Nonlocal transport models for capturing solute transport in one-dimensional sand columns: Model review,applicability, limitations and improvement

Modelling pollutant transport in water is one of the core tasks of computational hydrology, and various physical models including especially the widely used nonlocal transport models have been developed and applied in the last three decades. No studies, however, have been conducted to systematically assess the applicability, limitations and improvement of these nonlocal transport models. To fill this knowledge gap, this study reviewed, tested and improved the state-of-the-art nonlocal transport models, including their physical background, mathematical formula and especially the capability to quantify conservative tracers moving in one-dimensional sand columns, which represents perhaps the simplest real-world application. Applications showed that, surprisingly, neither the popular time-nonlocal transport models (including the multi-rate mass transfer model, the continuous time random walk framework and the time fractional advection-dispersion equation), nor the spatiotemporally nonlocal transport model (ST-fADE) can accurately fit passive tracers moving through a 15-m-long heterogeneous sand column documented in literature, if a constant dispersion coefficient or dispersivity is used. This is because pollutant transport in heterogeneous media can be scale-dependent (represented by a dispersion coefficient or dispersivity increasing with spatiotemporal scales), non-Fickian (where plume variance increases nonlinearly in time) and/or pre-asymptotic (with transition between non-Fickian and Fickian transport). These different properties cannot be simultaneously and accurately modelled by any of the transport models reviewed by this study. To bypass this limitation, five possible corrections were proposed, and two of them were tested successfully, including a time fractional and space Hausdorff fractal model which minimizes the scale-dependency of the dispersion coefficient in the non-Euclidean space, and a two-region time fractional advection-dispersion equation which accounts for the spatial mixing of solute particles from different mobile domains. Therefore, more efforts are still needed to accurately model transport in non-ideal porous media, and the five model corrections proposed by this study may shed light on these indispensable modelling efforts.     

Uptake of radioactivity by marine sediments and implications for monitoring metal pollutants

The value of studying artificially-produced radionuclides in the marine environment is discussed in the wider context of monitoring sediments for other metal pollutants. Differences in the dispersion of selected radionuclides discharged from the same known source are used to illustrate the sort of changes in phase or speciation which must occur with other metal pollutants, but which cannot be demonstrated directly because of the multiplicity of sources. Various chemical and physical procedures are discussed which can be applied to a study of heavy metal associations with marine sediments, as are questions such as the existence, or otherwise, of mechanisms for the slow release of adsorbed material from the buried sediment back into the water column. Suggestions are made as to how radionuclide studies may be helpful in answering questions such as these, which are considered to be vital for the meaningful interpretation of sediment analyses.     

混合ADI-FDTD亚网格技术在探地雷达频散媒质中的高效正演

提出混合ADI-FDTD亚网格技术开展频散介质GPR正演,即在物性参数变化剧烈局部区域采用细网格剖分ADI-FDTD计算,其他的区域采用粗网格剖分常规FDTD计算,ADI-FDTD突破了CFL条件的限制,可选取与粗网格一致的大时间步长,有效地提高了计算效率.本文首先基于Debye方程,推导了粗网格FDTD及细网格ADI-FDTD频散介质差分格式,着重对粗细两种网格结合的场值交换方式进行了深入探讨,给出了该算法的计算流程.然后以一个薄层模型为例,分别应用粗网格、细网格、混合ADI-FDTD亚网格算法对该模型进行正演,计算资源的占用及模拟精度说明了混合ADI-FDTD亚网格算法的优势.最后,建立频散介质与非频散介质的组合模型,应用3种方法对该模型进行正演,对比3种方法优劣,分析雷达剖面中非频散介质及频散介质中波形特征,有效地指导雷达资料的精确解释.     

