Hotspots of Diffusive CO 2 and CH 4 Emission From Tropical Reservoirs Shift Through Time

gross decreases and microbial Abstract The patterns of spatial and temporal variability in CO 2 and CH 4 emission from reservoirs are still poorly studied, especially in tropical regions where hydropower is growing. We performed spatially resolved measurements of dissolved CO 2 and CH 4 surface water concentrations and their gas-exchange coefficients ( k ) to compute diffusive carbon flux from four contrasting tropical reservoirs across Brazil during different hydrological seasons. We used an online equilibration system to measure dissolved CO 2 and CH 4 concentrations; we estimated k from floating chamber deployments in conjunction with discrete CO 2 and CH 4 water concentration measurements. Diffusive CO 2 emissions were higher during dry season than during rainy season, whereas there were no consistent seasonal patterns for diffusive CH 4 emissions. Our results reveal that the magnitude and the spatial within-reservoir patterns of diffusive CO 2 and CH 4 flux varied strongly among hydrological seasons. River inflow areas were often characterized by high seasonality in diffusive flux. Areas close to the dam generally showed low seasonal variability CH 4 flux but high variability in CO 2 flux. Overall, we found that reservoir areas exhibiting highest emission rates (“hotspots”) shifted substantially across hydrological seasons. Estimates of total diffusive carbon emission from the reservoir surfaces differed between hydrological seasons by a factor up to 7 in Chapéu D'Úvas, up to 13 in Curuá-Una, up to 4 in Furnas, and up to 1.8 in Funil, indicating that spatially resolved measurements of CO 2 and CH 4 concentrations and k need to be performed

respiration rates increase, leading to potentially high CO 2 and CH 4 emissions, especially in the first 10 years after reservoir construction (Abril et al., 2005;Barros et al., 2011). In addition to the production of CO 2 and CH 4 from flooded material, allochthonous, and autochthonous organic matter are also important fuels for CO 2 and CH 4 production in reservoirs, which presumably remain an active source long after reservoir formation (Prairie et al., 2017). A share of the microbially produced CO 2 and CH 4 is internally consumed (e.g., via microbial CH 4 oxidation or photosynthesis) (Granéli et al., 1996;Heilman & Carlton, 2001;Pacheco et al., 2015), whereas the surplus evades to the atmosphere by diffusion of dissolved gases or by ebullition (i.e., gas bubbles emerging from the sediment to air) from the reservoir surface, by plant-mediated emission, or by degassing at the turbine passage and from the river downstream the turbine (Abril et al., 2005;Bastviken et al., 2004;Cole & Caraco, 1998;Delsontro et al., 2011;Linkhorst et al., 2020).
CO 2 and CH 4 emission from reservoirs can be highly variable in space due to the heterogeneity of flooded terrestrial habitats, hydrological gradients (e.g., across the longitudinal axis from river to dam), and variability in internal primary production Linkhorst et al., 2020;Pacheco et al., 2015;Paranaíba et al., 2018;Teodoru et al., 2012). Moreover, the complex bathymetry and hydrodynamics of reservoirs imply that sedimentation is heterogeneous in space, which also contributes to the spatial variability in emission rates since both CO 2 and CH 4 are produced during organic matter degradation in sediments (Delsontro et al., 2011;Mendonça et al., 2014;Quadra et al., 2020;Sobek et al., 2012). Hence, accurate quantification of greenhouse gas (GHG) emission from reservoirs requires well-resolved spatial coverage to reduce the uncertainties behind the spatial estimates (Deemer et al., 2016;Paranaíba et al., 2018;Teodoru et al., 2012).
In addition to varying in space, reservoir CO 2 and CH 4 fluxes also vary in time, which is related, for instance, to variations in discharge and the load of C and nutrients from the watershed, water depth, and temperature (Abril et al., 2005;Linkhorst et al., 2020;Pacheco et al., 2015). The extent of the reservoir water body, both their depth and surface area, is strongly affected by seasonal shifts in precipitation regimes within the reservoir watersheds, as well as by demands for electricity production and water supply (Pacheco et al., 2015;Roland et al., 2010). In order to generate reliable estimates when upscaling to whole-reservoir emissions, representative measurements across space and time are therefore needed. Furthermore, due to its warming potential that is 34 times larger than that of CO 2 considering a 100-year time scale and including a carbon feedback loop (Clarke et al., 2014), CH 4 plays a disproportionately large role in the annual system-wide GHG emissions. CH 4 has been estimated to account for ∼80% of total reservoir water surface CO 2 -equivalent emissions, of which 35% are attributed to CH 4 diffusion and 65% to CH 4 ebullition, which thus generally is the major pathway of CO 2 -equivalent emission from reservoirs (Deemer et al., 2016). While there has been recent progress concerning the variability in CH 4 ebullition across domains of both space and time Hilgert et al., 2019;Linkhorst et al., 2020;Natchimuthu et al., 2016;Wik et al., 2016), the understanding of reservoir-internal processes affecting the concentration, emission and transformations of CO 2 and CH 4 remains poorly constrained in reservoirs worldwide, and therefore motivates research into magnitudes and spatiotemporal patterns of concentrations and diffusive emission of CO 2 and CH 4 (Duc et al., 2010;Reed et al., 2017).
