characteristics of secondary circulations over an...

Boundary-Layer Meteorol (2007) 123:239–261DOI 10.1007/s10546-006-9137-6

O R I G I NA L PA P E R

Characteristics of secondary circulations overan inhomogeneous surface simulated withlarge-eddy simulation

Thara V. Prabha · Anandakumar Karipot ·Michael W. Binford

Received: 19 May 2005 / Accepted: 16 October 2006 / Published online: 30 November 2006© Springer Science+Business Media B.V. 2006

Abstract Large-eddy simulation is used to study secondary circulations in the con-vective boundary layer modulated as a result of horizontally varying surface propertiesand surface heat fluxes over flat terrain. The presence of heat flux heterogeneity and itsalignment with respect to geostrophic wind influences the formation, strength and ori-entation of organized thermals. Results show boundary-attached roll formation alongheat flux maxima in the streamwise direction. The streamwise organization of theupdrafts and downdrafts formed downwind of heterogeneities leads to counter-rotat-ing secondary circulations in the crosswind plane. The distribution of resolved-scalepressure deviations shows large pressure gradients in the crosswind plane. Spanwiseand vertical velocity variances and heat flux profiles depict considerable spatial var-iability compared to a homogeneous forest simulation. Secondary circulations areobserved for various ambient wind scenarios parallel and perpendicular to hetero-geneities. In the presence of increased wind speed, thermals emerging from the heatflux heterogeneity are elongated, and organize along and downwind of large-scaleheterogeneity in the streamwise direction. Simulation with a reduced heat flux showsa shallower circulation with a lower aspect ratio. Point measurements of heat fluxinside the roll circulation could be overestimated by up to 15–25% compared to ahomogeneous case.

T. V. Prabha (B)Department of Biological and Agricultural Engineering,The University of Georgia,1109 Experiment st., Griffin, GA 30223, USAe-mail: [email protected]

A. KaripotLab for Environmental Physics, The University of Georgia,1109 Experiment st., Griffin, GA 30223, USA

M. W. BinfordDepartment of Geography, University of Florida,Gainsville, FL 32611, USA

240 Boundary-Layer Meteorol (2007) 123:239–261

Keywords Convective boundary layer · Eddy covariance · Large-eddy simulation ·Rolls · Secondary circulation · Surface heterogeneity

1 Introduction

Earlier theoretical studies (Pielke 1974; Avissar and Pielke 1989; André et al. 1990;Gopalakrishnan et al. 2000; Esau and Lyons 2002; Kustas and Albertson 2003; SilvaDias et al. 2004) have demonstrated that heat flux heterogeneities at scales of tensof kilometres can induce mesoscale circulations. When heterogeneity scales (h) aremuch larger than the boundary-layer height (zi) (h/zi � 1), convective boundary-layer (CBL) characteristics are significantly altered (Gopalakrishnan and Avissar2000; Cai et al. 2004; Patton et al. 2005), which can trigger temporal oscillations(Schumann 1991; Hadfield et al. 1991b; Letzel and Raasch 2003). The effect of surfaceheterogeneities at smaller scales (h/zi ≤ 1) is considerably reduced in the presenceof a background wind (Hadfield et al. 1991b; Hechtel et al. 1990; Dörnbrack andSchumann 1993; Shen and Leclerc 1994; Avissar and Schmidt 1998; Avissar et al.1998) compared to cases without a background wind (Hadfield et al. 1991a). Theeffect of surface heat flux heterogeneity also depends on the heat flux magnitude andthe pattern of heat flux variations. Most of these studies have used either a strip-like ora random, uncorrelated (Avissar et al. 1998) heat-flux pattern. In the presence of two-dimensional and continuous sinusoidal heat-flux heterogeneities, the surface heat-fluxheterogeneities of smaller scale (h < zi) could influence the variances, covariancesand third moments (Shen and Leclerc 1995). Heterogeneities at larger scales (≈ zi)produced more intense vertical energy transfer than smaller scales (h < zi). Raaschand Harbusch (2001) used two-dimensional discontinuous (similar to real heteroge-neous surfaces) surface heterogeneity (h ≤ 1.1 zi) in the heat flux and showed that amoderate increase in background wind speed (7.5 m s−1) does not necessarily weakenthe secondary circulations. Their results are contrary to earlier results of Shen andLeclerc (1994) and Avissar and Schmidt (1998). The disagreement is due to the factthat the strength of the secondary circulation depends on the orientation of hetero-geneities in relation to the ambient flow and the circulation itself has a more complexthree-dimensional structure. Characteristics of these circulations for more complexreal surface heterogeneities in the heat flux and roughness were not investigated.

However, signatures of quasi-stationary circulations have been reported in severalexperimental studies (Doran et al. 1992; Desjardins et al. 1997; Esau and Lyons 2002),which contributed to energy imbalance (Twine et al. 2000). Experimental sites mea-suring vertical fluxes of energy, heat and mass often fall short of idealized horizontallyhomogeneous conditions due to contrasting thermal and dynamical characteristicsof the study area. Contrasts in the surface characteristics may trigger circulations orintroduce flow features that can influence measurements by transport and diffusionof energy and mass (Sun et al. 1997, 1998; Lee 1998; Yi et al. 2000). These circulationsmight introduce a non-local (scales � h) contribution to the measured fluxes. Mahrt(1998) suggested that errors associated with surface heterogeneity might increasewith decreasing wind speed due to boundary-attached quasi-stationary circulations.Sakai et al. (2001) demonstrated that there could be up to 17% increase in surfaceeddy fluxes of heat, water vapour, and carbon dioxide attributed to large eddies withperiodicities in the range 4–30 min. The identification and characterization of such

Boundary-Layer Meteorol (2007) 123:239–261 241

local and/or non-local effects are necessary to infer the true flux devoid of randomand systematic errors.

