Momentum Absorption in Rough-Wall Boundary Layers with Sparse Roughness Elements in Random and Clustered Distributions

A wind-tunnel experiment has been used to investigate momentum absorption by rough surfaces with sparse random and clustered distributions of roughness elements. An unusual (though longstanding) method was used to measure the boundary-layer depth δ and friction velocity u _* and thence to infer the functional relationship z ₀/h = f(λ) between the normalised roughness length z ₀/ h and the roughness density λ (where z ₀ is the roughness length and h the mean height of the roughness elements). The method for finding u _* is based on fitting the velocity defect in the outer layer to a functional form for the dimensionless velocity-defect profile in a canonical zero-pressure-gradient boundary layer. For the conditions investigated here, involving boundary layers over sparse roughness with strong local heterogeneity, this velocity-defect-law method is found to be more robust than several alternative methods for finding u _* (uw covariance, momentum integral and slope of the logarithmic velocity profile).The experimental results show that, (1) there is general agreement in the relationship z ₀/h = f(λ) between the present experiment with random arrays and other wind-tunnel experiments with regular arrays; (2) the main effect of clustering is to increase the scatter in the z ₀/h = f(λ) relationship, through increased local horizontal heterogeneity; (3) this scatter obscures any trend in the z ₀/h = f(λ) relationship in response to clustering; and (4) the agreement between the body of wind-tunnel data (taken as a whole) and field data is good, though with scatter for which it is likely that a major contribution stems from local horizontal heterogeneity in the field.     

Shear stress partitioning in large patches of roughness in the atmospheric inertial sublayer

Drag partition measurements were made in the atmospheric inertial sublayer for six roughness configurations made up of solid elements in staggered arrays of different roughness densities. The roughness was in the form of a patch within a large open area and in the shape of an equilateral triangle with 60 m long sides. Measurements were obtained of the total shear stress (τ) acting on the surfaces, the surface shear stress on the ground between the elements (τ_S) and the drag force on the elements for each roughness array. The measurements indicated that τ_S quickly reduced near the leading edge of the roughness compared with τ, and a τ_S minimum occurs at a normalized distance (x/h, where h is element height) of (downwind of the roughness leading edge is negative), then recovers to a relatively stable value. The location of the minimum appears to scale with element height and not roughness density. The force on the elements decreases exponentially with normalized downwind distance and this rate of change scales with the roughness density, with the rate of change increasing as roughness density increases. Average τ_S : τ values for the six roughness surfaces scale predictably as a function of roughness density and in accordance with a shear stress partitioning model. The shear stress partitioning model performed very well in predicting the amount of surface shear stress, given knowledge of the stated input parameters for these patches of roughness. As the shear stress partitioning relationship within the roughness appears to come into equilibrium faster for smaller roughness element sizes it would also appear the shear stress partitioning model can be applied with confidence for smaller patches of smaller roughness elements than those used in this experiment.     

Detection and analysis of coherent structures in urban turbulence

Summary The continuous wavelet transform provides a suitable tool to visualize the vertical structure of turbulence and to detect coherent structures in turbulent time series. This is demonstrated with a simple example of an artificially ramp structured time series. In this study turbulence data, i.e. the fluctuations of the horizontal wind components u′ and v′, the vertical component w′ and temperature T′, sampled with 20.83 Hz and measured simultaneously at three levels (z/h=1.5, 2.1 and 3.2, with z as the sensor height and h the height of the roughness elements) over an urban canopy in the inner city of Basel, Switzerland, are analyzed. The detection of the coherent structures was performed using the Mexican hat wavelet and the zero-crossing method. The analysis for unstable conditions shows that organized structures (ejection-sweep cycles) cover about 45% of the total run time. A conditional average from a total of 116 detected ejection-sweep sequences during 7 hours was calculated over a time window of 100 seconds. This dominating time scale was derived from peak frequencies of the wavelet spectra as well as from the Fourier spectra. It is shown that the normalized amplitudes of fluctuations of temperature and longitudinal wind speed during the events are largest at the lowest measurement level just above the canopy and decrease with increasing distance from the roughness elements. A comparison of related studies over different non-urban surfaces (mainly forests) shows that the shape of conditionally averaged ejection-sweep sequences is very similar for all canopies, however, the dominating time scale in general increases the rougher the surface is and the higher the roughness elements are.     

