Lidar measurements of plume statistics

Surface-layer aerosol diffusion experiments have been conducted using artificial smoke plume releases at ground level over flat and homogeneously vegetated terrain at the Meppen proving grounds in the Federal Republic of Germany (1989). At fixed downwind locations in the range out to 800 m from the source, instantaneous crosswind plume profiles were detected repetitively at high spatial (1.5 m) and temporal (3 sec) intervals by use of a mini LIDAR system. The experiments were accompanied by measurement of the surface-layer mean wind and turbulence quantities by sonic anemometers. On the basis of measured crosswind concentration profiles, the following statistics were obtained: 1) Mean profile, 2) Root mean square profile, 3) Fluctuation intensities, and 4) Intermittency factors. Furthermore, some experimentally determined probability density functions (pdf's) of the fluctuations are presented. All the measured statistics are referred to a fixed and a moving frame of reference, the latter being defined as a frame of reference from which the (low frequency) plume meander is removed. Finally, the measured statistics are compared with statistics on concentration fluctuations obtained with a simple puff diffusion model (RIMPUFF) developed at Risø.     

Measurements of level-crossing statistics of concentration fluctuations in plumes dispersing in the atmospheric surface layer

The statistics of level crossings and local extremes in concentration fluctuations in plumes dispersing in the atmosphere have been investigated. A set of concentration fluctuation tracer experiments has been utilized to measure the statistical propertics of the upcrossing interval (inter-arrival time between consecutive concentration bursts), excursion duration (persistence or width of concentration bursts), and concentration amplitude (difference between the maximum and minimum concentrations between successive upcrossings) with respect to a range of concentration crossing levels. In particular, the effect of downwind distance and atmospheric stratification on the level-crossing statistics has been studied in detail. It is shown that the effect of increasing atmospheric stability on level-crossing statistics is similar to the effect of increasing distance from the source in the sense that level-crossing statistics of concentration fluctuations in stable stratification resemble those in neutral stratification, but at a greater downwind distance. It is also found that the distribution of the interval between consecutive upcrossings of a concentration level, as well as the duration of an excursion across a concentration level, can be approximated by a lognormal distribution, whereas the distribution of the concentration amplitude is best characterized by a gamma distribution. Some implications of these results for the modeling of level-crossing statistics of concentration fluctuations are discussed.     

The vertical profile of concentration fluctuations in near-surface plumes

Field experiments on concentration fluctuations have frequently measured horizontal cross-sections of fluctuation statistics through plumes at fixed heights near the surface, but have not considered the effect of height above the ground in any detail. A set of tracer experiments designed to measure vertical profiles of concentration fluctuations in plumes, with a range of source heights, is described, and profiles of statistics are presented. Considerable variation of the statistics with both source and detector height is found. Near the surface, fluctuation intensity is a minimum and the time and length scales of the fluctuations are greatly increased. Profiles are consistent with the idea that concentration fluctuations near the surface are like those higher up at a greater distance from the source. Lowering the source height reduces the fluctuation intensity at all heights, and also alters the form of the concentration PDF. Results may be explained by the reduced length scale of sheargenerated turbulence near the surface causing enhanced small-scale mixing, which rapidly smooths out much of the fine structure with the plume.     

Statistics of wind direction fluctuations in the surface layer over plant canopies

Boundary-Layer Meteorology - Height dependency of statistics of horizontal and vertical wind direction fluctuations over plant canopies have been studied, using observational data in the surface...     

The variations of the statistics of wind,temperature and humidity fluctuations with stability

Measurements of the turbulent fluctuations of wind, temperature and humidity were made in the atmospheric surface layer. The statistics of the fluctuations were investigated in both the time and frequency domains. The vertical wind, temperature and smaller-scale horizontal wind fluctuations appear to obey the Monin-Obukhov similarity hypothesis. The humidity fluctuations were found to be governed by a humidity flux stability parameter rather than the normal Monin-Obukhov length.     

