Stable Carbon Isotope Studies of CH4 Dynamics Via Water and Plant Pathways in a Tropical Thai Paddy: Insights Into Diel CH4 Transportation

Separate evaluation of methane (CH4) emission dynamics (e.g., oxidation, production, and transportation) at the soil‐plant‐atmosphere and soil‐water‐atmosphere interfaces has been limited in tropical rice paddies, but it is crucial for comprehending the entire CH4 cycles. We investigated CH4 oxidation, production, and transportation through plant and water pathways during the reproductive stage in a tropical Thailand rice paddy field using natural abundance carbon stable isotope ratios (δ13CH4 and δ13CO2). Mass balance equations using δ13CH4 and δ13CO2 in soil gases indicated that CH4 oxidation in the planted soil exceeded those in the interrow soil due to oxygen supply through rice roots. In addition, at 1–11 cm depth acetate fermentation was the dominant process in the planted soil, whereas in the interrow soil the dominant process was H2/CO2 reduction. The water pathway showed a significant negative correlation between CH4 flux and released δ13CH4 over 24 hr, driven by a diel change in episodic ebullition, steady ebullition, and diffusion, all due to diel changes in soil temperature and atmospheric pressure. In contrast, the plant pathway showed a significant positive relationship between CH4 flux and emitted δ13CH4 throughout one day. A comparison of the diel change in emitted δ13CH4 between the water and plant pathways showed that the rice plants transported CH4 in soil bubbles without any large isotopic fractionation. The diel change in the plant‐mediated CH4 transportation was mainly controlled by diel changes in soil bubble expansion and CH4 diffusion through plants, which were probably regulated by diel changes in soil temperature and atmospheric pressure.


Introduction
Increasing concentration of atmospheric methane (CH 4 ) contributes to global climate change (Bindoff et al., 2013). CH 4 emissions from anthropogenic sources account for 54-72% of the total global The CH 4 emission dynamics in rice paddies are mainly controlled by CH 4 production, oxidation, and transportation processes (Schütz et al., 1989). Plant-mediated transportation usually dominates overall CH 4 emission (90%) (Butterbach-Bahl et al., 1997;Schütz et al., 1989), so studies of CH 4 emission dynamics often do not pay enough attention to evaluating separately the plant-and water-mediated pathways (Chanton et al., 1997;Khalil et al., 2008;Marik et al., 2002;Miyata et al., 2005;Rao et al., 2008;Tyler et al., 1994;Yagi et al., 1994;Zhang et al., 2011Zhang et al., , 2012Zhang et al., , 2017. For example, a study showed that CH 4 ebullition through paddy water accounted for 35-62% of total CH 4 emissions when rice straw was applied to tropical rice paddy fields (Wassmann et al., 1996). The organic matter (e.g., rice straw, root exudates, and decayed root) supply stimulates production of CH 4 that generally exists in the gas-phase (i.e., soil bubbles) rather than the liquid-phase (i.e., soil solution) due to low CH 4 solubility; eventually this increases CH 4 ebullition through paddy water (Hayashi et al., 2015;Schütz et al., 1989;Tokida et al., 2013;Wassmann et al., 1996). Therefore, the potential for such large water-mediated CH 4 emission makes it difficult to accurately understand the true nature of CH 4 emission dynamics in rice paddy fields. Thus, the plant-mediated pathway needs to be assessed separately from the water-mediated pathway and vice versa. Separate investigation of CH 4 emission dynamics via plant-and water-mediated pathway is limited, but it is essential to properly understand the entire CH 4 dynamics (Bridgham et al., 2013).
Natural abundance stable carbon isotope methods are useful for understanding the main controlling processes of CH 4 emission dynamics in rice paddy fields: CH 4 production, oxidation, and transportation (Chanton, 2005;Conrad, 2005;Tyler et al., 1997). The different δ 13 C values of CH 4 , CO 2 , and acetate make it possible to estimate the relative contribution of acetate-and H 2 /CO 2 -dependent methanogenesis to total CH 4 production, and the proportion of CH 4 consumption by methanotrophs (Conrad, 2005;Krüger et al., 2002;Tyler et al., 1997). Additionally, differences in δ 13 C of emitted CH 4 between the plant-mediated pathway, bubble ebullition, and diffusion via paddy water would enable evaluation of the CH 4 transportation modes from paddy soil to the atmosphere (Chanton, 2005;Tokida et al., 2014). Therefore, the application of the natural abundance stable carbon isotope methods to plant-and water-mediated pathways individually should help to clarify the contributions of these three main processes to CH 4 emissions via each pathway.
To date, most δ 13 CH 4 studies in rice paddy fields have investigated seasonal variations in CH 4 production, oxidation, and transportation processes (Bilek et al., 1999;Krüger et al., 2002;Marik et al., 2002;Nakagawa et al., 2002;Tyler et al., 1994Tyler et al., , 1997Zhang et al., 2011Zhang et al., , 2012Zhang et al., , 2013Zhang et al., , 2016Zhang et al., , 2017, but few have focused on diel variations. Two studies that have focused on diel variations of δ 13 CH 4 showed that δ 13 CH 4 emitted from rice paddies positively correlated with increasing CH 4 flux due to increasing transpiration rate or bubble ebullition (Chanton et al., 1997;Marik et al., 2002). However, both these studies only measured δ 13 CH 4 emitted through the mixed (both plant-and water-mediated) pathways using chambers; that is, the chambers measured not only the plant-mediated CH 4 transportation but also water-mediated transport. Thus, the diel variations in the two pathways remain unclear.
In this study, we applied natural carbon stable isotope methods to soil gas measurement in interrow and planted soils and to automatic plant and water chamber measurements. By using the isotopic measurements, we evaluated CH 4 emission dynamics (i.e., CH 4 oxidation, production, and transportation) at the respective soil-plant-atmosphere and soil-water-atmosphere interfaces during the reproductive stage in a tropical rice paddy in Thailand, one of the largest rice producing countries in tropical Asia (FAOSTAT, 2018). In particular, we examined the differences in soil CH 4 oxidation and production (e.g., acetate fermentation and H 2 /CO 2 reduction) between interrow and planted soils. We used soil and emitted δ 13 CH 4 values to assess the soil depths at which the methane that was transported into the atmosphere through the respective water and plant pathways originated. Also, using the soil and chamber measurements we attempted to partition the water-mediated CH 4 transportation into bubble ebullition (episodic and steady) and diffusion, as well as examining diel CH 4 transportation through the respective water and plant pathways. The specific research questions are summarized below: 1. What are the differences in CH 4 oxidation and CH 4 production (i.e., acetate fermentation and H 2 /CO 2 reduction) processes between planted and interrow soils? 2. At which soil depths did the soil CH 4 transported into the atmosphere through the water and plant pathways originate? 3. What is the diel variation in CH 4 transportation through the water (e.g., episodic bubble ebullition, steady bubble ebullition, and diffusion) and plant pathways, and how is it regulated?

