Browsing by Author "Chang, Ching-Min"

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Heat transport in partially saturated heterogeneous aquifers
(2012-04-01)
Chang, Ching-Min
;
Yeh, Hund-Der
;
環境工程研究所
;
Institute of Environmental Engineering
This paper presents a stochastic analysis of the behaviour of heat transfer by soil moisture in a partially saturated heterogeneous aquifer. A spectral approach based on FourierStieltjes representations for the perturbed quantities is used to develop closed-form expressions that describe the field-scale heat advection and the variability of temperature profile. It is shown that the field-scale heat advection is related to the variability of the specific discharge, which, in turn, is related to the variation of hydraulic conductivity. Our analysis is, therefore, focused on the impact of the correlation scale of the log saturated hydraulic conductivity field on these analytical results. It is found that the correlation scale of log saturated hydraulic conductivity has an influence on enhancing the heat advection and the variability of the mean temperature field.
Induced Groundwater Flux by Increases in the Aquifer\'s Total Stress
(2015-01-01)
Chang, Ching-Min
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Yeh, Hund-Der
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環境工程研究所
;
Institute of Environmental Engineering
Fluid-filled granular soils experience changes in total stress because of earth and oceanic tides, earthquakes, erosion, sedimentation, and changes in atmospheric pressure. The pore volume may deform in response to the changes in stress and this may lead to changes in pore fluid pressure. The transient fluid flow can therefore be induced by the gradient in excess pressure in a fluid-saturated porous medium. This work demonstrates the use of stochastic methodology in prediction of induced one-dimensional field-scale groundwater flow through a heterogeneous aquifer. A closed-form of mean groundwater flux is developed to quantify the induced field-scale mean behavior of groundwater flow and analyze the impacts of the spatial correlation length scale of log hydraulic conductivity and the pore compressibility. The findings provided here could be useful for the rational planning and management of groundwater resources in aquifers that contain lenses with large vertical aquifer matrix compressibility values.
Investigation of flow and solute transport at the field scale through heterogeneous deformable porous media
(2016-09)
Chang, Ching-Min
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Yeh, Hund-Der
;
環境工程研究所
;
Institute of Environmental Engineering
This work describes an investigation of the spatial statistical structure of specific discharge field and solute transport process of a nonreactive solute at the field scale through a heterogeneous deformable porous medium. The flow field is driven by a vertical gradient in the excess pore water pressure induced by a step increase in load applied on the upper part of a finite-thickness aquifer. The non-stationary spectral representation is adopted to characterize the spatial covariance of the specific discharge field necessary for the development of the solute particle trajectory statistics using the Lagrangian formalism. We show that the statistics of the specific discharge and particle trajectory derived herein are non-stationary and functions of the coefficient of soil compressibility, mu, The effect of mu on the relative variation of specific discharge and the solute particle trajectory statistics are analyzed upon evaluating our expressions. (C) 2016 Elsevier B.V. All rights reserved.
Large-time behavior of macrodispersion in heterogeneous trending aquifers
(2007-11-03)
Chang, Ching-Min
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Yeh, Hund-Der
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環境工程研究所
;
Institute of Environmental Engineering
This paper presents a stochastic analysis of the large-time behavior of macrodispersion in a three-dimensional heterogeneous aquifer with a linear trend in the mean log hydraulic conductivity. To solve the problem analytically, focus is placed on the particular case where the linear trend is aligned in the direction of mean hydraulic head gradient. A spectral approach based on Fourier-Stieltjes representations for the perturbed quantities is used to develop closed-form expressions that describe variability of flow velocity, the second-order mean flow, and asymptotic macrodispersion. The impact of the mean log hydraulic conductivity gradient on these results is examined. It is found that the asymptotic longitudinal and transverse macrodispersion coefficients decrease with the increasing trend gradient of mean log hydraulic conductivity in the case of finite Peclet numbers. This feature is a consequence of the reduction in variability of flow velocity with the trend gradient.
