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New Hybrid Method to Model Extreme Rainfalls

Authors: A. Amar, Y. Laaroussi, Z. Guennoun


Modeling and forecasting dynamics of rainfall occurrences constitute one of the major topics, which have been largely treated by statisticians, hydrologists, climatologists and many other groups of scientists. In the same issue, we propose, in the present paper, a new hybrid method, which combines Extreme Values and fractal theories. We illustrate the use of our methodology for transformed Emberger Index series, constructed basing on data recorded in Oujda (Morocco). The index is treated at first by Peaks Over Threshold (POT) approach, to identify excess observations over an optimal threshold u. In the second step, we consider the resulting excess as a fractal object included in one dimensional space of time. We identify fractal dimension by the box counting. We discuss the prospect descriptions of rainfall data sets under Generalized Pareto Distribution, assured by Extreme Values Theory (EVT). We show that, despite of the appropriateness of return periods given by POT approach, the introduction of fractal dimension provides accurate interpretation results, which can ameliorate apprehension of rainfall occurrences.

Keywords: extreme values theory, fractals dimensions, rainfall occurrences, Peaks Over Threshold

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[1] A. mirataee, B., Montaseri, M. and Rezaei, H., “Assessment of goodness of fit methods in determining the best regional probability distribution of rainfall data” International Journal of Engineering-Transactions A: Basics, Vol. 27, No. 10, (2014), pp. 1537-1546.
[2] Evin, G. and Favre, A.C., “Further developments of a transient Poissoncluster model for rainfall”, Stochastic environmental research and risk assessment, vol. 27, (2013), pp. 831-847.
[3] Koutsoyiannis, D., “Statistics of extremes and estimation of extreme rainfall”, Theoretical investigation. Hydrological Sciences Journal, vol. 49, (2004), pp. 575–590.
[4] Ceresetti, D., Anquetin, S., Molinie, G., Leblois, E. and Creutin, J. D., “Multiscale Evaluation of Extreme Rainfall Event Predictions Using Severity Diagrams”, Weather and Forecasting, vol. 27, (2012), pp. 174- 188.
[5] Barkotulla, M. A. B., “Stochastic Generation of the Occurrence and Amount of Daily Rainfall”. Department of Crop Science and Technology University of Rajshahi Rajshahi-6205, Bangladesh. Pak.j.stat.oper.res, vol. 6, No. 1, (2010), pp. 61-73.
[6] Sayang, M. D. and Jemain, A. A., “Fitting the distribution of dry and wet spells with alternative probability models”. Meteorology and Atmospheric Physics, vol. 104, (2009), pp. 13-27.
[7] Masala and Giovanni, “Rainfall derivatives pricing with an underlying semi-Markov model for precipitation occurrences”. Stochastic Environmental Research and Risk Assessment, vol. 28, (2014), pp. 717 – 727.
[8] Vidal, I., “A Bayesian analysis of the Gumbel distribution: an application to extreme rainfall data”. Stochastic Environmental Research and Risk Assessment, vol. 28, (2014), pp. 571-582.
[9] Andrés, M. A., Patricia, Z. B. and Manuel, G. S., “Comparing Generalized Pareto models fitted to extreme observations: an application to the largest temperatures in Spain”. Stochastic Environmental Research and Risk Assessment, vol. 28, (2014), pp. 1221-1233.
[10] Christidis, Nikolaos, Peter A., Adam, S., Scaife, A., Alberto, A., Gareth, S. J., Dan, C., Jeff, R. K. and Warren, J. T., “A New HadGEM3-ABased System for Attribution of Weather and Climate-Related Extreme Events”. Journal of Climate, vol. 26, (2013), pp. 2756-2783.
[11] Hristidis, N., Stott, P.A., Scaife, A., Arribas, A., Jones, G.S., Copsey, D., Knight, J. R. and Tennant, W. J., “A new HadGEM3-A-based system for attribution of weather and climate-related extreme events”, Journal of Climate, vol. 26, (2013), pp. 2756–2783.
[12] Zu-Guo, Y., Yee, L., Yongqin, D. C., Qiang, Z., Vo, A. and Yu, Z., “Multifractal analyses of daily rainfall time series in Pearl River basin of China”, Physica A: Statistical Mechanics and its Applications, vol. 405, (2014), pp. 193-202.
[13] MORAT, Ph., “Note sur l'application à Madagascar du quotient pluviomètre d'Emberger”, Cah., ORSTOM, sér.bio1., vol. 10, (1969), pp. 117-132.
[14] Shaw, E. M., “Hydrology in Practice”. Second Edition, Van Nostrand Reinhold (Intemational), London, United Kingdom, (1988).
[15] Cook, G. D. and Heerdegen, R. G., “Spatial variation in the duration of the rainy season in monsoonal Australia”, International Journal of Climatology, vol.21, (2001), pp. 1723–1732.
[16] Moon, S. E., Ryoo, S. B. and Kwon, J. G., “A Markov chain model for daily precipitation occurrence in South Korea”, International Journal of Climatology, vol. 14, (1994), pp. 1009–1016.
[17] Reiser, H. and Kutiel, H., “Rainfall uncertainty in the Mediterranean: definitions of the daily rainfall threshold (DRT) and the rainy season length (RSL)”, Theoretical and Applied Climatolology, vol. 97, (2008), pp. 151-162.
[18] Reiser, H. and Kutiel, H., “Rainfall uncertainty in the Mediterranean: definition of the rainy season – a methodological approach”, Theoretical and Applied Climatolology, vol. 94, (2008), pp. 35-49.
[19] Zoglat, A., El Adlouni, S., Badaoui, F., Amar, A. and Okou, “Managing hydrological risk with extreme modeling: application of peaks over threshold model to the Lokkous basin”. Journal of Hydrologic Engineering, vol. 19, (2014).
[20] Naveau, P., Nogaj, M., Ammann, C., Yiou, P., Cooley, D. and Jomelli, V., “Statistical methods for the analysis of climate extremes”, Comptes Rendus Geoscience, vol. 337, (2005), pp. 1013– 1022.
[21] Deidda, R., “A multiple threshold method for fitting the generalized Pareto distribution to rainfall time series”, Hydrology and Earth System Sciences, vol. 14, (2010), pp. 2559-2575.
[22] Jibrael, F. J., “Multiband Cross Dipole Antenna Based On the Triangular and Quadratic Fractal Koch Curve”, International Journal of Engineering, Vol. 4, (1991).
[23] Anisheh, S.M. and Hassanpour, H., “adaptive segmentation with optimal window length scheme using fractal dimension and wavelet transform”, International Journal of Engineering, Transactions B: Applications, Vol. 22, No.3 (2009).
[24] Tricot, C., “Curves and Fractal Dimension”, Springer-Verlag, (1995).