Foundations of Forward and Inverse Groundwater Flow Models

Wouter Zijl, Florimond De Smedt, Mustafa El-Rawy, Okke Batelaan

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


This chapter deals with the basic equation governing groundwater flow. In Sect. 2.1, the equations are presented in their full four-dimensional form (three spatial dimensions + time) with emphasis on the parameters. Section 2.2 introduces Calderón’s approach to determination of the spatially heterogeneous hydraulic conductivity field. To avoid negative hydraulic conductivities in the double constraint methodology (DCM), this approach is based on the square root of the hydraulic conductivity (sqrt-conductivity α). Section 2.3 introduces Stefanescu’s α-center method for parameter estimation, while Sect. 2.4 analyzes Calderón’s approach in more depth using inspiration from Stefanesco’s method. Although this chapter sets the scene for the real subject matter of this book—the double constraint methodology (DCM)—its reading may be skipped by readers who want to go directly to the DCM treated in Chap. 3.

Original languageEnglish
Title of host publicationThe Double Constraint Inversion Methodology
Subtitle of host publicationEquations and Applications in Forward and Inverse Modeling of Groundwater Flow
EditorsWouter Zijl, Florimond De Smedt, Mustafa El-Rawy, Okke Batelaan
Number of pages19
ISBN (Print)9783319713410
Publication statusPublished - 2018

Publication series

NameSpringerBriefs in Applied Sciences and Technology
ISSN (Print)2191-530X
ISSN (Electronic)2191-5318

Bibliographical note

©The Author(s) 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.


  • Calderon's conjecture
  • smoothed conductivity fields
  • stefanescu's alpha centers
  • uncorrelated conductivity fields


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