Sources and processes sustaining surface CO2 and CH4 fluxes in a tropical reservoir: the importance of water column metabolism

Freshwaters are important emitters of carbon dioxide (CO2) and methane (CH4) to the atmosphere, two potent greenhouse gases (GHG). While aquatic surface GHG fluxes have been extensively measured, there is much less information about their underlying sources. In lakes and reservoirs, surface GHG can originate from horizontal riverine flow, the hypolimnion, littoral sediments, and water column metabolism. These processes are generally studied separately, leading to a 10 fragmented assessment of their relative role in sustaining CO2 and CH4 surface fluxes. In this study, we quantified sources / sinks of CO2 and CH4 in the epilimnion along a hydrological continuum in a permanently stratified tropical reservoir (Borneo Island). Results showed that horizontal inputs are an important source of both CO2 and CH4 (18 to 100 % of surface emissions) in the upstream reservoir branches. However, this contribution fades along the hydrological continuum, becoming negligible in the main basin of the reservoir, where CO2 and CH4 are uncoupled and driven by different processes. In the main basin, 15 vertical CO2 inputs and sediment CH4 inputs contributed to on average 60 and 23 % respectively to the surface fluxes of the corresponding gas. Water column metabolism exhibited wide amplitude and range for both gases, making it the most influential but uncertain component in the epilimnetic gas budgets. Overall our results show that while sources sustaining surface CO2 and CH4 fluxes vary spatially and between the two gases, internal water metabolism remains a dominant driver. However, this study also highlights challenges and knowledge gaps related to estimating ecosystem-scale CO2 and CH4 metabolism, which 20 hinder aquatic GHG flux predictions.

Physical mixing in lakes and reservoirs indirectly impacts C metabolic processes by shaping the O2 profile, and directly affects GHG surface diffusion by controlling the transport of CO2 and CH4 from deep to surface water layers (Barrette and Laprise, 2005;Kreling et al., 2014;Pu et al., 2020). Despite its potential importance (Kankaala et al., 2013), very few studies quantified 65 vertical gas transport and the role of this process in fueling surface GHG emissions. The movement of gases within a system depends on the structure of the water column, which changes spatially along the aquatic continuum. Reservoirs in particular exhibit strong gradients in morphometry and hydrology, translating into high spatial heterogeneity in surface GHG fluxes to the atmosphere (Paranaíba et al., 2018;Teodoru et al., 2011).
Understanding what regulates surface CO2 and CH4 concentrations and fluxes to the atmosphere requires knowledge of the 70 interplay between all physical and biogeochemical processes involved, and how they vary spatially. While a number of studies have assessed some processes individually or by difference, very few have measured all relevant components of the epilimnetic mass-balance simultaneously. Here we report on a field study in a tropical East Asian hydropower reservoir quantifying external inputs, sediments inputs, net CO2 and CH4 metabolism, vertical diffusion from deeper layers and gas exchange at the air-water interface. This allowed us to estimate the relative contribution of each process in shaping surface GHG emissions 75 from the reservoir, and to test whether the epilimnetic mass balance can be closed. The two major rivers feeding the reservoir flow into two elongated branches, acting as a transition zones, before reaching the main basin. This configuration, common in reservoirs, allowed us to quantify and compare epilimnetic CO2 and CH4 regulation in two morphometrically different areas (reservoir branches and main basin). Overall, the aim of this study is to provide an ecosystem-scale portrait of the processes sustaining surface CO2 and CH4 emissions and examine how they change when transitioning from a river delta to an open 80 basin.

Site and sampling description
The study was conducted in Batang Ai hydroelectric reservoir in Sarawak Malaysia (latitude 1.16º and longitude 111.9º). The reservoir is located on the Borneo Island in a tropical equatorial climate with a constantly high temperature averaging 23 ºC 85 and 32 ºC during nighttime and daytime respectively (Sarawak Government, 2019). The region experiences two weak monsoon seasons (November to February and June to October) with a yearly average rainfall of 3300 to 4600 mm (Sarawak Government, 2019). The reservoir was impounded in 1985 with a dam wall of 85 m, a surface area of ~68.4 km 2 and a watershed area of 1149 km 2 of mostly undisturbed forested land (limited rural habitations and small scale croplands).
We distinguish between three sections of the study site: inflows, reservoir branches, and reservoir main basin shown in Figure  90 1. The inflows are the two main reservoir inlets: Batang Ai and Engkari rivers (3 to 10 m deep where sampled). The two rivers flow into two arms that we refer to as the reservoir branches (10.8 km 2 , mean and max depths of 18 and 52 m respectively).
The reservoir branches merge into the main basin of the reservoir (58.9 km 2 , mean and max depths of 30 and 73 m respectively).

