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

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ISBN-10: 047177636X

ISBN-13: 9780471776369

Edition: 2007

Authors: Mary C. Hill, Claire R. Tiedeman

List price: $156.95
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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.
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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

Book and Associated Contributions: Methods, Guidelines, Exercises, Answers, Software, and PowerPoint Files
Model Calibration with Inverse Modeling
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
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
Residuals and Weighted Residuals
Least-Squares Objective-Function Surfaces
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Selected Statistical Tables