Kolmogorov Complexity Analysis and Prediction Horizon of the Daily Erythemal Dose Time Series

Abstract

Influenced by stratospheric total ozone column (TOC), cloud cover, aerosols, albedo, and other factors, levels of daily erythemal dose (Her) in a specific geographic region show significant variability in time and space. To investigate the degree of randomness and predictability of Her time series from ground-based observations in Novi Sad, Serbia, during the 2003–2012 time period, we used a set of information measures: Kolmogorov complexity, Kolmogorov complexity spectrum, running Kolmogorov complexity, the largest Lyapunov exponent, Lyapunov time, and Kolmogorov time. The result reveals that fluctuations in daily Her are moderately random and exhibit low levels of chaotic behavior. We found a larger number of occurrences of deviation from the mean in the time series during the years with lower values of Her (2007–2009, 2011–2012), which explains the higher complexity. Our analysis indicated that the time series of daily values of Her show a tendency to increase the randomness when the randomness of cloud cover and TOC increases, which affects the short-term predictability. The prediction horizon of daily Her values in Novi Sad given by the Lyapunov time corrected for randomness by Kolmogorov is between 1.5 and 3.5 days.

Keywords

• erythemal dose
• Novi Sad (Serbia)
• Kolmogorov complexity-based measures
• chaos
• largest Lyapunov exponent
• Lyapunov time