Area-Averaged Sensible Heat Flux and a New Method to Determine Zero-Plane Displacement Length over an Urban Surface using Scintillometry

Field observations of area-averagedturbulence characteristics were conducted in a densely built-up residential neighbourhood in Tokyo, Japan. In addition to eddy-correlation (EC) sensors a scintillometer was used for the first time in a city. Significant results include: (1) Scintillometer-derived sensible heat fluxes, Q_H, obtained at a height 3.5 times the building height agree well with those using the EC technique; (2) source areas for the scintillometer fluxes are larger than for the EC sensors, so that at low heights over inhomogeneous terrain scintillometry offers advantages; (3) new similarity relationships for dissipation rates are proposed for urban areas; (4) a new technique that uses simultaneous scintillation measurements at two heights to directly estimate area-averaged zero-plane displacement height, z_d, is proposed. z_d estimated in this way depends slightly on atmospheric stability (lower z_d under more unstable conditions).     

Equations for the Drag Force and Aerodynamic Roughness Length of Urban Areas with Random Building Heights

We use a conceptual model to investigate how randomly varying building heights within a city affect the atmospheric drag forces and the aerodynamic roughness length of the city. The model is based on the assumptions regarding wake spreading and mutual sheltering effects proposed by Raupach (Boundary-Layer Meteorol 60:375?C395, 1992). It is applied both to canopies having uniform building heights and to those having the same building density and mean height, but with variability about the mean. For each simulated urban area, a correction is determined, due to height variability, to the shear stress predicted for the uniform building height case. It is found that u _*/u _*R , where u _* is the friction velocity and u _*R is the friction velocity from the uniform building height case, is expressed well as an algebraic function of ?? and ?? _h /h _m , where ?? is the frontal area index, ?? _h is the standard deviation of the building height, and h _m is the mean building height. The simulations also resulted in a simple algebraic relation for z ₀/z _0R as a function of ?? and ?? _h /h _m , where z ₀ is the aerodynamic roughness length and z _0R is z ₀ found from the original Raupach formulation for a uniform canopy. Model results are in keeping with those of several previous studies.     

Aerodynamic Parameters of Regular Arrays of Rectangular Blocks with Various Geometries

The aerodynamic effects of various configurations of an urban array were investigated in a wind-tunnel experiment. Three aerodynamic parameters characterising arrays—the drag coefficient (C _d ), roughness length (z _o) and displacement height (d)—are used for analysis. C _d is based on the direct measurement of the total surface shear using a floating element, and the other two parameters are estimated by logarithmic fitting of the measured wind profile and predetermined total drag force. The configurations of 63 arrays used for measurement were designed to estimate the effects of layout, wind direction and the height variability of the blocks on these parameters for various roughness packing densities. The results are summarised as follows: (1) The estimated C _d and z _o of the staggered arrays peak against the plan area index (λ _p ) and frontal area index (λ _f ), in contrast with values for the square arrays, which are less sensitive to λ _p and λ _f . In addition, the square arrays with a wind direction of 45° have a considerably larger C _d , and the wind direction increases z _o/H by up to a factor of 2. (2) The effect of the non-uniformity of roughness height on z _o is more remarkable when λ _f exceeds 20%, and the discrepancy in z _o is particularly remarkable and exceeds 200%. (3) The effect of the layout of tall blocks on C _d is stronger than that of short blocks. These results indicate that the effects of both wind direction and the non-uniformity of the heights of buildings on urban aerodynamic parameters vary greatly with λ _p and λ _f ; hence, these effects should be taken into account by considering the roughness packing density.     

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.     

Aerodynamic Parameters of Urban Building Arrays with Random Geometries

It is difficult to describe the flow characteristics within and above urban canopies using only geometrical parameters such as plan area index (λ _p ) and frontal area index (λ _f ) because urban surfaces comprise buildings with random layouts, shapes, and heights. Furthermore, two types of ‘randomness’ are associated with the geometry of building arrays: the randomness of element heights (vertical) and that of the rotation angles of each block (horizontal). In this study, wind-tunnel experiments were conducted on seven types of urban building arrays with various roughness packing densities to measure the bulk drag coefficient (C _d ) and mean wind profile; aerodynamic parameters such as roughness length (z _o ) and displacement height (d) were also estimated. The results are compared with previous results from regular arrays having neither ‘vertical’ nor ‘horizontal’ randomness. In vertical random arrays, the plot of C _d and z _o versus λ _f exhibited a monotonic increase, and z _o increased by a factor of almost two for λ _f = 48–70%. C _d was strongly influenced by the standard deviation of the height of blocks (σ) when λ _p ≥ 17%, whereas C _d was independent of σ when λ _p = 7%. In the case of horizontal random arrays, the plot of the estimated C _d against λ _f showed a peak. The effect of both vertical and horizontal randomness of the layout on aerodynamic parameters can be explained by the structure of the vortices around the blocks; the aspect ratio of the block is an appropriate index for the estimation of such features.     

