Modelling the One-Dimensional Stable Boundary Layer with an E−ℓ Turbulence Closure Scheme

The atmospheric boundary layer (ABL) model of Weng and Taylor with E−ℓ turbulence closure is applied to simulate the one-dimensional stably stratified ABL. The model has been run for nine hours from specified initial wind, potential temperature and turbulent kinetic energy profiles, and with a specified cooling rate applied at the surface. Different runs are conducted for different cooling rates, geostrophic winds and surface roughnesses. The results are discussed and compared with other models, large-eddy simulations and published field data.     

Prediction of inversion strengths and heights from A 1-D nocturnal boundary layer model

A 1-D numerical model for the nocturnal boundary layer is developed which is capable of predicting inversion heights and strengths successfully. The model uses two distinct length scales for the dissipation of turbulent energy and for transfer of heat and momentum within the Planetary Boundary Layer (PBL). The wind and potential temperature profiles obtained from the present model are compared with observations and the agreement is found to be good, viz., the RMSE for inversion height is found to be 71 m and that for inversion strength is found to be 2.0 °C.     

The structure of the stably stratified internal boundary layer in offshore flow over the sea

Observations obtained mainly from a research aircraft are presented of the mean and turbulent structure of the stably stratified internal boundary layer (IBL) over the sea formed by warm air advection from land to sea. The potential temperature and humidity fields reveal the vertical extent of the IBL, for fetches out to several hundred of kilometres, geostrophic winds of 20–25 m s^–1, and potential temperature differences between undisturbed continental air and the sea surface of 7 to 17 K. The dependence of IBL depth on these external parameters is discussed in the context of the numerical results of Garratt (1987), and some discrepancies are noted.Wind observations show the development of a low-level wind maximum (wind component normal to the coast) and rotation of the wind to smaller cross-isobar flow angles. Potential temperature () profiles within the IBL reveal quite a different structure to that found in the nocturnal boundary layer (NBL) over land. Over the sea, profiles have large positive curvature with vertical gradients increasing monotonically with height; this reflects the dominance of turbulent cooling within the layer. The behaviour is consistent with known behaviour in the NBL over land where curvature becomes negative (vertical gradients of decreasing with height) as radiative cooling becomes dominant.Turbulent properties are discussed in terms of non-dimensional quantities, normalised by the surface friction velocity, as functions of normalised height using the IBL depth. Vertical profiles of these and the normalised wavelength of the spectral maximum agree well with known results for the stable boundary layer over land (Caughey et al., 1979).     

A study of multiple stable layers in the nocturnal lower atmosphere

The structure of nocturnal inversions in the first 300 m of the atmosphere is analyzed using observational data from the Boulder Atmospheric Observatory (BAO) from March through June 1981. The temperature profiles show more than one inversion layer 41% of the time during the observational period. The vertical distributions of wind speed and moisture also show evidence of stratification during these multiple-layer events. The relation between the radiative cooling rate in time and height, including moisture, and the vertical structure of the multiple layers is calculated. The vertical distribution of eddy kinetic energy and the turbulent vertical fluxes of heat and momentum are also calculated. Turbulent structure in the elevated inversion layers is more complicated than that in the single-layer, stable nocturnal boundary layer. The total heat budget for a multiple-layer case is calculated, and turbulent cooling is found to be negligible relative to radiative cooling and to horizontal advection and/or horizontal divergence of heat flux.     

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.     

Horizontal and Vertical Turbulent Fluxes Forced by a Gravity Wave Event in the Nocturnal Atmospheric Surface Layer Over the Amazon Forest

