The Effect of Vegetation Density on Canopy Sub-Layer Turbulence

The canonical form of atmospheric flows near theland surface, in the absence of a canopy, resembles a rough-wallboundary layer. However, in the presence of an extensive and densecanopy, the flow within and just above the foliage behaves as aperturbed mixing layer. To date, no analogous formulation existsfor intermediate canopy densities. Using detailed laser Dopplervelocity measurements conducted in an open channel over a widerange of canopy densities, a phenomenological model that describesthe structure of turbulence within the canopy sublayer (CSL) isdeveloped. The model decomposes the space within the CSL intothree distinct zones: the deep zone in which the flow field isshown to be dominated by vortices connected with vonKármán vortex streets, butperiodically interrupted by strong sweep events whose features areinfluenced by canopy density. The second zone, which is near thecanopy top, is a superposition of attached eddies andKelvin–Helmholtz waves produced by inflectional instability in themean longitudinal velocity profile. Here, the relative importanceof the mixing layer and attached eddies are shown to vary withcanopy density through a coefficient . We show that therelative enhancement of turbulent diffusivity over its surface-layer value near the canopy top depends on the magnitude of. In the uppermost zone, the flow follows the classicalsurface-layer similarity theory. Finally, we demonstrate that thecombination of this newly proposed length scale and first-orderclosure models can accurately reproduce measured mean velocity andReynolds stresses for a wide range of roughness densities. Withrecent advancement in remote sensing of canopy morphology, thismodel offers a promising physically based approach to connect theland surface and the atmosphere without resorting to empiricalmomentum roughness lengths.     

Improving a Two-Equation Turbulence Model for Canopy Flows Using Large-Eddy Simulation

Large-eddy simulations of the neutrally-stratified flow over an extended homogeneous forest were used to calibrate a canopy model for the Reynolds-averaged Navier–Stokes (RaNS) method with the $k-\varepsilon $ k - ε turbulence model. It was found that, when modelling the forest as a porous medium, the canopy drag dissipates the turbulent kinetic energy (acts as a sink term). The proposed model was then tested in more complex flows: a finite length forest and a forested hill. In the finite length forest, the destruction of the turbulent kinetic energy by the canopy was overestimated near the edge, for a length approximately twice the tree height. In the forested hill, the model was less accurate inside the recirculation zone and overestimated the turbulent kinetic energy, due to an incorrect prediction of the production term. Nevertheless, the canopy model presented here provided consistent results in both a priori and a posteriori tests and improved the accuracy of RaNS simulations with the $k-\varepsilon $ k - ε model.     

Organized structures in developing turbulent flow within and above a plant canopy,using a Large Eddy Simulation

A Large Eddy Simulation (LES) model representing the air flow within and above a plant canopy layer has been completed. Using this model, the organized structures of turbulent flow in the early developmental stages of a crop are simulated and discussed in detail.The effect of the drag due to vegetation is expressed by a term added to the three-dimensional Navier-Stokes equation averaged over the grid scale. For the formulation of sub-grid turbulence processes, the equations for the time-dependent SGS (Sub-Grid-Scale) turbulence energy equation is used, which includes the effects of dissipation (both by viscosity and leaf drag), shear production and diffusion.The organized structure of turbulent flow at the air-plant interface, obtained numerically by the model, yields its contribution to momentum transfer. The three-dimensional large eddy structures, which are composed of spanwise vortices (rolls) and streamwise vortices (ribs), are simulated near the air-plant interface. They are induced by the shear instability at inflection points of the velocity profile. The structure clearly has a life cycle. The instantaneous image of the structure is similar to those observed in the field observations of Gaoet al. (1989) and in the laboratory flume experiments of Ikeda and Ota (1992). These organized structures also account for the well known fact that the sweep motion of turbulence dominates momentum transport within and just above a plant canopy, and the motion of ejection prevails in the higher regions.     

