Applied Groundwater Modeling, 2nd Edition

Simulation of Flow and Advective Transport

Applied Groundwater Modeling, 2nd Edition,Mary Anderson,William Woessner,Randall Hunt,ISBN9780120581030
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This second edition provides an expanded discussion of the fundamentals of applied groundwater modeling focusing on finite-difference and finite-element models with updated coverage of particle tracking and advances in model calibration and uncertainty analysis.

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Key Features

    • Explains how to formulate a conceptual model of a groundwater system and translate it into a numerical model
    • Demonstrates how modeling concepts, including boundary conditions, are implemented in two groundwater flow codes-- MODFLOW (for finite differences) and FEFLOW (for finite elements)
    • Discusses particle tracking methods and codes for flowpath analysis and advective transport of contaminants
    • Summarizes parameter estimation and uncertainty analysis approaches using the code PEST to illustrate how concepts are implemented
    • Discusses modeling ethics and preparation of the modeling report
    • Includes Boxes that amplify and supplement topics covered in the text
    • Each chapter presents lists of common modeling errors and problem sets that illustrate concepts


This second edition is extensively revised throughout with expanded discussion of modeling fundamentals and coverage of advances in model calibration and uncertainty analysis that are revolutionizing the science of groundwater modeling. The text is intended for undergraduate and graduate level courses in applied groundwater modeling and as a comprehensive reference for environmental consultants and scientists/engineers in industry and governmental agencies.


Graduate students and practicing professionals in groundwater hydrology, civil engineers and environmental consultants, and USGS and state agencies dealing with groundwater.

Mary Anderson

Affiliations and Expertise

University of Wisconsin-Madison, USA

William Woessner

Affiliations and Expertise

University of Montana, Missoula, USA

Randall Hunt

Affiliations and Expertise

U.S. Geological Survey, Wisconsin Water Science Center, Middleton, WI

Applied Groundwater Modeling, 2nd Edition

List of Figures
List of Tables

Section 1 Modeling Fundamentals

1. Introduction
1.1 Motivation for Modeling
1.2 What Is a Model?
1.2.1 Physical Models
1.2.2 Mathematical Models
1.3 Purpose of Modeling
1.3.1 Forecasting/Hindcasting Models
1.3.2 Interpretative Models
1.4 Limitations of Models
1.4.1 Nonuniqueness
1.4.2 Uncertainty
1.5 Modeling Ethics
1.5.1 Model Design
1.5.2 Bias
1.5.3 Presentation of Results
1.5.4 Cost
1.6 Modeling Workflow
1.6.1 Steps in the Workflow
1.6.2 Verification and Validation
1.7 Common Modeling Errors
1.8 Use of This Text
1.9 Problems
Box 1.1 Data-Driven (Black-Box) Models

2. Modeling Purpose and Conceptual Model
2.1 Modeling Purpose
2.2 Conceptual Model: Definition and General Features
2.3 Components of a Conceptual Model
2.3.1 Boundaries
2.3.2 Hydrostratigraphy and Hydrogeological Properties
2.3.3 Flow Direction and Sources and Sinks
2.3.4 Groundwater Budget Components
2.3.5 Ancillary Information
2.4 Uncertainty in the Conceptual Model
2.5 Common Modeling Errors
2.6 Problems
Box 2.1 Geographical Information Systems (GIS)
Box 2.2 Describing the Void Space

3. Basic Mathematics and the Computer Code
3.1 Introduction
3.2 Governing Equation for Groundwater Flow
3.2.1 Assumptions
3.2.2 Derivation
3.3 Boundary Conditions
3.4 Analytical Models
3.4.1 Analytical Solutions
3.4.2 Analytic Element (AE) Models
3.5 Numerical Models
3.5.1 Finite Differences
3.5.2 Finite Elements
3.5.3 Control Volume Finite Differences
3.5.4 Solution Methods
3.6 Code Selection
3.6.1 Code Verification
3.6.2 Water Budget
3.6.3 Track Record
3.6.4 GUIs
3.7 Code Execution
3.7.1 Simulation Log
3.7.2 Execution Time
3.7.3 Closure Criteria and Solution Convergence
3.8 Common Modeling Errors
3.9 Problems
Box 3.1 The Hydraulic Conductivity Tensor
Box 3.2 Insights from Analytical Solutions

