Comparison of fractal dimension oscillations and trends of rainfall data from Pastaza Province, Ecuador and Veneto, Italy

Since climate trends are getting considerable attention in recent years, we aimed in this study to compare trends and rhythms of complexity (fractal dimension, FD) of rainfall data series between two continents: Latin America and Europe. Two parallel nonlinear methods for calculating FD of a temporal data series, Higuchi's and consecutive differences, were combined with Fast Fourier Transform (FFT) to obtain FD oscillations of monthly accumulated rainfall.

The data were collected for the last thirty years in Pastaza province, Ecuador and Veneto province, Italy. In order to calculate their FD time dependence, FD(t), moving windows of different lengths (short, 10–20 and long 21–350 samples), were applied. Both methods, each combined with FFT, detected identical (or very similar) rhythms of detrended FD(t) in the two data series, but frequencies with dominant amplitudes differed (4.4 years in Ecuador, 10.3 years in Italy).

Long-term FD(t) trends were also studied using optimized long window lengths (~200 samples). A linear positive trend was obtained for the Ecuadorian rainfall data over the whole recorded period. Italian fractal trend profile was, however, characterized by two periods: a constant high value for years 1974–1993, followed by a linear decrease for 1993–2005.

Trend results, obtained with two different methods, were also similar. Accordance of the results, reported in the present paper by applying these two methods, validates their use as a tool in future fractal meteorological measurements. As well, these results indicate that positive FD trend obtained for Pastaza (Ecuador) and negative trend computed for Veneto (Italy) account for a local or regional phenomenon, most probably caused by extensive deforestation and land use change (Ecuador) and continental or global atmospheric pattern variability (Italy).