## 1. Introduction

Forests cover a significant fraction of Earth’s land surface and provide a net land sink of carbon dioxide (CO_{2}) of over 10 GtCO_{2} yr^{−1} (Le Quéré et al. 2014); of this 10 GtCO_{2} yr^{−1}, about one-third arises through carbon uptake from undisturbed tropical forests and two-thirds from undisturbed temperate and boreal forests. Regrowth on previously cleared tropical forest land and in managed plantations contributes to an additional sink of 6.2 GtCO_{2} yr^{−1}, although this does not completely offset the even larger source (~10.25 GtCO_{2} yr^{−1}) resulting from ongoing clearing (Canadell and Schulze 2014). Even though deforestation is diminishing (FAO 2010), projections of the future global carbon balance are strongly influenced by our understanding of the response of the forest sink to climate change and disturbance. In addition to its involvement in the carbon cycle, forests play a critical role in Earth’s climate through their influence on energy, water, and nitrogen cycles (Bonan 2008), as well as through exchanges of reactive species that place stringent controls on the atmosphere’s oxidative capacity [or cleansing ability (e.g., Fuentes et al. 2000; Guenther et al. 2006)]. For all these reasons, understanding the processes controlling turbulent exchange of energy, momentum, and scalars between the vegetation and the atmosphere has never been more important.

Vegetation (and urban) canopies produce turbulence that is qualitatively different to that over a rough surface, which ultimately results from canopies absorbing momentum over a distributed height range rather than at the ground surface. Within the canopy airspace, the distribution of the mean velocity and the turbulence is controlled by the interplay of downward turbulent transport of momentum and canopy drag (e.g., Raupach and Thom 1981) modulated by diabatic influences. The aerodynamic drag of the canopy varies spatially based upon the distribution of the canopy elements, their efficiency at extracting momentum, and the velocity field itself. Similarly, within-canopy distributions of scalars like heat, water vapor, and carbon dioxide are determined by the balance between turbulent transfer and the distribution of scalar sources and sinks. These, in turn, respond to solar radiation as it attenuates through the foliage, the biological state of the plants (e.g., their access to soil water), the ambient concentration of the particular scalar in the canopy airspace, and, in the case of reactive scalars, their reaction rates.

Current theory describing canopy exchange largely hinges on the hydrodynamic instability associated with an inflection point in the vertical profile of the horizontal wind at canopy top (sometimes called an inflection-point instability) induced through the canopy’s distributed momentum absorption (e.g., Raupach et al. 1996; Finnigan et al. 2009). Parameterizations built upon this theory (Harman and Finnigan 2007, 2008) are showing great promise in predicting flux–gradient relationships (e.g., Weligepolage et al. 2012). However because the theory relies on the presence of wind speed shear at canopy top, its applicability across the broad stability variation that occurs outdoors remains uncertain. Consequently, this manuscript focuses on diabatically unstable conditions extending from high wind (near neutral) through increasingly weaker winds to no-wind situations (free convection).

Current understanding of the impact of atmospheric stability on canopy turbulence is based on a relatively limited number of studies (e.g., Leclerc et al. 1991; Su et al. 2004; Thomas and Foken 2007; Cava and Katul 2008; Dupont and Patton 2012a) where most of these are based upon measurements from a single tower and infer horizontal spatial variations in atmospheric properties by adopting Taylor’s frozen turbulence hypothesis. Critically, these studies all lack information regarding atmospheric stability-induced variability of atmospheric boundary layer (ABL)-scale turbulence and its impact on turbulence at canopy scale.

Because of the vast range of scales present in the ABL, numerical simulation efforts attempting to further the community’s understanding of canopy turbulence have largely ignored ABL-scale turbulence and instead allocated numerical resolution toward resolving canopy processes as opposed to investigating larger domains (e.g., Shaw and Schumann 1992; Su et al. 1998; Dupont and Brunet 2008). For simplicity, these efforts have also targeted neutral stability conditions. Albertson et al. (2001) investigated atmospheric stability variations on coupled canopy turbulence but were similarly unable to interrogate the influence of ABL-scale turbulence because of domain size limitations. Bohrer et al. (2009) investigated stability variations in relatively large domains but with uncoupled canopy scalar sources/sinks.

To test the hypothesis that the evolution of organized turbulence structure across a range of atmospheric stability variations alters canopy exchange, this manuscript analyzes results from five large-eddy simulations (LES) of atmospheric boundary layers interacting with a resolved and interactive forest canopy. The manuscript is organized as follows: Section 2 describes the essentials of the LES code, and similarly, section 3 outlines the basis behind the multilevel canopy model. Section 4 sketches each model’s configuration and the flow regimes investigated. Section 5 discusses how statistics are calculated and data normalization. Section 6 presents analysis of the results, and section 7 outlines the key findings regarding ABL control over canopy exchange that would not be possible with limited-domain numerical (or physical) simulations of canopy turbulence.

