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.     

Simplified expressions for vegetation roughness length and zero-plane displacement as functions of canopy height and area index

Using a previous treatment of drag and drag partition on rough surfaces, simple analytic expressions are derived for the roughness length (z ₀) and zero-plane displacement (d) of vegetated surfaces, as functions of canopy height (h) and area index (). The resulting expressions provide a good fit to numerous field and wind tunnel data, and are suitable for applications such as surface parameterisations in atmospheric models.     

Flux-gradient profiles for momentum and heat over an urban surface

Summary In this paper, we evaluate the applicability of flux-gradient relationships for momentum and heat for urban boundary layers within the Monin-Obukhov similarity (MOS) theory framework. Although the theory is widely used for smooth wall boundary layers, it is not known how well the theory works for urban layers. To address this problem, we measured the vertical profiles of wind velocity, air temperature, and fluxes of heat and momentum over a residential area and compared the results to theory. The measurements were done above an urban canopy whose mean height z_h is 7.3 m. 3-D sonic anemometers and fine wire thermocouples were installed at 4 heights in the region 1.5z_h < z < 4z_h. We found the following: (1) The non-dimensional horizontal wind speed has good agreement with the stratified logarithmic profile predicted using the semi-empirical Monin-Obukov similarity (MOS) function, when it was scaled by the surface friction velocity that is derived from the shear stress extrapolated to the roof-top level. (2) The scaled gradient of horizontal wind speed followed a conventional semi-empirical function for a flat surface at a level (z/z_h = 2.9), whereas, in the vicinity of the canopy height was larger than the commonly-used empirical relationship. (3) The potential temperature profile above the canopy shows dependency on the atmospheric stability and the scaled gradient of temperature is in good agreement with a conventional shear function for heat. In the case of heat, the dependency on height was not found. (4) The flux-gradient relationship for momentum and heat in the region 1.5z_h < z < 4z_h was rather similar to that for flat surfaces than that for vegetated canopies.     

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.     

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.     

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).     

Statistics of atmospheric turbulence within a natural black spruce forest canopy

Turbulence statistics were measured in a natural black-spruce forest canopy in southeastern Manitoba, Canada. Sonic anemometers were used to measure time series of vertical wind velocity (w), and cup anemometers to measure horizontal wind speed (s), above the canopy and at seven different heights within the canopy. Vertical profiles were measured during 25 runs on eight different days when conditions above the canopy were near-neutral.Profiles of s and of the standard deviation ( _w ) of w show relatively little scatter and suggest that, for this canopy and these stability conditions, profiles can be predicted from simple measurements made above the canopy. Within the canopy, a negative skewness and a high kurtosis of the w-frequency distributions indicate asymmetry and the persistence of large, high-velocity eddies. The Eulerian time scale is only a weak function of height within the canopy.Although w-power spectra above the canopy are similar to those in the free atmosphere, we did not observe an extensive inertial subrange in the spectra within the canopy. Also, a second peak is present that is especially prominent near the ground. The lack of the inertial subrange is likely caused by the presence of sources and sinks for turbulent kinetic energy within our canopy. The secondary spectral peak is probably generated by wake turbulence caused by form drag on the wide, horizontal spruce branches.     

Characteristics of air flow above and within soybean canopies

Air flow was observed above and within canopies of a number of kinds of soybeans. The Clark cultivar and two isolines of the Harosoy cultivar were studied in 1979 and 1980, respectively. Wind speed above the canopy was measured with cup anemometers. Heated thermistor anemometers were used to measure air flow within the canopy. Above-canopy air flow was characterized in terms of the zero-plane displacement (d), roughness parameter (z _o) and drag coefficient (C _d). d and z _o were dependent on canopy height but were independent of friction velocity in the range 0.55 to 0.75 m s^?1 · C _d for the various canopies ranged from 0.027 to 0.035. Greater C _d values were measured over an erectophile canopy than over a planophile canopy. C _d was not measurably affected by differences in leaf pubescence. Within-canopy wind profiles were measured at two locations: within and between rows. The wind profile was characterized by a region of great wind shear in the upper canopy and by a region of relatively weak wind shear in the middle canopy. Considerable spatial variability in wind speed was evident, however. This result has significant implications for canopy flow modeling efforts aimed at evaluating transport in the canopy. In the lower canopy, wind speed within a row increased with depth whereas wind speed between two rows decreased with depth. The wind speeds at the two locations tended to converge to a common value at a height near 0.10 m. The attenuation of within-canopy air flow was stronger in canopies with greater foliage density. Canopy flow attenuation seemed to decrease with increasing wind speed, suggesting that high winds distorted the shape of the canopy in such a manner that the penetration of wind into the canopy increased.     

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

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

A study of the structure of low-level katabatic winds at Mizuho Station,East Antarctica

Low-level katabatic wind profiles, which have shapes similar to those of the low-level jet (LLJ) wind profiles, are often observed during strong winds in the summer period at Mizuho Station, which is located at 70°42 S, 44°20 E in East Antarctica. The profiles may be classified according to the height of the maximum wind speed, z _m , found below 30 m height. The behavior of z m and of conditions in the layer above z mare explained well by the normalized frequency, f N = Nz/U at 30 m, whose value can be used to predict the existence of a LLJ wind profile. Subsidence and inertial oscillations above z m are related closely to the height and time variations of z m. Thus, not only effects emanating upward from surface but also momentum and heat transported downward from above are significant for the evolution of z m.     

