A Computational Approach to a Mathematical Model of Climate Change Using Heat Sources and Diffusion

Muhammad Shoaib Arif; Kamaleldin Abodayeh; Yasir Nawaz

doi:10.28991/CEJ-2022-08-07-04

Authors

Muhammad Shoaib Arif
marif@psu.edu.sa
Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh,, Saudi Arabia https://orcid.org/0000-0002-6009-5609
Kamaleldin Abodayeh Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh,, Saudi Arabia https://orcid.org/0000-0003-0735-6520
Yasir Nawaz Department of Mathematics, Air University, PAF Complex E-9, Islamabad 44000,, Pakistan https://orcid.org/0000-0002-7048-574X

Vol. 8 No. 7 (2022): July

Research Articles

Downloads

PDF

Abstract
How to Cite
Metrics
References
License

The present work aims to extend the climate change energy balance models using a heat source. An ordinary differential equations (ODEs) model is extended to a partial differential equations (PDEs) model using the effects of diffusion over the spatial variable. In addition, numerical schemes are presented using the Taylor series expansions. For the climate change model in the form of ODEs, a comparison of the presented scheme is made with the existing Trapezoidal method. It is found that the presented scheme converges faster than the existing scheme. Also, the proposed scheme provides fewer errors than the existing scheme. The PDEs model is also solved with the presented scheme, and the results are displayed in the form of different graphs. The impact of the climate feedback parameter, the heat uptake parameter of the deep ocean, and the heat source parameter on global mean surface temperature and deep ocean temperature is also portrayed. In addition, these recently developed techniques exhibit a high level of predictability.

Doi: 10.28991/CEJ-2022-08-07-04

Full Text: PDF

Arif, M. S., Abodayeh, K., & Nawaz, Y. (2022). A Computational Approach to a Mathematical Model of Climate Change Using Heat Sources and Diffusion. Civil Engineering Journal, 8(7), 1358–1368. https://doi.org/10.28991/CEJ-2022-08-07-04

