A Parameter Estimation Technique for a Groundwater Flow Model

Joseph Acquah; Francis Benyah; Jerry Samuel Yao-Kuma

doi:doi:10.11648/j.mma.20200504.11

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A Parameter Estimation Technique for a Groundwater Flow Model

Joseph Acquah, Francis Benyah, Jerry Samuel Yao-Kuma

Published in Mathematical Modelling and Applications (Volume 5, Issue 4)

Received: 31 August 2020 Accepted: 12 October 2020 Published: 16 December 2020

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Abstract

In this paper, the problem of ill-posedness of solution in identifying multiple groundwater flow parameters from hydraulic head data and other ancillary data was assessed. The solution approach to the parameter identification problem is sought by applying the Least Squares, the Adjoint, the Conjugate Gradient Method and a proposed Parameter Transformation Method. Numerical test for a 1D and 2D flow models governed by PDEs were used to assess the accuracy and stability of the proposed method. The proposed method gave an appreciable solution estimates with minimal error-norm compared with the o ptimisation techniques explored in the study as a measure to the PTM The results revealed that when the adapted methods and the PTM were simulated numerically on a 1D and 2D test problems, the PTM gave a more stable solution estimates with a residual norm-error value of 2.23500 for the 1D test problem compared with that of the Adjoint method which prove to be the comparing solution with a norm-error value of 2.66500. For the 2D test case, the results also revealed that the PTM was stable with a residual norm-error value of 10.98310 compared with that of the Conjugate Gradient method with value of 86.562. Thus in conclusion, the study revealed that the PTM is capable of yielding realistic solution estimates compared with the studied optimisation methods.

Published in	Mathematical Modelling and Applications (Volume 5, Issue 4)
DOI	10.11648/j.mma.20200504.11
Page(s)	202-213
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Ill-Posed Problem, Parameter Transformation Method, Optimisation Techniques

References

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APA Style

Joseph Acquah, Francis Benyah, Jerry Samuel Yao-Kuma. (2020). A Parameter Estimation Technique for a Groundwater Flow Model. Mathematical Modelling and Applications, 5(4), 202-213. https://doi.org/10.11648/j.mma.20200504.11

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ACS Style

Joseph Acquah; Francis Benyah; Jerry Samuel Yao-Kuma. A Parameter Estimation Technique for a Groundwater Flow Model. Math. Model. Appl. 2020, 5(4), 202-213. doi: 10.11648/j.mma.20200504.11

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AMA Style

Joseph Acquah, Francis Benyah, Jerry Samuel Yao-Kuma. A Parameter Estimation Technique for a Groundwater Flow Model. Math Model Appl. 2020;5(4):202-213. doi: 10.11648/j.mma.20200504.11

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@article{10.11648/j.mma.20200504.11,
  author = {Joseph Acquah and Francis Benyah and Jerry Samuel Yao-Kuma},
  title = {A Parameter Estimation Technique for a Groundwater Flow Model},
  journal = {Mathematical Modelling and Applications},
  volume = {5},
  number = {4},
  pages = {202-213},
  doi = {10.11648/j.mma.20200504.11},
  url = {https://doi.org/10.11648/j.mma.20200504.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20200504.11},
  abstract = {In this paper, the problem of ill-posedness of solution in identifying multiple groundwater flow parameters from hydraulic head data and other ancillary data was assessed. The solution approach to the parameter identification problem is sought by applying the Least Squares, the Adjoint, the Conjugate Gradient Method and a proposed Parameter Transformation Method. Numerical test for a 1D and 2D flow models governed by PDEs were used to assess the accuracy and stability of the proposed method. The proposed method gave an appreciable solution estimates with minimal error-norm compared with the o ptimisation techniques explored in the study as a measure to the PTM The results revealed that when the adapted methods and the PTM were simulated numerically on a 1D and 2D test problems, the PTM gave a more stable solution estimates with a residual norm-error value of 2.23500 for the 1D test problem compared with that of the Adjoint method which prove to be the comparing solution with a norm-error value of 2.66500. For the 2D test case, the results also revealed that the PTM was stable with a residual norm-error value of 10.98310 compared with that of the Conjugate Gradient method with value of 86.562. Thus in conclusion, the study revealed that the PTM is capable of yielding realistic solution estimates compared with the studied optimisation methods.},
 year = {2020}
}

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TY  - JOUR
T1  - A Parameter Estimation Technique for a Groundwater Flow Model
AU  - Joseph Acquah
AU  - Francis Benyah
AU  - Jerry Samuel Yao-Kuma
Y1  - 2020/12/16
PY  - 2020
N1  - https://doi.org/10.11648/j.mma.20200504.11
DO  - 10.11648/j.mma.20200504.11
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 202
EP  - 213
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20200504.11
AB  - In this paper, the problem of ill-posedness of solution in identifying multiple groundwater flow parameters from hydraulic head data and other ancillary data was assessed. The solution approach to the parameter identification problem is sought by applying the Least Squares, the Adjoint, the Conjugate Gradient Method and a proposed Parameter Transformation Method. Numerical test for a 1D and 2D flow models governed by PDEs were used to assess the accuracy and stability of the proposed method. The proposed method gave an appreciable solution estimates with minimal error-norm compared with the o ptimisation techniques explored in the study as a measure to the PTM The results revealed that when the adapted methods and the PTM were simulated numerically on a 1D and 2D test problems, the PTM gave a more stable solution estimates with a residual norm-error value of 2.23500 for the 1D test problem compared with that of the Adjoint method which prove to be the comparing solution with a norm-error value of 2.66500. For the 2D test case, the results also revealed that the PTM was stable with a residual norm-error value of 10.98310 compared with that of the Conjugate Gradient method with value of 86.562. Thus in conclusion, the study revealed that the PTM is capable of yielding realistic solution estimates compared with the studied optimisation methods.
VL  - 5
IS  - 4
ER  -

