Experimental Measurements of Expected Mass Fraction in a Contaminant Plume

The sudden release of a quantity of gas into the atmospheric boundary layer produces a contaminant cloud. The expected mass fraction function provides a relatively simple measure of the contaminant concentration values found within the cloud and represents the ensemble-averaged fraction of the conserved release mass found at the different contaminant concentration intervals as the cloud evolves. The plume generated by a line source in grid turbulence is used to investigate the expected mass fraction function as it applies to scalar concentration values found on a typical line normal to the plume axis. Simultaneous particle image velocimetry and planar laser induced fluorescence are used to measure velocity and concentration fields, respectively. The measured expected mass fraction functions are observed to be approximately self-similar when concentration values are normalized by the centreline mean concentration. The moments of the expected mass fraction function are observed to be simply related to the centreline moments of the probability density function of scalar concentration. Arguments based on a source fluid, non-source fluid decomposition of the scalar probability density function are used to explain these observations. The results are compared with the theoretical and experimental results established for a line source of scalar in grid turbulence.     

Modelling of concentration fluctuations in canopy turbulence

The knowledge of the concentration probability density function (pdf) is of importance in a number of practical applications, and a Lagrangian stochastic (LS) pdf model has been developed to predict statistics and concentration pdf generated by continuous releases of non-reactive and reactive substances in canopy generated turbulence. Turbulent dispersion is modelled using a LS model including the effects of wind shear and along-wind turbulence. The dissipation of concentration fluctuations associated with turbulence and molecular diffusivity is simulated by an Interaction by Exchange with the Conditional Mean (IECM) micromixing model. A general procedure to obtain the micromixing time scale needed in the IECM model useful in non-homogeneous conditions and for single and multiple scalar sources has been developed. An efficient algorithm based on a nested grid approach with particle splitting, merging techniques and time averaging has been used, thus allowing the calculation for cases of practical interest. The model has been tested against wind-tunnel experiments of single line and multiple line releases in a canopy layer. The approach accounted for chemical reactions in a straightforward manner with no closure assumptions, but here the validation is limited to non-reacting scalars.     

热带海洋对大气进行非绝热加热的随机效应的进一步研究

本文考虑了热带海洋对大气进行非绝热加热过程中海温起伏的随机效应,建立了朗之万方程形式的描写大气热量变化的发展方程。由该随机微分方程的定态解,给出了加热势函数和概率密度函数。在确定的热力学参数下,利用实际海温起伏方差值,计算求得了加热势函数的分布及概率密度分布曲线。文中还进一步计算了概率密度流,得到了在两种稳定状态之间穿透势垒的弛豫时间。计算结果表明,海温异常的随机效应是一个长周期过程,时间尺度约为140天,可以用实际测得的拖曳系数C_D和海温起伏方差q2值对它进行预测。      

Comparing Two Implementations of a Micromixing Model. Part I: Wall Shear-Layer Flow

A Lagrangian stochastic (LS) micromixing model is used for estimating concentration fluctuations in plumes of a passive, non-reactive tracer dispersing from elevated and ground-level compact sources into a neutral wall shear-layer flow. SPMMM (for sequential particle micromixing model) implements the familiar IECM (interaction by exchange with the conditional mean) micromixing scheme. The parametrization of the scalar micromixing time scale is identical to that proposed in a previously reported LS–IECM model (Cassiani et al., Atmos Environ 39:1457–1469, 2005a). However, while SPMMM is mathematically equivalent to the previously reported model, it differs in its numerical implementation: SPMMM releases N independent particles sequentially, whereas the previously reported model releases N independent particles simultaneously. In both implementations, the trajectories of the N particles are governed by single-point velocity statistics. The sequential particle implementation is computationally efficient, but cannot be applied to the case of reacting species. Results from both implementations are compared to experimental wind-tunnel dispersion data and to each other.     

