On the extension of the wind profile over homogeneous terrain beyond the surface boundary layer

Analysis of profiles of meteorological measurements from a 160 m high mast at the National Test Site for wind turbines at Høvsøre (Denmark) and at a 250 m high TV tower at Hamburg (Germany) shows that the wind profile based on surface-layer theory and Monin-Obukhov scaling is valid up to a height of 50–80 m. At higher levels deviations from the measurements progressively occur. For applied use an extension to the wind profile in the surface layer is formulated for the entire boundary layer, with emphasis on the lowest 200–300 m and considering only wind speeds above 3 m s^?1 at 10 m height. The friction velocity is taken to decrease linearly through the boundary layer. The wind profile length scale is composed of three component length scales. In the surface layer the first length scale is taken to increase linearly with height with a stability correction following Monin-Obukhov similarity. Above the surface layer the second length scale (L _MBL ) becomes independent of height but not of stability, and at the top of the boundary layer the third length scale is assumed to be negligible. A simple model for the combined length scale that controls the wind profile and its stability dependence is formulated by inverse summation. Based on these assumptions the wind profile for the entire boundary layer is derived. A parameterization of L _MBL is formulated using the geostrophic drag law, which relates friction velocity and geostrophic wind. The empirical parameterization of the resistance law functions A and B in the geostrophic drag law is uncertain, making it impractical. Therefore an expression for the length scale, L _MBL , for applied use is suggested, based on measurements from the two sites.     

An assessment of mixing-length closure schemes for models of turbulent boundary layers over complex terrain

The effectiveness of closure assumptions implemented in turbulent boundary-layer models is rather uncertain over complex terrain. Different closure schemes for Reynolds shear stress based on the mixing-length concept are compared with data from wind tunnel experiments over complex terrain and the results are analysed on the basis of second-order moment equations. A good estimation of the vertical momentum flux velocity scale turns out to be given by the standard deviation of the vertical velocity while the turbulent kinetic energy scaling gives less satisfactory results in regions where turbulence anisotropy is large. Fairly good results are given by closure models implementing a shear-limited mixing-length already proposed for non-logarithmic wind profiles, while large errors characterize traditional mixing-length formulations.     

Mesoscale modelling of wind energy over non-homogeneous terrain

The use of numerical mesoscale models for the evaluation of wind energy potential over non-homogeneous terrain is outlined, focusing on the following: (i) an overview of modelling investigations of relevance to wind energy; and (ii) a discussion of the optimal implementation of mesoscale models in wind energy studies.     

A wind tunnel boundary-layer simulation of wind flow over complex terrain: Effect of terrain and model construction

The report presents the results of a wind-tunnel study of the flow of the natural wind over complex terrain. A 1:4000 undistorted scale model of Gebbies Pass in the South Island of New Zealand was prepared and tested in the boundary-layer wind tunnel in the Department of Mechanical Engineering at the University of Canterbury.Three forms of construction, viz., terraced, contoured and roughness-added, were compared. Velocity and turbulence profiles, Reynolds stresses and spectra were measured, and correlation of results between different types of construction was calculated. The terraced form was much simpler to construct but was found to be unsatisfactory. The correlation between the contoured and roughness-added models was as high as 0.94, although the roughness-added model made a significant difference to the results in the lower 20%; of the boundary layer. The results of these tests will be compared with results from the field in a future report.     

Some turbulence characteristics of convectively mixed layers over rugged and homogeneous terrain

Turbulence characteristics of convectively mixed layers over rugged and homogenous terrain are presented, and their differences are sought. The data used in the study were obtained from aircraftborne instruments. Apart from statistics related to the mixing ratio q, there does not seem to be a marked difference between the two sets of data. This lack of difference is attributed to the degree of ruggedness of the terrain and the dominant wind direction. The behaviour of some statistics related to q is attributed to the entrainment effect of the unstable layer of the moist, cool air above the mixed layer.This work was initiated and a large part of it was completed while all three authors were with CSIRO (Commonwealth Scientific Industrial Research Organisation), Australia.Formerly at: Division of Atmospheric Research, CSIRO, Epping, NSW, Australia.Formerly at: Division of Mathematics and Statistics, CSIRO, Lindfield, NSW, Australia.     

Regional effects of large-scale extreme wind events over orographically structured terrain

Summary ?Above orographically structured terrain considerable differences of the regional wind field may be identified during large-scale extreme wind events. So far, these regional differences could not be resolved by climate models. To determine the relationships between large-scale atmospheric conditions, the influence of orography, and the regional wind field, data measured in the upper Rhine valley within the framework of the REKLIP Regional Climate Project were analyzed and calculations were made using the KAMM mesoscale model. In the area of the upper Rhine valley, ratios of the wind velocity in the Rhine valley at 10 m above ground level, ν_val, and the large-scale flow velocity, ν_lar, are between ν_val/ν_lar ≈ 0.1 and ν_val/ν_lar ≈ 1. The ν_val/ν_lar ratio exhibits a strong dependence on thermal stratification, δ, and decreases from ν_val/ν_lar ≈ 1 at δ = 0 K m⁻¹ to ν_val/ν_lar ≈ 0.2 at δ = 0.0075 K m⁻¹. In areas, where the lateral mountainous border of the Rhine valley is interrupted, the ν_val/ν_lar ratio increases again with increasing stability or decreasing Froude number. This is obviously due to flow around the Black Forest under stable stratification. It is demonstrated by model calculations that a complex wind field develops in the Rhine valley at small Froude numbers (Fr < 1) irrespective of the direction of large-scale flow. The ν_val/ν_lar ratio is characterized by small values in the direct lee side (ν_val/ν_lar ≈ 0.2) and high values on the windward side of the lateral mountainous border of the Rhine valley (ν_val/ν_lar ≈ 0.8). Received October 22, 2001; revised June 18, 2002; accepted June 23, 2002     

