Detection of Entrainment Influences on Surface-Layer Measurements and Extension of Monin–Obukhov Similarity Theory

We present a method to detect influences of boundary-layer processes on surface-layer measurements, using statistics and spectra of surface-layer variables only. We validated our detection method with boundary-layer measurements. Furthermore, we confirm that Monin–Obukhov similarity functions fit well to temperature-variance data obtained at two different homogeneous surfaces. However, we found that humidity variance measurements deviate from the universal functions above one of the two studied surfaces for days on which entrained air reached the surface layer. These results confirm that Monin–Obukhov similarity theory should be used with care in the analysis of surface-layer data. Finally, we propose the use of an extra term in flux-variance relations that depends on the entrainment ratio for humidity and on the boundary-layer height. If boundary-layer measurements are not available, we show how the entrainment ratio for humidity can be approximated from the skewness of the humidity distribution.     

On Monin–Obukhov Similarity In The Stable Atmospheric Boundary Layer

Atmospheric measurements from several field experiments have been combined to develop a better understanding of the turbulence structure of the stable atmospheric boundary layer. Fast response wind velocity and temperature data have been recorded using 3-dimensional sonic anemometers, placed at severalheights (1 m to 4.3 m) above the ground. The measurements wereused to calculate the standard deviations of the three components of the windvelocity, temperature, turbulent kinetic energy (TKE) dissipation andtemperature variance dissipation. These data were normalized and plottedaccording to Monin–Obukhov similarity theory. The non-dimensional turbulencestatistics have been computed, in part, to investigate the generalapplicability of the concept of z-less stratification for stable conditions. From the analysis of a data set covering almost five orders ofmagnitude in the stability parameter = z/L (from near-neutral tovery stable atmospheric stability), it was found that this concept does nothold in general. It was only for the non-dimensional standard deviation oftemperature and the average dissipation rate of turbulent kinetic energythat z-less behaviour has been found. The other variables studied here(non-dimensional standard deviations of u, v, and w velocity components and dissipation of temperature variance) did not follow the concept of z-less stratification for the very stable atmospheric boundary layer. An imbalance between production and dissipation of TKE was found for the near-neutral limit approached from the stable regime, which matches with previous results for near-neutral stability approached from the unstable regime.     

Monin–Obukhov Similarity Functions for the Structure Parameters of Temperature and Humidity

Monin–Obukhov similarity functions for the structure parameters of temperature and humidity are needed to derive surface heat and water vapour fluxes from scintillometer measurements and it is often assumed that the two functions are identical in the atmospheric surface layer. Nevertheless, this assumption has not yet been verified experimentally. This study investigates the dissimilarity between the turbulent transport of sensible heat and water vapour, with a specific focus on the difference between the Monin–Obukhov similarity functions for the structure parameters. Using two datasets collected over homogeneous surfaces where the surface sources of sensible heat and water vapour are well correlated, we observe that under stable and very unstable conditions, the two functions are similar. This similarity however breaks down under weakly unstable conditions; in that regime, the absolute values of the correlations between temperature and humidity are also observed to be low, most likely due to large-scale eddies that transport unsteadiness, advection or entrainment effects from the outer layer. We analyze and demonstrate how this reduction in the correlation leads to dissimilarity between the turbulent transport of these two scalars and the corresponding Monin–Obukhov similarity functions for their structure parameters. A model to derive sensible and latent heat fluxes from structure parameters without measuring the friction velocity is tested and found to work very well under moderately to strongly unstable conditions (−z/L > 0.5). Finally, we discuss the modelling of the cross-structure parameter over wet surfaces, which is crucial for correcting water vapour effects on optical scintillometer measurements and also for obtaining surface sensible and latent heat fluxes from the two-wavelength scintillometry.     

A Cautionary Note on the Use of Monin–Obukhov Similarity Theory in Very High-Resolution Large-Eddy Simulations

In several recent large-eddy simulation studies, the lowest grid level was located well within the roughness sublayer. Monin–Obukhov similarity-based boundary conditions cannot be used under this scenario, and in this note we elaborate on this fundamental problem and suggest potential solutions.     

