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

Wei Hu,Bing Cheng Si

doi:10.5194/hess-20-3183-2016

Abstract

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.

Highlights

Geoscience data such as topography, climate, and ocean waves usually present cyclic patterns, with high-frequency processes being superimposed on lowfrequency processes (Si, 2008)
Bivariate wavelet coherency has been widely used for untangling scale-specific and localized relationships for transient processes in areas including geophysics (Lakshmi et al, 2004; Müller et al, 2008), hydrology (Labat et al, 2005; Das and Mohanty, 2008; Tang and Piechota, 2009; Carey et al, 2013; Graf et al, 2014), soil science (Si and Zeleke, 2005; Biswas and Si, 2011), meteorology (Torrence and Compo, 1998), and ecology (Polansky et al, 2010)
There are two narrow, horizontal bands representing an MWC value of around 1, at the respective scales of 8 and 32 for all locations (Fig. 2a). These two bands correspond to the scales of 8 and 32, respectively, for the two predictor variables

Summary

Introduction

Geoscience data such as topography, climate, and ocean waves usually present cyclic patterns, with high-frequency (small-scale) processes being superimposed on lowfrequency (large-scale) processes (Si, 2008). Bivariate wavelet coherency has been widely used for untangling scale-specific and localized relationships for transient processes in areas including geophysics (Lakshmi et al, 2004; Müller et al, 2008), hydrology (Labat et al, 2005; Das and Mohanty, 2008; Tang and Piechota, 2009; Carey et al, 2013; Graf et al, 2014), soil science (Si and Zeleke, 2005; Biswas and Si, 2011), meteorology (Torrence and Compo, 1998), and ecology (Polansky et al, 2010) This method, is limited to two variables. A method is needed for analysing multivariate (> 2 variables) and localized relationships at multiple scales

Objectives

Results

Conclusion