Theory for Reconstruction of an Unknown Number of Contaminant Sources using Probabilistic Inference

We address the inverse problem of source reconstruction for the difficult case of multiple sources when the number of sources is unknown a priori. The problem is solved using a Bayesian probabilistic inferential framework in which Bayesian probability theory is used to derive the posterior probability density function for the number of sources and for the parameters (e.g., location, emission rate, release time and duration) that characterize each source. A mapping (source–receptor relationship) that relates a multiple source distribution to the concentration measurements made by an array of detectors is formulated based on a forward-time Lagrangian stochastic model. A computationally efficient methodology for determination of the likelihood function for the problem, based on an adjoint representation of the source–receptor relationship and realized in terms of a backward-time Lagrangian stochastic model, is described. An efficient computational algorithm based on a parallel tempered Metropolis-coupled reversible-jump Markov chain Monte Carlo (MCMC) method is formulated and implemented to draw samples from the posterior probability density function of the source parameters. This methodology allows the MCMC method to initiate jumps between the hypothesis spaces corresponding to different numbers of sources in the source distribution and, thereby, allows a sample from the full joint posterior distribution of the number of sources and the parameters for each source to be obtained. The proposed methodology for source reconstruction is tested using synthetic concentration data generated for cases involving two and three unknown sources.     

Simulation of Time Series of Concentration Fluctuations in Atmospheric Dispersion Using a Correlation-distortion Technique

Short-duration fluctuations in the concentration of airborne substances can be important in a variety of atmospheric dispersion problems, especially when assessing the risks posed by harmful materials. This paper discusses a simulation technique for generating individual realisations of fluctuating concentration time series in dispersing plumes based on target probability distributions and spectral functions. The scheme uses a correlation-distortion approach to simulate these time series. Gaussian processes with modified spectral characteristics are generated and then transformed to yield non-Gaussian processes with the desired spectral characteristics. The simulation scheme is initially developed for a single receptor, and is then extended to model pairs of correlated time series at two receptors. In fact, the modelling technique can be generalised to an arbitrary number of receptors and this provides, in principal, an approach that is applicable to a wide class of similar problems (such as the modelling of instantaneous puff releases or the response of line-of-sight detection systems). The simulation technique is illustrated using observations made during recent field experiments, conducted both in the United Kingdom and in the U.S.A., investigating the short-range dispersion of a passive tracer.     

多维非高斯系统最小熵控制

针对多维非高斯系统提出了最小熵控制方法,控制的目标是使系统的非高斯输出概率密度函数跟踪一个已知的联合概率密度函数.首先,根据系统模型和辅助映射,构建了系统状态、跟踪误差与扰动输入之间的泛函算子模型,然后基于梯度算法设计了递归的次优控制律,最后通过仿真验证了最小熵控制算法的有效性.     

The Interference of Higher-Order Statistics of the Concentration Field Produced by Two Point Sources According to a Generalized Fluctuating Plume Model

The higher-order correlation functions for the concentrationfluctuations arising from a two-point-source configuration have beencalculated analytically within the context of the phenomenology of afluctuating plume model (viz., a meandering plume model that explicitlyincorporates internal fluctuations). Explicit expressions for thesecond-, third-, and fourth-order correlationfunctions between the concentrationfluctuations produced by two point sources are given in terms of the sourceseparation d and the five physically based parameters that define thegeneralized fluctuating plume model: namely, the absolute plume dispersion,_a, which determines the outer plume length scale; the relative plume dispersion, _r, which determines the inner plume length scale; the fluctuation intensity, i_r, in relative coordinates, which determines the internal concentration fluctuation level; the correlation coefficient, r,between the positions of the centroids of the two interfering plumes; and,the correlation coefficient, r^*, between the concentration fluctuationsof the two plumes in relative coordinates, which determines the degree ofinternal mixing of the two scalars. Furthermore, the form of the totalconcentration probability density function arising from the interferenceproduced by two point sources is presented. Predictions for the second-ordercorrelation function, , and for the total concentration probabilitydensity function have been compared with some new experimental data fora two-point-source configuration in grid turbulence generated in awater-channel simulation. These results are in good agreement with the dataand suggest that the analytical model for the second-order correlationfunction and the total concentration probability density function canreproduce many qualitative trends in the interaction of plumes from twosources.     