Study Site and Measurement Period
Field experiments were carried out between 13 September and 28 September (DOY: 256-271) in 2014 in a farmer's rice paddy field at Kasetsart University (14°00′33″N, 99°59′03″E), Kamphaeng Saen campus in Nakhon Pathom Province, Thailand. The paddy soil was classified as clay soil (65.7% clay; 23.30% silt; 11.0% sand) with a dry bulk density of 1.69 Mg m −3 . The topsoil, sampled on DOY 260, had a soil pH of 5.98 (1:1, soil:water). Weeds and weedy rice were directly plowed into the paddy field soil on DOY 168 and 177, and then on DOY 181, seedlings of the rice variety "Homcholasit" were transplanted to the field with four to five seedlings planted in each location, 18 cm apart in the same row, with rows 30 cm apart. The heading of the rice plants began on DOY 265. The soil was continuously flooded from DOY 168 to 301 (harvest day) with the water depth ranging between 2-20 cm. During the gas measurement period, the flooding water depth was as follows. From the start of the gas measurements on DOY 256 until 10:50 a.m. local time (LT) on DOY 267, the water depth fell from 7.8 to 2.5 cm (Figure S1g in the supporting information). Then, after irrigation at 10:50 a.m. LT on DOY 267 and heavy rain on the same day (21.9 mm day −1 ), the water depth rose to 10.6 cm by 12:35 a.m. LT on DOY 268. Thereafter, it declined again to 6.9 cm by 5 p.m. LT on DOY 271 ( Figure S1g).

Soil Gas Sampling and Measurement
The gases in the paddy soil and water were collected using diffusive equilibration samplers. The diffusive equilibration samplers consisted of a PVC pipe (id = 38 mm, od = 39 mm, and length = 400 mm) with several drilled holes of 7 mm dia. and a 0.5 mm thick silicon sheet which entirely covered the pipe ( Figure S2), similar to Kato et al. (2013). The side of the silicon sheet in contact with the soil/water was protected by wrapping that side of the sheet in a plastic mesh. Both ends of the sampler were sealed with silicone rubber stoppers, and one of the rubber stoppers was connected to a nylon tube which was extended above ground in order to collect the gas samples from the samplers. On DOY 211, the soil gas samplers were buried horizontally at 1-5, 7-11, and 13-17 cm depths under both a rice hill and an interrow space between rice plants ( Figure S3). On the same day, the water gas sampler was submerged flat in the paddy water. Gas samples were taken from under the planted soil by plastic syringes at noon LT on DOY 257,260,261,263,and 269. The gases in the interrow soil and surface water were collected at noon LT on DOY 257, 260, 263, and 269. After each sampling of the water or soil gases, atmospheric air was drawn into the samplers automatically due to negative pressure inside the samplers themselves. Then, the above ground end of the nylon tube was sealed by a three-way stopcock to prevent gas exchange between the sampler and atmosphere during nonmeasurement periods. Since the samplers needed to equilibrate with surrounding gases for 11 hr, a gas sampling interval of at least 1 day was assumed to be enough for gas equilibration between air inside the samplers and the soil/water gases. We measured the concentration and δ 13 C of CH 4 , CO 2 in the soil/water gas samples, which were diluted 81× or 101× with high-purity nitrogen gas, using a wavelength-scanned cavity ring-down spectroscopy (WS-CRDS) analyzer (G2201-i, Picarro Inc., Santa Clara, CA, USA). In the laboratory test, we found an isotopic fractionation across the diffusive equilibration sampler for CH 4 : +1.8‰ (unfortunately not assessed for CO 2 ). The isotopic fractionation was subtracted from the δ 13 CH 4 measured by the samplers. This isotopic fractionation was also subtracted from the δ 13 CO 2 values measured by the samplers with the assumption that the isotopic fraction for CH 4 was as same as that for CO 2 .

