Turbulent transport of scalar quantities within and above a paddy field

An experiment was conducted to study turbulent transport processes of scalar quantities within and above a rice plant canopy. A sonic anemometer-thermometer and a Lyman- humidiometer were used to measure the turbulent fluxes of sensible and latent heat and related turbulence statistics within a paddy field. The sensible and latent heat fluxes measured at two heights within and above the plant canopy showed that the upper layer of this plant canopy was an active source region and that the source strength of sensible and latent heat depended on the solar radiation and physiology of rice plants. Analysis of joint probability distributions of w and T and of w and q within this plant canopy showed that downdrafts were remarkably efficient for upward transport of sensible and latent heat in the daytime. The vertical fluxes of temperature and humidity variance were also divergent from the upper layer of plant canopies. The power spectra of temperature and humidity within the plant canopy decreased rapidly in the high frequency range, compared with the - 2/3 law relationship of nS(n) vs log n observed above plant canopies.     

An Analytical one-Dimensional Second-Order Closure Model of Turbulence Statistics and the Lagrangian Time Scale Within and Above Plant Canopies of Arbitrary Structure

An analytical one-dimensional second-order closure model is developed to describe the within canopy velocity variances, turbulent intensities, dissipation rates, Lagrangian time scale and Lagrangian far field diffusivities for vegetation canopies of arbitrary structure and density. The model incorporates and extends the model of momentum transfer developed by Massman (1997) and the model of within canopy velocity variances developed by Weil (unpublished) from the second-order closure model of Wilson and Shaw (1977). Model predictions of within and above canopy velocity variances, turbulent intensities, dissipation rates and the Lagrangian time scale are in reasonable agreement with previously measured or estimated values for these parameters. The present model suggests that the Lagrangian time scale and the far field diffusivity could be strongly dependent upon foliage structure and density through the foliage effects on the velocity variances. A simple formulation for the Lagrangian time scale at canopy height is derived from model results. Taken as a whole, the present model may provide a relatively simple way to incorporate turbulence parameters into models of soil/canopy/atmosphere mass transfer.     

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.

     

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.     

NUMERICAL SIMULATIONS OF TURBULENT FLOW IN AND ABOVE PLANT CANOPIES

The turbulent flow in and above plant canopies is of fundamental importance to the understanding oftransport processes of momentum,heat and mass between plant canopies and atmosphere,and to microme-teorology.The Reynolds stress equation model(RSM)has been applied to calculate the turbulence in cano-pies in this paper.The calculated mean wind velocity profiles,Reynolds stress,turbulent kinetic energy andviscous dissipation rate in a corn canopy and a spruce forest are compared with field observed data and withWilson's and Shaw's model.The velocity profiles and Rynolds stress calculated by both models are in goodagreement,and the length scale of turbulence appears to be similar.     

A two-dimensional trajectory-simulation model for non-Gaussian,inhomogeneous turbulence within plant canopies

We report a two-dimensional (alongwind u, vertical w) trajectory-simulation model, consistent with Thomson's (1987) well-mixed criteria, that allows for the non-Gaussian turbulence typical of flow within a plant canopy. The effect of non-Gaussian turbulence was examined by formulating a non-Gaussian u, w joint probability density function (PDF) as the sum of two Gaussian joint-PDFs. The resultant PDF reproduced the desired means, variances, skewnesses, and kurtoses, and the correct covariance. In prediction of the location of maximum concentration downwind of a line source in homogeneous, slightly non-Gaussian turbulence, it proved advantageous to incorporate skewness and kurtosis. However, in the case of inhomogeneous, highly non-Gaussian turbulence, the addition of skewness and kurtosis in the model resulted in substantially worse agreement with measurements than the results of the model using Gaussian PDFs. This may be due to inaccuracy in our PDF formulation. Dispersion predictions from the model with Gaussian PDFs were generally not statistically different from measurements. These results indicate that a two-dimensional Gaussian trajectory-simulation approach is adequate to predict mean concentrations and fluxes resulting from sources within plant canopies.     

