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.     

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.     

An Analytical Approach to Shear Dispersion and Tracer Age

Solutions to the sheared Fickian advection–diffusion equation in a half-space with arbitrary surface source are given using a ‘transfer function’ method. The method uses Fourier transforms in two horizontal coordinates and time, along with complex Airy functions in the vertical coordinate. Surface deposition and tracer decay are included in the formulation. ‘Puff’ and steady ‘plume’ solutions are compared with Saffman’s moment formulae. The inclusion of a decay rate factor (α) allows the average tracer age to be computed from steady state solutions for concentration C(x, y, z) according to Age = − dln C/dα. A comparison between the puff centroid formula of Saffman and plume Age computations confirms that shear causes tracer puffs to accelerate horizontally as they diffuse upward into a different wind regime. In forward shear, tracer ages are younger than in unsheared flow but the range of ages is greater due to the existence of a high fast pathway and a low slow pathway. In reverse shear, concentrations, ages and the range of ages all rise markedly near the source. Large tracer age suggests that some tracer has taken a very distant path involving a low-level outbound trip and a high-level return. The effect of surface deposition is to reduce the influence of the distant path. In the case of reverse shear, deposition makes the tracer younger. In a turning wind, the time needed to reach a given radius increases due to the curved path of the plume.     

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 .     

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     

A Simple Model for Spatially-averaged Wind Profiles Within and Above an Urban Canopy

This paper deals with the modelling of the flow in the urban canopy layer. It critically reviews a well-known formula for the spatially-averaged wind profile, originally proposed by Cionco in 1965, and provides a new interpretation for it. This opens up a number of new applications for modelling mean wind flow over the neighbourhood scale. The model is based on a balance equation between the obstacle drag force and the local shear stress as proposed by Cionco for a vegetative canopy. The buildings within the canopy are represented as a canopy element drag formulated in terms of morphological parameters such as λ _f and λ _p (the ratios of plan area and frontal area of buildings to the lot area). These parameters can be obtained from the analysis of urban digital elevation models. The shear stress is parameterised using a mixing length approach. Spatially-averaged velocity profiles for different values of building packing density corresponding to different flow regimes are obtained and analysed. The computed solutions are compared with published data from wind-tunnel and water-tunnel experiments over arrays of cubes. The model is used to estimate the spatially-averaged velocity profile within and above neighbourhood areas of real cities by using vertical profiles of λ _f .     

Monin–Obukhov Similarity Functions of the Structure Parameter of Temperature and Turbulent Kinetic Energy Dissipation Rate in the Stable Boundary Layer

The Monin–Obukhov similarity theory (MOST) functions f_ε and f_T, of the dissipation rate of turbulent kinetic energy (TKE). ε, and the structure parameter of temperature, C_T², were determined for the stable atmospheric surface layer using data gathered in the context of CASES-99. These data cover a relatively wide stability range, i.e. ζ=z/L of up to 10, where z is the height and L the Obukhov length. The best fits were given by f_ε = 0.8 + 2.5ζ and f_T= 4.7[ 1+1.6(ζ)^2/3], which differ somewhat from previously published functions. ε was obtained from spectra of the longitudinal wind velocity using a time series model (ARMA) method instead of the traditional Fourier transform. The neutral limit f_ε =0.8 implies that there is an imbalance between TKE production and dissipation in the simplified TKE budget equation. Similarly, we found a production-dissipation imbalance for the temperature fluctuation budget equation. Correcting for the production-dissipation imbalance, the ‘standard’ MOST functions for dimensionless wind speed and temperature gradients (φ_m and φ_m) were determined from f_ε and f_T and compared with the φ_m and φ_h formulations of Businger and others. We found good agreement with the Beljaars and Holtslag [J. Appl. Meteorol. 30, 327–341 (1991)] relations. Lastly, the flux and gradient Richardson numbers are discussed also in terms of f_ε and f_T.     