Remote sensing and modelling of bio-physical distribution patterns at Porcupine and Rockall Bank,Northeast Atlantic

Monthly composites of multi-year sea surface temperature (SST) and chlorophyll-a (Chl-a) have been used in combination with ocean model simulations to study bio-physical distribution patterns at Porcupine and Rockall Bank, two large submarine banks in the Northeast Atlantic in close proximity to the European shelf edge. Seven years (January 1998–December 2004) of remotely sensed data have been collated to create monthly climatological fields and to analyse principal spatio-temporal characteristics. At both banks, a region of cooler SST is found over the summit region compared to warmer waters of the surrounding ocean, less apparent in summer when capped by the seasonal thermocline. Enhanced Chl-a levels are found over both banks with a lifetime partly exceeding the bloom period. At Rockall Bank, both SST and Chl-a signals are more pronounced and persistent showing a 30% increase in annual Chl-a levels over the summit area with an even higher ratio in spring and autumn. A combination of physical processes appears to promote the enhanced productivity over both banks through the generation of a quasi-steady dome of cold, dense water during winter convection and upwelling events. This cold dome is associated with the presence of a retentive circulation based on Taylor cap dynamics and tidal rectification processes. The larger and more persistent enhancement of Chl-a levels over Rockall Bank would appear due to its isolated nature as well as its size. In contrast, Porcupine Bank is partly attached to the Irish shelf edge and exposed to the poleward flowing shelf edge current which may strip passive particles from the central bank region. Satellite derived Chl-a spring/summer distributions over the banks have been used to initialise model simulations of passive tracer dispersion. Timescales for the observed lifetime of the remotely sensed Chl-a patches are consistent with model derived retention timescales and simple scaling for the dispersion of passive biological material over the banks. Surface particle residence times over Rockall Bank are estimated to exceed Porcupine Bank values by a factor of two. Finally, the tidal contribution to individual particle motion is found to be large in some Rockall Bank areas, but less important at Porcupine Bank.     

ABSENCE OF PREFERENTIAL FLOW IN THE PERCOLATING WATERS OF A CONIFEROUS FOREST SOIL

Evidence for the functioning of macropores and the presence of preferential flow in forest soils is equivocal. This is partly because many workers use only one diagnostic technique to indicate whether or not macropore flow occurs. In this paper three lines of evidence are used to suggest that preferential flow does not occur in the percolating waters of a coniferous forest soil under the range of hydrological conditions that prevail in the field. To simulate field conditions, realistic rainfall intensities were used in conservative solute transport experiments on four undisturbed soil columns. A method is described in which breakthrough data can be used to calculate the percentage of antecedent water displaced from a soil column during frontal-type breakthrough experiments. Calculations based on this method using the experimental data show that as little as five percent of the antecedent water was immobile. The simple form of the functional advection–dispersion equation, based on a single value for linear velocity and the dispersion coefficient was fitted to two of the breakthrough curves with reasonable accuracy, further suggesting that preferential flow did not occur in the experiments. Finally, soil moisture characteristic curves were determined for replicate soil samples from the forest soil. The operational water contents of the columns during the breakthrough experiments were compared with the soil moisture characteristics and it was found that pores exerting pressure heads greater than −0·5 kPa did not appear to contribute to flow through the columns, again suggesting an absence of preferential flow. © 1997 by John Wiley & Sons, Ltd.     

A physical study of low-frequency dispersion of rock conductivity in time-domain electromagnetics

Most rocks display conductivity dispersion in the low-frequency range, when the usual displacement currents are neglected. The strong influence this low-frequency dispersion (LFD), including the response sign reversals, was revealed by field experiments with the coincident-loop configuration widely used in transient electromagnetics (EM). Mathematical modelling of LFD has been the subject of numerous studies. However, confirmation of the role of LFD or induced polarization (IP) by comparing mathematical modelling and field data is rather poor, because knowledge of the properties of rocks in the area of the field measurements is usually insufficient. For this reason physical modelling of LFD has been carried out at Moscow State Geological-prospecting Academy (Russia) in 1994-95. In order to observe criteria of similarity for both induction and polarization transients, a ring-shaped model was chosen and was represented by an electric circuit, consisting of lumped elements (real rock samples included). Qualitatively different transients for dispersive models and their non-dispersive ohmic equivalents were observed.     

