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 .     

Models for estimating offshore winds from onshore meteorological measurements

To understand and estimate wind speed differences across the coastal zone, two models, one theoretical and another semi-empirical, have been developed and verified by available data sets. Assuming that: (1) mean horizontal motion exists across the coastal zone; and (2) the geostrophic wind does not change appreciably at the top of the planetary boundary layer (PBL), the equation of motion in the direction of the wind can be reduced so that 341-01, where U, H, and C _D are wind speed, height of PBL, and drag coefficient over the sea and land, respectively. For practice, C _D SEA has been modified from a formula with U _LAND as the only input. H _SEA may be estimated routinely from known H _{D LAND LAND} and the temperature difference between land and sea, which can be provided by such means as remote sensing from meteorological satellites. For a given coast, Cmay be estimated also. This formula is recommended for weather forecasters. The semiempirical formula is based mainly on the power law wind distribution with height in the PBL. The formula states that 341-02. Simultaneous offshore and onshore wind measurements made at stations ranging from Somalia, near the equator, to the Gulf of Alaska indicated that values of a and b are 2.98 and 0.34 with a correlation coefficient of -0.95. For oceanographic applications, a simplified equation, i.e., 341-03, is also proposed.     

Estimation of the Exchange Coefficient of Heat During Low Wind Convective Conditions

For the first time, the exchange coefficient of heat C_H has been estimated from eddy correlation of velocity and virtual temperature fluctuations using sonic anemometer measurements made at low wind speeds over the monsoon land atJodhpur (26°18' N, 73°04' E), a semi arid station. It shows strong dependence on wind speed, increasing rapidly with decreasing wind speed, and scales according to a power law C_H = 0.025U₁₀ ^-0.7 (where U₁₀ is the mean wind speed at 10-m height). A similar but more rapid increase in the drag coefficient C_Dhas already been reported in an earlier study. Low winds (<4 m s^-1) are associated with both near neutral and strong unstable situations. It is noted that C_H increases with increasing instability. The present observations best describe a low wind convective regime as revealed in the scaling behaviour of drag, sensible heat flux and the non-dimensional temperature gradient. Neutral drag and heat cofficients,corrected using Monin–Obukhov (M–O) theory, show a more uniform behaviour at low wind speeds in convective conditions, when compared with the observed coefficients discussed in a coming paper.At low wind convective conditions, M-O theory is unable to capture the observed linear dependence of drag on wind speed, unlike during forced convections. The non-dimensional shear inferred from the present data shows noticeable deviations from Businger's formulation, a forced convection similarity. Heat flux is insensitive to drag associated with weak winds superposed on true free convection. With heat flux as the primary variable, definition of new velocity scales leads to a new drag parameterization scheme at low wind speeds during convective conditionsdiscussed in a coming paper.     

Effects of local accelerations and baroclinity on the mean structure of the atmospheric boundary layer over the sea

Substitution of the geostrophic wind by the actual upper wind in the equations of motion for the boundary layer implies less sensitivity of the mean wind to inertial effects. This is confirmed by observations, although the problem of computing time or spatial derivatives from scattered data reduces the accuracy and the clarity of the results. It is found that acceleration (deceleration) increases (decreases) the cross-isobar angle whereas the geostrophic drag coefficient is a minimum (maximum) for crosswind acceleration (deceleration). On the other hand, cold air advection increases the cross-isobar angle whereas the geostrophic drag coefficient is a maximum when the thermal wind is parallel to the surface wind. The universal functions A _m and B _m based on vertically averaged winds are also rather insensitive to inertial influences.     

