1. MMC
  2. All Volumes and Issues
  3. Volume 12, Number 3, 2025
  4. Flood frequency analysis of daily water levels using the L-moment and TL-moment approaches at river stations in Pahang

Flood frequency analysis of daily water levels using the L-moment and TL-moment approaches at river stations in Pahang

MMC.
2025;
Volume 12, Number 3
: pp. 709–723
Received: December 17, 2024
Revised: April 07, 2025
Accepted: May 05, 2025

Arba F. A. N., Azahar A. A., Marsani M. F., Kasihmuddin M. S. K., Someetheram V., Mansor M. A., Jan N. A. M., Jamaludin S. Z. M.  Flood frequency analysis of daily water levels using the L-moment and TL-moment approaches at river stations in Pahang.  Mathematical Modeling and Computing. Vol. 12, No. 3, pp. 709–723 (2025)

Authors:
  1. F. A. N. Arba
  2. A. A. Azahar
  3. M. F. Marsani
  4. M. S. M. Kasihmuddin
  5. V. Someetheram
  6. M. A. Mansor
  7. N. A. M. Jan
  8. S. Z. M. Jamaludin
1
School of Mathematical Sciences, Universiti Sains Malaysia
2
School of Mathematical Sciences, Universiti Sains Malaysia
3
School of Mathematical Sciences, Universiti Sains Malaysia
4
School of Mathematical Sciences, Universiti Sains Malaysia
5
School of Mathematical Sciences, Universiti Sains Malaysia
6
School of Distance Education, Universiti Sains Malaysia
7
Department of Physical and Mathematical Science, Faculty of Science, Universiti Tunku Abdul Rahman
8
School of Mathematical Sciences, Universiti Sains Malaysia

The application of flood frequency analysis is essential for understanding and managing the risks associated with extreme water level events.  This study examines the Pahang River basin, specifically focusing on water levels at Sungai Pahang (Temerloh) and Sungai Lipis (Benta). Probability distributions and return period concepts are applied to assess flood occurrences.  The study has two main objectives: first, to determine the most suitable probability distribution for modeling flood events among the Generalized Extreme Value (GEV), Generalized Logistic (GLO), and Generalized Pareto (GPA) distributions, using both L-moments and TL-moments for parameter estimation; and second, to estimate expected water levels for return periods of 2, 5, 10, 50, and 100 years using the identified best-fit distributions.  The study employs the Mean Absolute Deviation Index (MADI) and Ratio Diagram tools to evaluate distribution performance to achieve these objectives. The results indicate that the GLO distribution, estimated using TL-moments (1;0), provides the best fit for the water level data.  The findings suggest that water levels in Sungai Pahang and Sungai Lipis will likely exceed the critical danger thresholds of 33 meters and 75 meters within the next 5 and 10 years, respectively, highlighting the need for proactive flood management strategies.