## 2. The large-eddy simulation

The National Center for Atmospheric Research’s LES code has been described in a variety of earlier manuscripts (e.g., Moeng 1984; Moeng and Wyngaard 1988; Sullivan et al. 1996; Sullivan and Patton 2011). The current model is based on the developments described in Patton et al. (2005), Finnigan et al. (2009), and Sullivan and Patton (2011), where the equations for an atmospheric boundary layer under the Boussinesq approximation are solved on a discretized three-dimensional grid. The equations include: (i) transport equations for momentum **u** = (*u*, *υ*, *w*) in the (streamwise *x*, spanwise *y*, and vertical *z*) directions, (ii) a transport equation for potential temperature *θ*, (iii) a transport equation for water vapor mixing ratio *q*, (iv) a discrete Poisson equation for pressure *π* to enforce incompressibility, and (v) an equation for subfilter-scale (SFS) turbulent kinetic energy *e*. Following Patton et al. (2005), buoyancy appears in the momentum equations as virtual potential temperature

*f*is the Coriolis parameter;

*z*;

*x*,

*y*) components (

*g*is Earth’s gravitational acceleration and

*e*are:

^{1}

*a*is a one-sided frontal plant area density (PAD),

Boundary conditions are periodic in the horizontal, and the upper-boundary condition is such that horizontal velocities, SFS energy, potential temperature, and specific humidity use a specified gradient method (Neumann conditions) and vertical velocity is forced to 0 m s^{−1} (Dirichlet condition). Beneath the canopy, rough-wall boundary conditions (i.e., specified roughness length ^{2} Spalart et al.’s (1991) third-order Runge–Kutta scheme advances the solutions in time. Horizontal spatial derivatives use Orszag’s (1969) pseudospectral methods for all field variables, while vertical derivatives use second-order finite differences for momentum and SFS energy and Beets and Koren’s (1996) monotone scheme for potential temperature and specific humidity.

## 3. The land surface model

### a. The model’s basis

The NOAA/NCEP–Oregon State University–Air Force Research Laboratory–NOAA/Office of Hydrology land surface model (Noah) serves as the primary basis describing the coupling between the atmosphere and the land surface. Noah is designed for weather forecasting focusing on hydrologic coupling in the soil–water–vegetation system (Chen et al. 1996; Chen and Dudhia 2001; Ek et al. 2003). In its standard form (e.g., Ek et al. 2003), Noah’s canopy exchanges heat and moisture as a single “big leaf” and assumes that emitted scalars are vented immediately from the canopy space (e.g., Pan and Mahrt 1987). Sensible and latent heat fluxes are determined through a coupling between radiation and photosynthesis models to obtain a surface resistance and the solution of the energy balance using Monteith’s (1973) resistance method. In the soil, Noah predicts vertical profiles of temperature and moisture using a one-dimensional model with specified lower-boundary conditions [see Ek et al. (2003) for further details]. Noah was previously coupled with NCAR’s LES code to investigate the effects of a horizontally varying soil moisture content on the mean and turbulence structure of the ABL (Patton et al. 2005); therefore, the interface between the two codes is already well established.

### b. The multilayer canopy

In the current implementation, Noah’s big-leaf model has been extended so that the canopy now spans multiple vertical levels. Noah remains a 1D column model implemented at every horizontal location, but the canopy extends vertically into the flow domain according to the prescribed PAD described in section 2. Leaf energy balances are now solved at each vertical level, resolving the canopy based upon the vertical distribution of radiant energy and LES-derived local atmospheric temperature, moisture and wind. The new vertically resolved canopy model arises through merging a number of previously developed models into Noah’s simpler canopy system.

New to Noah is a canopy radiation model that stems from Guenther et al.’s (1995, 2006) Model of Emissions of Gases and Aerosols from Nature (MEGAN). Incoming solar radiation is imposed as an external forcing. Sunlit leaves experience incoming direct longwave radiation according to local air temperature modified on the sunlit side to account for Brutsaert’s (1975) apparent clear-sky emissivity, while direct incoming longwave radiation for shaded leaves is calculated based solely upon local air temperature. MEGAN uses specified leaf scattering, reflection, and clumping coefficients for visible and near-infrared (NIR) wavelength radiation (Table 2). Using these coefficients in combination with an assumed spherical leaf angle distribution, the vertically varying absorption and scattering of direct/diffuse visible and NIR radiation by both sunlit and shaded leaves (Goudriaan and van Laar 1994; Leuning et al. 1995; Leuning 1997) is determined.

Stomatal resistance *a*. Currently, the atmospheric CO_{2} partial pressure is assumed constant at 34 Pa.

^{−1}factor in Eq. (12) follows from Leuning et al. (1995); the latter factor arises because of a different effective boundary layer thickness for mass versus heat under forced convection (Monteith and Unsworth 2008). The variables

## 4. Simulation design

### a. The atmosphere

The simulations use (2048, 2048, 1024) grid points in a Cartesian coordinate system resolving a (5120, 5120, 2048)-m domain using (2.5, 2.5, 2)-m resolution in the (*x*, *y*, *z*) directions, respectively. The horizontal domain size is chosen to span a distance approximately 5 times the anticipated ABL depth (

The simulation’s location is 38°N, 121°W, representative of Dixon, California [the location of the CHATS field campaign (Patton et al. 2011)]. The simulations begin at 1100 LT, with an imposed solar constant of 1367 W m^{−2} and an atmospheric transmissivity according to Stull (1988), where the transmissivity without clouds varies between 0.6 when the sun is at the horizon and 0.8 when the sun is at the solar zenith. Therefore, the incoming solar radiation impinging at the top of the trees starts at about 940 W m^{−2} at 1100 LT and evolves to approximately 1015 W m^{−2} throughout the simulation.