A new nonlinear analytical model for canopy flow over a forested hill

A new nonlinear analytical model for canopy flow over gentle hills is presented. This model is established based on the assumption that three major forces (pressure gradient, Reynolds stress gradient, and nonlinear canopy drag) within canopy are in balance for gentle hills under neutral conditions. The momentum governing equation is closed by the velocity-squared law. This new model has many advantages over the model developed by Finnigan and Belcher (Quart J Roy Meteorol Soc 130: 1–29 2004, hereafter referred to as FB04) in predicting canopy wind velocity profiles in forested hills in that: (1) predictions from the new model are more realistic because surface drag effects can be taken into account by boundary conditions, while surface drag effects cannot be accounted for in the algebraic equation used in the lower canopy layer in the FB04 model; (2) the mixing length theory is not necessarily used because it leads to a theoretical inconsistency that a constant mixing length assumption leads to a nonconstant mixing length prediction as in the FB04 model; and (3) the effects of height-dependent leaf area density (a(z)) and drag coefficient (C _d ) on wind velocity can be predicted, while both a(z) and C _d must be treated as constants in FB04 model. The nonlinear algebraic equation for momentum transfer in the lower part of canopy used in FB04 model is height independent, actually serving as a bottom boundary condition for the linear differential momentum equation in the upper canopy layer. The predicting ability of the FB04 model is largely restricted by using the height-independent algebraic equation in the bottom canopy layer. This study has demonstrated the success of using the velocity-squared law as a closure scheme for momentum transfer in forested hills in comparison with the mixing length theory used in FB04 model thus enhancing the predicting ability of canopy flows, keeping the theory consistent and simple, and shining a new light into land-surface parameterization schemes in numerical weather and climate models.     

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.     

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

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

Spatio-temporal Variability of Surface-layer Turbulent Fluxes Over the Bay of Bengal and Arabian sea During the ICARB Field Experiment

We report the spatio-temporal variability of surface-layer turbulent fluxes of heat, moisture and momentum over the Bay of Bengal (BoB) and the Arabian Sea (AS) during the Integrated Campaign for Aerosols, gases Radiation Budget (ICARB) field experiment. The meteorological component of ICARB conducted during March – May 2006 onboard the oceanic research vessel Sagar Kanya forms the database for the present study. The bulk transfer coefficients and the surface-layer fluxes are estimated using a modified bulk aerodynamic method, and then the spatio-temporal variability of these air-sea interface fluxes is discussed in detail. It is observed that the sensible and latent heat fluxes over the AS are marginally higher than those over the BoB, which we attribute to differences in the prevailing meteorological conditions over the two oceanic regions. The values of the wind stress, sensible and latent heat fluxes are compared with those obtained for the Indian Ocean Experiment (INDOEX) period. The variation of drag coefficient (C _D ), exchange coefficients of sensible heat and moisture (C _H = C _E ) and neutral drag coefficient (C _DN ) with wind speed is also discussed.

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Velocity and Surface Shear Stress Distributions Behind a Rough-to-Smooth Surface Transition: A Simple New Model

A simple new model is proposed to predict the distribution of wind velocity and surface shear stress downwind of a rough-to-smooth surface transition. The wind velocity is estimated as a weighted average between two limiting logarithmic profiles: the first log law, which is recovered above the internal boundary-layer height, corresponds to the upwind velocity profile; the second log law is adjusted to the downwind aerodynamic roughness and local surface shear stress, and it is recovered near the surface, in the equilibrium sublayer. The proposed non-linear form of the weighting factor is equal to ln(z/z ₀₁)/ln(δ _i /z ₀₁), where z, δ _i and z ₀₁ are the elevation of the prediction location, the internal boundary-layer height at that downwind distance, and the upwind surface roughness, respectively. Unlike other simple analytical models, the new model does not rely on the assumption of a constant or linear distribution for the turbulent shear stress within the internal boundary layer. The performance of the new model is tested with wind-tunnel measurements and also with the field data of Bradley. Compared with other existing analytical models, the proposed model shows improved predictions of both surface shear stress and velocity distributions at different positions downwind of the transition.     