植被内部及其上方湍流场的数值模拟

植被内部及其上方的湍流流场对于了解植被与大气之间的动量、热量和质量交换过程极其重要。本文把高阶湍流封闭模型的Reynolds应力方程模型(RSM)应用于植被湍流的计算,得到了风速、湍流动能、Reynolds应力及能量耗散率的垂直分布,与现场观测数据比较,甚为满意。     

An Analytical Model for Mean Wind Profiles in Sparse Canopies

Existing analytical models for mean wind profiles within canopies are applicable only in dense canopy scenarios, where all momentum is absorbed by canopy elements and, hence, the effect of the ground on turbulent mixing is not important. Here, we propose a new analytical model that can simulate mean wind profiles within sparse canopies under neutral conditions. The model adopts a linearized canopy-drag parametrization and a first-order turbulence closure scheme taking into account the effects of both the ground and canopy elements on turbulent mixing. The resulting wind profile within a sparser canopy appears to be more like a logarithmic form, with the no-slip condition at the ground being satisfied. The analytical solution converges exactly to the standard surface-layer logarithmic wind profile in the case of zero canopy density (i.e., no-canopy scenario) and tends to be an exponential wind profile for a dense canopy; this feature is unique compared with existing analytical models for canopy wind profiles. Results from the new model are in good agreement with those from laboratory experiments and numerical simulations.     

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.     

Turbulence Structure Within and Above a Canopy of Bluff Elements

Measurements of turbulence structure in a wind-tunnel model canopy of bluff elements show many of the features associated with vegetation canopies and roughness sublayers but also display features more characteristic of the inertial sublayer (ISL). Points of similarity include the existence of an inflexion point in the space-time averaged streamwise velocity at the canopy top, the variation with height of turbulent second moments and the departure of the turbulent kinetic energy budget from local equilibrium in and just above the canopy. Quadrant analysis shows characteristic dominance of sweep over ejection events within the canopy although sweeps are more frequent than usually seen in vegetation canopies. Points of difference are a u′, w′ correlation coefficient that is closer to the ISL value than to most canopy data, and a turbulent Prandtl number midway between canopy and ISL values. Within the canopy there is distinct spatial partitioning into two flow regimes, the wake and non-wake regions. Both time-mean and conditional statistics take different values in these different regions of the canopy flow. We explain many of these features by appealing to a modified version of the mixing-layer hypothesis that links the dominant turbulent eddies to the instability of the inflexion point at canopy top. However, it is evident that these eddies are perturbed by the quasi-coherent wakes of the bluff canopy elements. Based upon an equation for the instantaneous velocity perturbation, we propose a criterion for deciding when the eddies linked to the inflexion point will dominate flow structure and when that structure will be replaced by an array of superimposed element wakes. In particular, we show that the resemblance of some features of the flow to the ISL does not mean that ISL dynamics operate within bluff-body canopies in any sense.     

Seasonal and diurnal variations of coherent structures over a deciduous forest

Coherent structures in turbulent flow above a midlatitude deciduous forest are identified using a wavelet analysis technique. Coupling between motions above the canopy (z/h=1.5, whereh is canopy height) and within the canopy (z/h=0.6) are studied using composite velocity and temperature fields constructed from 85 hours of data. Data are classified into winter and summer cases, for both convective and stable conditions. Vertical velocity fluctuations are in phase at both observation levels. Horizontal motions associated with the structures within the canopy lead those above the canopy, and linear analysis indicates that the horizontal motions deep in the canopy should lead the vertical motions by 90°. On average, coherent structures are responsible for only about 40% of overall turbulent heat and momentum fluxes, much less than previously reported. However, our large data set reveals that this flux fraction comes from a wide distribution that includes much higher fractions in its upper extremes. The separation distanceL _s between adjacent coherent structures, 6–10h, is comparable to that obtained in previous observations over short canopies and in the laboratory. Changes in separation between the summer and winter (leafless) conditions are consistent withL _s being determined by a local horizontal wind shear scale.     

Dispersion of a Passive Scalar Within and Above an Urban Street Network

The transport of a passive scalar from a continuous point-source release in an urban street network is studied using direct numerical simulation (DNS). Dispersion through the network is characterized by evaluating horizontal fluxes of scalar within and above the urban canopy and vertical exchange fluxes through the canopy top. The relative magnitude and balance of these fluxes are used to distinguish three different regions relative to the source location: a near-field region, a transition region and a far-field region. The partitioning of each of these fluxes into mean and turbulent parts is computed. It is shown that within the canopy the horizontal turbulent flux in the street network is small, whereas above the canopy it comprises a significant fraction of the total flux. Vertical fluxes through the canopy top are predominantly turbulent. The mean and turbulent fluxes are respectively parametrized in terms of an advection velocity and a detrainment velocity and the parametrization incorporated into a simple box-network model. The model treats the coupled dispersion problem within and above the street network in a unified way and predictions of mean concentrations compare well with the DNS data. This demonstrates the usefulness of the box-network approach for process studies and interpretation of results from more detailed numerical simulations.     

An Investigation of Higher-Order Closure Models for a Forested Canopy

Simultaneous triaxial sonic anemometer velocity measurements vertically arrayed at six levels within and above a uniform pine forest were used to examine two parameterization schemes for the triple-velocity correlation tensor employed in higher-order closure models. These parameterizations are the gradient-diffusion approximation typically used in second-order closure models, and the full budget for the triple-velocity correlation tensor typically employed in third-order closure models. Both second- and third-order closure models failed to reproduce the measured profiles of the triple-velocity correlation within and above the canopy. However, the Reynolds stress tensor profiles (including velocity variances) deviated greatly from the measurements only within the lower levels of the canopy. It is shown that the Reynolds stresses are most sensitive to the parameterization of the triple-velocity correlation in these lower canopy regions where local turbulent production is negligible and turbulence is mainly sustained by the flux transport term. The failure of the third-order closure model to reproduce the measured third moments in the upper layers of the canopy-top contradicts conclusions from a previous study over shorter vegetation but agrees with another study for a deciduous forest. Whether the third-order closure model failure is due to the zero-fourth-cumulant closure approximation is therefore considered. Comparisons between measured and predicted quadruple velocity correlations suggest that the zero-fourth-cumulant approximation is valid close to the canopy-atmosphere in agreement with recent experiments.     

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 Comprehensive Modelling Approach for the Neutral Atmospheric Boundary Layer: Consistent Inflow Conditions, Wall Function and Turbulence Model

We report on a novel approach for the Reynolds-averaged Navier-Stokes (RANS) modelling of the neutral atmospheric boundary layer (ABL), using the standard k-ek-{\varepsilon} turbulence model. A new inlet condition for turbulent kinetic energy is analytically derived from the solution of the k-ek-{\varepsilon} model transport equations, resulting in a consistent set of fully developed inlet conditions for the neutral ABL. A modification of the standard k-ek-{\varepsilon} model is also employed to ensure consistency between the inlet conditions and the turbulence model. In particular, the turbulence model constant C _μ is generalized as a location-dependent parameter, and a source term is introduced in the transport equation for the turbulent dissipation rate. The application of the proposed methodology to cases involving obstacles in the flow is made possible through the implementation of an algorithm, which automatically switches the turbulence model formulation when going from the region where the ABL is undisturbed to the region directly affected by the building. Finally, the model is completed with a slightly modified version of the Richards and Hoxey rough-wall boundary condition. The methodology is implemented and tested in the commercial code Ansys Fluent 12.1. Results are presented for a neutral boundary layer over flat terrain and for the flow around a single building immersed in an ABL.     

Simulation of Meteorological Fields Within and Above Urban and Rural Canopies with a Mesoscale Model

Accurate simulation of air quality at neighbourhood scales (on order of 1-km horizontal grid spacing) requires detailed meteorological fields inside the roughness sub-layer (RSL). Since the assumptions of the roughness approach, used by most of the mesoscale models, are unsatisfactory at this scale, a detailed urban and rural canopy parameterisation, called DA-SM2-U, is developed inside the Penn State/NCAR Mesoscale Model (MM5) to simulate the meteorological fields within and above the urban and rural canopies. DA-SM2-U uses the drag-force approach to represent the dynamic and turbulent effects of the buildings and vegetation, and a modified version of the soil model SM2-U, called SM2-U(3D), to represent the thermodynamic effects of the canopy elements. The turbulence length scale is also modified inside the canopies. SM2-U(3D) assesses the sensible and latent heat fluxes from rural and urban surfaces in each of the computational layers inside the canopies by considering the shadowing effect, the radiative trapping by the street canyons, and the storage heat flux by the artificial surfaces. DA-SM2-U is tested during one simulated day above the city of Philadelphia, U.S.A. It is shown that DA-SM2-U is capable of simulating the important features observed in the urban and rural RSL, as seen in the vertical profiles of the shear stress, turbulent kinetic energy budget components, eddy diffusivity, potential air temperature, and specific humidity. Within the canopies, DA-SM2-U simulates the decrease of the wind speed inside the dense canopies, the skirting of the flow around the canopy blocks, warmer air inside the vegetation canopy than above open areas during the night and conversely during the day, and constantly warmer air inside the urban canopy. The comparison with measurements shows that the surface air temperature above rural and urban areas is better simulated by DA-SM2-U than by the `standard version' of MM5.     

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.     