Automatic Plant and Water Chamber Measurements
The emissions of CH 4 and δ 13 CH 4 through rice plants and paddy water were measured using two polycarbonate automated closed chambers (Green Blue Corp., Tokyo, Japan; Figure S3). On DOY 232 (20 August), one of the chambers (24 × 24 cm at the base and 140 cm tall) was placed over a rice hill with the lid left open. Starting on DOY 256, the water surface at the bottom of the plant chamber was covered by air bubble cushioning wrap, with assumed minimal gas permeability, to prevent methane emissions via paddy water, so that (as much as possible) the chamber only captured CH 4 transported through the rice plants. It is still possible that some water-mediated CH 4 emission could be captured in the chamber due to transported along the hydrophobic rice plant exterior. However, the uncovered water-surface area exposed to the atmosphere was very small, only a very small area between the plant culms, so we believe that this chamber, the plant chamber, predominantly measured CH 4 emitted through the plant pathway. The other chamber (50 × 20 cm at the base and 40 cm height) was inserted between rice plants on DOY 220 to measure the CH 4 exchanges via paddy water. From DOY 256 to 271, the top lids of both chambers were automatically closed for 10 min every hour, to measure the CH 4 fluxes and emitted δ 13 CH 4 . The headspace air in each chamber was mixed during lid closure using a small electric fan which was incorporated into each chamber. The fan in the plant chamber also ran during nonmeasurement periods when the lids were open in order to prevent gas residence at the bottom of the tall chambers. During the lid closure period, the headspace air in each chamber was circulated through a 250 ml buffer tank, placed inside a shed about 4 m from each chamber, at 500 ml min −1 flow rate by a diaphragm pump (TD-4X2N, Brailsford Co., Rye, NY, USA). Another diaphragm pump (UN84.4 ANDC-B, KNF Neuberger Inc., NJ, USA; flow rate~25 ml min −1 ) sucked the headspace air in the buffer tank through the WS-CRDS analyzer, calibrated as described in section 2.2.1, which monitored the change in CH 4 concentration and δ 13 CH 4 in each chamber at around 3.6 s intervals in the high precision (HP) and high dynamic range (HR) modes. In case of an abrupt CH 4 concentration increase for a short period time, measurement artifacts occurred in the HR mode data stream and afterwards the measurement returned to normal. No such artifacts occurred in the HP mode, but the HP mode could only measure CH 4 concentrations up to 15 ppm. So only the HR mode continuously measured CH 4 concentration and δ 13 CH 4 , including times when the CH 4 concentration exceeded 15 ppm. The analyzed air was returned to the loop line, but before the sampled air entered the analyzer, the air was dehumidified by a membrane dryer (SWG-A01-06, Asahi Glass Engineering Co., Chiba, Japan) to water vapor concentration of less than 0.1%. The initial air after closing the chambers reached the WS-CRDS analyzer in about 2 min, estimated from the internal volumes of the buffer tank and connecting tubes and also the flow rate of the two pumps. Each chamber measurement was finished when the lid of the chamber opened, so that one measurement cycle for each chamber ran for 8 min. The respective plant and water chamber measurements were conducted every hour at 32 and 50 min after the hour.
The methane flux was calculated using an exponential method (de Mello & Hines, 1994) following Komiya et al. (2015) ( Figure S4a). In cases when the exponential method did not fit well, a linear regression method was applied (Davidson et al., 1998). The emitted δ 13 CH 4 (δ 13 CH 4_emit ) for a chamber measurement period was obtained as the intercept of the Keeling plot ( Figure S4c). The Keeling plot intercept (=δ 13 CH 4_emit ) was acquired from a simple linear regression line between δ 13 CH 4 and a reciprocal of CH 4 concentration in the headspace air. When the Keeling correlation was weak (r < 0.20, p > 0.05, n > 66) or the analyzer was not able to precisely measure the change in δ 13 CH 4 due to a too rapid change in CH 4 concentration triggered by bubble ebullitions, the value of δ 13 CH 4_emit was approximately estimated from the following mass balance equation (Krüger et al., 2002): where CH 4_ini and δ 13 CH 4_ini are the 1-min averages of the concentration (ppm) and δ 13 C value of CH 4 in the chamber air, either at the start of the measurement (when analyzer in the HP mode) or up to 2.5 min before the start of measurement (when the analyzer was in the HR mode; see above). The CH 4_end and δ 13 CH 4_end are averages of the CH 4 concentration and δ 13 CH 4 in the head-space air for the last 1 min of a chamber measurement. The values of δ 13 CH 4_emit by the mass balance method agreed well with δ 13 CH 4_emit by the Keeling plot method using the plant chamber data sets which could obtain δ 13 CH 4_emit by both of the methods for most of the measurement period ( Figure S5). Thus, we believe that the mass balance method is valid for estimating δ 13 CH 4_emit .

Environmental Variables
Atmospheric pressure was measured with a barometer (MPXAZ6115A and MPXV7007DP, Freescale Inc., TX, USA), and air temperature was measured with a temperature sensor (HMP45A, Vaisala Inc., Helsinki, Finland). Soil temperatures were measured at 0, 3, 9, and 15 cm below the soil surface with type T thermocouples. Water depth above the soil surface was measured with a water level sensor (eTapeTM Continuous Fluid Level Sensor, Milone Technologies Inc., NJ, USA).

Analysis of Soil CH 4 Oxidation and Production
We estimated the CH 4 oxidation fraction of total soil CH 4 using the following mass balance equation with the in situ measured δ 13 CH 4 , based on the assumption that total CH 4 in soil was mainly composed of CH 4 oxidation (F ox(total) ) and production (1 − F ox(total) ): where δ 13 CH 4(total) is the measured δ 13 CH 4 value of soil gases, δ 13 CH 4(prod) is the δ 13 C value of CH 4 produced and unoxidized in paddy soil, and δ 13 CH 4(oxidized) is the δ 13 C value of CH 4 oxidized by methanotrophs. The value of δ 13 CH 4(prod) was assumed to be equivalent to δ 13 CH 4 values in emitted bubbles from the interrow soil because the released bubbles from the interrow soil were not thought to be affected by CH 4 oxidation, both due to rapid transportation from the soil without isotopic fractionation and low root availability in the interrow soil (Chanton, 2005). The value of δ 13 CH 4(oxidized) was deduced from the following mass balance equation for F ox(total) (Tyler et al., 1997): solved for δ 13 CH 4(oxidized) by assuming F ox = 1, where α ox is the isotopic fractionation during the CH 4 oxidation process. Chanton et al. (2008) reported values of α ox between 1.025 and 1.038 in landfill soil over a temperature range of 12-35°C, similar to temperatures in anaerobic paddy soil. A similar α ox range between 1.025 and 1.033 was also found in a Chinese paddy soil at 28.3°C (Zhang et al., 2013). Unfortunately, since we did not directly measure α ox in this paddy soil, we estimated δ 13 CH 4(oxidized) by using the two different α ox values (=1.025 and 1.038), and then calculated F ox(total) at each depth in the planted and interrow soils. The values of δ 13 CH 4(total) , δ 13 CH 4(prod) , δ 13 CH 4(oxidized) , and F ox(total) on each sampling day are shown in Tables S2 and S3.
The net CH 4 production (F prod = 1) in paddy soil is assumed to be mainly derived from acetate fermentation (F ac ) and H 2 /CO 2 reduction (1 − F ac ) processes, allowing us to obtain the following mass balance equation (Conrad, 2005;Krüger et al., 2002;Tyler et al., 1997), where δ 13 CH 4(acetate) and δ 13 CH 4 H2=CO2 ð Þ are the δ 13 C values of acetate-derived and H 2 /CO 2 -derived CH 4 , respectively. δ 13 CH 4(prod) is the δ 13 C value of CH 4 produced in paddy soil. As stated above, the value of δ 13 CH 4 in emitted bubbles from interrow was assumed to represent the unoxidized and produced δ 13 CH 4 (=δ 13 CH 4(prod) ). Values of δ 13 CH 4(acetate) in Japanese and Italian rice paddy soils have been reported ranging between −37‰ to −43‰ (Krüger et al., 2002;Sugimoto & Wada, 1993). Since the F ac values in our study did not largely vary from this δ 13 CH 4(acetate) range of −37‰ to −43‰ (Table S4), the value of δ 13 CH 4(acetate) was set as the average, −40‰. The values of F ac on each sampling day are also shown in Table S4.
The value of δ 13 CH 4 H2=CO2 ð Þ was calculated through the following definitional equation for the carbon isotope fractionation factor (α CO2=CH4 ), where δ 13 CO 2(prod) is the δ 13 C value of CO 2 produced in paddy soil. The δ 13 CO 2(prod) values were assumed to be the δ 13 CO 2 value in the soil gas at each depth. The value of α CO2=CH4 in submerged paddy soil generally varies from 1.045 to 1.083 (Conrad, 2005;Fey et al., 2004;Sugimoto & Wada, 1993;Zhang et al., 2011Zhang et al., , 2013. Given that some α CO2=CH4 can produce negative values of calculated F ac at some depths, an appropriate range of α CO2=CH4 for estimating F ac values of 0-1 at all depths was 1.057-1.083 in the planted soil, and 1.073-1.083 in the interrow soil ( Figure S6). The α CO2=CH4 in a submerged paddy soil decreased from 1.083 to 1.076 as temperature rose from 10°C to 37°C (Fey et al., 2004). In our study, the mean soil temperature at 1-15 cm depth was around 30°C on the gas sampling days, so the value of α CO2=CH4 was set to be 1.078 at 30°C (Fey et al., 2004). Finally, the acetate fermentation fraction of the total soil CH 4 (=F ac(total) ) was determined by multiplying F ac by (1 − F ox(total) ); presented and discussed in sections 3.2 and 4.1. The values of δ 13 CO 2(prod) , δ 13 CH 4 H2=CO2 ð Þ , and F ac(total) on each sampling day are shown in Tables S5 and S6.