Stably stratified flow in a marine atmospheric surface layer

Data from the marine atmospheric surface layer have been analysed. The data set consists of about two weeks with tower measurements up to 31 m of mean profiles of wind, temperature, and humidity, together with 20 Hz turbulence data. Mean wind, temperature, and humidity profiles up to 2000 m are also available from pibal trackings and radio soundings. Wave height was measured at 2 Hz, using an inverted echo-sounder.It was found from pibal wind profiles that low level jets were present during 2/3 of the measurements, having their maxima in the height interval 40 to 300 m. Here only data from the remaining 1/3 of the measurements, without low level jets, have been analysed.Non-dimensional wind and temperature gradients agree with results over homogeneous land surfaces as regards stability dependence during stable conditions that prevailed during this experiment. Linear regression gave _m = 1 + 6.8z/L and _m = 1 + 8.3z/L. No significant sea wave influence was found. The same was vrue for me dimensionless standard deviations of the three wind components, except for the vertical component. The expected wind speed dependence was found for the neutral drag coefficient, givingC _dN = 0.109U + 0.33 at 10 m, and a dependence on the wave parameter,C/u _*, was confirmed. Note, however, that the data set was restricted to low and moderate wind speeds and that stratification was mainly stable.Power spectra, non-dimensionalized according to suface-layer theories, do not follow the expected stability dependence. It was shown that this may be a consequence of the presence of gravity waves in the stable marine boundary layer. Indicators of gravity waves were found in most runs. The TKE budget agrees with findings over homogeneous land areas. The pressure transport term was found to be a source of energy also for near neutral conditions.     

Regional shear stress of broken forest from radiosonde wind profiles in the unstable surface layer

Mean wind speed profiles were measured by tracking radiosondes in the unstable atmospheric boundary layer (ABL) over the forested Landes region in southwestern France. New Monin-Obukhov stability correction functions, recently proposed following an, analysis by Kader and Yaglom, as well as the Businger-Dyer stability formulation were tested, with wind speeds in the surface sublayer to calculate the regional shear stress. These profile-derived shear stresses were compared with eddy correlation measurements gathered above a mature forest stand, at a location roughly, 4.5 km from the radiosonde launch site. The shear stress values obtained by means of the newly proposed stability function were in slightly better agreement with the eddy correlation values than those obtained by means of a Businger-Dyer type stability function. The general robustness of the profile method can be attributed in part to prior knowledge of the regional surface roughness (z ₀=1.2 m) and the momentum displacement height (d ₀=6.0 m), which were determined from neutral wind profile analysis. The 100 m drag coefficient for the unstable conditions above this broken forest surface was found to beu _* ² /V ₁₀₀ ² =0.0173.     

étude expérimentale de la couche limite de montagne

The characteristics of the boundary layer over complex terrain (Lannemezan - lat.: 43.7° N and, long.: 0.7 ° E) are analyzed for various scales, using measurements obtained during the COCAGNE Experiment. In this first part, the dynamic characteristics of the flow are studied with respect to atmospheric stability and the relief at small (~20 km) and medium scales (~100 km). These relief scales depend on the topographical profile of the Lannemezan Plateau along the dominant axis of the wind (E-W) and the Pyrénées Mountains located at the south of the experimental site. The terrain heterogeneities have a standard deviation of ~48 m and a wavelength of ~2 km.The averaged vertical profiles of wind speed and direction over the heterogeneous terrain are analyzed. The decrease of wind speed within the boundary layer is greater than over flat terrain (WANGARA Experiment). However, a comparison between ETTEX (complex terrain) and COCAGNE vertical wind speed profiles shows good agreement during unstable conditions. In contrast, during neutral conditions a more rapid increase with normalized height is found with COCAGNE than with ETTEX and WANGARA data. The vertical profiles of wind direction reveal an influence of the Pyrénées Mountains on the wind flow. The wind rotation in the BL is determined by the geostrophic wind direction-Pyrénées axis angle (negative deviation) as the geostrophic wind is connected with the Mountain axis.When the geostrophic wind does not interact with the Pyrénées axis, the mean and turbulent wind flow characteristics (drag coefficient C _D, friction velocity u _*) depend on the topography of the plateau. When the wind speed is strong (>6 m s ^-1), an internal boundary layer is generated from the leading edge of the Plateau.     

