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.
[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).
[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).
@article{"International Journal of Earth, Energy and Environmental Sciences:69615", author = "Y. Laaroussi and Z. Guennoun and A. Amar", title = "New Hybrid Method to Model Extreme Rainfalls", abstract = "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, Peaks
Over Threshold, Rainfall occurrences.", volume = "9", number = "4", pages = "331-6", }
