共查询到20条相似文献，搜索用时 15 毫秒
1.
《Advances in water resources》2004,27(8):775-784
In this study, we derive analytical solutions of the first two moments (mean and variance) of pressure head for one-dimensional steady state unsaturated flow in a randomly heterogeneous layered soil column under random boundary conditions. We first linearize the steady state unsaturated flow equations by Kirchhoff transformation and solve the moments of the transformed variable up to second order in terms of σY and σβ, the standard deviations of log hydraulic conductivity Y=ln(Ks) and of the log pore size distribution parameter β=ln(α). In addition, we also give solutions for the mean and variance of the unsaturated hydraulic conductivity. The analytical solutions of moment equations are validated via Monte Carlo simulations. 相似文献
2.
Non-local stochastic moment equations are used successfully to analyze groundwater flow in randomly heterogeneous media. Here we present a moment equations-based approach to quantify the uncertainty associated with the estimation of well catchments. Our approach is based on the development of a complete second order formalism which allows obtaining the first statistical moments of the trajectories of conservative solute particles advected in a generally non-uniform groundwater flow. Approximate equations of moments of particles’ trajectories are then derived on the basis of a second order expansion in terms of the standard deviation of the aquifer log hydraulic conductivity. Analytical expressions are then obtained for the predictors of locations of mean stagnation points, together with their associated uncertainties. We implement our approach on heterogeneous media in bounded two-dimensional domains, with and without including the effect of conditioning on hydraulic conductivity information. The impact of domain size, boundary conditions, heterogeneity and non-stationarity of hydraulic conductivity on the prediction of a well catchment is explored. The results are compared against Monte Carlo simulations and semi-analytical solutions available in the literature. The methodology is applicable to both infinite and bounded domains and is free of distributional assumptions (and so applies to both Gaussian and non-Gaussian log hydraulic conductivity fields) and formally includes the effect of conditioning on available information. 相似文献
3.
《Advances in water resources》1998,22(2):185-195
We present an efficient numerical method for solving stochastic porous media flow problems. Single-phase flow with a random conductivity field is considered in a standard first-order perturbation expansion framework. The numerical scheme, based on finite element techniques, is computationally more efficient than traditional approaches because one can work with a much coarser finite element mesh. This is achieved by avoiding the common finite element representation of the conductivity field. Computations with the random conductivity field only arise in integrals of the log conductivity covariance function. The method is demonstrated in several two- and three-dimensional flow situations and compared to analytical solutions and Monte Carlo simulations. Provided that the integrals involving the covariance of the log conductivity are computed by higher-order Gaussian quadrature rules, excellent results can be obtained with characteristic element sizes equal to about five correlation lengths of the log conductivity field. Investigations of the validity of the proposed first-order method are performed by comparing nonlinear Monte Carlo results with linear solutions. In box-shaped domains the log conductivity standard deviation σY may be as large as 1.5, while the head variance is considerably influenced by nonlinear effects as σY approaches unity in more general domains. 相似文献
4.
Traditional Ensemble Kalman Filter (EnKF) data assimilation requires computationally intensive Monte Carlo (MC) sampling, which suffers from filter inbreeding unless the number of simulations is large. Recently we proposed an alternative EnKF groundwater-data assimilation method that obviates the need for sampling and is free of inbreeding issues. In our new approach, theoretical ensemble moments are approximated directly by solving a system of corresponding stochastic groundwater flow equations. Like MC-based EnKF, our moment equations (ME) approach allows Bayesian updating of system states and parameters in real-time as new data become available. Here we compare the performances and accuracies of the two approaches on two-dimensional transient groundwater flow toward a well pumping water in a synthetic, randomly heterogeneous confined aquifer subject to prescribed head and flux boundary conditions. 相似文献
5.
