Spatio-Temporal Characterization with Wavelet Coherence: Anexus between Environment and Pandemic

Abstract

Identifying spatio-temporal synchrony in a complex, interacting and oscillatory coupled-system is a challenge. In particular, the characterization of statistical relationships between environmental or biophysical variables with the multivariate data of pandemic is a difficult process because of the intrinsic variability and non-stationary nature of the time-series in space and time. This paper presents a methodology to address these issues by examining the bivariate relationship between Covid-19 and temperature time-series in the time-localized frequency domain by using Singular Value Decomposition (SVD) and continuous cross-wavelet analysis. First, the dominant spatio-temporal trends are derived by using the eigen decomposition of SVD. The Covid-19 incidence data and the temperature data of the corresponding period are transformed into significant eigen-state vectors for each spatial unit. The Morlet Wavelet transformation is performed to analyse and compare the frequency structure of the dominant trends derived by the SVD. The result provides cross-wavelet transform and wavelet coherence measures in the ranges of time period for the corresponding spatial units. Additionally, wavelet power spectrum and paired wavelet coherence statistics and phase difference are estimated. The result suggests statistically significant coherency at various frequencies providing insight into spatio-temporal dynamics. Moreover, it provides information about the complex conjugate dynamic relationships in terms phases and phase differences.