A Stochastic Time Series Model for Threshold Crossing Statistics of Concentration Fluctuations in non-Intermittent Plumes

A numerical stochastic model is developed for the upcrossing rate across a specified threshold concentration. The model assumes that the concentration time series at a given spatial point within a dispersing plume can be approximated as a first-order Markovian process designed to be consistent with a given time-invariant concentration probability density function (pdf). The model requires only the specification of a concentration pdf with a given mean and variance and a concentration fluctuation integral time scale. Predicted upcrossing rates are compared with atmospheric plume concentration data obtained from a point source near the ground. For this data set, a log-normal pdf is found to give better estimates of the threshold crossing rate than a gamma pdf.     

类比法在暴雨灾害损失定量预估中的应用

从致灾因子角度,通过系统分析暴雨与其造成的灾害损失之间的关系,提取致灾关联度较高的暴雨因子,采用正态分布概率密度函数和最小距离法,建立区域性暴雨强度评价模型。在此基础上,通过分析历史暴雨个例之间灾害损失的相似性,采用类比法,建立了湖北5—9月暴雨灾害损失定量预估模型。2008—2009年的试验结果表明,类比法可作为暴雨灾害定量损失预估的实用方法。     

A model for sensible heat flux probability density function for near-neutral and slightly-stable atmospheric flows

The probability density function for sensible heat flux was measured above a uniform dry lakebed (Owens lake) in Owens Valley, California. It was found that for moderately stable to near neutral atmospheric stability conditions, the probability density function exhibits well defined exponential tails. These exponential tails are consistent with many laboratory boundarylayer measurements and numerical simulations. A model for the sensible heat flux probability density function was developed and tested. A key assumption in the model derivation was the near Gaussian statistics of the vertical velocity and temperature fluctuations. This assumption was verified from time series measurements of temperature and vertical velocity. The parameters for the sensible heat flux probability density function model were also derived from mean meteorological and surface conditions using surface-layer similarity theory. It was found that the best agreement between modeled and measured sensible heat flux probability density function was at the tails. Finally, a relation between the intermittency parameter, the probability density function, and the mean meteorological conditions was derived. This relation rigorously links the intermittency parameter to mean meteorological conditions.     

Analysis of Urban Atmosphere Plume Concentration Fluctuations

Concentration variability in the fast-response tracer dataset for continuous, near-surface, point source releases in the urban core from the Joint Urban 2003 field study is analyzed. Concentration variability for conditionally and unconditionally sampled time series is characterized by probability densities, concentration fluctuation intensity, skewness, and kurtosis. Significant day-night differences in plume dispersion are observed. Relative to daytime, nighttime plumes were more likely to have reduced concentration fluctuation intensities, higher normalized surface concentrations, suppressed vertical mixing, and a greater prevalence of Gaussian-like distributions rather than log-normal or mixed mode distributions. This was in spite of the similar stability and turbulence conditions in the urban core for day and night. The potential roles of flow meander and thermal stability in explaining these differences are examined. Probability densities of concentration are found to be a strong function of fluctuation intensity. There are few differences in probability densities between day and night when classified by fluctuation intensity. There are no appreciable differences between conditional and unconditional probability densities and only small differences between conditional and unconditional sampling statistics relative to the larger differences usually observed in more homogeneous settings. Fluctuation intensity, skewness, and kurtosis are higher for the daytime experiments, and closer to the source, but show little difference between conditional and unconditional results over most of their range of values. The log-normal distribution provides a better overall fit to a broader range of the dataset than the exponential or clipped-normal distributions.     

Probabilistic Model for Concentration Fluctuations in Compact-Source Plumes in an Urban Environment

A comprehensive model for the prediction of concentration fluctuations in plumes dispersing in the complex and highly disturbed wind flows in an urban environment is formulated. The mean flow and turbulence fields in the urban area are obtained using a Reynolds-averaged Navier-Stokes (RANS) flow model, while the standard k-ϵ turbulence model (k is the turbulence kinetic energy and ϵ is the viscous dissipation rate) is used to close the model. The RANS model provides a specification of the velocity statistics of the highly disturbed wind flow in the urban area, required for the solution of the transport equations for the mean concentration and concentration variance (both of which are formulated in the Eulerian framework). A physically-based formulation for the scalar dissipation time scale t _d , required for the closure of the transport equation for , is presented. This formulation relates t _d to an inner time scale corresponding to “internal” concentration fluctuation associated with relative dispersion, rather than an outer time scale associated with the entire portion of the fluctuation spectrum. The two lowest-order moments of concentration ( and ) are used to determine the parameters of a pre-chosen functional form for the concentration probability density function (clipped-gamma distribution). Results of detailed comparisons between a water-channel experiment of flow and dispersion in an idealized obstacle array and the model predictions for mean flow, turbulence kinetic energy, mean concentration, concentration variance, and concentration probability density function are presented.     

