Technical Note: Improved partial wavelet coherency for understanding scale-specific and localized bivariate relationships in geosciences

Abstract

Abstract. Bivariate wavelet coherency is a measure of correlation between two variables in the location–scale (spatial data) or time–frequency (time series) domain. It is particularly suited to geoscience, where relationships between multiple variables differ with locations (times) and/or scales (frequencies) because of the various processes involved. However, it is well-known that bivariate relationships can be misleading when both variables are dependent on other variables. Partial wavelet coherency (PWC) has been proposed to detect scale-specific and localized bivariate relationships by excluding the effects of other variables but is limited to one excluding variable and provides no phase information. We aim to develop a new PWC method that can deal with multiple excluding variables and provide phase information. Both stationary and non-stationary artificial datasets with the response variable being the sum of five cosine waves at 256 locations are used to test the method. The new method was also applied to a free water evaporation dataset. Our results verified the advantages of the new method in capturing phase information and dealing with multiple excluding variables. Where there is one excluding variable, the new PWC implementation produces higher and more accurate PWC values than the previously published PWC implementation that mistakenly considered bivariate real coherence rather than bivariate complex coherence. We suggest the PWC method is used to untangle scale-specific and localized bivariate relationships after removing the effects of other variables in geosciences. The PWC implementations were coded with Matlab and are freely accessible (https://figshare.com/s/bc97956f43fe5734c784, last access: 14 January 2021).

Multiscale coherence analysis of reference evapotranspiration of north-western Iran using wavelet transform

“…If both σ p 2 (Y, X1, X2) and σ p 2 (Y, X2, X1) still have significant bands, both X1 and X2 have a significant influence on Y. Very recently, Hu & Si (2021) extended this approach by simultaneous accounting for the removal of multiple variables simultaneously and phase differences. But the proposers reported some inconsistency of results in some cases, emphasizing the necessity of more investigations on their proposed formulation.…”

“…Instead, the role of large-scale climate oscillations along with local meteorological variables can be considered in analysis. The simultaneous removal of more than one variable in the PWC is a possible analysis to be explored and some of the very recent formulations by Hu & Si (2021) offer flexibility to perform such analysis. Also, improved formulations like terrestrial combined terrestrial evapotranspiration index (CTEI) (Dharpure et al 2020;Elbeltagi et al 2021) involving both satellite data and hydrometeorological parameters can be used instead of ET 0 .…”

Nexus Between COVID-19 Infections, Exchange Rates, Stock Market Return, and Temperature in G7 Countries: Novel Insights From Partial and Multiple Wavelet Coherence

“…The approach of partial wavelet coherence was employed. We defined the squared partial wavelet coherence (Hu and Si, 2021) between time series -Y and X, after excluding the effect of a pair of time series, Z (z 1 , z 2 ) at scale (s) and location (t) as…”

Improving the understanding of the influencing factors on sea level on various time scales based on wavelet coherence and partial wavelet coherence

“…It prevents errors caused by the interdependence between predictors and other variables (Kenney and Keeping, 1954) and reflects the relationship between control variables and response variables on various time scales. Several successful applications of PWC have been reported (Hu and Si, 2021;Tan et al, 2016;Rathinasamy et al, 2017;Aloui et al, 2018;Wu et al, 2020;Xin et al, 2018). For example, Hu et al (2021)…”

“…Several successful applications of PWC have been reported (Hu and Si, 2021;Tan et al, 2016;Rathinasamy et al, 2017;Aloui et al, 2018;Wu et al, 2020;Xin et al, 2018). For example, Hu et al (2021)…”