Δx = Δy = 100 m,


Fig. 8. Distribution of Df on (a, d) 700 hPa, (b, e) 600 hPa and (c, f) 500 hPa nearthe BDEX site. (a), (b) and (c) represent N1, and (d), (e), (f) represent N2. In eachfigure, the center of the cross indicates the BDEX site. Contour intervals are 0.4(units: 10−3 K s−1), and the zero lines are thickened. Light shade indicates values>0.4, and dark shades indicate values < −0.4.

and Δz = 20 m, respectively. The geostrophic wind,(Ug, Vg) = (5, 0) m s−1, was considered to be the samefor all simulation cases. The roughness length wasset to z0 = 0.06 m, and the Coriolis parameter wasf = 9.35×10−5 s−1. The surface kinematic heat flux,(wθ)0 = 0.12 K m s−1, was derived from mean Hs ofobservations on D1 (Fig. 6 a).

The initial vertical profiles of PT for all six simu-lation cases (called C1, C2, C3, C4, C5, and C6) areshown in Fig. 9, and γn for each case are listed inTable 1. The model was initialized assuming an initialheight of mixed layer at 400 m, with a PT of 313.5K. The inversion layer with the depth of 80 m abovethe mixed layer and the subinversion layer with thedepth of 40 m above the neutral layer were selected;

their vertical PT gradients were 37.5 K km−1and 50K km−1, respectively. The depth of the neutral layerwas chosen to be 2180 m.

We set the initial conditions as (u, v, w) = (2, 0, 0)m s−1 for all model grids for C1, C2, C3, C4, and C5,and we set (u, v, w) = (5, 0, 0) m s−1 for C6. Bothinitial wind fields represented a fairly weak wind fieldcompared with those considered by Moeng and Sulli-van (1994). The model automatically added a randomturbulence in PT and velocity fields before the firststep of integration.

The upper boundary conditions were assumed tobe stress-free for horizontal velocity components. Thevertical velocity and sub-grid-scale atmospheric activ-ities were set to zero, and the potential temperature


Fig. 9. Initial vertical profiles of PT for all six cases oflarge-eddy simulation.

lapse rate was 5 K km−1 in the free atmosphericlayer. A flux boundary condition was used in the lowerboundary, derived from the Monin–Obukhov similar-ity formulation (Foken, 2006).

Following Deardorff (1970), the convective velocityscale was defined as

w∗ =g

θ(wθ)0h0 , (2)

where θ is the mean PT inside the mixed layer, h0 isthe depth of CBL, (wθ)0 is the surface kinematic heatflux. The turbulence velocity scale (σw) of the mixedlayer can be written as

σ3w = w3

∗ + ηu3∗ . (3)

where u∗ is the friction velocity and was kept to0.3∼0.4 m s−1 during the simulations. Here η is sug-gested to be 12.5 (Driedonks, 1982). If h0 is assumedto be ∼400 m as in Fig. 2, then from Eq. (2) w∗ is is1.3 m s−1, which is greater than u∗. This indicatesthat the turbulence within the mixed layer is mainlycontrolled by underlying surface heating.

The three-stage Runge–Kutta scheme was used forthe time integration for the model (Sullivan et al.,1996). The time increment was adjusted at each timestep based on the Courant–Friedrichs–Levy stabilitycondition.

Table 1. γn, u (initial wind field), r1 and r2 for differentcases of large-eddy simulation

γn (K km−1) u (m s−1) r1 (m s−1) r2 (m s−1)

C1 0 2 0.0198 1.5924C2 0.07 2 0.0172 0.7791C3 0.14 2 0.0219 0.6124C4 0.28 2 0.0201 0.3452C5 0.56 2 0.0230 0.1658C6 0 5 / /

5.2 Simulated results

5.2.1 Intercomparison of CBL structures among allcases

The structures of kinematic heat flux (Hθ) av-eraged over the horizontal domain of model for allcases were plotted and are presented in Fig. 10. After11 000 s of integration, the CBL heights for all casesbegan to increase sharply. Hθ also increased signifi-cantly during this period.

Illustrated in Fig. 10, the negative Hθ highlightsthe features of the entrainment zone. In the earlystage, the entrainment zone was located near the in-version layer for all selected cases. After 10 000 s,the entrainment zone vanished when the thermals inthe mixed layer penetrated to the neutral layer. Af-ter a short time, a new entrainment zone was formednear the subinversion layer. Due to stronger Hθ withinthe neutral layer, the entrainment process in the newentrainment zone became more intense than the firstone.

