Optimizing the Determination of Roughness Parameters for Model Urban Canopies

We present an objective optimization procedure to determine the roughness parameters for very rough boundary-layer flow over model urban canopies. For neutral stratification the mean velocity profile above a model urban canopy is described by the logarithmic law together with the set of roughness parameters of displacement height d, roughness length \(z_0\), and friction velocity \(u_*\). Traditionally, values of these roughness parameters are obtained by fitting the logarithmic law through (all) the data points comprising the velocity profile. The new procedure generates unique velocity profiles from subsets or combinations of the data points of the original velocity profile, after which all possible profiles are examined. Each of the generated profiles is fitted to the logarithmic law for a sequence of values of d, with the representative value of d obtained from the minima of the summed least-squares errors for all the generated profiles. The representative values of \(z_0\) and \(u_*\) are identified by the peak in the bivariate histogram of \(z_0\) and \(u_*\). The methodology has been verified against laboratory datasets of flow above model urban canopies.     

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。     

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.     

Improvements in Sensible Heat-Flux Parametrization in the High-Resolution Regional Model (HRM) Through the Modified Treatment of the Roughness Length for Heat

We discuss the impact of the differential treatment of the roughness lengths for momentum and heat ( $z_{0\mathrm{m}}$ and $z_{0\mathrm{h}}$ ) in the flux parametrization scheme of the high-resolution regional model (HRM) for a heterogeneous terrain centred around Thiruvananthapuram, India (8.5°N, 76.9°E). The magnitudes of sensible heat flux (H) obtained from HRM simulations using the original parametrization scheme differed drastically from the concurrent in situ observations. With a view to improving the performance of this parametrization scheme, two distinct modifications are incorporated: (1) In the first method, a constant value of 100 is assigned to the $z_{0\mathrm{m}}/z_{0\mathrm{h}}$ ratio; (2) and in the second approach, this ratio is treated as a function of time. Both these modifications in the HRM model showed significant improvements in the H simulations for Thiruvananthapuram and its adjoining regions. Results obtained from the present study provide a first-ever comparison of H simulations using the modified parametrization scheme in the HRM model with in situ observations for the Indian coastal region, and suggest a differential treatment of $z_{0\mathrm{m}}$ and $z_{0\mathrm{h}}$ in the flux parametrization scheme.     

On the Mechanism of Air Pollutant Removal in Two-Dimensional Idealized Street Canyons: A Large-Eddy Simulation Approach

Flow resistance, ventilation, and pollutant removal for idealized two-dimensional (2D) street canyons of different building-height to street-width (aspect) ratios $AR$ are examined using the friction factor $f$ , air exchange rate (ACH), and pollutant exchange rate (PCH), respectively, calculated by large-eddy simulation (LES). The flows are basically classified into three characteristic regimes, namely isolated roughness, wake interference, and skimming flow, as functions of the aspect ratios. The LES results are validated by various experimental and numerical datasets available in the literature. The friction factor increases with decreasing aspect ratio and reaches a peak at $AR = 0.1$ in the isolated roughness regime and decreases thereafter. As with the friction factor, the ACH increases with decreasing aspect ratio in the wake interference and skimming flow regimes, signifying the improved aged air removal for a wider street canyon. The PCH exhibits a behaviour different from its ACH counterpart in the range of aspect ratios tested. Pollutants are most effectively removed from the street canyon with $AR = 0.5$ . However, a minimum of PCH is found nearby at $AR = 0.3$ , at which the pollutant removal is sharply weakened. Besides, the ACH and PCH are partitioned into the mean and turbulent components to compare their relative contributions. In line with our earlier Reynolds-averaged Navier–Stokes calculations (Liu et al., Atmos Environ 45:4763–4769, 2011), the current LES shows that the turbulent components contribute more to both ACH and PCH, consistently demonstrating the importance of atmospheric turbulence in the ventilation and pollutant removal for urban areas.     