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 Field Study of the Mean Pressure About a Windbreak

To provide additional field data for assessingwindbreak flow models, mean ground-level pressurehas been measured upstream and downstream from along porous fence (height H = 1.25 m, resistancecoefficient k _r = 2.4). Measurements were madeduring periods of near-neutral stability and near-normallyincident flow, with the fence standing on bare soil(roughness length, z ₀ 0.8 cm;H/z ₀ 160), or within a plant canopy. The mean pressure field,measured far from the ends of the fence, was foundto be quite insensitive to mean wind direction( , zero for perpendicular flow), for| | less than about 25°.In the absence of a canopy, during each measurementperiod the minimum pressure occurred at the closestsampling location to leeward of the windbreak, thepressure-gradient in most cases beingmaximally-adverse in the immediate lee, and decayingwith increasing downwind distance (x). On one day ofmeasurements, however, the pressure gradient over2 x/H 6 (H = windbreak height) resembled theleeward plateau identified by Wang and Taklein their numerical studies. Perhaps thisoccasional feature was only due to instrumenterror. Nevertheless a plateau of sorts wasindicated in similar measurements by Judd andPrendergast (with H = 1.92 m, z ₀ 1.2 cm;H/z ₀ 160, k _r 3). Therefore,existence of a leeward pressure plateau behind athin fence cannot be definitely ruled out.When the windbreak was placed in a canopy, minimumsurface pressure was displaced downwind. Thisagrees with the wind-tunnel study of Judd, Raupach and Finnigan,and is consistent with a simple simulation reported here.     

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     

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.     

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.     

Markov chain simulations of vertical dispersion in the neutral surface layer for surface and elevated releases

Vertical dispersion in the neutral surface layer is investigated using a Markov Chain simulation procedure. The conceptual basis of the procedure is discussed and computation procedures outlined. Wind and turbulence parameterizations appropriate to the neutral surface layer are considered with emphasis on the Lagrangian time scale. Computations for a surface release are compared with field data. Good agreement is found for the variation of surface concentration and cloud height to distances 500 m downwind of the source. The functional form of the vertical concentration profile is examined and an exponential with exponent 1.6 is found to give the best fit with simulations.For elevated releases, it is demonstrated that an initial dip of the mass mean height from the simulation can be normalized for various release heights using a non-dimensionalized downwind coordinate incorporating advective wind speed and wind shear. The vertical distribution standard deviation ( _z ), as employed in Gaussian models, shows a fair degree of independence with source height but close examination reveals an optimum source height for maximum _z at a given downwind distance,x. This source height increases with downwind distance. Also the simulations indicate that vertical wind shear is more important than vertical variation of Lagrangian time scale close to the source, with a reverse effect farther downwind.     

Variability of surface roughness and turbulence intensities at a coastal site in India

Surface-layer features with different prevailing wind directions for two distinct seasons (Southwest Monsoon and Northeast Monsoon) on the west coast of India are studied using data obtained from tower-based sensors at a site located about 500 m from the coast. Only daytime runs have been used for the present analysis. The surface boundary-layer fluxes have been estimated using the eddy correlation method. The surface roughnessz ₀ obtained using the stability-corrected wind profiles (Paulson, 1970) has been found to be low for the Southwest monsson season. For the other season,z ₀ is relatively high. The drag coefficientC _D varies with height in the NE monsoon season but not in the season with lowz ₀. This aspect is reflected in the wind profiles for the two seasons and is discussed in detail. The scaling behaviour of friction velocityu _* and the turbulence intensity of longitudinal, lateral and vertical winds _u, _v and _w, respectively) are further examined to study their dependence on fetch. Our study shows that for the non-dimensional case, _u/u_* and _v/u_* do not show any surface roughness dependence in either season. On the other hand, for _w/u_* for the season with lowz ₀, the values are seen to agree well with that of Panofskyet al. (1977) for homogeneous terrain whereas for the other season with highz ₀, the results seem to conform more to the values observed by Smedman and Högström (1983) for coastal terrain. The results are discussed in the light of observations by other investigators.     

Formulation of the thermal internal boundary layer in a mesoscale model

Mesoscale models using a non-local K-scheme for parameterization of boundary-layer processes require an estimate of the planetary boundary layer (PBL) height z _i at all times. In this paper, two-dimensional sea-breeze experiments are carried out to evaluate three different formulations for the advective contribution in the z _i prognostic equation of Deardorff (1974).Poor representation of the thermal internal boundary layer in the sea breeze is obtained when z _i is advected by the wind at level z _i . However, significantly better results are produced if the mean PBL wind is used for the advecting velocity, or if z _i is determined simply by checking for the first sufficiently stable layer above the ground.A Lagrangian particle model is used to demonstrate the effect of each formulation on plume dispersion by the sea breeze.     

The estimation of the surface-layer parameters from wind velocity,temperature and humidity profiles by least-squares methods

The estimation of the surface-layer parameters u _* (friction velocity), _* and q _* (temperature and humidity scales), _r and q _r (temperature and humidity reference values), z _o (roughness length) and d (zero-displacement) from vertical profiles of wind velocity, temperature and humidity by least-squares methods is described. The estimation is based on the flux-gradient relationships and the constant flux assumption for the transfer of momentum, sensible heat and matter near the Earth's surface.Test calculations were carried out with the vertical profile data from the GREIV I 1974 experiment and the Great Plains Turbulence Project.