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。     

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

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

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

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

Derivation of the relationship between the Obukhov stability parameter and the bulk Richardson number for flux-profile studies

Using the relationship between the bulk Richardson numberR _z and the Obukhov stability parameterz/L (L is the Obukhov length), formally obtained from the flux-profile relationships, methods to estimatez/L are discussed. Generally,z/L can not be uniquely solved analytically from flux-profile relationships, and it may be defined using routine observations only by iteration. In this paper, relationships ofz/L in terms ofR _z obtained semianalytically were corrected for variable aerodynamic roughnessz ₀ and for aerodynamic-to-temperature roughness ratiosz ₀/z _T, using the flux-profile iteration procedure. Assuming the so-called log-linear profiles to be valid for the nearneutral and moderately stable region (z/L<1), a simple relationship is obtained. For the extension to strong stability, a simple series expansion, based on utilisation of specified universal functions, is derived.For the unstable region, a simple form based on utilisation of the Businger-Dyer type universal functions, is derived. The formulae yield good estimates for surfaces having an aerodynamic roughness of 10^–5 to 10^–1 m, and an aerodynamic-to-temperature roughness ratio ofz ₀/z _T=0.5 to 7.3. When applied to the universal functions, the formulae yield transfer coefficients and fluxes which are almost identical with those from the iteration procedure.     

An analytical method for the determination of the roughness parameters over complex regions

The values of roughness length for momentum z ₀and zero-plane displacement d ₀over a hilly rough complex region with vegetation were evaluated without any assumption concerning z ₀and d ₀.It was found that for widely scattered profile data, the method of least squares will not give a reasonable result in determining the roughness parameters. For this purpose, the method of maximum correlation was introduced instead. This method gave a fair result for captive balloon observations conducted in hilly terrain mainly covered with forest in the northwestern part of the Kanto Plain, Japan.     

Momentum and scalar transfer coefficients over aerodynamically smooth antarctic surfaces

Vertical profiles of wind speed, temperature and humidity were used to estimate the roughness lengths for momentum (z ₀), heat (z _H ) and moisture (z _Q) over smooth ice and snow surfaces. The profile-measurements were performed in the vicinity of a blue ice field in Queen Maud Land, East Antarctica. The values ofz ₀ over ice (3·10^–6 m) seem to be the smallest ever obtained over permanent, natural surfaces. The settling of snow on the ice and the loss of momentum at saltating snow particles serve as momentum dissipating processes during snow-drift events, expressed as a strong dependence ofz ₀ on u_#.The scalar roughness lengths and surface temperature can be evaluated from the temperature and humidity profile measurements if the ratioz _H /z _Q is specified. This new method circumvents the difficult measurement of surface temperature. The scalar roughness lengths seem to be approximately equal toz0 for a large range of low roughness Reynolds numbers, despite the frequent occurrence of drifting snow. Possible reasons for this agreement with theory of non-saltating flow are discussed.     

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

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

Turbulent dispersion in the atmospheric surface layer

By non-dimensionalizing a trajectory-simulation (TS) model of turbulent dispersion, it is shown that the dimensionless concentration z ₀cu_*/kQ (cu _*/kQ) due to a continuous line (area) source of strength Q in the atmospheric surface layer depends only on z/z ₀, x/z ₀, z ₀/L and z _s/z₀, where z _s is the source height. The TS model is used to tabulate concentration profiles due to ground-level line and area sources. Concentration profiles generated by the TS model for elevated sources are shown to be inconsistent with the Reciprocal Theorems of Smith (1957) and it is suggested that this is because the flux-mean gradient closure scheme inherent in the Reciprocal Theorem is invalid for an elevated source.     