Download Citation

[1] Stroud, K. A., & Booth, D. J. (2009). Essential Mathematics for Science and Technology. Industrial Press, South Norwalk, United States.
[2] Riley, K. F., & Hobson, M. P. (2006). Student Solutions Manual for Mathematical Methods for Physics and Engineering. doi:10.1017/cbo9780511816130.
[3] Yevick, D., & Yevick, H. (2014). Fundamental Math and Physics for Scientists and Engineers. John Wiley & Sons, Hoboken, United States. doi:10.1002/9781118979792.
[4] Harshbarger, R. J., & Reynolds, J. J. (2012). Mathematical applications for the management, life, and social sciences. Cengage Learning, Boston, United States.
[5] Yang, X. S. (2009). Introductory mathematics for earth scientists. Dunedin, Edinburg, Scotland.
[6] Bröcker, J., Calderhead, B., Cheraghi, D., Cotter, C., Holm, D. D., Kuna, T., ... & Weller, H. (2017). Mathematics of Planet Earth: A Primer. World Scientific, Singapore. doi:10.1142/q0111.
[7] Stocker, T. F., Qin, D., Plattner, G. K., Tignor, M. M., Allen, S. K., Boschung, J., ... & Midgley, P. M. (2014). Climate Change 2013: The physical science basis. Contribution of working group I to the fifth assessment report of IPCC the intergovernmental panel on climate change. Cambridge University press, Cambridge, United Kingdom.
[8] Masson-Delmotte, V., Zhai, P., Pirani, A., Connors, S. L., Péan, C., Berger, S., ... & Zhou, B. (2021.) Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, United Kingdom.
[9] NOAA. (2018). State of the Climate. Global Climate Report. December 2018. National Centers for Environmental Information. Available online: www.ncdc.noaa.gov/sotc/global/201812 (accessed on March 2022).
[10] Soldatenko, S., Yusupov, R., & Colman, R. (2020). Cybernetic approach to problem of interaction between nature and human sosiety in context of unprecedented climate change. SPIIRAS Proceedings, 19(1), 5–42. doi:10.15622/sp.2020.19.1.1. (In Russian).
[11] Osipov, V., Kuleshov, S., Zaytseva, A., & Aksenov, A. (2021). Approach for the COVID-19 epidemic source localization in Russia based on mathematical modeling. Informatics and Automation, 20(5), 1065–1089. doi:10.15622/20.5.3. (In Russian).
[12] Simpson, N. P., Mach, K. J., Constable, A., Hess, J., Hogarth, R., Howden, M., ... & Trisos, C. H. (2021). A framework for complex climate change risk assessment. One Earth, 4(4), 489-501. doi:10.1016/j.oneear.2021.03.005.
[13] Soldatenko, S. A., & Alekseev, G. V. (2020). Managing climate risks associated with socio-economic development of the Russian Arctic. IOP Conference Series: Earth and Environmental Science, 606(1), 12060. doi:10.1088/1755-1315/606/1/012060.
[14] Taylor, K. E., Stouffer, R. J., & Meehl, G. A. (2012). An overview of CMIP5 and the experiment design. Bulletin of the American Meteorological Society, 93(4), 485–498. doi:10.1175/BAMS-D-11-00094.1.
[15] Meehl, G. A., Stocker, T. F., Collins, W. D., Friedlingstein, P. I. E. R. R. E., Gaye, A. T., Gregory, J. M., ... & Zhao, Z. C. (2007). Global climate projections. Climate change 2007: the physical science basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, United Kingdom.
[16] Collins, M., Knutti, R., Arblaster, J., Dufresne, J. L., Fichefet, T., Friedlingstein, P., ... & Booth, B. B. (2013). Long-term climate change: projections, commitments and irreversibility. Climate change 2013-The physical science basis: Contribution of working group I to the fifth assessment report of the intergovernmental panel on climate change, 1029-1136, Cambridge University Press, Cambridge, United Kingdom.
[17] Flato, G., Marotzke, J., Abiodun, B., Braconnot, P., Chou, S. C., Collins, W., ... & Rummukainen, M. (2014). Evaluation of climate models. Climate change 2013: the physical science basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, 741-866, Cambridge University Press, Cambridge, United Kingdom.
[18] Grose, M. R., Gregory, J., Colman, R., & Andrews, T. (2018). What Climate Sensitivity Index Is Most Useful for Projections? Geophysical Research Letters, 45(3), 1559–1566. doi:10.1002/2017GL075742.
[19] Colman, R., & Soldatenko, S. (2020). Understanding the links between climate feedbacks, variability and change using a two-layer energy balance model. Climate Dynamics, 54(7–8), 3441–3459. doi:10.1007/s00382-020-05189-3.
[20] Kaper, H., & Engler, H. (2013). Mathematics and climate. Society for Industrial and Applied Mathematics, Philadelphia, United States. doi:10.1137/1.9781611972610.
[21] Shen, S. S. P., & Somerville, R. C. J. Climate Mathematics: Theory and Applications (1st Ed.). Cambridge University Press, Cambridge, United Kingdom. doi:10.1017/9781108693882.
[22] Soldatenko, S. A. (2017). Weather and climate manipulation as an optimal control for adaptive dynamical systems. Complexity, 2017, 1-12. doi:10.1155/2017/4615072.
[23] Lynch, P. (2008). The origins of computer weather prediction and climate modeling. Journal of Computational Physics, 227(7), 3431–3444. doi:10.1016/j.jcp.2007.02.034.
[24] Harper, K., Uccellini, L. W., Kalnay, E., Carey, K., & Morone, L. (2007). Symposium of the 50th anniversary of operational numerical weather prediction. Bulletin of the American Meteorological Society, 88(5), 639–650. doi:10.1175/BAMS-88-5-639.
[25] Charney, J. G., FjÖrtoft, R., & Neumann, J. Von. (1950). Numerical Integration of the Barotropic Vorticity Equation. Tellus 2(4), 237–254. doi:10.3402/tellusa.v2i4.8607.
[26] Lohmann, G. (2020). Temperatures from energy balance models: The effective heat capacity matters. Earth System Dynamics, 11(4), 1195–1208. doi:10.5194/esd-11-1195-2020.
[27] Lovejoy, S. (2021). The half-order energy balance equation - Part 2: The inhomogeneous HEBE and 2D energy balance models. Earth System Dynamics, 12(2), 489–511. doi:10.5194/esd-12-489-2021.
[28] Chang, S., Wang, J., & Wang, X. (2015). A fitted finite volume method for real option valuation of risks in climate change. Computers and Mathematics with Applications, 70(5), 1198–1219. doi:10.1016/j.camwa.2015.07.003.
[29] Vilar, M. L., Tello, L., Hidalgo, A., & Bedoya, C. (2021). An energy balance model of heterogeneous extensive green roofs. Energy and Buildings, 250, 111265. doi:10.1016/j.enbuild.2021.111265.
[30] Budyko, M. I. (1969). The effect of solar radiation variations on the climate of the Earth. Tellus, 21(5), 611–619. doi:10.3402/tellusa.v21i5.10109.
[31] Alrwashdeh, S. S., Ammari, H., Madanat, M. A., & Al-Falahat, A. A. M. (2022). The effect of heat exchanger design on heat transfer rate and temperature distribution. Emerging Science Journal, 6(1), 128-137. doi:10.28991/esj-2022-06-01-010.
[32] Soldatenko, S., Bogomolov, A., & Ronzhin, A. (2021). Mathematical modelling of climate change and variability in the context of outdoor ergonomics. Mathematics, 9(22), 2920. doi:10.3390/math9222920.
[33] Nawaz, Y., Arif, M. S., & Abodayeh, K. (2022). An explicit-implicit numerical scheme for time fractional boundary layer flows. International Journal for Numerical Methods in Fluids, 94(7), 920–940. doi:10.1002/fld.5078.
[34] Nawaz, Y., Arif, M. S., & Shatanawi, W. (2022). A New Numerical Scheme for Time Fractional Diffusive SEAIR Model with Non-Linear Incidence Rate: An Application to Computational Biology. Fractal and Fractional, 6(2), 78. doi:10.3390/fractalfract6020078.

