Potential of plotting positions for intensity-duration-frequency curves with short rainfall records


  • Noratiqah Mohd Ariff Universiti Kebangsaan Malaysia
  • Abdul Aziz Jemain Universiti Kebangsaan Malaysia
  • Mohd Aftar Abu Bakar Universiti Kebangsaan Malaysia




Intensity-duration-frequency (IDF), plotting positions, storm events, L-moment


Intensity-duration-frequency (IDF) curves represent the relationship between storm intensity, storm duration and return period. The IDF curves available are mostly done by fitting series of annual maximum rainfall intensity to parametric distributions. However, the length of annual rainfall records, especially for small scaled data, are not always enough. Rainfall records of less than 50 years are usually deemed insufficient to unequivocally identify the probability distribution of the annual rainfall. Thus, this study introduces an alternative approach that replaces the need for parametric fitting by using empirical distribution based on plotting positions to represent annual maximum rainfall series. Subsequently, these plotting positions are used to build IDF curves. The IDF curves found are then compared to the IDF curves yielded from the parametric GEV distribution which is a common basis for IDF curves. This study indicates that IDF curves obtained using plotting positions are similar to IDF curves found using GEV distribution for storm events. Hence, researchers could model and subsequently build IDF curves for annual rainfall records of less than 50 years by using plotting positions and avoid any probability distribution fitting of insufficient data.

Author Biographies

Noratiqah Mohd Ariff, Universiti Kebangsaan Malaysia

School of Mathematical Sciences,

Senior Lecturer

Abdul Aziz Jemain, Universiti Kebangsaan Malaysia

School of Mathematical Sciences,


Mohd Aftar Abu Bakar, Universiti Kebangsaan Malaysia

School of Mathematical Sciences,

Senior Lecturer


Olsson, J. and Burlando, P. Reproduction of temporal scaling by a rectangular pulse rainfall model. Hydrological Processes. 2002. 16(3): 611-630.

Ellouze, M. and Abida, H. Regional flood frequency analysis in Tunisia: Identification of regional distributions. Water Resources Management. 2008. 22(8): 943-957.

Koutsoyiannis, D., Kozonis, D. and Manetas, A. A mathematical framework for studying rainfall intensity-duration-frequency relationships. Journal of Hydrology. 1998. 206(1-2): 118-135.

Chang, K. B., Lai, S. H. and Othman, F. Comparison of annual maximum and partial duration series of derivation of rainfall intensity-duration-frequency relationships in Peninsular Malaysia. Journal of Hydrologic Engineering. 2015. 21(1): 05015013.

Hosking, J. R. M. and Wallis, J. R. Regional frequency analysis: An approach based on L-moments. 2005. Cambridge: Cambridge University Press.

De, M. A new unbiased plotting position formula for Gumbel distribution. Stochastic Environmental Research and Risk Assessment. 2000. 14(1): 1-7.

Goel, N. K. and De, M. Development of unbiased plotting position formula for general extreme value distributions. Stochastic Hydrology and Hydraulics. 1993. 7(1): 1-13.

Kim, S., Shin, H., Joo, K. and Heo, J. H. Development of plotting position for the general extreme value distribution. Journal of Hydrology. 2012. 475: 259-269.

Kim, D., Olivera, F., Cho, H. and Lee, S. O. Effect of the inter-annual variability of rainfall statistics on stochastically generated rainfall time series: part 1. Impact on peak and extreme rainfall values. Stochastic Environmental Research and Risk Assessment. 2013. 27: 1601-1610.

Ariff, N. M., Jemain, A. A. and Bakar, M. A. A. Pengitlakan lengkung IDF untuk peristiwa ribut ekstrim di Semenanjung Malaysia. Journal of Quality Measurement and Analysis. 2015. 11(2): 31-46.

Bezak, N., Šraj, M. and Mikoš, M. Copula-based IDF curves and empirical rainfall thresholds for flash floods and rainfall-induced landslides. Journal of Hydrology. 2016. 541: 272-284.

Palynchuk, B. and Guo, Y. Threshold analysis of rainstorm depth and duration statistics at Toronto, Canada. Journal of Hydrology. 2008. 348(3-4): 535-545.

Leahy, P. G. and Kiely, G. Short duration rainfall extremes in Ireland: influence of climatic variability. Water Resources Management. 2011. 25(3): 987-1003.

De Michele, C., Zenoni, E., Pecora, S. and Rosso, R. Analytical derivation of rain intensity-duration-area-frequency relationships from event maxima. Journal of Hydrology. 2011. 399(3-4): 385-393.

Villarini, G., Smith, J. A., Baeck, M. L., Vitolo, R., Stephenson, D. B. and Krajewski, W. F. On the frequency of heavy rainfall for the midwest of the United States. Journal of Hydrology. 2011. 400(1-2): 103-120.

Ben-Zvi, A. Rainfall intensity–duration–frequency relationships derived from large partial duration series. Journal of Hydrology. 2009. 367(1-2): 104-114.

Nadarajah, S. and Shiau, J. T. Analysis of extreme flood events for the Pachang River, Taiwan. Water Resources Management. 2005. 19(4): 363-374.

Guo, S. L. Unbiased plotting position formulae for historical floods. Journal of Hydrology. 1990. 121(1): 45-61.

Jones, D. A. Plotting positions via maximum-likelihood for a non-standard situation. Hydrology and Earth System Sciences Discussions. 1997. 1(2): 357-366.

Cunnane, C. Unbiased plotting positions – a review. Journal of Hydrology. 1978. 37(3): 205-222.

Rao, A. R. and Hamed, K. Flood frequency analysis. Florida: CRC Press. 1999.

Gerold, L. A. and Watkins, D. W. Short duration rainfall frequency analysis in Michigan using scale-invariance assumptions. Journal of Hydrologic Engineering. 2005. 10(6): 450-457.

Nhat, L. M., Tachikawa, Y. and Takara, K. Establishment of intensity-duration-frequency curves for precipitation in the monsoon area of Vietnam. Annuals of Disaster Prevention Research Institute, Kyoto University 2006. 49 B: 93-102. Retrieved from


Ariff, N. M., Jemain, A. A. and Bakar, M. A. A. Regionalization of IDF curves with L-moments for storm events. International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering. 2016. 10(5): 172-178.