The Fallow Period Plays an Important Role in Annual CH 4 Emission in a Rice Paddy in Southern Brazil

: Paddy ﬁelds are signiﬁcant anthropogenic sources of methane (CH 4 ) emissions. In southern Brazil, rice is grown in lowland ﬂooded areas once a year, followed by a long fallow period. This study aimed to measure CH 4 ﬂuxes in a rice paddy ﬁeld in southern Brazil during the rice-growing season of 2015/2016 and the following fallow period. The ﬂuxes were estimated using the eddy covariance (EC) technique and soil chamber (SC). Diurnal and seasonal variations of CH 4 ﬂuxes and potential meteorological drivers were analyzed. The CH 4 ﬂuxes showed distinct diurnal variations in each analyzed subperiod (vegetative, reproductive, pre-harvest, no rice, and land preparation), characterized by a single-peak diurnal pattern. The variables that most inﬂuenced methane emissions were air and surface temperatures. In the growing season, the rice vegetative stage was responsible for most of the measured emissions. The accumulated annual emission estimated was 44.88 g CH 4 m − 2 y − 1 , being 64% (28.50 g CH 4 m − 2 ) due to the rice-growing season and 36% (16.38 g CH 4 m − 2 ) due to the fallow period. These results show the importance of including fallow periods in strategies to mitigate methane emissions in ﬂood irrigated rice-growing areas.

Flooded rice fields are responsible for 11-26% of the total anthropogenic CH 4 emissions and emit around 30-40 Tg CH 4 per year, with Asia accounting for 90% of emissions [1]. Additionally, these rice are generally grown in lowland areas and are major sources of CH 4 emissions [7,8]. In Brazil, 11.2 million tons of rice were produced in 2020 in a 1.67 million ha area [9], representing approximately 2.0% of world production [10]. In the 2019/2020 rice season, Rio Grande do Sul State, southern state of Brazil, produced about 8 million tons of rice in a 0.94 million ha area [11], in which river lowlands were developed to increase rice production.
Due to the subtropical climate in southern Brazil, only one annual rice-growing season is possible, unlike most of Asia with two annual rice-growing seasons [12,13]. As a result,

Data Collection
A flux tower was installed in a dike of an irrigation channel in one of the rice fields (Figure 1), and data were collected from 21 November 2015 (16 days after planting, DAP) to 18 August 2016. Four static soil chambers (SC) were installed, side by side, ~10 m from the flux tower. Rice was allowed to grow in three chambers, while in the fourth chamber the soil was devoid of vegetation. The SC measurements started 76 DAP (20 January 2016) in the rice field (hereafter SC cultivated) and 90 DAP (5 February 2016) in the area without rice plants (hereafter SC uncultivated). The last SC measurements occurred on 14 April 2016.
Leaf area index (LAI) data were obtained from the MOD15A2 product of the MODIS (Moderate Resolution Imaging Spectroradiometer) with an 8-day temporal resolution and 1 km spatial resolution. Souza et al. [38] compared LAI (MOD15A2) data with experimental measurements at the same Cachoeira do Sul site and reported similar seasonal behavior in most of the rice-growing season.

Soil Chamber (SC)
Surface CH4 fluxes were measured by the manually operated static closed chamber (soil chamber), according to Bayer et al. [15]. Each chamber consisted of an aluminum base (0.64 × 0.64 × 0.20 m) and an aluminum cover of the same size. The bases were inserted 5 cm into the soil. Each base had an open bottom and sealable channels on the sides to facilitate water flow. The channels on the sides were sealed during air sampling events. Additional 20-30 cm aluminum extensions were stacked on the bases as the plants grew taller. The chamber volume was considered in CH4 emission measurements. Each chamber cover had a rubber septum sampling port, a stainless steel thermometer, and a batteryoperated fan to circulate and homogenize air within the apparatus. Chamber closing and For this study, the 2015/2016 rice-growing season and following fallow period were evaluated. A late-cycle rice cultivar (Epagri 118) was planted on 5 November 2015, and harvested on 16 April 2016. Planting was carried out with pre-germinated seeds broadcast by airplane onto the flooded field with a standing water depth of 5 cm. The soil remained flooded with 5-10 cm of standing water during the growing season until one week before the harvest, and flooding was maintained by pumping water from the nearby river. The amount of N fertilizer applied was 68 kg N ha −1 , being in agreement with official technical recommendations for this region [36]. The average rice yield (Y) from the analyzed crop was 0.45 kg m −2 (4.5 ton ha −1 ). The rice phenological stages were estimated using the degree-day method [37]. This experimental site represents the rice paddy management system currently adopted by most farmers in southern Brazil.

Data Collection
A flux tower was installed in a dike of an irrigation channel in one of the rice fields (Figure 1), and data were collected from 21 November 2015 (16 days after planting, DAP) to 18 August 2016. Four static soil chambers (SC) were installed, side by side,~10 m from the flux tower. Rice was allowed to grow in three chambers, while in the fourth chamber the soil was devoid of vegetation. The SC measurements started 76 DAP (20 January 2016) in the rice field (hereafter SC cultivated) and 90 DAP (5 February 2016) in the area without rice plants (hereafter SC uncultivated). The last SC measurements occurred on 14 April 2016.
Leaf area index (LAI) data were obtained from the MOD15A2 product of the MODIS (Moderate Resolution Imaging Spectroradiometer) with an 8-day temporal resolution and 1 km spatial resolution. Souza et al. [38] compared LAI (MOD15A2) data with experimental measurements at the same Cachoeira do Sul site and reported similar seasonal behavior in most of the rice-growing season.

