This dissertation presents results of research in the development, testing and application of an automated calibration and uncertainty analysis framework for distributed environmental models based on Bayesian Markov chain Monte Carlo (MCMC) sampling and response surface methodology (RSM) surrogate models that use a novel random local fitting algorithm. Typical automated search methods for optimization and uncertainty assessment such as evolutionary and Nelder-Mead Simplex algorithms are inefficient and/or infeasible when applied to distributed environmental models, as exemplified by the watershed management scenario analysis case study presented as part of this dissertation. This is because the larger numbers of non-linearly interacting parameters and the more complex structures of distributed environmental models make automated calibration and uncertainty analysis more computationally demanding compared to traditional basin-averaged models. To improve efficiency and feasibility of automated calibration and uncertainty assessment of distributed models, recent research has been focusing on using the response surface methodology (RSM) to approximate objective functions such as sum of squared residuals and Bayesian inference likelihoods. This dissertation presents (i) results on a novel study of factors that affect the performance of RSM approximation during Bayesian calibration and uncertainty analysis, (ii) a new 'random local fitting' (RLF) algorithm that improves RSM approximation for large sampling domains and (iii) application of a developed automated uncertainty analysis framework that uses MCMC sampling and a spline-based radial basis approximation function enhanced by the RLF algorithm to a fully-distributed hydrologic model case study. Using the MCMC sampling and response surface approximation framework for automated parameter and predictive uncertainty assessment of a distributed environmental model is novel. While extended testing of the developed MCMC uncertainty analysis paradigm is necessary, the results presented show that the new framework is robust and efficient for the case studied and similar distributed environmental models. As distributed environmental models continue to find use in climate change studies, flood forecasting, water resource management and land use studies, results of this study will have increasing importance to automated model assessment. Potential future research from this dissertation is the investigation of how model parameter sensitivities and inter-dependencies affect the performance of response surface approximation.

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.