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.
Highlights
Scientists in different fields study the behavior of rivers, which is significantly influenced by human activities, climatic change and many other factors that change the mass and energy balance of the rivers.Influenced by the aforementioned factors, the river flow may range from being simple to complex, fluctuating in both time and space
The only exception is the Ukrina River (UKR_D) having greater randomness which is closer to the Kolmogorov complexity (KCL) of mountain rivers (0.981), which could be attributed to the fact that the KCL information measure neglects variability in time series amplitudes
The KCL as a measure does not “see” a difference between time series which have different amplitude variations but similar random components. This could be said for the Kolmogorov complexity spectrum highest value (KCM) information measure, it gives more information about complexity, in a broader context, than the KCL one does
Summary
Scientists in different fields (physicists, meteorologists, geologists, hydrologists, and engineers, among others) study the behavior of rivers, which is significantly influenced by human activities, climatic change and many other factors that change the mass and energy balance of the rivers.Influenced by the aforementioned factors, the river flow may range from being simple to complex, fluctuating in both time and space. According to [10] we should be careful in developing and using complex information metrics as with traditional statistics, since many of these methods are highly technical and not always useful [11,12]. These measures are good tools, which help us to investigate more deeply possible changes in river flow due to: human activities, climate change, catchments classification framework, improvement of application of the stochastic process concept in hydrology for its modeling, forecasting, and other purposes [13]
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