Soil Chamber (SC)
Surface CH 4 fluxes were measured by the manually operated static closed chamber (soil chamber), according to Bayer et al. [15]. Each chamber consisted of an aluminum base (0.64 × 0.64 × 0.20 m) and an aluminum cover of the same size. The bases were inserted 5 cm into the soil. Each base had an open bottom and sealable channels on the sides to facilitate water flow. The channels on the sides were sealed during air sampling events. Additional 20-30 cm aluminum extensions were stacked on the bases as the plants grew taller. The chamber volume was considered in CH 4 emission measurements. Each chamber cover had a rubber septum sampling port, a stainless steel thermometer, and a battery-operated fan to circulate and homogenize air within the apparatus. Chamber closing and initial air sampling began at 9:00 a.m. local time. Air samples were taken at 0, 5, 10, and 20 min after closing the chamber [15]. Air samples were obtained by polypropylene syringes, transferred to evacuated 12-mL vials, and analyzed for CH 4 by gas chromatograph. The chromatograph (Shimadzu GC 2014 "Greenhouse") was equipped with three packed columns at 70 • C, N 2 as carrier gas at a flow of 26 mL min −1 , an injector with 1 mL sample loop for direct injection at 250 • C, and a flame ionization detector (FID) at 250 • C for CH 4 detection. Air was sampled on a weekly basis during rice-growing season.
The CH 4 flux rates were calculated as follows [15]: where f is the CH 4 production rate (g m −2 h −1 ); ∆Q/∆t is the change in gas concentration (mol h −1 ); P is the atmospheric pressure in the chamber (1 atm); V is the chamber volume (L); R is the ideal gas constant (0.0825 atm L mol −1 K −1 ); T is the chamber temperature (K); M is the gas molar mass (g mol −1 ), and A is the chamber basal area (m 2 ). The gas production rate was subsequently converted to µmol CH 4 m −2 s −1 , with an average of the three rice chambers being calculated to obtain a single value representative of the rice field. The mean CH 4 flux from the air samples in each chamber was assumed to be equivalent to the mean daily flux [39]. Seasonal emissions were calculated by trapezoidal interpolation of the daily CH 4 fluxes during the evaluated period [15].

Eddy Covariance and Meteorological Measurements
The CH 4 concentrations were measured in the flux tower with an open-path gas analyzer using wavelength modulation spectroscopy (LI-7700, LI-COR Inc., Lincoln, NE, USA). Wind speed was measured with a three-dimensional sonic anemometer (CSAT3, Campbell Scientific Inc., Logan, UT, USA). Both sensors were installed 3 m above the ground. Data were recorded at 10 Hz via an analyzer interface unit (LI-7550, LI-COR Inc., Lincoln, NE, USA) and stored on a 16 GB hard drive.
Meteorological data were collected at 1 Hz using a data logger (CR1000, Campbell Scientific Inc., Logan, UT, USA). Air temperature (Tair) and relative humidity (RH) were measured using a thermohygrometer (CS215, Campbell Scientific Inc., Logan, UT, USA) installed 3 m above the ground. A rain gauge (TB4 Rain Gauge; Campbell Scientific Inc., Logan, UT, USA) 6 m above the ground measured precipitation (Prec). Photosynthetically active radiation (PAR) was measured at 4 m height using a quantum sensor (LI-190S, LI-COR Inc., Lincoln, NE, USA). Incident longwave (Ld) and emitted longwave (Lu) radiation were measured using a pyrgeometer (CGR3, Kipp & Zonen B.V., Delft, The Netherlands), and incident shortwave (Sd) and reflected shortwave (Su) radiation were measured using pyranometers (CMP3, Kipp & Zonen B.V., Delft, The Netherlands), which were all installed 5.6 m above the ground. Surface temperatures (Tskin) were measured using an infrared temperature sensor (SI-111, Apogee Instruments Inc., Logan, UT, USA). Soil temperatures (Tsoil) were measured at 5 cm depth using a thermometer (T-108, Campbell Scientific Inc., Logan, UT, USA), while soil heat flux (G) was measured at 15 cm depth using a heat flux plate (HFP01, Hukseflux Thermal Sensor Inc., Delft, The Netherlands). Soil water content (SWC) was measured using a reflectometer (CS616 water content reflectometer, Campbell Scientific Inc., Logan, UT, USA) at 30 cm depth. More details on the experimental site, data acquisition, and data processing are described in Diaz et al. [35] and Souza et al. [38].

Eddy Covariance Flux Data Processing
There were some technical problems until a useful dataset of CH 4 fluxes by EC was acquired (see Supplementary Material). The methane flux (CH 4 flux) was estimated using EC and consisted of calculating the covariance between turbulent fluctuations in the vertical wind speed and CH 4 concentration [30]. The CH 4 fluxes were measured at half-hour intervals using the EddyPro ® software, version 7 (Li-Cor, Lincoln, NE, USA). The raw data were filtered according to Vickers and Mahrt [40] and the peak counting and removal method proposed by Mauder et al. [41]. Turbulent fluctuations were also calculated in mean per block, with double rotation [42], correction of the density effect [43], flux mitigation due to instrument configuration [44], and high and low corrections of the filter according to the methods of Moncrieff et al. [45] and Moncrieff et al. [46], respectively.
EddyPro ® calculates three quality indicators for the CH 4 flux: 0 represents a good quality, 1 represents an intermediate quality, and 2 represents a low quality. Flux data with quality flags 1 and 2 were discarded. Moreover, CH 4 fluxes were discarded if the statistical quality of the raw time series failed (rigid flag test) in the following situations: spikes, amplitude resolution, dropouts, absolute limits, skewness and kurtosis, discontinuities, and time lag; in the case of failure in the rigid flags; when the relative signal strength indicator (RSSI) at the diagnostic output of the LI-7700 was below 10% [47][48][49]; in precipitation events and the following half-hour period [50]; and with values below −1 µmol CH 4 m −2 s −1 and above 1 µmol CH 4 m −2 s −1 that were established as physical limits for the experimental site. The limiting values of the friction velocity parameter (u*), which represent a situation of low turbulence, were estimated according to the method by Diaz et al. [35] for CO 2 flux in the same experimental site and period according to Reichstein et al. [51]. Values of CH 4 fluxes for u* threshold (u* < 0.11 m s −1 ) were also discarded.