The Florida AmeriFlux site of interest in the present study characterizes distinctdiscontinuities in both thermal and aerodynamic properties. Sodar measurements atthis site showed recurrence of vertical velocities up to 0.3–0.5 m s−1 and there areuncertainties in the tracer fluxes measured above the canopy (Leclerc et al. 2003).While there is a general understanding of the effects of heterogeneity on the flow fieldand turbulence from eddy-covariance and acoustic remote sensing measurements atthis site, knowledge of the spatial distribution of the secondary circulations and theirhorizontal and vertical extent is lacking due to inadequate spatial resolution of theexperiments. The main objectives of the present study are to identify the secondarycirculations and their spatial distributions in relation to the surface heterogeneitieswith the help of large-eddy simulation (LES) and evaluate their influence on pointflux measurements. The heterogeneous surface characteristics of the site are incor-porated in the LES with the help of eddy-covariance and sodar measurements, andremote sensing data. The study aims for a better understanding of the importance ofnon-local effects on flux measurements during typical observed conditions.

2 Materials and methods

2.1 Site characteristics and measurements

The Florida AmeriFlux study site is located in a slash pine (Pinus elliotti var elliotti L.)plantation (29◦45′ N, 82◦10′W), near Gainesville, Florida. Though this measurementsite is homogeneous, by and large, in species composition, management practices inthe immediate vicinity of the site have introduced considerable inhomogeneities inthe land-use pattern (Fig. 1a). Freshly logged areas with bare soil (clear-cut) existnearly 500 m away from the forest flux tower (see Fig. 1a) at the time of the study.The clear-cut extends from the north-west to south-west of the site. The width of theclear-cut varies from 50 m to 600 m (maximum at the south-west side) and has a lon-gitudinal extent of nearly 1500 m. The main clear-cut has an inverted ‘L’ shape, wherewesterly winds flow perpendicular to the north–south oriented portion (h ≈ 1.5 zi),and parallel to the east–west oriented portion (h ≈ 1.1 zi) of the clear-cut. There aretwo other small-scale clear-cuts (h ≈ 0.5 zi) in the upwind and downwind areas ofthe main ‘L’ shaped clear-cut. The mini-sodar observations in the surface layer haveshown that north-westerly and westerly flows are significantly modified by the clear-cut (Leclerc et al. 2003). Measurements during other ambient wind directions havealso shown large differences in turbulence characteristics. Observations of land-useinformation (Fig. 1a), normalized difference vegetation index (NDVI) and albedo areobtained with a horizontal resolution of 30 m. The radiometric temperature is obtainedfrom the Landsat Enhanced Thematic Mapper+(ETM+) at 60 m resolution, which isresampled to 30 m (Fig. 1b). The surface temperature contrasts between the clear-cutand forested areas are close to 10 K, and in agreement with other point measurementsat the site during convective conditions.

The eddy-covariance system consisting of a three-dimensional sonic anemometer(CSAT3, Campbell Scientific Inc., USA) and Krypton hygrometer (KH20, CampbellScientific Inc., USA), and net radiometer (NR LITE, Kipp and Zonen Inc., USA)and soil heat flux plates (HFT-3, Campbell Scientific Inc., USA) are used at locations


0 1 2 3

0

1

2

3

x (km))

mk( y +F+c

Clear-cut Slash pineRiparian forest and young pine

sparse vegetation

+F1

0 1 2 3

0

1

2

3

x (km)

)mk( y +303

0 1 2 3

0

1

2

3

x (km)

)mk( y +

N(a) (b)

(c)

Fig. 1 (a) Land-use type and (b) the radiometric temperature (K) derived from Landsat data used toobtain, (c) the kinematic heat flux (K m s−1) distribution used in the LES. The eddy-covariance fluxtower locations over the forest (F and F1) and clear-cut (C) are indicated in Fig. 1a. F1 is located at500 m north of F. The area used for streamwise and spanwise averages is highlighted in Fig. 1b withthick dashed lines

indicated in Fig. 1a to study the energy balance over the forest (F) and over the clear-cut. Eddy-covariance measurements are made at a height of 2.5 m over the clear-cutand at 14.5 m over the forest. Ancillary flow field measurements are made with amini-sodar (Meteoscience, Austria) over the forest.

An energy balance comparison (Fig. 2) over the forest and the clear-cut during1000–1200 h shows no significant difference in the heat flux (H) between the twolocations. The net radiation (RN) is significantly lower at the clear-cut (≈500 W m−2

over the clear-cut and 625 W m−2 over the forest) due to high albedo and highsurface temperature of the exposed soil at the clear-cut, and much of the energyis converted as sensible heat flux and soil heat flux (G). The forested area has a


Fig. 2 The energy balanceover the forest and theclear-cut. RN, H, LeE and Gare the net radiation, sensibleheat flux, latent heat flux andsoil heat flux, respectively. (Leis the latent heat ofevaporation and E is the rateof evaporation)

1000 1100 1200 1300 14000

200

400

600

800Forest R

n H L

eE G

Clear-cut Rn

H LeE G

mW(

xulF2-)

Time (hours)

higher net radiation and lower soil heat flux, and latent heat flux decreased withtime. The energy imbalance has a large magnitude over the forest (a maximum of250 W m−2) compared to that over the clear-cut (150 W m−2). Mini-sodar observa-tions typically showed mean vertical velocities of 0.5 m s−1 in the surface layer duringwesterly/north-westerly/northerly ambient flow conditions. Coherent motions with aperiodicity of 15 min characterizing thermals are noticed in the lowest 100 m probedwith the help of the mini-sodar. The variance of the crosswind velocity component isenhanced during such situations.