The primary parameter variation across the simulations involves the imposed geostrophic wind (^{−1}, resulting in atmospheric stability variations ranging from near-neutral to free-convective conditions (i.e.,

Parameters characterizing the simulated atmosphere for each simulation. (*U*_{g}, *V*_{g}) represents the imposed geostrophic wind in the (*x*, *y*) directions; *B*, *L*,

The initial conditions impose the following: 1) a constant mean horizontal wind (*u*, *υ*) everywhere in the domain equal to (*θ* profile of 300 K from the surface to a height of 40 m (twice the canopy height) and then linearly increasing with height at a constant rate of 3 K km^{−1} above that height; 3) a constant water vapor specific humidity *q* profile of 1 g kg^{−1}; and 4) a constant SFS energy *e* profile of 1 × 10^{−8} m^{2} s^{−2}. Divergence-free perturbations placed on the horizontal velocity fields across the five vertical grid points centered at canopy top with an amplitude of 0.001 m s^{−1} and an increased SFS energy to 1 m^{2} s^{−2} over the same vertical extent initiate the turbulence.

### b. The canopy-resolving land surface model

The vegetation is horizontally homogeneous, 20 m tall (*h* = 20 m), and vertically resolved by 10 grid points with a PAD profile *a* representative of a deciduous canopy with a relatively dense overstory and a relatively open trunk space (Fig. 2); vertical integration of the plant area density profile yields a one-sided plant area index (PAI) of 2. Following MEGAN (Guenther et al. 1995, 2006), the plant functional type (PFT) imposes characteristics similar to a generic broadleaf deciduous forest; the specifics for this PFT can be found in Table 2. The leaf area fraction considered sunlit or shaded is prescribed at each level according to an exponential function of cumulative leaf area downward from canopy top modulated by the PFT’s clustering coefficient (Fig. 2 and Table 2).

Vertical profiles relative to the height of the canopy *h* of horizontally homogeneous one-sided plant area density (m^{2} m^{−3}; solid) normalized by the canopy height (lower axis), the fraction of the one-sided plant area density that is sunlit (upper axis; dashed–dotted), and the fraction of the one-sided plant area density that is shaded (upper axis; long dashed).

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Vertical profiles relative to the height of the canopy *h* of horizontally homogeneous one-sided plant area density (m^{2} m^{−3}; solid) normalized by the canopy height (lower axis), the fraction of the one-sided plant area density that is sunlit (upper axis; dashed–dotted), and the fraction of the one-sided plant area density that is shaded (upper axis; long dashed).

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Vertical profiles relative to the height of the canopy *h* of horizontally homogeneous one-sided plant area density (m^{2} m^{−3}; solid) normalized by the canopy height (lower axis), the fraction of the one-sided plant area density that is sunlit (upper axis; dashed–dotted), and the fraction of the one-sided plant area density that is shaded (upper axis; long dashed).

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Parameters specified for the broadleaf deciduous canopy [from MEGAN (Guenther et al. 2006)]. Radiation is given as photosynthetically active radiation (PAR) and near-infrared (NIR).

The soil is resolved using four vertical levels centered at depths of (0.05, 0.20, 0.45, 0.80) m, with a specified lower temperature boundary condition of 295 K at 1 m. The soil characteristics mimic silty-clay loam, with hydraulic and thermal properties taken directly from Noah (Table 3; Chen et al. 1996; Chen and Dudhia 2001; Ek et al. 2003). The soil’s surface roughness

Parameters characterizing the silty-clay-loam soil, Noah’s soil class number 8.

The initial volumetric soil moisture content and soil temperature profiles.

### c. Computational aspects

The simulations required between 100 and 225 wall-clock hours running on 16 384 computer cores, totaling between 1.5 and 3.7 × 10^{−6} CPU hours per simulation. As described in Sullivan and Patton (2011), to accommodate pseudospectral differencing, the NCAR LES code uses the Message Passing Interface (MPI) to partition the computational domain into horizontal “bricks” or “pencils.” Because the vegetative canopy resides at the lowermost portion of the domain, the bricks are transposed vertically, allowing every processor to participate in solving the required energy balances determining the next time step’s scalar source distribution throughout the canopy and the underlying surface fluxes at each horizontal grid point. To allow checkpointing during the simulation, the code uses MPI input/output to read/write data volumes; a single instant in time for these simulations requires approximately 245 GB of storage.

## 5. Averaging and scaling

During the simulations, turbulent fluctuations are calculated at every time step as deviations from instantaneous horizontally averaged fields. Higher-order moments are then created by horizontally averaging fluctuation products. Using these time-varying horizontally averaged profiles, the boundary layer–averaged turbulent kinetic energy (TKE) is interrogated to determine whether the flow has reached quasi equilibrium with the forcing; that is, the TKE averaged over the depth of the ABL has become steady in time. Time averaging then commences, and profiles are averaged over the subsequent 3600 s (1 h) of simulated time. In what follows, angle brackets denote this time- and horizontal-averaging process, and a prime represents the fluctuations. For clarity, the overbar notation introduced in section 2 denoting the explicit filtering process will be dropped, and all turbulent moments presented will include the sum of resolved and subfilter-scale contributions.

