Model Calibration and Parameter Estimation : For Environmental and Water Resource Systems Introduction The Classical Inverse Problem The Gauss Newton Method Multiobjective Inversion and Regularization Statistical Methods for Parameter Estimation Model Differentiation Model Dimension Reduction Development of Data Driven Models Data Assimilation for Inversion Model Uncertainty Quantification Optimal Experimental Design Goal Oriented Modeling This three part book provides a comprehensive and systematic introduction to the development of useful models for complex systems. 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 useful for graduate and upper level undergraduate students majoring in environmental engineering hydrology and geosciences. It also serves as an essential reference book for petroleum engineers mining engineers chemists mechanical engineers ecologists biomedical engineers applied mathematicians and others who perform mathematical modeling