Necessary conditions for inverse modeling of flow through variably saturated porous media

Deqiang Mao, Tian-Chyi J Yeh, Li Wan, Kuo Chin Hsu, Cheng Haw Lee, Jet Chau Wen

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

Non-unique solutions of inverse problems arise from a lack of information that satisfies necessary conditions for the problem to be well defined. This paper investigates these conditions for inverse modeling of water flow through multi-dimensional variably saturated porous media. It shows that in order to obtain a unique estimate of hydraulic parameters, along each streamline of the flow field (1) spatial and temporal head observations must be given; (2) the number of spatial and temporal head observations required should be greater or equal to the number of unknown parameters; (3) the flux boundary condition or the pumping rate of a well must be specified for the homogeneous case and both boundary flux and pumping rate are a must for the heterogeneous case; (4) head observations must encompass both saturated and unsaturated conditions, and the functional relationships for unsaturated hydraulic conductivity/pressure head and for the moisture retention should be given, and (5) the residual water content value also need to be specified a priori or water content measurements are needed for the estimation of the saturated water content.For field problems, these necessary conditions can be collected or estimated but likely involve uncertainty. While the problems become well defined and have unique solutions, the solutions likely will be uncertain. Because of this uncertainty, stochastic approaches are deemed to be appropriate for inverse problems as they are for forward problems to address uncertainty. Nevertheless, knowledge of these necessary conditions is critical to reduce uncertainty in both characterization of the vadose zone and the aquifer, and prediction of water flow and solute migration in the subsurface.

Original languageEnglish (US)
Pages (from-to)50-61
Number of pages12
JournalAdvances in Water Resources
Volume52
DOIs
StatePublished - Feb 2013

Fingerprint

porous medium
water content
inverse problem
water flow
pumping
modeling
vadose zone
flow field
hydraulic conductivity
solute
boundary condition
moisture
aquifer
hydraulics
prediction
rate
parameter

Keywords

  • Inverse problem
  • Necessary condition
  • Uniqueness
  • Variably-saturated condition

ASJC Scopus subject areas

  • Water Science and Technology

Cite this

Necessary conditions for inverse modeling of flow through variably saturated porous media. / Mao, Deqiang; Yeh, Tian-Chyi J; Wan, Li; Hsu, Kuo Chin; Lee, Cheng Haw; Wen, Jet Chau.

In: Advances in Water Resources, Vol. 52, 02.2013, p. 50-61.

Research output: Contribution to journalArticle

Mao, Deqiang ; Yeh, Tian-Chyi J ; Wan, Li ; Hsu, Kuo Chin ; Lee, Cheng Haw ; Wen, Jet Chau. / Necessary conditions for inverse modeling of flow through variably saturated porous media. In: Advances in Water Resources. 2013 ; Vol. 52. pp. 50-61.
@article{9d9126ca0e8d4839950ba877f1642d61,
title = "Necessary conditions for inverse modeling of flow through variably saturated porous media",
abstract = "Non-unique solutions of inverse problems arise from a lack of information that satisfies necessary conditions for the problem to be well defined. This paper investigates these conditions for inverse modeling of water flow through multi-dimensional variably saturated porous media. It shows that in order to obtain a unique estimate of hydraulic parameters, along each streamline of the flow field (1) spatial and temporal head observations must be given; (2) the number of spatial and temporal head observations required should be greater or equal to the number of unknown parameters; (3) the flux boundary condition or the pumping rate of a well must be specified for the homogeneous case and both boundary flux and pumping rate are a must for the heterogeneous case; (4) head observations must encompass both saturated and unsaturated conditions, and the functional relationships for unsaturated hydraulic conductivity/pressure head and for the moisture retention should be given, and (5) the residual water content value also need to be specified a priori or water content measurements are needed for the estimation of the saturated water content.For field problems, these necessary conditions can be collected or estimated but likely involve uncertainty. While the problems become well defined and have unique solutions, the solutions likely will be uncertain. Because of this uncertainty, stochastic approaches are deemed to be appropriate for inverse problems as they are for forward problems to address uncertainty. Nevertheless, knowledge of these necessary conditions is critical to reduce uncertainty in both characterization of the vadose zone and the aquifer, and prediction of water flow and solute migration in the subsurface.",
keywords = "Inverse problem, Necessary condition, Uniqueness, Variably-saturated condition",
author = "Deqiang Mao and Yeh, {Tian-Chyi J} and Li Wan and Hsu, {Kuo Chin} and Lee, {Cheng Haw} and Wen, {Jet Chau}",
year = "2013",
month = "2",
doi = "10.1016/j.advwatres.2012.08.001",
language = "English (US)",
volume = "52",
pages = "50--61",
journal = "Advances in Water Resources",
issn = "0309-1708",
publisher = "Elsevier Limited",