2.2 Large-eddy simulation

The numerical model used in this study is based on Moeng (1984) and is adaptedto account for the heterogeneous land surface parameterizations. The subgrid-scale(SGS) parameterization is based on the two-part eddy viscosity model (Schumann1975; Sullivan et al. 1994),

τij = −2νtγ Sij − 2νT⟨Sij

⟩, (1)

where νt and νT are fluctuating and mean field eddy viscosities, γ (γ = S′/(S′ + 〈S〉),where S′ is the horizontally averaged fluctuating resolved strain and 〈S〉 is the meanstrain) is an isotropic factor. Sij is the resolved strain rate tensor and spatial averagingis performed at each timestep. The eddy viscosity varies in time and space with thestrain rate. Surface fluxes and heterogeneity are embedded in the lower boundarycondition through a heterogeneous land surface parameterization. Horizontal varia-tions in surface heat flux are incorporated by modifying the lower boundary condition(Moeng and Wyngaard 1986). The boundary condition for pressure (p) is derivedfrom

1ρ0

∂p∂z

= −∂τ ′13

∂x− ∂τ ′

23

∂y+ gθ ′

θ0, (2)


where ρ0 is air density, τ ′13 and τ ′

23 are the streamwise and spanwise shear stresses, gis acceleration due to gravity, θ0 is surface temperature and θ ′ is the potential tem-perature deviation from the horizontal mean. The additional buoyancy term is usedto ensure that vertical velocity vanishes at the surface. The SGS fluxes at the first gridlevel above the surface are prescribed using similarity relations (Businger et al. 1971)applied at each grid point. The surface subgrid parameterization is two-dimensionaland heterogeneous over the domain as ensemble averages are not taken. The aero-dynamic roughness length (z0 = 0.1 hc, where hc is the canopy height) is assignedto different land-use patterns, depending on the height of vegetation in the studyarea. The range of values used for the clear-cut and grassland areas is 0.01–0.2 m, and0.2–1.1 m for forested areas.

The NDVI, albedo and radiometric temperature obtained from a Landsat sceneare used for estimating sensible heat flux over the domain, following a method similarto that used by Albertson et al. (2001). The net radiation partitioned between the baresoil and the vegetation is estimated according to the two-source model of Normanet al. (1995) using the leaf area index (LAI) distribution derived from NDVI. Thealbedo is derived from the visible spectrum (Liang 2000) and the net radiation isfound from the radiation balance. The sensible heat flux over bare soil is estimatedfrom the aerodynamic exchange, while over the vegetation it is estimated as a residualin the energy balance. The estimated net radiation and heat flux are comparable tothe direct observations (Fig. 2) over the forest and the clear-cut during similar stabilityconditions.

The simulation is carried out for 120 × 120 × 100 grid points and the domain size is3.6×3.6×1.5 km, giving a horizontal resolution of 30 m, conforming to the resampledspatial resolution of the Landsat radiometric temperature. The vertical resolution of15 m is used since the length scales of the coherent motions in the surface layer asobserved with the mini-sodar are 20–30 m. In the LES, the horizontal derivatives areevaluated with a pseudo-spectral method and the vertical derivatives are found withthe help of a second-order central differencing method. The pressure field is derivedfrom the Poisson equation by satisfying continuity and a divergence free velocityfield. The SGS kinetic energy is obtained by solving the time dependent turbulentkinetic energy (TKE) equation. The upper boundary allows hydrostatic gravity waveradiation. A strong temperature gradient is initialized at the top boundary and nosubsidence is imposed. Coriolis effects are not considered for the simulations. Allsimulations are done for a dry CBL.

Periodic lateral boundary conditions are used in the model, which implies that sim-ilar heterogeneities are repeated at the inflow boundaries. The influence of the peri-odic boundary condition on the simulation is minimized with the help of an extendeddomain. The study domain is embedded in another homogeneous domain by extend-ing the actual domain by 1 km in all four directions. A homogeneous heat flux Q0(0.13 K m s−1) and roughness length (1.1 m) are predefined for this outer region basedon the degree of homogeneity in the inner domain, which ensures a smooth transitionat the boundaries. This domain configuration imposes a quasi-homogeneous inflow,while alleviating the impact of periodic boundary conditions in the streamwise andthe spanwise directions. Results presented here for all simulations correspond to theheterogeneous inner domain. The adequacy of the extent of the simulation domainis tested with the help of autocorrelation functions of vertical velocity, which showedthat the function drops to 0 at a distance of 750–1000 m. A constant timestep of 1 s isused in all simulations and the results presented here correspond to the data saved


after attaining stable statistics. The time averaging is 6000 s, which is approximately9–10 large-eddy turnover times (t∗ = zi/w∗). A temporal resolution of 20 s is used inthe analysis.

2.3 Description of cases

Table 1 provides details of simulations. The test cases are named according to thegeostrophic wind speed and direction used in each simulation; for example, W2 rep-resents the case with a westerly background wind and speed of 2 m s−1. An exceptionto this is H2, which is a homogeneous case with a 2 m s−1 westerly wind.

Case H2: Westerly wind 2 m s−1, Homogeneous forest with z0 = 1.1 m and Q0 =0.13 K m s−1

Case W2: Westerly wind 2 m s−1, flow perpendicular to the north–south orientedclear-cut.

Case W5: Westerly wind 5 m s−1, flow perpendicular to the north–south orientedclear-cut.

Case N2: Northerly wind 2 m s−1, flow parallel to the north–south oriented clear-cut.

Case E2: Easterly wind 2 m s−1, flow perpendicular to the north–south orientedclear-cut.

