Ordinal pattern and statistical complexity analysis of daily stream flow time series

Abstract

When calculating the Bandt and Pompe ordinal pattern distribution from given time series at depth D, some of the D! patterns might not appear. This could be a pure finite size effect (missing patterns) or due to dynamical properties of the observed system (forbidden patterns). For pure noise, no forbidden patterns occur, contrary to deterministic chaotic maps. We investigate long time series of river runoff for missing patterns and calculate two global properties of their pattern distributions: the Permutation Entropy and the Permutation Statistical Complexity. This is compared to purely stochastic but long-range correlated processes, the k-noise (noise with power spectrum f −k ), where k is a parameter determining the strength of the correlations. Although these processes closely resemble runoff series in their correlation behavior, the ordinal pattern statistics reveals qualitative differences, which can be phrased in terms of missing patterns behavior or the temporal asymmetry of the observed series. For the latter, an index is developed in the paper, which may be used to quantify the asymmetry of natural processes as opposed to artificially generated data.

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

“…, q). As one possible complexity measure associated with the permutation entropy, the Jensen-Shannon complexity, C JS [P π ], is defined as [36]:…”

“…As a recent example, we mention here the consideration of the complexity-entropy causality plane for the characterization of daily streamflow time series [36], vegetation dynamics based on remote sensing data [179] or the degree distribution of a complex network obtained from correlations among surface air temperature records in the ENSO region in the equatorial Pacific [180].…”

Análise da variabilidade espaço temporal da chuva mensal no estado de Pernambuco utilizando o método entropia de permutação

“…Este método foi utilizado em estudos relacionados a fisiologia (NICOLAOU e GEORGIOU, 2012;FERLAZZO et al, 2014)), engenharia (YAN; LIU e GAO, 2012), geofísica (CONSOLINI e MICHELIS, 2014)), hidrologia (FAN et al, 2013;SERINALDI;ZUNINO e ROSSO, 2014;LANGE;ROSSO e HAUHS, 2013), finanças (BARIVIERA et al, 2015) e em estudos de sistemas caóticos .…”

Ordinal pattern dependence between hydrological time series

“…Ordinal patterns were applied in hydrology for time series analyses, e.g. to separate deterministic and stochastic parts of daily discharge series ( [10]). [10] estimated two indices, the permutation entropy and the permutation statistical complexity to quantify order pattern distributions by their information content and complexity.…”