An empirical formula for the height of the coastal internal boundary layer

Observations of the height of the daytime coastal internal boundary layer at several sites are used to justify an empirical formula in the Offshore and Coastal Dispersion (OCD) model, which states that the boundary-layer slope is 0.1 in the first 2km from the shoreline, and 0.03 therafter.     

A note on estimating the height of the convective internal boundary layer near shore

When cool air flows from the sea over a warm coast, the air is thermally modified. It is shown that h = cX ^1/2, where h is the height (in meters) of this thermal or convective internal boundary layer (CIBL) over the coast, X is the distance downwind (in meters) from the shoreline (i.e., the fetch), and c is a coefficient that relates to the shear velocity and wind speed inside the CIBL, potential temperature difference and entrainment coefficient across the CIBL, and the lapse rate outside the CIBL. This equation is a simplification of a theoretical equation and is supported by three similar formulations based on thermodynamic and dimensional analyses. Pertinent field experiments conducted near shorelines in France, Sweden, and Japan indicate that c is approximately 1.91, with a standard deviation of 0.38. All observations are within 95% confidence limits.     

A model for the height of the internal boundary layer over an area with an irregular coastline

A model for the time and space variation of the internal boundary-layer height over a land area with an irregular coastline is presented. It is based on the analytical model of the boundary-layer height proposed by Gryning and Batchvarova (1990) and Batchvarova and Gryning (1991), The model accounts for the temperature jump and the mean vertical air motion at the top of the internal boundary-layer. Four cases from experiments in Nanticoke and Vancouver are used for model validation. The agreement between the calculated and measured internal boundary layer height at the observational sites is fairly good. The input information for the model consist of wind speed and direction, friction velocity and kinematic heat flux in time and space for the area, and the potential temperature gradient and the mean vertical air motion above the internal boundary layer. For the experiments used in the validation the effect of subsidence is relatively important in the afternoon under low wind speed high pressure conditions, lowering the height of the internal boundary layer by up to 10%, and it is negligible in the morning hours. The effect of the mixing height over the sea is found to be negligible.     

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.     

A parameterization of the stable atmospheric boundary layer

Two formulations of the stable atmospheric boundary layer are proposed for use in weather forecasting or climate models. They feature the log-linear profile near the surface, but are free from the associated critical Richardson number. The diffusion coefficients in the Ekman layer are a natural extension of the surface layer. They are locally determined using wind shear in one case and turbulent kinetic energy in the other. The parameterizations are tested in a one-dimensional model simulating the evolution of the nocturnal boundary layer with and without radiative cooling. Both formulations give very similar results, except near the top of the boundary layer where the transition to the free atmosphere is smoother with the wind shear formulation. A distinctive feature of these schemes is that they retain their simulating skill when resolution is reduced. This is verified for a wide range of situations. In practice, this means that there is no need for a large-scale model to have a level below 50 m or so.     

An examination of methods to estimate the height of the coastal internal boundary layer

This paper examines the assumptions and derivations that govern commonly used methods of estimating the height of the thermal internal boundary layer (TIBL) that occurs near shorelines. We show that nearly all these methods require inputs that can be defined only in the very limited context of the data set used to derive the empirical equations for the boundary-layer height. This analysis suggests that the current formulations have little general applicability, and it points to the need for more reliable methods for estimating the TIBL height.     

A note on estimating the height of the constant flux layer

A method is presented for estimating the height of the constant flux layer.     

On the evolution of the height and temperature difference across the nocturnal stable boundary layer

Evidence is furnished which indicates that in some cases the height of the stable boundary layer (SBL) and the magnitude of the temperature difference across the SBL may be more appropriately described by an error function erf(t/) rather than the generally accepted square root time dependence. The time constant was observed to have values of one to three hours. The discovery has been found to be site dependent, however, as data from other sites follow the usual square root time evolution.     

A model for eddy diffusivity in a stable boundary layer

Expressions for the vertical and the lateral diffusivity coefficients were derived from the Local Similarity Theory and the Statistical Diffusion Theory. For such, the spectral density energies for the turbulent velocities were used. The expressions here derived are compared with the diffusivity coefficients for momentum and heat suggested by Sorbjan (from the Minnesota experiments) and Nieuwstadt (from the Cabauw experiments). This comparison allows us to conclude that turbulence is equally efficient in transporting momentum, heat and contaminants in an ideally stable boundary layer.     

An analytical study on the urban boundary layer

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A case study of turbulence in the stable nocturnal boundary layer

Velocity and signal intensity data during stable conditions in the nocturnal boundary layer (NBL) were obtained with a minisodar on two consecutive nights with similar mean conditions. There was little turbulence activity during the first night, but during the second night, continuous background Kelvin-Helmholtz waves and instabilities having a 2-min period grew and penetrated above the mean NBL height at approximately 60-min intervals. Enhanced ozone concentrations at the surface occurred during the active periods even though most mean meteorological parameters were unchanged. Vertical profiles of vertical velocity standard deviation, dissipation rate, and temperature variance destruction rate in the NBL were measured and analyzed separately according to levels of turbulence activity. Well-defined differences between inactive and active periods of a factor of two to four were found for each parameter. The temperature structure parameter flux was large and in opposite directions in the upper and lower part of the NBL during active periods of turbulence, but small during other periods.     

