Characteristics of canopy turbulence over a deciduous forest on complex terrain

Canopy turbulence plays an important role in mass and energy exchanges at the canopy-atmosphere interface. Despite extensive studies on canopy turbulence over a flat terrain, less attention has been given to canopy turbulence in a complex terrain. The purpose of this study is to scrutinize characteristics of canopy turbulence in roughness sublayer over a hilly forest terrain. We investigated basic turbulence statistics, conditionally sampled statistics, and turbulence spectrum in terms of different atmospheric stabilities, wind direction and vertical structures of momentum fluxes. Similarly to canopy turbulence over a homogeneous terrain, turbulence statistics showed coherent structure. Both quadrant and spectrum analysis corroborated the role of intermittent and energetic eddies with length scale of the order of canopy height, regardless of wind direction except for shift of peak in vertical wind spectrum to relatively high frequency in the down-valley wind. However, the magnitude of the momentum correlation coefficient in a neutral condition was smaller than typical value over a flat terrain. Further scrutiny manifested that, in the up-valley flow, temperature skewness was larger and the contribution of ejection to both momentum and heat fluxes was larger compared to the downvalley flow, indicating that thermal instability and weaker wind shear in up-valley flow asymmetrically affect turbulent transport within the canopy.     

A simple unified theory for flow in the canopy and roughness sublayer

The mean flow profile within and above a tall canopy is well known to violate the standard boundary-layer flux–gradient relationships. Here we present a theory for the flow profile that is comprised of a canopy model coupled to a modified surface-layer model. The coupling between the two components and the modifications to the surface-layer profiles are formulated through the mixing layer analogy for the flow at a canopy top. This analogy provides an additional length scale—the vorticity thickness—upon which the flow just above the canopy, within the so-called roughness sublayer, depends. A natural form for the vertical profiles within the roughness sublayer follows that overcomes problems with many earlier forms in the literature. Predictions of the mean flow profiles are shown to match observations over a range of canopy types and stabilities. The unified theory predicts that key parameters, such as the displacement height and roughness length, have a significant dependence on the boundary-layer stability. Assuming one of these parameters a priori leads to the incorrect variation with stability of the others and incorrect predictions of the mean wind speed profile. The roughness sublayer has a greater impact on the mean wind speed in stable than unstable conditions. The presence of a roughness sublayer also allows the surface to exert a greater drag on the boundary layer for an equivalent value of the near-surface wind speed than would otherwise occur. This characteristic would alter predictions of the evolution of the boundary layer and surface states if included within numerical weather prediction models.     

Turbulence Over Urban-type Roughness: Deductions from Wind-tunnel Measurements

Turbulence data from experiments conducted over a staggered cube array, modelling a neutrally stable atmospheric boundary layer in an urban environment, are presented. The results support the contention that organised eddy structures in the near-wall region differ significantly from those in regular smooth-wall flows or in rough-wall boundary layers with much smaller h/δ ratios (where δ and h are the boundary-layer thickness and the height of the roughness elements, respectively). Attention is concentrated on spatial correlations, spectra (and thus the dominant length and time scales), maps of anisotropy invariants and quadrant analyses of the stress tensor. Results are obtained within both the roughness sublayer (i.e. the region above the roughness but within which the flow is spatially inhomogeneous) and the canopy region (i.e. below the height of the roughness elements) and discussion includes consideration of the turbulence kinetic energy balance at various heights.     

A Flume Experiment on the Adjustment of the Mean and Turbulent Statistics to a Transition from Short to Tall Sparse Canopies

Water-flume experiments are conducted to study the structure of turbulent flow within and above a sparse model canopy consisting of two rigid canopies of different heights. This difference in height specifies a two-dimensional step change from a rough to a rougher surface, as opposed to a smooth-to-rough transition. Despite the fact that the flow is in transition from a rough to a rougher surface, the thickness of the internal boundary layer scales as x ^4/5, consistent with smooth-to-rough boundary layer adjustment studies, where x is the downstream distance from the step change. However, the analogy with smooth-to-rough transitions no longer holds when the flow inside the canopy and near the canopy top is considered. Results show that the step change in surface roughness significantly increases turbulence intensities and shear stress. In particular, there is an adjustment of the mean horizontal velocity and shear stress as the flow passes over the rougher canopy, so that their vertical profiles adjust to give maximum values at the top of this canopy. We also observe that the magnitude and shape of the inflection in the mean horizontal velocity profile is significantly affected by the transition. The horizontal and vertical turbulence spectra compare well with Kolmogorov’s theory, although a small deviation at high frequencies is observed in the horizontal spectrum within the canopy. Here, for relatively low leaf area index, shear is found to be a more effective mechanism for momentum transfer through the canopy structure than vortex shedding.     