Physical and chemical analyses 100
Water temperature, dissolved oxygen, and pH were measured using a multi-parameter probe (YSI model 600XLM-M) equipped with a depth gauge and attached to a 12 Volt submersible pump (Proactive Environmental Products model Tornado) for water samples collection. Concentrations of dissolved organic carbon (DOC), total phosphorus (TP), total nitrogen (TN), and chlorophyll a (Chla) were measured during all campaigns in all surface sampling sites ( Figure 1). Methods for these analyses are described in detail in Soued et Prairie (2020). Briefly, TP and Chla (extracted with hot ethanol) were analyzed via 105 spectrophotometry, and TN and DOC (filtered at 0.45 μm) were measured on an Alpkem Flow Solution IV autoanalyser and on a Total Organic Carbon analyser 1010-OI respectively.
For each site, we defined the depths of the thermocline and the top and bottom of the metalimnion based on measured temperature profiles using the R package rLakeAnalyzer (Winslow et al., 2018). The epilimnion was defined from the surface to the top of the metalimnion, and was assumed to be a mixed layer. 110 2.3 Gas concentration, isotopic signature, and water-air fluxes CO2 and CH4 gas concentrations and isotopic signatures (δ 13 C) were measured in duplicates at the surface in 36 sites and along vertical profiles in 9 sites (P1 to P9, Figure 1) using the headspace technique described in details in Soued et Prairie (2020). In brief, sampling was done by equilibrating the water sample for two minutes with an air headspace inside a 60 mL syringe. The gas phase was then injected in a 12 mL pre-vacuumed air-tight vial, and analyzed on a gas chromatograph (Shimadzu GC-8A 115 with a flame ionization detector) for gas concentrations, and on a Cavity Ring Down Spectrometer (CRDS) equipped with a Small Sample Isotopic Module (SSIM, Picarro G2201 -i) for δ 13 CO2 and δ 13 CH4.
Surface diffusive fluxes of CO2 and CH4 were measured at all surface sampling sites during each campaigns. Flux rates were derived from linear changes in CO2 and CH4 concentrations in a static floating chamber (design described in Soued et Prairie (2020) and IHA (2010)) connected in a closed loop to a gas analyzer (model UGGA, from Los Gatos Research). Measured gas 120 concentrations, isotopic signature, and fluxes were spatially interpolated to the whole reservoir area by inverse distance weighting (given the absence of a suitable variogram for kriging) using package gstat version 1.1-6 in the R version 3.4.1 software (Pebesma, 2004). Mean values were calculated for each campaign based on the interpolated maps (Soued and Prairie, 2020). https://doi.org/10.5194/bg-2020-258 Preprint. Discussion started: 14 September 2020 c Author(s) 2020. CC BY 4.0 License.

Horizontal GHG inputs 125
In order to estimate the external horizontal inputs of CO2 and CH4, we considered that the total volume of water inflow and outflow (discharge) were equal, and equivalent to the mean of measured daily discharge (Q, in m 3 d -1 ) during each campaign (considering minimal changes in inflow / outflow rates during a campaign). Given that part of the water from the riverine inflows is colder and denser than the reservoir surface layer, only a fraction of the inflowing waters enters the epilimnion of the reservoir, and the rest plunges into the hypolimnion. We estimated the fraction of inflowing water entering the epilimnion 130 (fepi) based on temperature profiles at the two ends of the right branch. The areal rate of horizontal CO2 and CH4 inputs (H, in mmol m -2 d -1 ) over each section of the reservoir were then calculated following Eq. (1):

=
( 1) with A (in m 2 ) the area of the reservoir section considered, and Cin (in mmol m -3 ) the concentration of gas in the inflowing water. To estimate gas inputs form the inflows to the branches, Cin was considered as the average of gas concentrations 135 measured at the two upstream extremities of the branches (Figure 1). To estimate gas inputs form the branches to the main basin, Cin was considered as the gas concentrations measured at the confluence between the two branches (right upstream of the main basin).

Vertical GHG fluxes
We estimated CO2 and CH4 fluxes from the metalimnion to the epilimnion (V) based on the vertical gas diffusivity (Kz) and 140 the gradient in gas concentration across the epilimnion-metalimnion interface using Eq. (2) (Wüest and Lorke, 2009): where Cmeta and Cepi are the gas concentrations at the top of the metalimnion and at the bottom of the epilimnion respectively, measured in profile sites (P1 to P9, Figure 1). Kz was derived from the following Eq. (3) (Osborn, 1980): where Γ is the mixing ratio set to 0.2 (Oakey, 1982), ϵ is the dissipation rate of turbulent kinetic energy, and N 2 is the buoyancy frequency. N 2 was calculated from measured temperature profiles (YSI probe) using function buoyancy.freq from the rLakeAnalyzer package (Winslow et al., 2018) in the R software (R Core Team, 2017). ϵ was derived from measured vertical shear microstructure profiles performed in the Aug 2018 campaign in all profile sites shown in Figure 1 (except P1 due to floating logs). Shear profiles were measured with a high frequency (512 Hz) MicroCTD profiler (Rockland Scientific) 150 equipped with two velocity shear probes, two thermistors, tilt and vibration sensors, and a pressure sensor. At each site, the profiler was cast 10 times, 5 with an uprising configuration (from bottom to top of the water column) and 5 with a downward configuration (top to bottom), with a 4 min waiting time between profiles to allow water column disturbance to subside. Data quality check and ϵ calculation for each profile cast were performed with ODAS v4.3.03 Matlab library (developed by Rockland Scientific) based on Nasmyth shear spectrum (Oakey, 1982), with ϵ values averaged among the two shear probes 155 https://doi.org/10.5194/bg-2020-258 Preprint. Discussion started: 14 September 2020 c Author(s) 2020. CC BY 4.0 License. and binned over 1-2 m segments along the profile. For each site, continuous ϵ profiles were interpolated by fitting a smooth spline through all ϵ values from replicate casts as a function of depth.
At the epilimnion-metalimnion interface (top of the metalimnion ± 2 m), calculated ϵ averaged 7.7 x10 -9 (range from 3.4 x 10 -9 to 1.6 x 10 -8 ) m 2 s -3 across all sites sampled with the microCTD, with no significant difference between the main basin and branches sites. In order to estimate vertical gas diffusion, we applied the latter ϵ average to Eq. (2) and (3) for all measured gas 160 profiles (except P1). The resulting V values for each gas were averaged across sites in the main basin and branches separatel y to derive estimates of V for each of these two reservoir sections.