The variation of the profile of momentum flux (Mf)is shown in Fig. 11. Analogous to Hθ, after 11000 s,Mf grew rapidly within the neutral layer, althoughthose large values of Mf exhibited more random dis-tribution than Hθ.

5.2.2 The development of CBL in C1In section 3, we discussed the measured CBL5. To

simulate this monitored CBL5, let us define θm as themean of PT over the horizontal domain at each modellevel, and let us define two normalized indices to illus-trate the structure of CBL:

Fn(z) =< wlθl > + < wsθs >

(wθ)0, (4)

and

Rw(iz) =

∑ix,iy

δw(ix, iy, iz)

NxNy, (5)

δw(ix, iy, iz) =

{0, w(ix, iy, iz) < 0.4

1, w(ix, iy, iz) � 0.4. (6)

The angle brackets in Eq. (4) stand for averaging overthe horizontal domain, while wlθl and wsθs stand forlarge eddy scale and sub-grid scale kinematic heat fluxrespectively. The minimum value of Fn is written asFni, which is known as the entrainment ratio (Gar-ratt, 1992). The height of Fni is defined by Zi, whichis identical with Ht in a CBL3 (Fig. 1a). In Eq. (5),ix, iy, and iz are coordinates in three directions, Nx

and Ny are grid numbers on the x−axis and the y-axis,respectively. δw is used to highlight those model gridwith updraft (w) > 0.4 (m s−1). Several instantaneousprofiles of Fn, Rw, and θm are given in Fig. 12. The


Fig. 10. The development of kinematic heat flux (Hθ, calculated as wlθl+wsθs,units: 10−2 K m s−1) for (a) C1, (b) C2, (c) C3, (d) C4, (e) C5, and (f) C6.The values were averaged over the horizontal domain of model, and the timeof simulation for all figures is from 3000 s to 17 000 s.

three different stages of the CBL development were se-lected at 2000 s and 6000 s for S1; 10 000 s, 11 000 s,and 12 000 s for S2; and 16 000 s for S3.

At 2000 s (Zi = 420 m) and 6000 s (Zi = 520m), the neutral layer and the subinversion layer didnot seem to exert an influence on the developmentof the CBL. Under inversion layer, the CBL was notmuch different from a CBL3, and Fni were −0.173and −0.129, respectively, indicating significant en-trainment process in the entrainment zone at these twostages. Rw was >0.3 below Zi, showing well-developedthermals within the mixed layer.

At 10 000 s, although Zi was only 800 m, the inver-

sion layer could not be identified clearly from θm. Fni

at this time was just −0.03, and Rw was >0.3 belowa 1120 m height. This suggests that we might haveoverestimated the height of the CBL when we used Ht

to indicate the top of the CBL in section 3. At 11 000s and 12 000s, Zi was ∼2580 m, and Fni had a orderof magnitude of 10−3. Generally speaking, both theFn and Rw profiles indicated an intensive and rapidadjustment of the structure in the CBL during S2.

As seen in Fig. 12f, a typical CBL3 (compare withFig. 1a) developed beginning at 16 000 s. Accordingly,Ht and Zi were identical. Fn decreased linearly withheight under the subinversion layer. In this case, we


Fig. 11. Same as in Fig. 10, but for vertical profiles of momentum flux (Mf ,calculated as

p(ulwl + usws)2 + (vlwl + vsws)2, units: 10−2 m2 s−2)

found Fni = −0.13, which was comparable to that at6000 s, and Rw was >0.4 under the subinversion layer,representing fully developed thermals within the neu-tral layer.

To give a detailed description on the structures ofthermals like Lenschow and Stephens (1980), the dis-tributions of upward wind on 500 m height were de-termined (Fig. 13). In addition to the intensificationof upward wind within the CBL, small and weak ther-mals tended to be absorbed by large and strong onesduring S2.

In conclusion, the development of the CBL5 mod-eled in C1 agreed well with the CBL observation dataon D1. The results illustrate detailed features of the

CBL during S2, including θm that changed little, theweak entrainment process, and rapid penetration ofthe thermals within the mixed layer to the neutrallayer.

5.2.3 The effect of γn on the growth rate of CBLThe variations of Zi in C1, C2, C3, C4, and C5

are shown in Fig. 14. We predicted that Zi wouldgrow much more slowly in a more stable neutral layerthan in an absolutely neutral layer, because thermalsconvert their kinematic energy into available potentialenergy when they increase in a stable layer. To makefurther a quantitative comparison, we conducted twolinear-fit simulations on Zi for two separate periods.