Section 2 Designing the Numerical Model

4. Model Dimensionality and Setting Boundaries
4.1 Spatial Dimensions
4.1.1 Two-Dimensional Models
4.1.2 Three-Dimensional Models
4.2 Selecting Boundaries
4.2.1 Physical Boundaries
4.2.2 Hydraulic Boundaries
4.3 Implementing Boundaries in a Numerical Model
4.3.1 Setting Boundaries in the Grid/Mesh
4.3.2 Specified Head Boundaries
4.3.3 Specified Flow Boundaries
4.3.4 Head-dependent Boundaries
4.4 Extracting Local Boundary Conditions from a Regional Model
4.5 Simulating the Water Table
4.5.1 Fixed Nodes
4.5.2 Movable Nodes
4.5.3 Variably Saturated Codes
4.6 Common Modeling Errors
4.7 Problems
Box 4.1 Two-Dimensional or Three-Dimensional-- More about the D-F Approximation
Box 4.2 Profile Models
Box 4.3 Spreadsheet Solution of a Finite-Difference Profile Model
Box 4.4 The Freshwater--Seawater Interface
Box 4.5 Large Water Budget Errors Arising from an HDB
Box 4.6 What Controls the Water Table?

5. Spatial Discretization and Parameter Assignment
5.1 Discretizing Space
5.1.1 Orienting the Grid/Mesh
5.1.2 Finite-Difference Grid
5.1.3 Finite-Element Mesh
5.2 Horizontal Nodal Spacing
5.2.1 Solution Accuracy
5.2.2 Calibration Targets
5.2.3 Perimeter Boundary Configuration
5.2.4 Heterogeneity
5.2.5 Faults, Conduits, and Barriers
5.2.6 Internal Sources and Sinks
5.3 Model Layers
5.3.1 Vertical Discretization
5.3.2 Layer Types
5.3.3 Layer Elevations
5.3.4 Pinchouts and Faults
5.3.5 Dipping Hydrogeologic Units
5.4 Parameters
5.4.1 Material Property Parameters
5.4.2 Hydrologic Parameters
5.5 Parameter Assignment
5.5.1 General Principles
5.5.2 Assigning Storage Parameters to Layers
5.5.3 Populating the Grid or Mesh
5.6 Parameter Uncertainty
5.7 Common Modeling Errors
5.8 Problems
Box 5.1 Numerical Error Inherent to Irregular FD Grids
Box 5.2 Vertical Anisotropy and the Transformed Section
Box 5.3 Upscaling Hydraulic Conductivity: Layered Heterogeneity and Vertical Anisotropy
Box 5.4 When Infiltration becomes Recharge

6. More on Sources and Sinks
6.1 Introduction
6.2 Pumping and Injection Wells
6.2.1 FD Well Nodes
6.2.2 FE Well Nodes and Multinode Wells
6.2.3 Multinode Wells in FD Models
6.3 Areally Distributed Sources and Sinks
6.4 Drains and Springs
6.5 Streams
6.6 Lakes
6.7 Wetlands
6.8 Common Modeling Errors
6.9 Problems
Box 6.1 Guidelines for Nodal Spacing around a Well Node
Box 6.2 Watershed Modeling
Box 6.3 Surface Water Modeling

7. Steady-State and Transient Simulations
7.1 Steady-State Simulations
7.1.1 Starting Heads
7.1.2 Boundary Conditions
7.1.3 Evaluating Steady-State Conditions
7.2 Steady State or Transient?
7.3 Transient Simulations
7.4 Initial Conditions
7.5 Perimeter Boundary Conditions for Transient Simulations
7.6 Discretizing Time
7.6.1 Time Steps and Stress Periods
7.6.2 Selecting the Time Step
7.7 Characterizing Transient Conditions
7.8 Common Modeling Errors
7.9 Problems