Large-Eddy Simulations on the Effects of Surface Geometry of Building Arrays on Turbulent Organized Structures

Turbulent organized structures (TOS) above building arrays were investigated using a large-eddy simulation (LES) model for a city (LES-CITY). Square and staggered building arrays produced contrasting behaviour in terms of turbulence that roughly corresponded to the conventional classification of ‘D-type’ and ‘K-type’ roughness, respectively: (1) The drag coefficients (referred to the building height) for staggered arrays were sensitive to building area density, but those for square arrays were not. (2) The relative contributions of ejections to sweeps (S₂/S₄) at the building height for square arrays were sensitive to building area density and nearly equalled or exceeded 1.0 (ejection dominant), but those for staggered arrays were insensitive to building area density and were mostly below 1.0 (sweep dominant). (3) Streaky patterns of longitudinal low speed regions (i.e., low speed streaks) existed in all flows regardless of array type. Height variations of the buildings in the square array drastically increased the drag coefficient and modified the turbulent flow structures. The mechanism of D-type and K-type urban-like roughness flows and the difference from vegetation flows are discussed. Although urban-like roughness flows exhibited mixed properties of mixing layers and flat-wall boundary layers as far as S₂/S₄ was concerned, the turbulent organized structures of urban-like roughness flows resembled those of flat-wall boundary layers.     

Vertical Structure of Selected Turbulence Characteristics above an Urban Canopy

Summary In this paper the results of an urban measurement campaign are presented. The experiment took place from July 1995 to February 1996 in Basel, Switzerland. A total of more than 2000 undisturbed 30-minute runs of simultaneous measurements of the fluctuations of the wind vector u′, v′, w′ and the sonic temperature θ _s ′ at three different heights (z=36, 50 and 76 m a.g.l.) are analysed with respect to the integral statistics and their spectral behaviour. Estimates of the zero plane displacement height d calculated by the temperature variance method yield a value of 22 m for the two lower levels, which corresponds to 0.92 h (the mean height of the roughness elements). At all three measurement heights the dimensionless standard deviation σ _w /u _* is systematically smaller than the Monin-Obukhov similarity function for the inertial sublayer, however, deviations are smaller compared to other urban turbulence studies. The σ_θ/θ_* values follow the inertial sublayer prediction very close for the two lowest levels, while at the uppermost level significant deviations are observed. Profiles of normalized velocity and temperature variances show a clear dependence on stability. The profile of friction velocity u _* is similar to the profiles reported in other urban studies with a maximum around z/h=2.1. Spectral characteristics of the wind components in general show a clear dependence on stability and dimensionless measurement height z/h with a shift of the spectral peak to lower frequencies as thermal stability changes from stable to unstable conditions and as z/h decreases. Velocity spectra follow the −2/3 slope in the inertial subrange region and the ratios of spectral energy densities S _w (f)/S _u (f) approach the value of 4/3 required for local isotropy in the inertial subrange. Velocity spectra and spectral peaks fit best to the well established surface layer spectra from Kaimal et al. (1972) at the uppermost level at z/h=3.2. Received September 26, 1997 Revised February 15, 1998     

Velocity and Surface Shear Stress Distributions Behind a Rough-to-Smooth Surface Transition: A Simple New Model

A simple new model is proposed to predict the distribution of wind velocity and surface shear stress downwind of a rough-to-smooth surface transition. The wind velocity is estimated as a weighted average between two limiting logarithmic profiles: the first log law, which is recovered above the internal boundary-layer height, corresponds to the upwind velocity profile; the second log law is adjusted to the downwind aerodynamic roughness and local surface shear stress, and it is recovered near the surface, in the equilibrium sublayer. The proposed non-linear form of the weighting factor is equal to ln(z/z ₀₁)/ln(δ _i /z ₀₁), where z, δ _i and z ₀₁ are the elevation of the prediction location, the internal boundary-layer height at that downwind distance, and the upwind surface roughness, respectively. Unlike other simple analytical models, the new model does not rely on the assumption of a constant or linear distribution for the turbulent shear stress within the internal boundary layer. The performance of the new model is tested with wind-tunnel measurements and also with the field data of Bradley. Compared with other existing analytical models, the proposed model shows improved predictions of both surface shear stress and velocity distributions at different positions downwind of the transition.     