Wavelet Analysis
We used cross wavelet and wavelet coherence analysis that can suitably examine correlation between two nonstationary geophysical time series data sets at different time frequency (Torrence & Compo, 1998). The analysis helped us to identify any diel linkage between δ 13 CH 4_emit , CH 4 flux, and potentially associated parameters such as soil temperature and atmospheric pressure. The wavelet coherence (R n 2 (s)), representing local correlation coefficients in time frequency space, is defined as, where W n XY (s) represents the cross wavelet spectrum of two time series data sets (X n and Y n ). W n X (s) and W n Y (s) are the cross-wavelet power. S and s denote a smoothing operator and the time scale, respectively.
Further definitions can be found in Grinsted et al. (2004). The statistical significance test for wavelet 10.1029/2019JG005112

Journal of Geophysical Research: Biogeosciences
coherence was conducted using Monte Carlo methods according to Grinsted et al. (2004). We also estimated the time lag from the phase angle between the two time series data sets for statistically significant correlated periods. All wavelet analysis was performed using the freely available MatLab package developed by Grinsted et al. (2004) (available at https://sites.google.com/a/glaciology.net/ grinsted/wavelet-coherence). Before implementing wavelet analysis, we first checked whether all measured time series data sets were normally distributed following Grinsted et al. (2004). The Shapiro-Wilk test showed that none of the time series data sets were normally distributed, so we transformed the raw time series data into the time series of percentiles following Grinsted et al. (2004).
In addition, we gap-filled missing CH 4 flux and δ 13 CH 4_emit data because the wavelet analysis package does not accept time series data with missing values. Throughout the whole experimental period, the data gaps comprised 2.8% of the CH 4 flux and δ 13 CH 4_emit data for the plant chamber measurements and 2.5% of the equivalent water chamber measurements. To estimate the respective missing data we used the relationships found during the measurement period between CH 4 flux and soil surface temperature and between δ 13 CH 4_emit and soil surface temperature.

Soil CH 4 Oxidation and Production Fractions
At each depth, there was little difference in the mean CH 4 oxidation fraction (F ox(total) ) estimated using either α ox 1.025 or α ox 1.038, except at 13-17 cm depth in the planted soil which had the highest F ox(total) values ( Figure 1 and Table S3). The mean F ox(total) at each depth was higher in the planted soil than in the interrow soil ( Figure 1). Based on these F ox(total) values ( Figure 1 and Table S3), the fraction of CH 4 production (F prod = 1 − F ox(total) ) in the paddy soil ranged between 0.58 and 0.97.
The estimated mean acetate fermentation fraction (F ac(total) ) values were also similar for α ox 1.025 and 1.038 at each depth, except once again at 13-17 cm depth in the planted soil ( Figure 1 and Table S6). The mean F ac (total) values at each depth were higher in the planted soil than in the interrow soil, except at 13-17 cm soil depth. Additionally, the F ac(total) values in the interrow soil increased with soil depth (Figure 1b).
The remaining fraction was assumed to be CH 4 production by H 2 /CO 2 reduction   (F ox(total) ) and acetate fermentation (F ac(total) ) fractions of total CH 4 in the planted soil (a) and interrow soil (b). The values of F ox(total) were estimated by two previously reported α ox values (=1.025 and 1.038). The F ac(total) values were calculated from the F ox(total) values. All values were averaged for four to five gas sampling days. The bars show one standard deviation (n = 4-5).

