We propose novel metrics based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We consider the origins of the Kolmogorov complexity and discuss its physical meaning. To get better insights into the nature of complex systems and time series analysis we introduce three novel measures based on the Kolmogorov complexity: (i) the Kolmogorov complexity spectrum, (ii) the Kolmogorov complexity spectrum highest value and (iii) the overall Kolmogorov complexity. The characteristics of these measures have been tested using a generalized logistic equation. Finally, the proposed measures have been applied to different time series originating from: a model output (the biochemical substance exchange in a multi-cell system), four different geophysical phenomena (dynamics of: river flow, long term precipitation, indoor ²²²Rn concentration and UV radiation dose) and the economy (stock price dynamics). The results obtained offer deeper insights into the complexity of system dynamics and time series analysis with the proposed complexity measures.

Turbulence is often expressed in terms of either irregular or random fluid flows, without quantification. In this paper, a methodology to evaluate the randomness of the turbulence using measures based on the Kolmogorov complexity (KC) is proposed. This methodology is applied to experimental data from a turbulent flow developing in a laboratory channel with canopy of three different densities. The methodology is even compared with the traditional approach based on classical turbulence statistics.

Analysis of daily solar irradiation variability and predictability in space and time is important for energy resources planning, development, and management. The natural variability of solar irradiation is being complicated by atmospheric conditions (in particular cloudiness) and orography, which introduce additional complexity into the phenomenological records. To address this question for daily solar irradiation data recorded during the years 2013, 2014 and 2015 at 11 stations measuring solar irradiance on La Reunion French tropical Indian Ocean Island, we use a set of novel quantitative tools: Kolmogorov complexity (KC) with its derivative associated measures and Hamming distance (HAM) and their combination to assess complexity and corresponding predictability. We find that all half-day (from sunrise to sunset) solar irradiation series exhibit high complexity. However, all of them can be classified into three groups strongly influenced by trade winds that circulate in a “flow around” regime: the windward side (trade winds slow down), the leeward side (diurnal thermally-induced circulations dominate) and the coast parallel to trade winds (winds are accelerated due to Venturi effect). We introduce Kolmogorov time (KT) that quantifies the time span beyond which randomness significantly influences predictability.

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.

In this article we considered the extreme temperatures, precipitation and UV-B radiation in Vojvodina region, Serbia. We describe the actual climate conditions for the period 1981?2007 and applied a dynamic downscaling technique using the EBU-POM regional coupled climate model under the SRES-A2 scenario to assess the changes for the period 2021-2100. The results indicate that a warmer and drier climate in the Vojvodina region can be expected at the end of the century. Projection of climate indicates to a strong increase in the mean annual minimum temperatures, and much smaller increase in the mean annual maximum temperatures. The increase of both extreme temperatures is predicted to be the highest in the winter and the lowest in the summer. Mean annual precipitation is projected to increase toward the end of the first half of the 21st century and to decrease for the last 30 years of the 21st century. Precipitation amount will be the highest during the winter and spring. The model simulations show that, by the end of this century, annual mean UV-B dose will recover by 5.2%. Recovery will be faster in the first half of the 21st century and more slowly later on. The UV-B doses recovery is expected to be the highest during the autumn and spring.

Solar ultraviolet (UV) radiation is a significant health hazard in the warm part of the year. In order to assess the level of hazard and the effects of UV radiation on the living world, long-term measured or estimated data are needed. In Novi Sad, the measurement of UV radiation has been performed since 2003, while ozone measurements have been made since 2007. However, those data sets are too short for assessing long-term biological effects. Therefore, several techniques for reconstruction of UV radiation doses have been developed. Reconstruction techniques are based on using available ground-based measurements of the meteorological data and satellite measurements of the total ozone column. It is shown that techniques that use ozone data show better performance than those that use only ground-based meteorological measurements. However, the difference between the performances of the methods is smaller when it comes to the monthly values, indicating that the techniques which use only ground-based meteorological measurements are roughly as good as the ozone-based techniques for assessing long-term changes in the surface UV radiation. The statistically significant increasing long term-trend of annual mean erythemal UV doses (ERY) and the decreasing trend in the total ozone column in Novi Sad since 1981 have been noticed. An increase in ERY has been noticed in all the seasons except in autumn and it is the highest in winter. The analysis showed that the increase in the ERY in the period 1981-1996 was mainly caused by the total ozone column, while the increase after 1996 is largely caused by cloudiness.