A nocturnal gravity wave was detected over a south-western Amazon forest during the Large-Scale Biosphere–Atmosphere experiment in Amazonia (LBA) in the course of the dry-to-wet season campaign on October 2002. The atmospheric surface layer was stably stratified and had low turbulence activity, based on friction velocity values. However, the passage of the wave, an event with a period of about 180–300 s, caused negative turbulent fluxes of carbon dioxide (CO₂) and positive sensible heat fluxes, as measured by the eddy-covariance system at 60 m (≈30 m above the tree tops). The evolution of vertical profiles of air temperature, specific humidity and wind speed during the wave movement revealed that cold and drier air occupied the sub-canopy space while high wind speeds were measured above the vegetation. The analysis of wind speed and scalars high frequency data was performed using the wavelet technique, which enables the decomposition of signals in several frequencies allowed by the data sampling conditions. The results showed that the time series of vertical velocity and air temperature were −90° out of phase during the passage of the wave, implying no direct vertical transport of heat. Similarly, the time series of vertical velocity and CO₂ concentration were 90° out of phase. The wave was not directly associated with vertical fluxes of this variable but the mixing induced by its passage resulted in significant exchanges in smaller scales as measured by the eddy-covariance system. The phase differences between horizontal velocity and both air temperature and CO₂ concentration were, respectively, zero and 180°, implying phase and anti-phase relationships. As a result, the wave contributed to positive horizontal fluxes of heat and negative horizontal fluxes of carbon dioxide. Such results have to be considered in nocturnal boundary-layer surface-atmosphere exchange schemes for modelling purposes.     

Wavy Vertical Motions in the ABL Observed by Sodar

Some characteristics of wavelike motions in the atmospheric boundary layer observed by sodar are considered. In an experiment carried out in February 1993 in Milan, Italy, Doppler sodar measurements were accompanied by in situ measurements of temperature and wind velocity vertical profiles using a tethered balloon up to 600 m. The oscillations of elevated wavy layers containing intense thermal turbulence, usually associated with temperature-inversion zones, were studied by using correlation and spectral analysis methods. The statistics of the occurrence of wavelike and temperature-inversion events are presented. The height distributions of Brunt–Vaisala frequency and wind shear and their correlation within elevated inversion layers were determined, with a strong correlation observed between the drift rate of the wavy layers and the vertical velocity measured by Doppler sodar inside these layers. Spectral analysis showed similarities regarding their frequency characteristics. The phase speed and propagation direction of waves were estimated from the time delay of the signals at three antennae to provide estimates of wavelength. Moreover, wavelengths were estimated from the intrinsic frequency obtained from sodar measurements of the Doppler vertical velocity and oscillations of wavy turbulent layers. The two wavelength estimates are in good agreement.     

冬奥崇礼赛区一次冷湖过程形成及消散的数值模拟研究

本文利用中尺度数值预报模式(WRF)并采用谱逼近方法,对2021年冬奥测试赛期间的一次冷湖过程进行模拟研究,探究了冷湖发展前后风温场的垂直变化规律,揭示了冷湖形成及消亡的具体原因。研究结果表明,静稳的天气形势是冷湖过程维持及发展的大背景条件。冷湖发展期间,逆温层由上至下迅速建立,谷底出现偏东—东南向的冷径流。受重力下坡风的影响,冷空气不断向谷底堆积,冷湖深度增加。日出后,越山的系统风重新建立,逆温层从底部消蚀,冷湖结构破坏。夜间的强辐射冷却作用是冷湖形成的主要原因之一。辐射冷却强度的差异会引起冷湖降温幅度的差异,后半夜辐射冷却作用的突然加强为冷湖中后期的维持及发展创造有利条件。通过分析冷湖发生前后位温廓线、摩擦速度及边界层高度随时间的演变,均可印证湍流活动的发展是逆温消散、冷湖结构破坏的重要影响因素。     

Observation of a Self-Limiting,Shear-Induced Turbulent Inversion Layer Above Marine Stratocumulus

