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

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Abstract

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 (Hxy) were larger than the average exponents of the separate processes (Hx and Hy, 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.

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Availability of data and materials

All the data used in the present study are available upon request.

Code availability

R Language, Packages and Codes are under the terms of the General Public License (GPL-2) of the Free Software Foundation.

Abbreviations

A :

Density location parameter

B :

Skewness parameter

F :

Dispersion parameter

d :

Maximum norm distance

G :

Embedding delay vector

e°:

Saturated vapor pressure (kPa)

e a :

Actual vapor pressure (kPa)

τ :

Time lag vector

H ρ :

Reduced form of 2Hxy–Hx–Hy

H x :

Hurst exponent of the residual time series of x(t)

H xy :

Bivariate Hurst exponent

H y :

Hurst exponent of the residual time series of y(t)

LRCC:

Long-range cross-correlation coefficient

m :

Scale factor

p :

Number of variables in the multivariate multiscale entropy

s :

Local scale length in the DCCA method

S(G,τ,ε):

Entropy-based metric as a function of the G-length vector

β :

Scaling exponent of the climacogram

T :

Superscript indicating matrix transpose

T a :

Air temperature

\(\theta\) :

Fourier variable

α :

Scaling exponent of the Lévy-stable distribution

γ :

Exponent of the autocorrelation function

ε :

Distance parameter (usually 0.15*SD)

ρ[S(x,y,G,τ,ε)]:

Entropy correlation coefficient

ρ DCCA :

Detrended cross-correlation coefficient

\(\sigma ({y_{l,j}^m })\) :

Variance of the coarse-grained time series

\(C^g \left( \varepsilon \right)\) :

Probability that two vectors are within ε in the multivariate multiscale entropy analysis

\(\hat{f}\left( \theta \right)\) :

Fourier transform of the Lévy-stable probability density function f(x)

\(y_{l,j}^m\) :

Coarse-grained time series corresponding to the scale factor m

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Acknowledgements

H. M. wants to acknowledge Dr. John Nolan (American University) for his valuable comments on the statistics of Lévy-stable distributions. We also thank Dr. Danilo P. Mandic (Imperial College London) for providing the MATLAB code MMSEV3 used in the present work.

Funding

The present investigation was not funded by any person or organization.

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Authors and Affiliations

  1. Department of Physics, Mathematics and Applied Informatics, University of Granma, Apdo. 21, 85100, Bayamo, Granma, Cuba

    Humberto Millán & Ramiro Cumbrera

  2. Dipartimento di Geoscienze, Universitá degli Studi di Padova, Via Gradenigo 6, 35131, Padua, Italy

    Riccardo Biondi

  3. CIMA Research Foundation, Via A. Magliotto, 217100, Savona, Italy

    Riccardo Biondi

  4. Federal University of Recôncavo da Bahia, Exact and Technological Sciences Center, Cruz das Almas, Bahia, Brazil

    Everaldo Freitas-Guedes

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Contributions

Conceptualization: [HM], [EF-G], [RC], [RB]; methodology: [HM], [EF-G]; formal analysis and investigation: [HM], [RC], [RB], [EF-G]; writing—original draft preparation: [HM]; writing—review and editing: [RB], [RC]; resources: [HM], [RC]; supervision: [EF-G], [RB], [RC], [HM].

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Correspondence to Humberto Millán.

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Millán, H., Biondi, R., Cumbrera, R. et al. Associating daily meteorological variables of a local climate using DCCA, sample entropy, Lévy-index and Hurst–Kolmogorov exponents: a case study. Meteorol Atmos Phys 136, 7 (2024). https://doi.org/10.1007/s00703-024-01006-2

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