Effects of petrophysical parameters on attenuation and dispersion of seismic waves in the simplified poroelastic theory: Comparison between the Biot's theory and viscosity‐extended theory

The simplified macro‐equations of porous elastic media are presented based on Hickey's theory upon ignoring effects of thermomechanical coupling and fluctuations of porosity and density induced by passing waves. The macro‐equations with definite physical parameters predict two types of compressional waves (P wave) and two types of shear waves (S wave). The first types of P and S waves, similar to the fast P wave and S wave in Biot's theory, propagate with fast velocity and have relatively weak dispersion and attenuation, while the second types of waves behave as diffusive modes due to their distinct dispersion and strong attenuation. The second S wave resulting from the bulk and shear viscous loss within pore fluid is slower than the second P wave but with strong attenuation at lower frequencies. Based on the simplified porous elastic equations, the effects of petrophysical parameters (permeability, porosity, coupling density and fluid viscosity) on the velocity dispersion and attenuation of P and S waves are studied in brine‐saturated sandstone compared with the results of Biot's theory. The results show that the dispersion and attenuation of P waves in simplified theory are stronger than those of Biot's theory and appear at slightly lower frequencies because of the existence of bulk and shear viscous loss within pore fluid. The properties of the first S wave are almost consistent with the S wave in Biot's theory, while the second S wave not included in Biot's theory even dies off around its source due to its extremely strong attenuation. The permeability and porosity have an obvious impact on the velocity dispersion and attenuation of both P and S waves. Higher permeabilities make the peaks of attenuation shift towards lower frequencies. Higher porosities correspond to higher dispersion and attenuation. Moreover, the inertial coupling between fluid and solid induces weak velocity dispersion and attenuation of both P and S waves at higher frequencies, whereas the fluid viscosity dominates the dispersion and attenuation in a macroscopic porous medium. Besides, the heavy oil sand is used to investigate the influence of high viscous fluid on the dispersion and attenuation of both P and S waves. The dispersion and attenuation in heavy oil sand are stronger than those in brine‐saturated sandstone due to the considerable shear viscosity of heavy oil. Seismic properties are strongly influenced by the fluid viscosity; thus, viscosity should be included in fluid properties to explain solid–fluid combination behaviour properly.     

弹性波在含双裂纹岩体中的传播分析

岩石和岩体是具有复杂细微观结构的非均匀介质.弹性波在岩体中传播时,与岩体细微观缺陷相互作用表现出弹性波的频散效应.为研究岩体内部细观结构对弹性波频散效应的作用,本文采用双裂纹模型:在模型内部,考虑裂纹间的相互作用对弹性波的影响,以分析弹性波在双裂纹体系间的多次散射作用;在双裂纹体系间,采用线性叠加分析法,以考虑岩体缺陷影响的局部化.对波动方程应用Green函数基本解,利用边界积分方法,将双裂纹体系作为内边界处理,得到相应的频散方程,由此对比分析了双裂纹体系在上述两种分析方法下的区别,进一步探讨了双裂纹体系参数、孔隙流体压力和卸荷对岩体频散特性的影响.     

Eutrophication and drought disturbance shape functional diversity and life-history traits of aquatic plants in shallow lakes

Theories that link plant strategies and abiotic filters discriminate between three strategies: competitive, ruderal or stress-tolerant species, and suggest that functional diversity is higher at intermediate values along the gradients of productivity and disturbance. The mechanism by which abiotic filters screen plant traits in aquatic plant communities has been poorly tested and has led to contrasting results. The present study aimed to test whether functional diversity and abundance of life-history traits corresponding to morphology, fecundity and longevity of aquatic plants were linked to disturbance and productivity. Fifty-nine shallow lakes that were arranged along a gradient of productivity (estimated through total phosphorus concentration) and drought-disturbance frequency were sampled for aquatic plants. Species traits were documented and functional diversity was calculated (richness, dispersion and evenness) for each lake. Increasing total phosphorus concentration was associated with decreased functional richness and dispersion but not functional evenness. Functional diversity did not differ according to disturbance frequency, regardless of the index that was measured. High productivity favoured floating species with storage organs and vegetative reproduction, especially at low disturbance frequency. For all disturbance frequencies, low productivity favoured small species without storage organs and sexual reproduction. The present study partly supports the theoretical model. At high productivity levels, because phytoplankton is a better competitor for light than aquatic plants, plant traits are screened stringently, and species with traits that allow them to reach the photic zone are selected.     