Temperature–Humidity Dissimilarity and Heat-to-water-vapour Transport Efficiency Above and Within a Pine Forest Canopy: the Role of the Bowen Ratio

Over the past 15 years atmospheric surface-layer experiments over heterogeneous canopies have shown that the vertical transfer of sensible heat and water vapour exhibit a strong dissimilarity. In particular, the sensible-heat-to-water-vapour transport efficiencies generally exceed unity. One of the main consequences is that evaporation (latent heat flux) computed by the flux-variance method is overestimated, as persistently demonstrated by comparisons with evaporation obtained with the eddy-correlation method. Various authors proposed to take into account the temperature–humidity dissimilarity to extend the applicability of the flux-variance method in order to compute evaporation from non-uniform surfaces. They attempted to connect the sensible-heat-to-water-vapour transport efficiency (λ) to the correlation coefficient between temperature and humidity turbulent fluctuations (R _Tq ). This approach was found to be successful over ‘wet’ surfaces for which λ can be approximated by R _Tq and ‘dry’ surfaces for which λ can be approximated by 1/R _Tq . However, no solution has been proposed until now for intermediate hydrological conditions. We investigated this question using eddy-correlation measurements above and inside a pine forest canopy. For both levels, our data present a strong likeness with previously published results over heterogeneous surfaces. In particular, they confirm that λ is R _Tq in wet conditions and 1/R _Tq in dry conditions. Moreover, we defined the range of the Bowen ratio (Bo) values for which those two approximations are valid (below 0.1 and greater than 1, respectively) and established a relationship between λ, R _Tq and Bo for the intermediate range of Bo. We are confident that this new parameterization will enlarge the applicability of the flux-variance method to all kinds of heterogeneous surfaces in various hydrological conditions     

Discrepancy and Applicability of Various Similarity Functions in Flux Calculations Under Stable Conditions

Based on data obtained during the Hualhe River Basin Experiment （HUBEX） in 1999, this study intends to detect the quantitative discrepancies in the momentum （τ0）, sensible heat （H0） and latent heat （E0） fluxes among six sets of similarity functions with the aerodynamic method. It also aims to clarify the applicability of the functions under stable conditions. The relative discrepancy was studied with the normalized transfer coefficients for τ0, H0 and E0, namely CD, CH and CQ, respectively. Except for one set of functions that adopted a rather small von Kármán＇s constant （0.365）, the relative discrepancy in τ0 among the other functions was less than 10%, while that in H0（E0） sometimes reached 25% when the bulk Richardson number （R/B） was less than 0.07. The absolute discrepancy in the fluxes was studied with statistical computations. Among the six sets of functions, the discrepancy in τ0, H0 and E0 sometimes reached 0.03 kg m^-1 s^-2, 4 W m^-2 and 10 W m^-2, respectively, and the discrepancy in the energy balance ratio sometimes exceeded 0.1. Furthermore, when RiB exceeded the critical value （Ric） for a specific set of functions, no fluxes could be derived with the functions. It is therefore suggested that RiB be compared with Ric before computing the fluxes if RiB is less than Ric. Finally, two sets of nonlinear similarity functions are recommended, due to their unlimited applicability in terms of RiB.     

Effects of Wall Heating on Flow Characteristics in a Street Canyon

We develop a large-eddy simulation (LES) model based on a meteorological numerical model for a real scale street-canyon flow with rough building facets heated by a given temperature. The model is applied to a canyon with the aspect ratio of unity for two idealized heating scenarios: (1) the roof and the entire upstream wall are heated, named as ‘assisting cases’, and (2) the roof and the entire downstream wall are heated, named as ‘opposing cases’. These facets were heated up to 15 K above the air temperature. A wall function for temperature is proposed for a rough facet with an assumption that the thermal roughness length, z _0T, is much smaller than the aerodynamic roughness length, z ₀. It is demonstrated that the sensible heat flux and canyon-air temperature are significantly influenced by the near-facet process that is parametrized by z _0T as the primary factor; other processes such as in-canyon mixing and roof-level exchange are secondary. This new finding strongly suggests that it is vital to choose an appropriate value of z _0T in a numerical simulation of street-canyon flows with the facet-air exchange processes of heat or any scalar. The finding also raises an awareness of the demand for carefully designed laboratory or field experiments of quantifying z _0T values for various urban surfaces. For the opposing cases, an unsteady penetrating narrow updraft zone appears occasionally along the heated wall and this feature is consistent field observations. The unique result indicates the superior capability of LES. The results of this study can be used to guide the parametrization of turbulent processes inside the urban canopy layer.     

