Cross-Validation of Open-Path and Closed-Path Eddy-Covariance Techniques for Observing Methane Fluxes

Abstract

Methane (${\mathrm {CH}}_{4}$) fluxes observed with the eddy-covariance technique using an open-path ${\mathrm {CH}}_{4}$ analyzer and a closed-path ${\mathrm {CH}}_{4}$ analyzer in a rice paddy field were evaluated with an emphasis on the flux correction methodology. A comparison of the fluxes obtained by the analyzers revealed that both the open-path and closed-path techniques were reliable, provided that appropriate corrections were applied. For the open-path approach, the influence of fluctuations in air density and the line shape variation in laser absorption spectroscopy (hereafter, spectroscopic effect) was significant, and the relative importance of these corrections would increase when observing small ${\mathrm {CH}}_{4}$ fluxes. A new procedure proposed by Li-Cor Inc. enabled us to accurately adjust for these effects. The high-frequency loss of the open-path ${\mathrm {CH}}_{4}$ analyzer was relatively large (11 % of the uncorrected covariance) at an observation height of 2.5 m above the canopy owing to its longer physical path length, and this correction should be carefully applied before correcting for the influence of fluctuations in air density and the spectroscopic effect. Uncorrected ${\mathrm {CH}}_{4}$ fluxes observed with the closed-path analyzer were substantially underestimated (37 %) due to high-frequency loss because an undersized pump was used in the observation. Both the bandpass and transfer function approaches successfully corrected this flux loss. Careful determination of the bandpass frequency range or the transfer function and the cospectral model is required for the accurate calculation of ${\mathrm {CH}}_{4}$ fluxes with the closed-path technique.

Appendix 1: Maximal Overlap Discrete Wavelet Transform

In this study, the coherence among scalars was used in the bandpass approach as described in Sect. 3.2.1. The coherence with the maximal overlap discrete wavelet transform (MODWT) is defined below.

The $j$th level MODWT coefficients are defined for an arbitrary variable $x$ with a sample size $N$ as follows (Percival and Walden 2000),

$$\begin{aligned} \widetilde{W}_{x,j,t}\equiv \sum _{l=0}^{L_{j}-1} \widetilde{h}_{j,l}x_{t-l\,\hbox {mod}\, N} \end{aligned}$$

(8)

for $t=0,..., N-1$, where $\widetilde{h}_{j,l}$ are termed the $j$th level MODWT wavelet filters and are defined as $h_{j,l}/2^{j/2}$, where $h_{j,l}$ is the $j$th level wavelet filter; $L_{j}$ is the width of filters and is defined as $(2^{j}-1)(L-1)+1$, where $L$ is the width of the $j=1$ base filter. The cospectrum of $w$ and an arbitrary scalar, $x$, is given as follows,

$$\begin{aligned} C_{wx}(f)=\frac{1}{N}\sum _{t=0}^{N-1}\widetilde{W}_{w,j,t} \widetilde{W}_{x,j,t} \end{aligned}$$

(9)

where $f$ is defined as $f\equiv 1/(2^{j}\Delta t)$ with $\Delta t$ being the sampling interval. The MODWT is a non-orthogonal variant of the discrete wavelet transform (DWT); its decomposition is highly redundant in time. The redundancy of the MODWT coefficients modestly decreases the variance of certain wavelet-based statistical estimates (Cornish et al. 2006). This property may stabilize the characterization of turbulent transfer, especially over the frequency region below the spectral peak frequency.

The coherence between two arbitrary variables ($x$ and $y$), $\lambda _{xy}(f)$, was calculated using MODWT in a similar way to the DWT version (Scanlon and Albertson 2001) as follows,

$$\begin{aligned} \lambda {xy}(f)=\frac{C_{xy}(f)}{\sigma _{x,j}\sigma _{y,j}}, \end{aligned}$$

(10)

where $\sigma _{x,j}$ is the standard deviation of the $j$th level MODWT coefficients of variable $x$.

Wavelet analysis requires the determination of a wavelet filter function, and appropriate selection of the function depends on the objectives of the analysis and the time series being analyzed. We chose the least asymmetric wavelet with eight coefficients, LA(8) (Daubechies 1992), following Cornish et al. (2006). The LA(8) filter has better uncorrelatedness between wavelet coefficients across scales compared to the Haar filter, which has been more commonly used because of its simplicity, and thus the energy leakage problem from nearby frequencies (Qiu et al. 1995) has less influence on the calculated wavelet coefficients.