Rainfall data simulation by hidden Markov model and discrete wavelet transformation


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7 Citations (Scopus)


In many regions, monthly (or bimonthly) rainfall data can be considered as deterministic while daily rainfall data may be treated as random. As a result, deterministic models may not sufficiently fit the daily data because of the strong stochastic nature, while stochastic models may also not reliably fit into daily rainfall time series because of the deterministic nature at the large scale (i.e. coarse scale). Although there are different approaches for simulating daily rainfall, mixing of deterministic and stochastic models (towards possible representation of both deterministic and stochastic properties) has not hitherto been proposed. An attempt is made in this study to simulate daily rainfall data by utilizing discrete wavelet transformation and hidden Markov model. We use a deterministic model to obtain large-scale data, and a stochastic model to simulate the wavelet tree coefficients. The simulated daily rainfall is obtained by inverse transformation. We then compare the accumulated simulated and accumulated observed data from the Chao Phraya Basin in Thailand. Because of the stochastic nature at the small scale, the simulated daily rainfall on a point to point comparison show deviations with the observed data. However the accumulated simulated data do show some level of agreement with the observed data. Copyright © 2008 Springer-Verlag.
Original languageEnglish
Pages (from-to)863-877
JournalStochastic Environmental Research and Risk Assessment
Issue number7
Publication statusPublished - Oct 2009


Jayawardena, A. W., Xu, P. C., & Li, W. K. (2009). Rainfall data simulation by hidden Markov model and discrete wavelet transformation. Stochastic Environmental Research and Risk Assessment, 23(7), 863-877. doi: 10.1007/s00477-008-0264-0


  • Daily rainfall
  • Discrete wavelet transformation
  • Hidden Markov model
  • Expectation-maximization algorithm
  • False nearest neighbours
  • Phase space reconstruction


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