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

2016 ◽  
Author(s):  
Wei Hu ◽  
Bing Cheng Si
Keyword(s):  
Multiple Scales ◽  
Free Water ◽  
Technical Note ◽  
Wavelet Coherence ◽  
Predictor Variables ◽  
Water Evaporation ◽  
Multivariate Methods ◽  
Spectral Coherence ◽  
Multivariate Relationships ◽  
Multiple Wavelet Coherence

Abstract. The scale-specific and localized bivariate relationships in geosciences can be revealed using simple wavelet coherence. The objective of this study is to develop a multiple wavelet coherence method for examining scale-specific and localized multivariate relationships. Stationary and non-stationary artificial datasets, 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 dataset and revealed the optimal combination of factors for explaining temporal variation of free water evaporation at Changwu site in China at multiple scale-location domains. Matlab codes for multiple wavelet coherence are developed and provided in the supplement.

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

2016 ◽  
Vol 20 (8) ◽  
pp. 3183-3191 ◽  
Author(s):  
Wei Hu ◽  
Bing Cheng Si
Keyword(s):  
Multiple Scales ◽  
Free Water ◽  
Wavelet Coherence ◽  
Predictor Variables ◽  
Water Evaporation ◽  
Multivariate Methods ◽  
Spectral Coherence ◽  
Data Set ◽  
Multivariate Relationships ◽  
Multiple Wavelet Coherence

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.

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

2020 ◽  
Author(s):  
Wei Hu ◽  
Bing Si
Keyword(s):  
Free Water ◽  
Temporal Variations ◽  
Technical Note ◽  
New Method ◽  
Predictor Variables ◽  
Water Evaporation ◽  
Phase Information ◽  
Multivariate Relationships ◽  
Wavelet Coherency ◽  
Wavelet Methods

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.

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

2021 ◽  
Vol 25 (1) ◽  
pp. 321-331
Author(s):  
Wei Hu ◽  
Bing Si
Keyword(s):  
Spatial Data ◽  
Free Water ◽  
Technical Note ◽  
New Method ◽  
Water Evaporation ◽  
Phase Information ◽  
Time Frequency ◽  
Multiple Variables ◽  
Wavelet Coherency ◽  
Artificial Datasets

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

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