Sediment GHG inputs
We calculated CO2 and CH4 inputs from the sediments to epilimnetic waters using gas profiles in sediment cores collected in Apr-May 2017 and Feb-Mar 2018 at 7 sites (P1 to P3 in the reservoir branches and P4, P5, P7, and P9 in the main basin, Figure  165 1). Sediment cores were collected using a Glew gravity corer attached to a 6 cm wide plastic liner. The liner was pre-drilled with 1 cm holes covered with electric tape at each centimeter up to 40 cm. Upon recovery of the sediment core, 3 mL tip-less syringes were inserted into each hole to extract sediments from each centimeter. The sediment content of each syringe was emptied into a 25 mL glass vial prefilled with 6 mL nano-pure water and immediately air-tight sealed by a butyl rubber stopper crimped with an aluminum cap. Glass vials were pressurized with 40 mL of ambient air using a plastic syringe equipped with 170 a needle to pierce the rubber cap. Glass vials were shaken for 2 min for equilibration before extracting the gas with a syringe and injecting it into a pre-evacuated air-tight vial for analysis of CO2 and CH4 concentrations and isotopic signatures as described above. Additionally, samples of the water overlaying the sediments (~1 cm above) were collected for similar analyses of CO2 and CH4. Sediment CO2 and CH4 flux rates to the overlaying water column were derived from the vertical gradient of gas concentration 175 measured in the sediment cores and overlaying water. The slope of CO2 or CH4 concentration as a function of depth (g, in μmol L -1 m -1 ) was calculated for measured values in the first 5 cm of sediments and overlaying water. Most cores exhibited clear linear slopes (p-value < 0.05 and R 2 adj > 0.5). In the few cases where a linear slope was not evident, g was replaced by the gradient between the mean gas concentration in the first 3 cm of sediments and the overlaying water. The sediment gas flux rate (Sf in mmol m -2 d -1 ) were calculated with Eq. (4): 180 With d the diffusion coefficient set to 1.5 x 10 -5 cm 2 s -1 (Donis et al., 2017), and p the sediment porosity assumed to be 2 % based on previous results in Batang Ai (Tan, 2015).
At an ecosystem scale, sediment CO2 and CH4 inputs to the water column (S) were estimated based on average and standard deviation values of sites located in each section of the reservoir (branches and main basin). For each section, mean sediment 185 CO2 and CH4 flux rates were multiplied by the areal ratio of epilimnetic sediments (Aepi) versus total water area (A0). The latter ratio was calculated based on the hypsometric model (Ferland et al., 2014;Imboden, 1973) as shown in Eq. (5) to (7): https://doi.org/10.5194/bg-2020-258 Preprint. Discussion started: 14 September 2020 c Author(s) 2020. CC BY 4.0 License.
with q a parameter describing the general shape of the reservoir section, zmax and zmean the maximum and mean depths respectively, and zepi the mean depth of the epilimnion (8.0 and 10.5 m in the branches and main basin respectively).
Littoral sediments are known to be a source of CH4 not only through diffusion but also via ebullition. While this emission pathway was found to be important in other reservoirs (Deemer et al., 2016), it is surprisingly low in Batang Ai, equaling less than 2 % of CH4 surface diffusive emissions, and only 0.1 % of the reservoir total GHG footprint (Soued and Prairie, 2020). 195 Therefore, sediment ebullition was considered negligible in the epilimnetic CH4 budget of Batang Ai.

Metabolic rates
Net metabolic rates of CO2 and CH4 production in the epilimnetic water column were estimated with in situ incubations.
Incubations were performed in 5 sites (P2 and P3 in the branches and P4, P5 and P7 in the main basin, Figure 1). Water from 3 m deep was pumped into 5 L transparent glass jars with an air tight clamp lid. Before closing, jars were filled from the bottom 200 and allowed to overflow, then sampled for initial CO2 and CH4 concentrations. Closed jars were fixed at 3 m to an anchored line at the sampling site, and incubated in in situ temperature and light conditions for 22.0 to 24.2 hours. Upon retrieval, samples of final CO2 and CH4 concentrations were collected from the jars. Volumetric daily rates of net CO2 and CH4 production were calculated based on the difference between final and initial gas concentrations rescaled to a 24 h period.
In addition to incubations, open water high frequency O2 measurements were carried out to derive CO2 metabolism on larger 205 spatial and temporal scales. Rates of GPP, ER, and net ecosystem production (NEP) were estimated in the reservoir surface layer by monitoring and inverse modeling diel O2 changes in the epilimnion. O2 was measured at a one minute interval using high frequency O2 and temperature sensors (model miniDOT from Precision Measurement Engineering). Sensors were deployed in profile sites P1 to P3 in the branches and P4, P5, P7, and P9 in the main basin ( Figure 1). Note that not all sites were sampled in all sampling campaigns. Sensors were attached to an anchored line at a depth between 0.7 and 3 m and 210 deployment time varied between 4 days and two weeks. Upon retrieval of the sensors, a first data quality check and selection was made based on the sensor internal quality index and visual screening. Rates of ecosystem metabolism were then estimated based on an open system diel O2 model (Odum, 1956), where change in O2 concentration is a function of GPP, ER, and airwater gas exchange (KO2) following Eq. (8) (Hall and Hotchkiss, 2017): with O2sat the theoretical O2 concentration at saturation considering the in situ temperature and atmospheric pressure, and O2 is the actual measured O2 concentration in the water. A detailed description of the model equations can be found in (Hall and https://doi.org/10.5194/bg-2020-258 Preprint. Discussion started: 14 September 2020 c Author(s) 2020. CC BY 4.0 License. Hotchkiss, 2017). Daily estimates of GPP, ER, and K600 (based on KO2) were derived by maximum likelihood fitting of the data to the model in Eq. (8) using the R package StreamMetabolizer (Appling et al., 2018). Note that even though the package used was originally developed for streams, it is easily applicable to lakes / reservoirs systems by replacing the depth of the 220 stream by the depth of the mixed layer. In some cases, where the best predicted K600 was negative, the fitting process was rerun with a user defined positive K600, either equal to a value estimated for the previous or subsequent day at the same site (range of 0.03 -0.96 d -1 ) or fixed to 0.1 d -1 (if no other available estimate). When considering the epilimnion depth, predicted values of K600 translate into a 1 st to 3 rd quantiles range of 1.17 to 5.55 m d -1 , which is similar to the range of K600 values back-calculated from surface gas flux measurements with the floating chamber technique. A final selection of daily metabolic estimates was 225 done based on the model goodness of fit assessed by calculating Pearson correlation coefficient between modeled and measured O2 values and discarding days with a correlation lower than 0.9. Based on GPP and ER estimates, we calculated daily NEP as the balance between these two processes, and converted it to net CO2 production rate by assuming an O2:CO2 metabolic quotient of 1.
Areal metabolic rates were derived by integrating volumetric rates over the depth of the epilimnion. Average estimates of areal 230 metabolic rates per campaign were obtained for the branches and main basin by first averaging data within each site and then across sites for each reservoir section. Note that one value derived from incubations was excluded from the calculation of the average net CH4 production rate in the branches due to its high value of initial CH4 concentration (an order of magnitude higher than in all other incubations and all epilimnetic data from this site). The high CH4 concentration, unrepresentative of real conditions, was probably caused by CH4 contamination during sampling, and triggered a high oxidation rate that would 235 overestimate the real ecosystem average rate if included.

