Turbulent Pressure and Velocity Perturbations Induced by Gentle Hills Covered with Sparse and Dense Canopies

How the spatial perturbations of the first and second moments of the velocity and pressure fields differ for flow over a train of gentle hills covered by either sparse or dense vegetation is explored using large-eddy simulation (LES). Two simulations are investigated where the canopy is composed of uniformly arrayed rods each with a height that is comparable to the hill height. In the first simulation, the rod density is chosen so that much of the momentum is absorbed within the canopy volume yet the canopy is not dense enough to induce separation on the lee side of the hill. In the second simulation, the rod density is large enough to induce recirculation inside the canopy on the lee side of the hill. For this separating flow case, zones of intense shear stress originating near the canopy-atmosphere interface persist all the way up to the middle layer, ‘contaminating’ much of the middle and outer layers with shear stress gradients. The implications of these persistent shear-stress gradients on rapid distortion theory and phase relationships between higher order velocity statistics and hill-induced mean velocity perturbations (Δu) are discussed. Within the inner layer, these intense shear zones improve predictions of the spatial perturbation by K-theory, especially for the phase relationships between the shear stress (~ ?Δu/?z) and the velocity variances, where z is the height. For the upper canopy layers, wake production increases with increasing leaf area density resulting in a vertical velocity variance more in phase with Δu than with ?Δu/?z. However, background turbulence and inactive eddies may have dampened this effect for the longitudinal velocity variance. The increase in leaf area density does not significantly affect the phase relationship between mean surface pressure and topography for the two simulations, though the LES results here confirm earlier findings that the minimum mean pressure shifts downstream from the hill crest. The increase in leaf area density and associated flow separation simply stretches this difference further downstream. This shift increases the pressure drag, the dominant term in the overall drag on the hill surface, by some 15%. With regards to the normalized pressure variance, increasing leaf area density increases ${\sigma_p/u_{*}^{2}}$ near the canopy top, where u _* is the longitudinally averaged friction velocity at the canopy top and σ _p is the standard deviation of the pressure fluctuations. This increase is shown to be consistent with a primitive scaling argument on the leading term describing the mean-flow turbulent interaction. This scaling argument also predicts the spatial variations in σ _p above the canopy reasonably well for both simulations, but not inside the canopy.     

Flow Over Partially Forested Ridges

Numerical simulations of flow over hills that are partially covered with a forest canopy are performed. This represents a much more realistic situation than previous studies that have generally concentrated on hills that are fully-forested. The results show that the flow over the hill is sensitive to where on the hill the forest is positioned. In particular, for low slopes flow separation is predominantly located within the forest on the lee slope. This has implications for the transport of scalars in the forest canopy. For large hills the results show more variability in scalar concentrations within the canopy compared to either a fully-forested hill or a patch of forest over flat terrain. These results are likely to have implications for a range of applications including the siting and interpretation of flux measurements over forests in complex terrain, predicting wind damage to trees and wind-farm developments. Calculation of the hill-induced pressure drag and canopy-plus-surface stress shows a strong sensitivity to the position of the forest relative to the hill. Depending on the position of the forest the individual drag terms may be strongly enhanced or reduced and may even change sign. The net impact is generally to reduce the total drag compared to an equivalent fully-forested hill, but the amount of the reduction depends strongly on the position of the forest canopy on the hill. In many cases with large, wide hills there is a clear separation of scales between the adjustment of the canopy to a forest edge (of order 6 ? 8L _c, where L _c is the canopy adjustment length scale) and the width of the hill. This separation means that the hill-induced pressure and flow fields and the forest-edge induced pressure and flow fields can in some sense be considered as acting separately. This provides a means of explaining the combined effects of partial forestation and terrain. It also offers a simple method for modelling the changes in drag over a hill due to partial forest cover by considering the impact of the hill and the partial canopy separately. Scaling arguments based on this idea successfully collapse the modelled drag over a range of different hill widths and heights and for different canopy parameters. This offers scope for a relatively simple parametrization of the effects of partial forest cover on the drag over a hill.     