*h*. Since the flows in each simulation respond to the varying combinations of shear and buoyancy forcing, we use a velocity scale

*A*parameter is 1.

## 6. Results and discussion

### a. Velocity

#### 1) Horizontal slices

Horizontal slices of instantaneous streamwise and vertical velocity at *z*/*h* = 6 from four simulations (Figs. 3 and 4, respectively) reveal the variation of the ABL-scale motions with atmospheric stability. In shear-dominated weakly unstable conditions (WU; Figs. 3a, 4a), velocity fields tend to organize themselves into elongated roll-like structures aligned with the geostrophic wind, while in free convection (FC; Figs. 3d, 4d), the velocity fields organize in cellular patterns. Intermediate stabilities (Figs. 3b,c, 4b,c) reveal a progression between these two end-member states.

Horizontal slices of instantaneous streamwise velocity fluctuations relative to the horizontal mean normalized by

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Horizontal slices of instantaneous streamwise velocity fluctuations relative to the horizontal mean normalized by

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Horizontal slices of instantaneous streamwise velocity fluctuations relative to the horizontal mean normalized by

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Horizontal slices of instantaneous vertical velocity normalized by

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Horizontal slices of instantaneous vertical velocity normalized by

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Horizontal slices of instantaneous vertical velocity normalized by

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

This evolution of ABL-scale motions with stability has been well established over the years (e.g., Deardorff 1972; Moeng and Sullivan 1994; Khanna and Brasseur 1998). Using linear-stability analysis, H. Jonker et al. (2015, unpublished manuscript) shows that this variation results from a competing balance between shear- and buoyancy-generated instabilities leading to preferential growth of particular longitudinal or transverse modes.

Features to note in Figs. 3 and 4 include the following: first, the structures to scale approximately with the ABL depth

The elongated roll structures in WU [and near neutral (NN); not shown] and the transition to cellular structure [in moderately unstable (MU) → FC] remain observable in the canopy-top streamwise velocity fields (Fig. 5), reminiscent of the results of Hutchins and Marusic (2007) who found the signature of very large structures in their observations collected within a neutrally stratified log layer. Across all stabilities, the ABL-scale organized motions generate broad regions of negative vertical velocity, bringing high-streamwise-momentum fluid to canopy top with a visible smaller-scale structure embedded within. The signature of ABL-scale motions is less evident in instantaneous canopy-top vertical velocity (Fig. 6), as vertical motions are strongly impacted by proximity to the canopy and to the underlying soil surface. Compared to the vertical velocity’s cellular-like structure that was evident at *z*/*h* = 6, the smaller scales contained within the canopy-top vertical velocity fields appear more filament-like with increasing instability (NN → FC).

Horizontal slices of instantaneous streamwise velocity fluctuations relative to the horizontal mean normalized by

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Horizontal slices of instantaneous streamwise velocity fluctuations relative to the horizontal mean normalized by

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Horizontal slices of instantaneous streamwise velocity fluctuations relative to the horizontal mean normalized by

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Horizontal slices of instantaneous vertical velocity normalized by

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Horizontal slices of instantaneous vertical velocity normalized by

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Horizontal slices of instantaneous vertical velocity normalized by

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Based on observed streamwise velocity profiles averaged over short times (10 s), Gao et al. (1992) found that canopy-scale organized motions were preceded by profiles exhibiting strong streamwise velocity shear at canopy top; Shaw et al. (1990) suggested that favorable pressure gradients were likely responsible. The simulations discussed here demonstrate that the spatial distribution, magnitude, and duration of canopy-top streamwise velocity are strongly controlled by organized ABL-scale motions that modulate the local vertical shear.

#### 2) Statistics

The NCAR LES code’s ability to reproduce statistics of ABL flows across a range of stability conditions has been previously documented in the literature and compared against observations (e.g., Moeng and Sullivan 1994; Beare et al. 2006; Sullivan and Patton 2011; Lenschow et al. 2012). With the exception of Dwyer et al. (1997) and Patton et al. (2003), most studies of canopy flows using NCAR’s LES code have focused on neutral stability conditions (Patton 1997; Su et al. 2000; Shaw and Patton 2003; Finnigan et al. 2009). Dwyer et al. (1997) presented a study of buoyancy influences on turbulent kinetic energy budgets, but the simulations were carried out in small domains that were unable to capture the large scales of motion described in the previous section. Patton et al. (2003) overcame the limited-domain issue using nested grids to investigate the influence of a canopy on ABL flow and scalar statistics; statistics investigated in that study compared well with measurements but focused on a single atmospheric stability with an imposed canopy-source distribution. For these numerous reasons, the following discussion therefore refrains from presenting atmospheric stability impacts on the overall ABL flow statistics and instead focuses on stability’s impact on statistics of canopy turbulence.

