The Experts below are selected from a list of 5118 Experts worldwide ranked by ideXlab platform
Ibrahim Hoteit - One of the best experts on this subject based on the ideXlab platform.
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a bayesian consistent dual ensemble kalman filter for state parameter estimation in Subsurface Hydrology
Hydrology and Earth System Sciences, 2016Co-Authors: Boujemaa Aitelfquih, Mohamad El Gharamti, Ibrahim HoteitAbstract:Abstract. Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in Subsurface groundwater models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model's state and parameters. These are generally estimated following joint and dual filtering strategies, in which, at each assimilation cycle, a forecast step by the model is followed by an update step with incoming observations. The joint EnKF directly updates the augmented state-parameter vector, whereas the dual EnKF empirically employs two separate filters, first estimating the parameters and then estimating the state based on the updated parameters. To develop a Bayesian consistent dual approach and improve the state-parameter estimates and their consistency, we propose in this paper a one-step-ahead (OSA) smoothing formulation of the state-parameter Bayesian filtering problem from which we derive a new dual-type EnKF, the dual EnKFOSA. Compared with the standard dual EnKF, it imposes a new update step to the state, which is shown to enhance the performance of the dual approach with almost no increase in the computational cost. Numerical experiments are conducted with a two-dimensional (2-D) synthetic groundwater aquifer model to investigate the performance and robustness of the proposed dual EnKFOSA, and to evaluate its results against those of the joint and dual EnKFs. The proposed scheme is able to successfully recover both the hydraulic head and the aquifer conductivity, providing further reliable estimates of their uncertainties. Furthermore, it is found to be more robust to different assimilation settings, such as the spatial and temporal distribution of the observations, and the level of noise in the data. Based on our experimental setups, it yields up to 25 % more accurate state and parameter estimations than the joint and dual approaches.
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a bayesian consistent dual ensemble kalman filter for state parameter estimation in Subsurface Hydrology
arXiv: Data Analysis Statistics and Probability, 2015Co-Authors: Boujemaa Aitelfquih, Mohamad El Gharamti, Ibrahim HoteitAbstract:Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in Subsurface groundwater models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model's state and parameters. These are generally estimated following joint and dual filtering strategies, in which, at each assimilation cycle, a forecast step by the model is followed by an update step with incoming observations. The Joint-EnKF directly updates the augmented state-parameter vector while the Dual-EnKF employs two separate filters, first estimating the parameters and then estimating the state based on the updated parameters. In this paper, we reverse the order of the forecast-update steps following the one-step-ahead (OSA) smoothing formulation of the Bayesian filtering problem, based on which we propose a new dual EnKF scheme, the Dual-EnKF$_{\rm OSA}$. Compared to the Dual-EnKF, this introduces a new update step to the state in a fully consistent Bayesian framework, which is shown to enhance the performance of the dual filtering approach without any significant increase in the computational cost. Numerical experiments are conducted with a two-dimensional synthetic groundwater aquifer model to assess the performance and robustness of the proposed Dual-EnKF$_{\rm OSA}$, and to evaluate its results against those of the Joint- and Dual-EnKFs. The proposed scheme is able to successfully recover both the hydraulic head and the aquifer conductivity, further providing reliable estimates of their uncertainties. Compared with the standard Joint- and Dual-EnKFs, the proposed scheme is found more robust to different assimilation settings, such as the spatial and temporal distribution of the observations, and the level of noise in the data. Based on our experimental setups, it yields up to 25% more accurate state and parameters estimates.
Fred J Molz - One of the best experts on this subject based on the ideXlab platform.
