Model Calibration And Parameter Estimation

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.

This book presents a detailed examination of the estimation techniques and modeling problems. The theory is furnished with several illustrations and computer programs to promote better understanding of system modeling and parameter estimation.

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.

Mathematical modelling has become in recent years an essential tool for the prediction of environmental change and for the development of sustainable policies. Yet, many of the uncertainties associated with modelling efforts appear poorly understood by many, especially by policy makers. This book attempts for the first time to cover the full range of issues related to model uncertainties, from the subjectivity of setting up a conceptual model of a given system, all the way to communicating the nature of model uncertainties to non-scientists and accounting for model uncertainties in policy decisions. Theoretical chapters, providing background information on specific steps in the modelling process and in the adoption of models by end-users, are complemented by illustrative case studies dealing with soils and global climate change. All the chapters are authored by recognized experts in their respective disciplines, and provide a timely and uniquely comprehensive coverage of an important field.