Technical Note: Partial wavelet coherency for improved understanding of scale-specific and localized bivariate relationships in geosciences

Abstract. Bivariate wavelet coherency is widely used to untangle the scale-specific and localized bivariate relationships in geosciences. However, it is well-known that bivariate relationships can be misleading when both variables are correlated to other variables. Partial wavelet coherency (PWC) has been proposed, but is limited to one excluding variable and presents no phase information. The objective of this study was to develop a new PWC method that can deal with multiple excluding variables and presents phase information for the PWC. Tests with both stationary and non-stationary artificial datasets verified the known scale- and localized bivariate relationships after eliminating the effects of other variables. Compared with the previous PWC method, the new method has the advantages of capturing phase information, dealing with multiple excluding variables, and producing more accurate results. The new method was also applied to two field measured datasets. Results showed that the coherency between response and predictor variables was usually less affected by excluding variables when predictor variables had higher correlation with the response variable. Application of the new method also confirmed the best predictor variables for explaining temporal variations in free water evaporation at Changwu site in China and spatial variations in soil water content in a hummocky landscape in Saskatchewan Canada. We suggest the PWC method to be used in combination with previous wavelet methods to untangle the scale-specific and localized multivariate relationships in geosciences. Matlab codes for the PWC were developed and are provided in the supplement.