Gap-Filling and Uncertainty
During the study period, 5.5% missing half-hourly values for the meteorological and soil data were gap-filled using the REddyProc package (version 1.1.5) for RStudio software [51]. The precipitation data were not gap-filled and the whole day of these data were disregarded when they had more than 10% of failures.
Regarding the CH 4 fluxes measured by EC, 50.0% of the half-hour periods were lost due to equipment failure, and 23.5% were discarded for quality control. These gaps were gap-filled using an artificial neural network. According to Kim et al. [52], random forest (RF) performed well in filling CH 4 gaps across different sites, including rice paddies. In this way, we used the "randomForest" R package [53], which was implemented with 400 regression trees. In the exploratory analysis, were selected meteorological variables that show correlation index with CH 4 fluxes above 0.4 (results of Section 3.2.), including three fuzzy variables (day of the year and cosine and sine functions with a year-long wavelength) [52,54]. The data were randomly split into 80% as the RF algorithm training dataset and 20% as the validation dataset. The division, training, and validation procedure was repeated 50 times, totaling 50 RFs. The RF statistical validation parameters varied between 0.86 and 0.92 for r (Pearson correlation coefficient), 0.06 and 0.07 µmol m −2 s −1 for the RMSE (root mean square error), and between −3.9 and 3.5 for the PBias (percent Bias). The CH 4 gaps were filled by median prediction of 50 RFs.
Uncertainties in CH 4 fluxes can be caused by random errors associated with the gap filling approach. We followed the method described by Anderson et al. [55] and Knox et al. [56] to quantify the uncertainty in the cumulative fluxes applying a Monte Carlo simulation. In this work, a Monte Carlo simulation was used to randomly draw 1000 random errors for every original measurement binned by 0.05 µmol CH 4 m −2 s −1 of flux magnitude to quantify the random uncertainty of cumulative fluxes, followed by computing the variance of the cumulative sums. For the gap-filled values, the combined gap-filling and random uncertainty were calculated from the variance of the cumulative sums of the 50 RF predictions. The total uncertainty in the cumulative fluxes was then calculated by adding the cumulative gap-filling and random measurement uncertainties in quadrature, assuming that these sources of error were independent and normally distributed [57]. The uncertainty was calculated for the period with EC data in the study area (21 November 2015, to 18 August 2016).

Data Analysis
The study period was divided into five sub-periods according to the rice phenological stages and successive soil management: The vegetative, reproductive, and pre-harvest stages were integrated to represent the rice-growing season, and the no rice and land preparation stages represented the fallow period.
Before gap-filling, the CH 4 fluxes obtained from the EC were correlated with the available atmospheric and soil variables, throughout r, in different sub-periods. For this analysis, the CH 4 fluxes not gap-filled were used because the gap-fill procedure uses meteorological factors as the independent variables in the fitting process, which may introduce false relationships between the CH 4 fluxes and other factors into the dataset [48].
The correlation coefficient r is calculated as: where O i represents the ith experimental CH 4 flux value, M i represents the ith modeled value for a total of n observations, O and M are the observed and modeled mean value, and σ O and σ M are the standard deviation of observed and modeled data [58]. r is a measure of the strength of the linear relationship between two variables. If there is a perfect linear relationship with a positive slope between the two variables, r = 1; if there is a perfect linear relationship with a negative slope between the two variables r = −1; if there is no linear relationship between the variables, r = 0. The correlations were considered weak if r < |0.4|, moderate if |0.4| ≤ r < |0.7|, and strong if r ≥ |0.7|. The correlation coefficient was also used to evaluate the ANN to estimate the CH 4 fluxes, as described in Section 2.4. Additionally, the RMSE and PBias statistical indices [58] were used in this analysis and are presented below: Analysis of the daily and seasonal variations of the CH 4 fluxes were carried out for both EC and SC methods. To complete one year of data, we extrapolated the results of the period measured in situ with EC, which we considered with similar soil cover and environmental conditions, using the mean value of each period. To compare with other studies in the literature, daily average conversions were performed using the following conversion factors between units: 1 µmol CH 4 m −2 s −1 = 1.382 g CH 4 m −2 d −1 = 1.037 gC m −2 d −1 .