Publication Start Year:	2015
JCR 2023 Impact Factor (IF):	4.3
JIF QUARTILE:	Q1
SJR 2023 Quartile:	Q1
Acceptance Rate:	27%
Review Speed (Average):	76 days
Issue Per Year:	12
Number of Volumes:	10
Number of Issues:	107
Number of Articles:	1552
Number of Reviewers:	3417
Number of Contributors:	3604
Contributing Countries:	86
No. of WoS Citations:	7986
WoS h-index:	34
Scopus CiteScore:	7.0
No. of Google Citations:	17324
Google h-index:	47
Google i10-index:	393
Abstract Views:	5,819,908
PDF Download:	3,790,637

A Computational Approach to a Mathematical Model of Climate Change Using Heat Sources and Diffusion

Authors

Downloads

Login

Publisher and Affiliated Societies

Publisher & Affiliated Societies

Indexing & Abstracting

SidebarMenu

Journal Imprint

Journal Imprint

Journal Metrics

IndexedBy

Indexed In

Follow us

Follow Us

Most Cited Articles

Heavy Metal Removal Investigation in Conventional Activated Sludge Systems

Modeling of the Solar Thermal Energy Use in Urban Areas

Adsorption Behavior of Heavy Metal Ions by Hybrid Inulin-TEOS for Water Treatment

Modeling Finned Thermal Collector Construction Nanofluid-based Al2O3 to Enhance Photovoltaic Performance

visitors

Analytics

Information

Address

Contact Info: