Rainfall Frequency Analysis of Upper Part Distribution Events Using Higher Order L-Moments Approach
Moath Suleiman Ali Jarah (a), Zahrahtul Amani Zakaria (a*)

a) Faculty of Informatics and Computing,
Universiti Sultan Zainal Abidin,
Besut Campus, 22200 Besut, Terengganu, Malaysia
*zahrahtulamani[at]unisza.edu.my

Abstract

Extreme precipitation events such as floods, heavy rainfalls and many others are rare in nature, but they may have a strong impact on society. Therefore, analyzing these types of data is important in order to obtain the best probability distribution that could represent the event. Classical L-moments are widely used in determining the best-fit distribution of the hydrological events. However, this method is said to be oversensitive to the lower values data and give less weight to the upper part of the distribution. In this case, the method of higher order L-moments (LH-moments) was implemented as a more robust alternative compared to classical L-moments to characterize the upper part of the distribution. The main aim of the study is to conduct a frequency analysis of maximum monthly rainfalls using LH-moments approach in characterizing the large event data. The data of maximum monthly rainfall for several stations in Terengganu were obtained from Department of Irrigation and Drainage Terengganu. The parameters were estimated using LH-moments approach for six distributions considered in this study such as, generalized extreme value (GEV), generalized logistic (GLO), three parameter kappa type-II (K3D), generalized Pareto (GPD), normal (N), and Mielke-Johnsons kappa (K2D) distributions. The analyses were conducted using conventional L-moments method with n=0 and LH-moments methods with n=1, n=2, n=3, and n=4 for a complete data series and for the upper parts of the distributions. LH-moments with n = 0 are known as L-moments. LH-moments with n=1, 2, 3 and 4 imply LH-moments of the larger events in data and the upper part of the distributions. The most suitable distributions were determined based on the mean absolute deviation index (MADI), mean square deviation index (MSDI) and correlation (r). LH-moments methods which performed on different levels of the upper parts of the distribution and complete data series showed that the GPD is the best distribution to fit the data of maximum monthly rainfalls for the seven stations in Terengganu. The results also proved that whenever η increases, LH-moments reflect more and more characteristics of the upper part of the distribution. This seems to suggest that LH-moments estimates for the upper part of the distribution events are superior to L-moments for fitting the data of maximum monthly rainfalls for several stations in Terengganu.

Keywords: LH-moments; probability distribution; moment ratio diagram; parameter estimation

Topic: Mathematics