Graph theory defining non-local dependency of rainfall in Northeast Brazil

Abstract

This work shows that graph theory provides a framework to quantify the behavior of the time-correlation function among precipitation records within a given region. The method amounts to consider each station, where one data series was recorded, as a vertex in the graph. An edge, characterized by its geodesic distance d, is inserted between any pair of nodes, for which the Pearson correlation coefficient R, calculated from the corresponding series, is larger than a threshold value Rth. Then, the dependence between N(ɛ), the total number of Pearson-correlated pairs of stations with geodesic distance d ≤ ɛ, is evaluated as a function of ɛ. Results are presented for a set of spatially distributed pluviometric stations in Northeast Brazil. The reliability of the proposed procedure is tested in a two-fold way: First, values of N(ɛ) are evaluated for graphs built up by sets of regular and random distributions of nodes within the actual region where the data is collected. Next, an investigation of the influence of the choice for Rth on the results is performed. The results lead to the identification of a power law N(ɛ) ∼ ɛα for all time periods and regions that have been investigated, suggesting the presence of a robust non-metric fractal behavior. The value of α is found to depend both on seasonal and intrinsic features of the region rainfall distribution, but rather weakly on the value of Rth. The comparison of the results shows that, in contrast with the values obtained from Hurst exponent analysis, the values of α are related to the uniformity of Pearson correlation within the considered region, not with persistence of the signal.