Atmospheric and Soil Conditions
Daily variations of the environmental variables are shown in Figure 2. Soil temperature at 5 cm depth (Tsoil) had the highest daily temperature values with similar behavior to air (Tair) and surface temperatures (Tskin), which presented very close daily averages ( Figure 2a). The daily temperatures varied by more than 20 • C between the growing season (summer) and fallow periods (winter). The maximum daily Tair was verified during the summer (27.9 • C), and the minimum Tair was determined during the winter (4.8 • C). The soil heat flux (G) was positive in almost the entire growing season, which suggests that the surface layer warms the subsoil, while the subsoil warms the surface layer in the fallow period (G < 0).  The seasonality between the summer (growing season) and winter (fallow) seasons in this region is characterized by global solar radiation (Sd), with maximum values around 50% lower in the winter than in the summer (Figure 2b). Similar behavior was observed in the PAR since it is practically a fixed percentage of Sd [59] and Su, although the latter also depends on albedo that in general, is lower in fallow periods [60]. The Ld and Lu decreased, in absolute values, by around 25% in winter from the summer values due to lower air and soil temperatures. The negative values for radiations indicate their direction from the surface to the atmosphere.
Climatically, precipitation is well distributed throughout the year in the study region [35,38], varying from 83.9 mm (April) to 157.4 mm (August). On 22-23 December 2015, the daily accumulated precipitation amounted to 115 and 94.2 mm, respectively ( Figure 2c). After that there were nearly 30 days of no recorded precipitation. The regular precipitation returned in February 2016. Unfortunately, there was a long period without precipitation data collection in the experimental site due to equipment failure (after 25 March 2016), which was identified as a negative value in Figure 2c. However, the flooding in the rice paddy does not depend on precipitation because it was maintained by pumping water from the nearby river. In general, RH is high because the rice paddies cover large areas within a catchment, creating a microclimate with high amounts of water available for evapotranspiration [61]. The lowest daily average of RH was 59% in the summer when little rainfall occurred. The highest vapor pressure deficit (VPD) values were in the rice-growing period and mainly due to the high air temperatures, exceeding values of 15 hPa [38]. The daily average soil water content (SWC) at 30 cm depth recorded a maximum value of 0.4 m 3 m −3 and a minimum of 0.27 m 3 m −3 , being always above the soil field capacity, which is 0.21 m 3 m −3 for this experimental site [35].

Correlation between the Meteorological Conditions and CH 4 Fluxes Not Gap-Filled
The factors influencing CH 4 emissions may contribute differently to the analyzed periods due to seasonal variations in atmospheric conditions and land use. In this study, we analyzed the correlations between the CH 4 fluxes obtained by the EC without gapfilling and atmospheric and soil variables at a half-hour basis for the entire period and different subperiods (Figure 3). The variables Tair, Tskin, and Lu presented moderate or high correlations in all subperiods. The negative correlation with Lu was obtained because negative values were used for this variable (Figure 1), i.e., the largest negative values represent higher longwave radiation emissions on the surface (the same analysis can be done for Su, but reflecting Sd). The correlations with Lu were very similar to Tskin, but with an inverted sign, which is expected since Lu depends directly on the surface temperature according to Stefan-Boltzmann's law. A higher correlation between the CH 4 flux with Lu than with Tskin, despite slightly higher, must be related to the position of the sensor on the flux tower. The Lu sensor was installed 5.6 m above the ground and represents a larger and more homogeneous area than the Tskin sensor, which was installed 2.2 m above the ground and may represent either a more open area or with more plants. Except for the no rice subperiod, Tsoil and G also showed a moderate or high correlation in all subperiods. During land preparation, only Tsoil, Ld, and SWC had r below 0.6. Since the soil temperature is the variable as the main controller of methane fluxes [21,33,48,54,[62][63][64], the low correlations found here regarding the no rice and land preparation subperiods may be a result of the intermittent flooding caused by precipitation. In the pre-harvest period (drained soil), the correlation of the VPD with CH 4 flux decreased.

Figure 3.
Correlation coefficient matrixes (in percentage) using lattice between the half-hour CH4 fluxes and atmospheric and soil variables for the vegetative, reproductive, pre-harvest, no rice, and land preparation periods. A perfect positive correlation is presented as a 45-degree line, positive slope, red color, and a value of 100. The absence of correlation has a circular shape, light color, and a value of zero. A perfect negative correlation is presented as a −45-degree line, negative slope, blue color, and a value of −100.

CH4 Flux Gap-Filling
The RFs were implemented with a completely random division of training and validation data. The random division of training and validation of the dataset avoids biasing toward data periods with more flux coverage. The statistical indices between the CH4(EC) and CH4 obtained by the median of the 50 RFs predictions for the entire period and different subperiods are listed in Table 1. All statistical indices for the entire period showed better values than the validation of the 50 RFs. This means that the median of the CH4 fluxes predicted by the RFs better represents the measured data than each RF individually. Satisfactory statistical indices were found for all the rice cultivation periods and land preparation. Despite the RMSE being low in the No rice and Pre-harvest periods, the PBias was higher in these periods, overestimating No rice and underestimating Pre-harvesting, which was likely caused by the smaller data coverage. There is currently no consensus regarding CH4 gap-filling methods due to limited comparative research [52]. Implementing a neural network method is complex, and its applicability depends on the favorable temporal representation of variables and data availability. Nevertheless, the ability of the neural network to model data with variable periodicity from the functional relationship between dependent and independent varia- . Correlation coefficient matrixes (in percentage) using lattice between the half-hour CH 4 fluxes and atmospheric and soil variables for the vegetative, reproductive, pre-harvest, no rice, and land preparation periods. A perfect positive correlation is presented as a 45-degree line, positive slope, red color, and a value of 100. The absence of correlation has a circular shape, light color, and a value of zero. A perfect negative correlation is presented as a −45-degree line, negative slope, blue color, and a value of −100.
In the rice-growing season, the vegetative stage presented the most variables (9 in total) with a correlation greater than |0.5|. In the pre-harvest, no variable showed a correlation greater than |0.5|, which may be related to the area drainage as it changed the soil moisture conditions faster. The smallest correlations were for Ld and SWC in all subperiods.