Moving Beyond Monin–Obukhov Similarity Theory in Modelling Wind-Speed Profiles in the Lower Atmospheric Boundary Layer under Stable Stratification

Monin–Obukhov similarity theory (MOST) is commonly used to model the wind-speed profile at altitudes relevant to wind-power production (e.g. 10–200 m). Though reasonably accurate for unstable to weakly stable stratification, this approach becomes less accurate under increasingly stable stratification, largely due to the constant-flux surface layer assumed by MOST becoming shallower than the altitude range of interest. Furthermore, above the surface layer, the Coriolis force has a considerable influence on the wind-speed profile (in particular in the formation of low-level jets) that cannot be modelled using similarity theory. Our goal is to compare the accuracy of alternative extrapolation models that are more physically appropriate above the surface layer. Using data from the 213-m Cabauw meteorological tower in the Netherlands between July 2007 and June 2008, it is shown that MOST is accurate only at low altitudes and low stability, and breaks down at high altitudes and high stability. Local similarity is generally more accurate than MOST across all altitudes and stabilities, though the model requires turbulent flux data at multiple altitudes that is generally impractical. In contrast, a two-layer MOST–Ekman model is found to be comparable to the other models at low stability ranges and considerably more accurate in the high stability range, while requiring only a measure of surface stability and the geostrophic wind.     

On Monin–Obukhov Scaling in and Above the Atmospheric Surface Layer: The Complexities of Elevated Scintillometer Measurements

In scintillometry Monin–Obukhov similarity theory (MOST) is used to calculate the surface sensible heat flux from the structure parameter of temperature (C_T²){(C_{T^2})} . In order to prevent saturation a scintillometer can be installed at an elevated level. However, in that case the observation level might be located outside the atmospheric surface layer (ASL) and thus the validity of MOST questioned. Therefore, we examine two concepts to determine the turbulent surface sensible heat flux from the structure parameter at elevated levels with data obtained at 60-m height on the Cabauw tower (the Netherlands). In the first concept (MOSTs) C_T²{C_{T^2}} is still scaled with the surface flux, whereas in the second (MOSTl) C_T²{C_{T^2}} is scaled with the local sensible heat flux. The C_T²{C_{T^2}} obtained from both concepts is compared with direct observations of C_T²{C_{T^2}} using a sonic anemometer/thermometer. In the afternoon (when the measurement height is located within the ASL) both concepts give results that are comparable to the directly observed values of C_T²{C_{T^2}} . In the morning (data outside the ASL), our data do not unequivocally support either of the two concepts. First, the peak in C_T²{C_{T^2}} that occurs when the measurement height is located in the entrainment zone disqualifies the use of MOST. Second, during the morning transition, local scaling shows the correct pattern (zero flux and a minimum in C_T²{C_{T^2}}) but underestimates C_T²{C_{T^2}} by a factor of ten. Third, from the best linear fit a we found that the slope of MOSTl gave better results, whereas the offset is closer to zero for MOSTs. Further, the correlation between the direct observations and MOST-scaled results is low and similar for the two concepts. In the end, we conclude that MOST is not applicable for the morning hours when the observation level is above the ASL.     

Monin–Obukhov Similarity Functions of the Structure Parameter of Temperature and Turbulent Kinetic Energy Dissipation Rate in the Stable Boundary Layer

The Monin–Obukhov similarity theory (MOST) functions f_ε and f_T, of the dissipation rate of turbulent kinetic energy (TKE). ε, and the structure parameter of temperature, C_T², were determined for the stable atmospheric surface layer using data gathered in the context of CASES-99. These data cover a relatively wide stability range, i.e. ζ=z/L of up to 10, where z is the height and L the Obukhov length. The best fits were given by f_ε = 0.8 + 2.5ζ and f_T= 4.7[ 1+1.6(ζ)^2/3], which differ somewhat from previously published functions. ε was obtained from spectra of the longitudinal wind velocity using a time series model (ARMA) method instead of the traditional Fourier transform. The neutral limit f_ε =0.8 implies that there is an imbalance between TKE production and dissipation in the simplified TKE budget equation. Similarly, we found a production-dissipation imbalance for the temperature fluctuation budget equation. Correcting for the production-dissipation imbalance, the ‘standard’ MOST functions for dimensionless wind speed and temperature gradients (φ_m and φ_m) were determined from f_ε and f_T and compared with the φ_m and φ_h formulations of Businger and others. We found good agreement with the Beljaars and Holtslag [J. Appl. Meteorol. 30, 327–341 (1991)] relations. Lastly, the flux and gradient Richardson numbers are discussed also in terms of f_ε and f_T.     

