Methods and guidelines for developing and using mathematical models
Turn to Effective Groundwater Model Calibration for a set of methods and guidelines that can help produce more accurate and transparent mathematical models. The models can represent groundwater flow and transport and other natural and engineered systems. Use this book and its extensive exercises to learn methods to fully exploit the data on hand, maximize the model's potential, and troubleshoot any problems that arise. Use the methods to perform:
* Sensitivity analysis to evaluate the information content of data
* Data assessment to identify (a) existing measurements that dominate model development and predictions and (b) potential measurements likely to improve the reliability of predictions
* Calibration to develop models that are consistent with the data in an optimal manner
* Uncertainty evaluation to quantify and communicate errors in simulated results that are often used to make important societal decisions
Most of the methods are based on linear and nonlinear regression theory.
Fourteen guidelines show the reader how to use the methods advantageously in practical situations.
Exercises focus on a groundwater flow system and management problem, enabling readers to apply all the methods presented in the text. The exercises can be completed using the material provided in the book, or as hands-on computer exercises using instructions and files available on the text's accompanying Web site.
Throughout the book, the authors stress the need for valid statistical concepts and easily understood presentation methods required to achieve well-tested, transparent models. Most of the examples and all of the exercises focus on simulating groundwater systems; other examples come from surface-water hydrology and geophysics.
The methods and guidelines in the text are broadly applicable and can be used by students, researchers, and engineers to simulate many kinds systems.
Rezensionen / Stimmen
"This is an excellent textbook that addresses a topic, optimization of multiparameter models, which is of broad interest." (Journal of American Water Resources Association, October 2007) "The book represents a very good combination of long-time expert knowledge and being up to date." (Clean, January 2008)
"...a welcome addition to my collection of hydrogeologic books...a valuable reference for ground water scientists who use models." (Ground Water, January-February 2008)
Auflage
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Zielgruppe
Produkt-Hinweis
Maße
Höhe: 244 mm
Breite: 161 mm
Dicke: 28 mm
Gewicht
ISBN-13
978-0-471-77636-9 (9780471776369)
Schweitzer Klassifikation
MARY C. HILL, PhD, is Project Chief for the U.S. Geological Survey (USGS) and a recipient of the USGS Meritorious Service Award, the ASCE Walter Huber Research Prize, and the NGWA M. King Hubbert Award. Dr. Hill is President of the International Commission for Ground Water. She is Adjunct Professor at the University of Colorado at Boulder and the Colorado School of Mines.
CLAIRE R. TIEDEMAN, MS, is a Research Hydrologist at the U.S. Geological Survey, where her work involves calibrating and evaluating models of complex groundwater flow systems, developing methods to evaluate prediction uncertainty, and characterizing flow and transport in fractured-rock aquifers. She is a recipient of the USGS Superior Service Award and an Associate Editor of the journal Ground Water.
Preface.
1 Introduction.
2 Computer Software and Groundwater Management Problem Used in the Exercises.
Exercise 2.1: Simulate Steady-State Heads and Perform Preparatory Steps.
3 Comparing Observed and Simulated Values Using Objective Functions.
Exercise 3.1: Steady-State Parameter Definition.
Exercise 3.2: Observations for the Steady-State Problem.
Exercise 3.3: Evaluate Model Fit Using Starting Parameter Values.
4 Determining the Information that Observations Provide on Parameter Values using Fit-Independent Statistics.
Exercise 4.1: Sensitivity Analysis for the Steady-State Model with Starting Parameter Values.
5 Estimating Parameter Values.
Exercise 5.1: Modified Gauss-Newton Method and Application to a Two-Parameter Problem.
Exercise 5.2: Estimate the Parameters of the Steady-State Model.
6 Evaluating Model Fit.
Exercise 6.1: Statistical Measures of Overall Fit.
Exercise 6.2: Evaluate Graph Model fit and Related Statistics.
7 Evaluating Estimated Parameter Values and Parameter Uncertainty.
Exercise 7.1: Parameter Statistics.
Exercise 7.2: Consider All the Different Correlation Coefficients Presented.
Exercise 7.3: Test for Linearity.
8 Evaluating Model Predictions, Data Needs, and Prediction Uncertainty.
Exercise 8.1: Predict Advective Transport and Perform Sensitivity Analysis.
Exercise 8.2: Prediction Uncertainty Measured Using Inferential Statistics.
9 Calibrating Transient and Transport Models and Recalibrating Existing Models.
Exercises 9.1 and 9.2: Simulate Transient Hydraulic Heads and Perform Preparatory Steps.
Exercise 9.3: Transient Parameter Definition.
Exercise 9.4: Observations for the Transient Problem.
Exercise 9.5: Evaluate Transient Model Fit Using Starting Parameter Values.
Exercise 9.6: Sensitivity Analysis for the Initial Model.
Exercise 9.7: Estimate Parameters for the Transient System by Nonlinear Regression.
Exercise 9.8: Evaluate Measures of Model Fit.
Exercise 9.9: Perform Graphical Analyses of Model Fit and Evaluate Related Statistics.
Exercise 9.10: Evaluate Estimated Parameters.
Exercise 9.11: Test for Linearity.
Exercise 9.12: Predictions.
10 Guidelines for Effective Modeling.
11 Guidelines 1 Through 8--Model Development.
Guideline 1: Apply the Principle of Parsimony.
Guideline 2: Use a Broad Range of System Information to Constrain the Problem.
Guideline 3: Maintain a Well-Posed, Comprehensive Regression Problem.
Guideline 4: Include Many Kinds of Data as Observations in the Regression.
Guideline 5: Use Prior Information Carefully.
Guideline 6: Assign Weights that Reflect Errors.
Guideline 7: Encourage Convergence by Making the Model More Accurate and Evaluating the Observations.
Guideline 8: Consider Alternative Models.
12 Guidelines 9 and 10--Model Testing.
Guideline 9: Evaluate Model Fit.
Guideline 10: Evaluate Optimized Parameter Values.
13 Guidelines 11 and 12--Potential New Data.
Guideline 11: Identify New Data to Improve Simulated Processes, Features, and Properties.
Guideline 12: Identify New Data to Improve Predictions.
14 Guidelines 13 and 14--Prediction Uncertainty.
Guideline 13: Evaluate Prediction Uncertainty and Accuracy Using Deterministic Methods.
Guideline 14: Quantify Prediction Uncertainty Using Statistical Methods.
15 Using and Testing the Methods and Guidelines.
Appendix A: Objective Function Issues.
Appendix B: Calculation Details of the Modified Gauss-Newton Method.
Appendix C: Two Important Properties of Linear Regression and the Effects of Nonlinearity.
Appendix D: Selected Statistical Tables.
References.
Index.
