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Numerical models of flow and transport processes are heavily employed in the fields of surface, soil, and groundwater hydrology. They are used to interpret field observations, analyze complex and coupled processes, or to support decision making related to large societal issues such as the water-energy nexus or sustainable water management and food production. Parameter estimation and uncertainty quantification are two key features of modern science-based predictions. When applied to water resources, these tasks must cope with many degrees of freedom and large datasets. Both are challenging and require novel theoretical and computational approaches to handle complex models with large number of unknown parameters.
This three-part book provides a comprehensive and systematic introduction to these challenging topics such as model calibration, parameter estimation, reliability assessment, and data collection design. Part 1 covers the classical inverse problem for parameter estimation in both deterministic and statistical frameworks, Part 2 is dedicated to system identification, hyperparameter estimation, and model dimension reduction, and Part 3 considers how to collect data and construct reliable models for prediction and decision-making. For the first time, topics such as multiscale inversion, stochastic field parameterization, level set method, machine learning, global sensitivity analysis, data assimilation, model uncertainty quantification, robust design, and goal-oriented modeling, are systematically described and summarized in a single book from the perspective of model inversion, and elucidated with numerical examples from environmental and water resources modeling. Readers of this book will not only learn basic concepts and methods for simple parameter estimation, but also get familiar with advanced methods for modeling complex systems. Algorithms for mathematical tools used in this book, such as numerical optimization, automatic differentiation, adaptive parameterization, hierarchical Bayesian, metamodeling, Markov chain Monte Carlo, are covered in details. This book can be used as a reference for graduate and upper level undergraduate students majoring in environmental engineering, hydrology, and geosciences. It also serves as an essential reference book for professionals such as petroleum engineers, mining engineers, chemists, mechanical engineers, biologists, biology and medical engineering, applied mathematicians, and others who perform mathematical modeling.
Since the International Institute for Applied Systems Analysis began its study of water quality modeling and management in 1977, it has been interested in the relations between uncertainty and the problems of model calibration and prediction. The work has focused on the theme of modeling poorly defined environmental systems, a principal topic of the effort devoted to environmental quality control and management. Accounting for the effects of uncertainty was also of central concern to our two case studies of lake eutrophication management, one dealing with Lake Balaton in Hungary and the other with several Austrian lake systems. Thus, in November 1979 we held a meeting at Laxenburg to discuss recent method ological developments in addressing problems associated with uncertainty and forecasting of water quality. This book is based on the proceedings of that meeting. The last few years have seen an increase in awareness of the issue of uncertainty in water quality and ecological modeling. This book is relevant not only to contemporary issues but also to those of the future. A lack of field data will not always be the dominant problem for water quality modeling and management; more sophisticated measuring techniques and more comprehensive monitoring networks will come to be more widely applied. Rather, the important problems of the future are much more likely to emerge from the enhanced facility of data processing and to concern the meaningful interpretation, assimilation., and use of the information thus obtained.
Published by the American Geophysical Union as part of the Water Science and Application Series, Volume 6. During the past four decades, computer-based mathematical models of watershed hydrology have been widely used for a variety of applications including hydrologic forecasting, hydrologic design, and water resources management. These models are based on general mathematical descriptions of the watershed processes that transform natural forcing (e.g., rainfall over the landscape) into response (e.g., runoff in the rivers). The user of a watershed hydrology model must specify the model parameters before the model is able to properly simulate the watershed behavior.
This ground-breaking work is the first to cover the fundamentals of hydrogeophysics from both the hydrogeological and geophysical perspectives. Authored by leading experts and expert groups, the book starts out by explaining the fundamentals of hydrological characterization, with focus on hydrological data acquisition and measurement analysis as well as geostatistical approaches. The fundamentals of geophysical characterization are then at length, including the geophysical techniques that are often used for hydrogeological characterization. Unlike other books, the geophysical methods and petrophysical discussions presented here emphasize the theory, assumptions, approaches, and interpretations that are particularly important for hydrogeological applications. A series of hydrogeophysical case studies illustrate hydrogeophysical approaches for mapping hydrological units, estimation of hydrogeological parameters, and monitoring of hydrogeological processes. Finally, the book concludes with hydrogeophysical frontiers, i.e. on emerging technologies and stochastic hydrogeophysical inversion approaches.
