Markov-chain simulation of particle dispersion in inhomogeneous flows: The mean drift velocity induced by a gradient in Eulerian velocity variance

The Langevin equation is used to derive the Markov equation for the vertical velocity of a fluid particle moving in turbulent flow. It is shown that if the Eulerian velocity variance _wE is not constant with height, there is an associated vertical pressure gradient which appears as a force-like term in the Markov equation. The correct form of the Markov equation is: w(t + t) = aw(t) + b _wE + (1 – a)T _L ( _wE ²)/z, where w(t) is the vertical velocity at time t, a random number from a Gaussian distribution with zero mean and unit variance, T _L the Lagrangian integral time scale for vertical velocity, a = exp(–t/T _L), and b = (1 – a ²)^1/2. This equation can be used for inhomogeneous turbulence in which the mean wind speed, _wE and T _L vary with height. A two-dimensional numerical simulation shows that when this equation is used, an initially uniform distribution of tracer remains uniform.     

A Lagrangian stochastic model for the trajectories of particle pairs and its application to the prediction of concentration variance within plant canopies

A simple Lagrangian stochastic model for the trajectories of particle pairs in high Reynolds-number turbulent flows is presented. In this model, the velocities of particle pairs are initially correlated but subsequently each particle moves independently. The independent single-particle trajectories are simulated using Thomson's model [J. Fluid Mech. 180, 529–556, 1987]. This two-particle model exactly satisfies the well-mixed condition for Gaussian turbulence when length scales, characterizing the two-point Eulerian velocity correlation function, vanish. Temperature variances, due to heat released as a passive scalar from an elevated plane source, within a model plant canopy (Coppin et al. Boundary Layer Meteorol. 35, 167–191, 1986) are shown to be well predicted by the model. It is suggested that for strongly inhomogeneous flows, the two-point Eulerian velocity function is of secondary importance in determining the simulated trajectories of particle pairs compared to the importance of ensuring satisfaction of the two-to-one constraint (Borgas and Sawford. J. Fluid Mech. 279, 69–99, 1994); i.e ensuring that one-particle statistics obtained from the two-particle model are the same as those obtained from the corresponding one-particle model. Limitations of this modelling approach are discussed.     

Diurnal variations of the refractive index gradient variance in the eastern regions of Russia

Diurnal variations of the standard deviation σ _g of the refractive index vertical gradient g _n in the lower 300-meter atmospheric layer are first analyzed for the vast area of Eastern Siberia and Far East by using observation data obtained from 30 aerological stations for 10 years. This statistics is most variable in the Far North areas in the spring-summer period. The diurnal cycle of σ _g is most diverse (in terms of both its character and amplitude) in the moderate climatic belt of the territory under study. Here, the maximum diurnal variability of σ _g is observed in the summer and then, in the winter time. Diurnal variations of σ _g in this region have significant amplitudes that are in many regions comparable with the amplitudes of its interseasonal variations.     

Numerical simulation of particle trajectories in inhomogeneous turbulence,II: Systems with variable turbulent velocity scale

It is shown that for the purpose of trajectory simulation, the vertical velocityw _L (t) of a fluid element, which is moving in a system (such as a forest canopy, or the unstably stratified atmospheric surface layer) whose turbulent velocity scale _w is height-dependent, must be chosen from a frequency-distribution which is asymmetric aboutw _L = 0. If the gradient _w /z varies only slowly with height, correct trajectories may be obtained by adding a bias (where _L is the length scale) to a fluctuating velocity chosen from a symmetric distribution with variance _w ²(z).     

Numerical simulation of particle trajectories in inhomogeneous turbulence,I: Systems with constant turbulent velocity scale

A means of numerical simulation of particle trajectories in inhomogeneous turbulence is described. The method employs a simple coordinate transformation which allows a trajectory in inhomogeneous turbulence to be converted to a corresponding trajectory in homogeneous turbulence. Concentration distributions predicted by the trajectory-simulation method agree precisely with analytical solutions in the special cases of homogeneous turbulence, turbulence with power-law wind and eddy diffusivity profiles, and the neutral atmospheric surface layer.     