Vertical profiles from the ground up to ^{−1}. Horizontal wind speeds *w*_{m} for cases [NN, WU, MU, strongly unstable (SU), FC], respectively. Coincident with this wind speed reduction at canopy top, the mean wind speed’s vertical gradient at canopy top varies from

Horizontal- and time-averaged vertical profiles of (a) normalized horizontal wind speed

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Horizontal- and time-averaged vertical profiles of (a) normalized horizontal wind speed

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Horizontal- and time-averaged vertical profiles of (a) normalized horizontal wind speed

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Normalized standard deviations of velocity (Figs. 7b–d) decrease in a natural progression in response to increasing instability; (

For near-neutral conditions (WU, NN),

For comparison with the velocity standard deviations, it is useful to define a height-dependent measure of the vertical turbulent flux of horizontal momentum with the dimensions of velocity [e.g.,

Numerous investigations (e.g., Shaw et al. 1988; Brunet et al. 1994; Su et al. 1998) have shown that under near-neutral conditions, turbulence within the canopy is notably more efficient at transporting momentum

As discussed by Leclerc et al. (1991), atmospheric stability has a marked influence on velocity skewness (Figs. 7g,h). Consistent with observations (e.g., Dupont and Patton 2012a), horizontal velocity skewness

These skewness results suggest a switch in turbulent transport mechanisms within the canopy as instability increases. In NN and WU, infrequent downward sweeps of high momentum associated with shear-induced “mixing layer” eddies (i.e.,

The peak values of

#### 3) Spectra

In the surface layer above the canopy, one expects kinetic energy spectra to generally follow the Kaimal et al. (1972) spectrum. Su et al. (2004) used long-term data from a tower to modify Kaimal et al.’s (1972) formulations for a wider range of stability conditions above a forest canopy. These two studies (among numerous others) collectively show that spectral peaks shift toward lower frequencies (or wavenumbers) as the atmosphere evolves from neutral toward unstable stability.

Following Sullivan and Patton (2011), Fig. 8 presents one-dimensional power spectra of horizontal and vertical velocity at four heights for two stability conditions (NN and FC). These spectra are calculated by generating two-dimensional power spectra at a given height and averaging in circular rings at constant

Two-dimensional normalized energy spectra of (left) horizontal velocity *u* and (right) vertical velocity *w* for two stability regimes: (top) NN and (bottom) FC. The spectra are functions of the magnitude of the horizontal wavenumber vector *y*-axis ranges differ between the *u* and *w* figures but are the same between the two different stabilities.

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Two-dimensional normalized energy spectra of (left) horizontal velocity *u* and (right) vertical velocity *w* for two stability regimes: (top) NN and (bottom) FC. The spectra are functions of the magnitude of the horizontal wavenumber vector *y*-axis ranges differ between the *u* and *w* figures but are the same between the two different stabilities.

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Two-dimensional normalized energy spectra of (left) horizontal velocity *u* and (right) vertical velocity *w* for two stability regimes: (top) NN and (bottom) FC. The spectra are functions of the magnitude of the horizontal wavenumber vector *y*-axis ranges differ between the *u* and *w* figures but are the same between the two different stabilities.

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Well above the canopy (*E*_{u} above the canopy.

Compared to spectra near the top of the surface layer and above *z*/*h* = 2 → 1); horizontal velocity spectra maintain significant contributions at low wavenumbers, but the spectral peak for vertical velocity shifts to higher wavenumbers. At these heights, increased energy content at canopy-scale wavenumbers

Under FC conditions, amplification of horizontal velocity variance at low wavenumbers by wall blocking continues all the way down to *z*/*h* = 1 and 0.5), there is very little canopy-induced modification except for the rapid reduction across all scales at

### b. Scalars

A unique feature of the simulations discussed here involves the coupling between the turbulence and the within-canopy scalar sources. By incorporating a fully interactive and resolved canopy within simulations permitting full ABL-scale motions, we can investigate the coupling between atmospheric stability variations and canopy scalar exchange.

#### 1) Scalar source/sinks

##### (i) Instantaneous fields

Horizontal slices of instantaneous sunlit leaf temperature fluctuations

Instantaneous horizontal slices at *h*. Each panel is presented in a coordinate system relative to *h*; the small axis at the bottom right of each panel depicts the ABL depth

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Instantaneous horizontal slices at *h*. Each panel is presented in a coordinate system relative to *h*; the small axis at the bottom right of each panel depicts the ABL depth

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Instantaneous horizontal slices at *h*. Each panel is presented in a coordinate system relative to *h*; the small axis at the bottom right of each panel depicts the ABL depth

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

This spatial variability in *θ* and *q* (e.g., Lamaud and Irvine 2006) and occurs at ABL scales [i.e., notably larger scales than those discussed by Huang et al. (2013)].