Since the pioneering work of Shannon in the late 1940's on the development of the theory of entropy and the landmark contributions of Jaynes a decade later leading to the development of the principle of maximum entropy (POME), the concept of entropy has been increasingly applied in a wide spectrum of areas, including chemistry, electronics and communications engineering, data acquisition and storage and retreival, data monitoring network design, ecology, economics, environmental engineering, earth sciences, fluid mechanics, genetics, geology, geomorphology, geophysics, geotechnical engineering, hydraulics, hydrology, image processing, management sciences, operations research, pattern recognition and identification, photogrammetry, psychology, physics and quantum mechanics, reliability analysis, reservoir engineering, statistical mechanics, thermodynamics, topology, transportation engineering, turbulence modeling, and so on. New areas finding application of entropy have since continued to unfold. The entropy concept is indeed versatile and its applicability widespread. In the area of hydrology and water resources, a range of applications of entropy have been reported during the past three decades or so. This book focuses on parameter estimation using entropy for a number of distributions frequently used in hydrology. In the entropy-based parameter estimation the distribution parameters are expressed in terms of the given information, called constraints. Thus, the method lends itself to a physical interpretation of the parameters. Because the information to be specified usually constitutes sufficient statistics for the distribution under consideration, the entropy method provides a quantitative way to express the information contained in the distribution.
The importance of monitoring networks for resource-management decisions is becoming more recognized, in both theory and application. Quantitative computer models provide a science-based framework to evaluate the efficacy and efficiency of existing and possible future monitoring networks. In the study described herein, two suites of tools were used to evaluate the worth of new data for specific predictions, which in turn can support efficient use of resources needed to construct a monitoring network. The approach evaluates the uncertainty of a model prediction and, by using linear propagation of uncertainty, estimates how much uncertainty could be reduced if the model were calibrated with addition information (increased a priori knowledge of parameter values or new observations). The theoretical underpinnings of the two suites of tools addressing this technique are compared, and their application to a hypothetical model based on a local model inset into the Great Lakes Water Availability Pilot model are described. Results show that meaningful guidance for monitoring network design can be obtained by using the methods explored. The validity of this guidance depends substantially on the parameterization as well; hence, parameterization must be considered not only when designing the parameter-estimation paradigm but also-importantly-when designing the prediction-uncertainty paradigm.
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
During the past five decades, we have witnessed a tremendous evolution in water resource system management. Three characteristics of this evolution are of particular note: First, the application of the systems approach to complex water management problems has been established as one of the most important advances in the field of water resource management. Second, the past five decades have brought a remarkable transformation of attitude in the water resource management community towards environmental concerns and action to address these concerns. Third, applying the principles of sustainability to water resource decision-making requires major changes in the objectives on which decisions are based, and an understanding of the complicated inter-relationships between existing ecological, economic, and social factors. The Special Issue includes 15 contributions that offer insights into contemporary problems, approaches, and issues related to the management of complex water resources systems. It will be presumptuous to say that these 15 contributions characterize the success or failure of the systems approach to support water resources decision-making. However, these contributions offer interesting lessons from current experiences and highlight possible future work.
In this study, methodologies for modeling grey uncertainty in water resources systems are developed, specifically for the problems in two identified areas in water resources: waste load allocation in streams and floodplain planning. A water resources system is associated with some degree of uncertainty, due to randomness of hydrologic and hydraulic parameters, imprecision and subjectivity in management goals, inappropriateness in model selection, inexactness of different input parameters for inadequacy of data, etc. Uncertainty due to randomness of input parameters could be modeled by the probabilistic models, when probability distributions of the parameters may be estimated. Uncertainties due to imprecision in the management problem may be addressed by the fuzzy decision models. In addition, some parameters in any water resources problems need to be addressed as grey parameters, due to inadequate data for an accurate estimation but with known extreme bounds of the parameter values. Such inexactness or grey uncertainty in the model parameters can be addressed by the inexact or grey optimization models, representing the parameters as interval grey numbers. The research study presented in this thesis deals with the development of grey and fuzzy optimization models, and the combination of the two for water resources systems decision-making. Three grey fuzzy optimization models for waste load allocation, namely (i) Grey Fuzzy Waste Load Allocation Model (GFWLAM), (ii) two-phase GFWLAM and (iii) multiobjective GFWLAM, and a Grey Integer Programming (GIP) model for floodplain planning, are developed in this study. The Grey Fuzzy Waste Load Allocation Model (GFWLAM) for water quality management of river system addresses uncertainty in the membership functions for imprecisely stated management goals of the Pollution Control Agency (PCA) and dischargers. To address the imprecision in fixing the boundaries of membership functions (also known as membership parameters), the mem.