Fig. 12. The vertical profiles of θm (solid line), Fn (dashed line) andRw (dotted line) in C1 at the simulation time of (a) 2000 s, (b) 6000 s,(c) 10 000 s, (d) 11 000 s, (e) 12 000 s and (f) 16 000 s, respectively.

Fig. 13. Distribution of vertical velocity (w) on 500 m height obtainedfrom the results of C1 at the simulation time of (a) 10 000 s, (b) 11 000s, (c) 12 000 s, and (d) 16 000 s. Only values >0 are shown, with theintervals of 1 (units: m s−1). Light and dark shading represent values>1 and >2, respectively.


Fig. 14. The development of Zi (solid line) obtainedfrom the results of (a) C1, (b) C2, (c) C3, (d) C4 and (e)C5. The dashed line is L1, and the dotted Line is L2.

The first one was from 2000 s to 6000 s, standing forS1. The second started at 10 000 s and extended tothe time when Zi remained above 2580 m (the heightwhere subinversion layer initially located) for 200 s,representing S2. If Zi did not reach 2580 m duringthe simulation (as occurring in C5), we then took 18000 s as the ending time. The two linear-fit lines werenamed L1 and L2, respectively (Fig. 14). Their slopes,r1 and r2, are listed in Table 1, which can be approxi-mately regarded as the mean growth rate of Zi duringS1 and S2, respectively. The reason for the absence ofC6 in the comparisons is that its Zi varied irregularlyfrom 3000 s to 9000 s (figure omitted).

As seen in Table 1, r1 ≈ 0.02 m s−1 for all cases,implying that the development of the CBL might notbe sensitive to γn during S1. However, r2 decreasedsharply with increasing γn. The relationship betweenr2 and γn can be described using the following fittingfunction:

r2 = A exp(−γn/B) + C . (7)

where A, B, and C are 1.95, 0.97, and 0.22, respec-tively. The variation of r2 with γn is shown in Fig. 15.Equation (7) indicates that r2 tends to become a con-

Fig. 15. The distribution of γn versus r2(�), and thefunction curve of Eq. (9) (solid line).

stant with increase of γn. If C of Eq. (7) is assumed tobe 0.02, then the growth rate of Zi in S2 will be iden-tical to that in S1 when γn is great enough. In thatcase, the development of a CBL3 can be seen as a spe-cial case of CBL5. Because a CBL5 has also takes intoaccount the CBL features above the inversion layer, itappears to be a more reasonable conceptual model forCBL compared with CBL3.

5.2.4 The effect of wind shear on the development ofa CBL5

Stronger initial wind field and vertical shear withinthe surface layer resulted in a more intense momen-tum flux in CBL before 10 000 s (Fig. 10f). This ledto a greater σw in the mixed layer, as shown in Eq.(3), and it also benefitted the growth of a CBL3 (Mo-eng and Sullivan, 1994). However, based on the re-sults presented above, S2 is a more critical stage thanS1 during the development of a CBL5. Therefore, itis worthwhile to further investigate the impact of thewind shear during S1 and S2 on the CBL5.

First, we introduce the entrainment velocity as(Garratt, 1992):

we =dH

dt− ws , (8)

where H is the height of CBL, ws is the large-scalevertical velocity, taken to be zero for all cases in thisstudy. If the growth rate of CBL in C6 was assumedto be equivalent to C1 during S1, then we for all sixcases were approximately equal to each other. Defining

the depth of entrainment zone as Δh, then followingBeyrich and Gryning (1998) we have

Δh

H∝ (

we

σw)α , (9)

where σw is defined in Eq. (3), and the exponent αcan be determined from experiments and ranging from0.25 to 1. We can then deduce that Δh of C6 is much


shallower as a result of greater σw. This suggests thatthe inversion layer was much stable in C6 than in othercases during S1 (figure omitted). As a result (Fig. 10),the more stable inversion layer in C6 would extend S1and thus delay the second stage of CBL (S2), althoughthe kinematic heat and momentum fluxes in C6 ap-peared to be stronger than other cases during S2.