The extent to which spatial patterns of CO 2 and CH 4 emission from reservoirs vary among different hydrological seasons is currently insufficiently understood, probably because past studies have largely focused on either investigating variability across space (e.g., Beaulieu et al., 2020;Paranaíba et al., 2018;Roland et al., 2010), or variability in time (e.g., Beaulieu et al., 2014;Jacinthe et al., 2012;Kemenes et al., 2011;Wilkinson et al., 2015). Systematic studies of the variability in diffusive reservoir CO 2 and CH 4 emission across domains of both space and time are lacking or have a low spatial sampling resolution (e.g., Beaulieu et al., 2014;Jacinthe et al., 2012;Serça et al., 2016;Yang et al., 2013). It is therefore not known whether areas with especially high or low diffusive CO 2 and CH 4 emission rates (Paranaíba et al., 2018) are fixed in space over time, and whether their respective magnitude of emission varies over time, and these gaps in knowledge add uncertainty to current estimates of reservoir C emissions. Given that hydrological season can act as a dominant control on reservoir C emissions (Beaulieu et al., 2014;Jacinthe et al., 2012;Kemenes et al., 2011), particularly at low latitudes where the differences in key environmental conditions between dry and rainy season can be large (e.g., water flow, catchment load, temperature), and considering that the number of reservoirs that are being constructed is growing worldwide (Zarfl et al., 2015), it is desirable to PARANAÍBA ET AL.

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gain knowledge on how to best distribute measurement effort between spatial and seasonal coverage (Linkhorst et al., 2020;Wik et al., 2016).
Here, we quantified the diffusive flux of CO 2 and CH 4 from four tropical reservoirs across Brazil, using spatially resolved measurements of dissolved CO 2 and CH 4 concentrations and CO 2 and CH 4 gas-exchange coefficients (k) in hydrologically different seasons, in order to understand: (i) the patterns of the spatial changes in diffusive C fluxes across seasons and (ii) how these seasonal changes affect the annual diffusive C emissions in the studied reservoirs. We hypothesized that the diffusive flux of CO 2 and CH 4 is characterized by substantial variation across both space and seasons, which results in different patterns of spatial within-reservoir variability between seasons. Even though ebullition is the dominant pathway of reservoir CH 4 emissions (Deemer et al., 2016), ebullition and the relative quantitative importance of the different flux pathways are not considered here but treated in detail in a separate study (Linkhorst et al., submitted).

Study Sites and Sampling Strategy
Ten sampling campaigns were performed in four tropical reservoirs in Brazil between 2015 and 2017. The reservoirs are located in three different biomes, and are different in size, age, type of flooded soil, trophic state, and type of use. Reservoir and climate characteristics are shown in Table S1. We sampled each reservoir during at least two different hydrological seasons (Figure 1). The term "season" here refers to samplings performed at different times of the year, that is, at different hydrological periods (dry and rainy seasons) resulting from the precipitation patterns observed within each reservoir's watershed ( Figure 1). The rainy season in the southeastern region of Brazil, where three of the four studied reservoirs are located (see below: Chapéu D'Úvas, Furnas, and Funil), historically occurs between October and March, with the highest temperatures and rainfall in January to February. The dry season for this region tends to occur between April and September. Overall, the southeastern region of Brazil tends to experience an average annual rainfall of 1,300-1,800 mm (Alvares et al., 2014). The rainy period in the Amazon region, where the fourth reservoir studied here is located (Curuá-Una), historically occurs between December and April, with the highest temperatures and rainfall occurring between February and April. The dry season, or a period of a less intense rainfall, is expected for this region from May to October. Overall, the Brazilian Amazon region experiences an average annual rainfall of 1,900-2,200 mm (Alvares et al., 2014). Due to constraints beyond our control (short-term weather variability, reservoir operation, logistics), it was not possible to sample equivalent sections of the hydrograph for all four reservoirs. While three of the reservoirs were sampled during both dry and rainy seasons, one of the reservoirs (Funil) was sampled two times during the dry season, yet in consecutive years. In the following, we briefly describe each reservoir, and relate the sampling campaigns to precipitation and water level conditions (Figure 1).
The 12 km 2 oligotrophic Chapéu D'Úvas (CDU) drinking water reservoir, situated in the Atlantic Forest biome, was sampled four times: sampling 1 was at the beginning of the rainy season, at falling water level; sampling 2 was during the rainy season, at rising water level; sampling 3 was at the beginning of the dry season with high stagnant water level; sampling 4 was during the dry season with falling water level (Table S2). The 72 km 2 mesotrophic Curuá-Una hydroelectric reservoir, situated in the Amazonia biome, was sampled two times: sampling 1 was the beginning of the rainy season, at rising water level; sampling 2 was during the dry season, at falling water level (Table S2). The 1,342 km 2 meso-to-eutrophic Furnas hydroelectric reservoir, situated in the Cerrado biome (Brazilian Savannah), was sampled two times: sampling 1 was during the dry season with stagnant water level; sampling 2 was during the rainy season with falling water level (Table S2). The 40 km 2 eutrophic Funil hydroelectric reservoir, situated in the Atlantic forest biome, was sampled two times: sampling 1 was at the end of the dry season in 2016, at falling water level, and sampling 2 was during the middle of the dry season in 2017, at falling water level (Table S2). All measurements were performed during daylight between 9 and 18 h. While the spatial variability in diffusive CO 2 and CH 4 emission in three of the four reservoirs has been described for one season in a previous publication (Paranaíba et al., 2018), we present here, for the first time, an analysis of the seasonal difference in the spatial variability of diffusive CO 2 and CH 4 emission in four contrasting tropical reservoirs.