CH 4 Flux Gap-Filling
The RFs were implemented with a completely random division of training and validation data. The random division of training and validation of the dataset avoids biasing toward data periods with more flux coverage. The statistical indices between the CH 4(EC) and CH 4 obtained by the median of the 50 RFs predictions for the entire period and different subperiods are listed in Table 1. All statistical indices for the entire period showed better values than the validation of the 50 RFs. This means that the median of the CH 4 fluxes predicted by the RFs better represents the measured data than each RF individually. Satisfactory statistical indices were found for all the rice cultivation periods and land preparation. Despite the RMSE being low in the No rice and Pre-harvest periods, the PBias was higher in these periods, overestimating No rice and underestimating Pre-harvesting, which was likely caused by the smaller data coverage.
There is currently no consensus regarding CH 4 gap-filling methods due to limited comparative research [52]. Implementing a neural network method is complex, and its applicability depends on the favorable temporal representation of variables and data availability. Nevertheless, the ability of the neural network to model data with variable periodicity from the functional relationship between dependent and independent variables has increased its use for gap-filling (CH 4 ) flux time series [54,[65][66][67]. Generally speaking, the network used herein (RF) is a good choice for gap-filling (CH 4 ) and has shown the best results compared to other networks, as reported by Kim et al. [52]. The vegetative period had significant variation and a higher daily average of CH 4(EC) fluxes, with a daily average of approximately 0.18 g CH 4(EC) m −2 d −1 and a maximum of 0.44 g CH 4(EC) m −2 d −1 on 8 December 2015 (Figure 4). In this period, the main pathway of CH 4 transport between the soil and atmosphere occurs via aerenchyma in the root and stems of vascular plants [68,69]. Moreover, the daily average of CH 4(EC) fluxes significantly decreased during the period in which a large volume of precipitation was recorded (Figure 2), which is likely due to the lower Tsoil and VPD. Afterward, at the beginning of the reproductive stage with no precipitation and high soil temperature and VPD, the CH 4(EC) fluxes increased again, decreasing after the return of precipitation. This relationship is also confirmed by the high correlation between CH 4 and VPD, Tskin, and Tsoil ( Figure 3) for this period (r = 0.72, 0.64, and 0.62, respectively). The LAI also increased quickly in this period, reaching 3.2 m 2 m −2 . The average value in the reproductive stage was slightly higher than in the vegetative period, with an average of 0.21 g CH 4(EC) m −2 d −1 , although with lower values at the end of the period. As Weller et al. [62] reported, the reduced thermal amplitude within the canopy and soil layers due to increased LAI may be responsible for lower methane emissions as crops develop. In the pre-harvest period, the daily average was 0.16 g CH 4(EC) m −2 d −1 , with values decreasing until the beginning of the no rice subperiod, which was the period with the smallest variations and CH 4(EC) fluxes, reaching values near zero (average value of 0.05 g CH 4(EC) m −2 d −1 ) due to aerobic conditions that stimulate methanotrophic bacteria development, which convert CH 4 into CO 2 . During land preparation, fluxes increased once again (daily average of 0.09 g CH 4(EC) m −2 d −1 ) due to the supply of carbon derived from rice straw.
The daily cycle average of CH 4(EC) fluxes for each studied period is shown in Figure 5 with bootstrap confidence intervals (95%) in the mean. There is a diurnal pattern in CH 4(EC) fluxes in all periods. During the night, fluxes are almost constant and with little variation, and the highest values were found during the rice cultivation period. Furthermore, the CH 4(EC) fluxes increase at sunrise and peak around 3:00 p.m. (local time), decreasing significantly until sunset. This behavior is known as the single-peak diurnal pattern and is related to times with higher air and soil temperatures (data not shown). Similar results were also observed found by Hatala et al. [70], Knox et al. [54], and Ge et al. [48], analyzing daily cycle of CH 4(EC) over rice field in different place in the world.
sible for lower methane emissions as crops develop. In the pre-harvest period, the daily average was 0.16 g CH4(EC) m −2 d −1 , with values decreasing until the beginning of the no rice subperiod, which was the period with the smallest variations and CH4(EC) fluxes, reaching values near zero (average value of 0.05 g CH4(EC) m −2 d −1 ) due to aerobic conditions that stimulate methanotrophic bacteria development, which convert CH4 into CO2. During land preparation, fluxes increased once again (daily average of 0.09 g CH4(EC) m −2 d −1 ) due to the supply of carbon derived from rice straw. The daily cycle average of CH4(EC) fluxes for each studied period is shown in Figure 5 with bootstrap confidence intervals (95%) in the mean. There is a diurnal pattern in CH4(EC) fluxes in all periods. During the night, fluxes are almost constant and with little variation, and the highest values were found during the rice cultivation period. Furthermore, the This behavior is known as the single-peak diurnal pattern a related to times with higher air and soil temperatures (data not shown). Similar re were also observed found by Hatala et al. [70], Knox et al. [54], and Ge et al. [48], anal daily cycle of CH4(EC) over rice field in different place in the world. The vegetative period presented the highest CH4(EC) emission peaks and more s icant variability of CH4(EC) fluxes, with values of 0.34 μmol CH4(EC) m −2 s −1 . After the tative period, the peak emissions decreased, with values of 0.28 and 0.19 μmol CH4(E s −1 for the reproductive and pre harvest periods, respectively. Considering the averag the entire rice-growing season (vegetative, reproductive, and pre-harvest), the maxi value was 0.28 μmol CH4(EC) m −2 s −1 . Alberto et al. [21] analyzed CH4 emissions in paddy in the Philippines and also reported a single-peak diurnal pattern during the g ing season. The no rice period registered the lowest amplitudes with a maximum o μmol CH4(EC) m −2 s −1 , while the land preparation period had, on average, a maximum near the pre-harvest stage, 0.19 μmol CH4(EC) m −2 s −1 , although with more significant ability between the means. Nevertheless, the no rice and land preparation subperiod istered similar values during the night and showed the lowest values among all sub ods (~0.02 μmol CH4(EC) m −2 s −1 ). For rice cultivation periods, these values were aroun μmol CH4(EC) m −2 s −1 , with higher values in the pre-harvest subperiod.

