A Dynamic Urban Canopy Parameterization for Mesoscale Models Based on Computational Fluid Dynamics Reynolds-Averaged Navier–Stokes Microscale Simulations

Urban canopy parameterizations (UCPs) are necessary in mesoscale modelling to take into account the effects of buildings on wind and turbulent structures. This study is focused on the dynamical part of UCPs. The main objective is twofold: first, computing important UCP input parameters (turbulent length scales and the sectional drag coefficient) by means of Reynolds-averaged Navier–Stokes (RANS) simulations of turbulent flow; and second, comparing UCP variables with spatially-averaged properties obtained from RANS simulations for the same configurations. The results show the importance of using a suitable parameterization of the drag force for different packing densities. An urban canopy parameterization that is a compromise between simplicity and accuracy is proposed. This scheme accounts for the variation of drag coefficients with packing densities, and has a parameterization of turbulent length scales. The technique adopted ensures that, at least for the simple configurations studied, the urban canopy parameterization gives values of spatially-averaged variables similar to those computed from a more complex simulation, such as RANS that resolves explicitly the flow around buildings.     

CFD simulation of airflow over a regular array of cubes. Part II: analysis of spatial average properties

In the first part of this study, results of a computational fluid dynamics simulation over an array of cubes have been validated against a set of wind-tunnel measurements. In Part II, such numerical results are used to investigate spatially-averaged properties of the flow and passive tracer dispersion that are of interest for high resolution urban mesoscale modelling (e.g. non resolved obstacle approaches). The results show that vertical profiles of mean horizontal wind are linear within the canopy and logarithmic above. The drag coefficient, derived from the numerical results using the classical formula for the drag force, is height dependent (it decreases with height). However, a modification of the formula is proposed (accounting for subgrid velocity scales) that makes the drag coefficient constant with height. Results also show that the dispersive fluxes are similar in magnitude to the turbulent fluxes, and that they play a very important role within the canopy. Vertical profiles of turbulent length scales (to be used in k–l closure schemes, where k is the turbulent kinetic energy and l a turbulent length scale) are also derived. Finally the distribution of the values around the mean over the reference volumes are analysed for wind and tracer concentrations.     

Numerical Investigations of Mean Winds Within Canopies of Regularly Arrayed Cubical Buildings Under Neutral Stability Conditions

Recently, several attempts have been made to model the wind velocity in an urban canopy in order to accurately predict the mixing and transport of momentum, heat, and pollutants within and above the canopy on an urban scale. For this purpose, unverified assumptions made by Macdonald (Boundary-Layer Meteorol 97:25–45, 2000) to develop a model for the profile of the mean wind velocity within an urban canopy have been used. In the present study, in order to provide foundations for improving the urban canopy models, the properties of the spatially-averaged mean quantities used to make these assumptions have been investigated by performing large-eddy simulations (LES) of the airflow around square and staggered arrays of cubical blocks with the following plan area densities: λ _p = 0.05, 0.11, 0.16, 0.20, 0.25, and 0.33. The LES results confirm that the discrepancy between the spatial average of wind velocity and Macdonald’s five-point average of wind velocity can be large in both types of arrays for large λ _p . It is also confirmed that Prandtl’s mixing length varies significantly with height within the canopy, contrary to Macdonald’s assumption for both types of arrays and for both small and large λ _p . On the other hand, in accordance with Macdonald’s assumption, the sectional drag coefficient is found to be almost constant with height except in the case of staggered arrays with high λ _p .     

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.     

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.     

How to Parametrize Urban-Canopy Drag to Reproduce Wind-Direction Effects Within the Canopy

The mean wind direction within an urban canopy changes with height when the incoming flow is not orthogonal to obstacle faces. This wind-turning effect is induced by complex processes and its modelling in urban-canopy (UC) parametrizations is difficult. Here we focus on the analysis of the spatially-averaged flow properties over an aligned array of cubes and their variation with incoming wind direction. For this purpose, Reynolds-averaged Navier–Stokes simulations previously compared, for a reduced number of incident wind directions, against direct numerical simulation results are used. The drag formulation of a UC parametrization is modified and different drag coefficients are tested in order to reproduce the wind-turning effect within the canopy for oblique wind directions. The simulations carried out for a UC parametrization in one-dimensional mode indicate that a height-dependent drag coefficient is needed to capture this effect.     