CO 2 and CH 4 Partial Pressure (pCO 2 and pCH 4 )
Measurements of pCO 2 and pCH 4 were continuously recorded (1 Hz frequency) using a gas flow equilibration system similar to that described in Gonzalez-Valencia et al. (2014), which was connected to an Ultraportable Greenhouse Gas Analyzer (UGGA, Los Gatos Research; for more details, see Paranaíba et al., 2018). The inlet of the online equilibration system was mounted to a boat, and water from ∼0.5-m depth was continuously pumped into system (3 L min −1 ). The spatial variability in pCO 2 and pCH 4 was investigated performing shore-to-shore transects throughout each of the reservoirs by navigating at an average speed of 7 km h −1 (Figure 2). The boat was stopped approximately every hour for discrete measurements of pCO 2 and pCH 4 : 30 mL of surface water (∼0.05-m depth) and 10 mL of atmospheric air were collected with PARANAÍBA ET AL.  60 mL polyethylene syringes in triplicates to measure pCO 2 and pCH 4 according to the headspace equilibration technique (Cole & Caraco, 1998). After shaking the syringes vigorously for 1 min, the headspace was transferred to a 10 mL polyethylene syringe, and at the end of each sampling day, the discrete samples were manually injected into the UGGA (for details about manual injections, see Paranaíba et al., 2018). These discrete measurements of pCO 2 and pCH 4 were used to determine the equilibration efficiency of the online equilibration system ( Figure S1), and also to calculate the gas-exchange coefficient (k; further described below). Mean ± standard deviation of the equilibration efficiency for CO 2 and CH 4 was 89 ± 18% and 88 ± 20%, respectively ( Figure S1). The response times for the online equilibration system were 3 min for CO 2 and 5 min for CH 4 . Geographic coordinates were recorded concomitantly using a USB-GPS (Navilock 6002U with the software Coolterm, version 1.4.7) for the online equilibration measurements, and with a handheld GPS device (Garmin, eTrex 30x) for the discrete measurements.

Diffusive Flux and Gas-Exchange Coefficient (k and k 600 ) Calculations
At the same sites at which discrete samples of CO 2 and CH 4 surface water concentrations were taken (Figure 2), triplicate measurements of CO 2 and CH 4 diffusion were conducted using a transparent acrylic floating chamber (FC; total volume: 17 L, surface area: 0.07 m 2 ) connected to the UGGA in a closed gas loop. In addition, in the time between each FC deployment, atmospheric concentrations of CO 2 and CH 4 were measured with the online equilibration system over 1 min. Changes in CO 2 and CH 4 concentrations within the FC over 5 min were monitored in real-time. Measurements with apparent nonlinear concentration PARANAÍBA ET AL.  . The red arrows indicate where the main contributing rivers are located, with the path from the main river entrance toward the dam corresponding to the main channel, that is, the relict main river bed. The black arrows indicate where additional tributaries enter the reservoirs.
increase, indicative of bubble flux, were immediately aborted and a new measurement was started. Therefore, only linear CO 2 and CH 4 concentration changes during FC measurements, indicative of diffusive flux, were considered (Duchemin et al., 2000;. This was done with the intention of only capturing the diffusive C flux between the air-water interface, since this study sought to understand the spatial and seasonal patterns of diffusive flux only. The spatial and seasonal patterns of ebullition are considered in a separate study (Linkhorst et al., submitted). We did not observe any flattening of the concentration slope inside the chamber at any point, which would have indicated a weakening of flux due to gas accumulation inside the chambers. In order not to affect photosynthesis and thus natural CO 2 cycling, we used a transparent FC, and the short deployment time (5 min) minimizes the air temperature change inside the chamber (for details, see Paranaíba et al., 2018).
The gas flux (F g , mmol m −2 d −1 ) through the air-water interface is driven by the gas concentration difference between air and water, and regulated by the gas-exchange velocity (k g , m d −1 ), which is specific for each gas and temperature (MacIntyre, 1995) where C w (mmol m −3 ) is the concentration of the given gas in water and C eq (mmol m −3 ) is the theoretical concentration of the given gas in water if the water phase was in equilibrium with the atmosphere.
Combining the FC measurements and discrete partial pressure measurements at each site, k (hereafter named as k FCg , m d −1 ) was then calculated for both CO 2 and CH 4 according to the following equation: Given that the triplicate FC measurements in each reservoir were taken approximately at the same sites for the different samplings ( Figure 2, ∼50 m apart), we calculated the difference in k FC for CO 2 and CH 4 between seasons. We achieved this by averaging the triplicated k values for each sampling site and then subtracting the minimum k FCg value by the maximum k FCg value (i.e., the range) at each sampling site between seasons.
In order to analyze in how far the gas-exchange velocity was driven by wind speed, k FC for CO 2 and CH 4 were normalized to a Schmidt number of 600 (i.e., CO 2 at 20 °C), for both CO 2 and CH 4 , according to Jähne et al. (1987)     600 FC , , 600 / Sc , where Sc g , T is the Schmidt number for a given gas at a given temperature (Wanninkhof, 1992). We used n = 2/3 for wind speed <3.7 m s −1 at 10 m above water level and n = 1/2 for wind speed >3.7 m s −1 at 10 m above water level (Prairie & del Giorgio, 2013). We measured wind speed at 2 m above the water surface at the same sites where discrete samples were taken, using a portable anemometer (Skymaster Speedtech SM-28, accuracy: 3%). Then, we normalized wind speed measurements to the wind speed 10 m above the water surface according to Smith (1985).

Water Column Profile of Temperature and Dissolved Oxygen Concentrations
Water temperature and dissolved oxygen concentration were measured in depth profiles using a multiparameter probe (YSI model 6600 V2, Yellow Spring, OH, USA) in different zones of the reservoirs during each sampling campaign. The multiparameter probe was calibrated before each sampling campaign, and the measurements were taken at every meter from the surface to 15-m depth, and at every 5 m from 15-m depth to the bottom where applicable.

Data Analysis
Since FC and discrete pCO 2 and pCH 4 measurements were performed every hour, we used an interpolation algorithm (see below) to produce estimates of k FCg that matched the higher spatial resolution of the online equilibration system. We also spatially interpolated the between-season range in k FCg values that we calculated at each site. Inverse distance weighting (IDW; ArcGIS version 10.3.1, ESRI) was adopted to interpolate dissolved CO 2 and CH 4 concentrations from the online equilibration system and k FCg to nonmeasured areas. The maps of interpolated CO 2 and CH 4 concentrations (continuous measurement) as well as k FCg of both gases (discrete measurements) were used to calculate the diffusive fluxes according to Equation 1 and to generate maps of diffusive CO 2 and CH 4 fluxes.
