Logarithmic Wind Profile Research Articles

Observational verification of urban surface roughness parameters derived from morphological models

AbstractThis study focuses on how to verify the aerodynamic roughness parameters in an urban area by using observational data collected in the roughness sub‐layer. Anemometrical observations were made in the downtown area of Nanjing, China, in summer and winter. Data were collected using both slow and fast response anemometers mounted on a 36 m tower. The friction velocity was observed just above the top of the urban canopy layer, which is at the height of 19.7 m, while the mean wind speed was observed at a relatively low level that is generally thought to be in the roughness sub‐layer, of which the top usually ranges from 2 to 5 times the height of the urban canopy layer. The results of the measurements show that the dimensionless friction velocities (normalized by the mean wind speed at an upper level) maintain approximately a constant (0.20) and the fluctuations are small ( ± 0.02) in a period of 21 days. The results imply that the similarity relation for the mean wind profile is still valid and that the effect of stratification is negligibly small in the urban roughness sub‐layer.Based on the measurement results, the logarithmic wind profile was applied to verify the aerodynamic roughness parameters empirically derived from four morphological models: the rule of thumb (Rt) method, the Bottema (Ba) method, the Macdonald (Ma) method and the Raupach (Ra) method. The results show that they are not very different from each other. The good performance of the Rt method may be due to the fact that the distribution of buildings in the study area is regular. The Ba and Ra methods are likely to be better since they can give reasonable estimates of roughness parameters. Evidence indicates that the Ma method underestimates the roughness length. Copyright © 2008 Royal Meteorological Society

Extrapolation of Wind Profiles Using Indirect Measures of Stability

The dependence of wind shear on boundary layer stability can be described using Monin-Obukhov similarity theory and modified logarithmic wind profiles. Typical measurements for wind resource assessment, however, are insufficient to assess stability. We show that useful, indirect inferences of stability are possible using measurements from typical instrumentation found on a meteorological tower installed for the purpose of wind resource assessment. Traditional power-law parameterizations, stratified by time of day and season, are often sufficient despite inter-day variations in stability. The effect of various wind speed extrapolation methods on wind energy estimates are demonstrated using measurements made during fall 2007 from a 50 m wind monitoring tower.

Compensation of Bias in Lidar Wind Resource Assessment

A number of vector and volume averaging considerations arise in relation to remote sensing, and in particular, Lidar. 1) Remote sensing devices obtain vector averages. The magnitude of a vector average is less than or equal to the scalar average obtained over the same period. The use of Lidars in wind power applications has introduced practices entailing the estimation of scalar average point quantities by the measurement of vector averages over volumes and vice versa. The relationship between vector and scalar averages, and the relationship between volume and point measurements, must therefore both be understood. It is found that their ratio depends upon wind direction variability according to a Bessel function of the standard deviation of the wind direction during the averaging interval. The impact of wind direction variability on power production is also explored. 2) The finite probe length of remote sensing devices incurs a volume averaging bias if wind shear is non-linear. The sensitivity of the devices to signals from a range of heights produces volume averages representing wind speeds within that range. If the wind shear is described by a logarithmic wind profile the apparent height, at which the average wind speed occurs, is found to depend on simple geometrical arguments concerning configuration height and probe length independent of the degree of wind shear. Similar arguments are applied to determine the ideal height across the rotor at which to acquire wind speed data for power curves. 3) The common restriction of the locus of points at which radial velocity measurements are made to the circumference of a horizontally oriented disc at a particular height is seen to introduce ambiguity into results when dealing with wind vector fields which are not uniform.

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.