6. Discussion

Although the CBL5 investigated in this study ap-pears to be a special case, the CBL with similar fea-tures has been observed and reported previously. ThePT profile on 0900 LST on day 33 of the Wangara ex-periment also revealed a CBL5, as reported by Stull(1976); the subinversion layer was not very significantcompared with the one in our case. In that study, Stullsimulated the development of a CBL using a GSM,which defined the inversion layer as a zero-order jumpof PT. Stull’s results agreed well with observations duepartly to a shallow neutral layer (∼500 m), which ledto a quick conversion of the CBL from a CBL5 to aCBL3 structure. It is doubtful that a GSM would ap-ply to a deep neutral layer like the one monitored inthe BDEX experiment.

The warm advection caused by large-scale circu-lation (discussed in section 4) can also be regardedas a pattern typical of thermal wind as discussed bySorbjan (2004). In that study, the influence of fourtypical patterns of thermal wind on the mixed layerwas assessed, with primary attention to the influenceof thermal wind on the internal structure of turbulentflux below the inversion layer. In this study, the activ-ities of the large-scale circulation above the inversionlayer were also addressed, which helped to form theneutral layer and the subinversion layer. Therefore,the effect of the large-scale circulation on the turbu-lent flux within the CBL as well as on the verticalthermal structure of atmosphere above the nocturnalboundary layer should both be carefully considered.

It has been recognized that the CBL over a desert isalways deep during summer (Zhang et al., 2006). Thecauses of such a deep CBL over a desert are these:First and foremost, intensive surface heating createsthe energy for strong convective motions during thedaytime. Second, intensive surface cooling during thenighttime helps to maintain the residual layer, becausethe more stable nocturnal boundary layer suppressesturbulent activities and weakens the heat exchange be-tween nocturnal boundary layer and neutral layer (orresidual layer). Third, the air column over a desert isusually cooler than its surroundings during the night-time. Once the wind at a relatively higher atmosphericlevel blows towards the desert as in N1 (Fig. 7a), warm

advection is likely to occur, which may help to createa neutral layer. Although the second and third argu-ments listed here need to be tested more thoroughlyusing more observations and analysis, they providea potential interpretation of the formation of neutrallayer, as elaborated in this paper.

7. Conclusions

Based on the observed data collected from BDEX,we reported a CBL5 formed by the surface layer, themixed layer, the inversion layer, the neutral layer, andthe subinversion layer extending from the surface to ahigher atmospheric elevation. The development of theCBL5 spanned three stages, differing from a CBL3.We found that, in the second stage of the CBL5 de-velopment, the top of CBL rose rapidly, characterizingthe initial structure of the CBL.

The analysis for the nighttime large-scale circula-tion associated with this CBL5 event was conductedto interpret the initial thermal structure of the CBL5.We found that the warm advection at a relativelyhigher atmospheric level contributed to the generationof the subinversion layer and to the maintenance of theneutral layer.

Extensive model experiments using the NCAR-LES were performed to simulate the CBL5. This mod-eling investigation successfully simulated the three-stage development of a CBL5. The detailed processof the thermals penetration from the mixed layer tothe neutral layer was quantified. The growth rate ofthe CBL5 during S2 was demonstrated to have decayedexponentially and inversely with the vertical gradientof potential temperature in the neutral layer. Finally,the stronger vertical shear of mean wind would helpto maintain the inversion layer and delay the S2 of theCBL5.

Acknowledgements. We are thankful for the assis-

tance of Professor Sullivan, who offered us the NCAR-LES

codes and their instructions. We are grateful to the two

anonymous reviewers and the editors of Advances in At-

mospheric Science for their kind and patient correction of

errors, for polishing the English, and for their many valu-

able comments and suggestions for this paper. This re-

search was funded by National Basic Research Program

of China (Grant Nos. 2009CB421402 and 2010CB950503)

and National Natural Science Foundation of China (Grant

No. 40975007).

REFERENCES

Ayotte, K. W., and Coauthors, 1996: An evaluation ofneutral and convective planetary boundary layer par-


ameterizations relative to large eddy simulations.Bound.-Layer Meteor., 79, 131–175.

Beyrich, F., and S. E. Gryning, 1998: Estimation ofthe entrainment zone depth in a shallow convectiveboundary layer from Sodar data. J. Appl. Meteor.,37, 255–268.

Chen, C., and W. R. Cotton, 1983: A one-dimensionalsimulation of the stratocumulus-capped mixed layer.Bound.-Layer Meteor., 25, 289–321.

Conzemius, R. J., and E. E. Fedorovich, 2006: Dynamicsof sheared convective boundary layer entrainment.Part I: Methodological background and large-eddysimulations. J. Atmos. Sci., 63, 1151–1178.