Mathematical Derivation of Spatially-Averaged Momentum Equations for an Urban Canopy Model Using Underlying Concepts of the Immersed Boundary Method

We propose a new approach to derive spatially-averaged momentum equations for an urban canopy model that resolves buildings vertically and not horizontally. First, in order to mathematically describe the actual momentum field as a completely continuous field, the underling concepts of the immersed boundary method are employed, where we assume that (i) the entire simulation space, including that occupied by buildings, is filled with a fluid, and (ii) an external body force field exists that reduces the wind speed to zero at all positions coinciding with the space occupied by the buildings. Then, in order to obtain the required spatially-averaged momentum equations in a self-consistent manner, a spatial-averaging operation is applied to the Navier–Stokes equations that include a term representing the external force field. The applied spatial-averaging operation is equivalent to the conventional spatial filtering operation used in large-eddy simulations. To examine the significance of the subgrid-scale (SGS) stresses of the spatially-averaged momentum equations, a numerical simulation is performed for a flow around a regular array of cubical blocks with a grid resolution that is sufficient to resolve the blocks. By estimating the individual terms in the spatially-averaged momentum equations using the simulation results, we show that the SGS stresses contribute significantly to the spatially-averaged momentum budget, and therefore they should not be neglected in urban canopy modelling.     

Wind-tunnel Modelling of Dispersion from a Scalar Area Source in Urban-Like Roughness

A wind-tunnel study was conducted to investigate ventilation of scalars from urban-like geometries at neighbourhood scale by exploring two different geometries a uniform height roughness and a non-uniform height roughness, both with an equal plan and frontal density of λ _p = λ _f = 25%. In both configurations a sub-unit of the idealized urban surface was coated with a thin layer of naphthalene to represent area sources. The naphthalene sublimation method was used to measure directly total area-averaged transport of scalars out of the complex geometries. At the same time, naphthalene vapour concentrations controlled by the turbulent fluxes were detected using a fast Flame Ionisation Detection (FID) technique. This paper describes the novel use of a naphthalene coated surface as an area source in dispersion studies. Particular emphasis was also given to testing whether the concentration measurements were independent of Reynolds number. For low wind speeds, transfer from the naphthalene surface is determined by a combination of forced and natural convection. Compared with a propane point source release, a 25% higher free stream velocity was needed for the naphthalene area source to yield Reynolds-number-independent concentration fields. Ventilation transfer coefficients w _T /U derived from the naphthalene sublimation method showed that, whilst there was enhanced vertical momentum exchange due to obstacle height variability, advection was reduced and dispersion from the source area was not enhanced. Thus, the height variability of a canopy is an important parameter when generalising urban dispersion. Fine resolution concentration measurements in the canopy showed the effect of height variability on dispersion at street scale. Rapid vertical transport in the wake of individual high-rise obstacles was found to generate elevated point-like sources. A Gaussian plume model was used to analyse differences in the downstream plumes. Intensified lateral and vertical plume spread and plume dilution with height was found for the non-uniform height roughness.     

Coupling Mesoscale Modelling with a Simple Urban Model: The Lisbon Case Study

The ongoing trend of urbanisation worldwide is leading to a growing requirement for detailed flow and transport parameterisations to be included within numerical weather prediction (NWP) models. Such models often employ a simple roughness parameterisation for urban areas, which is not particularly accurate in predicting or assessing the flow and dispersion at street scale. Moreover, this kind of parameterisation offers too poor a representation of the mechanical and thermal forcing exerted by urban areas on the larger scale flow. At present, high computational costs and long simulation running times are among the constraints for the implementation of more detailed urban sub-models within NWP models. To overcome such limitations, a downscaling procedure from the atmospheric flow at the synoptic scale to the neighbourhood scale and below, is presented in this study. This is achieved by means of a simple urban model based on a parameterised formulation of the drag exerted by the building on the airflow. Application of the urban model for estimating spatially-averaged mean wind speed and the urban heat island over a selected neighbourhood area in Lisbon, Portugal, is presented. The results show the capability of the urban model to provide more accurate mean wind and temperature profiles. Moreover, the urban model has the advantage of being cost effective, as it requires small computational resources, and thus is suitable to be adopted in an operational context. The model is simple enough to be also used to assess how the resolving of urban surface processes may affect those at the larger scales.     