Determination of Roughness Lengths for Heat and Momentum Over Boreal Forests

The roughness length for momentum (z_0m), zero-plane displacementheight (d), and roughness length for heat (z_0h) are importantparameters used to estimate land-atmosphere energy exchange. Although many different approaches have been developed to parameterizemomentum and heat transfer, existing parameterizations generally utilizehighly simplified representations of vegetation structure. Further, a mismatch exists between the treatments used for momentum and heat exchange and those used for radiative energy exchanges. In this paper, parameterizations are developed to estimate z_0m, d, and z_0h for forested regimes using information related to tree crown density and structure. The parameterizations provide realistic representationfor the vertical distribution of foliage within canopies, and include explicit treatment for the effects of the canopy roughness sublayer and leaf drag on momentum exchange. The proposed parameterizationsare able to realistically account for site-to-site differences in roughness lengths that arise from canopy structural properties.Comparisons between model predictions and field measurements show good agreement, suggesting that the proposed parameterizations capture the most important factors influencing turbulent exchange of momentumand heat over forests.     

A Simple Model for Spatially-averaged Wind Profiles Within and Above an Urban Canopy

This paper deals with the modelling of the flow in the urban canopy layer. It critically reviews a well-known formula for the spatially-averaged wind profile, originally proposed by Cionco in 1965, and provides a new interpretation for it. This opens up a number of new applications for modelling mean wind flow over the neighbourhood scale. The model is based on a balance equation between the obstacle drag force and the local shear stress as proposed by Cionco for a vegetative canopy. The buildings within the canopy are represented as a canopy element drag formulated in terms of morphological parameters such as λ _f and λ _p (the ratios of plan area and frontal area of buildings to the lot area). These parameters can be obtained from the analysis of urban digital elevation models. The shear stress is parameterised using a mixing length approach. Spatially-averaged velocity profiles for different values of building packing density corresponding to different flow regimes are obtained and analysed. The computed solutions are compared with published data from wind-tunnel and water-tunnel experiments over arrays of cubes. The model is used to estimate the spatially-averaged velocity profile within and above neighbourhood areas of real cities by using vertical profiles of λ _f .     

Large-eddy Simulations of Flow Over Forested Ridges

Large-eddy simulations (LES) of flow over a series of small forested ridges are performed, and compared with numerical simulations using a one-and-a-half order mixing length closure scheme. The qualitative and quantitative similarity between these results provides some confidence in the results of recent analytical and numerical studies of flow over forested hills using first-order mixing length schemes. Time series of model velocities at various locations within the canopy allow the application of various experimental techniques to study the turbulence in the LES. The application of conditional analysis shows that the structure of the turbulence over a forested hill is broadly similar to that over flat ground, with sweeps and ejections dominating. Differences are seen across the hill, particularly associated with regions of mean flow separation and recirculation near the summit and in the lee of the hill. Detailed comparison of derived mixing lengths from the LES with the assumed values used in mixing-length closure schemes show that the mixing length varies with location across the hill and with height in the canopy. This is consistent with previous wind-tunnel measurements, and demonstrates that a constant mixing-length assumption is not strictly valid within the canopy. Despite this, the first-order mixing-length schemes do give similar results both for the mean flow and the turbulence in such situations.     

Momentum Transfer and Turbulent Kinetic Energy Budgets within a Dense Model Canopy

Second-order closure models for the canopy sublayer (CSL) employ aset of closure schemes developed for `free-air' flow equations andthen add extra terms to account for canopy related processes. Muchof the current research thrust in CSL closure has focused on thesecanopy modifications. Instead of offering new closure formulationshere, we propose a new mixing length model that accounts for basicenergetic modes within the CSL. Detailed flume experiments withcylindrical rods in dense arrays to represent a rigid canopy areconducted to test the closure model. We show that when this lengthscale model is combined with standard second-order closureschemes, first and second moments, triple velocity correlations,the mean turbulent kinetic energy dissipation rate, and the wakeproduction are all well reproduced within the CSL provided thedrag coefficient (C_D) is well parameterized. The maintheoretical novelty here is the analytical linkage betweengradient-diffusion closure schemes for the triple velocitycorrelation and non-local momentum transfer via cumulant expansionmethods. We showed that second-order closure models reproducereasonably well the relative importance of ejections and sweeps onmomentum transfer despite their local closure approximations.Hence, it is demonstrated that for simple canopy morphology (e.g.,cylindrical rods) with well-defined length scales, standard closureschemes can reproduce key flow statistics without much revision.When all these results are taken together, it appears that thepredictive skills of second-order closure models are not limitedby closure formulations; rather, they are limited by our abilityto independently connect the drag coefficient and the effectivemixing length to the canopy roughness density. With rapidadvancements in laser altimetry, the canopy roughness densitydistribution will become available for many terrestrialecosystems. Quantifying the sheltering effect, the homogeneity andisotropy of the drag coefficient, and more importantly, thecanonical mixing length, for such variable roughness density isstill lacking.     