Flux contribution of coherent structures and its implications for the exchange of energy and matter in a tall spruce canopy

The flux contribution of coherent structures to the total exchange of energy and matter is investigated in a spruce canopy of moderate density in heterogeneous, complex terrain. The study deploys two methods of analysis to estimate the coherent exchange: conditional averages in combination with wavelet analysis, and quadrant analysis. The data were obtained by high-frequency single-point measurements using sonic anemometers and gas analysers at five observation heights above and within the canopy and subcanopy, and represent a period of up to 2.5 months. The study mainly addresses the momentum transfer and exchange of sensible heat throughout the roughness sublayer, while results are provided for the exchange of carbon dioxide and water vapour above the canopy. The magnitude of the flux contribution of coherent structures largely depends on the method of analysis, and it is demonstrated that these differences are attributed to differences in the sampling strategy between the two methods. Despite the differences, relational properties such as sweep and ejection ratios and the variation of the flux contribution with height were in agreement for both methods. The sweep phase of coherent structures is the dominant process close to and within the canopy, whereas the ejections gain importance with increasing distance to the canopy. The efficiency of the coherent exchange in transporting scalars exceeds that for momentum by a factor of two. The occurrence of coherent structures results in a flux error less than 4% for the eddy-covariance method. Based on the physical processes identified from the analysis of the ejection and sweep phases along the vertical profile in the roughness sublayer, a classification scheme for the identification of exchange regimes is developed. This scheme allows one to estimate the region of the canopy participating in the exchange of energy and matter with the above-canopy air under varying environmental conditions.     

Flux–Profile Relationships Over a Fetch Limited Beech Forest

The influence of an internal boundary layer and a roughness sublayer on flux–profile relationships for momentum and sensible heat have been investigated for a closed beech forest canopy with limited fetch conditions. The influence was quantified by derivation of local scaling functions for sensible heat flux and momentum (_h and _m) and analysed as a function of atmospheric stability and fetch. For heat, the influences of the roughness sublayer and the internal boundary layer were in agreement with previous studies. For momentum, the strong vertical gradient of the flow just above the canopy top for some wind sectors led to an increase in _m, a feature that has not previously been observed. For a fetch of 500 m over the beech forest during neutral atmospheric conditions, there is no height range at the site where profiles can be expected to be logarithmic with respect to the local surface. The different influence of the roughness sublayer on _h and _m is reflected in the aerodynamic resistance for the site. The aerodynamic resistance for sensible heat is considerably smaller than the corresponding value for momentum.     

城市表面粗糙度长度的确定

讨论了动量粗糙度长度与热量和水汽等标量粗糙度长度在形式上和物理本质上的不同，以及造成这些不同的原因和条件，分析了决定动量粗糙度的几种因素，并给出了确定动量粗糙度长度的简化关系式，并且根据城市冠层与其上惯性次层能量和动量守衡的原因，建立了热量和水汽粗糙度与动量粗糙度之间的联系，得到了确定热量和水汽粗糙度长度的简化关系式，最后，通过数值试验，表明了动量粗糙度和标量粗糙度变化特征以及对一些主要参数的敏感程度，以及动量粗糙度与标量粗糙度的动态关系。     

An analysis of wind velocity fluctuations in the atmospheric surface layer using an orthonormal wavelet transform

A wavelet analysis can supply information of both the location (time) and the scale of fluctuations. This method is applied to the fluctuations of the natural wind and the turbulent transport of momentum in the atmospheric surface layer. The shapes of both the wavelet spectra and the Fourier spectra of the three components of the wind velocity fluctuations are similar to each other. The quadrant representation of momentum transport shows the scale difference of the transport. The large-scale fluctuations mainly contribute to the downward transport of momentum.     

