Information in complex physical systems: Kolmogorov complexity plane of interacting amplitudes

One of the most challenging tasks in studying complex physical systems is determining the contributions of complexities of individual components to the complexity of the entire system. To investigate these contributions, this paper proposed the Kolmogorov complexity plane (the KC plane) based on the Kolmogorov complexity. We applied both the Kolmogorov complexity plane and the Kolmogorov complexity to daily (measured) and monthly (simulated by a climate model) values of precipitation representing a complex physical system, and temperature and water vapor pressure as individual components of that system. From the KC plane, we determined the intervals of interacting amplitudes in which the contributions of the complexities of individual components to the overall complexity could be observed.