Dynamical System Analysis of Reference Evapotranspiration using Chaos Models in Some Selected States in Northern Nigeria

C. O.  Iyamu; L. W. Lumbi; Ibrahim Inusa Ewa; E. V. Tikyaa

doi:10.62050/ljsir2024.v2n2.340

Authors

C. O. Iyamu Department of Physics, Nasarawa State University, Keffi, Nigeria Author
L. W. Lumbi Department of Physics, Nasarawa State University, Keffi, Nigeria Author
Ibrahim Inusa Ewa Department of Physics, Nasarawa State University, Keffi, Nigeria Author
E. V. Tikyaa Department of Physics, Joseph Sarwuan Tarka University, Makurdi, Benue State, Nigeria Author

DOI:

https://doi.org/10.62050/ljsir2024.v2n2.340

Keywords:

Dynamical System, Evapotranspiration, Chaos, Lyapunov exponents, Seasonal Variation

Abstract

This study analyzed the dynamical system of reference evapotranspiration using chaos and maximum entropy models in some selected states in Northern Nigeria. The study covered 16 states in Northern Nigeria which were selected using purposive sampling techniques. The materials used for the study consist of secondary data of daily mean records of air temperature, wind speed, solar radiation and relative humidity from 1^st January 1984 to December 2022. From the data, the daily reference Evapotranspiration were computed using Penman-Monteith equation. The reference evapotranspiration obtained was further analyzed using Phase portrait, recurrent plot and Lyapunov exponent to characterize the dynamical system. The results showed that the dynamical system has a random and nonlinear trend which is aperiodic. The phase portrait exhibits sponge-like structures having distinct curves which indicates a low degree deterministic chaos. Also, the recurrent plots in 16 states had a dark short diagonal line diagonals and white ribbons which indicates seasonal variations. The largest Lyapunov exponents of the 16 states are all positive and range between 0.001983/day – 0.004419/day. This positive result indicated that the dynamical system is deterministic and chaotic in behavior.

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References

Feddes, R.A. & Raats, P.A.C. (2004). Parametrising the soil-water-plant root system. In Feddes, R., de Rooij, G.H., and Van Dan, J.C. (eds), Unsaturated zone Modelling, Progress, Challenges and Applications. Doordrecht: Kluwer Academic

Novak, V. (2014). Evapotranspiration. Encyclopedia of Agrophysics, pp. 280-283

Tong, L., Kang, S. & Zhang, L. (2007). Temporal and spatial variations of evapotranspiration for spring wheat in the shiyang river basin in northwest China. Agricultural Water Management, 87 (3), 241-250

Schwartz, P. & Randall, D. (2003). An Abrupt climate change scenario and its implications for United States National Security. Abrupt climate change. Pp.23. http://www.iatp.org.documents

Jung, M. (2010). Recent decline in the global land evapotranspiration trend due to limited moisture supply. Nature, 467, 951. https://doi.org/10.1038/nature09396

Lescarmontier, L. (2018). IPCC Special report ‘global warming of 1.50C’ Summary for teachers. Retrieved July 2, 2023 from http://oce.global

Wang, W.G., Zou, S., Luo, Z.H., Zhang, W., Chen, D. & Kong, J. (2014). Prediction of the Reference Evapotranspiration Usinga Chaotic Approach. The Scientific World Journal, 2014, 347625, 1-13. Hindawi Publishing Corporation. http://dx.doi.org/10.1155/2014/347625

Kizi, O., & Zournemat-Kermani, M. (2019). Polynomial chaos expansion and response surface method for nonlinear modeling of reference evapotranspiration. Hydrological Science Journal, 64 (6), 720-730

Allen, R. G., Pereira, L.S., Raes, D. & Smith, M. (1998). Crop evapotranspiration guidelines for computing crop water requirements - FAO Irrigation and drainage.FAO - Food and Agriculture Organization of the United Nations. paper 56

Tableau (2023). Time series forecasting: Definition, Applications and Examples. Retrieved August 5, 2023 from https://www.tableau.com/learn/articles/time-series-forecasting

Lorenz, E.N. (1963). Deterministic non-periodic flow. Journal of the Atmospheric Sciences, 20(2), 130-141

Bishop, R. (2017). Chaos in Zalta, Edward N. (ed.), The Standford Encyclopedia of Philosophy (Spring 2017 ed.). Metaphysics Research Lab, Stanford University

Echi, M.I., Tikyaa, E.V. & Isikwue, B.C. (2015). Dynamics of Rainfall and Temperature in Makurdi. International Journal of Science and Research, 4(7), 493-499

Fuwape, I. A., Ogunjo, S. T., Oluyamo, S. S. & Rabiu, A. B. (2016). Spatial variation of deterministic chaos in mean daily temperature and rainfall over Nigeria. TheorApplClimatol, 3(1), 122-125

Wang, W., Peng, S.Z. & Luo, Y. (2008). Chaotic behavior analysis and prediction of reference crop evapotranspiration. Shuili Xuebaol Journal of Hydraulic Engineering, 39 (9), 1030-1036

Wikipedia (2023). Chaos theory. Retrieved July 26, 2023 from https://en.m.wikipedia.org/wiki/Chaos_theory

Raymond, J. (2018). Dew point equations formulas. Retrieved October 16, 2023 from https://www.ajdesigner.com/phphumidity/dewpoint_equation_dewpoint_temperature

C. O. Iyamu, I. I. Ewa & L.W. Lumbi (2024). Estimation of Reference Evapotranspiration using Penman-Monteith Equation and Time Series Model in Some Selected States in Northern Nigeria. Lafia Journal of Scientific and Industrial Research, 2(2), 67-74. https://doi.org/10.62050/ljsir2024.v2n2.329