Articles | Volume 20, issue 8
Hydrol. Earth Syst. Sci., 20, 3183–3191, 2016
Hydrol. Earth Syst. Sci., 20, 3183–3191, 2016

Technical note 08 Aug 2016

Technical note | 08 Aug 2016

Technical note: Multiple wavelet coherence for untangling scale-specific and localized multivariate relationships in geosciences

Wei Hu1,3 and Bing Cheng Si2,3 Wei Hu and Bing Cheng Si
  • 1New Zealand Institute for Plant & Food Research Limited, Private Bag 4704, Christchurch 8140, New Zealand
  • 2College of Hydraulic and Architectural Engineering, Northwest A&F University, Yangling 712100, China
  • 3University of Saskatchewan, Department of Soil Science, Saskatoon, SK S7N 5A8, Canada

Abstract. The scale-specific and localized bivariate relationships in geosciences can be revealed using bivariate wavelet coherence. The objective of this study was to develop a multiple wavelet coherence method for examining scale-specific and localized multivariate relationships. Stationary and non-stationary artificial data sets, generated with the response variable as the summation of five predictor variables (cosine waves) with different scales, were used to test the new method. Comparisons were also conducted using existing multivariate methods, including multiple spectral coherence and multivariate empirical mode decomposition (MEMD). Results show that multiple spectral coherence is unable to identify localized multivariate relationships, and underestimates the scale-specific multivariate relationships for non-stationary processes. The MEMD method was able to separate all variables into components at the same set of scales, revealing scale-specific relationships when combined with multiple correlation coefficients, but has the same weakness as multiple spectral coherence. However, multiple wavelet coherences are able to identify scale-specific and localized multivariate relationships, as they are close to 1 at multiple scales and locations corresponding to those of predictor variables. Therefore, multiple wavelet coherence outperforms other common multivariate methods. Multiple wavelet coherence was applied to a real data set and revealed the optimal combination of factors for explaining temporal variation of free water evaporation at the Changwu site in China at multiple scale-location domains. Matlab codes for multiple wavelet coherence were developed and are provided in the Supplement.

Short summary
Bivariate wavelet coherence has been used to explore scale- and location-specific relationships between two variables. In reality, a process occurring on land surface is usually affected by more than two factors. Therefore, this manuscript is to develop a multiple wavelet coherence method. Results showed that new method outperforms other multivariate methods. Matlab codes for a new method are provided. This method can be widely applied in geosciences where a variable is controlled by many factors.