Quantitative Evaluation of Wavelet Analysis Method for Turbulent Flux Calculation of Non‐Stationary Series

• Published in: Geophysical research letters Vol. 50; no. 5
• Main Authors: Li, Yubin, Wu, Yujie, Tang, Jie, Zhu, Ping, Gao, Zhiqiu, Yang, Yuanjian
• Format: Journal Article
• Language: English
• Published: Washington John Wiley & Sons, Inc 16.03.2023; Wiley
• Subjects: Accuracy; Bias; Datasets; Decomposition; Eddies; Eddy covariance; Fluxes; Methods; Mexican hat wavelet; Morlet wavelet; non‐stationary turbulence; Time series; Turbulence; Turbulent fluxes; Uncertainty analysis; Wavelet analysis; United States > US
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1029/2022GL101591

This study evaluates the uncertainties of turbulent flux calculation using eddy covariance (EC) and wavelet analysis (WA) methods. First, a non‐stationary data set is concocted by adding periodic waves and random perturbations which mimic the large eddies, turbulent intermittency, and asymmetry into an observational stationary data set, and the theoretical “true” fluxes are used to quantitatively evaluate the accuracy of these methods. Results show that EC and Morlet‐wavelet generate biases ranging 50%–100% of the “true” values at different non‐stationarity grades, whereas the Mexican hat (Mexhat) wavelet has a bias of about half of them. Furthermore, there is a high correlation of the Mexhat‐derived fluxes to the benchmark values, the regression slopes of the values of these two can be improved to almost 1 by adding a correction coefficient. The results suggest the potential of using the Mexhat‐wavelet method to calculate turbulent fluxes with high accuracy under non‐stationary conditions. Plain Language Summary Eddy covariance (EC) method is the well‐accepted technique to calculate turbulent flux under stationary conditions. However, the observational turbulence data sometimes show non‐stationarity, and in this case, the EC method is not applicable and wavelet analysis (WA) is frequently used. However, because turbulent fluxes are calculated values, and there are no true flux measurements, the accuracy of WA‐calculated fluxes remains unknown. In this study, we constructed a non‐stationary data set and used their theoretical true values to evaluate the accuracy of EC and WA methods in flux calculation under non‐stationary conditions. It is found that EC and Morlet‐wavelet bias 50%–100% of the true values at different non‐stationarity grades, while the Mexican hat (Mexhat) wavelet has the bias about half of them. Besides, there is a high correlation of the Mexhat‐derived fluxes to the true values, and Mexhat‐derived fluxes can be corrected to near true values by adding a correction coefficient. Therefore, the Mexhat‐wavelet method has the potential to be used to calculate turbulent fluxes under non‐stationary conditions. Key Points A method to concoct non‐stationary data series is proposed Eddy covariance and wavelet analysis methods underestimate turbulent momentum flux under non‐stationary condition by about 50% Mexican hat wavelet method has the potential to accurately calculate flux of non‐stationary turbulence after correction