Rare earth element mobility during granite alteration: Evidence from southwest England

Geochemical analyses of granitic rocks from southwest England reveal that the rare earth elements (REE) were potentially mobile during hydrothermal and supergene alteration. In particular, trivalent REE were removed from the system during K-silicate alteration, Eu was lost during sericitic alteration; all REE were lost during tourmalinization, and light REE were lost during chloritization and argillic alteration. The fluids themselves had low concentrations of REE; in only one case (chloritization) were heavy REE introduced during alteration. Analysis of separated minerals indicated that the behaviour of the REE could be partly explained in terms of their different affinities for the primary and secondary assemblages. Thermodynamic calculations indicated that REE mobility is enhanced by the presence of fluorine in the alteration fluids partly because REE form more stable complexes with F than with Cl and partly because elements such as Ti, Zr and P that form REE-bearing minor phases are themselves potentially mobile.     

THE DISPERSION RELATION, OF EARTH''S ELECTROMAGNETIC RESPONSE FUNCTIONS AND THE JOINT INVERSION OF DATA

On the basis of the dispersion relations of MT field, the necessity and applied prospects of the joint inversions using a pair of MT response functions which are correlative with the dispersion relations, are infered. A filter coefficient algorithm is made, with which the corresponding impedance phase data can be estimated using a set of apparent resistivities. The tests for the observed MT data show that when comparing the impedance phase estimated using the dispersion relation with the ob served phase, it can be checked whether the dispersion relation between observed apparent resistivity and phase data is satisfied or not, and that the use of the phase data corrected using the dispersion relation in the joint inversion is advantageous to obtain more confident results. It is shown that joint inversions are more advantageous than single parameter inversions, and that in the most case the joint inversion using the apparent resistivities of impedance real and imaginary parts is more advantageous than the jointinversion using the normal apparent resistivity and impedance phase. The existence of the dipersion relations between the ratio apparent resistivity and corresponding impedance phase of the orthogonal electric and magnetic field horizontal Components in the frequency EM sounding with horizontal electric dipole(FEMS) are discussed, the better effect of the joint inversion using the pair of EM response functions is obtained. The problems on the one-dimensional joint inversion for the MT and FEMS apparent resistivities, for which the observed frequency bands partly overlape each other, are studied. It is shown that this joint inversion is applicable and effective:the joint inversions of the practical data for two kinds of EM methods at two sites give the results well corresponding to the drilling data. The simulated MT inversions for the data of two kinds of EM methods are made, and more confident results also are obtained.     

Mathematical Modeling of Diffusion and Transport of Pollutants in the Atmospheric Boundary Layer

— The process of dispersion of air pollutants, in a broad sense, can be considered as the net outcome of various mechanisms involved in the transport of air pollutants from the source to the receptor. The major mechanisms are: (1) advection of pollutants by mean air motion, (2) mixing of pollutants by atmospheric turbulence and (3) mass diffusion due to concentration gradients. In addition, the physical and chemical nature of the effluent, the location of the stack and the nature of the terrain downwind from the stack, effect the dispersion of the pollutants. Various physical and mathematical aspects related to the transport and diffusion of air pollutants in the atmospheric boundary layer are discussed here. Further, some aspects of dispersion in a weak wind stable boundary layer are described. Finally, the current issues in the modeling of weak wind boundary layer are illustrated.     

The multivariate controls of hydraulic geometry: A causal investigation in terms of boundary shear distribution

Most downstream hydraulic geometry exponents have been found to be very close to the classic values reported by Leopold and Maddock (1953). These have been viewed as the simplified cases to general trends because the hydraulic geometry of alluvial channels is actually the product of ‘multivariate controls’ (Richards, 1982). This paper is an attempt to develop a soundly based foundation for the explanation of the physical mechanisms of these controls. A quantitative relationship between channel shape and boundary shear distribution developed from experimental flume results is found to be applicable in some instances to alluvial channels, particularly to stable canals. On the basis of this relationship, it is shown that downstream hydraulic geometry is determined not only by flow discharge, but also by channel slope, channel average roughness and sediment composition of the channel boundary. This is strongly supported by our analysis of 529 observations from both stable canals and natural rivers in the U.S.A. and the U.K. The difference between regime relations in canals and the hydraulic geometry of rivers appears to be caused mainly by channel slope and average roughness, which can be regarded as constants only in stable canals. The close relationship between discharge and channel average roughness observed in canals is not repeated in natural channels, partly because of the variety of flow values used to define the channel-forming discharge. Furthermore, it is indicated that the effects of the sediment composition of the channel boundary on hydraulic geometry are significant and need further investigation.     