Soil and Emitted δ 13 CH 4
The carbon isotopic values of CH 4 in the interrow soil at all the depths ranged from −56.5‰ to −53.6‰.
These isotope values are similar to the emitted δ 13 CH 4 values (=δ 13 CH 4_emit ) through the water pathway throughout the entire measurement period, with an interquartile range between −57.4‰ and −51.8‰ (Figure 2a). Welch's t test showed that the interrow soil δ 13 CH 4 at 1-5 cm depth was not significantly different from the water-mediated δ 13 CH 4_emit (Figure 2a, p > 0.4). However, the δ 13 CH 4 values in the paddy water were significantly heavier than the water-mediated δ 13 CH 4_emit (Figure 2a, Welch's t test, p < 0.001).
In the planted soil, δ 13 CH 4 values at all depths were significantly heavier than the plant-mediated δ 13 CH 4_emit measured at the nearest equivalent sampling time (11:32 a.m. LT) on each day throughout the entire period ( Figure 2b, Welch's t test, p < 0.005). The planted soil δ 13 CH 4 were compared with only the plant-mediated δ 13 CH 4_emit at 11:32 a.m. LT on each day because it was considered that the planted soil δ 13 CH 4 values may have changed throughout the day due to a diel change in root oxygen and perhaps exudate supplies (Badri & Vivanco, 2009;Cho et al., 2012;Colmer & Pedersen, 2008;Waters et al., 1989;Watt & Evans, 1999). This was not considered to be a problem in the interrow soil which did not have a high density of plant roots. Figure 3 shows mean diel variations in CH 4 flux and δ 13 CH 4_emit via the water and plant pathways, obtained from measured data throughout the whole period (Figures S1a, S1b, S1c, and S1d). Methane fluxes through paddy water increased from 7:50 a.m. LT, reaching a maximum value in the afternoon, followed by a decrease to a minimum early the following morning (Figure 3a). In contrast, the water-mediated δ 13 CH 4_emit displayed minimum values in the afternoon and subsequently increased during the night, reaching a maximum peak between 7:50 and 10:00 a.m. LT (Figure 3b). The antiphase variations between the water-mediated CH 4 flux and the δ 13 CH 4_emit established a significant negative correlation between the water-mediated log 10 -CH 4 flux and δ 13 CH 4_emit (r = −0.77; p < 0.001; Figure 3c). A significant negative correlation was observed in all the measurement data (r = −0.57; p < 0.01; n = 352; Figure S7a). (b) Boxplot of planted soil δ 13 CH 4 at depths of 1-5 cm (P1-5), 7-11 cm (P7-11), and 13-17 cm (P13-17), δ 13 CH 4_emit through the plant pathway (emission via plant), and δ 13 CH 4_emit via bubble ebullition through the water pathway from DOY 256 to 271. Since the planted soil δ 13 CH 4 was assumed to vary during each day due to a diel change in root oxygen and perhaps exudate supplies (Badri & Vivanco, 2009;Cho et al., 2012;Colmer & Pedersen, 2008;Waters et al., 1989;Watt & Evans, 1999), the planted soil δ 13 CH 4 at each depth (n = 4-5) was compared with only the plant-mediated δ 13 CH 4_emit at 11:32 a.m. LT from DOY 256 to 271 (n = 15). In contrast, the lack of roots in the interrow soil meant little diel change in root oxygen and exudate supplies, so the interrow soil δ 13 CH 4 at each depth (n = 4) was assumed to be comparable with the water-mediated δ 13 CH 4_emit for the entire period (n = 352). The plant-mediated δ 13 CH 4_emit at 11:32 a.m. LT was also compared with the water-mediated δ 13 CH 4_emit through bubble ebullition observed at 11:50 a.m. LT from DOY 256 to 271 (n = 9) assuming no significant difference in δ 13 CH 4_emit due to the different timing (32 and 50 min past each hour) of the water and plant chamber measurements. The reason for the smaller number of samplers for water-mediated δ 13 CH 4_emit through bubble ebullition (n = 9) was because bubble ebullition was not observed in the water chamber on every measurement day.

Diel Variation in CH 4 Transportation Through the Water and Plant Pathways 3.3.1. Mean Diel CH 4 Variations
The CH 4 fluxes through the plant pathway followed a similar pattern to those through the water pathway, with a maximum flux in the afternoon, followed by lower fluxes at night (Figure 3d). The plant-mediated δ 13 CH 4_emit also followed a similar diel pattern (Figure 3e), meaning there was a significant positive correlation between the plant-mediated log 10 -CH 4 flux and δ 13 CH 4_emit (r = 0.80; p < 0.001; Figure 3f). This corresponds to the results in previous studies (Chanton et al., 1997;Marik et al., 2002). A significant positive relationship between log 10 -CH 4 flux and δ 13 CH 4_emit through the plant pathway was also found for all the data throughout the measurement period (r = 0.50; p < 0.01; n = 351; Figure S7b).
The mean diel cycles in CH 4 fluxes through the two pathways closely matched the mean diel change in soil surface temperature, with an increase from the early morning to the afternoon, followed by a decrease at nighttime (Figures 3a, 3d, and 3g). The mean diel change in plant-mediated δ 13 CH 4_emit also closely matched that of soil surface temperature (Figures 3e and 3g), but water-mediated δ 13 CH 4_emit showed an opposite pattern to soil surface temperature (Figures 3b and 3g). The diel variation in δ 13 CH 4_emit through the water pathway was more like the diel change in atmospheric pressure, with a minimum in the afternoon and a maximum in the early morning (Figures 3b and 3h). The mean diel pattern in atmospheric pressure was mostly converse to that for CH 4 flux through both the water and plant pathways, and also for plant-mediated δ 13 CH 4_emit (Figures 3a, 3d, 3e, and 3h).

Wavelet Coherence Results
The wavelet coherence analysis showed a significant antiphase coherence between the water-mediated CH 4 flux and δ 13 CH 4_emit at the daily timescale (Figure 4a). There was a 1.9-hr lag throughout most of the measurement period, obtained from the mean phase angle (=−151.5°) within the 5% significant region. This supports the significant negative relationship found between the mean diel log 10 -CH 4 flux and δ 13 CH 4_emit through the water pathway (cf. section 3.3.1; Figure 3c). Moreover, throughout most of the measurement period, the δ 13 CH 4_emit through paddy water showed significant antiphase coherence with soil surface temperature, with a daily lag of 0.8 hr (−168.0°) (Figure 4c). This reflected the opposite diel patterns of water-mediated δ 13 CH 4_emit and soil temperature (Figures 3b and 3g). In contrast, there was a significant in-phase coherence at the daily timescale between the δ 13 CH 4_emit via the water pathway and atmospheric pressure, with only a 0.7-hr lag (−10.9°) (Figure 4e). This in-phase relationship was also consistent with the similar mean diel patterns of δ 13 CH 4_emit and atmospheric pressure (Figures 3b and 3h).
Unlike the water pathway, the plant pathway usually showed a significant in-phase relationship between CH 4 flux and δ 13 CH 4_emit at the daily timescale, with a 1.5-hr lag (−22.6°) throughout the measurement period (Figure 4b). This supports the significant positive correlation between the mean diel log 10 -CH 4 flux and δ 13 CH 4_emit (Figure 3f). The plant-mediated δ 13 CH 4_emit also showed significant in-phase coherence with soil surface temperature, with a daily lag of only 0.6 hr (−8.8°), and antiphase coherence with atmospheric pressure when the daily lag was 2.1 hr (148.9°) (Figures 4d and 4f). The in-phase relationship between plant-mediated δ 13 CH 4_emit and soil temperature at the daily scale can also be seen from the mean diel variations in plant-mediated δ 13 CH 4_emit and soil temperature (Figures 3e and 3g). Similarly, the antiphase relationship between plant-mediated δ 13 CH 4_emit and atmospheric pressure can be seen from the mean diel variations in plant-mediated δ 13 CH 4_emit and atmospheric pressure (Figures 3e and 3h).

