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

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.