The influence of geometry on recirculation and CO2 transport over forested hills

Flow distortion over a forested hill is asymmetric, forming a recirculation region on the lee slope that increases the complexity in understanding atmosphere–biosphere interaction. To understand the complexity, we examine the effect of the geometry of forested hills on recirculation formation, structure, and related CO₂ transport by performing numerical simulations over double-forested hills. The ratio (0.8) of hill height (H) to half length (L) is a threshold value of flow patterns in the recirculation region: below 0.8, sporadic reversed flow occurs; at 0.8, one vortex is formed; and above 0.8, a pair of counter-rotating vortices is formed. The depth of recirculation increases with increasing H/L. The contribution of advection to the CO₂ budget is non-negligible and topographic-dependent. Vertical advection is opposite in sign to horizontal advection but cannot exactly offset in magnitude. Height-integrated advection shows significant variation in fluxes across hills. Gentle slopes can cause larger advection error. However, the relative importance of advection to CO₂ budget is slope-independent.     

Numerical Investigations of Mean Winds Within Canopies of Regularly Arrayed Cubical Buildings Under Neutral Stability Conditions

Recently, several attempts have been made to model the wind velocity in an urban canopy in order to accurately predict the mixing and transport of momentum, heat, and pollutants within and above the canopy on an urban scale. For this purpose, unverified assumptions made by Macdonald (Boundary-Layer Meteorol 97:25–45, 2000) to develop a model for the profile of the mean wind velocity within an urban canopy have been used. In the present study, in order to provide foundations for improving the urban canopy models, the properties of the spatially-averaged mean quantities used to make these assumptions have been investigated by performing large-eddy simulations (LES) of the airflow around square and staggered arrays of cubical blocks with the following plan area densities: λ _p = 0.05, 0.11, 0.16, 0.20, 0.25, and 0.33. The LES results confirm that the discrepancy between the spatial average of wind velocity and Macdonald’s five-point average of wind velocity can be large in both types of arrays for large λ _p . It is also confirmed that Prandtl’s mixing length varies significantly with height within the canopy, contrary to Macdonald’s assumption for both types of arrays and for both small and large λ _p . On the other hand, in accordance with Macdonald’s assumption, the sectional drag coefficient is found to be almost constant with height except in the case of staggered arrays with high λ _p .     

Estimation of atmospheric surface layer parameters and numerical simulation using MM5 at Mangalore, West Coast of India

Atmospheric surface layer meteorological observations obtained from 20-m-high meteorological tower at Mangalore, situated along the west coast of India are used to estimate the surface layer scaling parameters of roughness length (z _o) and drag coefficient (C _D), surface layer fluxes of sensible heat and momentum. These parameters are computed using the simple flux–profile relationships under the framework of Monin–Obukhov (M–O) similarity theory. The estimated values of z _o are higher (1.35–1.54 m) than the values reported in the literature (>0.4–0.9 m) probably due to the undulating topography surrounding the location. The magnitude of C _D is high for low wind speed (<1.5 m s^?1) and found to be in the range 0.005–0.03. The variations of sensible heat fluxes (SHF) and momentum fluxes are also discussed. Relatively high fluxes of heat and momentum are observed during typical days on 26–27 February 2004 and 10–11 April 2004 due to the daytime unstable atmospheric conditions. Stable or near neutral conditions prevail after 1700 h IST with negative SHF. A mesoscale model PSU/NCAR MM5 is run using a high-resolution (1 km) grid over the study region to examine the influence of complex topography on the surface layer parameters and the simulated fluxes are compared with estimated values. Spatial variations of the frictional velocity (u _*), C _D, surface fluxes, planetary boundary layer (PBL) height and surface winds are noticed according to the topographic variations in the simulation.     