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.     

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.     

Building morphological characteristics and their effect on the wind in Beijing

An urban boundary layer model (UBLM) is improved by incorporating the effect of buildings with a sectional drag coefficient and a height-distributed canopy drag length scale. The improved UBLM is applied to simulate the wind fields over three typical urban blocks over the Beijing area with different height-to-width ratios. For comparisons, the wind fields over the same blocks are simulated by an urban sub-domain scale model resolving the buildings explicitly. The wind fields simulated from the two different methods are in good agreement. Then, two-dimensional building morphological characteristics and urban canopy parameters for Beijing are derived from detailed building height data. Finally, experiements are conducted to investigate the effect of buildings on the wind field in Beijing using the improved UBLM.     

Relating Urban Surface-layer Structure to Upwind Terrain for the Salford Experiment (Salfex)

Profiles of wind and turbulence over an urban area evolve with fetch in response to surface characteristics. Sodar measurements, taken on 22 April 2002 during the Salford Experiment in the UK (Salfex), are here related to upstream terrain. A logarithmic layer up to z = 65m was observed in all half-hour averaged profiles. Above this height the profile showed a different vertical gradient, suggesting a change in surface cover upstream. The drag coefficient varied by a factor of two over only a 20° direction change. Turbulence intensity (σ _x ) for each wind component (x) decreased with height, but the ratio suggested an underestimate of σ _u compared to previous results. Mean urban and suburban cover fraction within the source area for each height decreased sharply between z = 20 and 50m, increasing slightly above. The near-convergence of cover fractions thus occured for source areas of minimum length ≈ 2,200 m. In comparison, the mean length scale of heterogeneity L _P was calculated from surface cover data to be 1,284 m, and the corresponding mean blending height h _b was 175 m. Finally, the mean streamline angle, α, was negative and the magnitude decreased with height. An exponential fit to α for z ≤ 65m gave an e-folding height scale of 159 m. A simple relationship between this height scale and L _P was assumed, giving L _P ≈ 1,080 m, which is in reasonable agreement with the estimate from surface cover type. The results suggest that more emphasis is required on modelling and measuring surface-layer flow over heterogeneous urban canopies.     

Spatio-Temporal Surface Shear-Stress Variability in Live Plant Canopies and Cube Arrays

This study presents spatiotemporally-resolved measurements of surface shear-stress τ _s in live plant canopies and rigid wooden cube arrays to identify the sheltering capability against sediment erosion of these different roughness elements. Live plants have highly irregular structures that can be extremely flexible and porous resulting in considerable changes to the drag and flow regimes relative to rigid imitations mainly used in other wind-tunnel studies. Mean velocity and kinematic Reynolds stress profiles show that well-developed natural boundary layers were generated above the 8 m long wind-tunnel test section covered with the roughness elements at four different roughness densities (λ = 0, 0.017, 0.08, 0.18). Speed-up around the cubes caused higher peak surface shear stress than in experiments with plants at all roughness densities, demonstrating the more effective sheltering ability of the plants. The sheltered areas in the lee of the plants are significantly narrower with higher surface shear stress than those found in the lee of the cubes, and are dependent on the wind speed due to the plants ability to streamline with the flow. This streamlining behaviour results in a decreasing sheltering effect at increasing wind speeds and in lower net turbulence production than in experiments with cubes. Turbulence intensity distributions suggest a suppression of horseshoe vortices in the plant case. Comparison of the surface shear-stress measurements with sediment erosion patterns shows that the fraction of time a threshold skin friction velocity is exceeded can be used to assess erosion of, and deposition on, that surface.     