Parametrization of orographical effects in the planetary boundary layer

Studies of the influence of orography on the dynamics of atmospheric processes usually assume the following relation as a boundary condition at the surface of the Earth, or at the top of the planetary layer: $$w = u\frac{{\delta z_0 }}{{\delta x}} + v\frac{{\delta z_0 }}{{\delta y}}$$ where u, v and w are the components of wind velocity along the x, y and z axes, respectively, and z ₀ = z₀(x, y) is the equation of the Earth's orography. We see that w, and consequently the influence of orography on the dynamics of atmospheric processes, depend on the wind (u, v) and on the slope of the obstacle (δz ₀/δx, δz₀/δy). In the present work, it is shown that the above relation for w is insufficient to describe the influence of orography on the dynamics of the atmosphere. It is also shown that the relation is a particular case of the expression: $$\begin{gathered} w_h = \left| {v_g } \right|\left[ {a_1 (Ro,s)\frac{{\delta z_0 }}{{\delta x}} + a_2 (Ro,s)\frac{{\delta z_0 }}{{\delta y}}} \right] + \hfill \\ + \frac{{\left| {v_g } \right|^2 }}{f}\left[ {b_1 (Ro,s)\frac{{\delta ^2 z_0 }}{{\delta x^2 }} + b_2 (Ro,s)\frac{{\delta ^2 z_0 }}{{\delta y^2 }} + b_3 (Ro,s)\frac{{\delta ^2 z_0 }}{{\delta x\delta y}}} \right] \hfill \\ \end{gathered} $$ where ¦vv _g¦ is the strength of the geostrophic wind, a ₁, a₂, b₁, b₂, b₃ are functions of Rossby number Ro and of the external stability parameter s. The above relation is obtained with the help of similarity theory, with a parametrization of the planetary boundary layer. Finally, the authors show that a close connection exists between the effects described by the above expression and cyclo- and anticyclogenesis.     

Surface influence upon vertical profiles in the nocturnal boundary layer

Near-surface wind profiles in the nocturnal boundary layer, depth h, above relatively flat, tree-covered terrain are described in the context of the analysis of Garratt (1980) for the unstable atmospheric boundary layer. The observations at two sites imply a surface-based transition layer, of depth z _*, within which the observed non-dimensional profiles Φ _M ⁰ are a modified form of the inertial sub-layer relation \(\Phi _M \left( {{z \mathord{\left/ {\vphantom {z L}} \right. \kern-0em} L}} \right) = \left( {{{1 + 5_Z } \mathord{\left/ {\vphantom {{1 + 5_Z } L}} \right. \kern-0em} L}} \right)\) according to $$\Phi _M^{\text{0}} \simeq \left( {{{1 + 5z} \mathord{\left/ {\vphantom {{1 + 5z} L}} \right. \kern-\nulldelimiterspace} L}} \right)\exp \left[ { - 0.7\left( {{{1 - z} \mathord{\left/ {\vphantom {{1 - z} z}} \right. \kern-\nulldelimiterspace} z}_ * } \right)} \right]$$ , where z is height above the zero-plane displacement and L is the Monin-Obukhov length. At both sites the depth z _* is significantly smaller than the appropriate neutral value (z _*N ) found from the previous analysis, as might be expected in the presence of a buoyant sink for turbulent kinetic energy.     

A Scale-Adaptive Approach for Spatially-Varying Urban Morphology Characterization in Boundary Layer Parametrization Using Multi-Resolution Analysis

Urban morphology characterization is crucial for the parametrization of boundary-layer development over urban areas. One complexity in such a characterization is the three-dimensional variation of the urban canopies and textures, which are customarily reduced to and represented by one-dimensional varying parametrization such as the aerodynamic roughness length $z_{0}$ and zero-plane displacement $d$ . The scope of the paper is to provide novel means for a scale-adaptive spatially-varying parametrization of the boundary layer by addressing this 3-D variation. Specifically, the 3-D variation of urban geometries often poses questions in the multi-scale modelling of air pollution dispersion and other climate or weather-related modelling applications that have not been addressed yet, such as: (a) how we represent urban attributes (parameters) appropriately for the multi-scale nature and multi-resolution basis of weather numerical models, (b) how we quantify the uniqueness of an urban database in the context of modelling urban effects in large-scale weather numerical models, and (c) how we derive the impact and influence of a particular building in pre-specified sub-domain areas of the urban database. We illustrate how multi-resolution analysis (MRA) addresses and answers the afore-mentioned questions by taking as an example the Central Business District of Oklahoma City. The selection of MRA is motivated by its capacity for multi-scale sampling; in the MRA the “urban” signal depicting a city is decomposed into an approximation, a representation at a higher scale, and a detail, the part removed at lower scales to yield the approximation. Different levels of approximations were deduced for the building height $\bar{{H}}$ and planar packing density $\lambda _\mathrm{p}$ . A spatially-varying characterization with a scale-adaptive capacity is obtained for the boundary-layer parameters (aerodynamic roughness length $z_{0}$ and zero-plane displacement $d$ ) using the MRA-deduced results for the building height and the planar packing density with a morphometric model; an attribute that is shown to be of great advantage to multi-scale and multi-resolution numerical weather prediction models.     