Measurements of spray at an air-water interface

The spray content in the surface boundary layer above an air—water interface was determined by a series of measurements at various feteches and wind speeds in a laboratory facility. The droplet flux density N(z) can be described in terms of the scaling flux density N_* and von Karman constant K throguh the equation, N(z)/N_* = −(1/K) ln(z/z_0d) where z is height above the mean water level and z_0d is the droplet boundary layer thickness. N_* is given by a unique relationship in terms of the roughness Reynolds number u_*σ/ν where σ is the root-mean-square surface displacement. Spray inception occurred for u_* 0.3. The dominant mode of spray generation in the present and most other laboratory tests, as well as in available field data, appears to be bubble bursting.     

Dependence of geostrophic drag on intensity of convection,baroclinicity, and acceleration

This paper examines the practical importance of stability, baroclinicity, and acceleration in the bulk ABL similarity formulations, in light of the random errors inherent in field measurements. This is done by propagating the measurement uncertainties through a theoretical model for the bulk ABL similarity functionsA ₀ andB ₀, under a range of assumed (but always unstable) conditions. It is shown that random measurement errors and acceleration effects may overwhelm most effects of baroclinicity and stability, once conditions are at least slightly unstable. Because of this, it is hard to discern a clear functional dependence ofA ₀ andB ₀ on degree of instability. Thus, for a given value ofh _i/z₀, whereh _i is the inversion height andz ₀ is the surface roughness, the geostrophic drag coefficient, which depends onA ₀ andB ₀, and weakly onh _i/z₀, may also be taken to be nearly independent of degree of instability.     

Radiometrically determined skin temperature and scalar roughness to estimate surface heat flux. Part I: Parameterization of radiometric scalar roughness

A series of experiments carried out in a pasture field during a growing season, allowed a radiometric determination of the scalar roughness for sensible heatz _oh,r . The values ofz _oh,r are shown to vary over the range of 10^–1–10^–7m both diurnally and seasonally, and an existing theoretical model for the estimation of scalar roughness for sensible heat is found to be inappropriate for the precise estimation ofz _oh,r . To parameterizez _oh,r better, a multiple regression analysis was performed, with predictor candidates such as solar elevation, solar radiationR _s , leaf area index LAI, canopy height, the ratio of the solar radiation and the extraterrestrial radiationR _s /R _e , the ratio of the direct and the total solar radiationR _d /R _s , and the roughness Reynolds number among others. The best regression equation which usesR _s , LAI,R _s /R _e , andR _d /R _s is derived withr=0.75; with smaller numbers of predictors, values ofr tend to deteriorate gradually down tor=0.52 when only one predictor, LAI, was incorporated into the equation.     

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

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

Heat and mass transfer to and from surfaces with dense vegetation or similar permeable roughness

A differential equation is obtained to describe the concentration of passive admixtures (water vapor, sensible heat, pollutants, CO₂, etc.) of turbulent flow inside a dense and uniform vegetational canopy. The profiles of eddy diffusivity, wind speed and shear stress are assumed to be exponential decay functions of depth below the top of the canopy. This equation is solved for the case of a vegetation with constant concentration of the admixture at the foliage surfaces. The solution is used to formulate bulk mass or heat transfer coefficients, which can be applied to practical problems involving surfaces covered with a vegetation or with similar porous or fibrous roughness elements. The results are shown to be consistent with experimental data presented by Chamberlain (1966), Garratt and Hicks (1973) and Garratt (1978). Calculations with the model illustrate that, as compared to its behavior over surfaces with bluff roughness elements, ln(z ₀/z _0c ) (wherez ₀ is the momentum roughness andz _0c , the scalar roughness) for permeable roughness elements is relatively insensitive tou _* and practically independent ofz ₀.     

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.     