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Do Heterogeneous Sediment Properties and Turbulent Velocity Fluctuations have Something in Common? Some History and a New Stochastic Process
2015Co-Authors: Anderson South Carolina, Fred J Molz, Mark M. Meerschaert, Tom J. Kozubowski, Paul D. HydenAbstract:It is increasingly apparent that sediment property distributions on sufficiently small scales are probably irregular. This has led to the development of stochastic theory in Subsurface Hydrology, including statistically heterogeneous concepts based mainly on the Gaussian and Lévy-stable probability density functions (PDFs), the mathematical basis for stochastic fractals. Gaussian and Levy-stable stochastic fractals have been applied both in the field of turbulence and Subsurface Hydrology. However, measurements have shown that the increment frequency dis-tributions do not always follow Gaussian or Lévy-stable PDFs. Provided herein is an overview of the origin and development of a new non-stationary stochastic process, called fractional Laplace motion (flam) with stationary, correlated, incre-ments called fractional Laplace noise (fLan). It is based on the Laplace PDF and known generalizations, and does not display self-similarity. Uncorrelated versions are equivalent to a Brownian motion subordinated to the gamma process. In anal-ogy to the development of fractional Brownian motion (fBm) from Brownian motion, fLam is equivalent to fBm subordinated to a gamma process. The ne
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a new type of stochastic fractal for application in Subsurface Hydrology
Geoderma, 2006Co-Authors: Fred J Molz, Paul HydenAbstract:Abstract Data suggest that many property distributions [P(x); p = property, x = length] are irregular [dP / dx discontinuous], exhibiting variations on all measurement scales. Logic then leads one to attempt to characterize these distributions through study of their increments or fluctuations [P(x + L) − P(x)], which results naturally in a statistical approach. Increment frequency distributions for a fixed L that fit the Levy/Gaussian family of probability density functions [PDFs] independent of position [statistically stationary in a spatial sense] have well-defined scaling properties characteristic of what are called self-affine stochastic fractals. Data show that measurements in natural systems display some of the scaling characteristics of this PDF family, but do not agree with theory in many important aspects. For example, increment ln(K) distributions show a consistently non-Gaussian shape for smaller values of L and become more Gaussian as L gets large. Particularly for smaller L, PDF tails display an approximate exponential decay and maintain a finite variance. In many cases they appear to be displaying a continuous change from exponential, or even sub-exponential, to Gaussian behavior with increasing L. Data supporting these observations are presented along with explanations of how the fractal-based concepts arise, both physically and mathematically. This is followed by the presentation and initial analysis of what appears to be a new type of stochastic fractal called fractional Laplace motion that displays more of the features observed in natural sedimentary systems.
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stochastic fractal based models of heterogeneity in Subsurface Hydrology origins applications limitations and future research questions
Reviews of Geophysics, 2004Co-Authors: Fred J Molz, Harihar RajaramAbstract:[1] Modern measurement techniques have shown that property distributions in natural porous and fractured media appear highly irregular and nonstationary in a spatial statistical sense. This implies that direct statistical analyses of the property distributions are not appropriate, because the statistical measures developed will be dependent on position and therefore will be nonunique. An alternative, which has been explored to an increasing degree during the past 20 years, is to consider the class of functions known as nonstationary stochastic processes with spatially stationary increments. When such increment distributions are described by probability density functions (PDFs) of the Gaussian, Levy, or gamma class or PDFs that converge to one of these classes under additions, then one is also dealing with a so-called stochastic fractal, the mathematical theory of which was developed during the first half of the last century. The scaling property associated with such fractals is called self-affinity, which is more general that geometric self-similarity. Herein we review the application of Gaussian and Levy stochastic fractals and multifractals in Subsurface Hydrology, mainly to porosity, hydraulic conductivity, and fracture roughness, along with the characteristics of flow and transport in such fields. Included are the development and application of fractal and multifractal concepts; a review of the measurement techniques, such as the borehole flowmeter and gas minipermeameter, that are motivating the use of fractal-based theories; the idea of a spatial weighting function associated with a measuring instrument; how fractal fields are generated; and descriptions of the topography and aperture distributions of self-affine fractures. In a somewhat different vein the last part of the review deals with fractal- and fragmentation-based descriptions of fracture networks and the implications for transport in such networks. Broad conclusions include the implication that models based on increment distributions, while more realistic, are inherently less predictive than models based directly on stationary stochastic processes; that there is presently an unresolved ambiguity when a measurement is attempted in a medium that exhibits property variations on all scales; the strong possibility that log(property) increment distributions that appear to be described by the Levy PDF are actually superpositions of several PDFs of finite variance, one for each facies; that there are apparent similarities in the transport behavior of heterogeneous porous media and fractured rock at the field scale that appear to be related to the existence of a few preferential flow paths in both types of media; and finally, that additional carefully collected data sets are needed to clarify and advance the fractal-based theories, particularly in the case of three-dimensional fracture networks where few data are available. Further refinement is needed also in the understanding of instrument spatial weighting functions in heterogeneous media and how measurements in media exhibiting variations on all scales should be interpreted.