Verification of a One-Dimensional Model of $$\hbox {CO}_{2}$$ Atmospheric Transport Inside and Above a Forest Canopy Using Observations at the Norunda Research Station

A model of \(\hbox {CO}_{2}\) atmospheric transport in vegetated canopies is tested against measurements of the flow, as well as \(\hbox {CO}_{2}\) concentrations at the Norunda research station located inside a mixed pine–spruce forest. We present the results of simulations of wind-speed profiles and \(\hbox {CO}_{2}\) concentrations inside and above the forest canopy with a one-dimensional model of profiles of the turbulent diffusion coefficient above the canopy accounting for the influence of the roughness sub-layer on turbulent mixing according to Harman and Finnigan (Boundary-Layer Meteorol 129:323–351, 2008; hereafter HF08). Different modelling approaches are used to define the turbulent exchange coefficients for momentum and concentration inside the canopy: (1) the modified HF08 theory—numerical solution of the momentum and concentration equations with a non-constant distribution of leaf area per unit volume; (2) empirical parametrization of the turbulent diffusion coefficient using empirical data concerning the vertical profiles of the Lagrangian time scale and root-mean-square deviation of the vertical velocity component. For neutral, daytime conditions, the second-order turbulence model is also used. The flexibility of the empirical model enables the best fit of the simulated \(\hbox {CO}_{2}\) concentrations inside the canopy to the observations, with the results of simulations for daytime conditions inside the canopy layer only successful provided the respiration fluxes are properly considered. The application of the developed model for radiocarbon atmospheric transport released in the form of \(^{14}\hbox {CO}_{2}\) is presented and discussed.     

Reynolds-Number Dependence of Gas Dispersion Over a Wavy Wall

Direct numerical simulations of an Ekman layer are performed to study flow evolution during the response of an initially neutral boundary layer to stable stratification. The Obukhov length, L, is varied among cases by imposing a range of stable buoyancy fluxes at the surface to mimic ground cooling. The imposition of constant surface buoyancy flux , i.e. constant-flux stability, leads to a buoyancy difference between the ground and background that tends to increase with time, unlike the constant-temperature stability case where a constant surface temperature is imposed. The initial collapse of turbulence in the surface layer owing to surface cooling that occurs over a time scale proportional to \(L/u_*\), where \(u_*\) is the friction velocity, is followed by turbulence recovery. The flow accelerates, and a “low-level jet” (LLJ) with inertial oscillations forms during the turbulence collapse. Turbulence statistics and budgets are examined to understand the recovery of turbulence. Vertical turbulence exchange, primarily by pressure transport, is found to initiate fluctuations in the surface layer and there is rebirth of turbulence through enhanced turbulence production as the LLJ shear increases. The turbulence recovery is not monotonic and exhibits temporal intermittency with several collapse/rebirth episodes. The boundary layer adjusts to an increase in the surface buoyancy flux by increased super-geostrophic velocity and surface stress such that the Obukhov length becomes similar among the cases and sufficiently large to allow fluctuations with sustained momentum and heat fluxes. The eventual state of fluctuations, achieved after about two inertial periods (\(ft \approx 4\pi \)), corresponds to global intermittency with turbulent patches in an otherwise quiescent background. Our simplified configuration is sufficient to identify turbulence collapse and rebirth, global and temporal intermittency, as well as formation of low-level jets, as in observations of the stratified atmospheric boundary layer.     

The Impact of Landscape Fragmentation on Atmospheric Flow: A Wind-Tunnel Study

Landscape discontinuities such as forest edges play an important role in determining the characteristics of the atmospheric flow by generating increased turbulence and triggering the formation of coherent tree-scale structures. In a fragmented landscape, consisting of surfaces of different heights and roughness, the multiplicity of edges may lead to complex patterns of flow and turbulence that are potentially difficult to predict. Here, we investigate the effects of different levels of forest fragmentation on the airflow. Five gap spacings (of length approximately 5h, 10h, 15h, 20h, 30h, where h is the canopy height) between forest blocks of length 8.7h, as well as a reference case consisting of a continuous forest after a single edge, were investigated in a wind tunnel. The results reveal a consistent pattern downstream from the first edge of each simulated case, with the streamwise velocity component at tree top increasing and turbulent kinetic energy decreasing as gap size increases, but with overshoots in shear stress and turbulent kinetic energy observed at the forest edges. As the gap spacing increases, the flow appears to change monotonically from a flow over a single edge to a flow over isolated forest blocks. The apparent roughness of the different fragmented configurations also decreases with increasing gap size. No overall enhancement of turbulence is observed at any particular level of fragmentation.     