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Author Information

Joseph Acquah

Mathematical Sciences Department, University of Mines and Technology (UMaT), Tarkwa, Ghana
Francis Benyah

Mathematics and Statistics Department, University of Cape Coast (UCC), Cape Coast, Ghana
Jerry Samuel Yao-Kuma

Geological Engineering Department, University of Mines and Technology (UMaT), Tarkwa, Ghana

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Plain Text BibTeX RIS

APA Style

Joseph Acquah, Francis Benyah, Jerry Samuel Yao-Kuma. (2020). A Parameter Estimation Technique for a Groundwater Flow Model. Mathematical Modelling and Applications, 5(4), 202-213. https://doi.org/10.11648/j.mma.20200504.11

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ACS Style

Joseph Acquah; Francis Benyah; Jerry Samuel Yao-Kuma. A Parameter Estimation Technique for a Groundwater Flow Model. Math. Model. Appl. 2020, 5(4), 202-213. doi: 10.11648/j.mma.20200504.11

Copy | Download

AMA Style

Joseph Acquah, Francis Benyah, Jerry Samuel Yao-Kuma. A Parameter Estimation Technique for a Groundwater Flow Model. Math Model Appl. 2020;5(4):202-213. doi: 10.11648/j.mma.20200504.11

Copy | Download

@article{10.11648/j.mma.20200504.11,
  author = {Joseph Acquah and Francis Benyah and Jerry Samuel Yao-Kuma},
  title = {A Parameter Estimation Technique for a Groundwater Flow Model},
  journal = {Mathematical Modelling and Applications},
  volume = {5},
  number = {4},
  pages = {202-213},
  doi = {10.11648/j.mma.20200504.11},
  url = {https://doi.org/10.11648/j.mma.20200504.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20200504.11},
  abstract = {In this paper, the problem of ill-posedness of solution in identifying multiple groundwater flow parameters from hydraulic head data and other ancillary data was assessed. The solution approach to the parameter identification problem is sought by applying the Least Squares, the Adjoint, the Conjugate Gradient Method and a proposed Parameter Transformation Method. Numerical test for a 1D and 2D flow models governed by PDEs were used to assess the accuracy and stability of the proposed method. The proposed method gave an appreciable solution estimates with minimal error-norm compared with the o ptimisation techniques explored in the study as a measure to the PTM The results revealed that when the adapted methods and the PTM were simulated numerically on a 1D and 2D test problems, the PTM gave a more stable solution estimates with a residual norm-error value of 2.23500 for the 1D test problem compared with that of the Adjoint method which prove to be the comparing solution with a norm-error value of 2.66500. For the 2D test case, the results also revealed that the PTM was stable with a residual norm-error value of 10.98310 compared with that of the Conjugate Gradient method with value of 86.562. Thus in conclusion, the study revealed that the PTM is capable of yielding realistic solution estimates compared with the studied optimisation methods.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - A Parameter Estimation Technique for a Groundwater Flow Model
AU  - Joseph Acquah
AU  - Francis Benyah
AU  - Jerry Samuel Yao-Kuma
Y1  - 2020/12/16
PY  - 2020
N1  - https://doi.org/10.11648/j.mma.20200504.11
DO  - 10.11648/j.mma.20200504.11
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 202
EP  - 213
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20200504.11
AB  - In this paper, the problem of ill-posedness of solution in identifying multiple groundwater flow parameters from hydraulic head data and other ancillary data was assessed. The solution approach to the parameter identification problem is sought by applying the Least Squares, the Adjoint, the Conjugate Gradient Method and a proposed Parameter Transformation Method. Numerical test for a 1D and 2D flow models governed by PDEs were used to assess the accuracy and stability of the proposed method. The proposed method gave an appreciable solution estimates with minimal error-norm compared with the o ptimisation techniques explored in the study as a measure to the PTM The results revealed that when the adapted methods and the PTM were simulated numerically on a 1D and 2D test problems, the PTM gave a more stable solution estimates with a residual norm-error value of 2.23500 for the 1D test problem compared with that of the Adjoint method which prove to be the comparing solution with a norm-error value of 2.66500. For the 2D test case, the results also revealed that the PTM was stable with a residual norm-error value of 10.98310 compared with that of the Conjugate Gradient method with value of 86.562. Thus in conclusion, the study revealed that the PTM is capable of yielding realistic solution estimates compared with the studied optimisation methods.
VL  - 5
IS  - 4
ER  -

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