Wind profile constants in a neutral atmospheric boundary layer over complex terrain

The roughness height z ₀ and the zero-plane displacement height d ₀ were determined for a region of complex terrain in the Pre-Alps of Switzerland. This region is characterized by hills of the order of 100 m above the valley elevations, and by distances between ridges of the order of 1 km; it lies about 20 to 30 km north from the Alps. The experimental data were obtained from radiosonde observations under near neutral conditions. The analysis was based on the assumption of a logarithmic profile for the mean horizontal wind existing over one half of the boundary layer. The resulting (z ₀/h) and (d ₀/h) (where h is the mean height of the obstacles) were found to be in reasonable agreement with available relationships in terms of placement density and shape factor of the obstacles, which were obtained in previous experiments with h-scales 2 to 4 orders of magnitude smaller than the present ones.     

A Study of the Internal Boundary Layer due to a Roughness Change in Neutral Conditions Observed During the LINEX Field Campaigns

Summary As an aspect of the LINEX field studies (1996–1997; Lindenberg near Beeskow, Germany), the characteristics of the internal boundary layer (IBL) that is associated with a step change of the surface roughnesses in neutral constant stress layers was investigated and is reported in this paper. Both smooth to rough (in 1996) and rough to smooth (in 1997) types of flow, have been studied based upon the profiles of mean wind and temperature realised from a 10-m mast and eddy correlation measurements taken at two levels (2 m and 5 m). Depending upon wind direction, the fetch at the site varied between 140 m and 315 m within the wind sector (200° to 340°) used for the field investigations. The height of the IBL, δ, had been determined from the intersect of the logarithmic wind-profiles below (< 2 m) and above (> 6 ) the interface. Values of δ obtained at the experimental site compared fairly well to the existing theoretical/empirical fetch-height relationships of the form: δ=aċx ^b , where a, b, are empirical constants. The ratio for the friction velocities below and above the IBL as measured directly by the eddy correlation techniques showed that for fetches less than 250 m there was an increase (decrease) of about 20% of the momentum flux arising from the smooth to rough (rough to smooth) transitions. Influences of distant obstructions (e.g., bushes, pockets of trees) on the surface flow were markedly important on the examined wind profiles and such can be indicative as multiple IBLs. Received September 1, 1997 Revised August 5, 1998     

Aerodynamic Scaling for Estimating the Mean Height of Dense Canopies

We used an aerodynamic method to objectively determine a representative canopy height, using standard meteorological measurements. The canopy height may change if the tree height is used to represent the actual canopy, but little work to date has focused on creating a standard for determining the representative canopy height. Here we propose the ‘aerodynamic canopy height’ h _a as the most effective means of resolving the representative canopy height for all forests. We determined h _a by simple linear regression between zero-plane displacement d and roughness length z ₀, without the need for stand inventory data. The applicability of h _a was confirmed in five different forests, including a forest with a complex canopy structure. Comparison with stand inventory data showed that h _a was almost equivalent to the representative height of trees composing the crown surface if the forest had a simple structure, or to the representative height of taller trees composing the upper canopy in forests with a complex canopy structure. The linear relationship between d and z ₀ was explained by assuming that the logarithmic wind profile above the canopy and the exponential wind profile within the canopy were continuous and smooth at canopy height. This was supported by observations, which showed that h _a was essentially the same as the height defined by the inflection point of the vertical profile of wind speed. The applicability of h _a was also verified using data from several previous studies.     