Applying single and two layer canopy models to derive conductances of a Scots pine plantation from micrometeorological measurements

Summary A single layer (Penman-Monteith) and a two layer (modified Shuttleworth-Wallace) evapotranspiration (ET) model are used alternatively to derive conductances related to the dominant fluxes of water vapor from a semi-closed Scots pine plantation. The derivations are based on micrometeorological measurements of above canopy energy flux densities and a simple resistance network. For a period of consecutive fine weather days, below canopy net radiation and below canopy ET were about 20 percent of the corresponding above canopy values. Resulting conductances for latent heat flux agreed well with porometric measurements of pines and understory scaled to canopy level. The shift from single to two layer modelling reduced the canopy conductance to pine conductance by the fraction of understory ET.However, characteristics of porometer results and micrometeorologically derived conductances were quite different: The porometer estimates of conductance were highly variable due to stomatal response to local environmental conditions or natural variability within the tree canopy and vegetation patches which characterized the forest understory. Micrometeorologically derived conductances integrate spatially resulting in relatively smooth and repetitive daily patterns that lack the information of small scale variability. This is seen as a favorable feature of micrometeorological derived conductances when used for the parameterization of atmospheric models for climate research as long as small scale bio-diversity is irrelevant.With 5 Figures     

E − ε − 〈θ 2〉 turbulence closure model for an atmospheric boundary layer including the urban canopy

A modified three-parameter model of turbulence for a thermally stratified atmospheric boundary layer (ABL) is presented. The model is based on tensor-invariant parameterizations for the pressure–strain and pressure–temperature correlations that are more complete than the parameterizations used in the Mellor–Yamada model of level 3.0. The turbulent momentum and heat fluxes are calculated with explicit algebraic models obtained with the aid of symbol algebra from the transport equations for momentum and heat fluxes in the approximation of weakly equilibrium turbulence. The turbulent transport of heat and momentum fluxes is assumed to be negligibly small in this approximation. The three-parameter $E - \varepsilon - {\left\langle {\theta ^{2} } \right\rangle }$ model of thermally stratified turbulence is employed to obtain closed-form algebraic expressions for the fluxes. A computational test of a 24-h ABL evolution is implemented for an idealized two-dimensional region. Comparison of the computed results with the available observational data and other numerical models shows that the proposed model is able to reproduce both the most important structural features of the turbulence in an urban canopy layer near the urbanized ABL surface and the effect of urban roughness on a global structure of the fields of wind and temperature over a city. The results of the computational test for the new model indicate that the motion of air in the urban canopy layer is strongly influenced by mechanical factors (buildings) and thermal stratification.     

Investigating a Hierarchy of Eulerian Closure Models for Scalar Transfer Inside Forested Canopies

Modelling the transfer of heat, water vapour, and CO₂ between the biosphere and the atmosphere is made difficult by the complex two-way interaction between leaves and their immediate microclimate. When simulating scalar sources and sinks inside canopies on seasonal, inter-annual, or forest development time scales, the so-called well-mixed assumption (WMA) of mean concentration (i.e. vertically constant inside the canopy but dynamically evolving in time) is often employed. The WMA eliminates the need to model how vegetation alters its immediate microclimate, which necessitates formulations that utilize turbulent transport theories. Here, two inter-related questions pertinent to the WMA for modelling scalar sources, sinks, and fluxes at seasonal to inter-annual time scales are explored: (1) if the WMA is to be replaced so as to resolve this two-way interaction, how detailed must the turbulent transport model be? And (2) what are the added predictive skills gained by resolving the two-way interaction vis-à-vis other uncertainties such as seasonal variations in physiological parameters. These two questions are addressed by simulating multi-year mean scalar concentration and eddy-covariance scalar flux measurements collected in a Loblolly pine (P. taeda L.) plantation near Durham, North Carolina, U.S.A. using turbulent transport models ranging from K-theory (or first-order closure) to third-order closure schemes. The multi-layer model calculations with these closure schemes were contrasted with model calculations employing the WMA. These comparisons suggested that (i) among the three scalars, sensible heat flux predictions are most biased with respect to eddy-covariance measurements when using the WMA, (ii) first-order closure schemes are sufficient to reproduce the seasonal to inter-annual variations in scalar fluxes provided the canonical length scale of turbulence is properly specified, (iii) second-order closure models best agree with measured mean scalar concentration (and temperature) profiles inside the canopy as well as scalar fluxes above the canopy, (iv) there are no clear gains in predictive skills when using third-order closure schemes over their second-order closure counterparts. At inter-annual time scales, biases in modelled scalar fluxes incurred by using the WMA exceed those incurred when correcting for the seasonal amplitude in the maximum carboxylation capacity (V _{cmax, 25}) provided its mean value is unbiased. The role of local thermal stratification inside the canopy and possible computational simplifications in decoupling scalar transfer from the generation of the flow statistics are also discussed.