An Analytical Formulation of the Monin–Obukhov Stability Parameter in the Atmospheric Surface Layer Under Unstable Conditions

A non-iterative analytical scheme is developed for unstable stratification that parametrizes the Monin–Obukhov stability parameter \(\zeta \) (\({=}z{/}L\), where z is the height above the ground and L is the Obukhov length) in terms of bulk Richardson number (\(Ri_B\)) within the framework of Businger–Dyer type similarity functions. The proposed scheme is valid for a wide range of roughness lengths of heat and momentum. The absolute relative error in the transfer coefficients of heat and momentum is found to be less than 1.5% as compared to those obtained from an iterative scheme for Businger–Dyer type similarity functions. An attempt has been made to extend this scheme to incorporate the similarity functions having a theoretically consistent free convection limit. Further, the performance of the scheme is evaluated using observational data from two different sites. The proposed scheme is simple, non-iterative and relatively more accurate compared to the schemes reported in the literature and can be used as a potential alternative to iterative schemes used in numerical models of the atmosphere.     

Modification Of The Standard ∈-Equation For The Stable Abl Through Enforced Consistency With Monin–Obukhov Similarity Theory

A condition is derived for consistency of the standard-equation with Monin–Obukhov (MO) similarity theory of thestably-stratified surface layer. The condition is derivedby extending the procedure used to derive the analogous condition forneutral theory to stable stratification. It is shown that consistencywith MO theory requires a function of flux Richardson number, Ri_f, to be absorbed into either of two closure parameters, c ₁ or c ₂.Inconsistency, on the other hand, results if constant values of these are maintained for all Ri_f, as is done in standardapplication of the equation, and the large overpredictions ofturbulence found in such application to the one-dimensionalstable atmospheric boundary layer (1D-SBL) are traced to thisinconsistency. Guided by this, we formulate a MO-consistent-equation by absorbing the aforementioned function intoc ₁, and combine this with a Level-2.5 second-orderclosure model for vertical eddy viscosity and diffusivities.Numerical predictions of the 1D-SBL by the modified model converge to a quasi-steady state, rectifying the predictive failure of the standard -equation for the case.Quasi-steady predictions of non-dimensional variables agree stronglywith Nieuwstadt's theory. Qualitative accuracy of predictionsis inferred from comparisons to field data, large-eddy simulationresults and Rossby-number similarity relationships.     

Application of Linear Thermodynamics to the Atmospheric System. Part Ⅰ: Linear Phenomenological Relations and Thermodynamic Property of the Atmospheric System

从一般的热力学原理或其它自然原理对唯象关系所强加的限制，能够演绎出大气系统的一系列热力学性质。利用非平衡态线性热力学导出了湍流K闭合理论中湍流交换系数同唯象系数的关系，从理论上证明大气系统热量湍流输送同水泡之间存在交叉耦合，还导出了湍流强度同速度和位温梯度的关系，从而证明速度和位温空间分布的非均匀性是湍流之源。并证明湍流强度定理，不可压缩气体和各向同性湍流大气中，湍流强度正比于速度与位温梯度的标积。进而证明大气涡旋定理，位温的切变将导致涡旋运动或各种环流运动，速度涡度等于速度同位温相对梯度的矢积。展现了线性热力学在大气系统的应用前景。     

Application of Linear Thermodynamics to the Atmospheric System.Part Ⅱ: Exemplification of Linear Phenomenological Relations in the Atmospheric System

将边界层相似性理论同线性热力学理论结合，间接地以观测实验事实证明大气边界层内线性唯象关系是成立的，而且线性湍流输送系数同相应的线性唯象系数成正比关系。但实验事实表明，大涡对流的混合层线性唯象系数成正比关系。但实验事实表明，大涡对流的混合层线性唯象关系是不成立的，混合层内湍流输送过程是一种强的非线性过程。所以，对流边界层是一种远离平衡态非线性区的热力学状态。地转风和热成风是一种大气系统特有的动力过程和热力过程和交叉耦合现象，这是大气系统交叉耦合现象的一个实际例证。     

On the Generalized Theory of Atmospheric Particle Systems

Unification is both necessary and challenging for studying atmospheric particle systems, which are polydisperse systems containing particles of different sizes and shapes. A general framework is proposed to realize the first order generalization. Within this generalized framework, (1) atmospheric particle shapes are unified into self-similar fractals; (2) a self-similar particle is characterized by various power-law relationships; (3) by combining these power-law relationships for a single particle with Shannon’s maximum entropy principle and some concepts in statis-tical mechanics, unified maximum likelihoood number size distributions are of the Weibull form for atmospheric particle systems. Frontier disciplines (e. g., scaling, fractal, chaos and hierarchy) are argued to provide potential “tools” for such unification. Several new topics are raised for future research.     