Aerodynamic Parameters of a UK City Derived from Morphological Data

Detailed three-dimensional building data and a morphometric model are used to estimate the aerodynamic roughness length z ₀ and displacement height d over a major UK city (Leeds). Firstly, using an adaptive grid, the city is divided into neighbourhood regions that are each of a relatively consistent geometry throughout. Secondly, for each neighbourhood, a number of geometric parameters are calculated. Finally, these are used as input into a morphometric model that considers the influence of height variability to predict aerodynamic roughness length and displacement height. Predictions are compared with estimations made using standard tables of aerodynamic parameters. The comparison suggests that the accuracy of plan-area-density based tables is likely to be limited, and that height-based tables of aerodynamic parameters may be more accurate for UK cities. The displacement heights in the standard tables are shown to be lower than the current predictions. The importance of geometric details in determining z ₀ and d is then explored. Height variability is observed to greatly increase the predicted values. However, building footprint shape only has a significant influence upon the predictions when height variability is not considered. Finally, we develop simple relations to quantify the influence of height variation upon predicted z ₀ and d via the standard deviation of building heights. The difference in these predictions compared to the more complex approach highlights the importance of considering the specific shape of the building-height distributions. Collectively, these results suggest that to accurately predict aerodynamic parameters of real urban areas, height variability must be considered in detail, but it may be acceptable to make simple assumptions about building layout and footprint shape.     

Aerodynamic Roughness Length of Fresh Snow

This study presents the results from a series of wind-tunnel experiments designed to investigate the aerodynamic roughness length z ₀ of fresh snow under no-drift conditions. A two-component hot-film anemometer was employed to obtain vertical profiles of velocity statistics in a zero pressure gradient turbulent boundary layer for flow over naturally deposited snow surfaces. The roughness of these snow surfaces was measured by means of digital photography to capture characteristic length scales that can be related to z ₀. Our results show that, under aerodynamically rough conditions, the mean value of the roughness length for fresh snow is \({\langle{z}_{0}\rangle= 0.24}\) mm with a standard deviation σ(z ₀) = 0.05 mm. In this study, we show that variations in z ₀ are associated with variations in the roughness geometry. The roughness measurements suggest that the estimated values of z ₀ are consistent with the presence of irregular roughness structures that develop during snowfalls that mimic ballistic deposition processes.     

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.     

Intercomparison of Methods for the Simultaneous Estimation of Zero-Plane Displacement and Aerodynamic Roughness Length from Single-Level Eddy-Covariance Data

We applied three approaches to estimate the zero-plane displacement $d$ through the aerodynamic measurement height $z$ (with $z = z_{m}- d$ and $z_{m}$ being the measurement height above the surface), and the aerodynamic roughness length $z_{0}$ , from single-level eddy covariance data. Two approaches (one iterative and one regression-based) were based on the universal function in the logarithmic wind profile and yielded an inherently simultaneous estimation of both $d$ and $z_{0}$ . The third approach was based on flux–variance similarity, where estimation of $d$ and consecutive estimation of $z_{0}$ are independent steps. Each approach was further divided into two methods differing either with respect to the solution technique (profile approaches) or with respect to the variable (variance of vertical wind and temperature, respectively). All methods were applied to measurements above a large, growing wheat field where a uniform canopy height and its frequent monitoring provided plausibility limits for the resulting estimates of time-variant $d$ and $z_{0}$ . After applying, for each approach, a specific data filtering that accounted for the range of conditions (e.g. stability) for which it is valid, five of the six methods were able to describe the temporal changes of roughness parameters associated with crop growth and harvest, and four of them agreed on $d$ to within 0.3 m most of the time. Application of the same methods to measurements with a more heterogeneous footprint consisting of fully-grown sugarbeet and a varying contribution of adjacent harvested fields exhibited a plausible dependence of the roughness parameters on the sugarbeet fraction. It also revealed that the methods producing the largest outliers can differ between site conditions and stability. We therefore conclude that when determining $d$ for canopies with unknown properties from single-level measurements, as is increasingly done, it is important to compare the results of a number of methods rather than rely on a single one. An ensemble average or median of the results, possibly after elimination of methods that produce outliers, can help to yield more robust estimates. The estimates of $z_{0}$ were almost exclusively physically plausible, although $d$ was considered unknown and estimated simultaneously with the methods and results described above.     

