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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/hess-2020-315
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2020-315
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

  07 Aug 2020

07 Aug 2020

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This preprint is currently under review for the journal HESS.

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

Wei Hu1 and Bing Si2 Wei Hu and Bing Si
  • 1The New Zealand Institute for Plant and Food Research Limited, Private Bag 4704, Christchurch 8140, New Zealand
  • 2University of Saskatchewan, Department of Soil Science, Saskatoon, SK S7N 5A8, Canada

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.

Wei Hu and Bing Si

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Wei Hu and Bing Si

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Short summary
Partial wavelet coherency method is developed to explore the bivariate relationships at different scales and locations after excluding the effects of other variables. The method was tested with artificial datasets and applied to two measured datasets. Compared with others, this method has the advantages of capturing phase information, dealing with multiple excluding variables, and producing more accurate results. This method can be used in different areas with spatial or temporal dataset.
Partial wavelet coherency method is developed to explore the bivariate relationships at...
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