Compensation of vector and volume averaging bias in lidar wind speed measurements

A number of vector and volume averaging considerations arise in relation to remote sensing, and in particular, Lidar. 1) Remote sensing devices obtain vector averages. These values are often compared to the scalar averages associated with cup anemometry. The magnitude of a vector average is less than or equal to the scalar average obtained over the same period. The use of Lidars in wind power applications has entailed the estimation of scalar averages by vector averages and vice versa. The relationship between the two kinds of average must therefore be understood. It is found that the ratio of the averages depends upon wind direction variability according to a Bessel function of the standard deviation of the wind direction during the averaging interval. 2) The finite probe length of remote sensing devices also incurs a volume averaging bias when wind shear is non-linear. The sensitivity of the devices to signals from a range of heights produces volume averages which will be representative of wind speeds at heights within that range. One can distinguish between the effective or apparent height the measured wind speeds represent as a result of volume averaging bias, and the configuration height at which the device has been set to measure wind speeds. If the wind shear is described by a logarithmic wind profile the apparent height is found to depend mainly on simple geometrical arguments concerning configuration height and probe length and is largely independent of the degree of wind shear. 3) The restriction of the locus of points at which radial velocity measurements are made to the circumference of a horizontally oriented disc at a particular height is seen to introduce ambiguity into results when dealing with wind vector fields which are not irrotational.

Characteristics of Wind–Wave Interaction During an Intense Extratropical Cyclogenesis

Abstract From November 2 to 5, 1996, an intense extratropical cyclone was near the National Data Buoy Center buoy 46035 in the Bering Sea. At the storm's extremes, the buoy measured minimum sea-level pressure (= 966.1 mbar), 10 m wind speed (= 28.2 m/s), peak gust (= 38.9 m/s), significant wave height (= 15.4 m), and peak period (= 16.7 s). During this period, 41 hourly observations were recorded when the waves were not fully developed; these records are the subject of our detailed analysis. It is shown that the wind–pressure relation was governed by the cyclostrophic equation; stability was neutral (i.e., the logarithmic wind profile law is useful); the relation between dimensionless wave height and period as normalized by the wind speed and the friction velocity follows the formulas found in the literature. Further determination of the friction velocity using the gust factor concept is successful to incorporate both tropical and extratropical cyclones.

Study of near-surface models for large-eddy simulations of a neutrally stratified atmospheric boundary layer

In large-eddy simulations (LES) of the atmospheric boundary layer (ABL), near-surface models are often used to supplement subgrid-scale (SGS) turbulent stresses when a major fraction of the energetic scales within the surface layer cannot be resolved with the temporal and spatial resolution at hand. In this study, we investigate the performance of both dynamic and non-dynamic eddy viscosity models coupled with near-surface models in simulations of a neutrally stratified ABL. Two near-surface models that are commonly used in LES of the atmospheric boundary layer are considered. Additionally, a hybrid Reynolds- averaged/LES eddy viscosity model is presented, which uses Prandtl’s mixing length model in the vicinity of the surface, and blends in with the dynamic Smagorinsky model away from the surface. Present simulations show that significant portions of the modelled turbulent stresses are generated by the near-surface models, and they play a dominant role in capturing the expected logarithmic wind profile. Visualizations of the instantaneous vorticity field reveal that flow structures in the vicinity of the surface depend on the choice of the near-surface model. Among the three near-surface models studied, the hybrid eddy viscosity model gives the closest agreement with the logarithmic wind profile in the surface layer. It is also observed that high levels of resolved turbulence stresses can be maintained with the so-called canopy stress model while producing good agreement with the logarithmic wind profile.

Characteristic Wind Speed Distributions and Reliability of the Logarithmic Wind Profile

Wind produces turbulence facilitating the exchange of pollutants and other environmentally important trace gases such as oxygen and greenhouse gases between stationary water bodies and the atmosphere. Whereas wind speeds continuously vary, different wind speed monitoring and characterization procedures have been used for the gas exchange studies. We assessed the impact of measurement time intervals, logarithmic wind speed profiles, and surface roughness values on wind characterizations. The Weibull probability density function effectively characterized yearly and seasonal wind speed distributions. It was not affected by various averaging time intervals (1–60 min) . However, averaging time interval of <10 min was necessary for reliable characterizations of shorter-periods ( <3–5 days). Vertical wind speed variations were effectively described by logarithmic profile irrespective of atmospheric stability conditions. Interestingly, use of the logarithmic profile allowed the actual U10 to be predicted with rea...

