Analytical Hydrogeology of Inland and Coastal Unconfined Dupuit-Type Aquifers

Publication year: 2026

Number of pages: 169

ISBN: 978-1-77470-151-5
https://doi.org/10.62592/IDJD7328

Citation: Chesnaux, R. (2026). Analytical Hydrogeology of Inland and Coastal Unconfined Dupuit-Type Aquifers. The Groundwater Project. https://doi.org/10.62592/IDJD7328.

Author:

Romain Chesnaux

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Released: June 30, 2026

Analytical Hydrogeology of Inland and Coastal Unconfined Dupuit-Type Aquifers

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Description

Analytical solutions still have a crucial role to play in hydrogeology on a global scale, and should be viewed as an equally powerful and complementary collaborator along with advanced numerical tools. In parallel with the most recent numerical modeling programs enriched by artificial intelligence learning models, analytical solutions using closed-form equations are still being developed and perfected. Analytical solutions are not only relevant for solving problems, but they can be useful for process understanding. They are still being used and perfected by hydrogeologists to solve groundwater problems and should always be considered an efficient tool available in the toolbox of hydrogeologists. This book focuses on compiling and presenting a series of analytical solutions for solving practical problems in unconfined Dupuit-type flow systems for both inland and coastal aquifers. These closed-form solutions can be used to improve knowledge of quantitative hydrogeology and to solve practical problems at an academic and professional level. Solving analytical solutions usually requires low-cost, low-tech, back-of-the-envelope calculations or a simple Excel spreadsheet. The book is composed of seven chapters providing solutions for solving groundwater flow, groundwater velocity and transit time, groundwater recharge, and groundwater volume equations in unconfined Dupuit-type aquifers. A specific application is proposed for assessing seawater intrusion and the impacts of climate change for different scenarios, specifically in Dupuit-type coastal and island aquifers. The book is intended for practitioners in hydrogeology, for undergraduate and graduate students in Earth sciences/hydrogeology or civil/environmental engineering, as well as for academic researchers.

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1 INTRODUCTION

1.1 Teaching Hydrogeology: Trying to Reveal “A Hidden Resource”

1.2 Groundwater Flow Modeling: Physical, Mathematical and Artificial Intelligence

1.3 Analytical vs Numerical Modeling: The Pros and Cons

1.4 Why Do Analytical Solutions Still Have a Role to Play? And How Can They Be Applied?

1.5 Objectives of This Book and Short Description of Its Contents

1.6 Practical Applications of the Closed-Form Analytical Solutions

2 DUPUIT-TYPE FLOW AQUIFERS: PRESENTATION AND ASSUMPTIONS

2.1 Groundwater Flow in an Unconfined Aquifer

2.2 Dupuit-Type Flow Description, Conditions and Assumptions

2.3 Dupuit-Forchheimer Model of Groundwater Flow, Water Table Profile Calculation and Calculation of Groundwater Divide Position

2.4 Verifying if the Aquifer Under Study Satisfies the Dupuit-Type Flow Conditions

2.5 Discussion on the Dupuit-Type Flow Conditions

3 INLAND AND INLAND-ISLAND DUPUIT-TYPE AQUIFERS

3.1 Conversion of the Natural System into a Single Conceptual Model

3.2 Groundwater Velocity

3.3 Groundwater Travel Times

3.4 Groundwater Recharge

3.5 Groundwater Volume

3.6 Groundwater Mean Residence Time

3.7 Specific Case of Inland-Island Aquifers

3.8 Advantages and Limitations of Using Analytical Solutions

4 OCEANIC COASTAL DUPUIT-TYPE AQUIFERS

4.1 Description of a Regional Dupuit-Type Coastal Aquifer Model with Seawater Intrusion

4.2 Conversion of the Natural System into a Single Conceptual Model

4.3 Regional Groundwater Flow Solutions and Determination of the Position of the Saltwater Toe

4.4 Groundwater Velocities

4.5 Groundwater Travel Times

4.6 Freshwater Volumes

4.7 Freshwater Residence Times

5 OCEANIC ISLAND DUPUIT-TYPE AQUIFERS

5.1 Description of the Regional Dupuit-Type Oceanic Island Aquifer Model: Freshwater Lens Model for Strip and Circular Islands

