Water Resources Management

, Volume 31, Issue 5, pp 1729–1744 | Cite as

Generating Synthetic Rainfall Total Using Multivariate Skew-t and Checkerboard Copula of Maximum Entropy

  • Noor Fadhilah Ahmad RadiEmail author
  • Roslinazairimah Zakaria
  • Julia Piantadosi
  • John Boland
  • Wan Zawiah Wan Zin
  • Muhammad Az-zuhri Azman


This study aims to test the appropriateness of multivariate skew-t copula and checkerboard copula of maximum entropy in generating monthly rainfall total data. The generation of synthetic data is important, as it provides hypothetical data in areas for which data availability remains limited. Three selected meteorological stations in Kelantan, Malaysia, Stesen Pertanian Melor, Rumah Pam Salor, and Ladang Lepan Kabu, are considered in this study. Monthly rainfall total data for the driest and wettest months in the year are tested in this study. For these three stations, the identified month with the least total of rainfall received (driest) is May, while the month with the highest total of rainfall received (wettest) is November. The data is fitted to gamma distribution with the corresponding parameters estimated. The observed data will be transformed to be in unit uniform using the gamma marginal. The resulting data is compared to simulated uniform data generated using multivariate skew-t copula and checkerboard copula of maximum entropy models based on the correlation values of the observed and simulated data. Next, the Kolmogorov-Smirnov test is used to assess the fit between the observed and generated data. The results show that the values of simulated correlation coefficients do not differ much for gamma distribution, multivariate skew-t, and maximum entropy approaches. This implies that the multivariate skew-t and maximum entropy may be used to generate monthly rainfall total for cases in which actual data is unavailable.


Multivariate skew-t Maximum entropy Copula Rainfall model 



The authors are grateful to Department of Irrigation and Drainage Malaysia for providing the rainfall data. This study was funded by Universiti Malaysia Pahang (RDU120101). We thanks two anonymous referees whose comments led to a clearer presentation.


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Noor Fadhilah Ahmad Radi
    • 1
    • 2
    Email author
  • Roslinazairimah Zakaria
    • 2
  • Julia Piantadosi
    • 3
  • John Boland
    • 3
  • Wan Zawiah Wan Zin
    • 4
  • Muhammad Az-zuhri Azman
    • 2
  1. 1.Institute of Engineering MathematicsUniversiti Malaysia Perlis, Taman Bukit Kubu JayaJalan SerawMalaysia
  2. 2.Faculty of Industrial Sciences and TechnologyUniversiti Malaysia PahangLebuhraya Tun RazakMalaysia
  3. 3.Centre for Industrial and Applied Mathematics, Scheduling and Control GroupUniversity of South AustraliaMawson LakesAustralia
  4. 4.School of Mathematical Sciences, Faculty of Science and TechnologyUniversiti Kebangsaan MalaysiaBangiMalaysia

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