Kolmogorov Complexity Based Information Measures Applied to the Analysis of Different River Flow Regimes

Abstract

We have used the Kolmogorov complexities and the Kolmogorov complexity spectrum to quantify the randomness degree in river flow time series of seven rivers with different regimes in Bosnia and Herzegovina, representing their different type of courses, for the period 1965–1986. In particular, we have examined: (i) the Neretva, Bosnia and the Drina (mountain and lowland parts), (ii) the Miljacka and the Una (mountain part) and the Vrbas and the Ukrina (lowland part) and then calculated the Kolmogorov complexity (KC) based on the Lempel–Ziv Algorithm (LZA) (lower—KCL and upper—KCU), Kolmogorov complexity spectrum highest value (KCM) and overall Kolmogorov complexity (KCO) values for each time series. The results indicate that the KCL, KCU, KCM and KCO values in seven rivers show some similarities regardless of the amplitude differences in their monthly flow rates. The KCL, KCU and KCM complexities as information measures do not “see” a difference between time series which have different amplitude variations but similar random components. However, it seems that the KCO information measures better takes into account both the amplitude and the place of the components in a time series.

Keywords

• river flow time series
• lower Kolmogorov complexity
• upper Kolmogorov complexity
• Kolmogorov complexity spectrum
• Kolmogorov complexity spectrum highest value
• overall Kolmogorov complexity