Nonstationary stochastic analysis of flow in a heterogeneous unconfined aquifer subject to spatially-random periodic recharge
(2010-12-15)
Chang, Ching-Min
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Yeh, Hund-Der
;
環境工程研究所
;
Institute of Environmental Engineering
The problem of two-dimensional groundwater flow in a heterogeneous unconfined aquifer under periodic random forcing in time is analyzed from a stochastic point of view It is assumed that the periodic random forcing namely random recharge can be represented by a sinusoidal function in time Analytical solutions are developed through the nonstationary spectral approach in conjunction with the principle of superposition The results namely the variances of hydraulic head and specific discharge are expressed in terms of statistical properties of hydraulic parameters and recharge field It can be concluded from the analytical results that the mean recharge rate and integral scale of spatially random recharge fluctuations play essential roles in enhancing the variability of hydraulic head and specific discharges (c) 2010 Elsevier B V All rights reserved
Probability density functions of the stream flow discharge in linearized diffusion wave models
(2016-12)
Chang, Ching-Min
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Yeh, Hund-Der
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環境工程研究所
;
Institute of Environmental Engineering
This article considers stream flow discharge moving through channels subject to the lateral inflow and described by a linearized diffusion wave equation. The variability of lateral inflow is manifested by random fluctuations in time, which is the only source of uncertainty as to flow discharge quantification. The stochastic nature of stream flow discharge is described by the probability density function (PDF) obtained using the theory of distributions. The PDF of the stream flow discharge depends on the hydraulic properties of the stream flow, such as the wave celerity and hydraulic diffusivity as well as the temporal correlation scale of the lateral inflow rate fluctuations. The focus in this analysis is placed on the influence of the temporal correlation scale and the wave celerity coefficient on the PDF of the flow discharge. The analysis demonstrates that a larger temporal correlation scale causes an increase of PDF of the lateral inflow rate and, in turn, the PDF of the flow discharge which is also affected positively by the wave celerity coefficient. (C) 2016 Elsevier B.V. All rights reserved.
Quantification of Lagrangian travel time statistics under nonstationary random groundwater flow conditions
(2018-05-30)
Chang, Ching-Min
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Yeh, Hund-Der
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環境工程研究所
;
Institute of Environmental Engineering
This study presents a Lagrangian description of advection dominated field-scale transport of inert solutes, namely, the statistics of advective solute travel time and trajectory, in nonstationary random groundwater flow fields. The vertical flow field is generated by the effects of changes in total stress applied in fluid-saturated heterogeneous deformable porous media. The Lagrangian statistics are developed directly from the velocity statistics based on the application of stochastic methodology such as the representation theorem and Fourier-Stieltjes integral representation. The focus of our numerical evaluation is placed on the influence of the soil compressibility on the Lagrangian statistics. The prediction on the statistics of solute travel time and trajectory may serve as the basic input to the environmental risk assessment.
Spatial variability of the poroelastic response of the heterogeneous medium
(2010-08-01)
Chang, Ching-Min
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Yeh, Hund-Der
;
環境工程研究所
;
Institute of Environmental Engineering
In this work, a stochastic methodology is applied to analyze the variability of the poroelastic response of the heterogeneous medium at the field scale. To solve the problem analytically, we restrict our attention to the one-dimensional models, where fluid flow as well as deformation occurs in one direction only under a constant applied stress Assuming statistic homogeneity, the closed-form solutions that describe the variability of fluid pressure head, and a solid's strain and displacement are developed using a spectral approach based on Fourier-Stieltjes representations for the perturbed quantities The influence of the correlation length of the log hydraulic conductivity on these results is investigated. It is found that the variances of the solid's strain and displacement increase with the correlation length of the log hydraulic conductivity, while the correlation length of the log hydraulic conductivity plays the role in reducing the variability of the specific discharge. (C) 2010 Elsevier Ltd All rights reserved
Spectral analysis of temporal non-stationary rainfall-runoff processes
(2018-04-01)
Chang, Ching-Min
;
Yeh, Hund-Der
;
環境工程研究所
;
Institute of Environmental Engineering
This study treats the catchment as a block box system with considering the rainfall input and runoff output being a stochastic process. The temporal rainfall-runoff relationship at the catchment scale is described by a convolution integral on a continuous time scale. Using the Fourier-Stieltjes representation approach, a frequency domain solution to the convolution integral is developed to the spectral analysis of runoff processes generated by temporal non-stationary rainfall events. It is shown that the characteristic time scale of rainfall process increases the runoff discharge variability, while the catchment mean travel time constant plays the role in reducing the variability of runoff discharge. Similar to the behavior of groundwater aquifers, catchments act as a low-pass filter in the frequency domain for the rainfall input signal. (C) 2018 Elsevier B.V. All rights reserved.