Estimating Aerodynamic Parameters of Urban-Like Surfaces with Heterogeneous Building Heights

There are many geometrical factors than can influence the aerodynamic parameters of urban surfaces and hence the vertical wind profiles found above. The knowledge of these parameters has applications in numerous fields, such as dispersion modelling, wind loading calculations, and estimating the wind energy resource at urban locations. Using quasi-empirical modelling, we estimate the dependence of the aerodynamic roughness length and zero-plane displacement for idealized urban surfaces, on the two most significant geometrical characteristics; surface area density and building height variability. A validation of the spatially-averaged, logarithmic wind profiles predicted by the model is carried out, via comparisons with available wind-tunnel and numerical data for arrays of square based blocks of uniform and heterogeneous heights. The model predicts two important properties of the aerodynamic parameters of surfaces of heterogeneous heights that have been suggested by experiments. Firstly, the zero-plane displacement of a heterogeneous array can exceed the surface mean building height significantly. Secondly, the characteristic peak in roughness length with respect to surface area density becomes much softer for heterogeneous arrays compared to uniform arrays, since a variation in building height can prevent a skimming flow regime from occurring. Overall the simple model performs well against available experimental data and may offer more accurate estimates of surface aerodynamic parameters for complex urban surfaces compared to models that do not include height variability.     

北京城市下垫面动力学参数的计算与分析

采用北京325 m铁塔2008—2012年的单层超声观测资料,基于莫宁-奥布霍夫相似理论(Monin-Obukhov similarity theory)和前人提出的最小误差分析方法,计算了铁塔周边下垫面的零平面位移高度和动力粗糙度长度。结果表明,由于铁塔位于北京市区,其周边下垫面呈现极其复杂的非均匀性,所以对应铁塔周边不同的扇区,零平面位移高度和动力粗糙度长度各有不同。平均而言,在2008—2012年间,铁塔周边下垫面的零平面位移高度为34.4 m,动力粗糙度长度为1.16 m。此外,综合前人的计算结果发现,铁塔周边的零平面位移高度和动力粗糙度长度在2001年之前呈显著增加的趋势,而在2001年以后并未增长,这一现象与铁塔周边的城市化进程相对应。     

Evaluation of Urban Local-Scale Aerodynamic Parameters: Implications for the Vertical Profile of Wind Speed and for Source Areas

Nine methods to determine local-scale aerodynamic roughness length \((z_{0})\) and zero-plane displacement \((z_{d})\) are compared at three sites (within 60 m of each other) in London, UK. Methods include three anemometric (single-level high frequency observations), six morphometric (surface geometry) and one reference-based approach (look-up tables). A footprint model is used with the morphometric methods in an iterative procedure. The results are insensitive to the initial \(z_{d}\) and \(z_{0}\) estimates. Across the three sites, \(z_{d}\) varies between 5 and 45 m depending upon the method used. Morphometric methods that incorporate roughness-element height variability agree better with anemometric methods, indicating \(z_{d}\) is consistently greater than the local mean building height. Depending upon method and wind direction, \(z_{0}\) varies between 0.1 and 5 m with morphometric \(z_{0}\) consistently being 2–3 m larger than the anemometric \(z_{0}\). No morphometric method consistently resembles the anemometric methods. Wind-speed profiles observed with Doppler lidar provide additional data with which to assess the methods. Locally determined roughness parameters are used to extrapolate wind-speed profiles to a height roughly 200 m above the canopy. Wind-speed profiles extrapolated based on morphometric methods that account for roughness-element height variability are most similar to observations. The extent of the modelled source area for measurements varies by up to a factor of three, depending upon the morphometric method used to determine \(z_{d}\) and \(z_{0}\).     

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.     

Impact of surface variations on the momentum flux above the urban canopy

Based on the momentum flux–wind profile relationship of the Monin–Obukhov Similarity (MOS) theory, the observational data from the urban boundary layer field campaign in Nanjing are used to calculate the friction velocity ( $ {u_*} $ ) at the top of the urban canopy and the calculated results are evaluated. The urban surface roughness parameters (the roughness length z ₀ and zero-plane displacement height z _d) are estimated with the Ba method (Bottema’s morphological method). Two different regimes are employed for the calculations. In the homogeneous approach, z ₀ and z _d are averagely derived from the surface elements in the whole study area; while in the heterogeneous approach, z ₀ and z _d are locally derived from the surface elements in the corresponding upwind fetches (or source areas). The calculated friction velocities are compared to the measurement data. The results show that the calculated friction velocities from the heterogeneous approach are in better agreement with the observed values than those from the homogeneous approach are. This study implies that the local roughness parameters can properly represent the dynamical heterogeneity of urban surface, and its application can significantly improve the performance of parameterizations based on the MOS theory in the urban roughness sublayer.     