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fractional brownian motion and fractional gaussian noise in Subsurface Hydrology a review presentation of fundamental properties and extensions
Water Resources Research, 1997Co-Authors: Fred J Molz, Huihai Liu, J SzulgaAbstract:Recent studies have shown that fractional Brownian motion (fBm) and fractional Gaussian noise (fGn) are useful in characterizing Subsurface heterogeneities in addition to geophysical time series. Although these studies have led to a fairly good understanding of some aspects of fBm/fGn, a comprehensive introduction to these stochastic, fractal functions is still lacking in the Subsurface Hydrology literature. In this paper, efforts have been made to define fBm/fGn and present a development of their mathematical properties in a direct yet rigorous manner. Use of the spectral representation theorem allows one to derive spectral representations for fBm/fGn even though these functions do not have classical Fourier transforms. The discrete and truncated forms of these representations have served as a basis for synthetic generation of fBm/fGn. The discrete spectral representations are developed and various implications discussed. In particular, it is shown that a discrete form of the fBm spectral representation is equivalent to the well known Weierstrass-Mandelbrot random fractal function. Although the full implications are beyond the scope of the present paper, it is observed that discrete spectral representations of fBm constitute stationary processes even though fBm is nonstationary. A new and general spectral density function is introduced for construction of complicated, anisotropic, (3-D) fractals, including those characterized by vertical fGn and horizontal fBm. Such fractals are useful for modeling anisotropic Subsurface heterogeneities but cannot be generated with existing schemes. Finally, some basic properties of fractional Levy motion and concepts of universal multifractals, which can be considered as generalizations of fBm/fGn, are reviewed briefly.
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a fractal based stochastic interpolation scheme in Subsurface Hydrology
Water Resources Research, 1993Co-Authors: Fred J Molz, Gerald K BomanAbstract:Real porosity and hydraulic conductivity data do not vary smoothly over space, so an interpolation scheme that preserves irregularity is desirable. Such a scheme based on the properties of fractional Brownian motion (fBm) and fractional Gaussian noise (fGn) is presented. Following the methodology of Hewett (1986), the authors test for the presence of fGn in a set of 459 hydraulic conductivity (K) measurements. The use of rescaled-range analysis strongly indicated the presence of fGn when applied to the natural logs of the K data, and the resulting Hurst coefficient (H) was determined to be 0.82. This H value was then used along with the methodology for successive random additions to generate a fBm K interpolation (realization) in the vertical cross section between two wells. The results appeared realistic, and the overall methodology presented herein may serve as an improved basis for a conditional simulation approach to the study of various transport processes in porous media. (Copyright (c) 1993 American Geophysical Union.)
Mohamad El Gharamti - One of the best experts on this subject based on the ideXlab platform.