To better understand the spatial variability in the diffusive CO 2 and CH 4 flux within and between seasons, the reservoirs were gridded using the Fishnet tool of ArcGIS to create a grid of identical squares (300 × 300 m) over each reservoir's shape. Then, the diffusive flux maps (for each gas and sampling campaign) were combined with the grid layer to extract the mean diffusive flux of all pixels within each grid cell by using the Zonal Statistics as Table function, available in the Spatial Analyst tool of ArcGIS ( Figure S2). Of all grid cells in the reservoirs, 48%, 23%, 5%, and 38% presented at least 1 sampling point (continuous measurements) in CDU (mean ± standard deviation: 9 ± 5 sampling points), CUN (5 ± 2 sampling points), FNS (3 ± 1 sampling points), and FUN (6 ± 4 sampling points), respectively. Grid cells with no interpolated data were excluded from the seasonal analysis (CDU: 8-24 of 283 grid cells were excluded; CUN: 93-153 of 1,413 grid cells were excluded; FNS: 2,448-3,112 of 16,741 grid cells were excluded; and FUN: 97-111 of 792 grid cells were excluded). Empty grid cells are those in which IDW does not extrapolate beyond measured location, but only interpolates between measurements (e.g., due to variability in water level, some areas were covered during one sampling, but not during the other). The number of pixels within grid cells, resulting from IDW interpolation, ranged from 10 to 760 pixels (mean ± standard deviation: 221 ± 177 pixels) in CDU, 12-108 pixels (73 ± 71 pixels) in CUN, 9-114 pixels (64 ± 25 pixels) in FNS, and 10-810 pixels (300 ± 235 pixels) in FUN. Because the grid cells are fixed in space, it was possible to calculate the between-season variability for each grid cell; it was calculated as the range, that is, for each grid cell, the minimum mean flux was subtracted from the maximum mean flux ( Figure S2). Then, all between-season ranges of diffusive flux were plotted in boxplot graphs for each reservoir.
In order to investigate if there are areas within the reservoirs that are characterized by particularly low or high seasonal variability in diffusive CO 2 and/or CH 4 flux, we identified the geographical locations at which the between-season flux difference was either below or above the interquartile range in the boxplots for each reservoir. In addition, to verify whether hotspot zones of diffusive C emission vary in the reservoirs between seasons, we geographically identified the upper quartile that contained 25% of the grid cells with the highest diffusive CO 2 and CH 4 fluxes.
In addition to the analysis of interpolated data, we also performed analyses of the measured data. Since the concentration transects as well as the floating chamber measurement locations were not at identical locations for the different sampling campaigns, not all measurements could be matched and the grid cell size had to be increased (from 300 × 300 m to 400 × 400 m). Analyses of the measured data returned patterns of spatial and temporal distribution ( Figures S3-S6) that were similar to the patterns of the interpolated data (Figures 3-6), indicating that the interpolation did not produce artifacts that could affect our conclusions.
In the following, we present results based solely on the interpolated data, since the interpolations allow us to use all of the measured data (in particular the highly resolved concentration measurements), and allow smaller grid cell sizes, and thus result in a more representative assessment of the reservoirs.
To investigate whether the observed spatial variability in diffusive CO 2 and CH 4 emissions among reservoirs and across seasons was driven rather by variability in gas concentration, or rather by variability in gas-exchange velocity, a Markov Chain Monte Carlo (MCMC) simulation followed by a variance-based sensitivity analysis was performed to calculate Sobol indices (Sobol, 2001). As the diffusive flux across the air-water interface is regulated by the difference in gas concentration and k (Equation 1), Sobol indices disentangle the variance in flux into fractions which are attributed to the input variables (i.e., gas concentration and k). For MCMC simulations and subsequent Sobol index calculations, we used the mean values of diffusive flux, concentration and k FCg of CO 2 and CH 4 , respectively, as extracted from each grid cell, in all reservoirs. We calculated: (i) diffusive flux by fixing k FCg (Flux|k)-diffusive CO 2 and CH 4 fluxes were calculated using fixed k FCg values against all grid-extracted gas concentrations in surface water; and (ii) diffusive flux by fixing surface water gas concentration (Flux|C w )-diffusive CO 2 and CH 4 fluxes were calculated using fixed C w values against all grid-extracted k FCg values Averaged and fixed C eq values based on all grid cells in each sampling campaign in each reservoir were used, given that C eq is based on the atmospheric gas concentration and thus is much less variable in space and time when compared to C w . Subsequently, we separately calculated the average of all fluxes resulting from (i) fixed k FCg and variable C w , and (ii) fixed C w and variable k FCg . We, then, calculated the variance of all diffusive fluxes from both scenarios together (Var(Flux|k U Flux|C w )) and the variance of all averaged diffusive fluxes calculated using fixed k FCg (Var(Flux|k); calculation i) and using fixed C w (Var(Flux|C w ); calculation ii). Finally, the Sobol indices (S k and S Cw ) were calculated dividing Var(Flux|k) and Var(Flux|C w ) by Var(Flux|k U Flux|C w ), for each gas and sampling campaign separately. Accordingly, the Sobol indices are values that range from 0 to 1, with higher values meaning larger data variability. A high S k indicates that a large share of the variance in diffusive flux is attributable to a high variability in gas concentration C w (since k FCg was fixed). A high S Cw indicates that a large share of the variance in diffusive flux is attributable to a high variability in gas-exchange velocity k (since C w was fixed). The remainder to 1 of S k + S Cw is attributable to the variance in diffusive flux that is attributable to the interaction between k FCg and C w .