Spectral analysis of temporal variability of nonlinear and nonstationary rainfall-runoff processes
(2019-08-01)
Chang, Ching-Min
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Yeh, Hund-Der
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Chuang, Mo-Hsiung
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環境工程研究所
;
Institute of Environmental Engineering
This study deals with the time-dependent nonlinear response of catchments to the variations in rainfall. Both the rainfall and runoff discharge fields are treated to be nonstationary in time. A functional series representation, a generalization of the linear convolution integral, is employed to quantify the nonlinear relation between the input and output. The Fourier-Stieltjes representation approach is used to evaluate the variance of runoff discharge in the spectral frequency domain. The analysis based on the spectral solution for the runoff discharge variance clearly demonstrates that larger values of rainfall characteristic time scale or catchment size parameter lead to larger variability of the runoff discharge, while a larger catchment scale parameter leads to smaller variability of the runoff discharge.
Stochastic analysis of bounded unsaturated flow in heterogeneous aquifers: Spectral/perturbation approach
(2009-01-01)
Chang, Ching-Min
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Yeh, Hund-Der
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環境工程研究所
;
Institute of Environmental Engineering
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):541-511, 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]. (C) 2008 Elsevier Ltd. All rights reserved.
Stochastic analysis of stream-groundwater interaction subject to temporally correlated recharge
(2013-01-07)
Chang, Ching-Min
;
Yeh, Hund-Der
;
環境工程研究所
;
Institute of Environmental Engineering
In this article, the coupled equations describing the transient groundwater flow and stream flow fluctuations are solved based on the Fourier-Stieltjes integral representation, where the lateral inflow term in the stream flow perturbation equation connects the process of groundwater flow to that of stream flow. The closed-form solutions describing the variability in groundwater flow specific discharge and stream flow discharge are developed to quantify the influence of the variability in temporally correlated recharge in an unconfined aquifer on the stream flow discharge. We found from the closed-form solutions that the temporal correlation scale and the variance of recharge fields influence the variability in groundwater flow specific discharge and the stream flow discharge positively. In addition, the hydraulic diffusivity coefficient takes the role of reducing the variability in stream flow discharge. (C) 2012 Elsevier B.V. All rights reserved.
Stochastic Analysis of Unsaturated Flow Subject to Temporally Correlated Infiltration
(2014-09-01)
Chang, Ching-Min
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Yeh, Hund-Der
;
環境工程研究所
;
Institute of Environmental Engineering
In this article, we attempt to quantify the variability of water pressure head in response to temporally correlated fluctuations in infiltration rate in partially saturated heterogeneous formations. This study concentrates on the unsaturated case of predominantly vertical movement of moisture. A closed-form solution is developed to analyze the impacts of the temporal correlation scale of infiltration fluctuations and the spatial correlation scale of log-saturated hydraulic conductivity () field on the variability in water pressure head. Our result indicates that the temporal correlation scale of infiltration process or the spatial correlation scale of field takes a role in increasing the variability in the pressure head.