Case W2h: Westerly wind 2 m s−1, flow perpendicular to the north–south orientedclear-cut, and with the heat flux reduced to 40%, maintaining the hori-zontal gradients.

The heat flux (Q0 = w′θ ′0, the kinematic heat flux is used throughout the dis-cussion and may vary with x and y) distributions are the same for all simulationsexcept for case H2 and W2h. H2 is used for comparison of a homogeneous forestcase with different heterogeneous cases. W2h with a reduced heat flux is consideredto represent cloudy conditions as observed during some of the periods in Fig. 2. Fivecases have the shear buoyancy ratio (u∗/w∗, where u∗ is the friction velocity given by[〈u′w′+τuw〉2+〈v′w′+τvw〉2]1/4

s , where τuw and τvw are subgrid-scale (SGS) momentumfluxes in the streamwise and spanwise directions, w∗ is the convective scaling velocity

(gQ∗zi/〈θ〉)1/3, where Q∗ = 〈w′θ ′0〉 is the LES spatially averaged heat flux, g is the

Table 1 Cases chosen for the study and their characteristic scales; boundary-layer height (zi), friction

velocity (u∗ = [〈u′w′ + τuw〉2 + 〈v′w′ + τvw〉2]1/4s , where τuw and τvw are SGS momentum fluxes

in the streamwise and spanwise directions), convective scaling velocity (w∗ = (gQ∗zi/〈θ〉)1/3, whereQ∗ = < w′θ ′

0 >, g is acceleration due to gravity and < θ > is mean potential temperature), temper-

ature scale (θ∗ = < w′θ ′0 >/w∗), Obukhov length (L = − < θ > u3∗/(kgQ∗), where k = 0.4 is von

Kármán constant) and large-eddy turnover time (t∗ = zi/w∗)

Case zi(m) u∗ (m s−1) w∗ (m s−1) θ∗ (K) zi/L t∗ (s)

H2 1020 0.25 1.55 0.07 −92.8 656W2 1050 0.25 1.65 0.08 −121.1 638W5 1080 0.39 1.67 0.08 −31.6 647N2 1050 0.24 1.64 0.08 −122.1 640E2 1065 0.24 1.64 0.08 −124.6 650W2h 1035 0.2 1.19 0.04 −88.0 869


acceleration due to gravity and 〈θ〉 is mean potential temperature) equal to 0.15 andfor W5 a value of 0.23 is noted (Table 1). This shows that all cases are approximatelyin the same shear-buoyancy regime.

Due to complex geometry and orientation of surface inhomogeneities, phase aver-ages used in idealized heterogeneity (Shen and Leclerc 1994; Raasch and Harbusch2001) studies could not be used here. Results are analyzed by means of domain-averaged cross-sections, time averaged and normalized with zi and other associatedscaling parameters from Table 1, for corresponding cases. The study area used inthe streamwise and the spanwise averaging is shown in Fig. 1b. In the presence ofwesterly and easterly winds, the north–south oriented part (h ≈ 1.5 zi) of the inverted‘L’-shaped clear-cut is located perpendicular to (Fig. 1a), and the east–west orientedpart (h ≈ 1.1 zi) of the clear-cut is parallel to, the mean flow. Horizontal averages arerepresented with angular brackets 〈〉 in the streamwise and in the spanwise directions.The orientation of the study domain is fixed and streamwise/spanwise averaging repre-sents a distribution in the alongwind/crosswind plane. A deviation from the horizontalmean is marked by a prime and time averages are indicated with the overbar.

3 Results and discussion

3.1 Comparison of bulk properties in the CBL

An examination of the temporal evolution of volume-averaged TKE (not shown)for all cases showed oscillatory behaviour even after integrations of 20 times thelarge-eddy turnover time (t∗ = zi/w∗). Persistent thermally induced oscillations inthe CBL over several large-eddy turnover times have also been noted by Letzel andRaasch (2003). During the integration period less than 10% variation from the meanTKE is noted, and the boundary-layer height is approximately constant during thisaveraging period.

Bulk profiles of potential temperature (Fig. 3a) corresponding to the heteroge-neous cases show a constant difference ≈0.3 K with the homogeneous case (H2) and≈0.6 K with W2h at all levels attributed to lower prescribed heat fluxes. Heat-fluxprofiles (Fig. 3b) show some difference for W5 with slightly higher values in the lowerhalf of the mixed layer. The SGS heat flux (thin lines in Fig. 3b) has very little var-iation between the cases, and peaks at the lowest grid point. The normalized windspeed (not shown in the Figure) in the mixed layer for case H2 (U/Ug = 0.75) isidentical to the LES with-canopy case of Patton et al. (2003). Cases H2 and W2hhave a nearly constant Reynolds stress (Fig. 3c) in the lower layers, which decreasessteadily with height. Cases W2, E2, and N2 characterize enhancement in the hori-zontal velocity (U/Ug > 0.75 at z = 0.05–0.3 zi) and relatively less stress than H2.With an increase in wind speed (W5), the stress increases three times more than H2in the lower levels due to higher background wind speed, and a consistent reduc-tion in the normalized wind speed (U/Ug = 0.65 in the mixed layer) is noted. Thetemperature variance for case H2 is lower than (Fig. 3d) that for the heterogeneouscases.

