Parametric Sensitivity Analysis of a Mathematical Model of the Effect of CO<sub>2</sub> on the Climate Change

Bazuaye Frank Etin-Osa; Ijomah Maxwell Azubike

doi:doi:10.11648/j.acm.20200903.16

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Parametric Sensitivity Analysis of a Mathematical Model of the Effect of CO₂ on the Climate Change

Bazuaye Frank Etin-Osa, Ijomah Maxwell Azubike

Published in Applied and Computational Mathematics (Volume 9, Issue 3)

Received: 3 October 2019 Accepted: 26 May 2020 Published: 8 June 2020

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Abstract

Mathematical modeling is a very powerful tool for the study and understanding of the climate system. Modern climate models used in different applications are derived from a set of many-dimensional nonlinear differential equations in partial derivatives. The Climate models contain a wide number of model parameters that can describe external forcing that can strongly affect the behavior of the climate. It is imperative to estimate the influence of variations in parameters on climate change. The methods of 1-norm, 2-norm, and infinity-norm were used to quantify different forms of the sensitivity of model parameters. The approach applied in this research involves coding the given system of continuous non-linear first order ordinary differential equation in a Matlab solver, modifying and coding a similar program which is used for a variation of a single parameter one-at-a-time while other model parameters are fixed. Finally, the program is used to calculate the 1-norm, 2-norm, 3-norm and infinity norm of the solution trajectories in the same manner. The study shows that the most sensitivity parameters in the model are the concentration of a suitable absorbent and the rate of inflow of absorbent in the absorption chamber.

Published in	Applied and Computational Mathematics (Volume 9, Issue 3)
DOI	10.11648/j.acm.20200903.16
Page(s)	96-101
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), 2020. Published by Science Publishing Group

Keywords

Sensitivity Analysis, Mathematical Model, Climate Change

References

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[6]	McGuffie K, Henderson-Sellers A (2014), The Climate Modeling Premier. 4th edition. New York: Wiley-Blackwell, 456 p.
[7]	Barry RG, Hall-McKim EA (2014). Essentials of the Earth’s Climate System. New York: Cambridge University Press, 271 p.
[8]	Goosse H (2015). Climate System Dynamics and Modeling. New York: Cambridge University Press, 378 p.
[9]	Rosenwasser E, Yusupov R (2000) Sensitivity of Automatic Control Systems. Boca Raton: CRC Press, 456 p.
[10]	Chang, C.-P.; Ghil, M.; Kuo, H.-C.; Latif, M.; Sui, C.-H.; Wallace, J. M (2014), Understanding multi decadal climate changes. Bull. Am. Meteorol. Soc., made a theoretical analysis.
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[17]	E. Ekaka-a, E. C. Nwachukwu, N. M. Nafo, I. A. Agwu (2013), Parametric sensitivity analysis of a mathematical model of facultative mutualism. IOSR Journal of Mathematics (IOSR) Volume 7, Issue 2 (Jul. - Aug. 2013), PP 19-22.

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Bazuaye Frank Etin-Osa, Ijomah Maxwell Azubike. (2020). Parametric Sensitivity Analysis of a Mathematical Model of the Effect of CO2 on the Climate Change. Applied and Computational Mathematics, 9(3), 96-101. https://doi.org/10.11648/j.acm.20200903.16

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Bazuaye Frank Etin-Osa; Ijomah Maxwell Azubike. Parametric Sensitivity Analysis of a Mathematical Model of the Effect of CO2 on the Climate Change. Appl. Comput. Math. 2020, 9(3), 96-101. doi: 10.11648/j.acm.20200903.16

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AMA Style

Bazuaye Frank Etin-Osa, Ijomah Maxwell Azubike. Parametric Sensitivity Analysis of a Mathematical Model of the Effect of CO2 on the Climate Change. Appl Comput Math. 2020;9(3):96-101. doi: 10.11648/j.acm.20200903.16

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@article{10.11648/j.acm.20200903.16,
  author = {Bazuaye Frank Etin-Osa and Ijomah Maxwell Azubike},
  title = {Parametric Sensitivity Analysis of a Mathematical Model of the Effect of CO2 on the Climate Change},
  journal = {Applied and Computational Mathematics},
  volume = {9},
  number = {3},
  pages = {96-101},
  doi = {10.11648/j.acm.20200903.16},
  url = {https://doi.org/10.11648/j.acm.20200903.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20200903.16},
  abstract = {Mathematical modeling is a very powerful tool for the study and understanding of the climate system. Modern climate models used in different applications are derived from a set of many-dimensional nonlinear differential equations in partial derivatives. The Climate models contain a wide number of model parameters that can describe external forcing that can strongly affect the behavior of the climate. It is imperative to estimate the influence of variations in parameters on climate change. The methods of 1-norm, 2-norm, and infinity-norm were used to quantify different forms of the sensitivity of model parameters. The approach applied in this research involves coding the given system of continuous non-linear first order ordinary differential equation in a Matlab solver, modifying and coding a similar program which is used for a variation of a single parameter one-at-a-time while other model parameters are fixed. Finally, the program is used to calculate the 1-norm, 2-norm, 3-norm and infinity norm of the solution trajectories in the same manner. The study shows that the most sensitivity parameters in the model are the concentration of a suitable absorbent and the rate of inflow of absorbent in the absorption chamber.},
 year = {2020}
}