A New Scheme for the Simulation of Microscale Flow and Dispersion in Urban Areas by Coupling Large-Eddy Simulation with Mesoscale Models

A coupling scheme is proposed for the simulation of microscale flow and dispersion in which both the mesoscale field and small-scale turbulence are specified at the boundary of a microscale model. The small-scale turbulence is obtained individually in the inner and outer layers by the transformation of pre-computed databases, and then combined in a weighted sum. Validation of the results of a flow over a cluster of model buildings shows that the inner- and outer-layer transition height should be located in the roughness sublayer. Both the new scheme and the previous scheme are applied in the simulation of the flow over the central business district of Oklahoma City (a point source during intensive observation period 3 of the Joint Urban 2003 experimental campaign), with results showing that the wind speed is well predicted in the canopy layer. Compared with the previous scheme, the new scheme improves the prediction of the wind direction and turbulent kinetic energy (TKE) in the canopy layer. The flow field influences the scalar plume in two ways, i.e. the averaged flow field determines the advective flux and the TKE field determines the turbulent flux. Thus, the mean, root-mean-square and maximum of the concentration agree better with the observations with the new scheme. These results indicate that the new scheme is an effective means of simulating the complex flow and dispersion in urban canopies.     

Exploring the Effects of Microscale Structural Heterogeneity of Forest Canopies Using Large-Eddy Simulations

The Regional Atmospheric Modeling System (RAMS)-based Forest Large-Eddy Simulation (RAFLES), developed and evaluated here, is used to explore the effects of three-dimensional canopy heterogeneity, at the individual tree scale, on the statistical properties of turbulence most pertinent to mass and momentum transfer. In RAFLES, the canopy interacts with air by exerting a drag force, by restricting the open volume and apertures available for flow (i.e. finite porosity), and by acting as a heterogeneous source of heat and moisture. The first and second statistical moments of the velocity and flux profiles computed by RAFLES are compared with turbulent velocity and scalar flux measurements collected during spring and winter days. The observations were made at a meteorological tower situated within a southern hardwood canopy at the Duke Forest site, near Durham, North Carolina, U.S.A. Each of the days analyzed is characterized by distinct regimes of atmospheric stability and canopy foliage distribution conditions. RAFLES results agreed with the 30-min averaged flow statistics profiles measured at this single tower. Following this intercomparison, two case studies are numerically considered representing end-members of foliage and midday atmospheric stability conditions: one representing the winter season with strong winds above a sparse canopy and a slightly unstable boundary layer; the other representing the spring season with a dense canopy, calm conditions, and a strongly convective boundary layer. In each case, results from the control canopy, simulating the observed heterogeneous canopy structure at the Duke Forest hardwood stand, are compared with a test case that also includes heterogeneity commensurate in scale to tree-fall gaps. The effects of such tree-scale canopy heterogeneity on the flow are explored at three levels pertinent to biosphere-atmosphere exchange. The first level (zero-dimensional) considers the effects of such heterogeneity on the common representation of the canopy via length scales such as the zero-plane displacement, the aerodynamic roughness length, the surface-layer depth, and the eddy-penetration depth. The second level (one-dimensional) considers the normalized horizontally-averaged profiles of the first and second moments of the flow to assess how tree-scale heterogeneities disturb the entire planar-averaged profiles from their canonical (and well-studied planar-homogeneous) values inside the canopy and in the surface layer. The third level (three-dimensional) considers the effects of such tree-scale heterogeneities on the spatial variability of the ejection-sweep cycle and its propagation to momentum and mass fluxes. From these comparisons, it is shown that such microscale heterogeneity leads to increased spatial correlations between attributes of the ejection-sweep cycle and measures of canopy heterogeneity, resulting in correlated spatial heterogeneity in fluxes. This heterogeneity persisted up to four times the mean height of the canopy (h _c ) for some variables. Interestingly, this estimate is in agreement with the working definition of the thickness of the canopy roughness sublayer (2h _c –5h _c ).     

The ejection-sweep cycle over bare and forested gentle hills: a laboratory experiment