Total (resolved + SGS) velocity variances and TKE show (Fig. 4) comparablevalues with earlier studies (Moeng and Sullivan 1994; Lin 2000) for a moderatelyunstable CBL. The normalized streamwise velocity variance (Fig. 4a) peaks (≈0.3 w2∗)close to the surface and throughout the CBL it is slightly higher than the laboratory


0.0

0.5

1.0

0.0

0.0

0.5

1.0

0.00 0.02 0.04 0.06

0.0

0.5

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302

0.0

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1.0

0

[<u'w'>2+<v'w'>2]1/2/w2

*

W2h E2 N2 W5 W2 H2

<w'θ'>/w∗θ

∗

z/zi

<θ> (Κ)

z/zi

(c) (d)

(b)(a)

<θ'2>/θ2

∗

304 0.5 1.0

2 4 6 8 10

Fig. 3 Vertical profiles of horizontally averaged and time-averaged (a) potential temperature (b)normalized resolved and subgrid-scale heat flux, (c) total momentum flux normalized with square offree-convective scaling velocity (w∗) and (d) normalized temperature variance from LES for six casesas described in Table 1. Thin continuous and dotted lines in (b) represents subgrid-scale heat flux forcases H2 and W5, respectively

simulations (denoted by ‘star’ in the figure) of Willis and Deardorff (1974) and com-parable to the with-canopy case of Patton et al. (2003). The spanwise velocity variance(Fig. 4b) increases in the presence of heterogeneity (0.4–0.6 w2∗; a 10–20% enhance-ment in the v component variance relative to H2 is noted for the heterogeneous caseW2). In the presence of increased wind speed (W5), peak values (0.6 w2∗) are morepronounced (50% more than H2, 40% more than W2) than all other cases. If wecompare W5 (zi/L = −31.6) with the homogeneous with-canopy case presented inPatton et al. (2003) having a similar background wind and a lower stability parameter(zi/L = −25), a 15–20% enhancement of the v variance in the lower and upper lay-ers is noticed. The v variance maximum is located at 0.05 zi as in Patton et al. (2003).Raasch and Harbush (2002) also noticed higher spanwise velocity variances associatedwith their heterogeneous simulation, which is an indication of the secondary circula-tion in the plane perpendicular to the flow field. The normalized w velocity variancefor the heterogeneous cases is higher (7–10% more than H2 at z = 0.3–0.4 zi) than thehomogeneous case H2. However, there are no significant differences between the ver-tical velocity variance (Fig. 4c) for the different heterogeneous cases. The mixed-layer


0.0

0.5

1.0

0.0

0.0

0.5

1.0

<v'2>/w*

2

(a)

<u'2>/w*

2 <w'2>/w*

2

(b) (c) W2h E2 N2 W5 W2 H2

(d)

<E>/w2

*

(e)

<w'E>/w*

3<w'2θ'>/w2

*θ

*

z/zi

z/zi

(f)

0.3 0.6 0.0 0.3 0.6 0.0 0.3 0.6

0.0 0.3 0.6 0.0 0.1 0.20.0 0.3 0.6

Fig. 4 Vertical profiles of mean (a) streamwise (u), (b) spanwise (v), and (c) vertical (w) velocityvariances, (d) TKE, (e) vertical transport of heat flux and (f) vertical flux of TKE. These profilesare normalized with scaling parameters given in Table 1. The dashed line in (c) is the best fitMonin–Obukhov similarity relationship (Stull 1988). The symbol ‘star’ in (a) and (c) correspondsto experimental values from Willis and Deardorff (1974)

similarity relationship w′2w2∗

= A(

zzi

)2/3 (1 − B z

zi

)2(Stull 1988) fitted to the case W5

(using w∗ and zi from Table 1) is also presented in Fig. 4c. Constants A and B in therelationship with values of 1.8 and 0.7 give a best fit to the LES results. The verticalvelocity variance in the mid-regions of the mixed layer for case W5 are 10% morethan the homogeneous with-canopy case of Patton et al. (2003), while below 0.2 zi,


no differences are noted. The simulated vertical velocity variances are slightly higherthan the laboratory simulation of Willis and Deardorff (1974).

The heterogeneous cases show a higher (Fig. 4d) TKE than the homogeneous case.

The TKE(⟨

E⟩ = 0.5(

⟨u′⟩2 + ⟨

v′⟩2 + ⟨w′⟩2 + ⟨

e⟩)

, where 〈e〉 is the SGS contribution of

TKE) profile shows an increase in TKE for increased wind speed (W5). The verticaltransport of heat flux is enhanced (Fig. 4e) for the heterogeneous cases and lowestvalues are noted for H2. The vertical flux of resolved-scale TKE (〈w′E〉) for the heter-ogeneous cases is not very different from the homogeneous case. These results showthat the homogeneous case (H2) differs in the CBL bulk properties in comparisonwith the heterogeneous cases. A moderate increase in wind speed in the heteroge-neous case has a significant effect on bulk CBL parameters over the domain, while theinfluence due to wind direction change in weak wind conditions is not clearly evidentin these mean, normalized profiles.

3.2 Identification of secondary circulations

3.2.1 Homogeneous case (H2)

In the homogeneous case, the streamwise circulation shows narrow, weak updrafts(maximum of 0.03 w∗) and wide downdrafts (maximum of −0.1 w∗) dominating thedomain with a relatively uniform heat-flux distribution (Fig. 5a, H2). The spanwisedistribution (Fig. 5a, right panel) shows a weak circulation (with updrafts of 0.3 w∗ and

downdrafts of 0.2 w∗) attributed to the pressure gradient((

ziρw2∗

)∂p∂y = 0.08

), which is

greater than in the streamwise distribution (0.04).