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TY  - JOUR
T1  - Parametric Sensitivity Analysis of a Mathematical Model of the Effect of CO2 on the Climate Change
AU  - Bazuaye Frank Etin-Osa
AU  - Ijomah Maxwell Azubike
Y1  - 2020/06/08
PY  - 2020
N1  - https://doi.org/10.11648/j.acm.20200903.16
DO  - 10.11648/j.acm.20200903.16
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 96
EP  - 101
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20200903.16
AB  - Mathematical modeling is a very powerful tool for the study and understanding of the climate system. Modern climate models used in different applications are derived from a set of many-dimensional nonlinear differential equations in partial derivatives. The Climate models contain a wide number of model parameters that can describe external forcing that can strongly affect the behavior of the climate. It is imperative to estimate the influence of variations in parameters on climate change. The methods of 1-norm, 2-norm, and infinity-norm were used to quantify different forms of the sensitivity of model parameters. The approach applied in this research involves coding the given system of continuous non-linear first order ordinary differential equation in a Matlab solver, modifying and coding a similar program which is used for a variation of a single parameter one-at-a-time while other model parameters are fixed. Finally, the program is used to calculate the 1-norm, 2-norm, 3-norm and infinity norm of the solution trajectories in the same manner. The study shows that the most sensitivity parameters in the model are the concentration of a suitable absorbent and the rate of inflow of absorbent in the absorption chamber.
VL  - 9
IS  - 3
ER  -

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Author Information

Bazuaye Frank Etin-Osa

Department of Mathematics and Statistics, University of Port Harcourt, Port Harcourt, Nigeria
Ijomah Maxwell Azubike

Department of Mathematics and Statistics, University of Port Harcourt, Port Harcourt, Nigeria

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APA Style

Bazuaye Frank Etin-Osa, Ijomah Maxwell Azubike. (2020). Parametric Sensitivity Analysis of a Mathematical Model of the Effect of CO2 on the Climate Change. Applied and Computational Mathematics, 9(3), 96-101. https://doi.org/10.11648/j.acm.20200903.16

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ACS Style

Bazuaye Frank Etin-Osa; Ijomah Maxwell Azubike. Parametric Sensitivity Analysis of a Mathematical Model of the Effect of CO2 on the Climate Change. Appl. Comput. Math. 2020, 9(3), 96-101. doi: 10.11648/j.acm.20200903.16

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AMA Style

Bazuaye Frank Etin-Osa, Ijomah Maxwell Azubike. Parametric Sensitivity Analysis of a Mathematical Model of the Effect of CO2 on the Climate Change. Appl Comput Math. 2020;9(3):96-101. doi: 10.11648/j.acm.20200903.16

Copy | Download

@article{10.11648/j.acm.20200903.16,
  author = {Bazuaye Frank Etin-Osa and Ijomah Maxwell Azubike},
  title = {Parametric Sensitivity Analysis of a Mathematical Model of the Effect of CO2 on the Climate Change},
  journal = {Applied and Computational Mathematics},
  volume = {9},
  number = {3},
  pages = {96-101},
  doi = {10.11648/j.acm.20200903.16},
  url = {https://doi.org/10.11648/j.acm.20200903.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20200903.16},
  abstract = {Mathematical modeling is a very powerful tool for the study and understanding of the climate system. Modern climate models used in different applications are derived from a set of many-dimensional nonlinear differential equations in partial derivatives. The Climate models contain a wide number of model parameters that can describe external forcing that can strongly affect the behavior of the climate. It is imperative to estimate the influence of variations in parameters on climate change. The methods of 1-norm, 2-norm, and infinity-norm were used to quantify different forms of the sensitivity of model parameters. The approach applied in this research involves coding the given system of continuous non-linear first order ordinary differential equation in a Matlab solver, modifying and coding a similar program which is used for a variation of a single parameter one-at-a-time while other model parameters are fixed. Finally, the program is used to calculate the 1-norm, 2-norm, 3-norm and infinity norm of the solution trajectories in the same manner. The study shows that the most sensitivity parameters in the model are the concentration of a suitable absorbent and the rate of inflow of absorbent in the absorption chamber.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Parametric Sensitivity Analysis of a Mathematical Model of the Effect of CO2 on the Climate Change
AU  - Bazuaye Frank Etin-Osa
AU  - Ijomah Maxwell Azubike
Y1  - 2020/06/08
PY  - 2020
N1  - https://doi.org/10.11648/j.acm.20200903.16
DO  - 10.11648/j.acm.20200903.16
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 96
EP  - 101
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20200903.16
AB  - Mathematical modeling is a very powerful tool for the study and understanding of the climate system. Modern climate models used in different applications are derived from a set of many-dimensional nonlinear differential equations in partial derivatives. The Climate models contain a wide number of model parameters that can describe external forcing that can strongly affect the behavior of the climate. It is imperative to estimate the influence of variations in parameters on climate change. The methods of 1-norm, 2-norm, and infinity-norm were used to quantify different forms of the sensitivity of model parameters. The approach applied in this research involves coding the given system of continuous non-linear first order ordinary differential equation in a Matlab solver, modifying and coding a similar program which is used for a variation of a single parameter one-at-a-time while other model parameters are fixed. Finally, the program is used to calculate the 1-norm, 2-norm, 3-norm and infinity norm of the solution trajectories in the same manner. The study shows that the most sensitivity parameters in the model are the concentration of a suitable absorbent and the rate of inflow of absorbent in the absorption chamber.
VL  - 9
IS  - 3
ER  -

Copy | Download