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.     

Application of transilient turbulent theory to study interactions between the atmospheric boundary layer and forest canopies

The new Forest-Land-Atmosphere ModEl called FLAME is presented. The first-order, nonlocal turbulence closure called transilient turbulence theory (Stull, 1993) is applied to study the interactions between a forested land-surface and the atmospheric boundary layer (ABL). The transilient scheme is used for unequal vertical grid spacing and includes the effects of drag, wake turbulence, and interference to vertical mixing by plant elements. Radiation transfer within the vegetation and the equations for the energy balance at the leaf surface have been taken from Norman (1979). Among others, the model predicts profiles of air temperature, humidity and wind velocity within the ABL, sensible and latent heat fluxes from the soil and the vegetation, the stomata and aerodynamic resistances, as well as profiles of temperature and water content in the soil. Preliminary studies carried out for a cloud free day and idealized initial conditions are presented. The canopy height is 30 m within a vertical domain of 3 km. The model is able to capture some of the effects usually observed within and above forested areas, including the relative wind speed maximum in the trunk space and the counter gradient-fluxes in the lower part of the plant stand. Of special interest is the determination of the location and magnitude of the turbulent mixing between model layers, which permits one to identify the effects of large eddies transporting momentum and scalar quantities into the canopy. A comparison between model simulations and field measurements will be presented in a future paper.     

The Influence of Hilly Terrain on Aerosol-Sized Particle Deposition into Forested Canopies

Virtually all reviews dealing with aerosol-sized particle deposition onto forested ecosystems stress the significance of topographic variations, yet only a handful of studies considered the effects of these variations on the deposition velocity (V _d ). Here, the interplay between the foliage collection mechanisms within a dense canopy for different particle sizes and the flow dynamics for a neutrally stratified boundary layer on a gentle and repeating cosine hill are considered. In particular, how topography alters the spatial structure of V _d and its two constitutive components, particle fluxes and particle mean concentration within and immediately above the canopy, is examined in reference to a uniform flat-terrain case. A two-dimensional and particle-size resolving model based on first-order closure principles that explicitly accounts for (i) the flow dynamics, including the two advective terms, (ii) the spatial variation in turbulent viscosity, and (iii) the three foliage collection mechanisms that include Brownian diffusion, turbo-phoresis, and inertial impaction is developed and used. The model calculations suggest that, individually, the advective terms can be large just above the canopy and comparable to the canopy collection mechanisms in magnitude but tend to be opposite to each other in sign. Moreover, these two advective terms are not precisely out of phase with each other, and hence, do not readily cancel each other upon averaging across the hill wavelength. For the larger aerosol-sized particles, differences between flat-terrain and hill-averaged V _d can be significant, especially in the layers just above the canopy. We also found that the hill-induced variations in turbulent shear stress, which are out-of-phase with the topography in the canopy sublayer, play a significant role in explaining variations in V _d across the hill near the canopy top. Just after the hill summit, the model results suggest that V _d fell to 30% of its flat terrain value for particle sizes in the range of 1–10 μm. This reduction appears consistent with maximum reductions reported in wind-tunnel experiments for similar sized particle deposition on ridges with no canopies.     

Heat and mass transfer to and from surfaces with dense vegetation or similar permeable roughness

A differential equation is obtained to describe the concentration of passive admixtures (water vapor, sensible heat, pollutants, CO₂, etc.) of turbulent flow inside a dense and uniform vegetational canopy. The profiles of eddy diffusivity, wind speed and shear stress are assumed to be exponential decay functions of depth below the top of the canopy. This equation is solved for the case of a vegetation with constant concentration of the admixture at the foliage surfaces. The solution is used to formulate bulk mass or heat transfer coefficients, which can be applied to practical problems involving surfaces covered with a vegetation or with similar porous or fibrous roughness elements. The results are shown to be consistent with experimental data presented by Chamberlain (1966), Garratt and Hicks (1973) and Garratt (1978). Calculations with the model illustrate that, as compared to its behavior over surfaces with bluff roughness elements, ln(z ₀/z _0c ) (wherez ₀ is the momentum roughness andz _0c , the scalar roughness) for permeable roughness elements is relatively insensitive tou _* and practically independent ofz ₀.     

