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 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.

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

Understanding groundwater recharge is essential for successful management of water resources and modeling fluid and contaminant transport within the subsurface. This book provides a critical evaluation of the theory and assumptions that underlie methods for estimating rates of groundwater recharge. Detailed explanations of the methods are provided - allowing readers to apply many of the techniques themselves without needing to consult additional references. Numerous practical examples highlight benefits and limitations of each method. Approximately 900 references allow advanced practitioners to pursue additional information on any method. For the first time, theoretical and practical considerations for selecting and applying methods for estimating groundwater recharge are covered in a single volume with uniform presentation. Hydrogeologists, water-resource specialists, civil and agricultural engineers, earth and environmental scientists and agronomists will benefit from this informative and practical book. It can serve as the primary text for a graduate-level course on groundwater recharge or as an adjunct text for courses on groundwater hydrology or hydrogeology. For the benefit of students and instructors, problem sets of varying difficulty are available at http://wwwbrr.cr.usgs.gov/projects/GW_Unsat/Recharge_Book/.

Intended to fill a void in the atmospheric science literature, this self-contained text outlines the physical and mathematical basis of all aspects of atmospheric analysis as well as topics important in several other fields outside of it, including atmospheric dynamics and statistics.

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.

Uncertainty Quantification in Multiscale Materials Modeling provides a complete overview of uncertainty quantification (UQ) in computational materials science. It provides practical tools and methods along with examples of their application to problems in materials modeling. UQ methods are applied to various multiscale models ranging from the nanoscale to macroscale. This book presents a thorough synthesis of the state-of-the-art in UQ methods for materials modeling, including Bayesian inference, surrogate modeling, random fields, interval analysis, and sensitivity analysis, providing insight into the unique characteristics of models framed at each scale, as well as common issues in modeling across scales.

This Scientific and Technical Report (STR) presents the findings of the IWA Task Group on River Water Quality Modelling (RWQM). The task group was formed to create a scientific and technical base from which to formulate standardized, consistent river water quality models and guidelines for their implementation. This STR presents the first outcome in this effort: River Water Quality Model No. 1 (RWQM1). As background to the development of River Water Quality Model No.1, the Task Group completed a critical evaluation of the current state of the practice in water quality modelling. A major limitation in model formulation is the continued reliance on BOD as the primary state variable, despite the fact BOD does not include all biodegradable matter. A related difficulty is the poor representation of benthic flux terms. As a result of these limitations, it is impossible to close mass balances completely in most existing models. These various limitations in current river water quality models impair their predictive ability in situations of marked changes in a river's pollutant load, streamflow, morphometry, or other basic characteristics. RWQM 1 is intended to serve as a framework for river water quality models that overcome these deficiencies in traditional water quality models and most particularly the failure to close mass balances between the water column and sediment. To these ends, the model incorporates fundamental water quality components and processes to characterise carbon, oxygen, nitrogen, and phosphorus (C, O, N, and P) cycling instead of biochemical oxygen demand as used in traditional models. The model is presented in terms of process and components represented via a 'Petersen stoichiometry matrix', the same approach used for the IWA Activated Sludge Models. The full RWQM1 includes 24 components and 30 processes. The report provides detailed examples on reducing the numbers of components and processes to fit specific water quality problems. Thus, the model provides a framework for both complicated and simplified models. Detailed explanations of the model components, process equations, stoichiometric parameters, and kinetic parameters are provided, as are example parameter values and two case studies. The STR is intended to launch a participatory process of model development, application, and refinement. RWQM1 provides a framework for this process, but the goal of the Task Group is to involve water quality professionals worldwide in the continued work developing a new water quality modelling approach. This text will be an invaluable reference for researchers and graduate students specializing in water resources, hydrology, water quality, or environmental modelling in departments of environmental engineering, natural resources, civil engineering, chemical engineering, environmental sciences, and ecology. Water resources engineers, water quality engineers and technical specialists in environmental consultancy, government agencies or regulated industries will also value this critical assessment of the state of practice in water quality modelling. Key Features presents a unique new technical approach to river water quality modelling provides a detailed technical presentation of the RWQM1 water quality process model gives an informative critical evaluation of the state of the practice in water quality modelling, and problems with those practices provides a step by step procedure to develop a water quality model Scientific & Technical Report No. 12