Some aspects of the turbulent stable boundary layer

We consider the structure of the stable boundary layer using the concept of local scaling. In this scaling approach turbulence variables, non-dimensionalized with measurements taken at the same height, can be expressed as a function of a single parameter z/, where z is the height and a local Obukhov length. One of the consequences is that locally scaled variables become constant above the surface layer. This behavior is illustrated with observations of the Richardson number. With local scaling as a closure hypothesis we then formulate a model of the stable boundary layer. Its solution for steady-state conditions is given. One result we obtain is the well-known Zilitinkevich equation for the boundary-layer height. A comparison of this equation with observations results in a reasonable agreement. Also we discuss some alternative expressions for the stable boundary-layer height and compare them with observations. Another result of our model is an explicit profile for the K-coefficient as a quadratic function of height. We discuss the consequences of this expression for the dispersion of a point source emission. We find that the time scale of diffusion in this case is about 5 hours.     

On the determination of the height of the Ekman boundary layer

The heighth of the Ekman turbulent boundary layer determined by the momentum flux profile is estimated with the aid of considerations of similarity and an analysis of the dynamic equations. Asymptotic formulae have been obtained showing that, with increasing instability,h increases as ¦¦^1/2 (where is the non-dimensional stratification parameter); with increasing stability, on the other hand,h decreases as ^–1/2. For comparison, a simple estimate of the boundary-layer heighth _u determined by the velocity profile is given. As is shown, in unstable stratification,h _u behaves asymptotically as ¦¦^–1, i.e., in a manner entirely different from that ofh .     

Evaluation of Sodar methods for the determination of the atmospheric boundary layer mixing height

Summary It is the purpose of this paper to evaluate the different Sodar approaches and methods for the determination of the atmospheric mixing height against direct measurements. To achieve this objective a specific experiment was designed and performed incorporating, a research home made Sodar, a tethered balloon and a radiosonde facility as well as a conventional ground based meteorological station. The obtained data were statistically treated and analyzed to high-light the advantages and disadvantages of the various methods during different meteorological conditions. The results indicate that all three manual methods produce reasonable estimates during convective conditions, while for the stable cases the acceptable techniques are reduced to two. For the automated approach however, the two methods produced quite acceptable estimates during convective conditions, while for the stable cases none was found suitable for use.     

大气边界层高度确定及应用研究进展

大气边界层高度是表征边界层特征的重要参量,影响边界层内水热、物质、能量的垂直分布,也是数值模拟、环境评估中的重要参数。从湍流运动、热力作用、动力作用以及物质分布等多视角总结了大气边界层高度的定义及确定方法,回顾了采用直接观测手段和遥感手段确定大气边界层高度的不同方法,对比了大气边界层高度不同获取手段的优缺点,梳理了大气边界层高度参数化方案,探讨了大气边界层高度确定中存在的问题,并提出未来相关研究和应用可能突破方向。     

Estimating the Monin-Obukhov length in the stable boundary layer for dispersion calculations

Analysis of data collected during the Prairie Grass, Kansas and Minnesota experiments reveals the following empirical relationship between the Monin-Obukhov length L and the friction velocity u _*: L = Au _* ², A = 1.1 × 10³s²m^-1. This result combined with the formulation for the height of the stable boundary layer h suggested by Zilitinkevich (1972) leads to h u _* ^3/2 f–^1/2 where f is the Coriolis parameter. Data from the Minnesota study (Caughey et al., 1979) provide ample support for this expression.These empirical equations for L and h are useful for routine dispersion estimates during stable conditions.     

Coherent structures in the very stable atmospheric boundary layer

This study examines the structure of horizontal modes (meandering, vortical modes or fossil turbulence) in a layer of intermittent turbulence occurring at the top of a strongly stratified nocturnal inversion layer as observed by fast response aircraft data. The spatial variation of the coefficients of the principal components identify regular coherent structures with mainly horizontal motions. Conditional sampling is formulated in terms of this spatial variation. The quasi-horizontal motions are characterized by relatively sharp edges (transition zones) where horizontal convergence or divergence, small-scale turbulence and vertical fluxes seem to be concentrated. Zones of horizontal divergence appear to be associated with ejection of cold air from the underlying surface inversion while the convergent zones might be due to random collisions between horizontal modes.     

The velocity spectra in the stable atmospheric boundary layer

A model for the logarithmic spectra of velocity in the stable boundary layer is developed using the concept of local scaling. The resulting expressions for peak wavelength are in agreement with empirical data from Minnesota 1973.Partially financed by CAPES and FINEP.On leave from Faculdade de Engenharia de Joinville, SC, Brasil.     

Investigation of the planetary boundary layer height variations over complex terrain

The effects of sea-breeze interactions with synoptic forcing on the PBL height over complex terrain are investigated through the use of a 3-D mesoscale numerical model. Two of the results are as follows. First, steep PBL height gradients—order of 1500 m over a grid interval of 10 km — are associated with the sea-breeze front and are enhanced by the topography. Second, a significant horizontal shift in the maximum PBL height relative to the mountains, is induced by a corresponding displacement of the thermal ridge due to the mountains, in the presence of large scale flow.     

The depth of the internal boundary layer over an urban area under sea-breeze conditions

Field data are analyzed in order to study the development of the Thermal Internal Boundary Layer (TIBL) under sea breeze conditions. The measurements were carried out by the National Observatory of Athens (NOA) during ATHens Internal Boundary Layer Experiment (ATHIBLEX) in summer 1989 and 1990.Several formulations found in the literature are tested against the measurements in order to investigate whether they are capable of predicting the depth of the TIBL. It is found that a slab model including mechanical production of turbulence gives overall good agreement with the measurements.Finally, the concept of local equilibrium is used to explain the discrepancies found between small-and meso-scale observations and models; a formula is proposed which is intended for use over a wide range of downwind fetches.