“The tree, tilting its leaves to capture bullets of light; inhaling, exhaling; its many thousand stomata breathing, creating the air”. Ruth Stone, 2002, In the Next Galaxy

     

A Note on k - ε Modelling of Vegetation Canopy Air-Flows

The k - turbulence model is a standard of computational software packages for engineering, yet its application to canopy turbulence has not received comparable attention. This is probably due to the additional source (and/or sink) terms, whose parameterization remained uncertain. This model must include source terms for both turbulent kinetic energy (k) and the viscous dissipation rate (), to account for vegetation wake turbulence budget. In this note, we show how Kolmogorov's relation allows for an analytical solution to be calculated within the portion of a dense and homogeneous canopy where the mixing length does not vary. By substitution within model equations, this solution allows for a set of constraints on source term model coefficients to be derived.Those constraints should meet both Reynolds averaged Navier–Stokes equationsand large-eddy simulation sub-grid scale turbulence modelling requirements.Although originating from within a limited portion of the canopy, the predictedcoefficients values must be valid elsewhere in order to make the model capable of predicting the whole canopy-layer flow with a single set of constants.     

A k - *epsiv Turbulence Closure Model For The Atmospheric Boundary Layer Including Urban Canopy

A numerical model for the computation of the wind field,air temperature and humidity in the atmospheric boundary layer (ABL) including the urbancanopy was developed for urban climate simulation. The governing equations of the modelare derived by applying ensemble and spatial averages to the Navier–Stokes equation, continuityequation and equations for heat and water vapour transfer in the air. With the spatial averagingprocedure, effects of buildings and other urban structures in the urban canopy can be accounted for byintroducing an effective volume function, defined as the ratio between the volume of air in acomputational mesh over the total volume of the mesh. The improved k - model accounts for the anisotropyof the turbulence field under density stratification. In the improved k - model, the transportof momentum and heat in the vertical direction under density stratification is evaluated based onthe assumption of a near-equilibrium shear flow where transport effects on the stresses andheat fluxes are negligible. The heating processes at surfaces of buildings and ground are alsomodelled. The comparison of the computational results obtained with the present modeland existing observational data and numerical models shows that the present model is capableof predicting the structure of turbulence in the urban canopy layer under density stratification.Numerical experiments with the new model show that the flow behaviour of the air in the urbancanopy layer is strongly affected by the existence of buildings and density stratification.     

Experiments on scalar dispersion within a model plant canopy part I: The turbulence structure

This is the first of a series of three papers describing experiments on the dispersion of trace heat from elevated line and plane sources within a model plant canopy in a wind tunnel. Here we consider the wind field and turbulence structure. The model canopy consisted of bluff elements 60 mm high and 10 mm wide in a diamond array with frontal area index 0.23; streamwise and vertical velocity components were measured with a special three-hot-wire anemometer designed for optimum performance in flows of high turbulence intensity. We found that:

1. The momentum flux due to spatial correlations between time-averaged streamwise and vertical velocity components (the dispersive flux) was negligible, at heights near and above the top of the canopy.
2. In the turbulent energy budget, turbulent transport was a major loss (of about one-third of local production) near the top of the canopy, and was the principal gain mechanism lower down. Wake production was greater than shear production throughout the canopy. Pressure transport just above the canopy, inferred by difference, appeared to be a gain in approximate balance with the turbulent transport loss.
3. In the shear stress budget, wake production was negligible. The role of turbulent transport was equivalent to that in the turbulent energy budget, though smaller.
4. Velocity spectra above and within the canopy showed the dominance of large eddies occupying much of the boundary layer and moving downstream with a height-independent convection velocity. Within the canopy, much of the vertical but relatively little of the streamwise variance occurred at frequencies characteristic of wake turbulence.
5. Quadrant analysis of the shear stress showed only a slight excess of sweeps over ejections near the top of the canopy, in contrast with previous studies. This is a result of improved measurement techniques; it suggests some reappraisal of inferences previously drawn from quadrant analysis.