Boundedness of Turbulent Temperature Probability Distributions,and their Relation to the Vertical Profile in the Convective Boundary Layer

Higher-order moments, minima and maxima of turbulent temperature and water vapour mixing ratio probability density functions measured with an eddy-covariance system near the ground were related to each other and to vertical boundary-layer profiles of the same scalars obtained through airborne soundings. The dependence of kurtosis on squared skewness showed a kurtosis intercept below the Gaussian expectation, suggesting a compression of the probability density function by the presence of natural boundaries. This hypothesis was corroborated by comparing actual minima and maxima of turbulent fluctuations to estimates obtained from the first four sample moments by fitting a four-parameter beta distribution. The most sharply defined boundaries were found for the minima of temperature datasets during the day, indicating that negative temperature fluctuations at the sensor are limited by the availability of lower temperatures in the boundary layer. By comparison to vertical profiles, it could be verified that the turbulent minimum of temperature near the ground is close to the minimum of potential temperature in the boundary layer. The turbulent minimum of water vapour mixing ratio was found to be equal to the mixing ratio at a height above the minimum of the temperature profile. This height roughly agrees with the top of the non-local unstable domain according to bulk Richardson number profiles. We conclude that turbulence statistics measured near the surface cannot be solely explained by local effects, but contain information about the whole boundary layer including the entrainment zone.     

Variations of carbon dioxide,air temperature,and horizontal wind within and above a maize crop

The mean and short-term fluctuations of carbon dioxide concentration, air temperature, and horizontal wind speed were measured simultaneously within and above a maize crop. Although fluctuations were large at each of the 10 measurement heights, the largest were at the 180-cm level, the densest part of the crop. These short-term fluctuations indicated the broad range of environmental conditions to which plants are exposed (and which plants create or modify) in the field. The statistics of the distributions of these meteorological elements are discussed and the deviations from steady-state conditions are examined by determining linear trends. Finally, variance spectra showed the periodicity of the variations of these meteorological elements.Contribution from the Agricultural Research Service, US Department of Agriculture in cooperation with N.Y. State College of Agriculture, Cornell University, Ithaca, No. 1205. CBRI Contribution No. 966.     

Vertical profiles of small-scale temperature structure in the atmosphere

Measurements of air temperature fluctuations at frequencies from 1–100 Hz have been made with instruments carried by free-flying balloons. Structure functions and spectra of the temperature field have been calculated for various heights within the range 0.1–8 km above ground. The frequent occurrence of shallow regions, possibly layers, which exhibit locally enhanced values of the structure coefficient has been confirmed.     

Application of a Large-Eddy Simulation Database to Optimisation of First-Order Closures for Neutral and Stably Stratified Boundary Layers

Large-eddy simulation (LES) is a well-established numerical technique, resolving the most energetic turbulent fluctuations in the planetary boundary layer. By averaging these fluctuations, high-quality profiles of mean quantities and turbulence statistics can be obtained in experiments with well-defined initial and boundary conditions. Hence, LES data can be beneficial for assessment and optimisation of turbulence closure schemes. A database of 80 LES runs (DATABASE64) for neutral and stably stratified planetary boundary layers (PBLs) is applied in this study to optimize first-order turbulence closure (FOC). Approximations for the mixing length scale and stability correction functions have been made to minimise a relative root-mean-square error over the entire database. New stability functions have correct asymptotes describing regimes of strong and weak mixing found in theoretical approaches, atmospheric observations and LES. The correct asymptotes exclude the need for a critical Richardson number in the FOC formulation. Further, we analysed the FOC quality as functions of the integral PBL stability and the vertical model resolution. We show that the FOC is never perfect because the turbulence in the upper half of the PBL is not generated by the local vertical gradients. Accordingly, the parameterised and LES-based fluxes decorrelate in the upper PBL. With this imperfection in mind, we show that there is no systematic quality deterioration of the FOC in the strongly stable PBL provided that the vertical model resolution is better than 10 levels within the PBL. In agreement with previous studies, we found that the quality improves slowly with the vertical resolution refinement, though it is generally wise not to overstretch the mesh in the lowest 500 m of the atmosphere where the observed, simulated and theoretically predicted stably stratified PBL is mostly located. The submission to a special issue of the “Boundary-Layer Meteorology” devoted to the NATO advanced research workshop “Atmospheric Boundary Layers: Modelling and Applications for Environmental Security”.     