Physical and chemical properties
Surface water temperature exhibited a marked increase from the inflows to the branches, averaging 27.1 and 30.7 ºC respectively (Table 1). There was no difference in surface water temperature between the branches and the main basin. The 240 depth of the epilimnion tended to increase and become more stable along the water flow, going from 1.3 (± 1.6) m in Batang Ai river delta, to 8.0 (± 2.3) m in its branch, and 10.6 (± 1.7) m in the main basin (Table 1). Light penetration exhibited t he same spatial pattern, with an increasing Secchi depth along the water flow averaging 1.3, 5.1, and 5.5 m in the inflows, branches, and main basin respectively (Table 1). All sections of the study system exhibited oligotrophic water properties (Table   1). 245 https://doi.org/10.5194/bg-2020-258 Preprint. Discussion started: 14 September 2020 c Author(s) 2020. CC BY 4.0 License.

Surface GHG concentrations, fluxes, and isotopic signatures
Surface CO2 and CH4 patterns are summarized in Figure  Surface CO2 concentration in the reservoir (branches and main basin) was most strongly correlated inversely with water temperature (R 2 adj = 0.22, p-value < 0.001, Figure S1 and Table S1). Except for the Apr-Mar 2017 campaign, there was a modest increase of surface δ 13 CO2 towards more enriched values (2.2 to 3.3 ‰) from the inflows to the branches (Figure 2). 255 Similarly, surface CH4 flux and concentration continually decreased along the water channel, being an order of magnitude higher in the inflows compared to the branches, and about twice as high in the branches compared to the main basin ( Figure   2). Of all measured water properties, TN was the most strongly linked to reservoir surface CH4 concentration (R 2 = 0.14, pvalue < 0.001, Figure S1 and Table S1). Surface δ 13 CH4 values varied widely, between -83.3 and -47.6 ‰, but did not show a consistent spatial pattern (Figure 2). 260 The degree of coupling between CO2 and CH4 followed a clear spatial pattern. While CO2 and CH4 surface concentrations were strongly linked in the inflows (R 2 adj = 0.54, p-value = 0.006), they became only weakly correlated in the branches (R 2 adj = 0.17, p=0.005) and not correlated at all in the main basin (R 2 adj = 0.01, p-value = 0.11) ( Figure S2).

Horizontal GHG flow
Horizontal inputs from the inflows to the surface layer of the branches were estimated to vary between 0.34 -0.71 mol s -1 for 265 CO2 and 0.02 -0.25 mol s -1 for CH4. When expressed as rates over the branches surface area (to facilitate comparison with other components), this results in 2.7 -5.7 and 0.16 -2.0 mmol m -2 d -1 for CO2 and CH4 respectively (Table S2 and S3). These values are in the same order of magnitude as surface fluxes calculated in the branches (Figure 3 and Table S2 and S3). However, the effect of horizontal inputs faded spatially, with much lower inputs from the branches to the main reservoir basin, averaging 0.31 and 0.004 mmol m -2 d -1 for CO2 and CH4, respectively (Figure 3 and Table S2 and S3). For CH4, this fits spatial and 270 temporal surface flux measurements, being systematically higher in the branches, and maximal during the two sampling campaigns with the highest recorded horizontal inputs from the inflows (Table S3). In contrast, CO2 surface flux were typically lower (sometimes negative) in the branches compared to the main basin, despite substantial riverine inputs to the branches (Table S2).

