We examined the relative roles of gross ecosystem photosynthesis (GEP) and soil temperature in modulating the temporal spectrum of CH4flux with high frequency micrometeorological data collected continuously over the course of a growing season. We measured landscape-scale fluxes of CO2, H2O, CH4, and energy at a rice paddy located on Twitchell Island, CA, USA (latitude: 38.1087°N, longitude: 121.6530°W; elevation: 4 m below sea level) from the emergence of rice seedlings on 15 June 2011 to harvest on 15 October 2011. The water table at the field was maintained at 5 cm above the soil surface for the duration of the growing season. Winds during the study period were strong in magnitude and stable in direction where the 90% flux area footprint fell entirely within the bounds of the rice paddy. We measured soil temperature at 2 cm depth below the soil surface with three replicate copper-constantan thermocouples at a rate of 0.2 Hz, recorded as half-hourly averages. At a height of 3.05 m and a rate of 10 Hz, we measured 3-dimensional wind velocities (u, v, w) with a sonic anemometer (Gill WindMaster Pro; Gill Instruments Ltd, Lymington, Hampshire, England), CO2 and H2O density with an open-path infrared gas analyzer (LI-7500; LI-COR Biogeosciences, Lincoln NE, USA), and CH4density with a closed-path tunable diode laser CH4analyzer (FMA, Los Gatos Research, CA, USA). This sampling rate allowed for a 5 Hz cut-off for the co-spectra between the scalars (CO2, CH4, H2O) and turbulence, which was adequate for eddy covariance measurements at this site [Detto et al., 2011]. Additional micrometeorological instrumentation (air temperature, humidity, barometric pressure, incoming and net radiation, precipitation, and water table depth) is detailed by Hatala et al. .
 Using standard eddy covariance processing techniques, we analyzed fluxes of CO2, H2O, CH4, and heat after applying corrections with in-house software [Detto et al., 2010] explained in detail by Hatala et al. . Briefly, the procedure removed artificial data spikes (greater than six standard deviations from the mean) from the 10 Hz data and filtered bad readings that resulted from very infrequent fog events. For each 30-minute block of 10 Hz values, we applied a coordinate rotation to align the mean vertical and lateral wind velocities to zero and removed effects of air density fluctuations by the Webb-Pearman-Leuning correction [Detto and Katul, 2007; Webb et al., 1980]. We applied co-spectral corrections to CO2, H2O, and CH4fluxes to account for sensor separation, and additional co-spectral corrections to CH4 fluxes to correct for tube attenuation, residence time in the analyzer cell, and small changes in analyzer flow rate [Detto et al., 2011]. We filtered 30-minute flux values with anomalously high and low friction velocity (u* > 1.2 m/s and ∣uw∣ < 0.02 m/s) to constrain our analysis to periods where the air near the sensors was well-mixed. Of all possible 30-minute flux values during the growing season period in this analysis, 9% of CO2, H2O, and CH4fluxes were eliminated due to low friction velocity and an additional 10% of half-hourly CH4 fluxes were not available due to brief FMA sensor malfunction.
 We gap-filled CO2 fluxes using an artificial neural network approach standardized within the international Fluxnet project with meteorological variables driving the fitting [Papale et al., 2006]. To partition CO2 fluxes into gross ecosystem photosynthesis (GEP) and ecosystem respiration (Reco), we extrapolated nighttime CO2 flux as Recousing a short-term (2 week) 2 cm-depth soil temperature response and subtracted daytime Reco from net CO2 flux to obtain GEP [Reichstein et al., 2005]. To avoid spurious correlations between CH4flux and GEP, we did not gap-fill CH4 flux data with the artificial neural network technique, and instead replaced missing values with the median for the entire growing season. There were no gaps in the soil temperature time series for this measurement period. For spectral analysis, we standardized the CH4 flux, GEP, and soil temperature time series to have zero mean and unit variance.
2.1. Spectral Analysis Methods
 We used the continuous wavelet transform (CWT) with the Morlet mother wavelet to examine correlation between the spectra of GEP, CH4 flux, and soil temperature [Torrence and Compo, 1998]. Compared with Fourier analysis, wavelet spectral analysis is a more powerful tool for analyzing geophysical time series with nonstationarity, including trace-gas flux data measured by eddy covariance [Katul et al., 2001; Vargas et al., 2010]. The wavelet coherence spectrum is interpreted as the local correlation between two variables in frequency-time space where high coherence indicates phase-locked behavior between the two time series [Grinsted et al., 2004]. We tested the statistical significance of wavelet power against the null hypothesis of a red noise first order autoregressive process with lag-1 autocorrelation [Grinsted et al., 2004]. For time periods with significant wavelet coherence, we used the phase angle to calculate the time lag between the correlated oscillations of the two series.
 We used the method of Granger causality to determine whether the patterns of wavelet coherence between the time series of GEP and temperature and CH4 flux represented causal relationships. Granger causality is a method whereby a time series of one variable is determined to cause a second time series if it can successfully be used to predict the response of the second lagged time series [Granger, 1988], and here we applied the principles of conditional Granger causality to the nonparametric spectral domain [Chen et al., 2006; Dhamala et al., 2008] (auxiliary material). We tested the significance of nonparametric Granger causality against the null hypothesis that no direct interaction exists by the iterative amplitude adjusted Fourier transform, which preserves the power spectrum and distribution of the original time series but eliminates the correlation structure [Molini et al., 2010]. We tested the hypothesis that the periodic signal of GEP caused a periodic response in CH4 flux after we conditioned the response for the effect of soil temperature on CH4 flux. Support for this hypothesis indicates that GEP modulates CH4 flux at the time lags indicated by the spectral analysis.