High-resolution measurements of thermodynamic, microphysical, and turbulence properties inside a turbulent inversion layer above a marine stratocumulus cloud layer are presented. The measurements are performed with the helicopter-towed measurement payload Airborne Cloud Turbulence Observation System (ACTOS), which allows for sampling with low true air speeds and steep profiles through cloud top. Vertical profiles show that the turbulent inversion layer consists of clear air above the cloud top, with nearly linear profiles of potential temperature, horizontal wind speed, absolute humidity, and concentration of interstitial aerosol. The layer is turbulent, with an energy dissipation rate nearly the same as that in the lower cloud, suggesting that the two are actively coupled, but with significant anisotropic turbulence at the large scales within the turbulent inversion layer. The turbulent inversion layer is traversed six times and the layer thickness is observed to vary between 37 and 85 m, whereas the potential temperature and horizontal wind speed differences at the top and bottom of the layer remain essentially constant. The Richardson number therefore increases with increasing layer thickness, from approximately 0.2 to 0.7, suggesting that the layer develops to the point where shear production of turbulence is sufficiently weak to be balanced by buoyancy suppression. This picture is consistent with prior numerical simulations of the evolution of turbulence in localized stratified shear layers. It is observed that the large eddy scale is suppressed by buoyancy and is on the order of the Ozmidov scale, much less than the thickness of the turbulent inversion layer, such that direct mixing between the cloud top and the free troposphere is inhibited, and the entrainment velocity tends to decrease with increasing turbulent inversion-layer thickness. Qualitatively, the turbulent inversion layer likely grows through nibbling rather than engulfment.     

Measurements and Modelling of the Wind Speed Profile in the Marine Atmospheric Boundary Layer

We present measurements from 2006 of the marine wind speed profile at a site located 18 km from the west coast of Denmark in the North Sea. Measurements from mast-mounted cup anemometers up to a height of 45 m are extended to 161 m using LiDAR observations. Atmospheric turbulent flux measurements performed in 2004 with a sonic anemometer are compared to a bulk Richardson number formulation of the atmospheric stability. This is used to classify the LiDAR/cup wind speed profiles into atmospheric stability classes. The observations are compared to a simplified model for the wind speed profile that accounts for the effect of the boundary-layer height. For unstable and neutral atmospheric conditions the boundary-layer height could be neglected, whereas for stable conditions it is comparable to the measuring heights and therefore essential to include. It is interesting to note that, although it is derived from a different physical approach, the simplified wind speed profile conforms to the traditional expressions of the surface layer when the effect of the boundary-layer height is neglected.     

Analysis of aircraft measurements of momentum flux in the subcloud layer over the tropical atlantic ocean during gate

The momentum flux data obtained by the gust probe aboard the NOAA DC-6 aircraft during GATE are analyzed. Vertical profiles are obtained for Phases I and III and correlated with vertical wind velocity profiles using the geostrophic departure method. Reasonable agreement is obtained using the horizontal equations of motion with negligible advective acceleration. The vertical profiles of momentum flux and wind speed variance compare well with the numerical model results of Deardorff (1972) and Wyngaard et al. (1974). Vertical distributions of power spectra for vertical eddy motion and cospectra corresponding to the momentum flux components are obtained along with the height variation of the dominant length scales of vertical eddy motion and the dissipation rate of turbulence kinetic energy. When normalized by mixed-layer similarity, these results agree well with previous determinations in the boundary layer over tropical oceans and over land.     

Numerical Simulation and Observational Analysis of the Bora of Pag’s Ribs

The severe bora case that lasted from 13 to 15 November 2004 has been selected for the analysis of the bora of Pag’s ribs, which occurs in the northern part of the eastern Adriatic coast over the Pag island area (Croatia). According to the measurements from automatic stations, the MM5 numerical model is successful in the 10-min mean wind speed prediction at 10-m height. The vertical analysis of the wind speed and potential temperature also gave satisfactory results. At the commencement of the bora the modelled wind had a magnitude of 20ms⁻¹ at 10-m height in the Pag island area, which sharply attenuated in the cross direction and to the open sea. In this way the model has proved successful in predicting the characteristics of the bora of Pag’s ribs. Potential vorticity (PV) at 600m has lower values within PV banners than during the developed bora. The consequence is a strong jet emanating from the nearest gap. The vertical cross-sections through the centre of the gap point out a permanent hydraulic-like flow. At the time of the bora of Pag’s ribs the highest modelled turbulent kinetic energy is found in the jump-like region above the inversion and within the boundary layer along the lower boundary, ranging from 6–8m² s⁻². It is concluded that the dissipation in the hydraulic jumps and the wave breaking regions are the reasons for PV generation.     