     

Turbulence Statistics Measurements in a Northern Hardwood Forest

Tower-based turbulence measurements were collected in and over a mixed hardwood forest at the University of Michigan BiologicalStation (UMBS) UMBSflux site in the northern summerof 2000. Velocity and temperature fluctuations were measured at five levels within the canopy (up to the canopy height, H = 21.4 m), using one- and three-dimensional sonic anemometers and fine-wire thermocouples. Six additional thermocouples were distributed over the canopy-layer depth. Three-dimensional velocities and sonic temperatures were also measured above the canopy at 1.6H and at 2.15H on the AmeriFlux tower located at the UMBSflux site. Vertical profiles of buoyancy flux, mean horizontal velocity, Reynolds stress, and standard deviation and skewness of velocity components were calculated. The analysis of these measurements aims at a multi-layer parameterization framework of turbulence statistics forimplementation in Lagrangian stochastic models. Turbulence profiles and power spectra above the canopy were analyzed in the context of Monin-Obukhov similarity theory (MOST) and Kolmogorov theory, as determined by stability at the top level (2.15H), to assess the extent to which surface scaling is valid as the canopy top is approached. Velocity spectra were computed to explore the potential of estimating the viscous dissipation rate, and results show that the high frequency range of the spectra above the canopy exhibits the roll-off predicted by Kolmogorov theory. Similarly, velocity standard deviations above the canopy converge to MOST predicted values toward the top level, and spectral peaks shift with stability, as expected. Within the canopy, both turbulence statistics profiles and spectral distributions follow the general known characteristics inside forests.     

Numerical analysis of flux footprints for different landscapes

Summary A model for the canopy – planetary boundary layer flow and scalar transport based on E- closure was applied to estimate footprint for CO₂ fluxes over different inhomogeneous landscapes. Hypothetical heterogeneous vegetation patterns – forest with clear-cuts as well as hypothetical heterogeneous relief – a bell-shaped valley and a ridge covered by forest were considered. The distortions of airflow caused by these heterogeneities are shown – the upwind deceleration of the flow at the ridge foot and above valley, acceleration at the crest and the flow separation with the reversed flow pattern at lee slopes of ridge and valley. The disturbances induce changes in scalar flux fields within the atmospheric surface layer comparing to fluxes for homogeneous conditions: at a fixed height the fluxes vary as a function of distance to disturbance. Correspondingly, the flux footprint estimated from model data depends on the location of the point of interest (flux measurement point) and may significantly deviate from that for a flat terrain. It is shown that proposed method could be used for the choice of optimal sensor position for flux measurements over complex terrain as well as for the interpretation of data for existing measurement sites. To illustrate the latter the method was applied for experimental site in Solling, Germany, taking into account the complex topography and vegetation heterogeneities. Results show that in certain situations (summer, neutral stratification, south or north wind) and for a certain sensor location the assumptions of idealized air flow structure could be used for measurement interpretation at this site, though in general, extreme caution should be applied when analytical footprint models are used in the interpretation of flux measurements over complex sites.     

Large-eddy simulation of plant canopy flows using plant-scale representation

Turbulent flow in a corn canopy is simulated using large-eddy simulation (LES) with a Lagrangian dynamic Smagorinsky model. A new numerical representation of plant canopies is presented that resolves approximately the local structure of plants and takes into account their spatial arrangement. As a validation, computational results are compared with experimental data from recent field particle image velocimetry (PIV) measurements and two previous experimental campaigns. Numerical simulation using the traditional modelling method to represent the canopy (field-scale approach) is also conducted as a comparison to the plant-scale approach. The combination of temporal PIV data, LES and spatial PIV data allows us to couple a wide range of relevant turbulence scales. There is good agreement between experimental data and numerical predictions using the plant-scale approach in terms of various turbulence statistics. Within the canopy, the plant-scale approach also allows the capture of more details than the field-scale approach, including instantaneous gusts that penetrate deep inside the canopy.     

Mean Flow and Turbulence Statistics Over Groups of Urban-like Cubical Obstacles

Direct numerical simulations of turbulent flow over regular arrays of urban-like, cubical obstacles are reported. Results are analysed in terms of a formal spatial averaging procedure to enable interpretation of the flow within the arrays as a canopy flow, and of the flow above as a rough wall boundary layer. Spatial averages of the mean velocity, turbulent stresses and pressure drag are computed. The statistics compare very well with data from wind-tunnel experiments. Within the arrays the time-averaged flow structure gives rise to significant ‘dispersive stress’ whereas above the Reynolds stress dominates. The mean flow structure and turbulence statistics depend significantly on the layout of the cubes. Unsteady effects are important, especially in the lower canopy layer where turbulent fluctuations dominate over the mean flow.     