Stability dependence of the drag and bulk transfer coefficients over a coastal sea surface

Bulk transfer coefficients were evaluated from eddy correlation flux measurements on a fixed pier during onshore winds. The mean values are C _D = 1.69 × 10^-3, C _H = 2.58 × 10^-3 and C _E = 1.51 × 10^-3. The drag coefficient, C _D, gradually increases with wind speed but C _H and C _E are independent of wind speed. According to theory and empirical formulas based on experimental results over flat grassland, the transfer coefficients should gradually increase with increasing instability. This is confirmed experimentally in the stable region in our case. However, the drag coefficient appears to decrease with increasing instability, which is against the theoretical result. A stability dependence is not clearly observed for C _H or C _E.     

Momentum and sensible heat fluxes calculated by the dissipation technique during the Ocean Storms Project

High frequency measurements of wind velocity and temperature were made during the Ocean Storms Project in November 1987. The dissipation method was applied to the resulting time series in order to determine friction velocities,u _*, and the characteristic temperature scale,t _*, at 1-min intervals. These values were then compared to the 1-min mean wind speed and air-sea temperature differences to determine relationships for the drag coefficient (C _d ) and Stanton number (C _h ). The drag coefficient was comparable to other values reported in the literature, although the variation with wind speed was greater than reported by other investigators. An examination of the residual time series indicated a systematic low frequency periodicity of about 2-hr duration which was attributed to a fluctuating wind interacting with the surface gravity wave field. The temperature fluctuations did not produce meaningful estimates ofC _h for stable conditions. For unstable conditions, a value of 1.09±0.02×10^–3 was found.     

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.     

Determination Of The Surface Drag Coefficient

This study examines the dependence of the surface drag coefficienton stability, wind speed, mesoscale modulation of the turbulent flux and method of calculation of the drag coefficient. Data sets over grassland, sparse grass, heather and two forest sites are analyzed. For significantly unstable conditions, the drag coefficient does not depend systematically on z/L but decreases with wind speed for fixed intervals of z/L, where L is the Obukhov length. Even though the drag coefficient for weak wind conditions is sensitive to the exact method of calculation and choice of averaging time, the decrease of the drag coefficient with wind speed occurs for all of the calculation methods. A classification of flux calculation methods is constructed, which unifies the most common previous approaches.The roughness length corresponding to the usual Monin–Obukhovstability functions decreases with increasing wind speed. This dependence on wind speed cannot be eliminated by adjusting the stability functions. If physical, the decrease of the roughness length with increasing wind speed might be due to the decreasing role of viscous effectsand streamlining of the vegetation, although these effects cannot be isolated from existing atmospheric data.For weak winds, both the mean flow and the stress vector often meander significantly in response to mesoscale motions. The relationship between meandering of the stress and wind vectors is examined. For weak winds, the drag coefficient can be sensitive to the method of calculation, partly due to meandering of the stress vector.     

Generation and atmospheric heat exchange of coastal polynyas in the Weddell Sea

The forcing mechanisms for Antarctic coastal polynyas and the thermodynamic effects of existing polynyas are studied by means of an air-sea-ice interaction experiment in the Weddell Sea in October and November 1986.Coastal polynyas develop in close relationship to the ice motion and form most rapidly with offshore ice motion. Narrow polynyas occur frequently on the lee side of headlands and with strong curvature of the coastline. From the momentum balance of drifting sea ice, a forcing diagram is constructed, which relates ice motion to the surface-layer wind vector v _z and to the geostrophic ocean current vector c _g . In agreement with the data, wind forcing dominates when the wind speed at a height of 3 m exceeds the geostrophic current velocity by a factor of at least 33. This condition within the ocean regime of the Antarctic coastal current usually is fulfilled for wind speeds above 5 m/s at a height of 3 m.Based on a nonlinear parameter estimation technique, optimum parameters for free ice drift are calculated. Including a drift dependent geostrophic current in the ice/water drag yields a maximum of explained variance (91%) of ice velocity.The turbulent heat exchange between sea ice and polynya surfaces is derived from surface-layer wind and temperature data, from temperature changes of the air mass along its trajectory and from an application of the resistance laws for the atmospheric PBL. The turbulent heat flux averaged over all randomly distributed observations in coastal polynyas is 143 W/m². This value is significantly different over pack ice and shelf ice surfaces, where downward fluxes prevail. The large variances of turbulent fluxes can be explained by variable wind speeds and air temperatures. The heat fluxes are also affected by cloud feedback processes and vary in time due to the formation of new ice at the polynya surface.Maximum turbulent fluxes of more than 400 W/m² result from strong winds and low air temperatures. The heat exchange is similarly intense in a narrow zone close to the ice front, when under weak wind conditions, a local circulation develops and cold air associated with strong surface inversions over the shelf ice is heated above the open water.     