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 ).     

Regional roughness of the landes forest and surface shear stress under neutral conditions

Mean wind velocity profiles were measured by means of radio-windsondes over the Landes region in southwestern France, which consists primarily of pine forests with scattered villages and clearings with various crops. Analysis of neutral profiles indicated the existence of a logarithmic layer between approximately z – d ₀ = 67(±18)z ₀ and 128(+-32)z ₀ (z is the height above the ground, z ₀ the surface roughness and d ₀ the displacement height). The upper limit can also be given as z – d ₀ = 0.33 (±0.18)h, where h is the height of the bottom of the inversion. The profiles showed that the surface roughness of this terrain is around 1.2 m and the displacement height 6.0 m. Shear stresses derived from the profiles were in good agreement with those obtained just above the forest canopy at a nearby location with the eddy correlation method by a team from the Institute of Hydrology (Wallingford, England).     

Regional moisture source changes inferred from late holocene stable isotope records

Qinghai Lake, China, is located near the northern limit of the East Asian summer monsoon （EASM） and thus is an ideal region for studies of past monsoonal changes. However, isotope records from this region reflect the combined effects of multiple climatic factors, and make climatic interpretations difficult. The authors use multi-proxy records, generated from the same sediment core from Qinghai Lake, to disentangle these multiple effects in isotope records and to infer EASM variability during the late Holocene. Records of leaf wax （C2s） δD, lake carbonate 5180 and the Dunde ice core δ18O all indicate a millennial-scale depletion of mean isotopic values at -1500-1250 years before present. Compared with independent lake temperature and salinity records, the authors suggest that this depletion of long-term mean isotopic values must have resulted from changes in moisture sources in this region. In contrast, the authors attribute high-frequency （centennial timescale） C2s δD and ice core δ18O variability dominantly to a temperature effect. The multiproxy records provide a coherent picture in that many aspects of this regional climate （temperature, dryness, and moisture source） are strongly linked to the EASM variability.     

A stable oxygen, but not carbon, isotope chronology of Callitris columellaris reflects recent climate change in north-western Australia

We investigated the dendroclimatic potential of stable carbon (δ¹³C) and oxygen (δ¹⁸O) abundances in tree rings of Callitris columellaris F. Muell. Tree-ring chronologies were constructed from the central Pilbara, north-western Australia and span 1919–1999. Variation in δ¹⁸O was more strongly related to climate than δ¹³C; ecological and physiological factors may have dampened the climate signal in the δ¹³C chronology. Tree-ring δ¹⁸O was most strongly correlated with relative humidity (RH) and rainfall (r = −0.36 and −0.39) of the wettest months of the summer period, January and February. The correlation with RH reflects its effect on evaporative enrichment of leaf water. However, tree-ring δ¹⁸O may also partly reflect the variability in ¹⁸O signatures of rainfall, which are influenced by the amount of rainfall and atmospheric humidity. From the δ¹⁸O chronology, we inferred that from 1919 to 1955 summers were relatively dry and warm, but since 1955, summers in the Pilbara region have become increasingly cooler and more humid. Since 1980, conditions have been the wettest and coolest of the last 80 years. These inferred changes in climate correspond to a measured increase in rainfall since 1980 in north-western Australia associated with a greater intensity of tropical cyclones. We conclude that δ¹⁸O abundances in tree rings of C. columellaris have significant potential for reconstructing the climate of semi-arid Australia, a region for which observational climate records are sparse.     

Flow over high roughness elements

The mean velocity and longitudinal turbulence-intensity distributions inside the zone of and above high roughness elements were investigated experimentally. This was accomplished by using a model forest canopy. The results indicate that the flow may be divided into transition and fully-developed flow regions, followed by a short adjustment distance near the downstream terminus of the rough boundary. The transition region has a strong effect on the flow characteristics within and above the layer of roughness elements. Generally, a similar qualitative variation for both velocity and turbulence was found inside and above the roughness zone, whose influence extends to more than three times the roughness height.Investigation of the modified universal logarithmic law for describing the velocity variation above the roughness zone revealed that both of the so-called similarity parameters, i.e., friction velocity and roughness length, are not local constants. On the contrary, for a given flow and local conditions they vary drastically with height. It is suspected that this is due to the fact that the classical assumption of constant shear stress throughout the boundary layer or significant portions of it is not satisfied in the case of roughness elements many times greater in height than the thickness of the viscous wall zone.     

