Theoretical and Applied Climatology

, Volume 122, Issue 3–4, pp 685–697 | Cite as

A large sample investigation of temporal scale-invariance in rainfall over the tropical urban island of Singapore

  • Pradeep V. Mandapaka
  • Xiaosheng QinEmail author
Original Paper


Scaling behavior of rainfall time series is characterized using monofractal, spectral, and multifractal frameworks. The study analyzed temporal scale-invariance of rainfall in the tropical island of Singapore using a large dataset comprising 31 years of hourly and 3 years of 1-min rainfall measurements. First, the rainfall time series is transformed into an occurrence–non-occurrence binary series, and its scaling behavior is analyzed using box-counting analysis. The results indicated that the rainfall support displays fractal structure, but within a limited range of scales. The rainfall support has a fractal dimension (D f ) of 0.56 for scales ranging from 1 min to 1.5 h and a D f of 0.37 from 1.5 h to 1.5 days. The results further showed that the fractal dimension decreases with the increase in the threshold used to define binary series. Spectral analysis carried out on the rainfall time series and the corresponding binary series showed three distinct scaling regimes of 4 min–2 h, 2–24 h, and 24 h–1 month. In all the scaling regimes, the spectral exponents for the rainfall series were smaller than those for the binary series. The study then investigated the presence of multiscaling behavior in rainfall time series using moment scaling analysis. The results confirmed that the rainfall fluctuations display a multiscaling structure, which was modeled in the framework of universal multifractals. The results from this study would not only improve our understanding of the temporal rainfall structure in Singapore and the surrounding Maritime Continent but also help us build and parameterize parsimonious models and statistical downscaling techniques for rainfall in this region.


Multifractal Analysis Rainfall Series Spectral Slope Rainfall Time Series Saturation Regime 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This study was supported by Singapores Ministry of Education (MOE) AcRF Tier 2 (M4020182.030) project. The authors appreciate the support from the National Environmental Agency of Singapore for providing rain gauge data.


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Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  1. 1.School of Civil and Environmental EngineeringNanyang Technological UniversityNanyangSingapore

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