Mixing cell method for solving the solute transport equation with spatially variable coefficients

The advection–dispersion equation with spatially variable coefficients does not have an exact analytical solution and is therefore solved numerically. However, solutions obtained with several of the traditional finite difference or finite element techniques typically exhibit spurious oscillation or numerical dispersion when advection is dominant. The mixing cell and semi-analytical solution methods proposed in this study avoid such oscillation or numerical dispersion when advection dominates. Both the mixing cell and semi-analytical solution methods calculate the spatial step size by equating numerical dispersion to physical dispersion. Because of the spatial variability of the coefficients the spatial step size varies in space. When the time step size Δt→0, the mixing cell method reduces to the semi-analytical solution method. The results of application to two cases show that the mixing cell and semi-analytical solution methods are better than a finite difference method used in the study. © 1998 John Wiley & Sons, Ltd.     

Shear velocity and density of an attenuating earth

The dispersion that must accompany absorption is taken into account in many recent body-wave investigations but has been largely ignored in surface-wave and free-oscillation studies. In order to compare body-wave and free-oscillation data a correction must be made to travel times or periods to account for absorption-related physical dispersion. The correction depends on the frequency and Q of the data and can be as high as 1% which is much larger than the uncertainty of the raw data. Corrected toroidal mode data is inverted to obtain shear velocity and density versus depth. The average shear velocity in the upper 600 km is ～2% greater than obtained from the uncorrected data. The resulting shear-wave travel times oscillate about the Jeffreys-Bullen values with an average baseline of only +0.5 second. Thus, the discrepancy between body-wave and free-oscillation studies is eliminated.     

Stochastic modeling of reactive transport in wetlands

This study describes the development of a general model for reaction in and performance of spatially heterogeneous bioreactors such as treatment wetlands. The modeled domain possesses local-scale velocities, reaction rates and transverse dispersion coefficients that are functions of an underlying heterogeneity variate representing one or more controlling biophysical attributes, for example, reactive surface area (submerged plant) density. Reaction rate coefficients are treated as related to local velocities in an inverse square fashion via their mutual dependence upon the variate. The study focuses on the solution for the steady-state case with constant inlet concentration. Results compare well with exact solutions developed for laterally-bounded systems in which the heterogeneity is represented explicitly. Employing the bicontinuum analogue of a second-order model, an expression for an effective longitudinal dispersion coefficient as a function of travel distance is developed using the method of moments. The result provides insights into the behavior of concentration as transverse mixing drives the system asymptotically toward Fickian longitudinal dispersion. The model may represent an improvement over other approaches for characterizing treatment wetland performance because it accounts for evolving shear flow dispersion, and because parameters are few in number, physically based, and invariant with mean velocity.     

The comparison of ensemble or deterministic dispersion modeling on global dispersion during Fukushima Dai-ichi nuclear accident

Ensemble forcasting,originally developed for weather prediction,is lately being extended to atmospheric dispersion applications,which is a new,effective methodology for improving the atmospheric dispersion numerical modeling.In March 2011,due to the massive 9.0 earthquakes and ensuing tsunami that struck off the northern coast of the island of Honshu,the Fukushima Nuclear Plant I had the substantial leak of radioactive materials into surrounding environment and atmosphere.To aim at the global dispersion modeling of atmospheric radionuclides from Fukushima Nuclear Accident,this paper presents two approaches of atmospheric dispersion forecasting:ensemble dispersion modeling(EDM) and deterministic dispersion modeling(DDM),conducts the globally dispersion modeling cases for Fukushima nuclear accident,and analyzes and evaluates the simulation results using observation data.In this paper,EDM includes three different perturbation methods:meteorological perturbation method,turbulence perturbation method,and physical parameterization ensemble forecasting method.The simulation results show that the trajectories from EDM have a better performance,which is in better agreement with the atmospheric circulation and observation data; the spread from DDM is slower and not as far as EDM.Additionally,the results from EDM display a better performance in the modeling of transport from Japan to China East Sea on April 4.The reasons for these results are:the techniques of MET and TUR are performed by adding perturbations on mean wind and turbulent velocity,respectively; the various different flow fields will result in far spreading in horizontal and the simulation results closer to observation; PHY is performed by using different diffusion physical parameterizations and produces the perturbations on vertical wind,which results the spreading in smaller range and discontinuous in horizontal.Finally,the comparative analysis between modeling results and observation data shows that all cases results are in good agreement with trends of observed radionuclides surface concentration; however,the modeling surface concentration is smaller than observation,especially in DDM and PHY.Furthermore,the EDM results show that MET and TUR are of more evolutionary advantage than PHY in modeling of average and maximum concentration.Therefore,this study can serve as a reference to atmospheric dispersion and environmental emergency response(EER).     