Assessment of Gradient-Based Similarity Functions in the Stable Boundary Layer Derived from a Large-Eddy Simulation

Most of our knowledge on forest-edge flows comes from numerical and wind-tunnel experiments where canopies are horizontally homogeneous. To investigate the impact of tree-scale heterogeneities (\({>}1\) m) on the edge-flow dynamics, the flow in an inhomogeneous forest edge on Falster island in Denmark is investigated using large-eddy simulation. The three-dimensional forest structure is prescribed in the model using high resolution helicopter-based lidar scans. After evaluating the simulation against wind measurements upwind and downwind of the forest leading edge, the flow dynamics are compared between the scanned forest and an equivalent homogeneous forest. The simulations reveal that forest inhomogeneities facilitate flow penetration into the canopy from the edge, inducing important dispersive fluxes in the edge region as a consequence of the flow spatial variability. Further downstream from the edge, the forest inhomogeneities accentuate the canopy-top turbulence and the skewness of the wind-velocity components while the momentum flux remains unchanged. This leads to a lower efficiency in the turbulent transport of momentum within the canopy. Dispersive fluxes are only significant in the upper canopy. Above the canopy, the mean flow is less affected by the forest inhomogeneities. The inhomogeneities induce an increase in the mean wind speed that was found to be equivalent to a decrease in the aerodynamic height of the canopy. Overall, these results highlight the importance of forest inhomogeneities when looking at canopy–atmosphere exchanges in forest-edge regions.     

A wind tunnel study of turbulent flow around single and multiple windbreaks, part I: Velocity fields

This paper describes wind-tunnel experiments on the flow around single and multiple porous windbreaks (height H), sheltering a model plant canopy (height H/3). The mean wind is normal to the windbreaks, which span the width of the wind tunnel. The incident turbulent flow simulates the adiabatic atmospheric surface layer. Five configurations are examined: single breaks of three solidities (low, medium, high; solidity = 1 - porosity), and medium-solidity multiple breaks of streamwise spacing 12H and 6H. The experimental emphases are on the interactions of the windbreak flow with the underlying plant canopy; the effects of solidity; the differences in shelter between single and multiple windbreaks; and the scaling properties of the flow. Principal results are: (1) the "quiet zones" behind each windbreak are smaller in multiple than single arrays, because of the higher turbulence level in the very rough-wall internal boundary layer which develops over the multiple arrays. Nevertheless, the overall shelter effectiveness is higher for multiple arrays than single windbreaks because of the "nonlocal shelter" induced by the array as a whole. (2) The flow approaching the windbreak decelerates above the canopy but accelerates within the canopy, particularly when the windbreak solidity is high. (3) A strong mixing layer forms just downwind of the top of each windbreak, showing some of the turbulence and scaling properties of the classical mixing layer formed between uniform, coflowing streams. (4) No dramatic increase in turbulence levels in the canopy is evident at the point where the deepening mixing layer contacts the canopy (around x/H = 3) but the characteristic inflection in the canopy wind profile is eliminated at this point.     

On the Formulation of Lagrangian Stochastic Models of Scalar Dispersion Within Plant Canopies

Lagrangian stochastic models, quadratic in velocity and satisfying the well-mixed condition for two-dimensional Gaussian turbulence, are used to make predictions of scalar dispersion within a model plant canopy. The non-uniqueness associated with satisfaction of the well-mixed condition is shown to be non-trivial (i.e. different models produce different predictions for scalar dispersion). The best agreement between measured and predicted mean concentrations of scalars is shown to be obtained with a small sub-class of optimal models. This sub-class of optimal models includes Thomson's model (J. Fluid Mech. 180, 529–556, 1987), the simplest model that satisfies the well-mixed condition for Gaussian turbulence, but does not include two other models identified recently as being in optimal agreement with the measured spread of tracers in a neutral boundary layer. It is therefore demonstrated that such models are not universal, i.e. applicable to a wide range of flows without readjustment of model parameters. Predictions for scalar dispersion in the model plant canopy are also obtained using the model of Flesch and Wilson (Boundary-Layer Meteorol. 61, 349–374, 1992). It is shown that, when used with a Gaussian velocity distribution or a maximum-missing-information velocity distribution, which accounts for the measured skewness and kurtosis of velocity statistics, the agreement between predictions obtained using the model of Flesch and Wilson and measurements is as good as that obtained using Thomson's model.