Stochastic modeling of variations in stream flow discharge induced by random spatiotemporal fluctuations in lateral inflow rate
(2016-08)
Chang, Ching-Min
;
Yeh, Hund-Der
;
環境工程研究所
;
Institute of Environmental Engineering
Due to natural heterogeneity in runoff processes, the analysis of response of stream channels to the variation of lateral inflow is therefore viewed in terms of stochastic spatiotemporal processes. Based on the representation theorem, a closed-form expression is derived to describe the spectral response characteristic of stream subject to spatiotemporal fluctuations in lateral inflow. It provides a basis for evaluating the induced discharge variability in stream channels. It is found that the evolutionary power spectrum of the stream flow discharge process and therefore the variance is increased with the distance from the upstream boundary and the characteristic length scale of the lateral inflow process. Flow discharge prediction in the downstream region has a high degree of uncertainty by solving the deterministic partial differential equation.
Temporal Variability in the Response of a Linear Time-Invariant Catchment System to a Non-Stationary Inflow Concentration Field
(2020-08-01)
Chang, Ching-Min
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Ma, Kuo-Chen
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Chuang, Mo-Hsiung
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環境工程研究所
;
Institute of Environmental Engineering
Predicting the effects of changes in dissolved input concentration on the variability of discharge concentration at the outlet of the catchment is essential to improve our ability to address the problem of surface water quality. The goal of this study is therefore dedicated to the stochastic quantification of temporal variability of concentration fields in outflow from a catchment system that exhibits linearity and time invariance. A convolution integral is used to determine the output of a linear time-invariant system from knowledge of the input and the transfer function. This work considers that the nonstationary input concentration time series of an inert solute to the catchment system can be characterized completely by the Langevin equation. The closed-form expressions for the variances of inflow and outflow concentrations at the catchment scale are derived using the Fourier-Stieltjes representation approach. The variance is viewed as an index of temporal variability. The closed-form expressions therefore allow to evaluate the impacts of the controlling parameters on the temporal variability of outflow concentration.
Two-dimensional stochastic analysis of flow in leaky confined aquifers subject to spatial and periodic leakage
(2009-11-01)
Yeh, Hund-Der
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Chang, Ching-Min
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環境工程研究所
;
Institute of Environmental Engineering
This paper addresses the issue of flow in heterogeneous leaky confined aquifers subject to leakage. The leakage into the confined aquifer is driven by spatial and periodic fluctuations of water table in an overlying phreatic aquifer. The introduction of leakage leads to non-uniformity in the mean head gradient and results in nonstationarity in hydraulic head and velocity fields. Therefore, a nonstationary spectral approach based on Fourier-Stieltjes representations for the perturbed quantities is adopted to account for the spatial variability of nonstationary head fields. Closed-form expressions for the variances of hydraulic head and specific discharge are developed in terms of statistical properties of hydraulic parameters. The results indicate that the spatiotemporal variations in leakage leads to enhanced variability of the hydraulic head and of the specific discharge, which increase with distance from any arbitrary reference point. The coefficient of leakage and the spatial structure of log transmissivity field and of the amplitude of water table fluctuation are critical in quantifying the variability of the hydraulic head and of the specific discharge. (C) 2009 Elsevier Ltd. All rights reserved.
Uncertainty Estimation in One-Dimensional Heat Transport Model for Heterogeneous Porous Medium
(2014-05-01)
Chang, Ching-Min
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Yeh, Hund-Der
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環境工程研究所
;
Institute of Environmental Engineering
In many practical applications, the rates for ground water recharge and discharge are determined based on the analytical solution developed by Bredehoeft and Papadopulos (1965) to the one-dimensional steady-state heat transport equation. Groundwater flow processes are affected by the heterogeneity of subsurface systems; yet, the details of which cannot be anticipated precisely. There exists a great deal of uncertainty (variability) associated with the application of Bredehoeft and Papadopulos\' solution (1965) to the field-scale heat transport problems. However, the quantification of uncertainty involved in such application has so far not been addressed, which is the objective of this wok. In addition, the influence of the statistical properties of log hydraulic conductivity field on the variability in temperature field in a heterogeneous aquifer is also investigated. The results of the analysis demonstrate that the variability (or uncertainty) in the temperature field increases with the correlation scale of the log hydraulic conductivity covariance function and the variability of temperature field also depends positively on the position.