Vertical GHG inputs 275
Vertical fluxes depend on the gas diffusivity and concentration gradient. Gas diffusivity is a function of the strength of stratification (N 2 ) and energy dissipation rate (ϵ). Measured values of N 2 and ϵ varied widely, from 5.9 x 10 -5 to 2.3 x 10 -3 s -2 and from 3.4 x10 -9 to 1.6 x 10 -8 m 2 s -3 respectively, but with no clear differences between the reservoir branches and main basin ( Figure S3). Similarly, CO2 and CH4 concentration gradients varied substantially in both space and time (from -18.4 to 94.3 μmol L -1 m -1 for CO2 and -0.19 to 0.4 μmol L -1 m -1 for CH4). CO2 concentration generally increased from the epilimnion 280 to the metalimnion as a result of the respiratory CO2 buildup in the deep layer. On rare occasions, an inverse gradient was observed, possibly due to autotrophic activity in the metalimnion. For CH4, metalimnion to epilimnion concentration gradients were generally modest averaging 0.04 μmol L -1 m -1 , and even negative in one third of the profiles leading to the diffusion of epilimnetic CH4 toward deeper layers instead of the reverse. The low to negative CH4 vertical flux results from a highly active methanotrophic layer reducing CH4 concentration in the metalimnion, as evidenced by the strong enrichment effect observed 285 in δ 13 CH4 profiles ( Figure S4). The combination of vertical diffusivity and gas concentration gradients resulted in vertical fluxes averaging 3.4 (-1.8 to 20.5) mmol m -2 d -1 for CO2, and 0.01 (-0.01 to 0.09) mmol m -2 d -1 for CH4, with no significant differences between the reservoir branches and main basin ( Figure S3).

GHG inputs from littoral sediments
Areal sediment gas fluxes ranged from 1.2 to 4.0 and -0.29 to 1.10 mmol m -2 d -1 for CO2 and CH4, respectively ( Figure S5 Figure S5). Applying measured averages to the area of epilimnetic sediments in each section yields estimates of sediment inputs to the epilimnion of 0.6 (± 0.03) and 0.5 (± 0.11) mmol m -2 d -1 for CO2, and 0.04 (± 0.02) and 0.10 (± 0.06) mmol m -2 d -1 for CH4 in the branches and main basin 295 respectively ( Figure 3 and Table S2 and S3). These inputs from littoral sediments likely represent an upper limit since they are based on deep pelagic sediment cores (littoral area were too compact for coring), where a higher organic matter accumulation and degradation is expected (Blais and Kalff, 1995;Soued and Prairie, 2020). Even as upper estimates, the calculated rates of sediment GHG inputs remain a relatively modest fraction of the average emissions to the atmosphere for the branches and main basin both for CO2 (13 % and 7 %, respectively) and CH4 (4 % and 23 %, respectively) (Tables S2 and S3). 300
In the reservoir branches, results from the diel O2 monitoring method suggested systematic net CO2 uptake ranging from -19.2 to -1.4 μmol L -1 d -1 , whereas results from two incubations were slightly above that range (-0.5 to 3.3 μmol L -1 d -1 ) (Figure 4). 310 In the main basin, the two methods matched fairly well, with the diel O2 technique capturing a wider variability in net CO2 metabolic rates ranging from -19.2 to 6.1 μmol L -1 d -1 , with an estimated CO2 uptake in 39 out of 54 cases (Figure 4). Areal net CO2 metabolic rates, as the average of the two methods, yielded an ecosystem-scale estimate of -23.2 and -11.8 mmol m -2 d -1 in the reservoir branches and main basin, respectively (Table S2).

CH4 metabolism 315
Net metabolic CH4 rates (from incubations) ranged from -0.026 to 0.078 μmol L -1 d -1 , indicating that the CH4 balance in the epilimnion of Batang Ai varied from net oxidation to net production (Table S3). CH4 metabolic rates measured in Batang Ai are within the range of values observed in other systems for oxidation (Guérin and Abril, 2007;Thottathil et al., 2019) and production (Bogard et al., 2014;Donis et al., 2017). No temporal or spatial (branches versus main basin) differences in net metabolic CH4 rate were detected due to a high variability and limited data points. 320

Ecosystem scale GHG budgets
Estimated sources / sinks of CO2 and CH4 were collated into a budget to evaluate their relative impact on epilimnetic gas concentration and to assess whether their sum matches the measured surface gas fluxes in each section of the reservoir. Figure   3 depicts such reconstruction of the epilimnetic CO2 and CH4 budgets in Batang Ai, as well as the uncertainty limits of each component. While each process varied in time, their relative importance in driving surface fluxes was generally similar from 325 one sampling campaign to another (Table S2 and S3).

CO2 budget
For CO2, epilimnetic sediment inputs had the smallest contribution, being typically an order of magnitude lower than measured surface fluxes in both sections of the reservoir (Figure 3 and Table S2). Vertical CO2 inputs from lower depths on the other hand contributed substantially to surface fluxes in both the branches and the main basin (mean of 0.7 and 4.5 mmol m -2 d -1 330 respectively ( Figure 3 and Table S2), indicating that hypolimnetic processes impact surface emissions despite the permanent stratification. Horizontal inputs of CO2 were in the same range as vertical inputs (mean of 4.3 mmol m -2 d -1 ) in the branches, however, they decreased by an order of magnitude when reaching the main basin (mean of 0.3 mmol m -2 d -1 ). Thus, direct CO2 inputs from the inflows notably increase surface flux rates in the reservoir branches but only minimally in the main basin. Net CO2 metabolism was surprisingly variable (switching from negative to positive NEP on a daily time scale), thus making it 335 difficult to derive a sufficiently precise ecosystem-scale estimate to close the epilimnetic budget (Figure 3), despite high https://doi.org/10.5194/bg-2020-258 Preprint. Discussion started: 14 September 2020 c Author(s) 2020. CC BY 4.0 License. sampling resolution (n = 66 daily metabolic rates). Nevertheless, estimated net water column CO2 metabolism had a considerable impact on the epilimnetic budget, but acts more likely as a CO2 sink rather than a source in Batang Ai (Figure 3 and Table S2). Our best assessment suggests that in the main basin, vertical transport from deeper layers is the main source sustaining surface CO2 out-flux. 340