An Analytical Model for the Distribution of CO2 Sources and Sinks, Fluxes, and Mean Concentration Within the Roughness Sub-Layer

A one-dimensional analytical model that predicts foliage CO₂ uptake rates, turbulent fluxes, and mean concentration throughout the roughness sub-layer (RSL), a layer that extends from the ground surface up to 5h, where h is canopy height, is proposed. The model combines the mean continuity equation for CO₂ with first-order closure principles for turbulent fluxes and simplified physiological and radiative transfer schemes for foliage uptake. This combination results in a second-order ordinary differential equation in which soil respiration (R) and CO₂ concentration well above the RSL are imposed as lower and upper boundary conditions, respectively. An inverse version of the model was tested against datasets from two contrasting ecosystems: a tropical forest (h = 40m) and a managed irrigated rice canopy (h = 0.7m), with good agreement noted between modelled and measured mean CO₂ concentration profiles within the entire RSL. Sensitivity analysis on the model parameters revealed a plausible scaling regime between them and a dimensionless parameter defined by the ratio between external (R) and internal (stomatal conductance) characteristics controlling the CO₂ exchange process. The model can be used to infer the thickness of the RSL for CO₂ exchange, the inequality in zero-plane displacement between CO₂ and momentum, and its consequences on modelled CO₂ fluxes. A simplified version of the solution is well suited for being incorporated into large-scale climate models. Furthermore, the model framework here can be used to a priori estimate relative contributions from the soil surface and the atmosphere to canopy-air CO₂ concentration, thereby making it synergetic to stable isotopes studies.     

Three-dimensional simulations and wind-tunnel experiments on airflow over isolated forest stands

Prediction of windthrow risk to individual or groups of retained trees in harvested stands requires an improved understanding of canopy airflow dynamics. Large-eddy simulations were used to simulate wind-tunnel experiments in two and three dimensions to compare with observations for model validation and to address parameter space considerations for the design of subsequent retention pattern experiments. The three-dimensional simulations were similar to the observed wind-tunnel data for the statistical profiles for but there were greater differences in skewness and kurtosis. These results were obtained using a common leaf-area drag formulation without either skin friction or speed dependent drag that enables scaling with U ₀ (ambient wind speed) and h (height of the canopy). This scaling results in a single non-dimensional parameter h/h _c where h _c (x, y, z) is the momentum range resulting from the canopy drag. The validity of the model scaling was tested using two-dimensional simulations. The irrotational component of the flow (potential flow) was found to be important when defining vertical domain limitations and has significant implications for time dependent flow (i.e. turbulent conditions) when considering retention pattern design. The sudden onset of drag associated with the isolated stand presents some unexpected challenges. The horizontal scales of the shearing instabilities were simulated in two dimensions and found to range between 2h for early times to 7h for later times. The early-time horizontal scales are in the range of logical retention pattern scales and as such need to be taken into account as part of the parameter space, i.e. a range of retention pattern lengths need consideration.     

Simplified expressions for vegetation roughness length and zero-plane displacement as functions of canopy height and area index

Using a previous treatment of drag and drag partition on rough surfaces, simple analytic expressions are derived for the roughness length (z ₀) and zero-plane displacement (d) of vegetated surfaces, as functions of canopy height (h) and area index (). The resulting expressions provide a good fit to numerous field and wind tunnel data, and are suitable for applications such as surface parameterisations in atmospheric models.     

Modelling of Turbulent Form Drag in Convective Conditions

Large-eddy and mixing length model simulations of convective flows over hills have been performed for a range of hill slopes and stabilities. For low hills, the fractional speed-up and normalized pressure drag are shown to decrease with increasing instability. For hills steep enough to cause separation in neutral conditions, the effect of convection is to reduce the size and strength of the separated bubble, although the normalized pressure drag is found to be almost independent of stability. Finally, the ability of effective roughness length parametrizations to represent the effects of the hills in convective conditions is assessed.     