Flux Footprints in the Convective Boundary Layer: Large-Eddy Simulation and Lagrangian Stochastic Modelling

We investigated the flux footprints of receptors at different heights in the convective boundary layer (CBL). The footprints were derived using a forward Lagrangian stochastic (LS) method coupled with the turbulent fields from a large-eddy simulation model. Crosswind-integrated flux footprints shown as a function of upstream distances and sensor heights in the CBL were derived and compared using two LS particle simulation methods: an instantaneous area release and a crosswind linear continuous release. We found that for almost all sensor heights in the CBL, a major positive flux footprint zone was located close to the sensor upstream, while a weak negative footprint zone was located further upstream, with the transition band in non-dimensional upwind distances −X between approximately 1.5 and 2.0. Two-dimensional (2D) flux footprints for a point sensor were also simulated. For a sensor height of 0.158 z _i, where z _i is the CBL depth, we found that a major positive flux footprint zone followed a weak negative zone in the upstream direction. Two even weaker positive zones were also present on either side of the footprint axis, where the latter was rotated slightly from the geostrophic wind direction. Using CBL scaling, the 2D footprint result was normalized to show the source areas and was applied to real parameters obtained using aircraft-based measurements. With a mean wind speed in the CBL of U = 5.1 m s⁻¹, convective velocity of w _* = 1.37 m s⁻¹, CBL depth of z _i = 1,000 m, and flight track height of 159 m above the surface, the total flux footprint contribution zone was estimated to range from about 0.1 to 4.5 km upstream, in the case where the wind was perpendicular to the flight track. When the wind was parallel to the flight track, the total footprint contribution zone covered approximately 0.5 km on one side and 0.8 km on the other side of the flight track.     

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.     

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.     

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).     

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.     

Field And Wind-Tunnel Studies Of Aerodynamic Roughness Length

The aerodynamic roughness length (z₀) values of three Gobi desert surfaces were obtained by measurement of the boundary-layer wind profile in the field. To clarify the factors affecting the Gobi surface aerodynamic roughness length, a wind-tunnel experiment was conducted. The wind-tunnel simulation shows that z₀ values increase with increasingsize and coverage of roughness elements. Especially, the shape and height of roughnesselements are more important than other factors in affecting roughness length. The roughness length increases with decreasing values of the geometric parameter (the ratio of element horizontal surface area to height, ) of roughness elements. But at a higher free stream velocity, the height is more important than the shape in affecting roughness length.     

Anomalies in Flux-Gradient Relationships Over Forest

Simultaneous profile and eddy correlation flux data gathered over Thetford Forest, U.K., have been analysed to find values of the vertical turbulent diffusivities K _M, K _H and K _E (for momentum, heat and water vapour transfer, respectively) at a reference height z _R, nine roughness lengths above the zero-plane displacement d. The results show: (i), that values of K _M over the forest are not significantly different from these predicted by semiempirical diabatic influence functions appropriate to much smoother surfaces such as short grass; and (ii), that K _H and K _E exceed their values predicted from the semiempirical functions by an average factor of 2 or more in unstable, near neutral and slightly stable conditions. These conclusions are strongly dependent on the assumed behaviour of d, here taken as 0.76 tree heights, independent of both property and stability. Consideration is given to an alternative analysis procedure, in which values of the zero-plane displacements d _H and d _E for heat and water vapour respectively, are obtained from the data by assuming K _H and K _E to be given by semiempirical diabatic influence functions; this procedure is shown to be unacceptable on both practical and physical grounds. To account for the anomalies in K _H and K _E, a mechanism is proposed in which the horizontally inhomogeneous temperature structure of the canopy causes free convection to be maintained by discrete; localized heat sources and/or sinks, effectively enhancing turbulent transport processes even in near neutral conditions.     

On the determination of zero-plane displacement and roughness length for flow over forest canopies

This paper discusses the importance of the aerodynamic characteristics of forest and other similar canopies to modelling of boundary-layer flow and to estimating the diffusivity coefficients of turbulence transfer mechanisms over such canopies.The hypothesis of Marunich (1971) reported by Tajchman (1981) that the zero-plane displacement, d, equals the upward displacement of the flow trajectory, is critically examined. It is concluded that Marunich's hypothesis is conceptually incorrect and that calculations of d based on Marunich's hypothesis are inherently in error.This paper presents a method based on the mass conservation principle and uses wind profiles in and above a forest canopy as the sole input for determining d, z ₀ and u _*.Sensitivities of calculated results to measurements errors of wind profile data are evaluated. It is found that an error of less than 1% in wind in the logarithmic regime above the canopy can introduce up to 100% errors in calculated values of d, z ₀ and u _*. It is also found that the high sensitivity to wind data accuracy, characteristic of the present method, can be used as a guide for the selection of high quality canopy wind data.     

Zero-plane displacement and roughness length for tall vegetation,derived from a simple mass conservation hypothesis

A method for the determination of the zero-plane displacement, d, and roughness length, z ₀, for tall vegetation is described. A new relationship between d and z ₀ is developed by imposing the condition of mass conservation on the logarithmic wind profile. Further, d and z ₀ can be evaluated directly if independent measurements of friction velocity are available in addition to wind profile measurements. The proposed method takes into account the existence of a transition layer immediately above the vegetation where the logarithmic wind profile law is not valid. Only one level of wind speed measurements is necessary within the inertial sub-layer.The method is applied to wind profile and eddy correlation measurements taken in and above an 18.5 m pine forest to yield d = 12.7 m and z ₀ = 1.28 m. The choice of height for the upper level of measurement and problems with measuring canopy flow are discussed.Work carried out while on leave at the Institute of Hydrology.     

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).