We calculated the total daily diffusive CO 2 and CH 4 emission per reservoir for each sampling campaign by multiplying the mean gas flux of each grid cell with its grid cell surface area and then summing up the flux values of all grid cells, for CO 2 and CH 4 , respectively. To achieve this, the daily diffusive CO 2 and CH 4 emission of each sampling campaign was multiplied by the number of days that correspond to each studied hydrological season. Thereby, we assumed that the sampling occasions covered the total seasonal variability, and that the flux during the sampling occasion is representative of a period of 3 months for CDU, 6 months for CUN and FNS, and 12 months for each sampling occasion in FUN; evidently, these assumptions add uncertainty to the annual emission estimate. Accordingly, for CDU, where four sampling occasions took place, a multiplication factor of 91 was applied, whereas for CUN and FNS, where only two sampling occasions took place, a multiplication factor of 182 was applied. In FUN, which was sampled two times but both times during the dry season, we calculated an annual average assuming that the sampling occasions were each representative for the entire respective year and, therefore, a multiplication factor of 365 was applied, PARANAÍBA ET AL.
10.1029/2020JG006014 8 of 19 followed by averaging the two annual estimates into an annual average estimate for each gas. Given that our calculations of total diffusive C emission are only based on daytime measurements (between 9 and 18 h), our results may be biased since they do not include any potential diel variations in diffusive C emissions and any specific mixing dynamics happening in the water column during the entire period of each hydrological season represented here (Podgrajsek et al., 2014;Rõõm et al., 2014;Sieczko et al., 2020).
Generalized linear mixed models (GLMM) were applied to assess the differences in the diffusive CO 2 and CH 4 fluxes and gas-exchange coefficients between the different spatial variability campaigns, and between the reservoirs. To do so, we used the glmer function in the "lmer4" package in R (v. 4.0.2) (R Core Team, 2018). We used the spatial variability campaigns of each reservoir as a fixed factor, and the variable "reservoir" was used as a random factor to account for the underlying characteristics of each reservoir. We used generalized models because preliminary analyses showed that the distribution of the residuals of the linear mixed models (LMM) followed a logarithmic distribution and, therefore, the gamma family (link = log) was applied PARANAÍBA ET AL.
10.1029/2020JG006014 9 of 19 in the GLMM. A Tukey post-hoc test was applied to compare each possible pair using the glht function as available in the "multcomp" package (Hothorn et al., 2008). Graphical analyses were performed using the software JMP (version 14.0.0), statistical analyses and discrete sample calculations were done using the software R (version 1.1.383), and all maps were created using the software ArcGIS (version 10.3.1, ESRI).

Spatial and Seasonal Variability in pCO 2 , pCH 4 , k, k 600 , and Diffusive CO 2 and CH 4 Fluxes
We observed large variability in pCO 2 and pCH 4 within reservoirs, among reservoirs, and among hydrological seasons ( Table 1). The average surface water pCO 2 and pCH 4 were supersaturated with respect to the atmosphere in all reservoirs and all sampling campaigns (Table 1), except for pCO 2 during the late dry season in FUN, a highly eutrophic system (Table S1). For all reservoirs and sampling campaigns together, the average pCO 2 and pCH 4 were 1.6 and 7.4 times higher than atmospheric levels, respectively.
The gas-exchange coefficient (k) also varied within reservoirs and among seasons (Tables S3-S6); overall, k ranged from 0.002 to 14 m d −1 for CO 2 and from 0.005 to 22 m d −1 for CH 4 . The mean ± standard deviation of k was 1.1 ± 1.4 m d −1 for CO 2 and 4.3 ± 3.5 m d −1 for CH 4 in CDU; 1.4 ± 2.5 m d −1 for CO 2 and 2.4 ± 1.6 m d −1 for CH 4 in CUN; 0.6 ± 0.7 m d −1 for CO 2 and 3.0 ± 3.1 m d −1 for CH 4 in FNS; and 0.02 ± 0.06 m d −1 for CO 2 and 0.07 ± 0.07 m d −1 for CH 4 in FUN. While the seasonal variability in k was small in most reservoirs, a few areas in each reservoir were characterized by relatively high seasonal variability (red areas in Figures S7 and S8; Tables S3-S6). Statistical outcomes of the GLMM of k values for CO 2 and CH 4 between seasons and reservoirs are shown in Table S7; within reservoirs: k FC -CO 2 seasonality was significant in all reservoirs except in CUN (z value: −2.6, p = 0.206), whereas k FC -CH 4 seasonality was not significant between seasons in any reservoir (Table S7). See Table S7 for comparisons between reservoirs. In PARANAÍBA ET AL.

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10 of 19 search for possible drivers controlling gas exchange in all reservoirs across seasons, we plotted the k FC and k 600 for both CO 2 and CH 4 against the corresponding water temperature and wind speed at the time of sampling, respectively. We found that wind speed was not correlated with k 600 estimates neither for CO 2 and nor for CH 4 (except for k 600 -CO 2 in CDU; Figure S9). We also could not observe consistent positive relationships between k FC and water temperature for both CO 2 and CH 4 in all reservoirs ( Figure S10). This indicates that neither wind speed, which can affect k at very short time scales (minutes-hours), nor water temperature, which can affect k at diurnal-seasonal time scales, rendered a detectable imprint on the gas-exchange velocity in our study. Potentially, the variability in k could be driven by the presumably complex hydrodynamics in these dendritic reservoirs with their multiple tributaries, or by convection-driven turbulence.
As a result of the variability in gas concentration and k, diffusive CO 2 and CH 4 fluxes also varied across both space and time in all reservoirs (Table 1 and Figure 3). The mean diffusive CO 2 and CH 4 fluxes of our studied reservoirs were within the diffusive CO 2 and CH 4 flux ranges reported by Deemer et al. (2016) for 228 reservoirs worldwide ( Figure S11). Overall, diffusive CO 2 emissions from these four reservoirs are in the lower range observed in global reservoirs, whereas CH 4 emissions are in the upper range ( Figure S11).
