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.     

Analysis of canopy index values for various canopy densities

Canopy wind profiles can often be represented by an exponential function such that wind-speeds in these vegetative canopies are a function of height and the attenuation coefficient of this wind profile relationship. To be more precise, canopy flow is a function of canopy density, element flexibility, and height. An index of canopy flow, therefore, can be defined as a conservative measure of the gross flow response to the presence of various types of roughness elements. For this study, windspeed profile data of two quite different canopy density experiments — field and wind tunnel - have been analyzed based on least-square fittings. The results indicate that the two sets of index values of canopy flow behave in a similar manner with maxima occurring for optimum densities of one-third the potential full array of roughness elements. These index values also differ by some 0.2, but are still compatible when one accounts for the respective levels of turbulence within these dissimilar canopies.     

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.     

Numerical studies on the two-dimensional flow in horizontally homogeneous canopy layers

The two-dimensional equation of motion containing the pressure gradient and Coriolis force is numerically solved for the wind field in and above the layers of a horizontally homogeneous canopy with a vertical distribution of leaf-area densities. The solution shows that, in the case of descending through the canopy, the wind vector turns with an angle which depends on the profile of leaf-area densities. In particular, for the canopy of a forest consisting of upper layers with higher densities and lower layers with smaller densities, the turning is striking; a secondary maximum in wind profile appears in the lower layers.Variations of the aerodynamic parameters for the flow above the canopy are indicated with respect to the leaf-area density. The roughness length varies in such a manner that a maximum appears in intermediate density values, depending on the shape of the profile of leaf-area density. In the case of very dense canopies, the shearing stress acting on the flow above the canopy is determined by the contribution from only the upper canopy elements, but not by that from the lower parts of the canopy.     

Mean canopy flow in an oak forest and estimation of the foliage profile by a numerical model

Summary The interaction of flow with the canopy structure is shown for an oak forest with hornbean trees (Carpinus betulus) as dense undergrowth using a large sample of 15 min mean profiles for the winter (without leaves) and the summer period (with leaves). The usefulness of the canopy flow index is analysed.To identify the processes involved in the momentum interaction a first-order closure model is interactively used. An approximation of the foliage area density from wind profile measurements is derived.With 7 Figures     

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.     

Analytically Modelling Mean Wind and Stress Profiles in Canopies

An analytical model for mean wind profiles in sparse canopies (W. Wang, Boundary-Layer Meteorol 142:383–399, 2012) has been further developed, with (1) an explicit solution being derived, and (2) a linear term being added to the $K$ -closure scheme to improve the shear-stress parametrization when the contribution of non-local transport is significant. Results from large-eddy simulations and from laboratory experiments are used to evaluate the model and adjust model parameters, showing that the model can well simulate canopy wind and stress profiles not only for sparse-canopy scenarios, but also for dense-canopy scenarios. The analytical solution converges exactly to the standard surface-layer logarithmic wind profile in the case of zero canopy density, and tends to an exponential wind profile for a dense canopy.     

The effect of time-variable fluxes on mean wind and temperature profile structure

Synthetic wind speed and air temperature profiles based on the sensible heat flux density and stress at the surface are averaged for the four possible ways in which the suface stress and heat flux density can vary maintaining the same average values. The analysis of the averaged wind and temperature profiles shows that, when the surface stress and/or heat flux density are time-variable, and wind speed and air temperature are averaged linearly, an erroneous estimate of surface roughness, surface stress, heat flux density and profile structure parameters will result.     

Estimation of sector roughness lengths and the effect on prediction of the vertical wind speed profile

An estimate of roughness length is required by some atmospheric models and is also used in the logarithmic profile to determine the increase of wind speed with height under neutral conditions. The choice of technique for determining roughness lengths is generally constrained by the available input data. Here, we compare sets of roughness lengths derived by different methods for the same site and evaluate their impact on the prediction of the vertical wind speed profile.Wind speed and direction data have been collected at four heights over a three-year period at the North Norfolk Wind Monitoring Site. Wind speed profiles were used to generate sector roughness lengths based on the logarithmic profile formula. This is the only direct way of determining roughness lengths. The simplest and cheapest method is to use maps with published tables giving roughness length estimates for different terrain types. Alternatively Wieringa (1976, 1986) and Beljaars (1987) give formulae for determining roughness lengths from wind speed gusts or standard deviations.The four sets of estimated roughness lengths vary considerably. They were used to estimate 34 m wind speeds from 12.7 m observations. The profile-derived roughnesses are used simply as a check on the prediction of the wind speed profiles. The terrain-derived roughness lengths give reasonable results. Gust-derived and standard deviation roughnesses both predict wind speeds which are lower than the observed ones. The error is greater in the case of standard deviation roughnesses. If stability corrections are applied in the prediction of the vertical wind speed profile, the results are considerably improved.     

