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

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