3.2.2 Low wind speed case (W2)

The mean heat flux for case W2 is much higher and circulations are stronger(Fig. 5a) than that for case H2. The high heat-flux region at the eastern part ofthe large clear-cut extends downwind and is advected over the forested area. Theheated air over the clear-cut rises at the leading edge of the clear-cut and over theadjacent forest. A return flow with an aspect ratio of 1.5 leads to downdrafts overthe centre of the clear-cut, which is driven by the streamwise and vertical pressure

gradients((

ziρw2∗

)∂p∂x = 0.08,

(zi

ρw2∗

)∂p∂z = 0.08

). A pair of closed circulating cells is

separated by zi in the spanwise distribution. The non-symmetric circulations (aspectratio of 1.5 on the north side, and 1 on the south side) are driven by strong span-

wise pressure gradients ((

ziρw2∗

)∂p∂y = −0.3 on the north side, and 0.08 on the south

side). Updrafts are narrow and strong (w = 0.6 w∗ at 0.5 zi) along the heat flux max-imum (Fig. 5, W2), while downdrafts (−0.23 w∗ on the north side, and −0.15 w∗ onthe south side) are weak. These features have characteristics of a type I circulationas in the case of chessboard-type heterogeneity (Raasch and Harbusch 2001). Thespanwise velocity variance increases at the top and bottom of the mixed layer (Fig. 5a,W2, right panel) on both sides of a strong updraft. This increase is noted in regionswhere spanwise momentum is transferred to updrafts/downdrafts associated with thecirculation.

There is strong convergence at the front edge of the updraft contributing to thereturn flow over the clear-cut and counter-rotating circulations on the crosswind plane


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F

0 1 2 3F

0 1 2 3F1 2 3F

1 2 3F

1 2 3F

)mk(

z)

mk(z

)mk(

z

W5W5

W2

0.35 w*

Streamwise distance (km)

0.7 w*

0.0

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Fig. 5 (a) The streamwise (on the left panel) and spanwise (on the right panel) distributions of thenormalized heat flux. Vectors in the streamwise distribution represent resolved scale turbulence field(u′, w′) and in the spanwise distribution vectors represent resultant of v′ and w′. Contours in the rightpanel represent the spanwise velocity variance normalized with w2∗. The location of the flux tower ismarked with ‘F’. The vector scale in the streamwise direction is half that of the spanwise vector scale(0.7 w∗). Different scales are used to make the vectors visible in all the cases. The area used in thestreamwise and spanwise averaging is highlighted in Fig. 1b. (b) Same as (a), but for the cases N2, E2and W2h


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Fig. 5 continued

over the forest. This circulation has a more complex three-dimensional distributionsimilar to that of a ‘coherent system’ (Lin 2000). The pressure deviation within thesecirculations is much higher than the surroundings and is stronger in the crosswindplane (Fig. 6, right panel). The pressure transport within the updraft is higher thanthe surrounding region, which leads to an increase in the TKE within these strongthermals. There is an increase in the SGS TKE (e/w2∗ = 0.014 compared to 0.001outside the thermal) and resolved-scale TKE (E/w2∗ = 0.25 compared to 0.16 outsidethe thermal).


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Fig. 6 The streamwise (on left panel) and spanwise (on right panel) distribution of normalizedpressure deviation for the cases W2, W5, and N2

3.2.3 The effect of wind speed

In comparison with case W2, the heat-flux maximum in case W5 (Fig. 5a, left panel)is advected further downwind from the eastern edge of the large clear-cut whereweak updrafts dominate. In the crosswind plane there are three heat-flux maxima andassociated circulations (Fig. 6a, W5, right panel). The ambient flow is parallel to thebulk of the heterogeneity (h ≈ 1.1 zi) on the southern side and strong crosswindpressure gradients (Fig. 6, W5, right panel) exists there. Mean spanwise eddy veloci-ties at the base of downdrafts increase up to ±0.7 w∗ due to the transport from higherlevels. The v velocity variance enhances (0.6 w2∗) at the top and base of the mixed layerand is higher than in case W2. Our results are in agreement with Raasch and Harbusch(2001), and show that the secondary circulation becomes strong with increased windspeed. The uniform streamwise distribution of heat flux below z = 0.45 zi (Fig. 5a, W5,left panel) along with a complex secondary circulation in the crosswind plane showselongated rolls (LeMone 1973; Khanna and Brasseur 1998) with a length scale of 3 zi.The increased wind speed and shear (Fig. 3c) in case W5 cause the boundary-layermotions to transform from three-dimensional cellular (e.g. case W2) to two-dimen-sional convection motions (Sykes and Henn 1989). Similar boundary-attached roll


(LeMone 1973) circulations have been found in the LES (Esau and Lyons 2002)studies of larger-scale heterogeneities and in measurements at the sharp boundary ofagricultural and tall native vegetation. Kropfli and Kohn (1978) observed convergenteddy velocity fields aligned along the heavily industrial part of urban areas and diver-gent zones were observed over the low heat-flux regions, as noted here. Organizationof eddy velocity fields was also observed with lidar over urban areas (Newsom et al.2005). The quasi-stationary nature of organized features suggests that these circu-lations are directly linked to the surface heterogeneity and contribute to non-localadvection.

3.2.4 The effect of wind direction and scale and orientation of heterogeneity

Northerly flow encounters a heterogeneity scale of h ≈ 1.5 zi along the north–southoriented clear-cut. The high heat-flux region is found directly over the clear-cut andthe spanwise distribution (Fig. 5b, N2, right panel) shows a strong updraft that hascounter-rotating vortices on both sides. The aspect ratio is 1.0 on the western side,and 1.5 on the eastern side with a weaker circulation. The crosswind velocity variancehas double maxima, similar to W2. Strong horizontal pressure gradients and vertical

pressure gradients((

ziρw2∗

)∂p∂z = 2.1

)give rise to strong circulations (Fig. 6, N2, right

panel). There is negative fluctuating vorticity over the clear-cut (−0.2 s−1) extend-ing to a height of 0.5 zi. The co-existence of large vorticity and negative pressurefluctuations has also been reported (Lin 2000) inside large-scale elongated thermals.