Solute leaching in unsaturated soil is influenced by the variability in hydraulic functions (water retention and conductivity) that govern the flow process. Variability in measured soil hydraulic functions of a coarse-, medium- and fine-textured soil group was quantified with the scaling theory of similar media. Solute leaching in these soils was calculated with Monte Carlo simulation assuming, successively, hydraulic conductivity, K, volumetric water content, 0, and pressure head, h, to be constant. In addition to variability in hydraulic functions, variability in the solute retardation factor was also taken into account. To examine this effect five solutes were considered: a conservative solute (chloride), a non-retarded solute subject to decay (nitrate), a retarded solute that does not decay (cadmium) and two organic solutes which are retarded but have different sorption and decay parameters (the pesticide atrazine and a chlorinated hydrocarbon). The numerical results obtained with Monte Carlo simulation were in a number of instances verified with analytical solutions. The three soil groups distinguished showed considerable differences in vulnerability for leaching of the five solutes, emphasizing the importance of the effect of variability in soil hydraulic functions when studying solute leaching. Numerical and analytical results showed good agreement. Therefore, in relatively simple situations analytical solutions are attractive. However, in complicated situations, analytical solutions are cumbersome and numerical solutions are the only realistic alternative. 相似文献
6.
Stochastic analysis is commonly used to address uncertainty in the modeling of flow and transport in porous media. In the stochastic approach, the properties of porous media are treated as random functions with statistics obtained from field measurements. Several studies indicate that hydrological properties depend on the scale of measurements or support scales, but most stochastic analysis does not address the effects of support scale on stochastic predictions of subsurface processes. In this work we propose a new approach to study the scale dependence of stochastic predictions. We present a stochastic analysis of immiscible fluid–fluid displacement in randomly heterogeneous porous media. While existing solutions are applicable only to systems in which the viscosity of one phase is negligible compare with the viscosity of the other (water–air systems for example), our solutions can be applied to the immiscible displacement of fluids having arbitrarily viscosities such as NAPL–water and water–oil. Treating intrinsic permeability as a random field with statistics dependant on the permeability support scale (scale of measurements) we obtained, for one-dimensional systems, analytical solutions for the first moments characterizing unbiased predictions (estimates) of system variables, such as the pressure and fluid–fluid interface position, and we also obtained second moments, which characterize the uncertainties associated with such predictions. Next we obtained empirically scale dependent exponential correlation function of the intrinsic permeability that allowed us to study solutions of stochastic equations as a function of the support scale. We found that the first and second moments converge to asymptotic values as the support scale decreases. In our examples, the statistical moments reached asymptotic values for support scale that were approximately 1/10000 of the flow domain size. We show that analytical moment solutions compare well with the results of Monte Carlo simulations for moderately heterogeneous porous media, and that they can be used to study the effects of heterogeneity on the dynamics and stability of immiscible flow. 相似文献
7.
Two models for estimating expected areal‐average infiltration rate, ī, at the hillslope scale are presented. The first relies upon the condition of a negligible infiltration of surface water running downslope (run‐on process) into a previous heterogeneous soil. It is an adapted version of an earlier semi‐analytical model. The second incorporates the run‐on process and is based on a lumped approach that uses an effective saturated hydraulic conductivity. This latter was parameterized in terms of the main characteristics of rainfall and soil. Both the models were tested by comparison with the results carried out by Monte‐Carlo simulations over different soil types. It was found that the first model simulated ī with maximum errors in magnitude typically less than 10%. The second model provided similar errors in the total volume of overland flow, and the rising limb of the hydrograph experienced a distortion. Lastly, satisfactory results were obtained by comparing the model without run‐on with an empirical approach particularly accurate for fine‐textured soils. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
8.
9.