近水面层温、湿、风廓线和湍流交换规律

本文分析了官厅水库近水面层的温、湿、风廓线规律,指出水面的波浪状况对廓线规律有影响。给出了中性层结时水面粗糙度、动力摩擦速度及阻力系数与风速和浪高的关系。得出了适用于水面的层结订正函数。还分析了不稳定层结条件下的温度廓线规律,并对温、湿、风廓线的相似性问题进行了讨论。     

Charnock’s Roughness Length Model and Non-dimensional Wind Profiles Over the Sea

An analysis tool for the study of wind speed profiles over the water has been developed. The profiles are analysed using a modified dimensionless wind speed and dimensionless height, assuming that the sea surface roughness can be predicted by Charnock’s roughness length model. In this form, the roughness dependency on wind speed is extracted and the variations on the wind profile are due solely to atmospheric stability. The use of the Charnock’s non-dimensional wind profile is illustrated using data collected from a meteorological mast installed in the Danish North Sea. The best fit with the observed mean non-dimensional wind profile under neutral atmospheric conditions is found using a value of 1.2 × 10⁻² for Charnock’s parameter. The stability correction on the neutral wind profile suggested by the Businger-Dyer relations was found to perform well over the sea.     

Determination of zero-plane displacement and roughness length of a forest canopy using profiles of limited height

Flux parameters, zero-plane displancement height and roughness length of a forest canopy are determined taking into consideration a transition layer and atmospheric diabatic influences. The present study, unlike previous studies by DeBruin and Moore (1985) and Lo (1990) that accounted for the velocity profile alone, make use of information from both wind and temperature profiles in formulating the governing equations. However, only the top level measurement is assumed to be within the logarithmic regime. In addition to the mass conservation principle (e.g., Lo, 1990; DeBruin and Moore, 1985), an analytic relationship between the Monin-Obukhov length and the bulk Richardson number is employed as the closure equation for the governing system.The present method is applied to profile measurements taken at Camp Borden (den Hartog and Neumann, 1984) in and above a forest canopy with mean crown height of about 18.5 m. Profile data under neutral or near-neutral conditions yieldedd=12.69 m andz ₀=0.97 m, which are realistic values. In general,z ₀ increases slightly with increasing wind yet remains relatively constant with respect to small variation of stabilities. On the other hand, increases of wind speed reduced values of displacement height,d, by as much as 50%. The influence, if any, of stability ond, however, is not clear from the results of the present study. The validity of using profile data of limited height is also carefully examined. At least for neutral or near-neutral stabilities, the present method can yield realistic results even though the profile heights are substantially below the transition layer height suggested by Garratt (1978).     

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.     

Characteristics of air flow above and within soybean canopies

Air flow was observed above and within canopies of a number of kinds of soybeans. The Clark cultivar and two isolines of the Harosoy cultivar were studied in 1979 and 1980, respectively. Wind speed above the canopy was measured with cup anemometers. Heated thermistor anemometers were used to measure air flow within the canopy. Above-canopy air flow was characterized in terms of the zero-plane displacement (d), roughness parameter (z _o) and drag coefficient (C _d). d and z _o were dependent on canopy height but were independent of friction velocity in the range 0.55 to 0.75 m s^?1 · C _d for the various canopies ranged from 0.027 to 0.035. Greater C _d values were measured over an erectophile canopy than over a planophile canopy. C _d was not measurably affected by differences in leaf pubescence. Within-canopy wind profiles were measured at two locations: within and between rows. The wind profile was characterized by a region of great wind shear in the upper canopy and by a region of relatively weak wind shear in the middle canopy. Considerable spatial variability in wind speed was evident, however. This result has significant implications for canopy flow modeling efforts aimed at evaluating transport in the canopy. In the lower canopy, wind speed within a row increased with depth whereas wind speed between two rows decreased with depth. The wind speeds at the two locations tended to converge to a common value at a height near 0.10 m. The attenuation of within-canopy air flow was stronger in canopies with greater foliage density. Canopy flow attenuation seemed to decrease with increasing wind speed, suggesting that high winds distorted the shape of the canopy in such a manner that the penetration of wind into the canopy increased.     