The variability in diffusive flux of each grid cell between sampling campaigns (blue boxes in Figure 3) was as large as the variability observed between grid cells for every sampling campaign and both gases in all reservoirs (black boxes in Figure 3). This finding adds to previously documented strong within-reservoir variability in diffusive CO 2 and CH 4 fluxes (Paranaíba et al., 2018) by showing that at any given point in space, the variability between sampling occasions can also be as strong as the difference between any two sampling locations. ( Table S8; see also for comparisons between reservoirs). CO 2 emission was higher in the dry season than in the rainy season (Table 1 and Figure 3). However, no consistent pattern was visible for CH 4 emission, which was higher during the dry season in CUN and FNS, but higher during the rainy season in CDU (Table 1 and Figure 3). For FUN, which was sampled two times during dry seasons, CO 2 and CH 4 emissions were higher during the middry season of 2017 than during the late dry season of 2016, but since the fluxes were very small at both occasions for both gases (Table 1 and Figure 3), this difference should be interpreted with caution. It rather seems that sampling FUN two times during dry seasons of consecutive years overall returned similar diffusive emission estimates for both CO 2 and CH 4 (Table 1 and Figure 3). Higher C emission rates (for both CO 2 and CH 4 ) during dry seasons have previously been reported for some tropical hydroelectric reservoirs. They were correlated to longer water residence time during dry periods when compared to rainy periods (Abril et al., 2005), to nonstratified water columns due to stagnant low air temperatures over the dry period in tropical regions (wintertime) (Pacheco et al., 2015;Roland et al., 2010), and to the increased influence of river inflow areas on the dissolved gas concentrations of a reservoir as a whole (Pacheco et al., 2015). We also want to emphasize that the seasonal differences reported in this study refer to the hydrologically different times of the year at which the reservoirs were sampled. We do not use the term "seasonality" to attribute the observed differences in emission to potential drivers that vary at the seasonal scale (e.g., water flow, catchment load, or temperature), and cannot exclude that additional sampling campaigns could identify sources of variability in emission that are not related to seasonal-scale variability in potential drivers of emission.
The daily emission of CO 2 and CH 4 from the reservoir surface via diffusion (exclusive of ebullition or downstream emission) varied largely between reservoirs (Table S9). We describe here the magnitude of seasonal variability by dividing the highest total daily diffusive emission by the lowest total daily diffusive emission for each gas and each reservoir. Accordingly, total daily diffusive C emission from the studied reservoirs varied by a factor of 1.1-13 between seasons (median 5, range 1.8-13 for CO 2 ; and median 1.9, range 1.1-4 for CH 4 ) ( Table S9). Low between-season variability was observed only for CH 4 emissions in CUN (factor 1.4) and FUN (factor 1.1) ( Table S9). The dry seasons were characterized by the highest daily diffusive CO 2 emission in all reservoirs (total daily diffusive emission ± standard error: 1,000 ± 0.5 kg C d −1 in PARANAÍBA ET AL.  0.08 ± 0.2 (0.002-1.7) Table 1 Average, standard deviation, and range of CO 2 and CH 4 partial pressure (upper table)
The Sobol indices showed that the spatial variability in diffusive CO 2 and CH 4 fluxes observed in each hydrological season in the four studied reservoirs was strongly affected by the variability in the gas-exchange velocity (k FCg ) between seasons (mean S Cw for all data: 0.56), followed by the variability in surface water gas concentration (mean S k for all data: 0.26), and by the interaction between the two (mean remainder, 0.19; Table 2). Even though we could not identify consistent relationships between the gas-exchange velocity and the suspected drivers wind speed and water temperature ( Figures S9 and S10), this finding is in accordance with previous findings of a strong effect of k on reservoir C emission at very short time scales (e.g., at the diel scale; Deshmukh et al., 2014;Liu et al., 2016). Our analysis also indicates that gas concentration in concert with the interaction between gas concentration and k contributed almost half of the within-reservoir variability in diffusive flux. Furthermore, the calculation of Sobol indices assumes that the predictor variables are orthogonal, and while this condition was given as indicated in the absence of a relationship between gas concentration and gas-exchange velocity (data not shown), it is conceptually evident that gas concentration and gas-exchange velocity are not independent. That is, with high k values, dissolved gases from mixed surface waters may rapidly outgas, thereby lowering the C w concentrations, whereas low k values may allow dissolved gases to build up in the surface waters, thereby leading to high C w values. Therefore, the high S Cw indices ( Table 2), indicating that more than half of the variability in diffusive flux is attributable to variability in k FCg , cannot be used to rule out the importance of the gas concentration C w , and of the interaction between C w and k FCg .
PARANAÍBA ET AL. Notes. Remainder variance (Int.) is attributed to the interaction between S k and S Cw . Higher Sobol indices, indicating a higher variance, are highlighted in bold. For S k indices, k FCg values were fixed and C w values were allowed to vary, and therefore express the influence of the variability in C w on the resulting diffusive flux. For S Cw indices, C w values were fixed and k FCg values were allowed to vary, and therefore express the influence of the variability in k FCg on the resulting diffusive flux.

Within-Reservoir Variability in Diffusive CO 2 and CH 4 Fluxes Across Seasons
Our results demonstrate that the patterns of spatial within-reservoir variability in diffusive CO 2 and CH 4 emission can be very different between sampling campaigns performed during different hydrological seasons (Table 1 and Figure 4). The within-reservoir hotspots of diffusive gas emission-defined as the upper quartile containing 25% of the grid cells with the highest fluxes in a given reservoir-shifted substantially across seasons for both CO 2 and CH 4 in all reservoirs (except for CH 4 in FUN) (Figures 5 and 6).
Mapping the grid cells with the lowest and highest seasonal variability (<Q 1 and >Q 3 ) reveals remarkable spatial diffusive flux patterns, which, however, were not equivalent for CO 2 and CH 4 (Figure 4). Variability in diffusive flux results from the variability in gas concentration (i.e., the net outcome of all processes that either add or remove the gas from the water) and/or variability in k (i.e., transport across the air-water interface). In the following, we discuss the spatial patterns of seasonal variability in diffusive flux in the light of processes that affect gas concentration as well as gas-exchange velocity, even if these two terms of the diffusive flux equation are not entirely independent (e.g., Rocher-Ros et al., 2019).