CH 4 Processes in the Planted and Interrow Soils 4.1.1. Soil CH 4 Oxidation
The F ox(total) values indicate that there was higher CH 4 oxidation in the planted soil than in the interrow soil. This finding is also strongly suggested from the differences in soil gas concentrations and isotope signatures between the two soils (Text S1 and Figure S8). The results further indicate that the planted soil had more aerobic soil conditions, probably from root oxygen supplied via rice aerenchyma to the rhizosphere during the daytime (Cho et al., 2012;Colmer & Pedersen, 2008;Waters et al., 1989), and this increased CH 4 oxidation by methantrophic bacteria. In contrast, the lower root availability in the interrow soil would have reduced oxygen supply, resulting in more anaerobic conditions that would have reduced methantrophic bacteria activity.
The F ox(total) values in the paddy soil indicate that the greatest soil CH 4 oxidation by methanotrophic bacteria occurred in the planted soil at 13-17 cm depth. The highly active CH 4 oxidation at this depth was probably because of aerobic conditions due to high oxygen supply via rice roots. Root tips generally release oxygen more than the basal part of roots where barriers to radial oxygen loss (ROL) are developed (Armstrong, 1979(Armstrong, , 2000Nishiuchi et al., 2012), suggesting that there was a high density of root tips at 13-17 cm depth in the planted soil. The rice cultivar used in our study is assumed to have roots extending to 15-40 cm depth, with a high root density at 0-15 cm depth during the reproductive stage. Schmidt et al. (2011) and Atulba et al. (2015) have also confirmed that the root-oxidized area is developed at 10-20 cm depth during the rice reproductive stage. These results support the high distribution of rice root tips at 13-17 cm depth in the planted soil.

Soil CH 4 Production and Dominant Soil CH 4 Process
Methane production was the dominant CH 4 process in both paddy soils during the reproductive growth stage (F prod ≥ 0.58). Acetate fermentation (F ac(total) ) was occurring more actively in the planted soil than CH 4_emit via the plant. The color represents the local coherence, corresponding to local correlation coefficients in time and frequency domains. The regions of significant coherence (at the 5% significance level determined using Monte Carlo methods) are the yellow regions enclosed by the thick black lines (Grinsted et al., 2004). Outside the cone of influence (the large cone shaped region bounded by the thin curved line), the wavelet transform suffers from edge effects (Grinsted et al., 2004). The black arrows in the water pathway plots indicate the phase angle relationship between the two time-series variables X (i.e., (a) CH 4 flux via water, (c) soil surface temperature, or (e) atmospheric pressure) and Y (δ 13 CH 4_emit via water). The black arrows in the plant pathway plots indicate the phase angle relationship between the two time-series variables X (i.e., (b) CH 4 flux via the plant, (d) soil surface temperature, or (f) atmospheric pressure) and Y (δ 13 CH 4_emit via the plant). Arrows pointing to the right without any phase shift signify the two variables are perfectly in-phase, whereas arrows pointing to the left without any phase shift mean they are perfectly antiphase. Arrows pointing vertically upward signify that Y leads X by 90°in in-phase. The lead of 90°can also be interpreted as Y lagging X by 270°in in-phase or Y lagging X by 90°in antiphase. The phase angles of the arrows increase in a clockwise direction and signify the time lag between the X and Y variables, dependent on the time period (y-coordinate) (e.g., 90°at the 1-day time period = 6-hr lag at the daily timescale). Further information can be found in Grinsted et al. (2004).

Journal of Geophysical Research: Biogeosciences
in the interrow soil at 1-11 cm depths, probably due to acetate supply from rice roots enhancing acetoclastic methanogens in the planted rhizosphere soil (Hayashi et al., 2015;Lee et al., 2015;Schütz et al., 1989). In contrast, the low root availability in the interrow soil would have limited root acetate supply, which would explain the larger contribution of H 2 /CO 2 reduction F H2=CO 2 total ð Þ ≥ 0:53 to CH 4 production at these depths.
However, at 13-17 cm depth in the interrow soil acetate fermentation was more dominant than H 2 /CO 2 reduction (F ac(total) > 0.5). This suggests that there were more acetoclastic methanogens available in the deeper paddy soil, as has also been found by Lee et al. (2015). In contrast, the CH 4 production from acetate fermentation in the planted soil was lower at 13-17 cm depth than at 1-11 cm depth. This was probably due to the more aerobic conditions in the planted soil at that depth (see section 4.1.1) reducing the activity of acetoclastic methanogens.

CH 4 Transportation Via Water 4.2.1. Water-Mediated CH 4 Transportation Partitioning
The lack of any significant difference in δ 13 CH 4 between the interrow soil CH 4 at 1-5 cm depth and CH 4 emission via the water pathway indicates that most of the observed CH 4 emission through the water pathway was derived from bubble ebullition. This is because bubble ebullition generally does not cause any large isotopic fractionation during the transportation from the soil to the atmosphere (i.e., δ 13 CH 4_emit ≈ soil δ 13 CH 4 ) (Chanton, 2005), whereas diffusion generally causes isotopic fractionation during gas transport, which would result in heavier δ 13 CH 4_emit than soil δ 13 CH 4 (Chanton, 2005;Happell et al., 1994). Although hydrodynamic transport, which is involved in the diffusion process, is assumed to cause less isotopic fractionation than molecular diffusion, it would still produce more isotopic discrimination than bubble ebullition.
Assuming that the bubble ebullition process emitted δ 13 CH 4 that was similar or lighter than the soil δ 13 CH 4 , we divided the water-mediated CH 4 emission for each chamber measurement into bubble ebullition (δ 13 CH 4_emit < −53.6‰) and diffusion (δ 13 CH 4_emit > −53.6‰) processes by using the maximum interrow soil δ 13 CH 4 (=−53.6‰) as the upper limit for bubble ebullition (Figure 5a). The diffusion process, including hydrodynamic transport, was assumed to release heavier δ 13 CH 4 than soil δ 13 CH 4 due to the influence of isotopic fractionation by diffusion and CH 4 oxidation at the soil-water interface (Chanton, 2005).