Due to the homogeneity of the forest in the eastern sector of the flux tower, condi-tions with a prevailing wind from this sector are presumed to have quasi-homogeneouscharacteristics. The distribution of heat flux and the eddy velocity field shows (Fig. 5b,E2, left panel) similar characteristics to that of case W2. Organized vertical motionin the crosswind plane is noted at the same location as that of W2 (Fig. 5b, E2, rightpanel), but is weaker than W2.

3.2.5 The effect of reduced heat flux

In the lower prescribed heat flux scenario (W2h), the simulated heat-flux maximum(Fig. 5b, W2h) is lower than for cases W2 and E2. Updrafts dominate directly overthe clear-cut and there is low-level convergence from the eastern part of the domain.There are two pairs of vortices and three heat-flux maxima in the spanwise distribution(Fig. 5b, W2h, right panel) resembling W5. One strong circulation is noted over theregion adjacent to the southern part of the ‘L’-shaped clear-cut. The counter-rotatingvortices on either side have an aspect ratio of 1.

3.3 Three-dimensional distribution of heat flux

Two-dimensional averages do not give the actual orientation and location of theorganized motion, which may be crucial for point or area flux measurements. Wepresent time averages of the heat flux for cases W2 and W5 for an averaging time of6000 s at all grid points. A three-dimensional distribution of normalized heat flux (iso-surface of w′θ ′/w∗θ∗ = 1 with a view from the south-east of the domain) is presentedfor cases W2 and W5 in Fig. 7a and b, respectively. The heat flux is overestimated


Fig. 7 Three-dimensional view of the normalized heat-flux distribution. Isosurface with heat fluxequal to w∗θ∗ is presented for the case (a) W2 and (b) W5. Four plots marked 1–4 are used to ana-lyze the area-averaged heat flux in a 1 × 1 km area presented in Fig. 9. Dashed lines represent theapproximate boundary of major clear-cuts

(higher than the domain average presented in Fig. 3b) at all locations within the iso-surface. For case W2 (Fig. 7a), high heat-flux regions are present upwind, over anddownwind of the main clear-cut. A streamwise organization of plumes and thermalsemanating from the clear-cuts is noted at 2 km from the southern boundary. There isanother organized feature over the southern (lower part of the L-shaped clear-cut)region, where flow is parallel to the bulk of the heterogeneity. The distribution of theisosurface suggests a streamwise organization of thermals over a significantly largearea with high (w′θ ′/w∗θ∗ > 1 inside the isosurface) heat flux. With increasing eleva-tion, the high heat-flux region occupies less surface area and shifts downwind of theheterogeneity.

With the increase in wind speed (W5), isosurfaces are more elongated (Fig. 7b)in the streamwise direction. The organized feature at a distance of 1 km from thesouthern boundary is a dominant feature, where h ≈ zi in the alongwind direction.


The influence from small-scale heterogeneities is smeared at higher wind speeds. Asingle organized heat-flux maximum is noticed for case N2 (figure not presented) overthe north-south oriented clear-cut where the bulk of the heterogeneity is parallel tothe flow. The isosurface of the heat flux in N2 is narrow in the horizontal plane andelongated in the vertical direction, indicating a strong influence due to the large areaof the clear-cut aligned parallel to the geostrophic wind.

3.4 Impact of secondary circulations on area-averaged heat flux

We examine the area-averaged heat flux in four 1 × 1 km plots in the study area asindicated in Fig. 7a, b. Plots 1 and 4 are over the southern and northern sides of theclear-cut, and Plots 2 and 3 are over the forested areas. A heterogeneous patch oflinear dimension ≈0.5 zi and with higher heat flux is also embedded in Plot 3; Plot 2is apparently homogeneous. The area-averaged heat flux for all six cases is foundfrom the time-averaged heat flux at all grid points within each plot and presentedin Fig. 8. The homogeneous case shows little variation between the four plots, whilethe heterogeneous cases show considerable variation from the mean heat flux of H2(presented with the thick broken line in the figures). Cases W2 and W5 show theinfluence of horizontal advection in Plot 2 at higher elevations, while in other plots,an overestimated heat flux (15–20%) is noted in the lower part of the mixed layer.The laboratory simulation of convection flow shows up to a 20% increase in heat fluxin the presence of increased roughness (Shen et al. 1996). Experimental results overthe heat-flux heterogeneities have indicated an increase in the heat flux downwind ofthe heterogeneity (Doran et al. 1995; Klaassen et al. 2002) due to advection effects.Sakai et al. (2001) reported a 17% of low-frequency contributions to the measuredflux over a rough canopy. A lack of energy balance closure (imbalance) are noted overseveral forest flux sites (Finnigan et al. 2003; Wilson et al. 2002), and in some cases(Malhi et al. 2002), an extended averaging period (accounting for the low-frequencyflux contribution) up to 4 h resulted in a reduced surface imbalance.

It is obvious from the results that, depending on the background wind and thedistribution and size of heat-flux heterogeneity, the axis of the secondary circula-tion changes and measurements in the vicinity are influenced. Signatures of suchquasi-stationary circulations induced by surface heterogeneity have been reportedin observational studies (Desjardins et al. 1997) and their effect on fluxes at higherlevels is significant (Mahrt 1998). However, when measurements are made inside theorganized features, lower level fluxes are also altered. The above results suggest thatthere is considerable spatial variability in the heat flux in heterogeneous cases andthe identification of secondary circulations is crucial in minimizing errors in the fluxmeasurement.

