Evaluation of longitudinal and transverse dispersivities/distance ratios for tracer test in a radially convergent flow field with scale-dependent dispersion

This study presents a novel mathematical model for analysis of non-axisymmetrical solute transport in a radially convergent flow field with scale-dependent dispersion. A two-dimensional, scale-dependent advection–dispersion equation in cylindrical coordinates is derived based on assuming that the longitudinal and transverse dispersivities increase linearly with the distance of the solute transported from its injected source. The Laplace transform finite difference technique is applied to solve the two-dimensional, scale-dependent advection–dispersion equation with variable-dependent coefficients. Concentration contours for different times, breakthrough curves of average concentration over concentric circles with a fixed radial distance, and breakthrough curves of concentration at a fixed observation point obtained using the scale-dependent dispersivity model are compared with those from the constant dispersivity model. The salient features of scale-dependent dispersion are illustrated during the non-axisymmetrical transport from the injection well into extraction well in a convergent flow field. Numerical tests show that the scale-dependent dispersivity model predicts smaller spreading than the constant-dispersivity model near the source. The results also show that the constant dispersivity model can produce breakthrough curves of averaged concentration over concentric circles with the same shape as those from the proposed scale-dependent dispersivity model at observation point near the extraction well. Far from the extracting well, the two models predict concentration contours with significantly different shapes. The breakthrough curves at observation point near the injection well from constant dispersivity model always produce lesser overall transverse dispersion than those from scale-dependent dispersivity model. Erroneous dimensionless transverse/longitudinal dispersivity ratio may result from parametric techniques which assume a constant dispersivity if the dispersion process is characterized by a distance-dependent dispersivity relationship. A curve-fitting method with an example is proposed to evaluate longitudinal and transverse scale-proportional factors of a field with scale-dependent dispersion.     

Dispersion modelling of air pollution caused by road traffic using a Markov Chain–Monte Carlo model

 Although the strict legislation regarding vehicle emissions in Europe (EURO 4, EURO 5) will lead to a remarkable reduction of emissions in the near future, traffic related air pollution still can be problematic due to a large increase of traffic in certain areas. Many dispersion models for line-sources have been developed to assess the impact of traffic on the air pollution levels near roads, which are in most cases based on the Gaussian equation. Previous studies gave evidence, that such kind of models tend to overestimate concentrations in low wind speed conditions or when the wind direction is almost parallel to the street orientation. This is of particular interest, since such conditions lead generally to the highest observed concentrations in the vicinity of streets. As many air quality directives impose limits on high percentiles of concentrations, it is important to have good estimates of these quantities in environmental assessment studies. The objective of this study is to evaluate a methodology for the computation of especially those high percentiles required by e.g. the EU daughter directive 99/30/EC (for instance the 99.8 percentile for NO₂). The model used in this investigation is a Markov Chain – Monte Carlo model to predict pollutant concentrations, which performs well in low wind conditions as is shown here. While usual Lagrangian models use deterministic time steps for the calculation of the turbulent velocities, the model presented here, uses random time steps from a Monte Carlo simulation and a Markov Chain simulation for the sequence of the turbulent velocities. This results in a physically better approach when modelling the dispersion in low wind speed conditions. When Lagrangian dispersion models are used for regulatory purposes, a meteorological pre-processor is necessary to obtain required input quantities like Monin-Obukhov length and friction velocity from routinely observed data. The model and the meteorological pre-processor applied here, were tested against field data taken near a major motorway south of Vienna. The methodology used is based on input parameters, which are also available in usual environmental assessment studies. Results reveal that the approach examined is useful and leads to reasonable concentration levels near motorways compared to observations. We wish to thank Andreas Schopper (Styrian Government) for providing air quality values, M. Kalina for providing the raw data of the air quality stations near the motorway and J. Kukkonen for providing the road site data set from the Finish Meteorological Institute (FMI). The study was partly funded by the Austrian science fund under the project P14075-TEC.     

MODELLING CLIMATE,TOPOGRAPHY AND PALAEOGLACIER FLUCTUATIONS IN THE CHILEAN ANDES

A one-dimensional flowline model has been constructed, tested and applied to two formerly glaciated valley basins within the Chilean Lake District. The vertically integrated ice flow model is similar to those used to study historical fluctuations of European Alpine glaciers and includes terms for internal deformation and basal sliding. In addition, longitudinal deviatoric stresses are computed and velocity terms are correspondingly adjusted. The model is driven through a mass balance term forced by a stepped lowering of the equilibrium line altitude (ELA) through time. Experiments, based on generating equilibrium glacier surface profiles corresponding to various ELAs, indicate that a lowering of at least 1000 m of the ELA from its present-day position is required to simulate the glacial maximum. Furthermore, the specific geometry of the two valleys provides an important control on the extent of the two glaciers, effectively decoupling them from further climatic deterioration once they have advanced beyond the constraining influence of their valleys into the piedmont zone. The tight nesting of terminal moraine loops provides evidence for this topographical control on palaeoglacier extent. The modelled response and sensitivity of the two palaeoglaciers to climate change differ markedly as a result of contrasting valley geometry. Glaciers resting on steeper gradients tend to have thinner profiles, faster mass turnover times and correspondingly shorter volume time-scales. Puyehue glacier has a response time of c. 1000 years whereas the Rupanco glacier has a response time of c. 2000 years. Hence, Puyehue is more sensitive to climatic fluctuations occurring on a time-scale of 500–1000 years. Furthermore, the Rupanco glacier may lag or even fail to respond at all to climatic fluctuations at these time-scales, a conclusion substantiated by field evidence. © 1997 by John Wiley & Sons, Ltd.     

耗散大气中的声波射线追踪

基于分层大气中声波的局地色散关系方程,建立一种计入真实大气衰减效应的有耗大气声波射线追踪模型.在色散方程的虚部中导出声波在运动大气中的耗散系数和竖直方向上的增长因子,并利用真实大气中的衰减理论对所得到的耗散系数进行修正.利用Hamilton方程组解出大气声波在考虑耗散效应下的射线微分方程组.该有耗射线追踪模型的数值模拟结果表明,声波的耗散效应对声波的传播路径存在一定影响,在近场情况下,这种影响可以忽略,但是对于声波的远场传播,则影响较大.     

Glacier mass balance simulation using SWAT distributed snow algorithm

Application of a temperature-index melt model incorporated into the Soil and Water Assessment Tool (SWAT) is presented to simulate mass balance (MB) and equilibrium line altitude (ELA) of three glaciers. The snow accumulation/melt parameters were adjusted to glacierized and free glacier areas, respectively. The SWAT snow algorithm enabled us to consider spatial variation of snow parameters by elevation bands across the sub-basins, while in the previous studies using SWAT, the related parameters were constant for an entire basin. The results show slight improvement in runoff simulation and significant improvement in simulated MB when considering ELA in model calibration. The results showed that SWAT can be applied to simulate MB, vertical MB distribution and annual ELA, with light calibration efforts for data-scarce catchments. The accuracy of the results depends on the modelled area of ablation zone from which most of the meltwater is released.     

Non-isothermal soil water transport and evaporation

A detailed model was formulated to describe the non-isothermal transport of water in the unsaturated soil zone. The model consists of the coupled equations of mass conservation for the liquid phase, gas phase and water vapor and the energy conservation equation. The water transport mechanisms considered are convection in the liquid phase, and convection, diffusion and dispersion of vapor in the gas phase. The boundary conditions at the soil–atmosphere interface include dynamical mass flux and energy flux that accounts for radiation transport. Comparison of numerical simulations results with published experimental data demonstrated that the present model is able to describe water and energy transport dynamics, including situations of low and moderate soil moisture contents. Analysis of field studies on soil drying suggests that that dispersion flux of the water vapor near the soil surface, which is seldom considered in soil drying models, can make a significant contribution to the total water flux.     

Developing a Lagrangian sediment transport model for open channel flows

A three-dimensional stochastic Lagrangian particle tracking sediment transport model is developed to solve the discrete advection-dispersion equation using a combination of empirical dispersion equations.The performance of three widely-used longitudinal dispersion coefficient equations was examined to select one of them as the primary dispersion equation term in the developed model. Also, a conditional empirical equation was used to consider the effect of vertical dispersion term in top layers n...     

Analysis of solute transport with a hyperbolic scale-dependent dispersion model

An empirical hyperbolic scale-dependent dispersion model, which predicts a linear growth of dispersivity close to the origin and the attainment of an asymptotic dispersivity at large distances, is presented for deterministic modelling of field-scale solute transport and the analysis of solute transport experiments. A simple relationship is derived between local dispersivity, which is used in numerical simulations of solute transport, and effective dispersivity, which is estimated from the analysis of tracer breakthrough curves. The scale-dependent dispersion model is used to interpret a field tracer experiment by nonlinear least-squares inversion of a numerical solution for unsaturated transport. Simultaneous inversion of concentration-time data from several sampling locations indicates a linear growth of the dispersion process over the scale of the experiment. These findings are consistent with the results of an earlier analysis based on the use of a constant dispersion coefficient model at each of the sampling depths.     

Effect of Sea‐Level Rise on Salt Water Intrusion near a Coastal Well Field in Southeastern Florida

A variable‐density groundwater flow and dispersive solute transport model was developed for the shallow coastal aquifer system near a municipal supply well field in southeastern Florida. The model was calibrated for a 105‐year period (1900 to 2005). An analysis with the model suggests that well‐field withdrawals were the dominant cause of salt water intrusion near the well field, and that historical sea‐level rise, which is similar to lower‐bound projections of future sea‐level rise, exacerbated the extent of salt water intrusion. Average 2005 hydrologic conditions were used for 100‐year sensitivity simulations aimed at quantifying the effect of projected rises in sea level on fresh coastal groundwater resources near the well field. Use of average 2005 hydrologic conditions and a constant sea level result in total dissolved solids (TDS) concentration of the well field exceeding drinking water standards after 70 years. When sea‐level rise is included in the simulations, drinking water standards are exceeded 10 to 21 years earlier, depending on the specified rate of sea‐level rise.     

Comparison of continuum and pore-scale models of nutrient biodegradation under transverse mixing conditions

Recent studies indicate that during in situ bioremediation of contaminated groundwater, degradation occurs primarily along transverse mixing zones. Classical reactive-transport models overpredict the amount of degradation because solute spreading and mixing are not distinguished. Efforts to correct this have focused on modifying both dispersion and reaction terms, but no consensus on the best approach has emerged. In this work, a pore-scale model was used to simulate degradation along a transverse mixing zone between two required nutrients, and a continuum model with fitted parameters was used to match degradation rates from the pore-scale model. The pore-scale model solves for the flow field, concentration field, and biomass development within pore spaces of porous medium. For the continuum model, the flow field and biomass distributions are assumed to be homogeneous, and the fitting parameters are the transverse dispersion coefficient (D_T) and maximum substrate utilization rate (k_S,c). Results from the pore-scale model show that degradation rates near the system inlet are limited by the reaction rate, while degradation rates downgradient are limited by transverse mixing. For the continuum model, the value of D_T may be adjusted so that the degradation rate with distance matches that from the pore-scale model in the mixing-limited region. However, adjusting the value of k_S only improves the fit to pore-scale results within the reaction-limited region. Comparison with field and laboratory experiments suggests that the length of the reaction rate-limited region is small compared to the length scale over which degradation occurs. This indicates that along transverse mixing zones in the field, values of k_S are unimportant and only the value of D_T must be accurately fit.     

Modeling and observations of high-frequency flow variability and internal waves at a Caribbean reef spawning aggregation site

The characteristics and forcing mechanisms of high-frequency flow variations (periods of minutes to days) were investigated near Gladden Spit, a reef promontory off the coast of Belize. Direct field observations and a high-resolution (50-m grid size) numerical ocean model are used to describe the flow variations that impact the initial dispersion of eggs and larvae from this site, which serves as a spawning aggregation site for many species of reef fishes. Idealized sensitivity model experiments isolate the role of various processes, such as internal waves, wind, tides, and large-scale flow variations. The acute horizontal curvature and steep topography of the reef intensify the flow, create small-scale convergence and divergence zones, and excite high-frequency oscillations and internal waves. Although the tides in this area are relatively small (∼10-cm amplitude), the model simulations show that tides can excite significant high-frequency flow variations near the reef, which suggests that the preference of fish to aggregate and spawn in the days following the time of full moon may not be coincidental. Even small variations in remote flows (2–5 cm s⁻¹) due to say, meso-scale eddies, are enough to excite near-reef oscillations. Model simulations and the observations further suggest that the spawning site at the tip of the reef provides initial strong dispersion for eggs, but then the combined influence of the along-isobath flow and the westward wind will transport the eggs and larvae downstream of Gladden Spit toward less turbulent region, which may contribute to enhanced larval survival.     

The New Potential for Understanding Groundwater Contaminant Transport

The groundwater remediation field has been changing constantly since it first emerged in the 1970s. The remediation field has evolved from a dissolved‐phase centric conceptual model to a DNAPL‐dominated one, which is now being questioned due to a renewed appreciation of matrix diffusion effects on remediation. Detailed observations about contaminant transport have emerged from the remediation field, and challenge the validity of one of the mainstays of the groundwater solute transport modeling world: the concept of mechanical dispersion (Payne et al. 2008). We review and discuss how a new conceptual model of contaminant transport based on diffusion (the usurper) may topple the well‐established position of mechanical dispersion (the status quo) that is commonly used in almost every groundwater contaminant transport model, and evaluate the status of existing models and modeling studies that were conducted using advection‐dispersion models.     

Multi-station analysis of surface wave dispersion

Methods based on multi-station recordings are presented for constructing the experimental dispersion curve of Rayleigh waves. Multi-station recording permits a single survey of a broad depth range, high levels of redundancy with a single field configuration, and the ability to adjust the offset, effectively reducing near field and far field effects. A method based on the linear regression of phase angles measured at multiple stations is introduced for determining data quality and filtering criteria. This method becomes a powerful tool for on site quality control in real time. The effects of multiple modes and survey line parameters, such as near offset, receiver spacing, and offset range, are investigated. Parametric studies result in general guidelines for the field data acquisition. A case study demonstrates how to easily deploy commonplace seismic refraction equipment to simultaneously record data for P-wave tomographic interpretation and multi-station analysis of surface wave.     

地脉动空间自相关方法反演 浅层S波速度结构

在近地表地球物理领域, 基于地脉动(或称背景噪声)提取的面波频散曲线反演地下S波速度结构是一种简单经济的工程勘察方法. 本文基于地脉动的空间自相关方法对一个微型台阵观测的背景噪声记录进行处理, 介绍了一种简单易行的提取频散曲线的数据处理方法, 获得了6.7—23 Hz频段的可靠频散曲线; 通过对该观测频散曲线与预测模型的频散曲线进行拟合, 反演得到S波速度结构. 结果表明, 该速度结构与钻孔直接测试的结果相吻合.      

