Gordan Mimić

Complexity analysis of the turbulent environmental fluid flow time series

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.

Novel measures based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis

Abstract 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.

Climate Predictions: The Chaos and Complexity in Climate Models

Some issues which are relevant for the recent state in climate modeling have been considered. A detailed overview of literature related to this subject is given. The concept in modeling of climate, as a complex system, seen through Godels Theorem and Rosens definition of complexity and predictability is discussed. It is pointed out to occurrence of chaos in computing the environmental interface temperature from the energy balance equation given in a difference form. A coupled system of equations, often used in climate models is analyzed. It is shown that the Lyapunov exponent mostly has positive values allowing presence of chaos in this systems. The horizontal energy exchange between environmental interfaces, which is described by the dynamics of driven coupled oscillators, is analyzed. Their behavior and synchronization, when a perturbation is introduced in the system, as a function of the coupling parameters, the logistic parameter and the parameter of exchange, was studied calculating the Lyapunov exponent under simulations with the closed contour of N=100 environmental interfaces. Finally, we have explored possible differences in complexities of two global and two regional climate models using their output time series by applying the algorithm for calculating the Kolmogorov complexity.

KOLMOGOROV COMPLEXITY AND CHAOTIC PHENOMENON IN COMPUTING THE ENVIRONMENTAL INTERFACE TEMPERATURE

In this paper, we consider the chaotic phenomenon and Kolomogorov complexity in computing the environmental interface temperature. First, the environmental interface is defined in the context of the complex system, in particular for autonomous dynamical systems. Then we consider the following issues in modeling procedure: (i) how to replace given differential equations by appropriate difference equations in modeling of phenomena in the environmental world? (ii) whether a mathematically correct solution to the corresponding differential equation or system of equations is always physically possible and (iii) phenomenon of chaos in autonomous dynamical systems in environmental problems, in particular in solving the energy balance equation to calculate environmental interface temperature. The difference form of this equation for computing the environmental interface temperature is discussed and analyzed depending on parameters of equation, using the Lyapunov exponent and sample entropy. Finally, the Kolmogorov complexity of time series obtained from this difference equation is analyzed.

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

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.

CHAOS IN COMPUTING THE ENVIRONMENTAL INTERFACE TEMPERATURE: NONLINEAR DYNAMIC AND COMPLEXITY ANALYSIS OF SOLUTIONS

In this paper, we consider an environmental interface as a complex system, in which difference equations for calculating the environmental interface temperature and deeper soil layer temperature are represented by the coupled maps. First equation has its background in the energy balance equation while the second one in the prognostic equation for deeper soil layer temperature, commonly used in land surface parametrization schemes. Nonlinear dynamical consideration of this coupled system includes: (i) examination of period one fixed point and (ii) bifurcation analysis. Focusing part of analysis is calculation of the Lyapunov exponent for a specific range of values of system parameters and discussion about domain of stability for this coupled system. Finally, we calculate Kolmogorov complexity of time series generated from the coupled system.

Stability analysis of turbulent heat exchange over the heterogeneous environmental interface in climate models

Based on a short review of the different parameterization schemes for sub-grid scale surface fluxes in climate and other atmospheric models of different scales, the flux aggregation effect over a heterogeneous grid-box leading to the occurrence of Schmidts paradox is considered. To investigate this effect in the sub-grid scale parameterization, we have introduced a dynamical system approach, where the horizontal energy exchange is taken into account and is represented by a matrix of coupling parameters. Since it is, in general, very difficult to specify the quantities in that matrix, a sufficient condition for the asymptotic stability that can be applied for any coupling matrix is derived. Two theorems that consider the flux aggregation effect over a heterogeneous grid-box are proved. Finally, we have showed how, by their application, Schmidts paradox can be overcome. It is demonstrated through a numerical example of turbulent energy exchange over the grid-box including the part of the Prospect park, New York, USA.

Randomness Representation of Turbulence in Canopy Flows Using Kolmogorov 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.