A Comparison of Two Canopy Radiative Models in Land Surface Processes

This paper compares the predictions by two radiative transfer models-the two-stream approximation model and the generalized layered model (developed by the authors) in land surface processes-for different canopies under direct or diffuse radiation conditions. The comparison indicates that there are significant differences between the two models, especially in the near infrared (NIR) band. Results of canopy reflectance from the two-stream model are larger than those from the generalized model. However, results of canopy absorptance from the two-stream model are larger in some cases and smaller in others compared to those from the generalized model, depending on the cases involved. In the visible (VIS) band, canopy reflectance is smaller and canopy absorptance larger from the two-stream model compared to the generalized model when the Leaf Area Index (LAI) is low and soil reflectance is high. In cases of canopies with vertical leaf angles, the differences of reflectance and absorptance in the VIS and NIR bands between the two models are especially large.Two commonly occurring cases, with which the two-stream model cannot deal accurately, are also investigated. One is for a canopy with different adaxial and abaxial leaf optical properties; and the other is for incident sky diffuse radiation with a non-uniform distribution. Comparison of the generalized model within the same canopy for both uniform and non-uniform incident diffuse radiation inputs shows smaller differences in general. However, there is a measurable difference between these radiation inputs for a canopy with high leaf angle. This indicates that the application of the two-stream model to a canopy with different adaxial and abaxial leaf optical properties will introduce non-negligible errors.     

A Comparison of Two Canopy Radiative Models in Land Surface Processes

This paper compares the predictions by two radiative transfer models-the two-stream approximation model and the generalized layered model （developed by the authors） in land surface processes -for different canopies under direct or diffuse radiation conditions. The comparison indicates that there are significant differences between the two models, especially in the near infrared （NIR） band. Results of canopy reflectance from the two-stream model are larger than those from the generalized model. However, results of canopy absorptance from the two-stream model are larger in some cases and smaller in others compared to those from the generalized model, depending on the cases involved. In the visible （VIS） band, canopy reflectance is smaller and canopy absorptance larger from the two-stream model compared to the generalized model when the Leaf Area Index （LAI） is low and soil reflectance is high. In cases of canopies with vertical leaf angles, the differences of reflectance and absorptance in the VIS and NIR bands between the two models are especially large. Two commonly occurring cases, with which the two-stream model cannot deal accurately, are also investigated. One is for a canopy with different adaxial and abaxial leaf optical properties; and the other is for incident sky diffuse radiation with a non-uniform distribution. Comparison of the generalized model within the same canopy for both uniform and non-uniform incident diffuse radiation inputs shows smaller differences in general. However, there is a measurable difference between these radiation inputs for a canopy with high leaf angle. This indicates that the application of the two-stream model to a canopy with different adaxial and abaxial leaf optical properties will introduce non-negligible errors.     

Evaluation of the Turbulent Kinetic Energy Dissipation Rate Inside Canopies by Zero- and Level-Crossing Density Methods

Inferring the vertical variation of the mean turbulent kinetic energy dissipation rate (ε) inside dense canopies remains a basic research problem to be confronted. Using detailed laser Doppler anemometry (LDA) measurements collected within a densely arrayed rod canopy, traditional and newly proposed methods to infer ε profiles are compared. The traditional methods for estimating ε at a given layer include isotropic relationships applied to the viscous dissipation scales that are resolved by LDA measurements, higher order structure function methods, and residuals of the turbulent kinetic energy budget in which production and transport terms are all independently inferred. The newly proposed method extends earlier approaches based on zero-crossing statistics, which were shown to be promising in a number of laboratory flows. The extension to account for an arbitrary threshold (hereafter referred to as the level-crossing method) instead of zero-crossing minimizes the effects of instrument noise on the inferred ε. While none of the ε methods employed here can be titled as ‘measured’, these methods differ in their underlying assumptions and simplifications. Above the canopy, where a balance between production and dissipation rate of turbulent kinetic energy is expected, the agreement among all the methods is reasonably good. In the lower-to-middle layers of the canopy, all the methods agree except for those based on a structure-function inference of ε. This departure can be attributed to the lack of a well-defined inertial subrange in these layers. In the upper canopy layers, the disagreements between the methods are largest. Even the higher order structure-function methods disagree with each other when ε is inferred from third- and fifth-order moments. However, for all layers within the canopy, the proposed zero- and threshold-crossing methods agree well with estimates of ε derived from the isotropic relationship applied to the viscous dissipation range. Finally, the advantages of introducing thresholds to minimize two types of instrument noises, additive and multiplicative, are briefly discussed.