Progress on practical problems such as quantifying gene flow and seed dispersal by wind or turbulent fluxes over nonflat terrain now demands fundamental understanding of how topography modulates the basic properties of turbulence. In particular, the modulation by hilly terrain of the ejection-sweep cycle, which is the main coherent motion responsible for much of the turbulent transport, remains a problem that has received surprisingly little theoretical and experimental attention. Here, we investigate how boundary conditions, including canopy and gentle topography, alter the properties of the ejection-sweep cycle and whether it is possible to quantify their combined impact using simplified models. Towards this goal, we conducted two new flume experiments that explore the higher-order turbulence statistics above a train of gentle hills. The first set of experiments was conducted over a bare surface while the second set of experiments was conducted over a modelled vegetated surface composed of densely arrayed rods. Using these data, the connections between the ejection-sweep cycle and the higher-order turbulence statistics across various positions above the hill surface were investigated. We showed that ejections dominate momentum transfer for both surface covers at the top of the inner layer. However, within the canopy and near the canopy top, sweeps dominate momentum transfer irrespective of the longitudinal position; ejections remain the dominant momentum transfer mode in the whole inner region over the bare surface. These findings were well reproduced using an incomplete cumulant expansion and the measured profiles of the second moments of the flow. This result was possible because the variability in the flux-transport terms, needed in the incomplete cumulant expansion, was shown to be well modelled using “local” gradient-diffusion principles. This result suggests that, in the inner layer, the higher-order turbulence statistics appear to be much more impacted by their relaxation history towards equilibrium rather than the advection-distortion history from the mean flow. Hence, we showed that it is possible to explore how various boundary conditions, including canopy and topography, alter the properties of the ejection-sweep cycle by quantifying their impact on the gradients of the second moments only. Implications for modelling turbulence using Reynolds-averaged Navier Stokes equations and plausible definitions for the canopy sublayer depth are briefly discussed.     

Near Wall Flow over Urban-like Roughness

In this study, comprehensive measurements over a number of urban-type surfaces with the same area density of 25% have been performed in a wind tunnel. The experiments were conducted at a free stream velocity of 10 m s^-1 and the main instrumentation was 120 ° x-wire anemometry, but measurement accuracy was checked using laser Doppler anemometry.The results haveconfirmed the strong three-dimensionalityof the turbulent flow inthe roughness sublayer and the depths of the inertial sublayer (log-law region) and roughness sublayer for each surface have been determined. Spatial averaging has been used to remove the variability of the flow in the roughness sublayer due to individual obstacles and it is shown that the spatially averaged mean velocity in the inertial sublayer and roughness sublayer can,together, be described by a single log-law with a mean zero-plane displacement and roughness length for the surface, provided that the proper surface stress is known. The spatially averaged shear stresses in the inertial sublayer and roughness sublayer are compared with the surface stress deduced from form drag measurements on the roughness elements themselves.The dispersive stress arising from the spatial inhomogeneity in the mean flow profiles was deduced from the data and is shown to be negligible compared with the usual Reynolds stresses in the roughness sublayer. Comparisons have been made between a homogeneous (regular element array) surface and one consisting of random height elements of the same total volume. Although the upper limits of the inertial sublayer for both surfaces were almost identical at equivalent fetch, the roughness sublayer was much thicker for the random surface than for the uniform surface, the friction velocity and the roughness length were significantly larger and the `roughness efficiency' was greater. It is argued that the inertial sublayer may not exist at all in some of the more extreme rough urban areas. These results will provide fundamental information for modelling urban air quality and forecasting urban wind climates.     

Turbulent Transport of Momentum and Scalars Above an Urban Canopy

Turbulent transport of momentum and scalars over an urban canopy is investigated using the quadrant analysis technique. High-frequency measurements are available at three levels above the urban canopy (47, 140 and 280 m). The characteristics of coherent ejection–sweep motions (flux contributions and time fractions) at the three levels are analyzed, particularly focusing on the difference between ejections and sweeps, the dissimilarity between momentum and scalars, and the dissimilarity between the different scalars (i.e., temperature, water vapour and $\hbox {CO}_{2})$ . It is found that ejections dominate momentum and scalar transfer at all three levels under unstable conditions, while sweeps are the dominant eddy motions for transporting momentum and scalars in the urban roughness sublayer under neutral and stable conditions. The flux contributions and time fractions of ejections and sweeps can be adequately captured by assuming a Gaussian joint probability density function for flow variables. However, the inequality of flux contributions from ejections and sweeps is more accurately reproduced by the third-order cumulant expansion method (CEM). The incomplete cumulant expansion method (ICEM) also works well except for $\hbox {CO}_{2}$ at 47 m where the skewness of $\hbox {CO}_{2}$ fluctuations is significantly larger than that for vertical velocity. The dissimilarity between momentum and scalar transfers is linked to the dissimilarity in the characteristics of ejection–sweep motions and is further quantified by measures of transport efficiencies. Atmospheric stability is the controlling factor for the transport efficiencies of momentum and heat, and fitted functions from the literature describe their behaviour fairly accurately. However, transport efficiencies of water vapour and $\hbox {CO}_{2}$ are less affected by the atmospheric stability. The dissimilarity among the three scalars examined in this study is linked to the active role of temperature and to the surface heterogeneity effect.     