flood frequency analysis
L-moments
TL-moments
generalized logistic distribution
return period
Pahang river basin
  1. Tekolla A.  Rainfall and Flood Frequency Analysis in Pahang River Basin, Malaysia.  TVVR10/5012 (2010).
  2. Badyalina B., Mokhtar N. A., Mat Jan N. A., Marsani M. F., Ramli M. F., Majid M., Ya’acob F. F.  Hydroclimatic Data Prediction Using a New Ensemble Group Method of Data Handling Coupled with Artificial Bee Colony Algorithm.  Sains Malaysiana.  51 (8), 2655–2668 (2022).
  3. Ni C., Marsani M. F., Shan F. P.  Flood Prediction Based on Feature Selection and a Hybrid Deep Learning Network.  Journal of Water and Climate Change.  15 (3), 1245–1261 (2024).
  4. Ni C., Marsani M. F., Fam P. S., Zou X.  Flood prediction with optimized gated recurrent unit-temporal convolutional network and improved KDE error estimation.  AIMS Mathematics.  9 (6), 14681–14696 (2024).
  5. Someetheram V., Marsani M. F., Mohd Kasihmuddin M. S., Mohd Jamaludin S. Z., Mansor M. A.  Double Decomposition with Enhanced Least-Squares Support Vector Machine to Predict Water Level.  Journal of Water and Climate Change.  15 (6), 2582–2594 (2024).
  6. Vinet F.  Geographical analysis of damage due to flash floods in southern France: The cases of 12–13 November 1999 and 8–9 September 2002.  Applied Geography.  28 (4), 323–336 (2008).
  7. Badyalina B., Mokhtar N. A., Mat Jan N. A., Hassim N. H., Yusop H.  Flood Frequency Analysis Using L-Moment for Segamat River.  Matematika.  37 (2), 47–62 (2021).
  8. Jan N. A., Marsani M. F., Thiruchelvam L., Abidin N. B. Z., Shabri A., Sani S. A. A. Mitigating infectious disease risks through non-stationary flood frequency analysis: a case study in Malaysia based on natural disaster reduction strategy.  Geospatial Health.  18 (2), 1236 (2023).
  9. Ni C., Fam P. S., Marsani M. F.  A Data–Driven Method and Hybrid Deep Learning Model for Flood Risk Prediction.  International Journal of Intelligent Systems.  2024 (1), 3562709 (2024).
  10. Shabri A. B., Daud Z. M., Mohd Ariff N.  Regional analysis of annual maximum rainfall using TL-moments method.  Theoretical and Applied Climatology.  104 (3–4), 561–570 (2011).
  11. Ahmad I., Ahmad T., Shahzad U., Ameer M. A., Emam W., Tashkandy Y., Badar Z.  Estimation of regional and at-site quantiles of extreme winds under flood index procedure.  Heliyon.  10 (1), e23388 (2024).
  12. Mat Jan N. A., Shabri A., Azuardi S. D.  TL-Moments: Application to the Generalized Logistic Distribution.  Proceedings of the International Conference on Science, Technology and Social Sciences (ICSTSS) 2012.  525–531 (2014).
  13. Anghel C. G., Ilinca C.  Predicting Future Flood Risks in the Face of Climate Change: A Frequency Analysis Perspective.  Water.  15 (22), 3883 (2023).
  14. Du H., Xia J., Zeng S., Tu Y.  Climate Change and Multi-Reservoirs Impacts on Extreme Flood: Nonstationary Regional Frequency Analysis and Uncertainty Estimation.  Water Resources Management.  38 (3), 951–965 (2024).
  15. Ilinca C., Stanca S. C., Anghel C. G.  Assessing Flood Risk: LH-Moments Method and Univariate Probability Distributions in Flood Frequency Analysis.  Water.  15 (19), 3510 (2023).
  16. Khan Z., Rahman A., Karim F.  An Assessment of Uncertainties in Flood Frequency Estimation Using Bootstrapping and Monte Carlo Simulation.  Hydrology.  10 (1), 18 (2023).
  17. Prahadchai T., Busababodhin P., Parka J.-S.  Regional Flood Frequency Analysis of Extreme Rainfall in Thailand, Based on $L$-Moments.  Communications for Statistical Applications and Methods.  31 (1), 37–53 (2024).
  18. Vidrio-Sahagún C. T., He J., Pietroniro A.  Nonstationary hydrological frequency analysis using the Metastatistical extreme value distribution.  Advances in Water Resources.  176, 104460 (2023).
  19. Vidrio-Sahagún C. T., He J., Pietroniro A.  Multi-distribution regula-falsi profile likelihood method for nonstationary hydrological frequency analysis.  Stochastic Environmental Research and Risk Assessment.  38 (3), 843–867 (2024).
  20. Hosking J. R. M., Wallis J. R.  Regional Frequency Analysis.  Cambridge University Press (1997).
  21. Tao D. Q., Nguyen V.-T.-V., Bourque A.  On Selection of Probability Distributions for Representing Extreme Precipitations in Southern Quebec.  Annual Conference of the Canadian Society for Civil Engineering.  5, 1–8 (2002).
  22. Abdulali B. A. A., Abu Bakar M. A., Ibrahim K., Ariff N. M.  Extreme Value Distributions: An Overview of Estimation and Simulation.  Journal of Probability and Statistics.  2022 (1), 5449751 (2022).
  23. Hamed K. H., Rao A. R.  A Modified Mann-Kendall Trend Test for Autocorrelated Data.  Journal of Hydrology.  204 (1–4), 182–196 (1998).
  24. Hosking J. R. M.  L-Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics.  Journal of the Royal Statistical Society, Series B (Methodological).  52 (1), 105–124 (1990).
  25. Elamir E. A. H., Seheult A. H.  Trimmed L-Moments.  Computational Statistics & Data Analysis.  43 (3), 299–314 (2003).
  26. Shiryaev A. N.  Kolmogorov: Life and Creative Activities.  The Annals of Probability.  17 (3), 866–944 (1989).
  27. Marsani M. F., Someetheram V., Mohd Kasihmuddin M. S., Mohd Jamaludin S. Z., Mansor M. A., Badyalina B., Mat Jan N. A.  Enhancing rainfall prediction in SVM by incorporating the autocorrelation function (ACF).  AIP Conference Proceedings.  3123 (1), 70006 (2024).
  28. Marsani M. F., Someetheram V., Mohd Kasihmuddin M. S., Mohd Jamaludin S. Z., Mansor M. A., Badyalina B.  The application of seasonal autoregressive integrated moving average (SARIMA) model in forecasting Malaysia mean sea level.  AIP Conference Proceedings.  3123 (1), 70005 (2024).
  29. Tehrany M. S., Jones S., Shabani F.  Identifying the essential flood conditioning factors for flood prone area mapping using machine learning techniques.  CATENA.  175, 174–192 (2019).
  30. Rao A. R., Hamed H. K.  Flood Frequency Analysis.  CRC Press (2000).
  31. Tolikas K.  Unexpected tails in risk measurement: Some international evidence.  Journal of Banking & Finance.  40, 476–493 (2014).
  32. Ahmad U. N., Shabri A., Zakaria Z. A.  Flood Frequency Analysis of Annual Maximum Stream Flows Using L-Moments and TL-Moments Approach.  Applied Mathematical Sciences.  5 (5), 243–253 (2011).
  33. Mat Jan N. A., Shabri A., Samsudin R.  Handling non-stationary flood frequency analysis using TL-moments approach for estimation parameter.  Journal of Water & Climate Change.  11 (4), 966–979 (2020).