CH4 budget
In contrast with CO2, vertical transport was the smallest source of CH4 to the epilimnion, contributing to less than 2 % to surface fluxes in both reservoir sections (Figure 3 and Table S3). In the branches, sediment inputs and net CH4 metabolic rates were both relatively low (mean of 0.04 ± 0.02 and 0.04 ± 0.05 mmol m -2 d -1 ) and had little impact on the budget, corresponding each to 4 % of surface fluxes in that section ( Figure 3 and Table S3). On the other hand, horizontal inputs were the dominant 345 and most variable source sustaining CH4 emissions in the branches, where the epilimnetic mass balance closed almost perfectly ( Figure 3 and Table S3). Despite being the main CH4 source in the branches, horizontal transport was a negligible component in the main basin (< 1 % of the flux, Figure 3 and Table S3). Instead, sediment inputs played a larger role in that section, with a mean of 0.10 (± 0.06) mmol m -2 d -1 , fueling 22 % of surface emissions in the main basin ( Figure 3 and Table S3). As with CO2, the most variable CH4 component of the mass balance in the main basin was the net metabolism within the epilimnion 350 (mean of -0.16 ± 0.19 mmol m -2 d -1 ). Considering all sources, the CH4 budget indicates a deficit of 0.34 mmol m -2 d -1 to explain measured surface emissions in the main basin ( Figure 3 and Table S3).

Discussion
Our results have highlighted both the importance and the challenges associated with quantifying simultaneously all the components of the epilimnetic CO2 and CH4 budgets, particularly in a hydrologically complex reservoir system. While mass 355 fluxes (hydrological, sedimentary, and air-water fluxes) are relatively easy to constrain, internal C processing, namely the net metabolic balances between production and consumption of CO2 and CH4 are highly dynamic in both time and space, leading to significant uncertainties when extrapolated to the ecosystem scale. In many studies, some components are only inferred by difference. While convenient from a mass-balance perspective, we argue that assessing all components together is necessary to clearly identify knowledge gaps as well as sources of uncertainty. 360

Spatial dynamics of CO2 and CH4
The decrease in gas concentration and air-water fluxes along the hydrological continuum observed across sampling campaigns and for both CH4 and CO2 reflects a robust spatial structure of the gases. Concurrently, estimates of the horizontal GHG inputs shows a clear and consistent spatial pattern, being high in the branches but negligible in the main basin. A temporal effect of riverine inputs was also observed as the two sampling campaigns with the highest horizontal CH4 inputs coincided with the 365 https://doi.org/10.5194/bg-2020-258 Preprint. Discussion started: 14 September 2020 c Author(s) 2020. CC BY 4.0 License. highest CH4 emissions in the branches (Table S3). All these results concord with the progressively reduced influence of direct GHG catchment inputs and greater preponderance of internal processes along the hydrological flow (Hotchkiss et al., 2015).
For CO2, the sharpest change in surface metrics (concentration, flux, and isotopic signature) was observed between the inflows and the reservoir branches (Figure 2). Despite large riverine inputs (Table S2), the branches exhibited low CO2 concentration and fluxes, as well as an increase in δ 13 CO2 matching with high GPP values (Figure 2 and 4). This may reflect increased light 370 availability for phytoplankton when transitioning from the turbid inflows to the reservoir branches (higher Secchi depth, Table   1), a pattern previously reported in other reservoirs (Kimmel and Groeger, 1984;Pacheco et al., 2015;Thornton et al., 1990).
While the branch areas are often associated with high CO2 outflux due to riverine inputs Paranaíba et al., 2018;Pasche et al., 2019;Roland et al., 2010;Rudorff et al., 2011), they are occasionally observed to have low air-water flux due to simultaneous nutrient inputs (Paranaíba et al., 2018;Wilkinson et al., 2016). In Batang Ai, inflows have a high 375 nutrients (TP and TN) to DOC ratio compared to the reservoir branches (Table 1), providing higher inputs of nutrients relative to organic matter, and thus likely stimulating primary production more than respiration. This hypothesis is consistent with a higher GPP: ER ratio and mean Chla concentrations measured in the branches compared to the main basin ( Figure 4 and Table   1). The variability of CO2 concentration within the reservoir (branches and main basin) was negatively correlated to temperature, likely due to its effect on GPP . This further highlights the important role of primary 380 production in modulating CO2 dynamics throughout the reservoir, and particularly in the branches.
The correlation between surface CH4 surface and TN in the reservoir suggests that primary production may also affect CH4 dynamics. Nutrient content was shown in previous studies to enhance CH4 production in the sediments (Beaulieu et al., 2019;Gebert et al., 2006;Isidorova et al., 2019) and in the oxic water column (Bogard et al., 2014), through its link with algal production and decomposition. However, CH4 concentration and flux variability were strongly driven by a spatial / 385 hydrological structure, gradually decreasing from the inflows to the main basin. This likely reflects the combined effect of terrestrial inputs and a decreasing contact of water with sediments along the water channel. Surface δ 13 CH4 signatures varied substantially but without a consistent spatial pattern (Figure 2), indicating that the surface CH4 pool is shaped by multiple sources / processes (metabolism, riverine, and sediment inputs) varying through space and time.
Overall, the changing relative contribution of sources and processes shaping surface CO2 and CH4 concentrations varies with 390 the system hydro-morphology, from the inflows to the main reservoir basin, and lead to a progressive decoupling between the two gases along the continuum ( Figure S2). Thus, while CO2 and CH4 were both influenced by horizontal inputs in the upstream section, their main drivers diverge in the main basin, with CO2 mostly shaped by vertical inputs and aerobic metabolism, and CH4 by sediment inputs and anaerobic metabolism. The spatial patterns reported here highlight the hydrodynamic zonation common in reservoirs and its diverging effect on CO2 versus CH4 cycling. 395