Simulation of three-dimensional wind flow over complex terrain in the atmospheric boundary layer

A three-dimensional model for wind prediction over rough terrain has been developed for practical use. It is a compromise between hydrodynamic and objective wind models. The proposed model includes: (1) a statistical model to predict the wind velocity and potential temperature at anemometer height at observing stations, (2) the drainage wind model expressed by Prandtl's analytic solution for the slope wind, (3) the Businger-Dyer surface-layer formulation which considers the surface energy budget and (4) the model for three-dimensional boundary-layer solutions to the stationary flow. In this model, mass consistency is guaranteed by using flow fields that satisfy the continuity equation. Model predictions show good agreement with the observations.     

Effects of a change of terrain height and roughness on a wind profile

We have measured profiles of an onshore wind 200 m upwind and 200 m downwind from an abruptly rising shore using a remote-sensing Doppler lidar anemometer. Data were taken at heights between 4.7 and 66.5 m above sea level. Results show that the onshore velocity vector slopes upward 16.6 to 9.6°, the amount depending on the height of measurement, due to the combined effects of a 1.7-m high bluff shoreline and the frictionally decelerated flow over land. The profile 200 m inland has the expected deceleration at lower levels because of increased surface roughness and implies a velocity vector at 66.5 m height with an upward slope of approximately 18° (2.6 m s^-1 upward component, 8.4 m s^-1 vector magnitude), an acceleration to 0.3 m s^-1 greater than the upwind value, or a combination of both effects. All three options are consistent with mass continuity. The experiment exhibits the usefulness and limitations of a backscatter Doppler lidar for boundary-layer profile measurements in a horizontally inhomogeneous environment.     

Validity of the log-linear profile relationship over a rough terrain during stable conditions

The applicability of the log-linear profile relationship over rough terrain to a height of 126 m is investigated. Simultaneous hourly averaged mean wind and temperature profiles measured at the Brookhaven meteorological tower during stable conditions are used in the analysis. The tower was surrounded by fairly homogeneous vegetation to a height of about 8 m. The results indicate that the log-linear profile relationship is valid at least for a height of 126 m for stabilities with Richardson numbers less than the critical value of 0.25. The mean value of in is found to be about 5.2 for these stabilities. The log-linear profile relation is found to be applicable for profiles observed beyond the critical stability; but the height of validity seems to decrease to about 100 m and the mean value of is about 1.6.Research performed under the auspices of the United States Energy Research and Development Administration (Contract E(30-1)-16).     

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.     

A statistical representation of sub-grid variation in mixing-length models of the boundary layer

In conventional gradient-transfer models of the atmospheric boundary layer, the fluxes are calculated using the gradients of buoyancy and momentum over the grid interval. When using finite-differences, these gradients are approximated using what are essentially the grid-volume means of the quantities involved. This is unrealistic, as within a large volume of the atmosphere fluxes are supported by an ensemble of small-scale motions, which may be organized by the presence of large coherent eddies. In this paper, a new method of computing the flux is developed, in which the gradients of grid-volume mean buoyancy and momentum are replaced by grid-volume ensembles. The distributional parameters of the ensembles are derived using dimensional arguments, augmented by the results of a large-eddy simulation.     

Numerical study of wind energy characteristics over heterogeneous terrain — Central Israel case study

A numerical mesoscale meteorological model has been applied over the heterogeneous terrain of central Israel in order to study wind energy characteristics of three typical synoptic situations. The supportive nature of this method for observationally oriented wind energy studies has been emphasized. Mesoscale forcing effects on the availability of wind energy and on the exponent, p, in the vertical wind power law are evaluated.     

Estimates of diabatic wind speed profiles from near-surface weather observations

In this paper we analyse diabatic wind profiles observed at the 213 m meteorological tower at Cabauw, the Netherlands. It is shown that the wind speed profiles agree with the well-known similarity functions of the atmospheric surface layer, when we substitute an effective roughness length. For very unstable conditions, the agreement is good up to at least 200 m or z/L–7(z is height, L is Obukhov length scale). For stable conditions, the agreement is good up to z/L1. For stronger stability, a semi-empirical extension is given of the log-linear profile, which gives acceptable estimates up to ~ 100 m. A scheme is used for the derivation of the Obukhov length scale from single wind speed, total cloud cover and air temperature. With the latter scheme and the similarity functions, wind speed profiles can be estimated from near-surface weather data only. The results for wind speed depend on height and stability. Up to 80 m, the rms difference with observations is on average 1.1 m s^–1. At 200 m, 0.8 m s^–1 for very unstable conditions increasing to 2.1 m s^–1 for very stable conditions. The proposed methods simulate the diurnal variation of the 80 m wind speed very well. Also the simulated frequency distribution of the 80 m wind speed agrees well with the observed one. It is concluded that the proposed methods are applicable up to at least 100 m in generally level terrain.     