The Effects of Inner- and Outer-Layer Turbulence in a Convective Boundary Layer on the Near-Neutral Inertial Sublayer Over an Urban-Like Surface

A large-eddy simulation of the atmospheric boundary layer, large enough to contain both an urban surface layer and a convective mixed layer, was performed to investigate inner-layer and outer-layer scale motions. The objective was to determine the applicability of Monin–Obukhov similarity theory to inner-layer motions, to investigate the influence of outer-layer motions on surface-layer structure, as well as to assess the interaction of the two scales of motion. The urban surface roughness consisted of square-patterned cubic buildings of dimension H (40 m). A spatial filter was used to decompose the two scales in the inertial sublayer. The horizontal square filter of size 10H was effective in separating the inner-layer (surface-layer height ≈ 2 H) and outer-layer scales (boundary-layer height δ ≈ 30H), where the Reynolds stress contribution of the inner layer dominates in the logarithmic layer (depth 2H). Similarity coefficients for velocity fluctuations were successfully determined for inner-layer motions in the surface layer, proving the robustness of Monin–Obukhov similarity for surface-layer turbulence. The inner-layer structures exhibit streaky structures that have similar streamwise length but narrower spanwise width relative to the streamwise velocity fluctuation field, consistent with observations from an outdoor scale model. The outer-layer motions to some extent influence the location of ejections and sweeps through updraft and downdraft motions, respectively, thus, disturbing the homogeneity and similarity of inner-layer motions. Although the horizontal averages of the variances and covariance of motions reveal that the Reynolds stresses are dominated by inner-layer structures, the localized influence of the interaction of outer-layer horizontal and inner-layer vertical motions on the Reynolds stress is not insignificant.     

SHEBA flux–profile relationships in the stable atmospheric boundary layer

Measurements of atmospheric turbulence made during the Surface Heat Budget of the Arctic Ocean Experiment (SHEBA) are used to examine the profile stability functions of momentum, φ _m , and sensible heat, φ _h , in the stably stratified boundary layer over the Arctic pack ice. Turbulent fluxes and mean meteorological data that cover different surface conditions and a wide range of stability conditions were continuously measured and reported hourly at five levels on a 20-m main tower for 11 months. The comprehensive dataset collected during SHEBA allows studying φ _m and φ _h in detail and includes ample data for the very stable case. New parameterizations for φ _m (ζ) and φ _h (ζ) in stable conditions are proposed to describe the SHEBA data; these cover the entire range of the stability parameter ζ = z/L from neutral to very stable conditions, where L is the Obukhov length and z is the measurement height. In the limit of very strong stability, φ _m follows a ζ ^1/3 dependence, whereas φ _h initially increases with increasing ζ, reaches a maximum at ζ ≈ 10, and then tends to level off with increasing ζ. The effects of self-correlation, which occur in plots of φ _m and φ _h versus ζ, are reduced by using an independent bin-averaging method instead of conventional averaging.     