Use of a High-Resolution Sodar to Study Surface-layer Turbulence at Night

Measurements in the atmospheric surface layer are generally made with point sensors located in the first few tens of metres. In most cases, however, these measurements are not representative of the whole surface layer. Standard Doppler sodars allow a continuous display of the turbulent thermal structure and wind profiles in the boundary layer up to 1000 m, with a few points, if any, in the surface layer. To overcome these limitations a new sodar configuration is proposed that allows for a higher resolution in the surface layer. Because of its capabilities (echo recording starting at 2 m, echo intensity vertical resolution of approximately 2 m, temporal resolution of 1 s) this sodar is called the surface-layer mini-sodar (SLM-sodar). Features and capabilities of the SLM-sodar are described and compared with the sodar. The comparison of the thermal vertical structure given by the SLM-sodar and the sodar provides evidence that, in most cases, the surface layer presents a level of complexity comparable to that of the entire boundary layer. Considering its high vertical resolution, the SLM-sodar is a promising system for the study of the nocturnal surface layer. The nocturnal SLM-sodar measurements have shown that, depending on wind speed, the structure of the surface layer may change substantially within a short time period. At night, when the wind speed is greater than 3 m s⁻¹, mechanical mixing destroys the wavy structure present in the nocturnal layer. Sonic anemometer measurements have shown that, in such cases, also the sensible heat flux varies with height, reaching a peak in correspondence with the wind speed peak. Under these conditions the assumption of horizontal homogeneity of the surface layer and the choice of the averaging time need to be carefully treated.     

Estimating the turbulent energy dissipation rate in an airport environment

This note reports on the influence of aircraft wake vortices on the estimation of the turbulent energy dissipation rate using sonic anemometer measurements near the runway threshold. The wake vortex traces, which are generated at a height of about 65 m and subsequently evolve in ground effect, are clearly visible in the velocity components and temperature. The observed temperature increase of 1 K appears related to the stably stratified atmospheric surface layer. The dissipation rate is estimated from the longitudinal velocity power spectrum for a sample in a nocturnal boundary layer with and without a wake vortex signal. In both cases an inertial subrange is found. For the analyzed sample the estimated dissipation rate is a factor of ten larger compared to the undisturbed sample. Implications for operational wake avoidance systems are discussed.     

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.     

Sensitivity of Turbine-Height Wind Speeds to Parameters in Planetary Boundary-Layer and Surface-Layer Schemes in the Weather Research and Forecasting Model

We evaluate the sensitivity of simulated turbine-height wind speeds to 26 parameters within the Mellor–Yamada–Nakanishi–Niino (MYNN) planetary boundary-layer scheme and MM5 surface-layer scheme of the Weather Research and Forecasting model over an area of complex terrain. An efficient sampling algorithm and generalized linear model are used to explore the multiple-dimensional parameter space and quantify the parametric sensitivity of simulated turbine-height wind speeds. The results indicate that most of the variability in the ensemble simulations is due to parameters related to the dissipation of turbulent kinetic energy (TKE), Prandtl number, turbulent length scales, surface roughness, and the von Kármán constant. The parameter associated with the TKE dissipation rate is found to be most important, and a larger dissipation rate produces larger hub-height wind speeds. A larger Prandtl number results in smaller nighttime wind speeds. Increasing surface roughness reduces the frequencies of both extremely weak and strong airflows, implying a reduction in the variability of wind speed. All of the above parameters significantly affect the vertical profiles of wind speed and the magnitude of wind shear. The relative contributions of individual parameters are found to be dependent on both the terrain slope and atmospheric stability.     

