Comparison of L-Moments of Extreme Value Family of Probability Distributions for Determination of Design Rainfall Depth

Vivekanandan N.*
Central Water and Power Research Station, Pune, Maharashtra, India.
Periodicity:January - March'2025

Abstract

Accurate estimation of extreme (i.e., 1-day maximum) rainfall is essential for water resources management, flood forecasting, agricultural planning, and climate change impact studies. This can be achieved through fitting the extreme value family of probability distributions (EVD) that consists of Extreme Value Type-1 (EV1), Extreme Value Type-2 (EV2), Generalized Extreme Value (GEV), and Generalized Pareto (GPA) to the series of observed annual 1-day maximum rainfall (AMR), whereas the parameters are determined by the Method of L-Moments (LMO). This paper presents a study on the comparison of LMO estimators of EVD for the determination of design rainfall depth at Akkalkuwa, Kamrej, Navapur, Sakri, Shahada, and Taloda rain gauge sites. For this purpose, the AMR series was generated from the daily rainfall data observed at the sites during the period 1960 to 2022 and used. The adequacy of fitting LMO of EVD to the AMR series was examined through Goodness-of-Fit (GoF) tests, viz., Chi-Square and Kolmogorov-Smirnov (KS), while the selection of the best-fit distribution was made through model performance analysis with various indicators, viz., correlation coefficient (CC), Nash- Sutcliffe model efficiency (NSE), root mean squared error (RMSE), and cross-correlation matrix analysis (CCMA). The Chi- Square test results uniformly supported the use of EV1 and GEV for modelling the AMR data of six sites, whereas KS test results supported all four distributions of EVD for all six sites. The results indicated that the CC values obtained from four distributions vary between 0.960 and 0.994. The study showed that the NSE computed by EV1, GEV, and GPA varies from 91.7% to 98.7%. The outcomes of CCMA showed that there is a perfect correlation between the estimated rainfall by EV1 and GEV, and also nearer to 1.000. On the basis of evaluation of the results with quantitative (viz., CC, NSE, and RMSE) and qualitative assessments, it was found that GEV is the best choice for rainfall estimation for Akkalkuwa, Kamrej, Navapur, Sakri, Shahada, and Taloda. The estimated extreme rainfall by GEV distribution could be considered as a design rainfall depth while planning water resources management projects and their related activities in the respective sites.

Keywords

Chi-Square, Extreme Value Type-1, Generalized Extreme Value, Kolmogorov-Smirnov, Method of L-Moments, Rainfall.

How to Cite this Article?

Vivekanandan, N. (2024). Comparison of L-Moments of Extreme Value Family of Probability Distributions for Determination of Design Rainfall Depth. i-manager’s Journal on Structural Engineering, 13(4), 1-9.

References

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