Atmospheric Aerosol Characterization Over Naples During 2000–2003 EARLINET Project: Planetary Boundary-Layer Evolution and Layering

The evolution of the planetary boundary layer and the influence of local circulation phenomena over Naples (southern Italy, 40.838° N, 14.183° E, 118 m above sea level) have been studied by systematic lidar measurements of aerosol optical properties and vertical distributions carried out from May 2000 to August 2003, in the course of the EARLINET project. In particular, our data show the development of aerosol layers typically located in the range between 1,000 and 2,300 m, with variable thickness. The optical properties of the observed layers have been determined. In order to analyse the evolution of the planetary boundary layer, detailed observations of complete diurnal cycles have also been performed. The analysis of lidar measurements of vertical profiles of wind speed and wind direction and air mass back-trajectories allowed us to characterize the sea-breeze circulation influence on both the planetary boundary-layer evolution and the observed aerosol vertical distribution.     

On the Unified Theory of Atmospheric Particle Systems Part Ⅱ:Self-affine Particles

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Turbulent Flow at 190 m Height Above London During 2006–2008: A Climatology and the Applicability of Similarity Theory

Flow and turbulence above urban terrain is more complex than above rural terrain, due to the different momentum and heat transfer characteristics that are affected by the presence of buildings (e.g. pressure variations around buildings). The applicability of similarity theory (as developed over rural terrain) is tested using observations of flow from a sonic anemometer located at 190.3 m height in London, U.K. using about 6500 h of data. Turbulence statistics—dimensionless wind speed and temperature, standard deviations and correlation coefficients for momentum and heat transfer—were analysed in three ways. First, turbulence statistics were plotted as a function only of a local stability parameter z/Λ (where Λ is the local Obukhov length and z is the height above ground); the σ _i /u _* values (i = u, v, w) for neutral conditions are 2.3, 1.85 and 1.35 respectively, similar to canonical values. Second, analysis of urban mixed-layer formulations during daytime convective conditions over London was undertaken, showing that atmospheric turbulence at high altitude over large cities might not behave dissimilarly from that over rural terrain. Third, correlation coefficients for heat and momentum were analyzed with respect to local stability. The results give confidence in using the framework of local similarity for turbulence measured over London, and perhaps other cities. However, the following caveats for our data are worth noting: (i) the terrain is reasonably flat, (ii) building heights vary little over a large area, and (iii) the sensor height is above the mean roughness sublayer depth.     

Lettau’s Contribution to the Obukhov Length Scale: A Scientific Historical Study

Boundary-Layer Meteorology - It has been repeatedly assumed that Heinz Lettau found the Obukhov length in 1949 independently of Obukhov in 1946. However, it was not the characteristic length scale,...     

A Velocity–Dissipation Lagrangian Stochastic Model for Turbulent Dispersion in Atmospheric Boundary-Layer and Canopy Flows

An extended Lagrangian stochastic dispersion model that includes time variations of the turbulent kinetic energy dissipation rate is proposed. The instantaneous dissipation rate is described by a log-normal distribution to account for rare and intense bursts of dissipation occurring over short durations. This behaviour of the instantaneous dissipation rate is consistent with field measurements inside a pine forest and with published dissipation rate measurements in the atmospheric surface layer. The extended model is also shown to satisfy the well-mixed condition even for the highly inhomogeneous case of canopy flow. Application of this model to atmospheric boundary-layer and canopy flows reveals two types of motion that cannot be predicted by conventional dispersion models: a strong sweeping motion of particles towards the ground, and strong intermittent ejections of particles from the surface or canopy layer, which allows these particles to escape low-velocity regions to a high-velocity zone in the free air above. This ejective phenomenon increases the probability of marked fluid particles to reach far regions, creating a heavy tail in the mean concentration far from the scalar source.     

Impacts of Boundary-Layer Structure and Turbulence on the Variations of PM2.5 During Fog–Haze Episodes

Boundary-Layer Meteorology - The precise cause of PM2.5 (fine particular matter with a diameter smaller than 2.5 μm) explosive growth and the contribution of intermittent turbulence...     

Nonlinear Retrieval of Atmospheric Ozone Profile from Solar Backscatter Ultraviolet Measurements:Theory and Simulation

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