An Auxiliary Tool to Determine the Height of the Boundary Layer

Results from radiosoundings, performed both over land and over sea, show that the ascent rate of a radiosounding balloon, the vertical velocity of the balloon, can be used to determine the height of the boundary layer. In many cases the balloon has a higher ascent rate in the boundary layer and a lower, less variable, ascent rate above. The decrease in ascending velocity appears as a jump at the top of the boundary layer. Two examples of potential temperature profiles for unstable stratification and one profile for stable conditions are shown with the corresponding ascent rates. A comparison between the boundary-layer height determined from potential temperature profiles and from ascent rates is presented for a larger dataset. The different ascent rates of the balloon in the boundary layer and above can be explained by a decrease in drag on the balloon in combination with a lowering of the critical Reynolds number in the boundary layer caused by turbulence. Hence, by simply logging the time from release of a radiosonde, it is possible to obtain additional information that can be used to estimate the height of both the unstable and stable boundary layers.     

Reconstruction of the surface-layer vertical structure from measurements of wind,temperature and humidity at two levels

We present a comparison between several methods used to reconstruct fluxes and vertical profiles of wind, temperature and humidity from measurements at two levels in the atmospheric surface layer for different practical applications. An analytical method and an iterative method are tested by evaluating the quality of estimations of surface fluxes from detailed field measurements obtained during a campaign on the site of Lannemezan in the south-west of France. The iterative method yields better results, but the analytical one can give results of the same level of accuracy provided that specific constants in its formulation are modified. Then these techniques are applied to wind and temperature reconstruction for an experiment dedicated to wind power estimates over flat terrain. If turbulent fluxes are not needed, a simple power law appears to be sufficient, as the method based on Monin–Obukhov theory does not improve the accuracy of the vertical profile reconstruction.     

Nocturnal stable boundary layer height model and its application

A model of the evolution of the nocturnal stable boundary layer height, based on the heat conservation equation for a turbulent flow, is presented. This model is valid for nights with weak winds and little cloudiness in rural areas. The model includes an expression of vertical profile of potential temperature within the boundary layer, which is obtained using micrometeorological information from Prairie Grass, Wangara and O'Neill Projects. The expression turned out to be a second-grade polynomial of the dimensionless height of the nocturnal stable boundary layer. The resulting model is a function of the Monin–Obukhov length, the surface potential temperature of air and the roughness length. This model was satisfactorily compared with micrometeorological data. It was applied at three stations of Argentina, using surface hourly meteorological information. From the results that were obtained, the monthly average values of the stable boundary layer thickness were analysed. The maximum monthly average values occur during the cold season and the minimum ones take place during the hot season. It was observed that the monthly average thickness increases with latitude.     

On the Scale-dependence of the Gradient Richardson Number in the Residual Layer

We present results of a technique for examining the scale-dependence of the gradient Richardson number, Ri, in the nighttime residual layer. The technique makes use of a series of high-resolution, in situ, vertical profiles of wind speed and potential temperature obtained during CASES-99 in south-eastern Kansas, U.S.A. in October 1999. These profiles extended from the surface, through the nighttime stable boundary layer, and well into the residual layer. Analyses of the vertical gradients of both wind speed, potential temperature and turbulence profiles over a wide range of vertical scale sizes are used to estimate profiles of the local Ri and turbulence structure as a function of scale size. The utility of the technique lies both with the extensive height range of the residual layer as well as with the fact that the sub-metre resolution of the raw profiles enables a metre-by-metre ‘sliding’ average of the scale-dependent Richardson number values over hundreds of metres vertically. The results presented here show that small-scale turbulence is a ubiquitous and omnipresent feature of the residual layer, and that the region is dynamic and highly variable, exhibiting persistent turbulent structure on vertical scales of a few tens of metres or less. Furthermore, these scales are comparable to the scales over which the Ri is less than or equal to the critical value of Ri _c of 0.25, although turbulence is also shown to exist in regions with significantly larger Ri values, an observation at least consistent with the concept of hysteresis in turbulence generation and maintenance. Insofar as the important scale sizes are comparable to or smaller than the resolution of current models, it follows that, in order to resolve the observed details of small Ri values and the concomitant turbulence generation, future models need to be capable of significantly higher resolutions.