Simplified expressions for adjusting higher-order turbulent statistics obtained from open path gas analyzers

When density fluctuations of scalars such as CO₂ are measured with open-path gas analyzers, the measured vertical turbulent flux must be adjusted to take into account fluctuations induced by ‘external effects’ such as temperature and water vapour. These adjustments are needed to separate the effects of surface fluxes responsible for ‘natural’ fluctuations in CO₂ concentration from these external effects. Analogous to vertical fluxes, simplified expressions for separating the ‘external effects’ from higher-order scalar density turbulence statistics are derived. The level of complexity in terms of input to these expressions are analogous to that of the Webb–Pearman–Leuning (WPL), and are shown to be consistent with the conservation of dry air. It is demonstrated that both higher-order turbulent moments such as the scalar variances, the mixed velocity-scalar covariances, and the two-scalar covariance require significant adjustments due to ‘external effects’. The impact of these adjustments on the turbulent CO₂ spectra, probability density function, and dimensionless similarity functions derived from flux-variance relationships are also discussed.     

An Experimental Study of the Statistics of Temperature Fluctuations in the Atmospheric Boundary Layer

A statistical characterization for two-point temperature fluctuations in the planetary boundary layer (PBL) is analyzed and its implications on the long-standing closure problem discussed. Despite the non-triviality of the dynamics of temperature fluctuations, our analysis supports the idea that the most relevant statistical properties can be captured solely in terms of two scaling exponents. They turned out to be weakly dependent on the stability properties of the PBL. Its statistics have been investigated by collecting data from a field experiment carried out in the urban area of Turin (Italy) from January 2007 to March 2008. Our results confirm those from a large-eddy simulation (LES) analysis carried out for the convective PBL with different level of convection. We extend the scenario to the stable PBL, a regime much more difficult to simulate when exploiting LES.     

The effects of source size on concentration fluctuations in plumes

The effects of source size on plume behaviour have been examined in a 1.2 m wind tunnel boundary layer for isokinetic sources with diameters from 3 to 35 mm at source heights of 230 mm and at ground level. Experimental measurements of mean concentration and the variance, intermittency and probability density functions of the concentration fluctuations were obtained. In addition, a fluctuating Gaussian plume model is presented which reproduces many of the observed features of the elevated emission. The mean plume width becomes independent of source size much more rapidly than the instantaneous plume width. Since it is the meandering of the instantaneous plume which generates most of the concentration fluctuations near the source, these are also dependent on source size. The flux of variance in the plume reaches a maximum, whose value is greatest for the smallest source size, close to the source and thereafter is monotonically decreasing. The intermittency factor reaches a minimum, whose value is lowest for the smallest source, and increases back towards one. Concentration fluctuations for the ground-level source are much less dependent on source size due to the effects of the surface.     

Statistics of Air Temperature Spatial Variability in the Atmospheric Surface Layer

Surface-layer convection is investigated by analyzing multi-point measurements of temperature and velocity fluctuations at different sets of spatial points.The visual analysis of temperature and velocity fluctuations measured by sensors mounted on a mast of 36-m height clearly reveals the presence of large-scale convective cells (known as ramp structures) making large contributions to the heat transfer from the ground to lower atmosphere. The vertical temperature variability is described with the aid of empirical orthogonal functions derived from temperature covariance matrices for the heights of 1, 2, 5, 10, 18 and 36 m. Temporal-spatial correlation functions obtained allow estimates of a characteristic velocity scale, which may be interpreted as the downwind velocity of ramp structures.     

On the relation between ENSO and global climate change

Summary Two lines of research into climate change and El Niño/Southern Oscillation (ENSO) converge on the conclusion that changes in ENSO statistics occur as a response to global climate (temperature) fluctuations. One approach focuses on the statistics of temperature fluctuations interpreted within the framework of random walks. The second is based on the discovery of correlation between the recurrence frequency of El Niño and temperature change, while developing physical arguments to explain several phenomena associated with changes in El Niño frequency. Consideration of both perspectives leads to greater confidence in, and guidance for, the physical interpretation of the relationship between ENSO and global climate change. Topics considered include global dynamics of ENSO, ENSO triggers, and climate prediction and predictability.Revised November 14, 2002; accepted November 28, 2002 Published online: June 12, 2003     

Similarity of atmospheric Reynolds shear stress and heat flux fluctuations over a rough surface

Horizontal u and vertical w velocity fluctuations have been measured together with temperature fluctuations in the atmospheric surface layer, at a small height above a wheat crop canopy. Marginal probability density functions are presented for both individual fluctuations u, w, and for the instantaneous Reynolds stress uw, and heat fluxes w and u. Probability density functions of the velocity fluctuations deviate less significantly from the Gaussian form than the probability density of temperature. There appears to be closer similarity between statistics of the instantaneous heat fluxes than between the momentum flux and either of the heat fluxes investigated. The mean momentum flux receives equal contributions from the events referred to as ejections and sweeps in laboratory boundary layers. Sweeps provide the largest contribution to the heat fluxes.     