3.5 Impact of secondary circulations on point measurements

Finally, the time-averaged vertical velocity and the resolved-scale heat flux at the twolocations (F and F1 indicated in Fig. 1a, which are 500 m apart) over the forest areexamined (Fig. 9) to assess the impact of the secondary circulations on point measure-ments. All cases show a non-zero vertical velocity. The homogeneous case (H2) showsa weak vertical velocity irrespective of the location (‘F’ in Fig. 9a and ‘F1’ in Fig. 9b),and the heterogeneous cases display a wide range of variation in the vertical velocityat both locations. The location F1 is profoundly influenced due to the presence of the


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0.5 1.0 0.0 0.5 1.0

Fig. 8 Vertical profiles of time-averaged and area-averaged normalized heat flux over four 1 ×1 km plots (as indicated in Fig. 7a,b), for all six cases. Thick grey dashed lines represent total heatflux (given by (〈w′θ ′〉 + 〈τwθ 〉)/(w∗θ∗), where 〈τwθ 〉 is the SGS heat flux) for the case H2 used forcomparison

secondary circulation. For cases W5, W2h and N2, the location F is under the influ-ence of roll circulation and thus updrafts are stronger. The mini-sodar observationsat the site also show considerable changes in the hourly mean vertical velocities inthe surface layer. For cases W2, W2h and W5, the heat flux is overestimated (>totalflux for H2 presented in thick dotted lines) up to 15–25% at F1 and F (‘F1’ in Fig. 9c


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Fig. 9 Vertical profiles of time-averaged normalized vertical velocity and heat flux at the two locations(marked as F and F1 in Fig. 1a) over the forest (500 m apart in the north–south direction)

and ‘F’ in Fig. 9d). If the measurement point falls inside a quasi-stationary roll, over-estimation is more than 10%, and if the point lies under the influence of downdraftregions, an underestimation in the flux is noted. These results emphasize the needto re-examine the site selection criteria for flux measurements over heterogeneoussurfaces.

3.6 Remarks

Results presented in this study are sensitive to the sensible heat flux prescribed at thesurface in the simulation, which is derived from remote sensing and eddy-covariancemeasurements. It should also be noted that simulations carried out in this study havenot taken into account the effect of latent heat flux. Experimental studies in the pasthave found that evaporation and evapotranspiration rates are enhanced by the localadvection (Guo and Schuepp 1994) of sensible heat in the case of small-scale stepchanges. This is an important issue for advection over forests. Another aspect is thatthe characterization of surface roughness in this study is based on the canopy height.The drag force associated with the bluff canopy is not explicitly represented in thesimulations. The explicit characterization of the canopy at the lower boundary of LES


models might influence the bottom-up diffusion and thus fluxes as demonstrated byPatton et al. (2003). The use of higher vertical resolution near the lower boundaryand the inclusion of bluff canopy effects might introduce still smaller scale coherentstructures scaled to the canopy height as noted in their study. The grid size (15 m) usedin our simulations is chosen based on the eddy length scale observed in the surfacelayer over the forest with the mini-sodar. Coherent structures of 30 m wavelength areresolved in the simulations, while eddies of 10–15 m length near the canopy top are notresolved. Higher-order moments from LES results are sensitive to the grid spacing,the domain size and the SGS parameterization (Agee and Gluhovsky 1999), and sucheffects are not evaluated in this study. The grid size used here is comparatively smallerthan other studies (Shen and Leclerc 1994; Avissar and Schmidt 1998; Raasch andHarbusch 2001).

4 Conclusions

Specific conclusions from this study are:

– In comparison with a homogeneous forest, the introduction of heterogeneity pro-duces differences in the bulk properties of CBL turbulence such as spanwise andvertical velocity variances and TKE.

– Enhancement in spanwise velocity variance is closely associated with the roll for-mation and double maxima at the lower and upper parts of the mixed layer andis an indication of the transfer of spanwise momentum to the vertical direction.Spanwise circulations become shallow with a reduction in the heat flux.

– The orientation of heterogeneity with respect to geostrophic wind, horizontal scale(h) and amplitude of the heat flux influences the strength, location, aspect ratioand orientation of the secondary circulations.

– For low wind speeds, quasi-stationary convective thermals characterize a‘coherent system’ (Lin 2000), with a streamwise return circulation and spanwisecounter-rotating vortices that are driven by strong pressure gradients. The quasi-two dimensional elongated roll appears with increased wind speed, and the sec-ondary circulation strengthens.

– Strong updrafts induce enhanced entrainment at the mixed-layer top, and thustop-down diffusion is affected downwind of the heterogeneity.

– Area-averaged heat fluxes for the heterogeneous cases are up to 20% higher thanthat for a homogeneous forest.

– The flux tower locations in the forest characterize non-zero vertical velocities andheat flux is overestimated up to 20–25% in the presence of a moderate wind speedand when the upwind heterogeneity scale (h/zi) is large. The underestimation/overestimation of flux at a location depends whether the tower is located in thedowndraft /updraft region of the roll.

Our analyses indicate that the quasi-stationary roll formation induced as a result ofheat-flux heterogeneity has a profound influence on the flux measurements at the site.Large eddies that scale to the CBL introduce a ‘stationary heat flux’ (Mahrt 1998).The location of the roll formation is a strong function of wind direction and speed,and the prescribed surface heat flux. Point measurements can sometimes be under theconstant influence of these circulations or can miss the flux contributions due to thesestationary eddies, depending on their location, and may be interpreted as a randomor as a systematic error.


Acknowledgements Authors would like to thank Dr. Monique Y. Leclerc of the University ofGeorgia for her support and several useful comments on the manuscript. Mike Binford gratefullyacknowledges NASA Earth Science Enterprise Land Cover-Land Use Change Program; Grant No.NAG5-9331 and U.S. Department of Energy for funds provided through Office of Science under theTerrestrial Carbon Processes (TCP) program through a subcontract to the University of Florida. Theauthors also acknowledge the many constructive comments of three anonymous reviewers.

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