SC
The CH4 fluxes measured by the SC (hereafter CH4(SC)) had similar seasonal those obtained with EC, decreasing at the beginning of the reproductive stage and inc The vegetative period presented the highest CH 4(EC) emission peaks and more significant variability of CH 4(EC) fluxes, with values of 0.34 µmol CH 4(EC) m −2 s −1 . After the vegetative period, the peak emissions decreased, with values of 0.28 and 0.19 µmol CH 4(EC) m −2 s −1 for the reproductive and pre harvest periods, respectively. Considering the average for the entire rice-growing season (vegetative, reproductive, and pre-harvest), the maximum value was 0.28 µmol CH 4(EC) m −2 s −1 . Alberto et al. [21] analyzed CH 4 emissions in a rice paddy in the Philippines and also reported a single-peak diurnal pattern during the growing season. The no rice period registered the lowest amplitudes with a maximum of 0.07 µmol CH 4(EC) m −2 s −1 , while the land preparation period had, on average, a maximum value near the pre-harvest stage, 0.19 µmol CH 4(EC) m −2 s −1 , although with more significant variability between the means. Nevertheless, the no rice and land preparation subperiods registered similar values during the night and showed the lowest values among all subperiods (~0.02 µmol CH 4(EC) m −2 s −1 ). For rice cultivation periods, these values were around 0.1 µmol CH 4(EC) m −2 s −1 , with higher values in the pre-harvest subperiod.

SC
The CH 4 fluxes measured by the SC (hereafter CH 4(SC) ) had similar seasonality to those obtained with EC, decreasing at the beginning of the reproductive stage and increasing until the middle of this period when CH 4(SC) fluxes decreased (Figure 4). At the beginning of the reproductive stage, the first two weekly samplings with the soil chambers showed lower CH 4(SC) flux values than those determined by EC (CH 4(EC) ) (including a negative value, −0.07 ± 0.04 g CH 4(SC) m −2 d −1 ). From the third sampling on, the CH 4(SC) values were almost always higher than CH 4(EC) , with maximum values of 0.61 ± 0.12 g CH 4(SC) m −2 d −1 . Therefore, the measurements of soil chambers represented well the seasonal variability of CH 4(EC) , increasing until half of the reproductive stage, shortly after decreasing. For the same period, uncultivated SC showed little variability in flux values with values around zero (maximum values of 0.04 g CH 4(SC) m −2 d −1 and minimum values of −0.019 g CH 4(SC) m −2 d −1 ). These values were similar to those obtained by EC during the fallow period, even without the water layer. Therefore, these results demonstrate the considerable emissions of CH 4 of the rice paddies, as also highlighted by Holzapfel-Pschorn and Seiler [71] and Schütz et al. [72].
In this study, the SC collections were carried out on clear days and under intense solar radiation (summer in the southern hemisphere), which may overestimate the CH 4 fluxes of the ecosystem. Moreover, the soil chambers are made of aluminum, which has high thermal conductivity, leading to quick temperature rises after closing and possibly altering gas fluxes due to the modified internal microenvironment, affecting microbiota activity and CH 4 transport processes [73]. The liquid CH 4 flux is controlled by bacteria that produce and consume CH 4 , and three main processes carry out its transport in the rice paddy: transport through aerenchyma in roots and stems of vascular plants, ebullition as gas bubbles, and diffusion via the soil-floodwater interface [7]. The higher temperatures may also lead to different CH 4 concentrations between the soil surface and the top of the chamber [74,75]. Thus, three fans were installed inside each chamber to minimize these effects. Although the flux estimation using the chamber technique considers the temperature inside the chamber at the time of measurement (Equation (1)), the temperature has already changed the concentrations due to its effects on the transport processes. The effects of temperature may be minimized by insulating the chambers with thermal insulation material and protecting against direct solar radiation incidence, which is especially important in tropical and subtropical regions.