Journal of Geophysical Research: Biogeosciences
There was usually only a gradual increase in CH 4 concentration during a chamber closure period due to diffusion (δ 13 CH 4_emit > −53.6‰), with almost all CH 4 flux rates of less than 5 mg m −2 hr −1 , significantly lower than bubble ebullition (Figure 5a, Welch's t test, p < 0.001). The upper value of the diffusive CH 4 flux rate (5 mg m −2 hr −1 ) agrees with the mean diffusive CH 4 flux rate at the water-atmosphere interface in a flooded fen site (Hoffmann et al., 2017), so the value was considered as the upper threshold diffusive CH 4 flux rate. Furthermore, in another flooded wetland study (Poindexter et al., 2016), the maximum diffusive CH 4 flux rate by hydrodynamic transport was 200 nmol m −2 s −1 (=11.52 mg m −2 hr −1 ), which covers the maximum outlier diffusive CH 4 flux rates in our study (Figure 5a). Therefore, these wetland field data support the division between diffusion and bubble ebullition based on soil δ 13 CH 4 (=−53.6‰).
In contrast, bubble ebullition (δ 13 CH 4_emit < −53.6‰) usually produced CH 4 flux rates higher than the maximum limit for CH 4 diffusion (=5 mg m −2 hr −1 ) (Figure 5a). Bubble ebullition is mainly classified into episodic and steady ebullitions (Coulthard et al., 2009;Green, 2013). The episodic ebullition process rapidly releases bubbles from the soil into the atmosphere and therefore usually shows high CH 4 flux rates (Komiya et al., 2015;Tokida et al., 2007), which suggests that most of the measured bubble ebullition in our study was derived from episodic ebullition.
During the study period, episodic ebullition, steady ebullition, and diffusion were confirmed as the respective dominant CH 4 emission pathways in 40.9%, 19.3%, and 39.8% of the water chamber measurements (n = 352) (Figure 5b). Episodic ebullition was the predominant pathway during high CH 4 emissions from paddy water (CH 4 flux >5 mg m −2 hr −1 ), whereas the diffusion process was the dominant pathway during low CH 4 emission via water (CH 4 flux <5 mg m −2 hr −1 ). The low contribution of steady ebullition may have been due to the influence of CH 4 oxidation on small CH 4 bubbles as they gradually passed through the soil-water surface (Green, 2013).

From Which Soil Depth Are Bubbles Released Via Water?
The δ 13 CH 4_emit via steady ebullition was similar to the interrow soil δ 13 CH 4 at 7-11 cm depth (Figures 2a and 5b, Welch's t test, p > 0.9). This indicates that bubbles released via steady ebullition originated from 7-11 cm soil depth. In contrast, the δ 13 CH 4_emit via episodic ebullition was significantly lighter than the interrow soil δ 13 CH 4 at any depth (Figures 2a and 5b, Welch's t test, p < 0.005). This would suggest that the episodic ebullition process released bubbles from below 17 cm soil depth. However, clay paddy soil is not very porous, so it is unlikely that episodic ebullition could rapidly and smoothly release bubbles from deep soil (below 17 cm) into the atmosphere. Also, episodic ebullition releases bubbles rapidly from the soil meaning it is possible that the gas samplers in our study did not have enough time to adequately equilibrate with the soil gas and so accurately detect the carbon isotopic signal of CH 4 in the rapidly released bubbles. Based on the points in the previous sentences, it is more likely that the bubbles emitted via episodic ebullition were actually expanded from small bubbles in the soil. These small bubbles were mainly produced at 7-11 cm depth and then transferred to the soil surface layer and then the atmosphere. In the afternoon the soil temperature in the surface soil (e.g., 0-7 cm) increased more sharply than in deeper soil ( Figure S9), and this probably would have enabled the small bubbles in the shallower soil to expand more easily, which would have triggered the episodic ebullition.

Diel CH 4 Transportation Via Water (Bubble Ebullition and Diffusion)
The wavelet analysis results indicate that diel CH 4 transportation through the water pathway was significantly related to diel variations in soil surface temperature and atmospheric pressure. As discussed in section 4.2.1, there are three main CH 4 emission pathways via paddy water: episodic ebullition, steady ebullition, and diffusion. Based on δ 13 CH 4_emit and CH 4 flux, we apportioned the number of times that each of the three CH 4 emission pathways was the dominant pathway contributing to the total CH 4 in each hourly water chamber measurement ( Figure 6).

CH 4 Transportation Via Plants 4.3.1. From Which Soil Depth Is Methane Released Via Rice Plants?
The plant-mediated δ 13 CH 4_emit , measured at 11:32 a.m. LT, was significantly different from the planted soil δ 13 CH 4 at all the depths, but not significantly different from the water-mediated δ 13 CH 4_emit by bubble ebullition at the nearest equivalent time (11:50 a.m. LT) (Figure 2b, Welch's t test, p > 0.17). The water-mediated δ 13 CH 4_emit by bubble ebullition normally represents bubble δ 13 CH 4 in the soil (i.e., emitted bubble δ 13 CH 4_emit ≈ soil bubble δ 13 CH 4 ). Therefore, these results indicate that, at least around the noon chamber measurement time, the rice plants transported CH 4 in bubbles from the paddy soil through the plant aerenchyma into the atmosphere without any large isotope fractionation.
To further examine whether the rice plants transported methane in bubbles at other times, we compared δ 13 CH 4_emit values between the plant and water pathways at each hour of the day (plant and water chamber measurements at 32 and 50 min past each hour, respectively) ( Figure 7). There was no significant difference in δ 13 CH 4_emit between the plant and water pathways from 11:32 a.m. to 6:50 p.m. LT when bubble ebullition dominated the water pathway, as discussed in section 4.2.3 (emitted bubble δ 13 CH 4_emit ≈ soil bubble δ 13 CH 4 ) (Figure 7, Welch's t test, p > 0.05). This finding strongly suggests that methane emitted through the plant pathway in the afternoon originated from CH 4 in soil bubbles, just like at noon. The bubbles were mainly produced at 7-11 cm depth and expanded in the afternoon throughout 0-11 cm depth (cf. section 4.2.3). This indicates that rice roots could easily come into contact with the expanded bubbles at 0-11 cm and then transfer methane in the bubbles through the rice aerenchyma into the atmosphere. Therefore, the CH 4 emitted through rice plants in the afternoon was probably derived from the expanded bubbles at 0-11 cm depth. This soil depth was also the site with the highest CH 4 production fraction area in the planted soil (i.e., 1-11 cm soil depth, F prod > 0.87, Figure 1).

