Periodicities and scaling parameters of daily rainfall over semi-arid Botswana

Periodicities and several fractal parameters were determined for time series of daily rainfall records for eight synoptic stations in semi-arid Botswana, representing a total of 540 station years of data. Harmonic analysis showed reasonably well-defined deterministic annual and semi-annual periodicities. These periodicities appeared to be related to increasing insolation from the passage of the sun over Botswana following the June winter solstice, as evidenced by the latitudinal shifts of the annual and semi-annual peaks. Hurst exponent computed via R/S analysis for the residual series obtained after filtering periodicities, showed that they have statistical properties close to the ordinary Brownian noise. Fractal scaling of cumulative distributions of the number of days N(P) per year with daily rainfall depth greater than a specified value (P), and the number of times N(T) a run of dry days (defined as zero daily rainfall) exceeded a specified value (T) was tested. The linear log-log fitting corresponding to the scaling test gave positive results for N(P). This fractal analysis seems to indicate that the causative mechanisms for rainfall over Botswana were spatially uniform. The combination of harmonic and fractal analyses techniques appear useful for the characterization of periodicities and randomness present in rainfall records at the scale (24-h) used. This characterization might be used in further research for prediction purposes.