This study addresses estimation of net irrigation requirement over a growing season under climate uncertainty. An ecohydrological model, building upon the stochastic differential equation of soil moisture dynamics, is employed as a basis to derive new analytical expressions for estimating seasonal net irrigation requirement probabilistically. Two distinct irrigation technologies are considered. For micro irrigation technology, probability density function of seasonal net irrigation depth (SNID) is derived assessing transient behavior of a stochastic process which is time integral of dichotomous Markov process. Probability mass function of SNID which is a discrete random variable for traditional irrigation technology is also presented using a marked renewal process with quasi-exponentially-distributed time intervals. Comparing the results obtained from the presented models with those resulted from a Monte Carlo approach verified the significance of the probabilistic expressions derived and assumptions made. 相似文献
10.
This paper describes a stochastic analysis of steady state flow in a bounded, partially saturated heterogeneous porous medium subject to distributed infiltration. The presence of boundary conditions leads to non-uniformity in the mean unsaturated flow, which in turn causes non-stationarity in the statistics of velocity fields. Motivated by this, our aim is to investigate the impact of boundary conditions on the behavior of field-scale unsaturated flow. Within the framework of spectral theory based on Fourier–Stieltjes representations for the perturbed quantities, the general expressions for the pressure head variance, variance of log unsaturated hydraulic conductivity and variance of the specific discharge are presented in the wave number domain. Closed-form expressions are developed for the simplified case of statistical isotropy of the log hydraulic conductivity field with a constant soil pore-size distribution parameter. These expressions allow us to investigate the impact of the boundary conditions, namely the vertical infiltration from the soil surface and a prescribed pressure head at a certain depth below the soil surface. It is found that the boundary conditions are critical in predicting uncertainty in bounded unsaturated flow. Our analytical expression for the pressure head variance in a one-dimensional, heterogeneous flow domain, developed using a nonstationary spectral representation approach [Li S-G, McLaughlin D. A nonstationary spectral method for solving stochastic groundwater problems: unconditional analysis. Water Resour Res 1991;27(7):1589–605; Li S-G, McLaughlin D. Using the nonstationary spectral method to analyze flow through heterogeneous trending media. Water Resour Res 1995; 31(3):541–51], is precisely equivalent to the published result of Lu et al. [Lu Z, Zhang D. Analytical solutions to steady state unsaturated flow in layered, randomly heterogeneous soils via Kirchhoff transformation. Adv Water Resour 2004;27:775–84]. 相似文献
11.
David Ching-Fang Shih 《水文研究》2024,38(2):e15071
In the context of the heterogeneity in the unsaturated or vadose zone, accurately representing the analytical mechanisms and in-situ water content within the soil layer poses a significant challenge. Particularly in shallow layers, thermal conditions exhibit rapid changes in response to evolving surface temperatures. This study proposes a hypothesis suggesting that the in situ heat mechanism may notably impact the soil water layer. The research introduces an innovative approach to theoretically uncover thermal conditions, including soil temperature, soil temperature gradients, and heat flux, within the shallow Quaternary gravel layer at various depths through spectral analysis of temporal observations. The study presents a stochastic inverse solution to estimate thermal conductivity by leveraging spectral analysis of soil heat flux and temperature gradients. The findings reveal that thermal conditions exhibit the most prominent periodic fluctuations during the diurnal process over a 24-hour cycle. The soil temperature gradients and heat flux measurements at depths of 0.1, 0.3, 0.6, and 1.2 m demonstrate their ability to capture changes in soil temperature and air temperature to a certain extent within the frequency domain. Furthermore, the analysis highlights the intrinsic uncertainty and sensitivity of estimating thermal conductivity in heterogeneous soil environments. The wide variability observed in thermal conductivity values, coupled with their dependence on soil type and environmental conditions, underscores the need for careful consideration of these factors in future studies and modeling efforts. Applying the derived inverse spectral solution allows for determining thermal conductivity throughout the soil-water system across depths ranging from 0.1 to 1.2 m. As a result, this research demonstrates the feasibility and practicality of assessing the thermal conductivity of the soil layer in conjunction with heat flux and temperature gradients through spectral analysis. 相似文献
12.
