Fractal analysis of temporal rainfall structure in Peninsular Malaysia

The temporal structure of rainfall in Peninsular Malaysia was investigated and characterized by exploring scale-invariant properties in a fractal framework, i.e. by estimating the dimension of rainfall occurrences. This is done using a box-counting method to datasets from 56 selected rain gauge stations in Peninsular Malaysia. The stations were grouped according to four regions, namely northwest, west, southwest and east for a better understanding of the effect of topography and local climatology on the temporal structure of rainfall. Results from box-counting analyses have shown that the distribution of rainfall occurrences in Peninsular Malaysia can be characterized by a fractal behaviour for three different scaling regimes: regime 1 from 15 min to 2 hours, regime 2 from 2 hours to about 2 days and regime 3 over 11 days. The breaks in scaling regimes were found to be closely related to the average of rainfall event and dry period durations. The first regime is characterized by a higher value of fractal dimension compared to the second regime. This implies that the distribution of rainfall within 15 min to 2 hours is densely structured with rainy intervals closely clustered together, while rainfall series in 2 hours-∼2 days regime are sparsely distributed in time. For regimes over than 11 days, the occurrence of rainfall is assumed to be evenly distributed as this regime is characterized by a fractal dimension 1. The analysis of spatial patterns on the fractal behaviour showed that rainfall in Peninsular Malaysia is influenced by topography, seasonal wind flow patterns and local climatology. The northeast monsoon rainfall is clearly having a greater influence on the rainfall distribution of peninsula than the southwest monsoon rainfall as the former monsoon displayed a close resemblance of spatial patterns to those obtained for the total rainfall series. In general, the rainfall occurrences in the east region is characterized by a large fractal dimension in both regimes. This could be reasoned by the flow of wind during northeast monsoon that brings heavy rain for durations from minutes up to 3 days. Meanwhile, stations in the west and southwest regions, particularly the west region which received heavy rainfall and usually in a form of convective rains during the transitional period between southwest and northeast monsoons, displayed large and moderate fractal dimensions in the regime of 15 min to 2 hours but small within regime of 2 hours to about 2 days. The results from this study may help to improve our knowledge about the temporal structure of rainfall in Peninsular Malaysia as well as help us in providing a platform to develop practical tools to produce high-resolution synthetic rainfall for the uses in hydrologic modelling, analysis and design of water resource systems.