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.     

Effects of the Upstream-Flow Regime and Canyon Aspect Ratio on Non-linear Interactions Between a Street-Canyon Flow and the Overlying Boundary Layer

Large-scale structures within a rough-wall boundary layer generated over a cube array have recently been linked to small-scale fluctuations close to the roughness through a dynamical mechanism similar to amplitude modulation. Demonstrating the existence of this mechanism for different roughness types is a crucial step towards the development of a generic model for wind fluctuations in the urban canopy. Here the influence of the upstream roughness geometry (two-dimensional (2D) and three-dimensional (3D)) and planform packing density (\( \lambda_{p} \)) and street-canyon aspect ratio on the non-linear interactions between large-scale momentum regions and the small scales induced by the presence of the roughness is studied within a wind tunnel using combined particle-image velocimetry and hot-wire anemometry. A multi-time delay linear stochastic estimation is used to decompose the flow into large scales that participate in modulation and the remaining small scales. Using three different upstream roughness configurations composed of either 3D cubes or 2D rectangular blocks it is shown that the upstream roughness configuration has an influence on the non-linear interactions in the rough-wall boundary layer. Analysis of the turbulence skewness decomposition shows a change in the location of the maximum of the term \( \overline{{u_{L}^{\prime} u_{S}^{\prime 2}}} \), which represents the influence of the large-scale momentum regions on the small scales, whilst the temporal correlation shows a modification of the interaction located closer to the roughness with a change from 3D to 2D roughness. Furthermore, a two-point spatio–temporal correlation demonstrates that the non-linear relationship is significantly modified in the wake-interference-flow regime compared to the skimming-flow regime. Through skewness decomposition and temporal correlations the canyon aspect ratio is shown to have no influence on the non-linear interactions, indicating that the mechanism depends only on the flow developing upstream. Finally, although the upstream roughness configuration is shown to influence the non-linear interactions, the nature of the mechanism remains the same in all configurations.     

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.     

Incorporation of a high-roughness lower boundary into a mesoscale model for studies of dry deposition over complex terrain

For flow over natural surfaces, there exists a roughness sublayer within the atmospheric surface layer near the boundary. In this sublayer (typically 50z ₀ deep in unstable conditions), the Monin-Obukhov (M-O) flux profile relations for homogeneous surfaces cannot be applied. We have incorporated a modified form of the M-O stability functions (Garratt, 1978, 1980, 1983) in a mesoscale model to take account of this roughness sublayer and examined the diurnal variation of the boundary-layer wind and temperature profiles with and without these modifications. We have also investigated the effect of the modified M-O functions on the aerodynamic and laminar-sublayer resistances associated with the transfer of trace gases to vegetation. Our results show that when an observation height or the lowest level in a model is within the roughness sublayer, neglect of the flux-profile modifications leads to an underestimate of resistances by 7% at the most.     

Interpretation of Crown Radiation Temperatures of a Dense Douglas fir Forest with Similarity Theory

Infrared crown radiation temperatures as observed over a dense Douglas fir forest are analyzed in the context of similarity theory and the concept of transport resistances. As such we obtain a rather high value of the roughness length for heat, which is about equal to the roughness length for momentum. This value can be explained by the more efficient transport of heat relative to momentum in the roughness sublayer of the forest. Correcting for this effect we arrive at the classic value for homogeneous terrain of about 0.1 times the roughness length for momentum. For unstable cases the presence of enhanced mixing of heat in the roughness sublayer leads to a modified integral stability function for the dimensionless potential temperature difference between the surface and the top of the roughness sublayer. The observations give some evidence for this different stability behaviour. The analysis suggests that during daytime the radiative surface temperature and the aerodynamic surface temperature are not significantly different when used to estimate fluxes. Daytime trunk space air temperature is satisfactory parameterized with the concept of gusts and with surface renewal analysis. As such it is related to the sensible heat flux and the storage heat flux. Night time radiation temperatures at times strongly deviate from the expected behaviour based on similarity theory and the roughness length for heat, suggesting that the concept of a single surface temperature is too simple for such cases.