CO2 metabolism
Our observation that GPP often exceeded ER (Figure 4) was not unexpected given the very low DOC concentration (< 1 mg L -1 ). Previous work has reported that DOC > 4 mg L -1 is required to sustain persistent net heterotrophy and CO2 evasion https://doi.org/10.5194/bg-2020-258 Preprint. Discussion started: 14 September 2020 c Author(s) 2020. CC BY 4.0 License. (Hanson et al., 2003;Prairie et al., 2002). Throughout the reservoir, we found high day-to-day variability in both ER and GPP, but with no apparent link to weather data (light and rain, data not shown). The absence of such a link at a daily time scale has 400 been previously reported (Coloso et al., 2011), while other studies associated daily variations in metabolism with changes in water inflows carrying nutrients (Pacheco et al., 2015;Staehr and Sand-Jensen, 2007), or thermocline stability regulating hypolimnetic water incursions to the epilimnion. Such variations in thermocline depth are thought to be more common in warm tropical systems (Lewis, 2010), and were observed across sampling campaigns in Batang Ai, especially in the branches where the depth of the mixed layer varied considerably (SD = 2.3 m, Table 1). Hence, hydrological and physical factors may regulate 405 spatial and daily patterns of GPP and ER rates in Batang Ai through their influence on nutrient dynamics.
The accuracy of rates derived from diel O2 monitoring partly depends on the respiratory and photosynthetic quotients (RQ and PQ) assumed for the conversion of metabolic rates from O2 to CO2. A quotient differing from the assumed 1:1 ratio can lead to an under or over-estimation of net CO2 production. The fact that net CO2 metabolic rates were on average higher in incubations, based on direct CO2 measurements compared to diel O2 monitoring ( Figure 4 and Table S2), hints at a deviation 410 of the metabolic quotients form unity in Batang Ai. Additionally, surface O2 versus CO2 concentrations shows that the departure of these gases from saturation varies widely around the expected 1:-1 line ( Figure 5). O2 oversaturation was observed in 44 % of cases in the main basin and 81 % in the branches (Figure 5), which corresponds with the spatial patterns of net metabolic rates (Figure 4). CO2 oversaturation was also widespread (74 % of cases), making half the surface samples oversaturated in both O2 and CO2. This indicates an excess O2 and / or CO2 that can be due to a PQ and / or a RQ higher than 415 1, or to external CO2 inputs to the epilimnion , for instance from the inflows or the bottom layer (Table   S2). Metabolic quotients have been shown to vary widely, depending on the type and magnitude of photochemical and biological reactions at play (Berggren et al., 2012;Lefèvre and Merlivat, 2012;Vachon et al., 2020;Williams and Robertson, 1991). For instance, CH4 oxidation and production, evidently occurring in Batang Ai's epilimnion (Table S2 and S3), diverge from the metabolic O2:CO2 ratio of one, with CH4 oxidation consuming two moles of O2 for each mole of CO2 produced, and 420 acetoclastic methanogenesis producing CO2 without O2 consumption. Even though net CH4 processing rates are a minor portion of the epilimnetic C cycling in Batang Ai (1-2 orders of magnitudes lower than CO2 metabolic rates, Tables S2 and S3), these reactions (and other unmeasured processes) have the potential to alter the O2:CO2 metabolic quotient at an ecosystem scale. The lack of direct measure of metabolic quotients in Batang Ai adds uncertainty to the net CO2 metabolism estimates based on O2 data. The observed decoupling of O2 and CO2 metabolism in Batang Ai highlights the need for a deeper 425 understanding of the biochemical reactions occurring in the epilimnion, and their effect on metabolic quotients.
Overall, our results from Batang Ai reservoir point to water column metabolism as both a major process in the CO2 epilimnetic budget and a challenging one to estimate at an ecosystem scale (Figure 3). Improving this requires a better mechanistic knowledge of the physical and biochemical processes at play and how they interact to shape NEP. 430 https://doi.org/10.5194/bg-2020-258 Preprint. Discussion started: 14 September 2020 c Author(s) 2020. CC BY 4.0 License.

CH4 metabolism
Incubation results exhibited a wide range of net CH4 metabolism: from net oxidation to net production. CH4 oxidation is known to be highly dependent on CH4 availability and is optimal in low oxygen and low light conditions (Borrel et al., 2011;Thottathil et al., 2018Thottathil et al., , 2019, whereas CH4 production in the oxic water is still poorly understood but have been frequently linked to phytoplankton growth (Berg et al., 2014;Bogard et al., 2014;Lenhart et al., 2015;Wang et al., 2017). A large variability in 435 results exists among the studies that have assessed the net balance of CH4 metabolism in the water column, with some studies reporting pelagic CH4 production as a largely dominant process (Donis et al., 2017) while others find no trace of it (Bastviken et al., 2008). Based on spatial patterns of surface CH4 concentration and isotopic signature with distance to shore, DelSontro et al. (2018b) showed that, in 30 % of their studied temperate lakes, CH4 oxidation was dominant versus 70 % dominated by net pelagic production. In Batang Ai, surface δ 13 CH4 values were highly variable (-82.5 to -47.7 ‰) but mostly uncorrelated 440 with distance to shore, except a positive correlation indicative of oxidation in the Nov-Dec 2016 (R 2 adj = 0.29, p-value = 0.01) coinciding with a strong inverse pattern for CH4 concentration (R 2 adj = 0.54, p-value < 0.001, Figure 6). This suggests a temporal shift in processes driving surface CH4 patterns. Also, some measured surface δ 13 CH4 values were lower than the mean δ 13 CH4 form the sediments (-66.0 ‰, unpublished data), suggesting another highly depleted source of pelagic CH4 in the system. This is in line with water incubation results often showing positive net CH4 production (Table S3). When reported as 445 mean areal rates, CH4 metabolism ranged from net consumption to net production of CH4 (-0.29 to 0.94 mmol.m -2 .d -1 ), and had a strong influence on the epilimnetic CH4 budget at the reservoir scale ( Figure 3 and Table S3). Results in Batang Ai show that the net balance of CH4 metabolic processes varies widely even within a single system. However, the factors regulating this balance remain largely unknown. Investigating such factors constitute a key step in resolving CH4 budgets in lakes and reservoirs. 450