An observational study of wind-induced waving of plants

The motions of individual plants and the turbulence statistics of surface winds measured near the top of a canopy are obtained over a wheat field and a rush field. Two typical cases of motions of individual plants are presented. The displacements of the ear of wheat (the plant height is 1.0 m) showed a natural oscillation in wind speeds of 1.6 m s^–1 measured at a height of 30 cm over a wheat canopy, while displacements of the stem of a rush plant were closely related to the fluctuations of surface winds in wind speeds of 1.7 m s^–1 measured at the top of the rush plant. The power spectra of displacements of a rush plant seem to support the negative seven-third power hypothesis proposed by Inoue. The frequency responses of displacements of plants to fluctuations of the instantaneous momentum flux are also presented.     

An Observational Study of Wind-Induced Waving of Plants

The motions of individual plants and the turbulence statistics of surface winds measured near the top of a canopy are obtained over a wheat field and a rush field. Two typical cases of motions of individual plants are presented. The displacements of the ear of wheat (the plant height is 1.0 m) showed a natural oscillation in wind speeds of 1.6 m s⁻¹ measured at a height of 30 cm over a wheat canopy, while displacements of the stem of a rush plant were closely related to the fluctuations of surface winds in wind speeds of 1.7 m s⁻¹ measured at the top of the rush plant. The power spectra of displacements of a rush plant seem to support the negative seven-third power hypothesis proposed by Inoue. The frequency responses of displacements of plants to fluctuations of the instantaneous momentum flux are also presented.     

Statistical characteristics of concentration fluctuations in dispersing plumes in the atmospheric surface layer

Measurements have been made of concentration fluctuations in a dispersing plume from an elevated point source in the atmospheric surface layer using a recently developed fast-response photoionization detector. This detector, which has a frequency response (–6 dB point) of about 100 Hz, is shown to be capable of resolving the fluctuation variance contributed by the energetic subrange and most of the inertial-convective subrange, with a reduction in the fluctuation variance due to instrument smoothing of the finest scales present in the plume of at most 4%.Concentration time series have been analyzed to obtain the statistical characteristics of both the amplitude and temporal structure of the dispersing plume. We present alongwind and crosswind concentration fluctuation profiles of statistics of amplitude structure such as total and conditional fluctuation intensity, skewness and kurtosis, and of temporal structure such as intermittency factor, burst frequency, and mean burst persistence time. Comparisons of empirical concentration probability distributions with a number of model distributions show that our near-neutral data are best represented by the lognormal distribution at shorter ranges, where both plume meandering and fine-scale in-plume mixing are equally important (turbulent-convective regime), and by the gamma distribution at longer ranges, where internal structure or spottiness is becoming dominant (turbulent-diffusive regime). The gamma distribution provides the best model of the concentration pdf over all downwind fetches for data measured under stable stratification. A physical model is developed to explain the mechanism-induced probabilistic schemes in the alongwind development of a dispersing plume, that lead to the observed probability distributions of concentration. Probability distributions of concentration burst length and burst return period have been extracted and are shown to be modelled well with a powerlaw distribution. Power spectra of concentration fluctuations are presented. These spectra exhibit a significant inertial-convective subrange, with the frequency at the spectral peak decreasing with increasing downwind fetch. The Kolmogorov constant for the inertial-convective subrange has been determined from the measured spectra to be 0.17±0.03.     

A wind tunnel study of mean and fluctuating concentrations in a plume dispersing over a two-dimensional hill

This paper describes an experimental investigation of the behaviour of the statistics of concentration fluctuations in a passive plume dispersing over a two-dimensional hill of moderate steepness. Recently developed high frequency response Flame Ionization Detector (FID) technology with a frequency response in excess of 200 Hz was utilized to obtain an extensive set of measurements of the mean and fluctuating plume concentrations. Plumes dispersing over flat terrain and over a hill with a maximum slope of 0.3 were studied. For both cases, extensive turbulent flow measurements were also carried out.The measured mean plume concentration profiles were of a generally Gaussian form and showed the expected effects of surface reflection for the flat terrain and hill. Plume intermittency and concentration fluctuation intensity were calculated at all measurement locations. Conditional and unconditional plume concentration statistics were calculated. The conditional (in-plume) concentrations and intensities were more uniform with height than for the unconditional ones.