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Q-triplet characterization of atmospheric time series at Antofagasta: A missing values problem

Hishan Farfán-Bachiloglu, Francisco A. Calderón, Darío G. Pérez

TL;DR

The paper tackles missing-data atmospheric time series from Antofagasta to characterize non-equilibrium dynamics using the $q$-triplet framework from Tsallis statistics. It combines Singular Spectrum Analysis (SSA) to extract deseasonalized residuals with a three-part $q$-triplet analysis: $q_{ ext{stat}}$ from a $q$-log PDF fit, $q_{ ext{rel}}$ from a $q$-exponential fit to the autocorrelation, and $q_{ ext{sens}}$ from extrapolated multifractal spectrum via $ rac{1}{1 - q_{ ext{sens}}} = rac{1}{eta_{ ext{min}}} - rac{1}{eta_{ ext{max}}}$. The results yield $q_{ ext{stat}} o [1.26,1.44]$, $q_{ ext{rel}} o [1.91,4.61]$, and $q_{ ext{sens}} o [-0.23,0.32]$, with PDFs well described by $q$-Gaussians, $q$-exponential autocorrelation, and clear multifractality, signaling strong nonlinearity and long-range dependence. This demonstrates the utility of non-extensive statistics for climate time series with gaps and points to broader applicability across regions and variables beyond conventional ARIMA models.

Abstract

Located in northern Chile (23.7°S, 70.4°W), Antofagasta has an exceptionally arid and stable climate characterized by minimal precipitation and consistent weather patterns. Nevertheless, despite these climate conditions being meaningful for several research and practical applications, our understanding of weather dynamics remains limited. The available meteorological data from 1969 to 2016 is analogical, which presents a significant challenge to analyze because these records are riddled with missing values, some measurements were taken at irregular measuring intervals, making it an interesting puzzle to grasp the Antofagasta's climate scenario. To overcome this issue, we present a comprehensive statistical analysis of atmospheric temperature, pressure, and humidity time series. Our analytical approach involves the q-triplet calculation method, serving as a powerful tool to identify distinctive behavior within systems under non-equilibrium states. Our results suggest that, in general, the q-triplet values satisfy the condition $q_\text{sens}<1<q_\text{stat}<q_\text{rel}$, a pattern that has been observed in previous studies.

Q-triplet characterization of atmospheric time series at Antofagasta: A missing values problem

TL;DR

The paper tackles missing-data atmospheric time series from Antofagasta to characterize non-equilibrium dynamics using the -triplet framework from Tsallis statistics. It combines Singular Spectrum Analysis (SSA) to extract deseasonalized residuals with a three-part -triplet analysis: from a -log PDF fit, from a -exponential fit to the autocorrelation, and from extrapolated multifractal spectrum via . The results yield , , and , with PDFs well described by -Gaussians, -exponential autocorrelation, and clear multifractality, signaling strong nonlinearity and long-range dependence. This demonstrates the utility of non-extensive statistics for climate time series with gaps and points to broader applicability across regions and variables beyond conventional ARIMA models.

Abstract

Located in northern Chile (23.7°S, 70.4°W), Antofagasta has an exceptionally arid and stable climate characterized by minimal precipitation and consistent weather patterns. Nevertheless, despite these climate conditions being meaningful for several research and practical applications, our understanding of weather dynamics remains limited. The available meteorological data from 1969 to 2016 is analogical, which presents a significant challenge to analyze because these records are riddled with missing values, some measurements were taken at irregular measuring intervals, making it an interesting puzzle to grasp the Antofagasta's climate scenario. To overcome this issue, we present a comprehensive statistical analysis of atmospheric temperature, pressure, and humidity time series. Our analytical approach involves the q-triplet calculation method, serving as a powerful tool to identify distinctive behavior within systems under non-equilibrium states. Our results suggest that, in general, the q-triplet values satisfy the condition , a pattern that has been observed in previous studies.

Paper Structure

This paper contains 4 sections, 2 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Results
  4. Concluding remarks

Figures (3)

  • Figure 1: Illustration of $q$-triplet calculation at 08:00. Top row: Probability density functions $p(z)$ with q-Gaussian fits for atm. pressure (blue), air temperature (red), and rel. humidity (magenta). Middle row: (Log) Autocorrelation function $\ln_q[C(\tau)]$ versus time lag $\tau$, showing linear fits indicating relaxation dynamics. Bottom row: Multifractal spectra $f(\alpha)$ demonstrating multifractality of data.
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