Foundations of Forward and Inverse Groundwater Flow Models

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

doi:10.1007/978-3-319-71342-7_2

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 proceeding › Chapter › peer-review

Abstract

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 language	English
Title of host publication	The Double Constraint Inversion Methodology
Subtitle of host publication	Equations and Applications in Forward and Inverse Modeling of Groundwater Flow
Editors	Wouter Zijl, Florimond De Smedt, Mustafa El-Rawy, Okke Batelaan
Publisher	Springer
Chapter	2
Pages	15-33
Number of pages	19
Edition	9783319713410
ISBN (Print)	9783319713410
DOIs	https://doi.org/10.1007/978-3-319-71342-7_2
Publication status	Published - 2018

Publication series

Name	SpringerBriefs in Applied Sciences and Technology
Number	9783319713410
ISSN (Print)	2191-530X
ISSN (Electronic)	2191-5318

Keywords

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

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Zijl, W., De Smedt, F., El-Rawy, M., & Batelaan, O. (2018). Foundations of Forward and Inverse Groundwater Flow Models. In W. Zijl, F. De Smedt, M. El-Rawy, & O. Batelaan (Eds.), The Double Constraint Inversion Methodology: Equations and Applications in Forward and Inverse Modeling of Groundwater Flow (9783319713410 ed., pp. 15-33). (SpringerBriefs in Applied Sciences and Technology; No. 9783319713410). Springer . https://doi.org/10.1007/978-3-319-71342-7_2

Zijl, Wouter ; De Smedt, Florimond ; El-Rawy, Mustafa et al. / Foundations of Forward and Inverse Groundwater Flow Models. The Double Constraint Inversion Methodology: Equations and Applications in Forward and Inverse Modeling of Groundwater Flow. editor / Wouter Zijl ; Florimond De Smedt ; Mustafa El-Rawy ; Okke Batelaan. 9783319713410. ed. Springer , 2018. pp. 15-33 (SpringerBriefs in Applied Sciences and Technology; 9783319713410).

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abstract = "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 Calder{\'o}n{\textquoteright}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{\textquoteright}s α-center method for parameter estimation, while Sect. 2.4 analyzes Calder{\'o}n{\textquoteright}s approach in more depth using inspiration from Stefanesco{\textquoteright}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.",

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Zijl, W, De Smedt, F, El-Rawy, M & Batelaan, O 2018, Foundations of Forward and Inverse Groundwater Flow Models. in W Zijl, F De Smedt, M El-Rawy & O Batelaan (eds), The Double Constraint Inversion Methodology: Equations and Applications in Forward and Inverse Modeling of Groundwater Flow. 9783319713410 edn, SpringerBriefs in Applied Sciences and Technology, no. 9783319713410, Springer , pp. 15-33. https://doi.org/10.1007/978-3-319-71342-7_2

Foundations of Forward and Inverse Groundwater Flow Models. / Zijl, Wouter; De Smedt, Florimond; El-Rawy, Mustafa et al.
The Double Constraint Inversion Methodology: Equations and Applications in Forward and Inverse Modeling of Groundwater Flow. ed. / Wouter Zijl; Florimond De Smedt; Mustafa El-Rawy; Okke Batelaan. 9783319713410. ed. Springer , 2018. p. 15-33 (SpringerBriefs in Applied Sciences and Technology; No. 9783319713410).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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AU - El-Rawy, Mustafa

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N2 - 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.

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Zijl W, De Smedt F, El-Rawy M, Batelaan O. Foundations of Forward and Inverse Groundwater Flow Models. In Zijl W, De Smedt F, El-Rawy M, Batelaan O, editors, The Double Constraint Inversion Methodology: Equations and Applications in Forward and Inverse Modeling of Groundwater Flow. 9783319713410 ed. Springer . 2018. p. 15-33. (SpringerBriefs in Applied Sciences and Technology; 9783319713410). doi: 10.1007/978-3-319-71342-7_2

Foundations of Forward and Inverse Groundwater Flow Models

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