. Diel CH 4 Transportation Via Plants
The wavelet analysis results indicate that diel variations in soil surface temperature and atmospheric pressure significantly affected diel CH 4 transportation through the plant pathway. As discussed in section 4.3.1, rice plants transported methane in expanded bubbles in the afternoon. The bubble expansion mainly stemmed from both the increase in soil temperature and the decrease in atmospheric pressure in the afternoon (cf. section 4.2.3), which also helped the bubbles to come in contact with the rice roots. There is generally a larger amount of CH 4 in bubbles than in soil solution, because of insolubility (Himmelblau, 1964;Tokida et al., 2013). In addition, methane in bubbles can diffuse much faster than CH 4 in soil solution (Himmelblau, 1964;Tokida et al., 2013). Therefore, large amounts of CH 4 in expanded bubbles would have transferred into the rice plants. Then, once in the plant the CH 4 gas would move diffusively through the rice plant arenchyma (Chanton et al., 1997). In the daytime the rise in soil temperature and decrease in atmospheric pressure would probably have enhanced gas diffusive transport, following the Chapman-Enskog diffusion theory. Hosono and Nouchi (1998) found that CH 4 emission increased with increasing diffusive conductance of rice plants for CH 4 due to the increase in soil temperature. Therefore, the afternoon temperature and atmospheric pressure conditions would have enhanced diffusive CH 4 transport through the rice plants and resulted in an increase in CH 4 flux. The enhanced plant-mediated CH 4 transportation in the afternoon probably contributed to the lack of any significant isotopic difference between the CH 4 emitted through the rice plants and soil bubble CH 4 (cf. section 4.3.1).
In contrast, at night both the low soil temperature and high atmospheric pressure probably diminished the nighttime bubble expansion in the soil (cf. section 4.2.3). This probably made it more difficult for CH 4 -rich bubbles to come into contact with roots, thereby reducing nighttime CH 4 transport from bubbles through rice plants to the atmosphere. Furthermore, the soil temperature and atmospheric pressure conditions at night also probably decreased the diffusive CH 4 transportation through rice plants, following the Chapman-Enskog diffusion theory. Since the light carbon isotope (= 12 CH 4 ) can move faster than the heavy one (= 13 CH 4 ), the reduced plant-mediated diffusive transportation at night would probably have transported 12 CH 4 more easily than 13 CH 4 , which would explain the lighter value of the plant-mediated δ 13 CH 4_emit at night.
Collectively, the above discussion regarding plant-mediated CH 4 transportation shows that the diel changes in soil temperature and atmospheric pressure mainly regulated the diel variations in bubble expansion in the soil and plant-mediated CH 4 diffusion, both of which drove the diel variations in the plant-mediated CH 4 transport. The subsequent wavelet analysis of the water-mediated CH 4 flux and plant-mediated δ 13 CH 4_emit also confirmed a significant in-phase coherency at the daily timescale, with a lag of 0.7 hr (9.8°) ( Figure S10). Since the diel CH 4 emission through the water pathway was mainly regulated by soil bubble expansion, the wavelet coherence results also support the theory that diel change in CH 4 bubble expansion in soil is a key diel controller of plant-mediated CH 4 transportation.

Summary and Conclusions
We examined the CH 4 oxidation, production, and transportation processes at both the soil-plant-atmosphere and soil-water-atmosphere interfaces during the reproductive growth period of tropical paddy rice using natural δ 13 CH 4 and δ 13 CO 2 . Our results reveal that more CH 4 oxidation and production by acetate fermentation occurred in the planted soil compared with the interrow soil, due to increased oxygen and organic matter supply through rice roots in the planted soil. Furthermore, we found that the acetate fermentation was the dominant soil CH 4 process in the planted soil except at 13-17 cm depth where active CH 4 oxidation occurred. In contrast, the H 2 /CO 2 reduction was the dominant CH 4 process in the interrow soil, except at 13-17 cm depth where the acetate fermentation occurred more actively.
Assessing both CH 4 flux and emitted δ 13 CH 4 through the water pathway showed that methane in the interrow soil moved upward into the atmosphere by three transportation modes: episodic ebullition, steady ebullition, and diffusion at the water-atmosphere interface. Episodic and steady ebullitions released bubbles mainly from 7-11 cm soil depth. In addition, high CH 4 emissions (>5 mg m −2 hr −1 ) through the paddy water were dominated by episodic ebullition, whereas low (<5 mg m −2 hr −1 ) emissions were dominated by diffusion. The water pathway showed a significant negative correlation between the mean diel CH 4 flux and emitted δ 13 CH 4 ; this negative relationship was identified throughout most of the measurement period by the wavelet coherence analysis. The diel variations in CH 4 flux and emitted δ 13 CH 4 through the water pathway showed that episodic bubble ebullitions dominated the water-mediated CH 4 transportation in the daytime, whereas diffusion dominated the water pathway at night. The daily variations in episodic ebullition, steady ebullition, and diffusion were mainly regulated by the diel changes in soil temperature and atmospheric pressure.
In contrast, the plant pathway showed a significant positive correlation between the mean diel CH 4 flux and emitted δ 13 CH 4 . Comparison of the mean diel emitted δ 13 CH 4 by the water and plant pathways revealed that the rice plants transported CH 4 in bubbles, developed at 0-11 cm depth. The key factors for regulating the diel variation in CH 4 transportation through rice plants were changes in bubble expansion and plant-mediated CH 4 diffusion, regulated by diel changes in soil temperature and atmospheric pressure.
These results demonstrate that the diel pattern of CH 4 transportation through the plant pathway is strongly related to diel change in bubble expansion in soil. Better understanding of diel and longer-term changes in CH 4 bubbles in paddy soil would help to improve our knowledge of the temporal changes in CH 4 flux, and prediction of the CH 4 budget in rice paddies. This perspective is also important for other wetland field studies that have similar characteristics to rice paddies.

Erratum
In the originally published version of this article, the in-text citations to the panels of Figure 4 were transposed in Section 3.3.2. In Section 4.2.3, the in-text citations to Figures 3a, 3b, and 3h did not include Figure 6.
Additionally, an incorrect version of the Supporting Information published.
The article and Supporting Information have since been corrected, and this version may be considered the authoritative version of record.