The area close to the dam was characterized by high seasonal variability in diffusive CO 2 flux in CDU, FNS, and FUN (but not in CUN), which is probably linked to the fact that the dam area is typically the most lake-like part of a reservoir (deepest, i.e., with longest water residence time), which may favor the growth of phytoplankton and thus allow more biologically driven CO 2 dynamics ( Figure 4). On the other hand, the dam areas of all reservoirs were characterized by low seasonal variability in diffusive CH 4 flux (Figure 4), which may potentially be explained by the water column close to the dam being relatively deep compared to the rest of the reservoir (depth at dam and mean reservoir depth for CDU, CUN, FNS, and FUN were 30 and 19 m, 7 and 6 m, 61 and 15 m, and 58 and 22 m, respectively) (Figures S12-S15). A deep water minimizes the mixing of CH 4 -rich bottom waters with surface water, and favors aerobic oxidation of CH 4 during transport from the sediment to the atmosphere (Bastviken et al., 2004;McGinnis et al., 2006).
High seasonal variability in the diffusive CH 4 flux was sometimes observed in areas close to riverside communities in CDU and CUN (represented as small black houses in Figure 4). Such a pattern was not observed for CO 2 . Potentially, direct anthropogenic organic matter inputs via untreated sewage in these relatively shallow areas of the reservoirs (CDU: 9 ± 3 m, CUN: 5 ± 2 m) may favor methanogenesis in sediments.
Methanogenesis is expected to vary seasonally in response to temperature changes and sediment inputs (Grasset et al., 2018;Yvon-Durocher et al., 2014), leading to occasional venting to the atmosphere during water column mixing events (Liu et al., 2016). Moreover, total nitrogen (TN) and total phosphorus (TP) concentrations found near these riverside communities in CDU and CUN (mean ± standard deviation of TN in CDU: 810 ± 14 µg L −1 , TP in CDU: 23 ± 1 µg L −1 , n = 2; TN in CUN: 720 ± 19 µg L −1 , TP in CUN: 27 ± 2 µg L −1 , n = 3) were higher than the average TN and TP of each reservoir (TN in CDU: 452 ± 273 µg L −1 , TP in CDU: 12 ± 9 µg L −1 , n = 11; TN in CUN: 661 ± 77 µg L −1 , TP in CUN: 19 ± 6 µg L −1 , n = 10) (Paranaíba et al., 2018). The occurrence of high TN and TP levels near riverside communities in CDU and CUN may represent another indication that these communities are locally influencing water quality and biogeochemical processes. Even if high nutrient levels can affect the magnitude of CO 2 emission (e.g., Hanson et al., 2003), the variability in CO 2 emission between sampling occasions was apparently not affected. In FNS, which is much larger in area, depth, and total water volume than the other three reservoirs, there was no observable link between riverside communities and seasonal variability in CO 2 and CH 4 fluxes ( Figure 4).
The main channel of FUN and FNS was mostly low in CO 2 flux magnitude and variability (Figure 4), possibly because large open-water areas are typically more well-mixed and often have a higher gas-exchange velocity (Vachon & Prairie, 2013), which spatially homogenizes diffusive fluxes. Moreover, the influence of the surrounding land ecosystem and the ratio of sediment area to water column depth has a stronger influence in shallow narrow areas than in deep open-water areas (Holgerson & Raymond, 2016;Kortelainen et al., 2006).
In all reservoirs, some areas close to river inflows (as indicated by the arrows in Figure 4) showed high seasonal variability in diffusive CO 2 and CH 4 fluxes. It has been previously shown that river inflow areas may strongly affect the C dynamics in freshwater ecosystems (Delsontro et al., 2011;Pacheco et al., 2015;Paranaíba et al., 2018). The allochthonous inputs of organic matter and nutrients to the reservoir via river inflows is highly variable depending on weather and human activities in the catchment, and can directly affect the C dynamics in the reservoir (Butman & Raymond, 2011;Pacheco et al., 2015). High water flow from an incoming river also affects the hydrodynamics of the reservoir and can induce resuspension as well as intermittent vertical and lateral instabilities in the water column. These water column instabilities may contribute to a seasonally occurring lack of thermal stratification (Figures S12-S15) (Winton et al., 2019), increasing the connectivity between the sediments and the atmosphere, thus the diffusive transport of CO 2 and CH 4 , which is produced in the sediments and/or water column, to the atmosphere (Abril et al., 2005;Delsontro et al., 2011;Pacheco et al., 2015;Roland et al., 2010). Moreover, fluctuations in the magnitude of the river water flow may affect water turbulence in inflow areas, such that the river water flow could seasonally influence the gas-exchange rates at the atmosphere-water interface Long et al., 2015;Paranaíba et al., 2018;Zappa et al., 2007). Accordingly, we observed a strong seasonal difference in k in some river inflow areas of the four reservoirs ( Figures S7 and S8).
Finally, it is noteworthy that the high seasonal variability in the diffusive CO 2 and CH 4 flux in some areas in the main channel of some of the reservoirs (e.g., in CDU, CUN, and FNS; Figure 4) may be associated with the local k measurements that also varied spatially between seasons in all reservoirs (Figures S7 and S8, and  Tables S3-S6), and thus reflect conditions at the time of sampling. Our k values are products of FC measurements over short time intervals (5 min), and can, in response to meteorological and hydrological conditions as well as local basin morphology, strongly vary in space and time (Cole & Caraco, 1998;Long et al., 2015;Paranaíba et al., 2018;Zappa et al., 2007). The small-scale variability in k makes it difficult to observe clear patterns at larger scales of space or time ( Figures S7 and S8, and Tables S3-S6) (Paranaíba et al., 2018).