5.2 Regional Groundwater Flow Solutions

5.3 Groundwater Velocities

5.4 Groundwater Travel Times

5.5 Freshwater Volumes

5.6 Freshwater Mean Residence Times

6 ANALYTICAL SOLUTIONS FOR PREDICTING THE EFFECTS OF SEA-LEVEL RISE AND COASTAL EROSION ON GROUNDWATER RESOURCES IN OCEANIC COASTAL AND ISLAND AQUIFERS

6.1 Effects of Climate Change: Land-Surface Inundation Resulting from Sea-Level Rise and Coastal Erosion

6.2 Case of Oceanic Coastal Aquifers

6.3 Case of Oceanic Island Aquifers

6.4 Climate Change Prediction and Scenarios of Land-Surface Inundation

6.5 Discussion

7 SUMMARY AND EXAMPLES

7.1 Summary of the Closed-Form Analytical Solutions

7.2 Building the Spreadsheets for Solving the Equations

8 WRAP-UP/CONCLUSION

9 REFERENCES

10 EXERCISES

11 EXERCISE SOLUTIONS

12 NOTATIONS

13 ABOUT THE AUTHOR

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Analytical Hydrogeology of Inland and Coastal Unconfined Dupuit-Type Aquifers

Description

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Contents

1 INTRODUCTION

1.1 Teaching Hydrogeology: Trying to Reveal “A Hidden Resource”

1.2 Groundwater Flow Modeling: Physical, Mathematical and Artificial Intelligence

1.3 Analytical vs Numerical Modeling: The Pros and Cons

1.4 Why Do Analytical Solutions Still Have a Role to Play? And How Can They Be Applied?

1.5 Objectives of This Book and Short Description of Its Contents

1.6 Practical Applications of the Closed-Form Analytical Solutions

2 DUPUIT-TYPE FLOW AQUIFERS: PRESENTATION AND ASSUMPTIONS

2.1 Groundwater Flow in an Unconfined Aquifer

2.2 Dupuit-Type Flow Description, Conditions and Assumptions

2.3 Dupuit-Forchheimer Model of Groundwater Flow, Water Table Profile Calculation and Calculation of Groundwater Divide Position

2.4 Verifying if the Aquifer Under Study Satisfies the Dupuit-Type Flow Conditions

2.5 Discussion on the Dupuit-Type Flow Conditions

3 INLAND AND INLAND-ISLAND DUPUIT-TYPE AQUIFERS

3.1 Conversion of the Natural System into a Single Conceptual Model

3.2 Groundwater Velocity

3.3 Groundwater Travel Times

3.4 Groundwater Recharge

3.5 Groundwater Volume

3.6 Groundwater Mean Residence Time

3.7 Specific Case of Inland-Island Aquifers

3.8 Advantages and Limitations of Using Analytical Solutions

4 OCEANIC COASTAL DUPUIT-TYPE AQUIFERS

4.1 Description of a Regional Dupuit-Type Coastal Aquifer Model with Seawater Intrusion

4.2 Conversion of the Natural System into a Single Conceptual Model

4.3 Regional Groundwater Flow Solutions and Determination of the Position of the Saltwater Toe

4.4 Groundwater Velocities

4.5 Groundwater Travel Times

4.6 Freshwater Volumes

4.7 Freshwater Residence Times

5 OCEANIC ISLAND DUPUIT-TYPE AQUIFERS

5.1 Description of the Regional Dupuit-Type Oceanic Island Aquifer Model: Freshwater Lens Model for Strip and Circular Islands

5.2 Regional Groundwater Flow Solutions

5.3 Groundwater Velocities

5.4 Groundwater Travel Times

5.5 Freshwater Volumes

5.6 Freshwater Mean Residence Times

6 ANALYTICAL SOLUTIONS FOR PREDICTING THE EFFECTS OF SEA-LEVEL RISE AND COASTAL EROSION ON GROUNDWATER RESOURCES IN OCEANIC COASTAL AND ISLAND AQUIFERS

6.1 Effects of Climate Change: Land-Surface Inundation Resulting from Sea-Level Rise and Coastal Erosion

6.2 Case of Oceanic Coastal Aquifers

6.3 Case of Oceanic Island Aquifers

6.4 Climate Change Prediction and Scenarios of Land-Surface Inundation

6.5 Discussion

7 SUMMARY AND EXAMPLES

7.1 Summary of the Closed-Form Analytical Solutions

7.2 Building the Spreadsheets for Solving the Equations

8 WRAP-UP/CONCLUSION

9 REFERENCES

10 EXERCISES

11 EXERCISE SOLUTIONS

12 NOTATIONS

13 ABOUT THE AUTHOR

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