Effective Groundwater Model Calibration With Analysis of Data, Sensitivities, Predictions, and Uncertainty

Name: Effective Groundwater Model Calibration With Analysis of Data, Sensitivities, Predictions, and Uncertainty
Availability: OutOfStock
ISBN: 9780471776369

ISBN-10: 047177636X

ISBN-13: 9780471776369

Edition: 2007

Authors: Mary C. Hill, Claire R. Tiedeman

List price: $156.95

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Description:

Presenting a set of methods and guidelines for calibrating and analysing mathematical groundwater models, this text helps readers address societal issues related to natural and engineered systems that are conducive to quantitative modeling, and to the use the models and available data more effectively.

Book details

List price: $156.95
Copyright year: 2007
Publisher: John Wiley & Sons, Incorporated
Publication date: 1/22/2007
Binding: Hardcover
Pages: 480
Size: 6.46" wide x 9.15" long x 1.17" tall
Weight: 1.738
Language: English



Preface



Introduction



Book and Associated Contributions: Methods, Guidelines, Exercises, Answers, Software, and PowerPoint Files



Model Calibration with Inverse Modeling



Parameterization



Objective Function



Utility of Inverse Modeling and Associated Methods



Using the Model to Quantitatively Connect Parameters, Observations, and Predictions



Relation of this Book to Other Ideas and Previous Works



Predictive Versus Calibrated Models



Previous Work



A Few Definitions



Linear and Nonlinear



Precision, Accuracy, Reliability, and Uncertainty



Advantageous Expertise and Suggested Readings



Overview of Chapters 2 Through 15



Computer Software and Groundwater Management Problem Used in the Exercises



Computer Programs MODFLOW-2000, UCODE_2005, and PEST



Groundwater Management Problem Used for the Exercises



Purpose and Strategy



Flow System Characteristics



Exercises



Simulate Steady-State Heads and Perform Preparatory Steps



Comparing Observed and Simulated Values Using Objective Functions



Weighted Least-Squares Objective Function



With a Diagonal Weight Matrix



With a Full Weight Matrix



Alternative Objective Functions



Maximum-Likelihood Objective Function



L[subscript 1] Norm Objective Function



Multiobjective Function



Requirements for Accurate Simulated Results



Accurate Model



Unbiased Observations and Prior Information



Weighting Reflects Errors



Additional Issues



Prior Information



Weighting



Residuals and Weighted Residuals



Least-Squares Objective-Function Surfaces



Exercises



Steady-State Parameter Definition



Observations for the Steady-State Problem



Evaluate Model Fit Using Starting Parameter Values



Determining the Information that Observations Provide on Parameter Values using Fit-Independent Statistics



Using Observations



Model Construction and Parameter Definition



Parameter Values



When to Determine the Information that Observations Provide About Parameter Values



Fit-Independent Statistics for Sensitivity Analysis



Sensitivities



Scaling



Dimensionless Scaled Sensitivities (dss)



Composite Scaled Sensitivities (css)



Parameter Correlation Coefficients (pcc)



Leverage Statistics



One-Percent Scaled Sensitivities



Advantages and Limitations of Fit-Independent Statistics for Sensitivity Analysis



Scaled Sensitivities



Parameter Correlation Coefficients



Leverage Statistics



Exercises



Sensitivity Analysis for the Steady-State Model with Starting Parameter Values



Estimating Parameter Values



The Modified Gauss-Newton Gradient Method



Normal Equations



An Example



Convergence Criteria



Alternative Optimization Methods



Multiobjective Optimization



Log-Transformed Parameters



Use of Limits on Estimated Parameter Values



Exercises



Modified Gauss-Newton Method and Application to a Two-Parameter Problem



Estimate the Parameters of the Steady-State Model



Evaluating Model Fit



Magnitude of Residuals and Weighted Residuals



Identify Systematic Misfit



Measures of Overall Model Fit



Objective-Function Value



Calculated Error Variance and Standard Error



AIC, AIC[subscript c], and BIC Statistics



Analyzing Model Fit Graphically and Related Statistics



Using Graphical Analysis of Weighted Residuals to Detect Model Error



Weighted Residuals Versus Weighted or Unweighted Simulated Values and Minimum, Maximum, and Average Weighted Residuals