Day, B. M., B. Rappengluck, C. B. Clements, S. C.Tucker, and W. A. Brewer, 2010: Nocturnal bound-ary layer characteristics and land breeze developmentin Houston, Texas during TexAQS II. Atmos. Envi-ron., 44, 4014–4023.

Deardorff, J. W., 1970: Convective velocity and tem-perature scale for the unstable planetary boundarylayer and for Rayleigh convection. J. Atmos. Sci.,27, 1211–1213.

Deardorff, J. W., 1972: Numerical investigation of neutraland unstable planetary boundary layers. J. Atmos.Sci., 29, 91–115.

Deardorff, J. W., 1974: Three-dimensional numericalstudy of turbulence in an entraining mixed layer.Bound.-Layer Meteor., 7, 199–226.

Deardorff, J. W., 1979: Prediction of convective mixed-layer entrainment for realistic capping inversionstructure. J. Atmos. Sci., 36, 424–436.

Deardorff, J. W., G. E. Willis, and D. K. Lilly, 1969:Laboratory investigation of non-steady penetrativeconvection. J. Fluid. Mech., 35, 7–31.

Driedonks, A. G. M., 1982: Models and observationsof the growth of the atmospheric boundary layer.Bound.-Layer Meteor., 23, 283–306.

Fedorovich, E. E., and D. V. Mironov, 1995: A model fora shear-free convective boundary layer with param-eterized capping inversion structure. J. Atmos. Sci.,52, 83–95.

Fedorovich, E. E., R. J. Conzemius, and D. V. Mironov,2004: Convective entrainment into a shear-free, lin-early stratified atmosphere: bulk models reevaluatedthrough large eddy simulation. J. Atmos. Sci., 61,281–295.

Fochesatto, G. J., P. Drobinski, C. Flamant, D. Guedalia,C. Sarrat, P. H. Flament, and J. Pelon, 2001: Ev-idence of dynamical coupling between the residuallayer and the developing convective boundary layer.Bound.-Layer Meteor., 99, 451–464.

Foken, T., 2006: 50 years of Monin-Obukhov similaritytheory. Bound.-Layer Meteor., 119, 431-447.

Garratt, J. R., 1992: The Atmospheric Boundary Layer.Cambridge University Press, 316pp.

Grimsdell, A. W., and W. M. Angevine, 1998: Convec-tive boundary layer height measurement with windprofilers and comparison to cloud base. J. Atmos.Oceanic. Technol., 15, 1331–1338.

Hourdin, F., F. Couvreux, and L. Menut, 2002: Parame-terization of the dry convective boundary layer basedon a mass flux representation of thermals. J. Atmos.Sci., 59, 1105–1123.

Huang, J., X. Lee, and E. G. Patton, 2008: A modellingstudy of flux imbalance and the influence of entrain-ment in the convective boundary layer. Bound.-LayerMeteor., 127, 273–292.

Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40year reanalysis project. Bull. Amer. Meteor. Soc., 77,437–471.

Kuo, H. L., 1974: Further study of the parameterizationof the influence of cumulus convection on large-scaleflow. J. Atmos. Sci., 31, 1232–1240.

Lenschow, D. H., and P. L. Stephens, 1980: The role ofthermals in the convective boundary layer. Bound.-Layer Meteor., 19, 509–532.

Lilly, D. K., 1968: Models of cloud-topped mixed lay-ers under a strong inversion. Quart. J. Roy. Meteor.Soc., 10, 1162–1173.

Lock, A. P., A. R. Brown, M. R. Bush, G. M. Martin, andR. N. B. Smith, 2000: A new boundary layer mix-ing scheme. Part I: Scheme description and single-column model tests. Mon. Wea. Rev., 128, 3187–3199.

Mason, P. J., 1989: Large eddy simulation of the convec-tive atmospheric boundary layer. J. Atmos. Sci., 46,1492–1516.

McWilliams, J. C., P. P. Sullivan, and C. H. Moeng, 1997:Langmuir turbulence in the ocean. J. Fluid Mech.,334, 1–30.

Moeng, C. H., 1984: A large-eddy-simulation model forthe study of planetary boundary layer turbulence. J.Atmos. Sci., 41, 2052–2062.

Moeng, C. H., and J. C. Wyngaard, 1988: Spectral analy-sis of large-eddy-simulations of the convective bound-ary layer. J. Atmos. Sci., 45, 3573–3587.

Moeng, C. H., and P. P. Sullivan, 1994: A comparison ofshear- and buoyancy-driven boundary layer flows. J.Atmos. Sci., 51, 999–1022.