Wind profiles,momentum fluxes and roughness lengths at Cabauw revisited

We describe the results of an experiment focusing on wind speed and momentum fluxes in the atmospheric boundary layer up to 200 m. The measurements were conducted in 1996 at the Cabauw site in the Netherlands. Momentum fluxes are measured using the K-Gill Propeller Vane. Estimates of the roughness length are derived using various techniques from the wind speed and flux measurements, and the observed differences are explained by considering the source area of the meteorological parameters. A clear rough-to-smooth transition is found in the wind speed profiles at Cabauw. The internal boundary layer reaches the lowest k-vane (20 m) only in the south-west direction where the obstacle-free fetch is about 2 km. The internal boundary layer is also reflected in the roughness lengths derived from the wind speed profiles. The lower part of the profile (< 40 m) is not in equilibrium and no reliable roughness analysis can be given. The upper part of the profile can be linked to a large-scale roughness length. Roughness lengths derived from the horizontal wind speed variance and gustiness have large footprints and therefore represent a large-scale average roughness. The drag coefficient is more locally determined but still represents a large-scale roughness length when it is measured above the local internal boundary layer. The roughness length at inhomogeneous sites can therefore be determined best from drag coefficient measurements just above the local internal boundary layers directly, or indirectly from horizontal wind speed variance or gustiness. In addition, the momentum and heat fluxes along the tower are analysed and these show significant variation with height related to stability and possibly surface heterogeneity. It appears that the dimensionless wind speed gradients scale well with local fluxes for the variety of conditions considered, including the unstable cases.     

Determining surface roughness and displacement height

Vertical flux densities of momentum and sensible heat, obtained from simultaneous wind speed and air temperature profiles in the surface layer, depend on the displacement height of the profile system and the surface roughness. A criterion for selecting the displacement height and the surface roughness is introduced, which requires a minimum value for the error squares between the observed and a calculated wind speed profile as determined by diabatic surface layer theory. Values of displacement height and surface roughness, which provide a minimum error squares fit within a desired tolerance, are selected by the rule of false position. The method is programmed for digital computer solution and applied to a total number of 628 profiles obtained during a 7-day period at a micrometeorological test site near Davis, California, using five measurement levels to 160 cm height.     

Mean Flow and Turbulence Characteristics in an Urban Roughness Sublayer

In this study, a detailed model of an urban landscape has been re-constructed inthe wind tunnel and the flow structure inside and above the urban canopy has beeninvestigated. Vertical profiles of all three velocity components have been measuredwith a Laser-Doppler velocimeter, and an extensive analysis of the measured meanflow and turbulence profiles carried out. With respect to the flow structure inside thecanopy, two types of velocity profiles can be distinguished. Within street canyons,the mean wind velocities are almost zero or negative below roof level, while closeto intersections or open squares, significantly higher mean velocities are observed.In the latter case, the turbulent velocities inside the canopy also tend to be higherthan at street-canyon locations. For both types, turbulence kinetic energy and shearstress profiles show pronounced maxima in the flow region immediately above rooflevel.Based on the experimental data, a shear-stress parameterization is proposed, inwhich the velocity scale, u_s, and length scale, z_s, are based on the level and magnitude of the shear stress peak value. In order to account for a flow region inside the canopy with negligible momentum transport, a shear stress displacement height, d_s, is introduced. The proposed scaling and parameterization perform well for the measured profiles and shear-stress data published in the literature.The length scales derived from the shear-stress parameterization also allowdetermination of appropriate scales for the mean wind profile. The roughnesslength, z₀, and displacement height, d₀, can both be described as fractions of the distance, z_s - d_s, between the level of the shear-stress peak and the shear-stress displacement height. This result can be interpreted in such a way that the flow only feels the zone of depth z_s - d_s as the roughness layer. With respect to the lower part of the canopy (z < d_s) the flow behaves as a skimming flow. Correlations between the length scales z_s and d_s and morphometric parameters are discussed.The mean wind profiles above the urban structure follow a logarithmic windlaw. A combination of morphometric estimation methods for d₀ and z₀ with wind velocity measurements at a reference height, which allow calculation of the shear-stress velocity, u_*, appears to be the most reliable and easiest procedure to determine mean wind profile parameters. Inside the roughnesssublayer, a local scaling approach results in good agreement between measuredand predicted mean wind profiles.     

A quantitative method for estimating Pasquill stability class from windspeed and sensible heat flux density

A simple exponential expression, based upon a form of the Kazanski-Monin stability parameter, modified to account explicitly for effects of surface roughness, and semi-empirically derived from both qualitative and quantitative observations, is presented that relates windspeed and sensible heat flux density to Pasquill stability class. The method, though simple in mathematical form, gives results consistent with physical intuition and reproduces, quantitatively, the essential features of previously published nomograms with an added capability for treating all stability classes and any surface roughness from 0.10 to 100 cm. For the stable classes, a new expression for the wind profile stability factor, predicted by similarity theory, is introduced that produces results more consistent than the more common linear form.     

峨眉山地区近地层微气象特征研究

基于2019年12月至2020年11月峨眉山站梯度塔资料、辐射观测资料和地表通量资料,采用涡动相关法对峨眉山地区近地层的地表通量和蒸散发量的变化进行分析,并估算了零平面位移、空气动力粗糙度、空气热力粗糙度、动量通量输送系数和感热通量输送系数等重要的空气动力学和热力学参数.研究表明:近地面风速呈现高层高、低层低的特征,且...