ABSTRACT
Two parallel methods, Higuchi and consecutive differences, for calculating fractal dimension (FD) of temporal data series, were applied to accumulated rainfall, recorded in Pastaza Province, Ecuador and Véneto Province, Italy. Both series were recorded regularly, each month, for over 30 years (January 1974 - September 2005). In order to calculate their FD time dependence, DF(t), moving windows of different lengths (10 - 350 samples) were applied. Presence of fractal oscillations (> 1.67 year periods), was detected by applying FFT on detrended FD(t), obtained with short windows (10-20 samples). Long-term FD(t) trends were studied using long windows (100 - 300, optimal ~ 200 samples). Both methods detected identical (or very similar) rhythms of FD(t) in the two data series, but the intercontinental frequencies differed: 4.4 years dominating in Ecuadorian, 10.3 years in Italian data. A linear positive trend of fractal dimension values (1.93 to 1.99), with a significant slope, was obtained for the Ecuadorian data over the whole recorded period. Italian rainfall fractal trend profile was, however, characterized by two phases: a constant high value (-1.99) for the period 1974 - 1993, followed by a linear decrease (1.99 to 1.95) for 1993 - 2005. Trend results, obtained with two different methods, were also in accordance. Whether, and to what extent, the 4.4 years oscillation in the Ecuadorian fractal values could be associated with the ENSO phenomenon, similarly the 10.3 years rhythm in Véneto fractal rainfall with the solar activity, remains to be explored, perhaps by analyzing corresponding data from other European and South American locations. Accordance of the results, reported in the present paper by applying two different methods, validates their use as a tool in future fractal measurements.
