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

Received: 3 October 2019     Accepted: 26 May 2020     Published: 8 June 2020
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
 [1] Palmer T. (2000) Shadowing in Dynamical Systems. Theory and Applications. Dordrecht: Kluwer, 299-313. [2] Panchev S, Spassova T (2005) Simple general circulation and climate models with memory. Advances in Atmospheric Sciences 22: 765–769. [3] Lea D, Allen M, Haine T (2000) Sensitivity analysis of the climate of a chaotic system. Tellus 52A: 523–532. [4] Soldatenko S, Steinle P, Tingwell C, Chichkine D (2015) Some aspects of sensitivity analysis in variational data assimilation for coupled dynamical systems. Advances in Meteorology 2015: 1–22. [5] Soldatenko S, Chichkine D (2014) Correlation and spectral properties of a coupled nonlinear dynamical system in the context of numerical weather prediction and climate modeling. Discrete Dynamics in Nature and Society 2014: 498184. [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. [11] Han J., Elimera D. A, Melaaena M. C. (2013). Liquid phase mass transfer coefficient of carbon dioxide absorption by water droplet, Energy procedia, 37: 1728-1735. [12] Bai and Yeh, (1997; Removal of CO2 greenhouse gs by ammonia scrubbing Industrial and Engineering Chemistry Research. 36 (6): 2490-2493. [13] Resnik K. P., Yeh J. T, Pennline H. W. (2004); Aqua ammonia process for simultaneous removal of CO2, SO2 and NOx. International Journal of Environmental Technology and Management, 4 (1/2): 89-104. [14] Zeman and Lackner, (2004); Capturing carbon dioxide directly from the atmosphere. World Resource Review, 16 (2): 157-172. [15] Stolaroff J. K, Keith D, W, Lowry G. V. (2008). Carbon dioxide capture from atmospheric air using sodium hydroxide spray. Environmental Science and Technology, 42: 2728-2735. [16] Yeh AC, Bai H. (1999). Comparison of ammonia and monoethanolamine solvents to reduce CO2 greenhouse gas emissions. Science of the Total Environment, 228 (2-3): 121-133. [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.
• 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

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

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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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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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.
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Author Information
• Department of Mathematics and Statistics, University of Port Harcourt, Port Harcourt, Nigeria

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

• Sections