Associating daily meteorological variables of a local climate using DCCA, sample entropy, Lévy-index and Hurst–Kolmogorov exponents: a case study

The nonlinear scaling of meteorological processes is an issue of much interest. The objectives of the present work were (a) to investigate cross-correlations between pairs of meteorological time series using different resolutions and (b) to explore the long-range cross-correlations through different scaling exponents. We used 13 years of daily records of rainfall, relative humidity, cloudiness and vapor pressure ranging from January 1st 1996 to December 31st 2009. Data sets were compiled from Veguita agro-meteorological station at Granma province, Cuba. Detrended cross-correlation analysis, multiscale sample entropy, Lévy-stable laws and Hurst–Kolmogorov dynamics were the main methodological and theoretical tools. The detrended cross-correlation coefficient showed significant cross-correlation between rainfall, relative humidity, cloudiness and actual vapor pressure at all investigated time scales. The individual Hurst exponents were in the range 0.62 ≤ H ≤ 0.72 which is consistent with long-range correlated patterns. Bivariate Hurst exponents (H_xy) were larger than the average exponents of the separate processes (H_x and H_y, respectively). The Hurst–Kolmogorov exponents estimated from the climacograms were in the range 0.6 ≤ H ≤ 0.7 (0.603 ≤ β ≤ 0.798) consistent with the values estimated from detrended fluctuation analysis. Each pair of meteorological variables fitted reasonably well bistable distributions with approximately the same Lévy index (α ≅ 0.736). Hurst–Kolmogorov and infinite variance processes are important drivers of the atmospheric dynamics which can explain the persistence of extreme events (droughts) usually observed in the studied region. The multivariate multiscale sample entropy method and multivariate stable distributions could be valuable candidates for describing daily atmospheric processes.