Analysis of the long-term surface wind variability over complex terrain using a high spatial resolution WRF simulation

This work uses a WRF numerical simulation from 1960 to 2005 performed at a high horizontal resolution (2 km) to analyze the surface wind variability over a complex terrain region located in northern Iberia. A shorter slice of this simulation has been used in a previous study to demonstrate the ability of the WRF model in reproducing the observed wind variability during the period 1992–2005. Learning from that validation exercise, the extended simulation is herein used to inspect the wind behavior where and when observations are not available and to determine the main synoptic mechanisms responsible for the surface wind variability. A principal component analysis was applied to the daily mean wind. Two principal modes of variation accumulate a large percentage of the wind variability (83.7%). The first mode reflects the channeling of the flow between the large mountain systems in northern Iberia modulated by the smaller topographic features of the region. The second mode further contributes to stress the differentiated wind behavior over the mountains and valleys. Both modes show significant contributions at the higher frequencies during the whole analyzed period, with different contributions at lower frequencies during the different decades. A strong relationship was found between these two modes and the zonal and meridional large scale pressure gradients over the area. This relationship is described in the context of the influence of standard circulation modes relevant in the European region like the North Atlantic Oscillation, the East Atlantic pattern, East Atlantic/Western Russia pattern, and the Scandinavian pattern.     

非均匀地面近地层风速廓线的实验研究

本文以Monin-Obukhov(1954)相似理论为基础,分析研究了北京西郊八角村地区80米高的铁塔上观测的风速和温度资料。 指出在均匀粗糙地面条件下,中性平均风速廓线在77米高度内很好地满足对数规律;稳定层结下,对数一线性规律在(0.03 ≤R_i≤0.69)一个很宽的稳定范围内都是适用的,但是必须十分注意其线性项常数β是随稳定度R_i而变的。本文给出了β-R_i之间的经验关系为β=0.35R(-0.9)对于不稳定层结描写风速切变函数φ_m,我们得到:弱不稳定范围使用|z/L| ~((-1)/4)规律     

On the measurement of second moments of turbulent wind velocity with a single Doppler radar over non-homogeneous terrain

The measurement of turbulent wind quantities with a single Doppler radar requires a horizontal homogeneity assumption. When the terrain is not horizontally homogeneous, then the measurement of the various moments is contaminated by the gradients of these moments. However, by scanning the radar at three different elevation angles, the contamination from these gradients can be removed from the second-moment quantities of interest.     

The use of mesoscale numerical models to assess wind distribution and boundary-layer structure in complex terrain

Mesoscale models which can be used to assess wind and turbulent structure in complex terrain are overviewed. The different types of models — diagnostic and prognostic are discussed and the significant physical processes which each can handle realistically are reviewed. Examples of specific applications of these models are presented.     

Mass consistent models for wind distribution in complex terrain — Fast algorithms for three dimensional problems

Mass consistent models for wind distribution in complex terrain are extremely useful and readily applied to many practical situations, such as the siting of wind turbines, or as input in the estimation of diffusion and transport of pollutants in complex terrain. These models are based on the numerical solution of the steady state three dimensional continuity equation for the mean wind components. The momentum and energy equations are not solved explicitly, but considered indirectly using parametric relations and wind data. In practical applications the equations must be solved numerous times (e.g. for each time interval). Standard techniques for numerical solution of three dimensional problems are frequently very expensive and thus not suitable for practical needs. In the present work, great emphasis is given to the development of fast algorithms, and techniques based on the multigrid approach are shown. Two mass consistent programs are described, the first based on the parametric representation of one of the wind components, and the second based on a few wind measurements and a variational principle. To verify the reliability of the variational approach, a measurement program related to a project of wind energy, is being performed at Har-Ahim, a site located in the Galilee.     

On the log-linear wind profile and the relationship between shear stress and stability characteristics over the sea

Wind and stability characteristics in the atmospheric surface boundary layer at a height,Z, less than 20 m above the sea were examined in nine oceanic investigations. The analysis lends further support to the utility of the log-linear wind-profile law in the stability region of –0.4Z/L0.9, whereL is the Monin-Obukhov length. However, it is also shown that, inasmuch as better than 90% of the measurements fall within the range of ¦Z/L¦ 0.25, and inasmuch as this correction to the drag coefficient under neutral conditions amounts to less than 10%, the familiar logarithmic wind law may be used rather than the log-linear form. A wind-stress drag coefficient,C _d (=1.2×10^–3 between 1.0 m Z 18.3 m), is thus recommended for general deepwater oceanic applications. The situation over shallow water, which is different, is discussed briefly.