Numerical simulation of particle trajectories in inhomogeneous turbulence,III: Comparison of predictions with experimental data for the atmospheric surface layer

It is shown that predictions of a numerical trajectory-simulation method agree closely with the Project Prairie Grass observations of the concentrations 100 m downwind of a continuous point source of sulphur dioxide if the height (z) dependence of the Lagrangian length scale Λ _L is chosen as: whereL is the Monin-Obukhov length. The value of 0.5 for Λ _L /z in neutral conditions is consistent with the findings of Reid (1979) for the Porton experiment, and is also shown to be the best choice for simulation of an experiment in which concentration profiles were measured a short distance (< 40 m) downwind of an elevated point source of glass beads (40 μn diameter). $$\begin{gathered} \Lambda _L = 0.5z\left( {1 - 6\frac{z}{L}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} L< 0 \hfill \\ \Lambda _L = 0.5z/\left( {1 + 5\frac{z}{L}} \right)L > 0 \hfill \\ \end{gathered} $$      

On the motion of a small particle in the atmosphere

Equations of motion, valid for a water droplet or a dust particle less than about 50Μm in radius moving through the air, are derived. Thus, the behaviour of a particle in some simple nonuniform fluid flows is discussed. In particular, it is found that a particle may follow an approximately closed trajectory in an axisymmetric flow about a horizontal axis. Thus, it is argued that turbulence should cause particles to fall at a much slower rate than their terminal velocity, even in the absence of a mean updraft.     

Spatio-temporal variance and meteorological drivers of the urban heat island in a European city

Urban areas are especially vulnerable to high temperatures, which will intensify in the future due to climate change. Therefore, both good knowledge about the local urban climate as well as simple and robust methods for its projection are needed. This study has analysed the spatio-temporal variance of the mean nocturnal urban heat island (UHI) of Hamburg, with observations from 40 stations from different suppliers. The UHI showed a radial gradient with about 2 K in the centre mostly corresponding to the urban densities. Temporarily, it has a strong seasonal cycle with the highest values between April and September and an inter-annual variability of approximately 0.5 K. Further, synoptic meteorological drivers of the UHI were analysed, which generally is most pronounced under calm and cloud-free conditions. Considered were meteorological parameters such as relative humidity, wind speed, cloud cover and objective weather types. For the stations with the highest UHI intensities, up to 68.7 % of the variance could be explained by seasonal empirical models and even up to 76.6 % by monthly models.     

Energy transfer in a fluid with a uniform density gradient

Energy transfer via resonance in a stratified fluid with a constant Brunt–Väisälä frequency is studied through the Manley–Rowe relation and direct numerical simulations. The objectives of this study are two-fold. One is to determine if there is a limitation on the lengthscale of small-scale waves to which primary energy can be effectively transferred. The other is to study factors affecting the growth of parametric subharmonic instability. Resonantly interacting modes are classified into three groups: local sum modes, quasi-subharmonic modes and remote parametric subharmonic instability modes (characterized by interaction with very small-scale waves). The latter two involve energy transfer from a primary wave to secondary waves with half the frequency. Most energy transfer is through local sum resonant modes and quasi-subharmonic modes. Energy cannot effectively transfer to higher wavenumber modes since dynamical systems are altered as wavenumbers of excited modes increase. In the remote modes, the solution is sinusoidal with high angular frequency and very small energy capacity. As a consequence, these modes are inactive in energy transfer despite their high energy growth rates. Effects of non-uniform white noise amplitude and primary mode propagation angle on the quasi-subharmonic modes are also investigated. Implications for energy transfer in the ocean are discussed.     