Surface Heterogeneity Effects on Regional-Scale Fluxes in the Stable Boundary Layer: Aerodynamic Roughness Length Transitions

The effects of abrupt streamwise transitions of the aerodynamic roughness length ( $z_\mathrm{o}$ z o ) on the stable atmospheric boundary layer are evaluated using a series of large-eddy simulations based on the first Global Energy and Water Cycle Experiment Atmospheric Boundary Layer intercomparison study (GABLS1). Four $z_\mathrm{o}$ z o values spanning three orders of magnitude are used to create all possible binary distributions with each arranged into patches of characteristic length scales equal to roughly one-half, one, and two times the equivalent homogeneous boundary-layer height. The impact of the heterogeneity on mean profiles of wind speed and temperature, on surface fluxes of heat and momentum, and on internal boundary-layer dynamics are considered. It is found that $z_\mathrm{o}$ z o transitions do not significantly alter the functional relationship between the average surface fluxes and the mean profiles of wind speed and potential temperature. Although this suggests that bulk similarity theory is applicable for modelling the stable boundary layer over $z_\mathrm{o}$ z o heterogeneity, effective surface parameters must still be specified. Existing models that solve for effective roughness lengths of momentum and heat are evaluated and compared to values derived from the simulation data. The existing models are unable to accurately reproduce both the values of the effective aerodynamic roughness lengths and their trends as functions of patch length scale and stability. A new model for the effective aerodynamic roughness length is developed to exploit the benefits of the other models tested. It accurately accounts for the effects of the heterogeneity and stratification on the blending height and effective aerodynamic roughness length. The new model provides improved average surface fluxes when used with bulk similarity.     

Periodic solutions of the set of equations governing the nonadiabatic convection of dry isolated thermals

The changes with timet of a temperature deviation δT(t,α) and of a vertical velocityW _i(t,α) of an isolated dry thermal have been investigated theoretically. Solutions for the functionW _i(t, α) have been derived for stable and unstable environmental stratifications. Comparing these solutions with the corresponding ones for the rise of an adiabatic thermal yield some interesting conclusions. Firstly, there is the evident relation between the rate of entrainment of environmental air (expressed by the parameter α=(1/M _i) dM _i/dz whereM _i is the mass of the thermal) and the vertical velocity of the thermal: an increase in α decreases the velocity. Two similar thermals in stably stratified surroundings, one of them moving adiabatically (α=0) the other nonadiabatically (α>0), would rise for the same length of timet ₂=π/N, whereN is a typical Brunt-Väisälä frequency, but with different velocities and to different heights: the ascent timet ₂ depends only on environmental parameters. In an unstable stratification, the vertical non-adiabatic velocity of the thermal, instead of increasing without limit, tends towards a finite asymptotic velocity $$W_t (\infty ) = (\sqrt { - \mathcal{N}^2 } )/\alpha $$ the value of which depends upon both the stratification of the surroundings and upon the entrainment rate α. In a real atmosphere, where additional retarding forces exist, the motion will certainly be damped.     

Velocity Adjustment and Passive Scalar Diffusion in and Above an Urban Canopy in Response to Various Approach Flows

We used wind-tunnel experiments to investigate velocity-field adjustment and scalar diffusion behaviour in and above urban canopies located downwind of various roughness elements. Staggered arrays of rectangular blocks of various heights H and plan area ratios λ_p were used to model the urban canopies. The velocity field in the roughness sublayer (height \({z \lesssim 2H}\)) reached equilibrium at distances proportional to \({\sqrt{L_{\rm c}H}}\) where L _c is the canopy-drag length scale determined as a function of λ_p and the block side length L. A distance of about \({20\sqrt{L_{\rm c}H}}\) was required for adjustment at z = H/2 (in the canopy), and a distance of about \({10\sqrt{L_{\rm c}H}}\) was required at z = 2H (near the top of the roughness sublayer). Diffusion experiments from a ground emission source revealed that differences in upwind roughness conditions had negligible effects on the plume growth near the source (up to a few multiples of L from the source) if the source was located at a fetch F larger than about \({10\sqrt{L_{\rm c}H}}\) from the upwind edge of the canopy. However, at locations farther downwind (more than several multiples of L from the source), upwind conditions had considerable effects on the plume growth. For a representative urban canopy, it was shown that a much larger fetch than required for velocity-field adjustment in the roughness sublayer was necessary to eliminate the effects of upwind conditions on plume widths at 24L downwind from the source.     