}

TY - JOUR

T1 - Necessary conditions for inverse modeling of flow through variably saturated porous media

AU - Mao, Deqiang

AU - Yeh, Tian-Chyi J

AU - Wan, Li

AU - Hsu, Kuo Chin

AU - Lee, Cheng Haw

AU - Wen, Jet Chau

PY - 2013/2

Y1 - 2013/2

N2 - Non-unique solutions of inverse problems arise from a lack of information that satisfies necessary conditions for the problem to be well defined. This paper investigates these conditions for inverse modeling of water flow through multi-dimensional variably saturated porous media. It shows that in order to obtain a unique estimate of hydraulic parameters, along each streamline of the flow field (1) spatial and temporal head observations must be given; (2) the number of spatial and temporal head observations required should be greater or equal to the number of unknown parameters; (3) the flux boundary condition or the pumping rate of a well must be specified for the homogeneous case and both boundary flux and pumping rate are a must for the heterogeneous case; (4) head observations must encompass both saturated and unsaturated conditions, and the functional relationships for unsaturated hydraulic conductivity/pressure head and for the moisture retention should be given, and (5) the residual water content value also need to be specified a priori or water content measurements are needed for the estimation of the saturated water content.For field problems, these necessary conditions can be collected or estimated but likely involve uncertainty. While the problems become well defined and have unique solutions, the solutions likely will be uncertain. Because of this uncertainty, stochastic approaches are deemed to be appropriate for inverse problems as they are for forward problems to address uncertainty. Nevertheless, knowledge of these necessary conditions is critical to reduce uncertainty in both characterization of the vadose zone and the aquifer, and prediction of water flow and solute migration in the subsurface.

AB - Non-unique solutions of inverse problems arise from a lack of information that satisfies necessary conditions for the problem to be well defined. This paper investigates these conditions for inverse modeling of water flow through multi-dimensional variably saturated porous media. It shows that in order to obtain a unique estimate of hydraulic parameters, along each streamline of the flow field (1) spatial and temporal head observations must be given; (2) the number of spatial and temporal head observations required should be greater or equal to the number of unknown parameters; (3) the flux boundary condition or the pumping rate of a well must be specified for the homogeneous case and both boundary flux and pumping rate are a must for the heterogeneous case; (4) head observations must encompass both saturated and unsaturated conditions, and the functional relationships for unsaturated hydraulic conductivity/pressure head and for the moisture retention should be given, and (5) the residual water content value also need to be specified a priori or water content measurements are needed for the estimation of the saturated water content.For field problems, these necessary conditions can be collected or estimated but likely involve uncertainty. While the problems become well defined and have unique solutions, the solutions likely will be uncertain. Because of this uncertainty, stochastic approaches are deemed to be appropriate for inverse problems as they are for forward problems to address uncertainty. Nevertheless, knowledge of these necessary conditions is critical to reduce uncertainty in both characterization of the vadose zone and the aquifer, and prediction of water flow and solute migration in the subsurface.

KW - Inverse problem

KW - Necessary condition

KW - Uniqueness

KW - Variably-saturated condition

UR - http://www.scopus.com/inward/record.url?scp=84870206661&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870206661&partnerID=8YFLogxK

U2 - 10.1016/j.advwatres.2012.08.001

DO - 10.1016/j.advwatres.2012.08.001

M3 - Article

AN - SCOPUS:84870206661

VL - 52

SP - 50

EP - 61

JO - Advances in Water Resources

JF - Advances in Water Resources

SN - 0309-1708

ER -