Review of Lagrangian stochastic models for trajectories in the turbulent atmosphere

We review the theoretical basis for, and the advantages of, random flight models for the trajectories of tracer particles in turbulence. We then survey their application to calculate dispersion in the principal types of atmospheric turbulence (stratified, vertically-inhomogeneous, Gaussian or non-Gaussian turbulence in the surface layer and above), and show that they are especially suitable for some problems (e.g., quantifying ground emissions).     

最小方差准则的判别分析

从引入判别参数的概念出发,导出了在最小均方误差准则下的线性判别函数,证明了在二类问题中等价于Fisher准则的判别,且作了实例计算和讨论。     

Characteristics of pressure gradient force errors in a terrain-following coordinate

"地形追随坐标系中气压梯度力误差的特征分析"一文通过几何分析和理想实验,对比了地形追随坐标系两种方案(经典方案和协变方案)中气压梯度力(PGF)误差的特征。结果表明:(1)经典方案的PGF误差受"垂直气压梯度","气压梯度的方向(α)","垂直层的坡度(φ)"三者影响,垂直气压梯度越大,气压梯度与水平方向的夹角越大,垂直层坡度越大,误差越大;(2)协变方案的PGF误差不受上述三因子影响。此外,通过定义参数TT(TT=tanφ·tanα)能定量分析经典方案的PGF误差。     

Note on the viscous heating term in the temperature variance equation

Experimental results in the atmospheric surface layer indicate that the viscous heating term in the equation for the mean-square value of the turbulent temperature fluctuation is small, but the correlation between temperature and turbulent energy dissipation fluctuations is significant.     

Relationship between turbulent flux and variance in the urban canopy

The relationship between fluxes and variances has been widely studied in the frame of the similarity theory. However, the dynamics of urban morphology should be highlighted in the urban canopy. Therefore, the relationship between fluxes and variances of turbulent quantities (wind velocity, temperature, carbon dioxide, and water vapor concentration) without stability parameters has been investigated with data collected from the Beijing 325-m meteorological tower in the urban canopy. Though the similarity theory is available for the statistics of wind velocity and temperature, urban land use plays an important role in the linear relationship between momentum fluxes and velocity variances, while the linear relationship between sensible heat fluxes and temperature variances is influenced at large by stratification. As for carbon dioxide and water vapor, the linear relationship between their fluxes and variances is a better way compared to the similarity theory to describe their motion, though the plots are a little scattered owing to their fugitive source.     

On the temporal variance of stratospheric trace gas concentrations

The relative variances in stratospheric observations of longlived trace gases CH₄, N₂O, CF₂Cl₂, CFCl₃ show large differences. These differences are greatly reduced when the local mean standard deviation is normalized to the local vertical gradient. This ratio, called ‘equivalent displacement height’ exhibits a characteristic vertical profile which is very similar for all the longlived trace gases, as well as for O₃. With the help of this ratio, it is demonstrated that the variances are essentially due to natural causes, i.e., transport. Using the mixing length hypothesis a theoretical expression for the equivalent displacement height is derived. From it the meridional slope of the mixing surfaces and the mixing length can be calculated as function of the altitude. Additional information is obtained on the variance of that slope. The uncertainty of the measured mean trace gas profiles is defined.     

Maladaptive trajectories of change in Makira, Solomon Islands

Trajectories of change are dynamic processes of individual, group and/or societal responses to change which create further change and responses, with outcomes that reflect the cumulative properties of those processes. Understanding trajectories of change is an important initial step for designing appropriate adaptation strategies because even though responses may enable people to cope with change in the short term, the accumulated responses of individuals can generate undesirable maladaptive outcomes over longer periods of time. This paper examines trajectories of change in Kahua, Solomon Islands, where people have traditionally relied on subsistence activities and have in the past been subsistence affluent. Participatory methods, including 76 focus group discussions in 38 communities with 821 individuals, were used to determine changes in the region and its drivers. A conceptual model was developed of the underlying feedback processes within the Kahua social–ecological system. The results show that communities are facing rapid and extensive changes. Most changes, however, are being driven by the two key drivers of population growth and a strong desire for monetary prosperity that act synergistically to generate stress in communities. People are generally responding by focusing on income generation, which is reinforcing stress in communities and resulting in maladaptive trajectories of change. The results suggest development policy in the Solomon Islands needs to: (1) take the challenges of population growth much more seriously; (2) place greater effort on development activities that reduce per capita impact on the environment; (3) improve management of the high expectations for monetary prosperity; (4) increase emphasis on wellbeing aspects of development rather than income generation per se, and (5) better align development with existing adaptation strategies to ensure that vulnerability to future global change does not increase.     