Interreservoir Variability in pCO 2 , pCH 4 , and Diffusive CO 2 and CH 4 Fluxes
The highest pCO 2 and areal diffusive CO 2 flux were found in the Amazonian reservoir (CUN , Table 1 and Figure 3), and our findings are in accordance with previous results described by other studies on Amazonian inland waters (Belger et al., 2011;Duchemin et al., 2000;Kemenes et al., 2011;Richey et al., 2002). Amazonian freshwater systems are important sources of both CO 2 and CH 4 to the atmosphere, due to their connectivity with wetlands and extensive floodplains and high temperatures throughout the year (Abril et al., 2013;Almeida et al., 2017;Barbosa et al., 2016;Fearnside & Pueyo, 2012;Melack et al., 2004), even though Deemer et al. (2016) did not find a difference in CH 4 emission between Amazonian and non-Amazonian reservoirs. We found that in CUN, pCH 4 and areal diffusive CH 4 flux were relatively low, similar to an earlier report of low diffusive CH 4 emission in CUN (Duchemin et al., 2000) (Table 1 and Figure 3). This low diffusive CH 4 flux in CUN may be linked to microbial CH 4 oxidation in the water column. The entire shallow water column in CUN was well-oxygenated (surface water concentration: 7 ± 0.6 mg L −1 ; bottom water concentration: 5 ± 1 mg L −1 ) throughout the seasons ( Figure S13). In contrast, oxygen-poor bottom water was more common in the water columns of the other reservoirs (CDU, FNS, and FUN; Figures S12, S14, and S15). Importantly, CH 4 ebullition, which typically is the main emission pathway of CH 4 emission in shallow waters (Bastviken et al., 2004) and particularly in reservoirs (Deemer et al., 2016), was not measured in this study. Instead, we dealt with ebullition in CDU and FUN in a separate study, which revealed that CH 4 ebullition alone made up for 60% and 99% of CO 2 -equivalent C emission in CDU and FUN, respectively (Linkhorst et al., submitted). High potential for CH 4 ebullition from sediments of CUN has also been reported before (Quadra et al., 2020). Accordingly, any assessment of total reservoir CH 4 emission, which, again, we did not intended to do here, needs to include measurements of CH 4 ebullition, at high spatial resolution and during different hydrological seasons (Grinham et al., 2018;Linkhorst et al., 2020).
The lowest diffusive fluxes of both CO 2 and CH 4 in all four reservoirs was observed in the eutrophic reservoir FUN (Table 1 and Figure 3). This was surprising since both diffusive and ebullitive CH 4 emissions tend to increase with productivity (Beaulieu et al., 2019;Deemer et al., 2016), due to the high loads of labile autochthonous organic matter to the generally anoxic sediments. In FUN (Table 1), the average diffusive CH 4 flux was about one order of magnitude lower than in another eutrophic reservoir in the Brazilian semiarid region (Almeida et al., 2016), but similar to values observed in a eutrophic lake with a similar climate in eastern China (Xiao et al., 2017). Interestingly, the diffusive CO 2 flux that we observed in both sampling campaigns in FUN (Table 1) was also one to two orders of magnitude lower than reported previously for the same reservoir by Pacheco et al. (2015) and Roland et al. (2010). The pCO 2 in our study, however, was within the same order of magnitude as in the above-mentioned studies, indicating that k was comparatively low during our sampling campaigns in FUN. We may attribute such differences in the magnitude of diffusive CO 2 emissions to different meteorological conditions during sampling, to different methodologies, and to different sampling coverage. Moreover, this study was focused on diffusive fluxes and thus did not include ebullition measurements, which together with low k FCg values may explain why CH 4 emission from the highly productive FUN reservoir was low (Table S6, see Tables S3-S5 for the other reservoirs). Also, we did not perform any measurements in FUN during the rainy season.

Implications
By combining spatially resolved measurements of CO 2 and CH 4 surface water concentrations and k during different seasons, we show pronounced differences between hydrological seasons in spatial within-reservoir variability in the diffusive CO 2 and CH 4 fluxes of four tropical reservoirs. To the best of our knowledge, we showed for the first time that hotspot areas of diffusive C emission shift substantially between sampling occasions conducted during different hydrological seasons. Ignoring spatial and seasonal within-reservoir variability in gas concentration and k may introduce a serious bias in annual diffusive emission estimates; more specifically, the estimates in our four studied reservoirs differed by a factor of up to 13 for CO 2 , and by a factor of up to 4 for CH 4 . The seasonal and spatial variability patterns of CO 2 and CH 4 diffusion in this study were not consistent within and between reservoirs, which emphasizes the need of spatially resolved sampling campaigns at least during two hydrological seasons to constrain annual diffusive C emission estimates in tropical reservoirs. However, our analyses addressed diffusive emission only, while in many reservoirs, CH 4 ebullition is the pathway contributing most to CO 2 -equivalent emission (Deemer et al., 2016). Accordingly, we also found that CH 4 ebullition accounted for the largest fraction of the total CO 2 -equivalent emission from CDU and FUN reservoir surfaces during our sampling campaigns in 2016 (Linkhorst et al., submitted). This indicates that sampling effort not only needs to be distributed in space and time, but also between flux pathways. If the primary purpose of a study is quantification of CO 2 -equivalent emission, focusing sampling effort on CH 4 ebullition seems warranted. If addressing CO 2 emission or reservoir-internal processes regulating gas concentrations, gas exchange, or gas transformations (e.g., CH 4 ebullition and CH 4 oxidation in mixed layer; Thottathil et al., 2018), investing effort in spatially and seasonally resolved measurements of dissolved gases and diffusive emission will be conducive. the data analysis. We are also grateful to CESAMA and Eletronorte S/A for their logistical support during our fieldwork in CDU and CUN, respectively.