The extent of the unstable Monin-Obukhov layer for temperature and humidity above complex hilly grassland

Potential temperature, specific humidity and wind profiles measured by radiosondes under unstable but windy conditions during FIFE in northeastern Kansas were analyzed within the framework of Monin-Obukhov similarity. Around 86% of these profiles were found to have a height range over which the similarity, formulated in terms of the Businger-Dyer functions, is valid and for which the resulting surface fluxes are in good agreement with independent measurements at ground stations. When scaled with the surface roughness z ₀ = 1.05 m and the displacement height d ₀ = 26.9 m, for the potential temperature this height range was 45 (±31) (z – d ₀ )/z ₀ 104 (±54) and the comparison of the profile-derived surface fluxes with the independent measurements gave a correlation coefficient of r = 0.96. For the specific humidity these values are 42 (±29) (z – d ₀ )/z ₀ 96 (±38) and r = 0.94. In terms of the height of the bottom of the inversion H _i , in the morning hours the upper limit of (z – d ₀ ) in the Monin-Obukhov layer is approximately 0.3H _i , whereas for a fully developed ABL it is closer to 0.1H _i . Probably, as a result of the short sampling times and perhaps also of the small gradients under the windy conditions, the exact height range of validity was difficult to establish from a mere inspection of these profiles.     

A note on finite-difference schemes for the surface and planetary boundary layers

The solution of the planetary boundary-layer equations by finite-difference methods has recently become very popular. Among recent papers using such methods, several use somewhat arbitrary finite-difference meshes and some do not make use of a constant flux or wall layer near the ground. It is shown that the use of finite differences right down to the ground can be a very inaccurate procedure when used in conjunction with an eddy viscosity or mixing length proportional to (z +z ₀) orz near the ground. Such an approach can lead to results that are highly dependent on the finite-difference scheme used and virtually independent of the roughness length,z ₀. A scheme using an expanding grid, based on the form chosen for mixing length or eddy viscosity, is proposed which gives good results with or without a surface layer in the case of a neutrally stratified atmosphere.     

Aerodynamic roughness of vegetated surfaces

Available experimental results indicate that as the density of roughness elements over a horizontally homogeneous surface is varied, the roughness length, z ₀, varies in a manner that exhibits a maximum at intermediate density values. In an attempt to explain this behaviour, the available analytical solutions for the wind profile inside dense homogeneous canopies were reviewed. The review indicated that the variation of z ₀ with density depends on the interrelationship between the leaf density, a, and the mixing length, l. In view of this finding, a numerical model was devised based on a simple rule for constructing mixing-length profiles in the canopy. The rule states that the actual value of l is the maximum possible under the two constraints: l l _i and ¦dl/dz¦ k, where k is the von Karman constant and the intrinsic mixing length, l _i, is a function of the local internal structure of the canopy. The model which ensures a smooth transition from dense to thin canopy, was used to reproduce the observed maximum of z ₀. The model is also capable of handling vertically non-homogeneous canopies.     

Spectra of temperature derivatives in the atmospheric surface layer

Measured spectra ofθ _x,θ _y,θ _z, the derivatives of temperature in streamwise, lateral and vertical directions, respectively, indicate that the spectral densities ofθ _z andθ _y are nearly similar but significantly different from the spectral density ofθ _x. The high-frequency parts of the three spectra satisfy, in a qualitative sense, local isotropy requirements. In the high-frequency end of the inertial subrange, the relative behaviour of spectra ofθ _x,θ _y andθ _z is also consistent with local isotropy.     

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.     

An empirical expression for aerodynamic resistance in the unstable boundary layer

In unstable conditions, the set of equations defining the aerodynamic resistance to sensible heat transfer, r _a , cannot be solved analytically. An iterative technique must be used to obtain r _a exactly, but this is cumbersome and time consuming. In this paper, a new, empirical equation is presented relating the ratio, Q, of the aerodynamic resistances in neutral and unstable conditions, to the bulk Richardson number, Ri _B . The equation takes the form Q = a + b(–Ri) ^c , where a, b and c are empirical functions of (z – d)/z _om . This model is shown to predict r _awith a mean absolute error of 0.06 s m^–1 over the ranges -15 < Ri _B < 0 and 10 < (z – d)/z _om < 2300. Statistical comparison with other equations that have been proposed for r _a in unstable conditions indicates the superior precision of the model presented here.