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a bayesian consistent dual ensemble kalman filter for state parameter estimation in Subsurface Hydrology
Hydrology and Earth System Sciences, 2016Co-Authors: Boujemaa Aitelfquih, Mohamad El Gharamti, Ibrahim HoteitAbstract:Abstract. Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in Subsurface groundwater models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model's state and parameters. These are generally estimated following joint and dual filtering strategies, in which, at each assimilation cycle, a forecast step by the model is followed by an update step with incoming observations. The joint EnKF directly updates the augmented state-parameter vector, whereas the dual EnKF empirically employs two separate filters, first estimating the parameters and then estimating the state based on the updated parameters. To develop a Bayesian consistent dual approach and improve the state-parameter estimates and their consistency, we propose in this paper a one-step-ahead (OSA) smoothing formulation of the state-parameter Bayesian filtering problem from which we derive a new dual-type EnKF, the dual EnKFOSA. Compared with the standard dual EnKF, it imposes a new update step to the state, which is shown to enhance the performance of the dual approach with almost no increase in the computational cost. Numerical experiments are conducted with a two-dimensional (2-D) synthetic groundwater aquifer model to investigate the performance and robustness of the proposed dual EnKFOSA, and to evaluate its results against those of the joint and dual EnKFs. The proposed scheme is able to successfully recover both the hydraulic head and the aquifer conductivity, providing further reliable estimates of their uncertainties. Furthermore, it is found to be more robust to different assimilation settings, such as the spatial and temporal distribution of the observations, and the level of noise in the data. Based on our experimental setups, it yields up to 25 % more accurate state and parameter estimations than the joint and dual approaches.
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a bayesian consistent dual ensemble kalman filter for state parameter estimation in Subsurface Hydrology
arXiv: Data Analysis Statistics and Probability, 2015Co-Authors: Boujemaa Aitelfquih, Mohamad El Gharamti, Ibrahim HoteitAbstract:Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in Subsurface groundwater models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model's state and parameters. These are generally estimated following joint and dual filtering strategies, in which, at each assimilation cycle, a forecast step by the model is followed by an update step with incoming observations. The Joint-EnKF directly updates the augmented state-parameter vector while the Dual-EnKF employs two separate filters, first estimating the parameters and then estimating the state based on the updated parameters. In this paper, we reverse the order of the forecast-update steps following the one-step-ahead (OSA) smoothing formulation of the Bayesian filtering problem, based on which we propose a new dual EnKF scheme, the Dual-EnKF$_{\rm OSA}$. Compared to the Dual-EnKF, this introduces a new update step to the state in a fully consistent Bayesian framework, which is shown to enhance the performance of the dual filtering approach without any significant increase in the computational cost. Numerical experiments are conducted with a two-dimensional synthetic groundwater aquifer model to assess the performance and robustness of the proposed Dual-EnKF$_{\rm OSA}$, and to evaluate its results against those of the Joint- and Dual-EnKFs. The proposed scheme is able to successfully recover both the hydraulic head and the aquifer conductivity, further providing reliable estimates of their uncertainties. Compared with the standard Joint- and Dual-EnKFs, the proposed scheme is found more robust to different assimilation settings, such as the spatial and temporal distribution of the observations, and the level of noise in the data. Based on our experimental setups, it yields up to 25% more accurate state and parameters estimates.
Harihar Rajaram - One of the best experts on this subject based on the ideXlab platform.
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debates stochastic Subsurface Hydrology from theory to practice introduction
Water Resources Research, 2016Co-Authors: Harihar RajaramAbstract:This paper introduces the papers in the “Debates—Stochastic Subsurface Hydrology from Theory to Practice” series. Beginning in the 1970s, the field of stochastic Subsurface Hydrology has been an active field of research, with over 3500 journal publications, of which over 850 have appeared in Water Resources Research. We are fortunate to have insightful contributions from four groups of distinguished authors who discuss the reasons why the advanced research framework established in stochastic Subsurface Hydrology has not impacted the practice of groundwater flow and transport modeling and design significantly. There is reasonable consensus that a community effort aimed at developing “toolboxes” for applications of stochastic methods will make them more accessible and encourage practical applications.