Modulation of the heat and water vapor source strengths (

In addition, since some canopies emit reactive gases (e.g., isoprene) according to a combination of a leaf’s absorbed radiation and temperature (e.g., Guenther et al. 1993), ABL-scale modulation of leaf temperature

##### (ii) Mean source/sink profiles and their standard deviation

The temporally and spatially varying scalar source distributions (Fig. 9) permit investigation into the influence of atmospheric stability on canopy scalar source statistics. For all stabilities, ^{−1}, and ^{−1} at

(top) Horizontal- and time-averaged vertical profiles of normalized (a) potential temperature source per grid volume *h*. The thin black line marks canopy top

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

(top) Horizontal- and time-averaged vertical profiles of normalized (a) potential temperature source per grid volume *h*. The thin black line marks canopy top

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

(top) Horizontal- and time-averaged vertical profiles of normalized (a) potential temperature source per grid volume *h*. The thin black line marks canopy top

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Vertical profiles of scalar source standard deviations (Figs. 10b,f) peak at similar heights to those of their respective mean. For these simulations,

##### (iii) Production/loss of scalar variance and flux

*c*, these correlations appear on the right-hand side of the equations as

For the current simulations, potential temperature fluctuations in the canopy air space are generally negatively correlated with leaf-level potential temperature sources (Fig. 10c), while water vapor fluctuations are positively correlated with leaf-level water vapor sources (Fig. 10g). According to Eq. (11), regions of high potential temperature coincide with low

In a broad sense,

Examining the percent contributions of the correlation terms in Eqs. (16) and (17) relative to the total variance or flux production quantifies the importance of these terms; Table 5 presents these ratios evaluated at *θ* (*q*), with a general trend that the contribution from *q* compared to *θ*. The percentage contribution of these terms varies with height and becomes increasingly more important in regions where scalar variance and/or flux production are small (e.g., in the subcanopy’s relatively open trunk space; not shown).

#### 2) Scalar statistics

Vertical profiles of normalized

(top) Horizontal- and time-averaged vertical profiles of (a) the normalized potential temperature

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

(top) Horizontal- and time-averaged vertical profiles of (a) the normalized potential temperature

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

(top) Horizontal- and time-averaged vertical profiles of (a) the normalized potential temperature

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Above the canopy

Even though vertical scalar gradients vary little at canopy top with transition from NN to FC (Figs. 11a,e), scalar standard deviations (*q* skewness in the upper ABL. On the other hand, potential temperature

The influence that these ABL-scale motions have on canopy-top scalar moments can be seen in Fig. 11. Above-canopy scalar skewness profiles are positive and generally increase with increasing instability (Figs. 11c,g); however, above-canopy

### c. Spatial integral length scales

To calculate integral length scales from single-point tower measurements, Taylor’s hypothesis is required to convert integral time scales to length scales (e.g., Baldocchi and Meyers 1988). However, Taylor’s hypothesis requires *χ* is calculated as the time average of the horizontal separation at which the instantaneous autocorrelation function falls to

Under NN conditions, streamwise integral length scales for streamwise velocity *h* (Fig. 12a), which is directly comparable to that found by Shaw et al. (1995) in the wind tunnel. Within the canopy, *h* near the underlying surface. At *h*, which also matches the results of Shaw et al. (1995). Above the canopy, *h* at *h* in FC. Compared to NN, *h* near the surface in FC. With the transition from ABL-scale rolls to cells when transitioning from NN to FC conditions (Figs. 3–6), above-canopy

Streamwise integral length scales of (a) streamwise velocity *h*.

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Streamwise integral length scales of (a) streamwise velocity *h*.

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Streamwise integral length scales of (a) streamwise velocity *h*.

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

In NN conditions, streamwise integral length scales for vertical velocity *h* (i.e., canopy scale) from the surface up to approximately

Scalar streamwise integral length scales diminish at all levels with increasing instability (Fig. 12c,d). In general, both *q* peaking at much larger scales than *θ*.

### d. Momentum and scalar flux correlation

Katul et al. (1997) noticed that the ejection/sweep cycles for momentum and scalars are closely coupled but not identical. Using single-point measurements above a vineyard and a lake, Li and Bou-Zeid (2011) showed that the correlation between momentum and scalar (temperature and water vapor) fluxes decreases with transition from neutral to unstable conditions, and they put forward a hypothesis that this results from an evolution from hairpin structures to thermal plumes occurring across the evolution of atmospheric stability. Using vertical profiles from the CHATS field campaign [within and above a walnut orchard (Patton et al. 2011)], Dupont and Patton (2012b) also found the correlation between momentum and scalar fluxes to decrease with increasing instability but noted that the correlations were 1) nearly independent of height above the canopy, but within the canopy they decreased toward zero near the ground; and 2) largest when the trees were in full leaf because of collocation of the primary momentum sink and scalar sources in the canopy. Important in both of those investigations (Li and Bou-Zeid 2011; Dupont and Patton 2012b) is that they hinged on time-averaged statistics.

*ϕ*is either the atmospheric potential temperature

*θ*or specific humidity

*q*, and

Vertical profiles of the correlation coefficient between (a) the vertical flux of streamwise momentum and vertical potential temperature flux

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Vertical profiles of the correlation coefficient between (a) the vertical flux of streamwise momentum and vertical potential temperature flux

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Vertical profiles of the correlation coefficient between (a) the vertical flux of streamwise momentum and vertical potential temperature flux

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Under NN conditions, momentum and scalar fluxes are generally negatively correlated above the canopy (Figs. 13a,b): that is, upward motions typically carry low horizontal momentum and high scalar fluxes, with the opposite for downward motions. Consistent with Li and Bou-Zeid (2011) and Dupont and Patton (2012b), the magnitude of

It is extremely difficult to ascertain the linkage between ABL-scale motions and canopy-top exchange and their control over these correlations using single-point-based (Li and Bou-Zeid 2011) or single-tower-based measurements (Dupont and Patton 2012b). To this end, Fig. 14 presents instantaneous horizontal slices of vertical velocity at ^{2} subset of the domain for cases WU and FC. Overlaid on the grayscale image are quadrant analyses (e.g.,Wallace et al. 1972; Willmarth and Lu 1972) of momentum and potential temperature flux at canopy top (*χ*,

Instantaneous horizontal slices of low-pass-filtered vertical velocity at *z*/*h* = 1) and broken down by quadrants are overlaid in color. Using notation such that for any variable *χ*, ^{2} s^{−2} and ^{−1} are shown. In (b), only regions with ^{2} s^{−2} and ^{−1} are shown.

