Inverse Problems In Groundwater Modeling

... A diskette with the updated programme of Appendix C and examples is available through the author at a small fee. email: [email protected] fax: 1--310--825--5435 ... This book systematically discusses basic concepts, theory, solution methods and applications of inverse problems in groundwater modeling. It is the first book devoted to this subject. The inverse problem is defined and solved in both deterministic and statistic frameworks. Various direct and indirect methods are discussed and compared. As a useful tool, the adjoint state method and its applications are given in detail. For a stochastic field, the maximum likelihood estimation and co-kriging techniques are used to estimate unknown parameters. The ill-posed problem of inverse solution is highlighted through the whole book. The importance of data collection strategy is specially emphasized. Besides the classical design criteria, the relationships between decision making, prediction, parameter identification and experimental design are considered from the point of view of extended identifiabilities. The problem of model structure identification is also considered. This book can be used as a textbook for graduate students majoring in hydrogeology or related subjects. It is also a reference book for hydrogeologists, petroleum engineers, environmental engineers, mining engineers and applied mathematicians.

​This book describes a novel physics-based approach to inverse modeling that makes use of the properties of the equations governing the physics of the processes under consideration. It focuses on the inverse problems occurring in hydrogeology, but the approach is also applicable to similar inverse problems in various other fields, such as petroleum-reservoir engineering, geophysical and medical imaging, weather forecasting, and flood prediction. This approach takes into consideration the physics – for instance, the boundary conditions required to obtain a well-posed mathematical problem – to help avoid errors in model building and therefore enhance the reliability of the results. In addition, this method requires less computation time and less computer memory. The theory is presented in a comprehensive, not overly mathematical, way, with three practice-oriented hydrogeological case studies and a comparison with the conventional approach illustrating the power of the method. Forward and Inverse Modeling of Groundwater Flow is of use to researchers and graduate students in the fields of hydrology, as well as to professional hydrologists within industry. It also appeals to geophysicists and those working in or studying petroleum reservoir modeling and basin modeling.

The Workshop on Parameter Identification and Inverse Problems in Hydrology, Geology and Ecology, Karlsruhe, April 10-12, 1995, was organized to bring to gether an interdisciplinary group drawn from the areas of science, engineering and mathematics for the following purposes: - to promote, encourage and influence more understanding and cooperation in the community of parameter identifiers from various disciplines, - to forge unity in diversity by bringing together a variety of disciplines that attempt to understand the reconstruction of inner model parameters, un known nonlinear constitutive relations, heterogeneous structures inside of geological objects, sources or sinks from observational data, - to discuss modern regularization tools for handling improperly posed pro blems and strategies of incorporating a priori knowledge from the applied problem into the model and its treatment. These proceedings contain some of the results of the workshop, representing a bal anced selection of contributions from the various groups of participants. The reviewed invited and contributed articles are grouped according to the broad headings of hydrology, non-linear diffusion and soil physics, geophysical methods, mathematical analysis of inverse and ill-posed problems and parallel algorithms for inverse problems. Some of the issues adressed by the articles in these proceedings include the rela tion between least squares and direct formulations of inverse problems for partial differential equations, nonlinear regularization, identification of nonlinear consti tutive relations, fast parallel algorithms for large scale inverse problems, reduction of model structures, geostatistical inversion techniques.

This second edition is extensively revised throughout with expanded discussion of modeling fundamentals and coverage of advances in model calibration and uncertainty analysis that are revolutionizing the science of groundwater modeling. The text is intended for undergraduate and graduate level courses in applied groundwater modeling and as a comprehensive reference for environmental consultants and scientists/engineers in industry and governmental agencies. Explains how to formulate a conceptual model of a groundwater system and translate it into a numerical model Demonstrates how modeling concepts, including boundary conditions, are implemented in two groundwater flow codes-- MODFLOW (for finite differences) and FEFLOW (for finite elements) Discusses particle tracking methods and codes for flowpath analysis and advective transport of contaminants Summarizes parameter estimation and uncertainty analysis approaches using the code PEST to illustrate how concepts are implemented Discusses modeling ethics and preparation of the modeling report Includes Boxes that amplify and supplement topics covered in the text Each chapter presents lists of common modeling errors and problem sets that illustrate concepts

Groundwater is one of the most important resources in the world. In many areas, water supplies for industrial, domestic, and agricultural uses are de pendent on groundwater. As an "open" system, groundwater may exchange mass and energy with its neighboring systems (soil, air, and surface water) through adsorption, ion-exchange, infiltration, evaporation, inflow, outflow, and other exchange forms. Consequently, both the quantity and quality of groundwater may vary with environmental changes and human activities. Due to population growth, and industrial and agricultural development, more and more groundwater is extracted, especially in arid areas. If the groundwater management problem is not seriously considered, over extraction may lead to groundwater mining, salt water intrusion, and land subsidence. In fact, the quality of groundwater is gradually deteriorating throughout the world. The problem of groundwater pollution has appeared, not only in developed countries, but also in developing countries. Ground water pollution is a serious environmental problem that may damage human health, destroy the ecosystem, and cause water shortage.

This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods. Key Features: Brings together the perspectives of researchers in areas of inverse problems and data assimilation. Assesses the current state-of-the-art and identify needs and opportunities for future research. Focuses on the computational methods used to analyze and simulate inverse problems. Written by leading experts of inverse problems and uncertainty quantification. Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.

Methods and guidelines for developing and using mathematical models Turn to Effective Groundwater Model Calibration for a set of methods and guidelines that can help produce more accurate and transparent mathematical models. The models can represent groundwater flow and transport and other natural and engineered systems. Use this book and its extensive exercises to learn methods to fully exploit the data on hand, maximize the model's potential, and troubleshoot any problems that arise. Use the methods to perform: Sensitivity analysis to evaluate the information content of data Data assessment to identify (a) existing measurements that dominate model development and predictions and (b) potential measurements likely to improve the reliability of predictions Calibration to develop models that are consistent with the data in an optimal manner Uncertainty evaluation to quantify and communicate errors in simulated results that are often used to make important societal decisions Most of the methods are based on linear and nonlinear regression theory. Fourteen guidelines show the reader how to use the methods advantageously in practical situations. Exercises focus on a groundwater flow system and management problem, enabling readers to apply all the methods presented in the text. The exercises can be completed using the material provided in the book, or as hands-on computer exercises using instructions and files available on the text's accompanying Web site. Throughout the book, the authors stress the need for valid statistical concepts and easily understood presentation methods required to achieve well-tested, transparent models. Most of the examples and all of the exercises focus on simulating groundwater systems; other examples come from surface-water hydrology and geophysics. The methods and guidelines in the text are broadly applicable and can be used by students, researchers, and engineers to simulate many kinds systems.