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stochastic fractal based models of heterogeneity in Subsurface Hydrology origins applications limitations and future research questions
Reviews of Geophysics, 2004Co-Authors: Fred J Molz, Harihar RajaramAbstract:[1] Modern measurement techniques have shown that property distributions in natural porous and fractured media appear highly irregular and nonstationary in a spatial statistical sense. This implies that direct statistical analyses of the property distributions are not appropriate, because the statistical measures developed will be dependent on position and therefore will be nonunique. An alternative, which has been explored to an increasing degree during the past 20 years, is to consider the class of functions known as nonstationary stochastic processes with spatially stationary increments. When such increment distributions are described by probability density functions (PDFs) of the Gaussian, Levy, or gamma class or PDFs that converge to one of these classes under additions, then one is also dealing with a so-called stochastic fractal, the mathematical theory of which was developed during the first half of the last century. The scaling property associated with such fractals is called self-affinity, which is more general that geometric self-similarity. Herein we review the application of Gaussian and Levy stochastic fractals and multifractals in Subsurface Hydrology, mainly to porosity, hydraulic conductivity, and fracture roughness, along with the characteristics of flow and transport in such fields. Included are the development and application of fractal and multifractal concepts; a review of the measurement techniques, such as the borehole flowmeter and gas minipermeameter, that are motivating the use of fractal-based theories; the idea of a spatial weighting function associated with a measuring instrument; how fractal fields are generated; and descriptions of the topography and aperture distributions of self-affine fractures. In a somewhat different vein the last part of the review deals with fractal- and fragmentation-based descriptions of fracture networks and the implications for transport in such networks. Broad conclusions include the implication that models based on increment distributions, while more realistic, are inherently less predictive than models based directly on stationary stochastic processes; that there is presently an unresolved ambiguity when a measurement is attempted in a medium that exhibits property variations on all scales; the strong possibility that log(property) increment distributions that appear to be described by the Levy PDF are actually superpositions of several PDFs of finite variance, one for each facies; that there are apparent similarities in the transport behavior of heterogeneous porous media and fractured rock at the field scale that appear to be related to the existence of a few preferential flow paths in both types of media; and finally, that additional carefully collected data sets are needed to clarify and advance the fractal-based theories, particularly in the case of three-dimensional fracture networks where few data are available. Further refinement is needed also in the understanding of instrument spatial weighting functions in heterogeneous media and how measurements in media exhibiting variations on all scales should be interpreted.
Cass T Miller - One of the best experts on this subject based on the ideXlab platform.
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optimal design for problems involving flow and transport phenomena in saturated Subsurface systems
Advances in Water Resources, 2002Co-Authors: Alex S Mayer, C T Kelley, Cass T MillerAbstract:Estimation problems arise routinely in Subsurface Hydrology for applications that range from water resources management to water quality protection to Subsurface restoration. Interest in optimal design of such systems has increased over the last two decades and this area is considered an important and active area of research. In this work, we review the state of the art, assess important challenges that must be resolved to reach a mature level of understanding, and summarize some promising approaches that might help meet some of the challenges. While much has been accomplished to date, we conclude that more work remains before comprehensive, efficient, and robust solution methods exist to solve the most challenging applications in Subsurface science. We suggest that future directions of research include the application of direct search solution methods, and developments in stochastic and multi-objective optimization. We present a set of comprehensive test problems for use in the research community as a means for benchmarking and comparing optimization approaches.
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optimal design for problems involving flow and transport phenomena in saturated Subsurface systems
Advances in Water Resources, 2002Co-Authors: Alex S Mayer, C T Kelley, Cass T MillerAbstract:Estimation problems arise routinely in Subsurface Hydrology for applications that range from water resources management to water quality protection to Subsurface restoration. Interest in optimal design of such systems has increased over the last two decades and this area is considered an important and active area of research. In this work, we review the state of the art, assess important challenges that must be resolved to reach a mature level of understanding, and summarize some promising approaches that might help meet some of the challenges. While much has been accomplished to date, we conclude that more work remains before comprehensive, efficient, and robust solution methods exist to solve the most challenging applications in Subsurface science. We suggest that future directions of research include the application of direct search solution methods, and developments in stochastic and multi-objective optimization. We present a set of comprehensive test problems for use in the research community as a means for benchmarking and comparing optimization approaches.
