Stochastic modelling of seasonal and yearly rainfalls with low-frequency variability

  • Jing Lin Ng
  • Samsuzana Abd Aziz
  • Yuk Feng Huang
  • Aimrun Wayayok
  • M. K. Rowshon
Original Paper


Stochastic rainfall models are important for many hydrological applications due to their appealing ability to simulate synthetic series that resemble the statistical characteristics of the observed series for a location of interest. However, an important limitation of stochastic rainfall models is their inability to preserve the low-frequency variability of rainfall. Accordingly, this study presents a simple yet efficient stochastic rainfall model for a tropical area that attempts to incorporate seasonal and inter-annual variabilities in simulations. The performance of the proposed stochastic rainfall model, the tropical climate rainfall generator (TCRG), was compared with a stochastic multivariable weather generator (MV-WG) in various aspects. Both models were applied on 17 rainfall stations at the Kelantan River Basin, Malaysia, with tropical climate. The validations were carried out on seasonal (monsoon and inter-monsoon) and annual basis. The third-order Markov chain of the TCRG was found to perform better in simulating the rainfall occurrence and preserving the low-frequency variability of the wet spells. The log-normal distribution of the TCRG was consistently better in modelling the rainfall amounts. Both models tend to underestimate the skewness and kurtosis coefficient of the rainfall. The spectral correction approach adopted in the TCRG successfully preserved the seasonal and inter-annual variabilities of rainfall amounts, whereas the MV-WG tends to underestimate the variability bias of rainfall amounts. Overall, the TCRG performed reasonably well in the Kelantan River Basin, as it can represent the key statistics of rainfall occurrence and amounts successfully, as well as the low-frequency variability.


Stochastic rainfall model Low-frequency variability TCRG MV-WG Tropical climate 



The authors wish to express their appreciation to the Malaysian Meteorological Department (MMD) for providing the rainfall data and to the Ministry of Education Malaysia (MOE) for the financial support. The authors also would like to acknowledge the sincere appreciation to the reviewers for their valuable comments.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Jing Lin Ng
    • 1
  • Samsuzana Abd Aziz
    • 1
  • Yuk Feng Huang
    • 2
  • Aimrun Wayayok
    • 1
  • M. K. Rowshon
    • 1
  1. 1.Department of Biological and Agricultural Engineering, Faculty of EngineeringUniversiti Putra Malaysia (UPM)SerdangMalaysia
  2. 2.Department of Civil Engineering, Lee Kong Chian Faculty of Engineering and ScienceUniversiti Tunku Abdul RahmanKuala LumpurMalaysia

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