Epilimnetic GHG budgets
For CO2, measured surface fluxes in both reservoir sections fall in the range of possible values estimated by the sum of epilimnetic processes and their uncertainties (Figure 3 and Table S2). However, the averages of those two terms differ substantially, due to negative values of metabolism shifting the mean of the mass balance towards net CO2 consumption whereas, on average, surface out-flux was measured from the reservoir. This discrepancy indicates either a missing source of 455 CO2 in the budget or the underestimation of one of the processes. While lateral groundwater input is a potential source not explicitly considered, it is probably modest given the small ratio of littoral area to epilimnion volume, and is unlikely to account for the large CO2 deficit in the budget. On the other hand, underestimation of the CO2 metabolic balance is much more likely, given its large variability and uncertainty around its mean value. Additionally, a systematic underestimation of the CO2 metabolic rates derived from the diel O2 method is very possible in Batang Ai given the likely deviation of metabolic quotients 460 around the 1:1 line. As an example, when setting the photosynthetic quotient to 1.2 instead of 1, which remains well within the literature range (Lefèvre and Merlivat, 2012;Williams and Robertson, 1991), the average epilimnetic CO2 mass balance https://doi.org/10.5194/bg-2020-258 Preprint. Discussion started: 14 September 2020 c Author(s) 2020. CC BY 4.0 License. would increase from -17.7 to 4.3 mmol m -2 d -1 in the branches and from -6.5 to 6.2 mmol m -2 d -1 in the main basin, closely matching measured surface fluxes of 4.7 and 7.5 mmol m -2 d -1 in the respective sections. Thus, constraining the metabolic component, especially the O2: CO2 quotients, is key for closing the CO2 epilimnetic budget. 465 In the case of CH4, the epilimnetic mass balance in the branches is surprisingly close to the observed surface flux, largely fueled by horizontal inputs. Hence, CH4 emissions from the branches reflect catchment CH4 loads rather than internal processes. However, in the main basin, these inputs become negligible and the estimated budget does not match measured emissions, indicating a deficit of 0.49 mmolCH4 m -2 d -1 . This amount cannot be explained by a potential underestimation of horizontal or vertical inputs since they are two orders of magnitude lower. Similarly, sediment inputs would need to be six 470 time higher than estimated to fulfill the budget deficit, which is unlikely given their much lower range of uncertainty. Thus, the most plausible source to close the mass balance in the main basin would be water column CH4 production. Although the estimated CH4 metabolism indicates an average net consumption rather than a net production (-0.16 mmol m -2 d -1 ), this mean value is based on only 3 data points and has a high uncertainty associated to it (SE = 0.19 mmol m -2 d -1 , Table S3). Closing the mass balance would require a net volumetric CH4 production of about 0.03 μmol L -1 d -1 in the water column of the main 475 basin. This value seems plausible since an equal production rate was measured in one of the incubations, and it is at the low end of the range reported in other systems (Bogard et al., 2014 ;DelSontro et al., 2018b ;Donis et al., 2017). The combination of our results point to water column metabolism as the dominant source of CH4 in the main basin of Batang Ai, sustaining up to 75 % of surface emissions in that reservoir section. However, this process seems highly dynamic and requires more intensive research into its controls at spatial and temporal scales, commensurate with CH4 emissions. 480

Conclusion
The estimated epilimnetic CO2 and CH4 budgets in Batang Ai has helped define the role of different processes in shaping the reservoir surface GHG fluxes to the atmosphere. Results showed that horizontal riverine inputs are important sources of GHG in the reservoir branches (especially for CH4). This creates a coupling between CO2 and CH4 close to the river deltas, which gradually fades along the water flow, until the surface concentrations of the two gases become completely uncoupled in the 485 main basin being driven by different sources. For instance, vertical inputs from the bottom layer contributed significantly to surface CO2 saturation, while being negligible in the case of CH4 due to metalimnetic oxidation. Inversely, sediment inputs played a notably greater role in sustaining epilimnetic oversaturation of CH4 compared to CO2 in the main basin. Nonetheless, the epilimnetic budgets of both gases were heavily impacted by their respective water column metabolism. This result is likely representative of large systems with a high volume of water versus sediments, which is common for hydroelectric reservoirs. 490 The metabolic balances of CO2 and CH4 were also extremely variable in space and time, switching from a net production to a net consumption of the gases, and leading to highly uncertain ecosystem-scale estimates. Factors driving these metabolic changes are not well constrained based on current knowledge, highlighting the need for further research on the subject. Overall, this study gives an integrative portrait of the relative contribution of different sources to surface CO2 and CH4 fluxes in a https://doi.org/10.5194/bg-2020-258 Preprint. Discussion started: 14 September 2020 c Author(s) 2020. CC BY 4.0 License.