A Eulerian analytical method is developed for nonreactive solute transport in heterogeneous, dual-permeability media where the hydraulic conductivities in fracture and matrix domains are both assumed to be stochastic processes. The analytical solution for the mean concentration is given explicitly in Fourier and Laplace transforms. Instead of using the fast fourier transform method to numerically invert the solution to real space (Hu et al., 2002), we apply the general relationship between spatial moments and concentration (Naff, 1990; Hu et al., 1997) to obtain the analytical solutions for the spatial moments up to the second for a pulse input of the solute. Owing to its accuracy and efficiency, the analytical method can be used to check the semi-analytical and Monte Carlo numerical methods before they are applied to more complicated studies. The analytical method can be also used during screening studies to identify the most significant transport parameters for further analysis. In this study, the analytical results have been compared with those obtained from the semi-analytical method (Hu et al., 2002) and the comparison shows that the semi-analytical method is robust. It is clearly shown from the analytical solution that the three factors, local dispersion, conductivity variation in each domain and velocity convection flow difference in the two domains, play different roles on the solute plume spreading in longitudinal and transverse directions. The calculation results also indicate that when the log-conductivity variance in matrix is 10 times less than its counterpart in fractures, it will hardly influence the solute transport, whether the conductivity field is matrix is treated as a homogeneous or random field. 相似文献
13.
C. -M. Chang M. W. Kemblowski 《Stochastic Environmental Research and Risk Assessment (SERRA)》1994,8(4):281-300
In this article, we are concerned with the statistics of steady unsaturated flow in soils with a fractal hydraulic conductivity distribution. It is assumed that the spatial distribution of log hydraulic conductivity can be described as an isotropic stochastic fractal process. The impact of the fractal dimension of this process, the soil pore-size distribution parameter, and the characteristic length scale on the variances of tension head and the effective conductivity is investigated. Results are obtained for one-dimensional and three-dimensional flows. Our results indicate that the tension head variance is scale-dependent for fractal distribution of hydraulic conductivity. Both tension head variance and effective hydraulic conductivity depend strongly on the fractal dimension. The soil pore-size distribution parameter is important in reducing the variability of the unsaturated hydraulic conductivity and of the fluxes. 相似文献
14.
ABSTRACTThis study investigates the impact of hydraulic conductivity uncertainty on the sustainable management of the aquifer of Lake Karla, Greece, using the stochastic optimization approach. The lack of surface water resources in combination with the sharp increase in irrigation needs in the basin over the last 30 years have led to an unprecedented degradation of the aquifer. In addition, the lack of data regarding hydraulic conductivity in a heterogeneous aquifer leads to hydrogeologic uncertainty. This uncertainty has to be taken into consideration when developing the optimization procedure in order to achieve the aquifer’s sustainable management. Multiple Monte Carlo realizations of this spatially-distributed parameter are generated and groundwater flow is simulated for each one of them. The main goal of the sustainable management of the ‘depleted’ aquifer of Lake Karla is two-fold: to determine the optimum volume of renewable groundwater that can be extracted, while, at the same time, restoring its water table to a historic high level. A stochastic optimization problem is therefore formulated, based on the application of the optimization method for each of the aquifer’s multiple stochastic realizations in a future period. In order to carry out this stochastic optimization procedure, a modelling system consisting of a series of interlinked models was developed. The results show that the proposed stochastic optimization framework can be a very useful tool for estimating the impact of hydraulic conductivity uncertainty on the management strategies of a depleted aquifer restoration. They also prove that the optimization process is affected more by hydraulic conductivity uncertainty than the simulation process.
Editor Z.W. Kundzewicz; Guest editor S. Weijs 相似文献
15.
