In 20, this feature was probably associated with bubble growth and collapse due to the interaction between the aquifer and high temperature magma. PE also exhibited a spike-like increase just before the onset of the three eruptions. By combining these results with other observations we can attribute this decrease in PE to two reasons: first, to the occurrence of volcanic tremor that is a deterministic signal, and second, to magma migration at shallower depth beneath Shinmoedake which can attenuate high-frequency seismic waves and thus result in a less stochastic signal.
The results showed that PE values decreased before the occurrence of each eruption. The frequency range 1–7 Hz was used in order to infer temporal changes of PE in seismic noise and minimize any human contributions. The volcano is monitored by a dedicated seismic network and by infrasound microphones that recorded continuously during the aforementioned eruptions. This study investigates PE variations in seismic noise during three eruption cycles in 2011, 2017, and 2018 at Shinmoedake volcano, Japan.
#18 permute 3 series#
Permutation entropy (PE) is a complexity metric that encodes a time series into sequences of symbols and can be used to decipher between deterministic and stochastic behavior. The results confirm the suitability of the approach proposed, using a mixture of the two methods. Afterwards, these bounds are refined using heuristics about the behaviour of the number of patterns found in deterministic and random time series. First, an analytic normalisation is proposed using known but very conservative bounds. It is based on a max–min normalisation scheme, described in two steps. This paper describes a method to keep SlpEn results within this interval, and improves the interpretability and comparability of this measure in a similar way as for other methods. Although this interval is not necessary at all for time series classification purposes, it is a convenient and common reference framework when entropy analyses take place. This maximises the information captured by the method but, as a consequence, SlpEn results do not usually fall within the classical interval. As the histogram normalisation value, SlpEn uses the actual number of unique patterns found instead of the theoretically expected value.
It is based on the differences between consecutive values in a time series and two new input thresholds to assign a symbol to each resulting difference interval.
Slope Entropy (SlpEn) is a very recently proposed entropy calculation method. The other streamflow alteration unrelated to the construction of the two largest dams was identified in the upstream unimpacted São Francisco station, as an increase in the entropy around 1960s, indicating that some natural factors could also play a role in the decreased predictability of streamflow dynamics.
#18 permute 3 windows#
The time evolution of streamflow predictability was analyzed by applying CECP in 2 year sliding windows that revealed the influence of the Paulo Alfonso complex (located between Sobradinho and Xingó dams), construction of which started in the 1950s and was identified through the increased streamflow entropy in the downstream Pão de Açúcar station. Weighted CECP provides some finer details in the predictability of streamflow due to the inclusion of amplitude information in the probability distribution of ordinal patterns. By comparing the values of CECP information quantifiers (permutation entropy and statistical complexity) for the periods before and after the construction of Sobradinho (1979) and Xingó (1994) dams, we found that the reservoirs’ operations changed the temporal variability of streamflow series toward the less predictable regime as indicated by higher entropy (lower complexity) values. We analyzed daily streamflow time series recorded in three fluviometric stations: São Francisco (upstream of cascade dams), Juazeiro (downstream of Sobradinho dam), and Pão de Açúcar station (downstream of Sobradinho and Xingó dams). We investigated the influence of the construction of cascade dams and reservoirs on the predictability and complexity of the streamflow of the São Francisco River, Brazil, by using complexity entropy causality plane (CECP) in its standard and weighted form.
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