Temporal and Spatial Growth of Wind Waves

Abstract A solution of Rayleigh’s instability equation, which circumvents the apparent critical-layer singularity, is provided. The temporal and spatial growth rates of water waves exposed to a logarithmic wind profile are calculated and discussed. The findings are similar to previously published results, except for shear velocity–to–wave celerity ratios larger than 2, where the newly calculated growth rates start to decrease after having reached a distinct maximum. The ratio of the spatial to temporal growth rates is examined. It is shown to deviate by up to 20% from the leading-order value of 2. The implications of the growth rate to the modal distributions of energy input from wind to waves, for young and mature seas, and in temporal/spatial growth scenarios, are analyzed.

Airflow characteristics, energy balance and eddy covariance measurements in a banana screenhouse

Shading banana and other orchard crops with screens is increasing in popularity due to decreased water use, increased fruit quality and other reasons. This study focused on airflow, turbulence, ventilation rate, evapotranspiration and energy balance in a large commercial flat-roof banana screenhouse in northern Israel. Measurements were made during 14 days. An eddy covariance system, consisting of a one-dimensional sonic anemometer, a fine-wire thermocouple and a Krypton hygrometer, was deployed at 5 m height, in a location allowing a minimum fetch of 100 m in all directions. Net radiation, soil heat flux and storage, soil evaporation, air temperature and humidity and turbulent airflow characteristics were measured. Comparison between wind speed inside and outside of the screenhouse suggests that the logarithmic wind profile model is approximately valid within the screenhouse. Airflow direction inside the screenhouse was usually the same as that of the external wind. Friction velocity scaled with the mean horizontal wind speed inside the screenhouse. Integral length scale calculations showed that eddies were always narrow and long and high air velocities caused eddies to become even narrower, as expected. Average turbulence intensity within the screenhouse for all data was 0.49 ± 0.12 (± standard deviation). Spectral energy density depended on frequency to the power of about −5/3, typical of the inertial subrange in turbulent boundary layers. Air exchange rate increased with wind speed, as expected. Evapotranspiration averaged 5.6 ± 0.47 mm day −1, in accord with the 7–8 mm day −1 irrigation. Analysis of energy balance closure resulted in a slope of 0.94 and an intercept of 2.4 W m −2.

Surface roughness around a 325-m meteorological tower and its effect on urban turbulence

Based on slow- and fast-response measurements under neutral stratification conditions from a 325-m meteorological tower located in a built-up area of north-central Beijing as well as a descriptive survey of surface roughness elements (i.e., buildings and trees) around the tower site, urban roughness lengths,z 0, with zero-plane displacement height are estimated using logarithmic wind profile and morphometric methods in eight 45° directional sectors. When comparing their results with each other, the slow-response method tends to give smallerz 0 values. At a given location, considerable directional variations in values are observed. The effect of surface roughness on urban turbulence characteristics in terms of non-dimensional standard deviations of three-component velocity, σi/u*1 (wherei = u,v,w andu *1 is local friction velocity), is investigated.

Sulfur dioxide dry deposition on the loess surface–surface reaction concept for measuring dry deposition flux

As an effort to obtain more extensive data on sulfur dioxide dry deposition in northern China, experiments were carried out in Beijing by trying a new approach to the deposition flux determination. In this approach we determined the flux by a traditional concentration gradient method in the cases where the wind velocity profile conformed to the logarithmic law. In the cases outside the efficacy of the logarithmic law, in which considerable difficulty had been experienced in the traditional method, we resorted to a new concept of regarding the deposition as a reaction between sulfur dioxide and the ground surface. We introduced a mathematical model for the surface reaction, and, determining the reaction parameters on the basis of the logarithmic wind profile data, used the model to evaluate the flux in the non-logarithmic law cases. This method should enable us to obtain the dry deposition data for much more situations, including those which are difficult to be dealt with by the traditional method.