Valentina Ciriello Vittorio Di Federico Monica Riva Francesco Cadini Jacopo De Sanctis Enrico Zio Alberto Guadagnini 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(4):945-954
We perform global sensitivity analysis (GSA) through polynomial chaos expansion (PCE) on a contaminant transport model for the assessment of radionuclide concentration at a given control location in a heterogeneous aquifer, following a release from a near surface repository of radioactive waste. The aquifer hydraulic conductivity is modeled as a stationary stochastic process in space. We examine the uncertainty in the first two (ensemble) moments of the peak concentration, as a consequence of incomplete knowledge of (a) the parameters characterizing the variogram of hydraulic conductivity, (b) the partition coefficient associated with the migrating radionuclide, and (c) dispersivity parameters at the scale of interest. These quantities are treated as random variables and a variance-based GSA is performed in a numerical Monte Carlo framework. This entails solving groundwater flow and transport processes within an ensemble of hydraulic conductivity realizations generated upon sampling the space of the considered random variables. The Sobol indices are adopted as sensitivity measures to provide an estimate of the role of uncertain parameters on the (ensemble) target moments. Calculation of the indices is performed by employing PCE as a surrogate model of the migration process to reduce the computational burden. We show that the proposed methodology (a) allows identifying the influence of uncertain parameters on key statistical moments of the peak concentration (b) enables extending the number of Monte Carlo iterations to attain convergence of the (ensemble) target moments, and (c) leads to considerable saving of computational time while keeping acceptable accuracy. 相似文献
16.
《Advances in water resources》1998,21(4):315-324
The paper deals with numerical solutions to the Richards equation to simulate one-dimensional flow processes in the unsaturated zone of layered soil profiles. The equation is expressed in the pressure-based form and a finite-difference algorithm is developed for accurately estimating the values of the hydraulic conductivity between two neighboring nodes positioned in different soil layers, often referred to as the interlayer hydraulic conductivity. The algorithm is based upon flux conservation and continuity of pressure potential at the interface between two consecutive layers, and does not add significantly to simulation run time. The validity of the model is established for a number of test problems by comparing numerical results with the analytical solutions developed by Srivastava and Yeh29 which hold for vertical infiltration towards the water table in a two-layer soil profile. The results show a significant reduction in relative mass balance errors when using the proposed model. Some specific insights into its numerical performance are also gained by comparisons with a numerical model in which the more common geometric averaging operator acts on the interlayer conductivities. 相似文献
17.
The interaction of geomechanics and flow within a soil body induces deformation and pore pressure change. Deformation may change hydrogeological and elastic properties, which alters the mechanical behaviour and results in non‐linearity. To investigate this interaction effect in a heterogeneous porous medium, a stochastic poroelastic model is proposed. Monte Carlo simulations are performed to determine the mean and uncertainty of the parameter changes, displacement, and change in pore water pressure. Hydraulic conductivity is treated as the only random variable in the coupled geomechanics‐flow system due to its large variation compared to other mechanical and hydrogeological properties in natural environments. The three considered non‐linear models for the interaction between parameters and deformation are those that consider (1) porosity and hydraulic conductivity; (2) porosity and Young's modulus; and (3) a combined effect that includes porosity, hydraulic conductivity, and Young's modulus. Boundary effects on the coupled system are also explored. The relationships between changes of porosity, hydraulic conductivity, and Young's modulus are analytically shown to be non‐linear. Among the considered parameters, the deformation effect induces the largest reduction in hydraulic conductivity. The deformation‐induced change in hydraulic conductivity shows the most significant effect on the mean and variance of the change in pore water pressure and displacement, while changes in Young's modulus have the least effect. When the deformation effect is considered, the superposition relationship does not exist in the mean displacement and mean change in pore water pressure for the three scenarios considered; it exists for the case without deformation effects. Deformation also causes a reduction in the effective hydraulic conductivity for the whole domain. The scenario that considers both loading and discharge boundaries has larger changes in hydrogeological and geo‐mechanical parameters than those in scenarios that consider loading and discharge boundaries separately. The results indicate that the interaction between deformation and changes in parameters has a profound effect on the poroelastic system. The effect of deformation should thus be considered in modelling and practice. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
18.
