Assessing the Adequacy of Probability Distribution for Extreme Value Analysis of Rainfall and Temperature using Goodness-Of-Fit And Diagnostic Tests

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Scientist-B, Central Water and Power Research Station, Pune, Maharashtra, India.
Periodicity:February - April'2018
DOI : https://doi.org/10.26634/jfet.13.3.14225

Abstract

Assessment of rainfall and temperature for a desired return period is of utmost importance for planning and design of hydraulic structures and also for installation of nuclear power projects. This can be achieved through Extreme Value Analysis (EVA) by fitting of probability distribution to the observed series of meteorological data. This paper illustrates the study on EVA of rainfall and temperature recorded at Mandla observatory adopting Gumbel and Frechet distributions. The annual series of 1-day maximum rainfall, maximum and minimum temperature derived from daily data are used for EVA. The parameters of the probability distributions are determined by order statistics approach and used in EVA. The adequacy of probability distribution is quantitatively assessed by using Goodness-of-Fit (GoF) test viz., Kolmogorov- Smirnov and Diagnostic test, using correlation coefficient and root mean squared error. The GoF and Diagnostic tests’ results show that Gumbel is better suited probability distribution for EVA of rainfall and temperature for the region under study.

Keywords

Correlation, Frechet, Gumbel, Kolmogorov-Smirnov Test, Mean Squared Error.

How to Cite this Article?

Vivekanandan, N. (2018). Assessing the Adequacy of Probability Distribution for Extreme Value Analysis of Rainfall and Temperature using Goodness-Of-Fit And Diagnostic Tests. i-manager’s Journal on Future Engineering and Technology, 13(3), 1-8. https://doi.org/10.26634/jfet.13.3.14225

References

[1]. AERB. (2008). Extreme values of meteorological parameters. Atomic Energy Regulatory Board (AERB) Guide No. NF/SG/ S-3.
[2]. AlHassoun, S. A. (2011). Developing an empirical formulae to estimate rainfall intensity in Riyadh region. Journal of King Saud University Engineering Sciences, 23(1), 81–88.
[3]. Ang, A. H. S., & Tang, W. H. (1984). Probability Concepts in Engineering Planning and Design: Volum IIDecision, Risk, and Reliability. John Wiley & Sons.
[5]. Baratti, E., Montanari, A., Castellarin, A., Salinas, J. L., Viglione, A., & Bezzi, A. (2012). Estimating the flood frequency distribution at seasonal and annual time scales. Hydrology and Earth System Sciences, 16(12), 4651-4660.
[6]. Chen, J., & Adams, B. J. (2006). Integration of artificial neural networks with conceptual models in rainfall-runoff modeling. Journal of Hydrology, 318(1-4), 232-249.
[7]. Esteves, L. S. (2013). Consequences to flood management of using different probability distributions to estimate extreme rainfall. Journal of Environmental Management, 115(1), 98-105.
[8]. Ghorbani, A. M., Ruskeep, A. H., & Singh, V. P., & Sivakumar, B. (2010). Flood frequency analysis using mathematica. Turkish Journal of Engineering and Environmental Sciences, 34(3), 171-188.
[9]. Hughes, G. L., Rao, S. S., & Rao, T. S. (2007). Statistical analysis and time-series models for minimum/maximum temperatures in the Antarctic Peninsula. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (Vol. 463, No. 2077, pp. 241- 259). The Royal Society.
[10]. IAEA. (2003). Meteorological events in site evaluation for nuclear power plants-IAEA Safety Guide (No. Ns-G-3.4). International Atomic Energy Agency (IAEA), Vienna.
[11]. Lieblein, J. (1974). Note on Simplified Estimators for Type-I Extreme Value Distribution (NBSIR 75-647). National Bureau of Standards, U.S. Department of Commerce, Washington D.C.
[12]. Mujere, N. (2011). Flood frequency analysis using the Gumbel distribution. International Journal of Computer Science and Engineering, 3(7), 2774-2778.
[13]. Rao, A. R., & Hameed, K. H. (2000). Flood Frequency Analysis. CRC Publications, Washington, New York.
[14]. Rasel, M. M., & Hossain, S. M. (2015). Development of rainfall intensity duration frequency equations and curves for seven divisions in Bangladesh. International Journal of Scientific & Engineering Research, 6(5), 96- 101.
[15]. Varathan, N., Perera, K., & Nalin (2010). Board of Study in Statistics and Computer Science of the Postgraduate Institute of Science. University of Peradeniya, Sri Lanka.
[16]. Vivekanandan, N., Roy, S. K., & Jagtap, R. S. (2012). Assessment of rainfall and temperature using OSA estimators of extreme value distributions. Bonfring International Journal of Software Engineering and Soft Computing, 2(3), 16-21.
[17]. Vivekanandan, N. (2014). Rainfall frequency analysis using order statistics approach of extreme value distributions. SSRG International Journal of Civil Engineering, 1(4), 6-12.
[18]. Vivekanandan, N. (2015). Modelling of annual extreme rainfall, temperature and wind speed Using OSA of EV1 and EV2 distributions. International Journal of Innovative Research in Computer Science and Technology, 3(4), 57-60.
[19]. Vivekanandan, N. (2016). Statistical analysis of rainfall data and estimation of peak flood discharge for ungauged catchments. International Journal of Research in Engineering and Technology, 5(2), 27-31.
[20]. Vivekanandan, N. (2017). Evaluation of parameter estimation methods of probability distributions for extreme value analysis of temperature. International Journal of Research Studies in Science, Engineering and Technology, 4(8), 1-9.
[21]. Zhang, J. (2002). Powerful goodness of fit tests based on the likelihood ratio. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(2), 281- 294.
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