Can a Time Fractional‐Derivative Model Capture Scale‐Dependent Dispersion in Saturated Soils?

Time nonlocal transport models such as the time fractional advection‐dispersion equation (t‐fADE) were proposed to capture well‐documented non‐Fickian dynamics for conservative solutes transport in heterogeneous media, with the underlying assumption that the time nonlocality (which means that the current concentration change is affected by previous concentration load) embedded in the physical models can release the effective dispersion coefficient from scale dependency. This assumption, however, has never been systematically examined using real data. This study fills this historical knowledge gap by capturing non‐Fickian transport (likely due to solute retention) documented in the literature (Huang et al. 1995) and observed in our laboratory from small to intermediate spatial scale using the promising, tempered t‐fADE model. Fitting exercises show that the effective dispersion coefficient in the t‐fADE, although differing subtly from the dispersion coefficient in the standard advection‐dispersion equation, increases nonlinearly with the travel distance (varying from 0.5 to 12 m) for both heterogeneous and macroscopically homogeneous sand columns. Further analysis reveals that, while solute retention in relatively immobile zones can be efficiently captured by the time nonlocal parameters in the t‐fADE, the motion‐independent solute movement in the mobile zone is affected by the spatial evolution of local velocities in the host medium, resulting in a scale‐dependent dispersion coefficient. The same result may be found for the other standard time nonlocal transport models that separate solute retention and jumps (i.e., displacement). Therefore, the t‐fADE with a constant dispersion coefficient cannot capture scale‐dependent dispersion in saturated porous media, challenging the application for stochastic hydrogeology methods in quantifying real‐world, preasymptotic transport. Hence improvements on time nonlocal models using, for example, the novel subordination approach are necessary to incorporate the spatial evolution of local velocities without adding cumbersome parameters.     

A portable experimental hillslope for frozen ground studies

Frozen ground hydrological effects on runoff, storage, and release have been observed in the field and tested in numerical models, but few physical models of frozen slopes (at scales from 1 to 15 m) exist partly because the design of such an experiment requires new engineering design for realistic whole‐slope freezing and physical model innovation. Here, we present a new freezable tilting hillslope physical model for hydrological system testing under a variety of climate conditions with the ability to perform multiple (up to 20 per year) freeze–thaw cycles. The 4 × 2 m hillslope is mobile and tiltable on the basis of a modified tri‐axle 4.88‐m (16′) dump trailer to facilitate testing multiple configurations. The system includes controllable boundary conditions on all surfaces; examples of side and baseflow boundary conditions include permeable membranes, impermeable barriers, semipermeable configurations, and constant head conditions. To simulate cold regions and to freeze the hillslope in a realistic and controlled manner, insulation and a removable freezer system are incorporated onto the top boundary of the hillslope. The freezing system is designed to expedite the freezing process by the addition of a 10,130‐KJ (9,600‐BTU) refrigeration coil to the top‐centre of the insulated ceiling. Centre placement provides radial freezing of the hillslope in a top‐down fashion, similar to what natural systems encounter in the environment. The perimeter walls are insulated with 100 mm of spray foam insulation, whereas the base of the hillslope is not insulated to simulate natural heat fluxes beneath the frozen layer of soil. Our preliminary testing shows that covers can be frozen down to ?10 °C in approximately 7 days, with subsequent thaw on a similar time frame.     

On uniqueness of dispersion curve of surface love-waves

Summary Possibility of non-uniqueness of dispersion curve for various distributions of physical properties has been discussed. It has been concluded that number of layers in a model should be moderate in order to give a representative picture.