Revisiting meridional overturing bistability using a minimal set of state variables: stochastic theory

A stochastic analytical model of the Atlantic meridional overturning circulation (AMOC) is presented and tested against climate model data. AMOC stability is characterised by an underlying deterministic differential equation describing the evolution of the central state variable of the system, the average Atlantic salinity. Stability of an equilibrium implies that infinitesimal salinity perturbations are damped, and violation of this requirement yields a range of unoccupied salinity states. The range of states is accurately predicted by the analytical model for a coupled climate model of intermediate complexity. The introduction of climatic noise yields an equation describing the evolution of the probability density function of the state variable, and therefore the AMOC. Given the hysteresis behaviour of the steady AMOC versus surface freshwater forcing, the statistical model is able to describe the variability of the AMOC based on knowledge of the variability in the forcing. The method accurately describes the wandering between AMOC-On and AMOC-Off states in the climate model. The framework presented is a first step in relating the stability of the AMOC to more observable aspects of its behaviour, such as its transient response to variable forcing.     

用一维时间序列确定吸引子维数应注意的两个问题

该文给出了严格自相似和统计自相似的区别，并由此讨论了用一维时间序列确定吸引子维数应注意的两个问题，即维数计算公式中的标度范围及比例系数问题和双对数图与Ｄ－ｍ图的关系问题。     

The exponential probability density function and concentration fluctuations in smoke plumes

Observations of 1-s average concentration fluctuations during two trials of a U.S. Army diffusion experiment are presented and compared with model predictions based on an exponential probability density function (pdf). The source is near the surface and concentration monitors are on lines about 30 to 100 m downwind of the source. The observed ratio of the standard deviation to the mean of the concentration fluctuations is about 1.3 on the mean plume axis and 4 to 5 on the mean plume edges. Plume intermittency (fraction of non-zero readings) is about 50%; on the mean plume axis and 10%; on the mean plume edges. A meandering plume model is combined with an exponential pdf assumption to produce predictions of the intermittency and the standard deviation of the concentration fluctuations that are within 20%; of the observations.     

Simulating Concentration Fluctuation Time Series with Intermittent Zero Periods and Level Dependent Derivatives

Intermittent concentration fluctuation time series were produced with a stochastic numerical model derived from the assumption that the concentration fluctuations at a fixed receptor in a point-source plume can be modelled as a first order Markov process. The time derivative of concentration was assumed to be level-dependent and constrained by a stationary lognormal probability density function. The input parameters required to reconstruct the intermittent time series are the intermittency factor , the conditional fluctuation intensity i _p ² , and the time scale T _c . A clipped lognormal probability distribution was used to describe the fluctuation time series. Good agreement between the stochastic simulation and experimental water-channel data was demonstrated by comparing the time derivative of concentration and the upcrossing rates over a range of intermittency factors = 0.7 to 0.01 and fluctuation intensities i _w ² = 2.2 to 7.5.     

多元均生函数模型及其在短期气候预测中的应用

在原均生数模型的基础上，对模型进行改进，首次引入预报因子变量，建立一个多元的均生函数模型。它适应于气温、降水、热带气旋个数等多种要素预报。新建的多元均生函数模型包含了原模型的优点。而且比原有均生函数模型具有更物理基础。     

基于遗传算法的试题库智能组卷系统研究

采用自适应交叉率和变异率的生物遗传学算法，建立一个智能组卷的数学模型，并对该数学模型的编码方法和遗传操作进行了详细介绍和讨论。对该数学模型的应用求解表明，该方法是对以前的随机法和简单遗传算法组卷的一个显著改善。