Section 3 Particle Tracking, Calibration, Forecasting and Uncertainty Analysis

8. Particle Tracking
8.1 Introduction
8.2 Velocity Interpolation
8.2.1 Effect of Spatial Discretization
8.2.2 Effect of Temporal Discretization
8.2.3 Interpolation Methods
8.3 Tracking Schemes
8.3.1 Semianalytical Method
8.3.2 Numerical Methods
8.4 Weak Sinks
8.5 Applications
8.5.1 Flow System Analysis
8.5.2 Capture Zones and Contributing Areas
8.5.3 Advective Transport of Contaminants
8.6 Particle Tracking Codes
8.7 Common Errors in Particle Tracking
8.8 Problems
Box 8.1 Effective Porosity
Box 8.2 Flow Nets
Box 8.3 More on Capture Zones and Contributing Areas

9. Model Calibration: Assessing Performance
9.1 Introduction
9.2 Limitations of History Matching
9.3 Calibration Targets
9.3.1 Head Targets
9.3.2 Flux Targets
9.3.3 Ranking Targets
9.4 Manual History Matching
9.4.1 Comparing Model Output to Observations
9.4.2 Choosing the Parameters to Adjust
9.4.3 Manual Trial-and-Error History Matching
9.4.4 Limitations of a Manual Approach
9.5 Parameter Estimation: Automated Trial-and-Error History Matching
9.5.1 Weighting the Targets
9.5.2 Finding a Best Fit
9.5.3 Statistical Analysis
9.6 Highly Parameterized Model Calibration with Regularized Inversion
9.6.1 Increasing the Number of Calibration Parameters
9.6.2 Stabilizing Parameter Estimation
9.6.3 Speeding the Parameter Estimation Process
9.7 A Workflow for Calibration and Model Performance Evaluation
9.8 Common Modeling Errors
9.9 Problems
Box 9.1 Historical Context for Parameter Estimation
Box 9.2 Tips for Running a Parameter Estimation Code
Box 9.3 Tips for Effective Pilot Point Parameterization

Box 9.4 A "Singularly Valuable Decomposition"— Benefits for Groundwater Modeling
Box 9.5 Code/Model Verification and Model Validation
Box 9.6 Additional Parameter Estimation Tools

10. Forecasting and Uncertainty Analysis
10.1 Introduction
10.2 Characterizing Uncertainty
10.3 Addressing Uncertainty
10.4 Basic Uncertainty Analysis
10.4.1 Scenario Modeling
10.4.2 Linear Uncertainty Analysis
10.5 Advanced Uncertainty Analysis
10.5.1 Analysis Using One Conceptualization
10.5.2 Analysis Using Multiple Conceptualizations
10.6 Reporting Forecast Uncertainty
10.7 Evaluating Forecasts: Postaudits
10.8 Common Modeling Errors
10.9 Problems
Box 10.1 Historical Overview of Uncertainty Analysis in Groundwater Modeling
Box 10.2 Travel Time in Heterogeneous Aquifers: Impossible to Forecast Accurately?
Box 10.3 Cost-Benefit Analyses of Future Data Collection
Box 10.4 Using Monte Carlo Methods to Represent Forecast Uncertainty


Section 4 The Modeling Report and Advanced Topics

11. The Modeling Report, Archive, and Review
11.1 Introduction
11.2 The Modeling Report
11.2.1 Title
11.2.2 Executive Summary and Abstract
11.2.3 Introduction
11.2.4 Hydrogeologic Setting and Conceptual Model
11.2.5 Numerical Model
11.2.6 Forecasting Simulations and Uncertainty Analysis
11.2.7 Discussion
11.2.8 Model Assumptions, Simplifications, and Limitations
11.2.9 Summary and Conclusions
11.2.10 References Cited
11.2.11 Appendices
11.3 Archiving the Model
11.4 Reviewing the Modeling Report
11.5 Common Errors in Report/Archive Preparation and Review
11.6 Problems

12. Beyond Basic Modeling Concepts
12.1 Introduction
12.2 Complex Groundwater Flow Processes
12.2.1 Flow through Fractures and Conduits
12.2.2 Aquifer Compaction
12.2.3 Variably Saturated Flow
12.2.4 Variable Density Flow
12.2.5 Multiphase Flow
12.2.6 Linked and Coupled Models
12.3 Transport Processes
12.4 Surface Water Processes
12.5 Stochastic Groundwater Modeling
12.6 Decision-Support and Optimization
12.7 Final Comments



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