Hourly estimation of soil heat flux density at the soil surface with three models and two field methods

Heat flux density at the soil surface (G ₀) was evaluated hourly on a vegetal cover 0.08 m high, with a leaf area index of 1.07 m² m^?2, during daylight hours, using Choudhury et al. (Agric For Meteorol 39:283–297, 1987) ( $ G_0^{\text{rn}} $ ), Santanello and Friedl (J Appl Meteorol 42:851–862, 2003) ( $ G_0^{\text{s}} $ ), and force-restore ( $ G_0^{\text{fr}} $ ) models and the plate calorimetry methodology ( $ G_0^{\text{pco}} $ ), where the gradient calorimetry methodology (G _0R ) served as a reference for determining G ₀. It was found that the peak of G _0R was at 1 p.m., with values that ranged between 60 and 100 W m^?2 and that the G ₀/Rn relation varied during the day with values close to zero in the early hours of the morning and close to 0.25 in the last hours of daylight. The $ G_0^{\text{s}} $ model presented the best performance, followed by the $ G_0^{\text{rn}} $ and $ G_0^{\text{fr}} $ models. The plate calorimetry methodology showed a similar behavior to that of the gradient calorimetry referential methodology.     

étude expérimentale de la couche limite au-dessus d'un relief modéré proche d'une chaîne de montagne

Doppler sodar derived values of the temperature structure parameter C _infT ^sup2 , the vertical velocity variance ¯′w ², and the rate of dissipation of turbulent energy ?, were measured during unstable conditions above the Lannemezan heterogeneous site. The vertical profiles of these turbulent parameters, normalized by the classical convective scales are compared with those obtained using the same acoustic sounder above an homogeneous site during convective conditions. The typical decrease of C _infT ^sup2 as Z ^-4/3 is partially verified on the heterogeneous site: for the lower levels, C _infT ^sup2 exhibits an increase with Z whereas for the intermediate levels C _infT ^sup2 . decreases as Z ^-4/3. For the upper levels, C _infT ^sup2 increases with Z due to a signal-to-noise ratio lower than 1. The vertical profiles of ¯′w ² above the two sites are rather similar. However, near the base of the convective inversion Z _i , the values measured on the heterogeneous site are more scattered. The same scattering is also observed with the ? values; moreover, for the lower levels (Z<0.17Z _i ) the increase of ? as Z decreases is more important at the homogeneous site than at the heterogeneous one. It is suggested that these particular features observed at lower levels above the heterogeneous site are mainly related to a complex local boundary layer induced by the near environment of the sodar (vegetation and relief).     

Momentum- and Heat-Flux Parametrization at Dome C,Antarctica: A Sensitivity Study

An extensive meteorological observational dataset at Dome C, East Antarctic Plateau, enabled estimation of the sensitivity of surface momentum and sensible heat fluxes to aerodynamic roughness length and atmospheric stability in this region. Our study reveals that (1) because of the preferential orientation of snow micro-reliefs (sastrugi), the aerodynamic roughness length \(z_{0}\) varies by more than two orders of magnitude depending on the wind direction; consequently, estimating the turbulent fluxes with a realistic but constant \(z_{0}\) of 1 mm leads to a mean friction velocity bias of \(24\,\%\) in near-neutral conditions; (2) the dependence of the ratio of the roughness length for heat \(z_{0t}\) to \(z_{0}\) on the roughness Reynolds number is shown to be in reasonable agreement with previous models; (3) the wide range of atmospheric stability at Dome C makes the flux very sensitive to the choice of the stability functions; stability function models presumed to be suitable for stable conditions were evaluated and shown to generally underestimate the dimensionless vertical temperature gradient; as these models differ increasingly with increases in the stability parameter z / L, heat flux and friction velocity relative differences reached \(100\,\%\) when \(z/L > 1\); (4) the shallowness of the stable boundary layer is responsible for significant sensitivity to the height of the observed temperature and wind data used to estimate the fluxes. Consistent flux results were obtained with atmospheric measurements at heights up to 2 m. Our sensitivity study revealed the need to include a dynamical parametrization of roughness length over Antarctica in climate models and to develop new parametrizations of the surface fluxes in very stable conditions, accounting, for instance, for the divergence in both radiative and turbulent fluxes in the first few metres of the boundary layer.     

Characteristics of the Drag Coefficient in the Roughness Sublayer over a Complex Urban Surface

The statistics of momentum exchange in the urban roughness sublayer are investigated. The analysis focuses on the characteristics of the dimensionless friction velocity, \({u_{*}}/U\) , which is defined as the square root of the drag coefficient. The turbulence observations were made at a height of 47 m above the ground on the 325-m meteorological tower, which is located in a very inhomogeneous urban area in Beijing. Under neutral conditions, the dependence of the drag coefficient on wind speed varies with wind direction. When the airflow is from the area of densely built-up buildings, the drag coefficient does not vary with wind speed, while when the airflow is from the area covered by vegetation, the drag coefficient appears to decrease with increasing wind speed. Also, the drag coefficient does not vary monotonically with the atmospheric stability. Both increasing stability and increasing instability lead to the decrease of the drag coefficient, implying that the roughness length and zero-plane displacement may vary in urban areas.