Mean and variance evolutions of the hot and cold temperatures in Europe

In this paper, we examine the trends of temperature series in Europe, for the mean as well as for the variance in hot and cold seasons. To do so, we use as long and homogenous series as possible, provided by the European Climate Assessment and Dataset project for different locations in Europe, as well as the European ENSEMBLES project gridded dataset and the ERA40 reanalysis. We provide a definition of trends that we keep as intrinsic as possible and apply non-parametric statistical methods to analyse them. Obtained results show a clear link between trends in mean and variance of the whole series of hot or cold temperatures: in general, variance increases when the absolute value of temperature increases, i.e. with increasing summer temperature and decreasing winter temperature. This link is reinforced in locations where winter and summer climate has more variability. In very cold or very warm climates, the variability is lower and the link between the trends is weaker. We performed the same analysis on outputs of six climate models proposed by European teams for the 1961–2000 period (1950–2000 for one model), available through the PCMDI portal for the IPCC fourth assessment climate model simulations. The models generally perform poorly and have difficulties in capturing the relation between the two trends, especially in summer.     

隐式等权重粒子滤波在高维准地转模式中的特性研究

粒子滤波自从被引入资料同化领域以来,对于高维系统存在的粒子衰退问题一直困扰着资料同化领域的研究。隐式等权重粒子滤波（Implicit Equal-Weights Particle Filter,IEWPF）通过在高维的状态空间维数的前提下,隐式从每个粒子都具有特殊协方差的提议密度中进行采样,构建等权重的粒子集合,从而解决高维系统的粒子衰退问题。通过在高维准地转模式中应用IEWPF方法,验证了IEWPF的系统一致性和资料同化效果。通过对水平动能谱的检验,验证了IEWPF可以保持系统的原始平衡特性。通过IEWPF与等权重粒子滤波（Equivalent Weights Particle Filter,EWPF）的对比试验发现,两者的资料同化分析场非常接近,但在运行效率上,IEWPF远优于EWPF。同时,IEWPF也为解决一系列的资料同化问题,比如参数估计,提供了新的解决途径。      

Graupel growth and trajectories in a shallow cb cloud determined by a forced 1‐D model

Abstract

A kinematic model is applied to graupel growth. The vertical velocity and ther‐modynamic field data are taken from the forced 1‐D time‐dependent model of Cb cloud developed by Curie and Jane (1988). The graupel embryo pocket was released at the height of the — 10°C isotherm. The influence of the forced lifting on further graupel growth and its trajectory is analysed by sensitivity experiments based on the amplitude of the forced lifting, and initial graupel radius, density and cloud droplet concentration for the forced lifting initiation time derived from the model and the forced lifting duration time that agreed with observations. In particular, the sensitivity analysis was carried out for the forced lifting initiation and duration times.

It is shown that for large values of the forced lifting amplitudes, the residence time of the graupel within cloud and the final graupel radius may be significantly larger compared with those in the non‐forced case. The residence time in a cloud can also be significantly larger for the smallest amplitude, whereas the final radius is rather insensitive owing to oscillations around the melting level. For some cases the forced lifting causes recycling inside the updraft, contrary to the results of previous non‐forced numerical models. The recycling mechanism is sensitive to the forced lifting duration time and the time interval between the graupel pocket injection in cloud and the initiation of the forced lifting. Initially the observed recycling mechanism is a consequence of the periodic forced lifting mechanism, but then combines with recycling of the Pflaum type (1980).