Large-Eddy Simulation of Flow and Pollutant Transports in and Above Two-Dimensional Idealized Street Canyons

A large-eddy simulation (LES) model, using the one-equation subgrid-scale (SGS) parametrization, was developed to study the flow and pollutant transport in and above urban street canyons. Three identical two-dimensional (2D) street canyons of unity aspect ratio, each consisting of a ground-level area source of constant pollutant concentration, are evenly aligned in a cross-flow in the streamwise direction x. The flow falls into the skimming flow regime. A larger computational domain is adopted to accurately resolve the turbulence above roof level and its influence on the flow characteristics in the street canyons. The LES calculated statistics of wind and pollutant transports agree well with other field, laboratory and modelling results available in the literature. The maximum wind velocity standard deviations σ _i in the streamwise (σ _u ), spanwise (σ _v ) and vertical (σ _w ) directions are located near the roof-level windward corners. Moreover, a second σ _w peak is found at z ≈ 1.5h (h is the building height) over the street canyons. Normalizing σ _i by the local friction velocity u _*, it is found that σ _u /u _* ≈ 1.8, σ _v /u _* ≈ 1.3 and σ _w /u _* ≈ 1.25 exhibiting rather uniform values in the urban roughness sublayer. Quadrant analysis of the vertical momentum flux u′′w′′ shows that, while the inward and outward interactions are small, the sweeps and ejections dominate the momentum transport over the street canyons. In the x direction, the two-point correlations of velocity R _v,x and R _w,x drop to zero at a separation larger than h but R _u,x (= 0.2) persists even at a separation of half the domain size. Partitioning the convective transfer coefficient Ω _T of pollutant into its removal and re-entry components, an increasing pollutant re-entrainment from 26.3 to 43.3% in the x direction is revealed, suggesting the impact of background pollutant on the air quality in street canyons.     

Turbulence measurements above a pine forest

Eddy fluxes of momentum, sensible and latent heat, and turbulence spectra measured over the Thetford Forest during 10 days in the Spring of 1973 are described. The measured total heat flux (H + E) for 122 20-min periods agreed closely on average with independent estimates from an energy balance method. There was evidence that the energy balance data gave small systematic overestimates of available energy during the hours before noon, compensated by slight underestimates for the remainder of the day. A comparison of measured wind speeds and friction velocities in neutral stability confirmed the validity of the aerodynamic method for estimating momentum fluxes at heights of a few roughness lengths above the canopy. In stable conditions the log-linear wind profileU = (u _*/k)(ln ((z -d)/z _o) + (z -d -z _o)/L) with = 3.4 ± 0.4 provided a good fit to the data. Spectra in unstable conditions were generally more sharply peaked than those measured by other workers over smoother terrain: differences were less marked in the case of vertical velocity in stable conditions. Temperature spectra in these stable conditions showed high energy at relatively low wavenumbers, andwT cospectra showed a cospectral gap; both of these results were associated with an intermittent sawtooth structure in the temperature fluctuations.Now at the Meteorological Office, Bracknell     

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.     

Variance Method to Determine Turbulent Fluxes of Momentum And Sensible Heat in The Stable Atmospheric Surface Layer

Evidence is presented that in the stable atmospheric surface layer turbulent fluxes of heat and momentum can be determined from the standard deviations of longitudinal wind velocity and temperature, σ _u and σ _T respectively, measured at a single level. An attractive aspect of this method is that it yields fluxes from measurements that can be obtained with two-dimensional sonic anemometers. These instruments are increasingly being used at official weather stations, where they replace the standard cup anemometer–wind vane system. With methods such as the one described in this note, a widespread, good quality, flux network can be established, which would greatly benefit the modelling community. It is shown that a ‘variance’ dimensionless height (ζ _σ) defined from σ _u and σ _T is highly related to the ‘conventional’ dimensionless stability parameter ζ=z/L, where z is height and L is the Obukhov length. Empirical functions for ζ _σ are proposed that allow direct calculation of heat and momentum fluxes from σ _u and σ _T. The method performs fairly well also during a night of intermittent turbulence.     

A Comparative Study of the Atmospheric Layers below First Lifting Condensation Level for Instantaneous Pre-Monsoon Thunderstorm Occurrence at Agartala (23o30’N, 91o15’E) and Ranchi (23o14’N, 85o14’E) of India