Annual Integrated Flux
During the entire EC analyzed period, from 21 November 2015, to 18 April 2016, the integrated CH 4 flux value was 36.05 ± 2.52 g CH 4(EC) m −2 (±represents the total uncertainty of 7%). These CH 4 flux value results from simultaneous CH 4 production and consumption processes between the soil and the atmosphere, measured at the height of 3 m for 272 days. The daily accumulated CH 4 flux is presented in Figure 6. There are two periods with different average emission rates: one during the rice-growing season (vegetative, reproductive, and pre-harvest stages) and the other during the fallow period (no rice and land preparation). The change in the slope of the CH 4 accumulation curve occurred in April when the flood water was removed and the rice was harvested; hence, the CH 4(EC) emission rate decreased significantly. Schrier-Uijl et al. [32] proposed that the accumulated seasonal fluxes obtained by SC measurements can be calculated with models that consider the daily effects of temperatures on fluxes. However, in this study, we only used linear interpolation as it is the most widely used method and facilitates comparing results of other studies in the literature [16,76]. In the period that EC and SC measurements were performed simultaneously (5 February 2016, to 14 April 2016, totaling 70 days), the accumulated EC was 12.86 g CH4(EC) m −2 , while the SC registered 22.5 g CH4(SC) m −2 for the cultivated plot and 1.1 g CH4(SC) m −2 for the uncultivated plot. Therefore, a SC for the cultivated plot measured a CH4 emission that accumulated 74% higher than the EC in the same period. Studies have shown that fluxes measured with the SC method are greater in flooded areas (e.g., irrigated rice) than those with the EC method, with variations between 20 and 90% [76][77][78].
Possible reasons for the significant differences between SC and EC measurements could be the non-homogeneous characteristics of the surface in the field and different spatial and temporal scales of the collections. Chamber measurements capture emissions from small areas, which may not represent natural spatial variations in soil and plant growth because of possible irregular fertilizer spread or localized variations in water level [79]. In addition, weekly measurements are taken with the chambers, while half-hourly measurements are performed with the EC, capturing the diurnal variations in fluxes due to daily variations in climate and plant growth. Nonetheless, the EC data can also present gaps due to lack of power or after proper filtering of the data due to low turbulence, control quality, or the small CH4 sensor (as described in Section 2.3). Thus, both methods need gap-filling to generate full periods of data. In general, the weekly data from the cameras are linearly interpolated and may present overestimation, as collections usually occur on days with clear skies, and climatic variations are not taken into account.
Using SC to estimate CH4 fluxes in irrigated rice fields with and without rice plants (cultivated and uncultivated), it is estimated that rice plants contribute about 95% to CH4 emissions from the soil to the atmosphere. This occurs due to the transport of gases by diffuse exchange and mainly by internal convective fluxes [21,64]. The internal convective CH4 fluxes result from the pressure gradient in different parts of the plant [21]. Other authors have also reported the contribution of plants to CH4 emission from the soil into the atmosphere, including Holzapfel-Pschorn and Seiler [71] and Schütz et al. [72], who estimated the contribution of rice plants for CH4 emissions as 80 and 90%, respectively. Schrier-Uijl et al. [32] proposed that the accumulated seasonal fluxes obtained by SC measurements can be calculated with models that consider the daily effects of temperatures on fluxes. However, in this study, we only used linear interpolation as it is the most widely used method and facilitates comparing results of other studies in the literature [16,76]. In the period that EC and SC measurements were performed simultaneously (5 February 2016, to 14 April 2016, totaling 70 days), the accumulated EC was 12.86 g CH 4(EC) m −2 , while the SC registered 22.5 g CH 4(SC) m −2 for the cultivated plot and 1.1 g CH 4(SC) m −2 for the uncultivated plot. Therefore, a SC for the cultivated plot measured a CH 4 emission that accumulated 74% higher than the EC in the same period. Studies have shown that fluxes measured with the SC method are greater in flooded areas (e.g., irrigated rice) than those with the EC method, with variations between 20 and 90% [76][77][78].
Possible reasons for the significant differences between SC and EC measurements could be the non-homogeneous characteristics of the surface in the field and different spatial and temporal scales of the collections. Chamber measurements capture emissions from small areas, which may not represent natural spatial variations in soil and plant growth because of possible irregular fertilizer spread or localized variations in water level [79]. In addition, weekly measurements are taken with the chambers, while halfhourly measurements are performed with the EC, capturing the diurnal variations in fluxes due to daily variations in climate and plant growth. Nonetheless, the EC data can also present gaps due to lack of power or after proper filtering of the data due to low turbulence, control quality, or the small CH 4 sensor (as described in Section 2.3). Thus, both methods need gap-filling to generate full periods of data. In general, the weekly data from the cameras are linearly interpolated and may present overestimation, as collections usually occur on days with clear skies, and climatic variations are not taken into account.
Using SC to estimate CH 4 fluxes in irrigated rice fields with and without rice plants (cultivated and uncultivated), it is estimated that rice plants contribute about 95% to CH 4 emissions from the soil to the atmosphere. This occurs due to the transport of gases by diffuse exchange and mainly by internal convective fluxes [21,64]. The internal convective CH 4 fluxes result from the pressure gradient in different parts of the plant [21]. Other authors have also reported the contribution of plants to CH 4 emission from the soil into the atmosphere, including Holzapfel-Pschorn and Seiler [71] and Schütz et al. [72], who estimated the contribution of rice plants for CH 4 emissions as 80 and 90%, respectively.
Unfortunately, the EC system did not have a full year of CH 4 flux measurements, which may characterize a limitation for this study. However, according to our results and similar studies with irrigated rice, CH 4 fluxes are high during the vegetative period (beginning of the vegetative phase until the end of pre-harvest period) and reduced during the fallow period until planting [20,21,33,76]. Therefore, to complete one year of data, we extrapolated the results of the period measured in situ, which we considered had similar soil cover and environmental conditions for days without measurements. For the days at the beginning of the growing season (between 5-20 November 2015), the average daily rate of CH 4 emission of the growing season (0.19 g CH 4(EC) m −2 d −1 ) was used. From 19 August 2016, to 4 November 2016, the average daily CH 4 emission rate for no rice and land preparation (0.06 g CH 4(EC) m −2 d −1 ) was used, thus completing 365 days. In general, two or three weeks after land preparation, the field is kept fallow until the next rice-growing season. Therefore, by extrapolating the results for one year, we reached the total annual accumulated value of 44.88 g CH 4(EC) m −2 y −1 , with the rice-growing season being responsible for 28.50 g CH 4(EC) m −2 and the fallow period for 16.38 g CH 4(EC) m −2 , i.e., the rice-growing season accounts for 64% of the annual CH 4 emission, while the fallow is responsible for 36%. Hence, the CH 4 emissions during the fallow period represent 57% of the emissions in the rice-growing season. The accumulated value of CH 4(EC) fluxes in the growing season may likely be lightly overestimated because we do not have CH 4 flux measurements in the first days after flooding, which is when emissions are lower [33]. In addition, emissions during the fallow period may have been overestimated, as the gap-filling method presented positive PBias in this period (Table 1). Although the number of gaps in this period increased, the lower diurnal variability in CH 4 fluxes may improve RF representation.
In a rice paddy in northern Italy and with similar management practices, Meijide et al. [76] obtained annual accumulated values of 37.42 and 21.03 g CH 4(EC) m −2 for 2009 and 2010, respectively, i.e., approximately 17 and 53% lower than the values reported herein. These authors attributed the differences found in the two years to climatic conditions and mainly the water level in the field. These differences demonstrate the importance of long-term studies to understand interannual variability.
A critical comparison to be done is with the CH 4 emission factor for rice fields, as proposed by IPCC [80]. The IPCC [80] emission factor for the growing season is estimated as 0.13 g CH 4 m −2 d −1 , being almost 30% lower than the value reported herein (0.19 g CH 4(EC) m −2 d −1 ), representing a significant underestimation of CH 4 emission in rice paddy fields in southern Brazil. CH 4 has a global warming potential (GWP) 28 times greater than CO 2 , while N 2 O has a contribution 265 times greater than the CO 2 (both for a 100-year time horizon not considering the climate-carbon feedbacks [1]). Nonetheless, N 2 O had an almost insignificant contribution in the rice paddies [16,76], and this is because the N 2 O is mostly converted into N 2 via denitrification under flooded soil conditions [81]. Hence, by converting the CH 4 into CO 2-eq , the rice-growing season was responsible for 798 g CO 2-eq m −2 and the fallow period for 458 g CO 2-eq m −2 . In a previous study by our research group, Diaz et al. [35] estimated the CO 2 net exchange ecosystem (NEE) for five years in the same experimental area (20 October 2010 to 16 April 2016) and reported that the NEE = −1334 g CO 2 m −2 for the same rice paddy growing season (2015/2016) and NEE = 981 g CO 2 m −2 for the fallow period in five-year average (2011)(2012)(2013)(2014)(2015). By adding the contributions of CO 2 and CH 4 in the partial GWP (GWPp), the growing season GWPp represents an absorber of −536 g CO 2-eq m −2 , while the GWPp represents an emitter of 1439 g CO 2-eq m −2 in the fallow period, totaling at an annual emission of 903 g CO 2-eq m −2 . Therefore, CH 4 was dominantly responsible for the GWPp, as also reported by Meijide et al. [76]. The CH 4 emitter in the fallow accounted for almost 50% of the annual GWPp. Furthermore, the fallow emitted almost threefold the GWPp that was absorbed by the growing season. As 450 g of rice was produced in the growing season, we can consider that for each gram of rice produced, 2.0 g CO 2-eq was annually emitted per area, making the irrigated rice cultivation area a strong emitter of greenhouse gases.