Scalar Transport over Forested Hills

Numerical simulations of scalar transport in neutral flow over forested ridges are performed using both a 1.5-order mixing-length closure scheme and a large-eddy simulation. Such scalar transport (particularly of CO₂) has been a significant motivation for dynamical studies of forest canopy–atmosphere interactions. Results from the 1.5-order mixing-length simulations show that hills for which there is significant mean flow into and out of the canopy are more efficient at transporting scalars from the canopy to the boundary layer above. For the case with a source in the canopy this leads to lower mean concentrations of tracer within the canopy, although they can be very large horizontal variations over the hill. These variations are closed linked to flow separation and recirculation in the canopy and can lead to maximum concentrations near the separation point that exceed those over flat ground. Simple scaling arguments building on the analytical model of Finnigan and Belcher (Q J Roy Meteorol Soc 130:1–29, 2004) successfully predict the variations in scalar concentration near the canopy top over a range of hills. Interestingly this analysis suggests that variations in the components of the turbulent transport term, rather than advection, give rise to the leading order variations in scalar concentration. The scaling arguments provide a quantitative measure of the role of advection, and suggest that for smaller/steeper hills and deeper/sparser canopies advection will be more important. This agrees well with results from the numerical simulations. A large-eddy simulation is used to support the results from the mixing-length closure model and to allow more detailed investigation of the turbulent transport of scalars within and above the canopy. Scalar concentration profiles are very similar in both models, despite the fact that there are significant differences in the turbulent transport, highlighted by the strong variations in the turbulent Schmidt number both in the vertical and across the hill in the large-eddy simulation that are not represented in the mixing-length model.     

The influence of the geostrophic wind advection approximation on a well-mixed layer

Numerical results indicate that advection of momentum in the boundary layer may significantly alter both the structure of the planetary boundary layer and its influence on the overlying free atmosphere. However, due to the nonlinearity of the inertial terms, it is always difficult to obtain the analytical solution of the boundary-layer model that retains the flow acceleration. In order to overcome this difficulty, the geostrophic momentum (hereafter GM) approximation has been introduced into boundary-layer models. By replacing the advected momentum with the geostrophic wind, the effect of the flow acceleration is partially considered and the original nonlinear partial differential equation set is converted to ordinary differential equations, the solutions of which can be obtained easily with standard techniques. However, the model employing GM fails to capture the features of the boundary layer when the spatio-temporal variation of the boundary-layer flow cannot be properly approximated by the geostrophic wind. In the present work, a modified boundary-layer model with the inertial acceleration in a different approximate form is proposed, in which the advecting wind instead of the advected momentum is approximated by the geostrophic wind (hereafter GAM).Comparing the horizontal velocity and boundary-layer pumping obtained from the classical Ekman theory, and the model incorporating (i) GM and (ii) GAM, it is found that the model with GAM describes most facets of the steady well-mixed layer beneath a north-westerly flow with embedded mesoscale perturbations that is considered in the present work. Inspection of the solution of the model with GAM shows that, within the limit of the validation of the model (i.e., the Rossby number R_O is not very large and the drag coefficient C_D is not too small), the horizontal convergence (divergence) is strengthened by the effect of the inertial acceleration in the region of maximum positive (negative) geostrophic vorticity. Consequently, the boundary-layer pumping there is intensified. It is found that the intensification is firstly strengthened and then weakened as R_O or C_D increases.     

Are Urban-Canopy Velocity Profiles Exponential?

Using analyses of data from extant direct numerical simulations and large-eddy simulations of boundary-layer and channel flows over and within urban-type canopies, sectional drag forces, Reynolds and dispersive shear stresses are examined for a range of roughness densities. Using the spatially-averaged mean velocity profiles these quantities allow deduction of the canopy mixing length and sectional drag coefficient. It is shown that the common assumptions about the behaviour of these quantities, needed to produce an analytical model for the canopy velocity profile, are usually invalid, in contrast to what is found in typical vegetative (e.g. forest) canopies. The consequence is that an exponential shape of the spatially-averaged mean velocity profile within the canopy cannot normally be expected, as indeed the data demonstrate. Nonetheless, recent canopy models that allow prediction of the roughness length appropriate for the inertial layer’s logarithmic profile above the canopy do not seem to depend crucially on their (invalid) assumption of an exponential profile within the canopy.