Local advection processes in the surface layer of the marginal ice zone

Micro-scale turbulent transport processes over the marginal ice zone have been studied by use of a two-dimensional numerical model. It has been found that internal boundary layers (IBLs) of horizontal mean velocity, temperature, and specific humidity reveal a near field and a far field. In the near field, the change in surface roughness dominates the height and growth rate of a velocity IBL. The change in surface heat flux governs the near field of a temperature and humidity IBL. In the far field, approximately x/¦L _*2 ¦ ~ 20, where L _*2 is the downstream Obukhov length, the downstream stratification more and more influences the growth rate of IBLs basically by modifying the eddy viscosity.Above more complex terrain consisting of an ensemble of ice strips and leads, a merging height h ^M develops, below which the horizontal variability of the surface modification is clearly observed; h ^M varies with the length scale L of surface modification approximately in proportion to h ^M /L ~ 1/20 – 1/10, as a rule of thumb. Above the merging height, an enveloping IBL exists, whose growth depends on the ice cover, i.e., on the integral of surface modification, but changes very little with L.Local advection of momentum, heat, and moisture clearly affects the local surface heat fluxes. Sensible and latent heat fluxes are found to show also a near and far field. However, if areally averaged surface fluxes are to be deduced from grid-averaged flow variables, then details of local advection can be neglected to a reasonably good approximation.     

On the Correlation between Convective Plume Updrafts and Downdrafts,Lidar Reflectivity and Depolarization Ratio

We question the correlation between vertical velocity (w) on the one hand and the occurrence of convective plumes in lidar reflectivity (i.e. range corrected backscatter signal Pz ²) and depolarization ratio (Δ) on the other hand in the convective boundary layer (CBL). Thermal vertical motion is directly investigated using vertical velocities measured by a ground-based Doppler lidar operating at 2 μm. This lidar provides also simultaneous measurements of lidar reflectivity. In addition, a second lidar 200 m away provides reflectivities at 0.53 and 1 μm and depolarization ratio at 0.53 μm. The time series from the two lidars are analyzed in terms of linear correlation coefficient (ρ). The main result is that the plume-like structures provided by lidar reflectivity within the CBL as well as the CBL height are not a clear signature of updrafts. It is shown that the lidar reflectivity within the CBL is frequently anti-correlated (ρ (w, Pz ² )) with the vertical velocity. On the contrary, the correlation coefficient between the depolarization ratio and the vertical velocity ρ (w, Δ ) is always positive, showing that the depolarization ratio is a fair tracer of updrafts. The importance of relative humidity on the correlation coefficient is discussed. An erratum to this article can be found at     

Flux-gradient profiles for momentum and heat over an urban surface

Summary In this paper, we evaluate the applicability of flux-gradient relationships for momentum and heat for urban boundary layers within the Monin-Obukhov similarity (MOS) theory framework. Although the theory is widely used for smooth wall boundary layers, it is not known how well the theory works for urban layers. To address this problem, we measured the vertical profiles of wind velocity, air temperature, and fluxes of heat and momentum over a residential area and compared the results to theory. The measurements were done above an urban canopy whose mean height z_h is 7.3 m. 3-D sonic anemometers and fine wire thermocouples were installed at 4 heights in the region 1.5z_h < z < 4z_h. We found the following: (1) The non-dimensional horizontal wind speed has good agreement with the stratified logarithmic profile predicted using the semi-empirical Monin-Obukov similarity (MOS) function, when it was scaled by the surface friction velocity that is derived from the shear stress extrapolated to the roof-top level. (2) The scaled gradient of horizontal wind speed followed a conventional semi-empirical function for a flat surface at a level (z/z_h = 2.9), whereas, in the vicinity of the canopy height was larger than the commonly-used empirical relationship. (3) The potential temperature profile above the canopy shows dependency on the atmospheric stability and the scaled gradient of temperature is in good agreement with a conventional shear function for heat. In the case of heat, the dependency on height was not found. (4) The flux-gradient relationship for momentum and heat in the region 1.5z_h < z < 4z_h was rather similar to that for flat surfaces than that for vegetated canopies.     

The Effect of Stratification on the Aerodynamic Roughness Length and Displacement Height

The roughness length, z _0u , and displacement height, d _0u , characterise the resistance exerted by the roughness elements on turbulent flows and provide a conventional boundary condition for a wide range of turbulent-flow problems. Classical laboratory experiments and theories treat z _0u and d _0u as geometric parameters independent of the characteristics of the flow. In this paper, we demonstrate essential stability dependences—stronger for the roughness length (especially in stable stratification) and weaker but still pronounced for the displacement height. We develop a scaling-analysis model for these dependences and verify it against experimental data.