Uncertainty in applying the linear poroelasticity model to field situations as a result of periodic loading in heterogeneous aquifers
(2015-05-15)
Chang, Ching-Min
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Yeh, Hund-Der
;
環境工程研究所
;
Institute of Environmental Engineering
The solid Earth\'s surface frequently experience changes in total stresses as a result of periodic loading. When the fluid-saturated porous media deform in response to changes in stress, the induced variations in pore volume affect the pore water pressure. The fluid flow therefore occurs in response to the gradient in the induced excess pore water pressure. This work aims at quantifying the spatial variability in excess pressure head produced by the periodic loading accounting for the variation of log hydraulic conductivity (lnK). It is important for the rational management of groundwater resources. A closed-form expression is developed by the nonstationary spectral approach to analyse the influence of the statistical properties of lnK process, the hydraulic parameters, and the spatial position. The general stochastic framework outlined in this work provides a basis for assessing the impact of statistical properties of input aquifer parameters on the output variability (or uncertainty). Copyright (c) 2014 John Wiley & Sons, Ltd.
Uncertainty in applying the temperature time-series method to the field under heterogeneous flow conditions
(2014-11-27)
Chang, Ching-Min
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Yeh, Hund-Der
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環境工程研究所
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Institute of Environmental Engineering
Due to the irregular distributions of aquifer hydraulic properties, the detail on the characterization of flow field cannot be anticipated. There can be a great degree of uncertainty in the prediction of heat transport processes anticipated in applying the traditional deterministic transport equation to field situations. This article is therefore devoted to quantification of uncertainty involving predictions over larger scales in terms of the temperature variance. A stochastic frame of reference is adopted to account for the spatial variability in hydraulic conductivity and specific discharge. Within this framework, the use of the first-order perturbation approximation and spectral representation leads to stochastic differential equations governing the mean behavior and perturbation of the temperature field in heterogeneous aquifers. It turns out that the mean equation developed in this sense is equivalent to the traditional deterministic transport equation and the temperature variance gives a measure of the prediction uncertainty from the traditional transport equation. The closed-form expression for the temperature variance developed here indicates that the controlling parameters such as the correlation scale of specific discharge, which measures the spatial persistence of the flow field, and the periodicity of the source term tend to increase the variability in temperature field in heterogeneous aquifers. The uncertainty of the traditional heat transport model increases as the penetration depth of thermal front through the aquifer increases. This suggests that prediction of temperature distribution using the traditional heat transport model in heterogeneous aquifers is expected to be subject to large uncertainty at a large depth (in the downstream region). For the management purpose, the variance of temperature could serve as a calibration target when applying the traditional model to field situations. It may be more reasonable to make conclusions from, say, the mean temperature with one or two standard deviations rather than only the mean temperature drawn from the traditional heat transport equation. (C) 2014 Elsevier B.V. All rights reserved.
Uncertainty in the Volume Strain Field of the Solid in Unsaturated Heterogeneous Deforming Media
(2011-11-01)
Chang, Ching-Min
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Yeh, Hund-Der
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環境工程研究所
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Institute of Environmental Engineering
In a partially saturated, heterogeneous deforming aquifer, we analyzed the solid's volume strain field within a stochastic framework. The differential equations describing the first two moments of the solid's volume strain field were developed through the perturbation approach. To solve the problem analytically, focus was placed on the one-dimensional model. The resulting closed-form solutions (namely, the first two moments of the solid's volume strain field) were obtained using the nonstationary spectral approach in conjunction with the principle of superposition. They are functions of the statistical properties of the logarithm of the saturated hydraulic conductivity and a soil pore size distribution parameter. It can be concluded from the analytical solutions that the correlation length of the logarithm of the hydraulic conductivity is important in increasing the variability of the solid's volume strain field, while the soil pore size distribution parameter plays the role of decreasing the variability in the solid's volume strain field.