Weighted or Unweighted Observations Versus Simulated Values and Correlation Coefficient R



Graphs and Maps Using Independent Variables and the Runs Statistic



Normal Probability Graphs and Correlation Coefficient [Characters not reproducible]



Acceptable Deviations from Random, Normally Distributed Weighted Residuals



Exercises



Statistical Measures of Overall Fit



Evaluate Graph Model fit and Related Statistics



Evaluating Estimated Parameter Values and Parameter Uncertainty



Reevaluating Composite Scaled Sensitivities



Using Statistics from the Parameter Variance-Covariance Matrix



Five Versions of the Variance-Covariance Matrix



Parameter Variances, Covariances, Standard Deviations, Coefficients of Variation, and Correlation Coefficients



Relation Between Sample and Regression Statistics



Statistics for Log-Transformed Parameters



When to Use the Five Versions of the Parameter Variance-Covariance Matrix



Some Alternate Methods: Eigenvectors, Eigenvalues, and Singular Value Decomposition



Identifying Observations Important to Estimated Parameter Values



Leverage Statistics



Influence Statistics



Uniqueness and Optimality of the Estimated Parameter Values



Quantifying Parameter Value Uncertainty



Inferential Statistics



Monte Carlo Methods



Checking Parameter Estimates Against Reasonable Values



Testing Linearity



Exercises



Parameter Statistics



Consider All the Different Correlation Coefficients Presented



Test for Linearity



Evaluating Model Predictions, Data Needs, and Prediction Uncertainty



Simulating Predictions and Prediction Sensitivities and Standard Deviations



Using Predictions to Guide Collection of Data that Directly Characterize System Properties



Prediction Scaled Sensitivities (pss)



Prediction Scaled Sensitivities Used in Conjunction with Composite Scaled Sensitivities



Parameter Correlation Coefficients without and with Predictions



Composite and Prediction Scaled Sensitivities Used with Parameter Correlation Coefficients



Parameter-Prediction (ppr) Statistic



Using Predictions to Guide Collection of Observation Data



Use of Prediction, Composite, and Dimensionless Scaled Sensitivities and Parameter Correlation Coefficients



Observation-Prediction (opr) Statistic



Insights About the opr Statistic from Other Fit-Independent Statistics



Implications for Monitoring Network Design



Quantifying Prediction Uncertainty Using Inferential Statistics



Definitions



Linear Confidence and Prediction Intervals on Predictions



Nonlinear Confidence and Prediction Intervals



Using the Theis Example to Understand Linear and Nonlinear Confidence Intervals



Differences and Their Standard Deviations, Confidence Intervals, and Prediction Intervals



Using Confidence Intervals to Serve the Purposes of Traditional Sensitivity Analysis



Quantifying Prediction Uncertainty Using Monte Carlo Analysis



Elements of a Monte Carlo Analysis



Relation Between Monte Carlo Analysis and Linear and Nonlinear Confidence Intervals



Using the Theis Example to Understand Monte Carlo Methods



Quantifying Prediction Uncertainty Using Alternative Models



Testing Model Nonlinearity with Respect to the Predictions



Exercises



Predict Advective Transport and Perform Sensitivity Analysis



Prediction Uncertainty Measured Using Inferential Statistics



Calibrating Transient and Transport Models and Recalibrating Existing Models



Strategies for Calibrating Transient Models



Initial Conditions



Transient Observations



Additional Model Inputs



Strategies for Calibrating Transport Models



Selecting Processes to Include



Defining Source Geometry and Concentrations



Scale Issues



Numerical Issues: Model Accuracy and Execution Time



Transport Observations



Additional Model Inputs



Examples of Obtaining a Tractable, Useful Model



Strategies for Recalibrating Existing Models



Exercises (optional)