The influence of the geostrophic wind advection approximation on a well-mixed layer

Numerical results indicate that advection of momentum in the boundary layer may significantly alter both the structure of the planetary boundary layer and its influence on the overlying free atmosphere. However, due to the nonlinearity of the inertial terms, it is always difficult to obtain the analytical solution of the boundary-layer model that retains the flow acceleration. In order to overcome this difficulty, the geostrophic momentum (hereafter GM) approximation has been introduced into boundary-layer models. By replacing the advected momentum with the geostrophic wind, the effect of the flow acceleration is partially considered and the original nonlinear partial differential equation set is converted to ordinary differential equations, the solutions of which can be obtained easily with standard techniques. However, the model employing GM fails to capture the features of the boundary layer when the spatio-temporal variation of the boundary-layer flow cannot be properly approximated by the geostrophic wind. In the present work, a modified boundary-layer model with the inertial acceleration in a different approximate form is proposed, in which the advecting wind instead of the advected momentum is approximated by the geostrophic wind (hereafter GAM).Comparing the horizontal velocity and boundary-layer pumping obtained from the classical Ekman theory, and the model incorporating (i) GM and (ii) GAM, it is found that the model with GAM describes most facets of the steady well-mixed layer beneath a north-westerly flow with embedded mesoscale perturbations that is considered in the present work. Inspection of the solution of the model with GAM shows that, within the limit of the validation of the model (i.e., the Rossby number R_O is not very large and the drag coefficient C_D is not too small), the horizontal convergence (divergence) is strengthened by the effect of the inertial acceleration in the region of maximum positive (negative) geostrophic vorticity. Consequently, the boundary-layer pumping there is intensified. It is found that the intensification is firstly strengthened and then weakened as R_O or C_D increases.     

Geostrophic drag coefficients

Data on the relationship of the surface wind to the geostrophic wind at Porton Down, Salisbury Plain, are presented for various stability conditions and analysed in the light of the Rossbynumber similarity theory. For near-neutral conditions, the geostrophic drag coefficients for geostrophic wind speeds 5 to 15 m s^-1 are close to those found by other workers but at higher speeds the values are low. Comparisons of geostrophic and radar wind speeds for ⋍900-m height, suggest that undetectably small mean cyclonic curvatures of the trajectories of the air are responsible for this departure. A value of the geostrophic drag coefficient for the open sea at wind speeds around 8 m s^-1 (neutral conditions) is deduced from recent observations of the drag in relation to the surface wind, combined with the ratios of 900-mb radar wind to surface wind obtained from the North Atlantic weather ship data tabulations of Findlater et al. (1966).     

Drag coefficient modeling for the near coastal zone

Using the JONSWAP spectrum for describing the surface wave state in the near coastal zone, models for the roughness length and the drag coefficient are used to simulate the dependence of the wind stress on fetch and depth. The results of each model are then compared with a compiled set of past investigations of the neutral drag coefficient over a variety of conditions. It is found that the models of Donelan, Hsu, and Kitaigorodskii correctly predict the trends in the drag coefficient with fetch and depth. Although it did not account for all the observed variations in the neutral drag coefficient. Kitaigorodskii's model, when incorporating the JONSWAP spectrum, more accurately simulated the slopes of the various C_DN regressions against windspeed.