Moeng, C. H., J. Dudhia, J. Klemp, and P. P. Sullivan,2007: Examining two-way grid nesting for large eddysimulation of the PBL using the WRF Model. Mon.Wea. Rev., 135, 2295–2311.

Nieuwstadt, F. T. M., P. J. Mason, C. H. Moeng, andU. Schumann, 1993: Large-eddy simulation of theconvective boundary layer: A comparison of fourcomputer codes. Turbulent Shear Flows, Durst et al.,Eds., Springer–Verlag, 343–367.

Patton, E. G., P. P. Sullivan, and C. H. Moeng, 2005:The influence of idealized heterogeneity on wet anddry planetary boundary layers coupled to the landsurface. J. Atmos. Sci., 62, 2078–2097.

Piringer, M., K. Baumann, and M. Langer, 1998: Sum-mertime mixing heights at Vienna, Austria, esti-mated from vertical soundings and by a numericalmodel. Bound.-Layer Meteor., 89, 25–45.

Pul, W. A. J., A. A. M. Holtslag, and D. P. J. Swart, 1994:A comparison of ABL heights inferred routinely from


lidar and radiosondes at noontime. Bound.-LayerMeteor., 68, 173–191.

Schmidt, H., and U. Schhumann, 1989: Coherent struc-ture of the convective boundary layer derived fromlarge eddy simulation. J. Fluid Mech., 200, 511–562.

Sorbjan, Z., 2004: Large-eddy simulations of the baro-clinic mixed layer. Bound.-Layer Meteor., 112, 57–80.

Stensrud, D. J., 1993: Elevated residual layers and theirinfluence on surface boundary-layer evolution. J. At-mos. Sci., 50, 2284–2293.

Stull, R. B., 1976: Mixed-layer depth model based onturbulent energetics. J. Atmos. Sci., 33, 1268–1278.

Stull, R. B., 1988: Introduction to Boundary-LayerMeterology. Kluwer Academic Publishers, Boston,666pp.

Sullivan, P. P., J. C. McWilliams, and C. H. Moeng,1994: A subgrid-scale model for large-eddy simula-tion of planetary boundary-layer flows. Bound-LayerMeteor., 71, 247–276.

Sullivan, P. P., J. C. McWilliams, and C. H. Moeng, 1996:A grid nesting method for large-eddy simulation ofplanetary boundary-layer flows. Bound.-Layer Me-teor., 80, 167–202.

Tennekes, H., 1973: A model for the dynamics of the in-version above a convective boundary layer. J. Atmos.Sci., 30, 558–567.

Tjernstrom, M., B. B. Balsley, G. Svensson, and C. J.Nappo, 2009: The effect of critical layers on residuallayer turbulence. J. Atmos. Sci., 66, 468–480.

Trainer, M., B. A. Ridley, M. P. Buhr, G. Kok, J. Walega,G. Hubler, D. D. Parrish, and F. C. Fehsenfeld, 1995:Regional ozone and urban plumes in the southeasternUnited States: Birmingham, a case study. J. Geo-phys. Res. 100, 18823–18834.

Vomel, H., and Coauthors, 2007: Radiation dry bias ofthe Vaisala RS92 humidity sensor. J. Atmos. OceanicTechnol., 24, 953–963.

Webb, E. K., G. I. Pearman, and R. Leuning, 1980: Cor-rection of flux measurements for density effects dueto heat and water vapor transfer. Quart. J. Roy. Me-teor. Soc., 106, 85–100.

Wilczak, J. M., E. E. Gossard, W. D. Neff, and W. L.Eberhard, 1996: Ground-based remote sensing of theatmospheric boundary layer: 25 years of progress.Bound.-Layer Meteor., 78, 321–349.

Wyngaard, J. C., 1985: Structure of the planetary bound-ary layer and implications for its modeling. J. Appl.Meteor., 24, 1131–1142.

Zeman, O., and J. L. Lumley, 1976: Modeling buoyancydriven mixed layers. J. Atmos. Sci., 33, 1974–1988.

Zeman, O., and H. Tennekes, 1977: Parameterization ofthe Turbulent Energy Budget at the Top of the Day-time Atmospheric Boundary Layer. J. Atmos. Sci.,34, 111–123.

Zhang, Q., S. Wang, and Y. Li, 2006: The depth of at-mospheric boundary layer in arid region of NorthwestChina. Acta Meteorologica Sinica, 20(Suppl.), 1–12.(in Chinese)

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