Simulate Transient Hydraulic Heads and Perform Preparatory Steps



Transient Parameter Definition



Observations for the Transient Problem



Evaluate Transient Model Fit Using Starting Parameter Values



Sensitivity Analysis for the Initial Model



Estimate Parameters for the Transient System by Nonlinear Regression



Evaluate Measures of Model Fit



Perform Graphical Analyses of Model Fit and Evaluate Related Statistics



Evaluate Estimated Parameters



Test for Linearity



Predictions



Guidelines for Effective Modeling



Purpose of the Guidelines



Relation to Previous Work



Suggestions for Effective Implementation



Guidelines 1 Through 8-Model Development



Apply the Principle of Parsimony



Problem



Constructive Approaches



Use a Broad Range of System Information to Constrain the Problem



Data Assimilation



Using System Information



Data Management



Application: Characterizing a Fractured Dolomite Aquifer



Maintain a Well-Posed, Comprehensive Regression Problem



Examples



Effects of Nonlinearity on the css and pcc



Include Many Kinds of Data as Observations in the Regression



Interpolated "Observations"



Clustered Observations



Observations that Are Inconsistent with Model Construction



Applications: Using Different Types of Observations to Calibrate Groundwater Flow and Transport Models



Use Prior Information Carefully



Use of Prior Information Compared with Observations



Highly Parameterized Models



Applications: Geophysical Data



Assign Weights that Reflect Errors



Determine Weights



Issues of Weighting in Nonlinear Regression



Encourage Convergence by Making the Model More Accurate and Evaluating the Observations



Consider Alternative Models



Develop Alternative Models



Discriminate Between Models



Simulate Predictions with Alternative Models



Application



Guidelines 9 and 10-Model Testing



Evaluate Model Fit



Determine Model Fit



Examine Fit for Existing Observations Important to the Purpose of the Model



Diagnose the Cause of Poor Model Fit



Evaluate Optimized Parameter Values



Quantify Parameter-Value Uncertainty



Use Parameter Estimates to Detect Model Error



Diagnose the Cause of Unreasonable Optimal Parameter Estimates



Identify Observations Important to the Parameter Estimates



Reduce or Increase the Number of Parameters



Guidelines 11 and 12-Potential New Data



Identify New Data to Improve Simulated Processes, Features, and Properties



Identify New Data to Improve Predictions



Potential New Data to Improve Features and Properties Governing System Dynamics



Potential New Data to Support Observations



Guidelines 13 and 14-Prediction Uncertainty



Evaluate Prediction Uncertainty and Accuracy Using Deterministic Methods



Use Regression to Determine Whether Predicted Values Are Contradicted by the Calibrated Model



Use Omitted Data and Postaudits



Quantify Prediction Uncertainty Using Statistical Methods



Inferential Statistics



Monte Carlo Methods



Using and Testing the Methods and Guidelines



Execution Time Issues



Field Applications and Synthetic Test Cases



The Death Valley Regional Flow System, California and Nevada, USA



Grindsted Landfill, Denmark



Objective Function Issues



Derivation of the Maximum-Likelihood Objective Function



Relation of the Maximum-Likelihood and Least-Squares Objective Functions



Assumptions Required for Diagonal Weighting to be Correct



References



Calculation Details of the Modified Gauss-Newton Method



Vectors and Matrices for Nonlinear Regression



Quasi-Newton Updating of the Normal Equations



Calculating the Damping Parameter



Solving the Normal Equations



References



Two Important Properties of Linear Regression and the Effects of Nonlinearity



Identities Needed for the Proofs



True Linear Model



True Nonlinear Model



Linearized True Nonlinear Model



Approximate Linear Model



Approximate Nonlinear Model



Linearized Approximate Nonlinear Model



The Importance of X and X



Considering Many Observations



Normal Equations



Random Variables



Expected Value



Variance-Covariance Matrix of a Vector



Proof of Property 1: Parameters Estimated by Linear Regression are Unbiased



Proof of Property 2: The Weight Matrix Needs to be Defined in a Particular Way for Eq. (7.1) to Apply and for the Parameter Estimates to have the Smallest Variance



References



Selected Statistical Tables



References


References


Index