An attempt has been made to investigate the role of vertical wind shear, corrective instability and the thermodynamic parameter (θes - θe) below the first lifting condensation level (FLCL) in the occurrence of instanta-neous premonsoon thunderstorm over Agartala (AGT) and Ranchi (RNC) at 12 GMT Radiosonde data of 1988 have been utilized here. The study has however been confined to 1000 hPa-500 hPa range at most Here the convectively unstable layers with positive vertical wind shear upto 500 hPa have been termed as ‘Fa?vourable Layers’ (FL) and the level at which an initially stable layer turns out to be convectively unstable for the first time has been termed as ‘Transition Level’ (TL). It is observed that the changes in vertical wind shear are positive at TL at the time of occurrence of thunderstorm (TS) and the corresponding change is negative on fair-weather situa?tion Moreover, the 90% confidence interval for (θes - θe) reveals that for AGT the upper layer thermodynamic characteristic is important at the time of occurrence of TS whereas for RNC, the value of (θes - θe) at the surface is much more effective     

The stability of large—scale horizontal air motion in the non—linear basic zephyr flow under the effect of rossby parameter

The stability of large-scale horizontal motion in the atmosphere is discussed in this paper by using qualitative analysis theory of non-linear ordinary differential equations. Both the non-linear distribution of basic Zephyr flow and the variation of geostrophic vorticity along the latitude (f=f0 + βδy ) are all included in this paper's mathematical model so as to analogue the background field of large-scale horizontal air motion more really in the rotating reference frame of the earth. Some significant results are drawn out from this paper and the conclusions of Li(1986)'s and Wan et al.(1990)'s are extended widely.     

Scaling Properties of Temperature Spectra and Heat-Flux Cospectra in the Surface Friction Layer Beneath an Unstable Outer Layer

Temperature variance and temperature power spectra in the unstable surface layer have always presented a problem to the standard Monin-Obukhov similarity model. Recently that problem has intensified with the demonstration by Smedman et al. (2007, Q J Roy Meteorol Soc 133: 37–51) that temperature spectra and heat-flux cospectra can have two distinct peaks in slightly unstable conditions, and by McNaughton et al. (2007, Nonlinear Process Geophys 14: 257–271) who showed that the wavenumber of the peak of temperature spectra in a convective boundary layer (CBL), closely above the surface friction layer (SFL), can be sensitive to the CBL depth, z _i. Neither the two-peak form at slight instability nor the dependence of peak position on z _i at large instability is compatible with the Monin-Obukhov model. Here we examine the properties of temperature spectra and heat-flux cospectra from between these extremes, i.e. from within the unstable SFL, in two experiments. The analysis is based on McNaughton’s model of the turbulence structure in the SFL. According to this model, heat is transported through most of the SFL by sheet plumes, created by the action of impinging outer eddies. The smallest and most effective of these outer eddies have sizes that scale on SFL depth, z _s. The z _s-scale eddies and plumes are organised within the overall convection pattern in the CBL, and in turn they organise the motion of smaller eddies within the SFL, whose sizes scale on height, z. The main experimental results are: (1) the peak amplitudes of the temperature spectra in the SFL are collapsed with a scaling factor (z_sz)^1/3e_o^2/3{(z_{\rm s}z)^{1/3}\varepsilon_{\rm o}^{2/3}} divided by the square of the surface temperature flux, where e_o{\varepsilon_{\rm o}} is the dissipation rate of turbulent energy in the outer CBL (above the SFL); (2) the peak wavenumbers of the temperature spectra are collapsed with the mixed length scale (z _i z _s)^1/2; (3) the peak wavenumbers of the heat-flux cospectra are collapsed with the doubly-mixed length scale (z _i z _s)^1/4 z ^1/2; (4) for z/z _s < 0.03, the peak in the cospectrum is replaced by another peak at a wavenumber about a magnitude larger. This peak’s position scales on z; (5) all these findings are consistent with the observations of Smedman et al.     

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.     

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.     

Formation of horizontal convective rolls in urban areas

The formation of horizontal convective rolls (HCRs) in urban areas is investigated in this paper using observations and fine-scale numerical simulations. Cloud streets organized parallel to the mean boundary-layer wind (a manifestation of HCRs) are seen in the Fengyun-2C satellite imagery around local noon in Beijing. Observed vertical velocity and horizontal wind fields from an urban wind profiler suggest that the time scale for alternating updraft and downdraft in the boundary layer is about 30 min, and the length of the updraft/downdraft is about 9 km. Numerical simulations show that most HCRs occur in the urban areas with − z_i / L < 25 (z_i: the boundary-layer depth, L: the Monin–Obukhov length). Sensitivity tests reveal that HCRs are common in urban boundary layers, while rural areas are more conducive to forming cellular convection; the aspect ratio of HCRs in urban areas is smaller than the typical value over natural landscapes.