Complexity analysis of the turbulent environmental fluid flow time series

Abstract

We have used the Kolmogorov complexities, sample and permutation entropies to quantify the randomness degree in river flow time series of two mountain rivers in Bosnia and Herzegovina, representing the turbulent environmental fluid, for the period 1926–1990. In particular, we have examined the monthly river flow time series from two rivers (the Miljacka and the Bosnia) in the mountain part of their flow and then calculated the Kolmogorov complexity (KL) based on the Lempel–Ziv Algorithm (LZA) (lower—KLL and upper—KLU), sample entropy (SE) and permutation entropy (PE) values for each time series. The results indicate that the KLL, KLU, SE and PE values in two rivers are close to each other regardless of the amplitude differences in their monthly flow rates. We have illustrated the changes in mountain river flow complexity by experiments using (i) the data set for the Bosnia River and (ii) anticipated human activities and projected climate changes. We have explored the sensitivity of considered measures in dependence on the length of time series. In addition, we have divided the period 1926–1990 into three subintervals: (a) 1926–1945, (b) 1946–1965, (c) 1966–1990, and calculated the KLL, KLU, SE, PE values for the various time series in these subintervals. It is found that during the period 1946–1965, there is a decrease in their complexities, and corresponding changes in the SE and PE, in comparison to the period 1926–1990. This complexity loss may be primarily attributed to (i) human interventions, after the Second World War, on these two rivers because of their use for water consumption and (ii) climate change in recent times.