Solution of Rayleighs instability equation for arbitrary wind profiles

A different approach to the solution of the singular Rayleigh equation is presented in the context of the water wave growth problem as modelled by wind-induced shear instabilities. The approach is based on the analytical solution of a Bessel equation in the vicinity of the singular point, which is obtained from Rayleigh's equation with an arbitrary wind profile. Wave growth rates are computed using an integral expression derived from the dispersion relation of the air–sea interface. Computations of the present approach agree well with those of Conte &amp; Miles (1959) for the special case of a logarithmic wind profile. Effects of the shape of the wind profile on the wave growth rate are investigated by using the 1/7-power law to represent the wind profile. Comparisons of the growth rates for the logarithmic wind profile and for the 1/7 profile reveal appreciable differences which must be investigated further, possibly using measured wind profiles within 10 m above the sea surface.

New Findings concerning the Structure of the Marine Atmospheric Boundary Layer over the Baltic Sea – Possible Implications for Wind Energy Installations

Seven years worth of meteorological tower data from the site Östergarnsholm in the Baltic Sea have provided new information on the structure of the marine atmospheric boundary layer, of high relevance for off-shore wind energy siting. The present paper is a review based on a series of original papers, which have appeared recently or are about to appear in the meteorological literature. Waves on the water surface modify the flow considerably as soon as they become of sufficient length. Thus, during neutral conditions, a logarithmic wind profile is observed only when the waves are growing actively. During unstable stratification, which occurs at this site during more than half the time, several factors act together to reduce the magnitude of the wind shear to a considerable extent. Velocity spectra during neutral conditions and growing sea agree with corresponding spectra over land, which have recently been shown to have appreciably more low-frequency energy than previously assumed. The marine spectra are shown to be strongly dependent on wave-state. The effect of limited water depth on the structure of the marine surface layer is discussed.

Scaling Effects of Standing Crop Residues on the Wind Profile

Standing senescent stems increase the aerodynamic roughness of the surface, reducing wind energy available for momentum transfer at the soil surface, such as for wind erosion, and also the soil–atmosphere convective exchanges of heat, water vapor, and trace gases. We conducted studies to determine the predictive accuracy of an algorithm derived for plant canopies to scale effects of standing crop residues on the wind profile. We used this algorithm to calculate aerodynamic properties (displacement height and roughness length) of standing crop residues related to the log wind profile equation. We also calculated apparent roughness length from wind profiles measured under neutral stability conditions over stems of wheat (Triticum aestivum L.), corn (Zea mays L.), millet (Panicum miliaceum L.), and sunflower (Helianthus annuus L.) using calibrated single‐needle and cup anemometers. A least‐squares fit of roughness length calculated by an algorithm derived for crop canopies indicated a systematic, positive bias when it was applied to standing stems. After adjusting for bias, calculated windspeeds generally were contained in 80% confidence intervals for observations above and within the crop stubble. Predictive root mean square errors (RMSE) within profiles ranged from 0.6 to 4.6% of reference wind speed. The nonlinear forms of the scaling algorithms are consistent with theory and wind tunnel observations, representing an advance over parameterization schemes assuming a linear relation with residue height. This advance warrants evaluation of the adjusted algorithm for simulation of microclimate in the soil–residue–crop canopy regime. Application to momentum transfer problems requires further investigation of drag partitioning.