Are Urban-Canopy Velocity Profiles Exponential?

Using analyses of data from extant direct numerical simulations and large-eddy simulations of boundary-layer and channel flows over and within urban-type canopies, sectional drag forces, Reynolds and dispersive shear stresses are examined for a range of roughness densities. Using the spatially-averaged mean velocity profiles these quantities allow deduction of the canopy mixing length and sectional drag coefficient. It is shown that the common assumptions about the behaviour of these quantities, needed to produce an analytical model for the canopy velocity profile, are usually invalid, in contrast to what is found in typical vegetative (e.g. forest) canopies. The consequence is that an exponential shape of the spatially-averaged mean velocity profile within the canopy cannot normally be expected, as indeed the data demonstrate. Nonetheless, recent canopy models that allow prediction of the roughness length appropriate for the inertial layer’s logarithmic profile above the canopy do not seem to depend crucially on their (invalid) assumption of an exponential profile within the canopy.     

A 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.     

Large-Eddy Simulation of Flows over Random Urban-like Obstacles

Further to our previous large-eddy simulation (LES) of flow over a staggered array of uniform cubes, a simulation of flow over random urban-like obstacles is presented. To gain a deeper insight into the effects of randomness in the obstacle topology, the current results, e.g. spatially-averaged mean velocity, Reynolds stresses, turbulence kinetic energy and dispersive stresses, are compared with our previous LES data and direct numerical simulation data of flow over uniform cubes. Significantly different features in the turbulence statistics are observed within and immediately above the canopy, although there are some similarities in the spatially-averaged statistics. It is also found that the relatively high pressures on the tallest buildings generate contributions to the total surface drag that are far in excess of their proportionate frontal area within the array. Details of the turbulence characteristics (like the stress anisotropy) are compared with those in regular roughness arrays and attempts to find some generality in the turbulence statistics within the canopy region are discussed.     

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.     

An intra-urban thermal breeze in Göteborg, Sweden

Summary ?The existence and character of an intra-urban thermal breeze (IUTB) in the city centre of G?teborg, Sweden was examined. The study was carried out in a 10 ha open area covered with gravel, asphalt and grass, surrounded by narrow street canyons. Measurements included an array of fixed wind and temperature sensors and smoke in the open area; temperature of the surrounding neighbourhood from mobile thermal mapping and fixed temperature sensors; standard climate measurements from four automatic weather stations in and around G?teborg. The results based on sixteen field surveys performed between December 1998 and March 2000 showed that the open urban area might generate a special type of IUTB under certain conditions. The IUTB was shown to be a rare nocturnal winter phenomenon developing during clear and calm weather conditions, with snow covered ground, strong ground based inversions and high stability (Ri _b  > 1). The most important driving forces for the generation of an IUTB were large intra-urban horizontal air temperature differences and strong atmospheric stability which led to decoupling of the canopy layer atmosphere from wind flow aloft. In order to estimate the physical principles underlying an IUTB of this type a simple 1.5-dimensional model was devised. Results indicated that the horizontal intra-urban air temperature difference recorded in G?teborg was enough to develop an IUTB. Received May 6, 2002; revised November 20, 2002; accepted January 7, 2003 Published online May 20, 2003     

A Note on Spatial Averaging and Shear Stresses Within Urban Canopies

One-dimensional urban models embedded in mesoscale numerical models may place several grid points within the urban canopy. This requires an accurate parametrization for shear stresses (i.e. vertical momentum fluxes) including the dispersive stress and momentum sinks at these points. We used a case study with a packing density of 33% and checked rigorously the vertical variation of spatially-averaged total shear stress, which can be used in a one-dimensional column urban model. We found that the intrinsic spatial average, in which the volume or area of the solid parts are not included in the average process, yield greater time–spatial average of total stress within the canopy and a more evident abrupt change at the top of the buildings than the comprehensive spatial average, in which the volume or area of the solid parts are included in the average.