Fractal analysis of rainfall occurrence observed in the synoptic stations of Benin (west Africa)

Abstract

Fractal analysis is important for characterizing and modeling rainfall’s space-time variations in hydrology. The purpose of this study consists on determining, in a mono-fractal framework, the scale invariance of rainfall series in Benin synopticstations located in two main geographical area: Cotonou, Bohicon , Savè in a sub equatorial climate and Parakou, Natitingou, Kandi in a Sudanian climate. Daily rainfall data for 1963 to 2008 have been used. It’s provided by the Agency for the Aerial Navigation’s Security in Africa and Madagascar. This study characterizes, for the first time in Benin, the rainfall occurrence using fractal’s theories. Box counting method permits us to determine the fractal dimension (D_ƒ) of the support. Afterward, a sensitivity analysis of the previously estimated fractal dimension is performed by varying the series length, as well as, the intensity threshold for the detection of rain. The results show that, the fractal dimension of the rainfall field depends strongly on: (i) the intensity threshold for the detection of rain fixed and (ii) the geographical position of the stations. The fractal dimension of these stations decreases with the increasing values of the threshold and confers to the synoptic stations’ rainy field a multifractal character. Three main regimes of scale invariance are obtained from the stations whatever the values of detection threshold of rain chosen between 0 mm/ day and 50 mm/day. For example, in a null detection threshold of rain, the first regime of scale invariance is delimited from 1 day to 8 days (meso-scale) whatever the geographical position of the stations. The associated fractal dimension varies from 0.52 to 0.65, such as: D _ƒ (Bohicon) < D _ƒ (Cotonou) < D _ƒ (Savè) < D _ƒ (Parakou) < D _ƒ (Kandi) < D _ƒ (Natitingou). However the second regime of scale invariance is delimited from 8 days to 128 days (synoptic scale) for stations located in sub equatorial region with a fractal dimensions varying from 0.86 to 0.90 respectively as: D _ƒ (Savè) < D _ƒ (Bohicon) < D _ƒ (Cotonou); in the Sudanian climate, the second regime is delimited from 8 days to 256 days (synoptic scale) for with a fractal dimensions varying from 0.81 to 0.87 respectively as: D _ƒ (Kandi) < D _ƒ(Parakou) < D _ƒ (Natitingou). The last regime of scale invariance starts from 128 days to above for the stations located in sub equatorial area which are characterized by a fractal dimension equal to 1; it starts from 256 days to above for the stations located in the Sudanian area and characterized by a fractal dimension equal to 1. For successive sequences of sub-periods of different sizes (3 years, 9 years and 15 years), the variation of the fractal dimension (for meso-scale and synoptic-scale) is essentially the same regardless of the size of the sequence and the geographical position of the stations. The occurrence of daily rainfall on all the six synoptic stations of Benin has the same properties as those studied in different parts of the world under different climatic conditions. So they check the universal properties of the occurrence of rain.

Keywords: Fractal dimension, rainfall time series, scale-invariance, on-off intermittency, mono-fractal, box counting method.