Effective aerodynamic roughness estimated from airborne laser altimeter measurements of surface features

Aerodynamic roughness length (z 0) and displacement height (d 0) are important surface parameters for estimating surface fluxes in numerical models. These parameters are generally determined from wind flow characteristics using logarithmic wind profiles measured at a meteorological tower or by balloon release. It would be an advantage to use measurements of land surface characteristics instead of wind flow characteristics to estimate the z 0 and d 0 for large areas. Important land surface characteristics are the size and distribution of roughness elements (obstacles). This research evaluates the use of high resolution laser altimeter data to obtain these land surface characteristics. Data were collected at the US Department of Agriculture, Agricultural Research Service (USDA‐ARS), Jornada Experimental Range in southern New Mexico, USA over a coppice dune dominated area. These dunes are covered by honey mesquite (Prosopis glandulosa Torr.) with flat and mostly bare interdunal areas. For this analysis, three 450 m laser transects with a 2 cm measurement interval were used. The distribution and size of dunes were calculated from these laser transects and used to compute z 0. Analysis gave an average z 0 = 4.3 cm and d 0 = 70 cm for the three laser transects, which compares to z 0 = 7 ± 4 cm and d 0 = 98 ± 48 cm calculated from wind profile data measured at a 10 m tower near the laser transects. These results show that the estimation of z 0 and d 0 for a complex terrain is possible using simple land surface features computed from high resolution laser altimeter data.

MODELING THE ROUGHNESS PROPERTIES OF ARTIFICIAL SOIL CLODS

Knowledge of the aerodynamic roughness length (Z0) resulting from management practices that include soil clods, vegetation, and ridges is essential to describing their protective roles in wind erosion. The usual method of obtaining Z0 from a logarithmic wind profile has limited accuracy because the

Simple expressions for correcting wind speed data for elevation

Using the logarithmic wind profile and typical values of dimensionless sea roughness for different sea states, simple power expressions are derived for the wind profile over water. The power expressions are useful for correcting measured wind speed data at a given elevation (up to an elevation of 60 m) to the standard elevation of 10 m commonly used in coastal engineering studies. The analysis shows that the 1/7 power expression (suggested in [U.S. Army Corps of Engineers, 1984. Shore Protection Manual, Vol. 1. Coastal Engineering Research Center, Vicksburg, USA.] and commonly used today) is a good approximation (<3% error) of the logarithmic profile for various sea states up to an elevation of 20 m. Above this elevation, the 1/7 power expression underestimates the wind speed for moderate to fully developed sea states.

A Study of the Internal Boundary Layer due to a Roughness Change in Neutral Conditions Observed During the LINEX Field Campaigns

As an aspect of the LINEX field studies (1996–1997; Lindenberg near Beeskow, Germany), the characteristics of the internal boundary layer (IBL) that is associated with a step change of the surface roughnesses in neutral constant stress layers was investigated and is reported in this paper. Both smooth to rough (in 1996) and rough to smooth (in 1997) types of flow, have been studied based upon the profiles of mean wind and temperature realised from a 10-m mast and eddy correlation measurements taken at two levels (2 m and 5 m). Depending upon wind direction, the fetch at the site varied between 140 m and 315 m within the wind sector (200° to 340°) used for the field investigations. The height of the IBL, δ, had been determined from the intersect of the logarithmic wind-profiles below ( 6 ) the interface. Values of δ obtained at the experimental site compared fairly well to the existing theoretical/empirical fetch-height relationships of the form: δ=aċx b , where a, b, are empirical constants. The ratio for the friction velocities below and above the IBL as measured directly by the eddy correlation techniques showed that for fetches less than 250 m there was an increase (decrease) of about 20% of the momentum flux arising from the smooth to rough (rough to smooth) transitions. Influences of distant obstructions (e.g., bushes, pockets of trees) on the surface flow were markedly important on the examined wind profiles and such can be indicative as multiple IBLs.

Near-wake behaviour of wind turbines

For studies of the flow downstream wind turbines, the initial state of the flow is of importance. In this study the flow generated by a wind turbine has been calculated. The purpose is to study how a logarithmic wind profile and yaw, modifies the initial state. For validation of the model, measurements from the Alsvik wind farm are used.