Conclusions
This study presents the first CH 4 estimates using eddy covariance in a paddy field in southern Brazil, covering a growing season and a fallow period. The diurnal and seasonal variations of CH 4 fluxes were analyzed. The seasonal integrations showed that the rice-growing season emitted 28.50 g CH 4 m −2 and the fallow period emitted 16.38 g CH 4 m −2 , i.e., the fallow emitted 35% of annual CH 4 flux. Although lower than the growing season, the emission in fallow is significant to the annual estimation. The diurnal cycle was characterized by a single-peak diurnal pattern in different phenological stages and the fallow period. The most significant daily CH 4 flux variation and highest values occurred during the vegetative stage. Air and surface temperatures were the variables that most influenced those dynamics.
Measuring CH 4 fluxes using EC and SC in the cultivated plot was compared for the reproductive and pre-harvest stages, resulting in SC overestimating EC by 74%. Nevertheless, a comparison of integrated CH 4 fluxes from EC in the growing season with other studies using SC in southern Brazil demonstrated similar findings. In uncultivated plots, the CH 4 flux from SC was similar to those obtained using EC during the fallow period. Moreover, the SC results shows that rice plants contribute about 95% to CH 4 emissions from the soil to the atmosphere, highlighting the importance of rice cultivation in the CH 4 emission rate.
Using estimates based on EC to obtain annual integrations of GWPp, our results show that the paddy field is an annual sink of 903 g CO 2-eq m −2 . The fallow emitted almost threefold the GWPp that was absorbed by the rice-growing season. This study adds further support to the evidence that CH 4 emissions from areas used for flood irrigated rice cultivation significantly influence annual carbon balances and GWP. Therefore, it is fundamental to stimulate technological practices that reduce CH 4 emissions in the ricegrowing season of different processes and during the fallow period.
As a complementary part of this work, our results can be used in the verification and calibration of the Brazilian Global Atmospheric Model-BAM [82], the atmospheric component of the Brazilian Earth System Model (BESM), since no studies including CH 4 flux emissions over paddy field in southern Brazil have been carried out with this model.