The parallel physically-based surface–subsurface model PARFLOW was used to investigate the spatial patterns and temporal dynamics of river–aquifer exchange in a heterogeneous alluvial river–aquifer system with deep water table. Aquifer heterogeneity at two scales was incorporated into the model. The architecture of the alluvial hydrofacies was represented based on conditioned geostatistical indicator simulations. Subscale variability of hydraulic conductivities (K) within hydrofacies bodies was created with a parallel Gaussian simulation. The effects of subscale heterogeneity were investigated in a Monte Carlo framework. Dynamics and patterns of river–aquifer exchange were simulated for a 30-day flow event. Simulation results show the rapid formation of saturated connections between the river channel and the deep water table at preferential flow zones that are characterized by high conductivity hydrofacies. Where the river intersects low conductivity hydrofacies shallow perched saturated zones immediately below the river form, but seepage to the deep water table remains unsaturated and seepage rates are low. Preferential flow zones, although only taking up around 50% of the river channel, account for more than 98% of total seepage. Groundwater recharge is most efficiently realized through these zones. Subscale variability of Ksat slightly increased seepage volumes, but did not change the general seepage patterns (preferential flow zones versus perched zones). Overall it is concluded that typical alluvial heterogeneity (hydrofacies architecture) is an important control of river–aquifer exchange in rivers overlying deep water tables. Simulated patterns and dynamics are in line with field observations and results from previous modeling studies using simpler models. Alluvial heterogeneity results in distinct patterns and dynamics of river–aquifer exchange with implications for groundwater recharge and the management of riparian zones (e.g. river channel-floodplain connectivity via saturated zones). 相似文献
19.
Dale F. Rucker 《Advances in water resources》2011,34(2):215-226
Modeling unsaturated flow in porous media requires constitutive relations that describe the soil water retention and soil hydraulic conductivity as a function of either potential or water content. Often, the hydraulic parameters that describe these relations are directly measured on small soil cores, and many cores are needed to upscale to the entire heterogeneous flow field. An alternative to the forward upscaling method using small samples are inverse upscaling methods that incorporate soft data from geophysical measurements observed directly on the larger flow field. In this paper, we demonstrate that the hydraulic parameters can be obtained from cross borehole ground penetrating radar by measuring the first arrival travel time of electromagnetic waves (represented by raypaths) from stationary antennae during a constant flux infiltration experiment. The formulation and coupling of the hydrological and geophysical models rely on a constant velocity wetting front that causes critical refraction at the edge of the front as it passes by the antennae. During this critical refraction period, the slope of the first arrival data can be used to calculate (1) the wetting velocity and (2) the hydraulic conductivity of the wet (or saturated) soil. If the soil is undersaturated during infiltration, then an estimate of the saturated water content is needed before calculating the saturated hydraulic conductivity. The hydraulic conductivity value is then used in a nonlinear global optimization scheme to estimate the remaining two parameters of a Broadbridge and White soil. 相似文献
20.
《Advances in water resources》1998,21(3):203-215
Transport of inert solutes in two-dimensional bounded heterogeneous porous media is investigated in a stochastic framework. After adopting a first-order approximation of the flow equations, analytical expressions are derived for the velocity covariances. Effects of the boundary conditions and aquifer size upon the statistical moments are analyzed. While the size of the domain is shown to have small influence on the covariances in most cases, the solutions are considerably modified by the boundaries. The results are compared with analytical solutions on infinite domains, and several discrepancies are demonstrated. For example, while the velocity variances on infinite domains are homogeneous, the present results are strongly non-stationary. Finally, the problem is solved numerically by the Monte Carlo simulation method. The results, including the behavior near the boundaries, are shown to be in close agreement with analytical solutions. 相似文献