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Instantaneous horizontal slices of low-pass-filtered vertical velocity at *z*/*h* = 1) and broken down by quadrants are overlaid in color. Using notation such that for any variable *χ*, ^{2} s^{−2} and ^{−1} are shown. In (b), only regions with ^{2} s^{−2} and ^{−1} are shown.

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Instantaneous horizontal slices of low-pass-filtered vertical velocity at *z*/*h* = 1) and broken down by quadrants are overlaid in color. Using notation such that for any variable *χ*, ^{2} s^{−2} and ^{−1} are shown. In (b), only regions with ^{2} s^{−2} and ^{−1} are shown.

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Looking at Fig. 14, one can immediately notice that the ABL-scale structures organize exchange at canopy top. In Fig. 14a, canopy-top regions of ^{2} s^{−2} (ejections; green) predominantly coincide with canopy-top regions of ^{−1} (red), and locations where they coincide largely occur at the edges of the ABL-scale updrafts at

Figure 14b shows that canopy-top momentum and scalar exchange occurs quite differently when there is no mean shear. ABL-scale updrafts (downdrafts) create regions of convergence (divergence) beneath them at canopy top. These regions of convergence and divergence generate near-surface horizontal winds acting as the near-surface component of a closed ABL-scale circulation, thereby spatially separating regions of *x* direction (green) and *x* direction (blue). For scalars, warm air is largely transported upward (

## 7. Conclusions

Aspects of atmospheric stability’s influence on ABL-scale structure and its impact on canopy exchange have been investigated by analyzing results from five large-eddy simulations of ABLs interacting with a resolved and interactive broadleaf forest canopy. To perform these simulations, a multilevel canopy version of Noah was developed; its basis and implementation are briefly described. The multilevel canopy model allows for the coupled interaction between the turbulent atmosphere and the scalar source distribution (and vice versa)—an essential feature, especially when studying the range of atmospheric stabilities under investigation here.

Key findings arising from analyzing the simulation data include the following:

ABL-scale structure maintains and imposes its signature at canopy top (especially for streamwise velocity

*u*), creating regions where high-momentum fluid is brought down to canopy top (or low-momentum fluid is ejected from the canopy) at scales tied to the ABL depth, which modifies the horizontal distribution of vertical shear of the horizontal wind at canopy top and places controls on canopy exchange of momentum and scalars.Increasing instability reduces mean canopy-top vertical shear of the horizontal wind. As a result, velocity variance, momentum stress, and transport efficiency systematically diminish with increasing instability and importance of buoyant plumes. With transition to free convection, canopy-top velocity skewness values reduce in magnitude but maintain the same sign as found under near-neutral conditions; velocity skewness profiles also transition toward their surface-layer values at lower elevations above the canopy and change sign in the lower canopy as buoyant plumes emanating from the surface become increasingly important.

Because of the relatively rapid response time of the leaves, organized ABL-scale structures interact with the plant physiology to generate spatially varying leaf temperatures and scalar sources. Potential temperature sources peak above the level of maximum canopy density, while water vapor specific humidity sources peak just below. Standard deviations of the potential temperature source are as large as about 10% of the source strength, while those for water vapor are only about 1%. Spatially varying sources generate additional terms in the equations for resolved-scale scalar variance and flux. For variances,

acts to reduce within-canopy potential temperature fluctuations, while acts to produce water vapor mixing ratio fluctuations; the same is true for and for scalar fluxes. The sign and magnitude of these terms contributing to scalar variance and flux are most certainly dependent on soil moisture availability. Increasing instability from near neutral to free convection decreases vertical scalar gradients above the canopy and increases scalar variances and scalar skewness. ABL-scale downwelling motions bring dry air to increasingly lower altitudes with increasing instability impacting above-canopy scalar statistics. Increasing instability also reduces within-canopy scalar skewness as the importance of shear-driven canopy-scale motions diminishes.

Momentum and scalar length scales in the vicinity of the canopy reflect the influence of atmospheric stability and the organized ABL-scale motions. At canopy top,

increases from about 2 *h*for near neutral conditions to about 8.5*h*for free-convective conditions; but, well above the canopy, increases much more rapidly in near-neutral conditions than it does under free-convective conditions as ABL-scale motions transition from cells to rolls. Below *z*/*h*= 3,is nearly constant with height at a value of about 1 *h*under near-neutral conditions but rapidly increases above the canopy with a transition to free convection, suggesting the continual coalescence of finescale plumes into larger and larger updrafts. Near canopy top, scalar length scales are notably larger thanand shrink with increasing instability. The evolution of ABL-scale structures with atmospheric stability (i.e., the transition from rolls to cells as stability varies from near neutral to free convection) spatially separates momentum and scalar fluxes, which explains their decreasing correlation with increasing instability.