Wideband dipole logging based on segment linear frequency modulation excitation

A wideband dipole signal is required for dipole dispersion correction and near-borehole imaging. To obtain the broadband flexural wave dispersion, we use a nonlinear frequency modulation (NLFM) signal and propose a segment linear frequency modulation (SLFM) signal as the dipole excitation signal to compensate for the excitation intensity. The signal-to-noise ratio (SNR) of the signal over the entire frequency band is increased. The finite-difference method is used to simulate the responses from a Ricker wavelet, a linear frequency modulation (LFM) signal, an NLFM signal, and an SLFM signal in two borehole models of a homogeneously hard formation and a radially stratified formation. The dispersion and radial tomography results at low SNR of the sound source signals are compared. Numerical modeling suggests that the energy of the flexural waves excited by the Ricker wavelet source is concentrated near the Airy phase. In this case, the dispersion is incomplete and information regarding the formation near or far from the borehole cannot be obtained. The LFM signal yields dispersion information near the Airy phase and the high-frequency range but not in the low-frequency range. Moreover, the information regarding the formation far from the borehole is not accurate. The NLFM signal extends the frequency range of the flexural waves by compensating for the excitation intensity and yields information regarding the formation information, but it is not easy to obtain. The SLFM signal yields the same results as the NLFM signal and is easier to implement. Consequently, the dipole detection range expands and the S-wave velocity calculation accuracy improves.     

Pollutant transport in coastal areas with and without background wind

A three-dimensional meteorological model and a Lagrangian particle dispersion model are used to study the effects of a uniform large-scale wind on the dispersion of a non-reactive pollutant in a coastal region with complex terrain. Simulations are carried out both with and without a background wind. A comparison between model results and measured data (wind and pollutant concentrations) indicates that the coupled model system provides a useful mechanism for analyzing pollutant dispersion in coastal regions.     

Apparent phase velocities and fundamental-mode phase velocities of Rayleigh waves

Rayleigh wave dispersion data usually appear in the form of multimodal spectra for a layered model structure. The number of dispersion modal curves depends on the number of layers in the model. The measured dispersion velocities from the frequency–wavenumber (F–K) space, however, may not represent the true phase velocities of the fundamental-mode dispersion curve, but apparent phase velocities. The present study discusses how multimode curves are generated in the multichannel analysis of surface waves (MASW) method and the cause of the apparent velocity produced by the F–K method. Results from a field trial demonstrate that apparent phase velocities fail to reveal thin layers with low velocities. A better agreement of the inverted model with the geotechnical record is obtained by using the data points extracted from the fundamental-mode curve of the MASW spectral image.     

Rayleigh波频散曲线“交叉”及多模式耦合作用研究

Rayleigh波可以用来反演近地表结构,在工程物探、石油物探、地球内部结构探测中均有重要意义.数值计算得到的含低速层的层状介质对应的Rayleigh波频散曲线会出现看似“交叉”的现象,但是对于这种现象目前还没有进行系统的研究.事实上可以验证,有些看似交叉的频散曲线实际上不相交.改变低速层的厚度和横波速度发现低速层越明显（即低速层速度越低或层厚越厚）频散曲线越不容易相交.凡友华等在2007年提出频散曲线对应着四种基本模式,在频散曲线发生“交叉”现象的区域实际上存在两个以上模式的频散曲线.本文主要研究了存在R模和S2模的区域内频散曲线的“交叉”现象.首先利用竖直本征振动曲线研究R模和S2模Rayleigh 波的振动特点,发现R模对应的本征振动主要集中在地表,随着深度变化能量快速衰减,S2模对应的本征振动主要集中在第2层.研究“交叉点”附近频散点对应的本征振动曲线发现这一区域有些Rayleigh波同时具有R模和S2模的振动特点,对应着一种耦合模式.通过对实例的研究发现,在“交叉点”附近,若两条频散曲线不发生交叉,则每条曲线对应的模式会发生R模和S2模之间经由耦合模式的转变,本文称这种现象为两种模式发生耦合;若两条频散曲线相交,则同一条频散曲线上的Rayleigh波模式几乎相同,只是在离交点很近的区域会存在一些耦合模式,本文称此时两种模式不发生耦合.本文研究结果主要供Rayleigh波对低速层结构的反演研究参考.     

A deterministic method for designing near field and far field earthquakes

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