In combination, our analysis confirms the hypothesis that the evolution of ABL-scale organized turbulent motions across stability variations from near neutral to free convection significantly alters turbulent exchange at the canopy–atmosphere interface. In particular, the evolution of spatial integral length scales and the evolution of spatial separation of momentum and scalar exchange with buoyancy suggest that, in order to transition from near-neutral to free-convective conditions, currently available parameterizations of roughness sublayer turbulence hinging on the shear-induced hydrodynamic instability at canopy top need to incorporate an additional length and/or time scales associated with the ABL-scale organized motions.

The coupled canopy–atmosphere system also shows that the evolution of ABL-scale organized turbulent motions across variations in stability can link with the underlying biologically controlled scalar source/sinks to segregate heat and moisture sources contributing to dissimilarity in their vertical transport—a result that implies that tower-based observations need to be averages over time scales associated with ABL-scale motions (as opposed to canopy-scale motions) when designing measurement strategies to evaluate energy or carbon budgets.

## Acknowledgments

We would like to acknowledge Alex Guenther, Fei Chen, Anil Kumar, Peter Harley, Ian Harman, Ray Leuning, Bill Massman, Laurent Perret, and Rich Rotunno, who provided some of the initial code base used to create this multilayer canopy system, contributed the HRLDAS-derived initial soil conditions, and/or offered suggestions along the way. We also thank Arnold Moene and two anonymous reviewers for substantial suggestions/commentary, from which the manuscript benefited greatly.

Support for this project came largely from the Army Research Office (Grant W911NF-09-1-0572) courtesy of Dr. Walter Bach, from the Bio–Hydro–Atmosphere Interactions of Energy, Aerosols, Carbon, H_{2}O, Organics and Nitrogen (BEACHON) program at NCAR, and through the Center for Multiscale Modeling of Atmospheric Processes (CMMAP) at Colorado State University, NSF Grant ATM-0425247 and Contract G-3045-9 to NCAR. Numerous collaboration visits sponsored by NCAR and CSIRO were an essential aspect of this effort. Additionally, this research would not have been possible without the high-performance computing support from: 1) Yellowstone (ark:/85065/d7wd3xhc) provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation, and 2) the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract DE-AC02-05CH11231.

## APPENDIX

### Multilayer Canopy Model: Test against Observations

The new multilevel canopy model is not intended to represent all leaf-level processes and their atmospheric coupling. Rather, it is intended to provide sufficient realism to investigate the importance of leaf-level processes on turbulence–canopy coupling.

The new multilevel canopy model is tested against field observations from the 30-m tower at CHATS (Patton et al. 2011). The CHATS tower included seven levels of winds, temperature, and specific humidity characterizing the within-canopy structure of mean and turbulent quantities within and above a deciduous Chandler walnut orchard (Dupont and Patton 2012a,b). The CHATS tower also included observations of above-canopy four-component radiation, soil temperature and moisture profiles, and soil heat flux. The CHATS campaign took place over a 3-month period, where the final month sampled the canopy layers while the deciduous walnut canopy was in full leaf. See Patton et al. (2011) for more complete details regarding CHATS.

*θ*is potential temperature,

*w*is vertical velocity,

*z*is height,

*t*is time, and

A test of the multilayer canopy model. Here, the multilayer canopy model is driven by within-canopy vertical profiles of 5-min-averaged observations taken during the final month of the CHATS field campaign (Patton et al. 2011). Presented is a comparison of measured vs modeled portions of a horizontally averaged thermodynamic heat budget vertically integrated over the canopy depth [Eq. (A1)]; if the measurements and the model were perfect, all points would lie on the 1:1 line (long dashed).

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

A test of the multilayer canopy model. Here, the multilayer canopy model is driven by within-canopy vertical profiles of 5-min-averaged observations taken during the final month of the CHATS field campaign (Patton et al. 2011). Presented is a comparison of measured vs modeled portions of a horizontally averaged thermodynamic heat budget vertically integrated over the canopy depth [Eq. (A1)]; if the measurements and the model were perfect, all points would lie on the 1:1 line (long dashed).

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

A test of the multilayer canopy model. Here, the multilayer canopy model is driven by within-canopy vertical profiles of 5-min-averaged observations taken during the final month of the CHATS field campaign (Patton et al. 2011). Presented is a comparison of measured vs modeled portions of a horizontally averaged thermodynamic heat budget vertically integrated over the canopy depth [Eq. (A1)]; if the measurements and the model were perfect, all points would lie on the 1:1 line (long dashed).

Citation: Journal of the Atmospheric Sciences 73, 4; 10.1175/JAS-D-15-0068.1

Figure A1 shows that the multilevel canopy model provides sufficient realism to investigate the importance of leaf-level processes on turbulence–canopy coupling; this is especially the case since the parameters describing the canopy properties came directly from MEGAN [see Table 2 (Guenther et al. 2006)], are representative of a generic broadleaf forest, and have not been tuned for the CHATS walnut canopy.

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