Diurnal Pumped‐Storage Operation Minimizes Methane Ebullition Fluxes From Hydropower Reservoirs

Hydropower is considered green energy and promoted to reduce greenhouse warming. However, hydropower is typically generated using reservoirs and reservoirs are known to emit substantial amounts of the greenhouse gas methane (CH4) to the atmosphere. In many reservoirs ebullition is the dominant pathway of CH4 emission. We show that continuous diurnal pumped‐storage operation, which combines water pumping into the reservoir typically during the night and water drawdown during high demand of electricity, is beneficial for reducing CH4 ebullition associated with hydropower generation. This conclusion is based on ebullition fluxes and water levels measured over 3 months in Schwarzenbach reservoir located in Germany. The reservoir was managed using three modes of operation: (1) diurnal pumping and turbination, (2) no pumping and no turbination, and (3) diurnal turbination. Cross‐correlation analysis indicates that ebullition fluxes predominantly occur during diurnal water level decrease associated with turbination. Consistently, average ebullition fluxes of CH4 were negligible during Mode (2) and substantial during Modes (1) and (3). During Mode (3) the average CH4 ebullition flux was ~197 mg m−2day−1, ~12 times larger than during Mode (1) (16 mg m−2day−1). Our data indicate that overall CH4 ebullition is about 3 times larger during 51 days of operation consisting of 38 days of no turbination followed by 13 days of diurnal turbination than during 51 days of continuous diurnal pumped‐storage operation. This suggests that continuous diurnal pumped‐storage operation leads to reduced CH4 ebullition from reservoirs and is therefore advantageous compared to modes of operations involving long‐term, large‐amplitude turbination cycles.


Introduction
Reservoirs are anthropogenic systems constructed to collect, store, and manage water by blocking the natural water flow of streams and rivers with artificial dams and/or by complex pumped-storage operation in artificial water systems. Reservoirs provide important services to society such as a reliable supply of drinking water, flood control, water for irrigation, hydroelectric power generation, and storage of energy . Each reservoir is managed according to the specific use of the system. The mode of operation typically consists of time periods during which water is accumulated in the reservoir and drawdown periods during which the water is withdrawn again. In case of hydroelectric power generation, the water is withdrawn through turbines (called turbination). Some hydropower reservoirs are designed as pumped-storage systems in which water is pumped from a reservoir at a lower elevation during low energy demands and turbinated during periods of peak energy demand. Pumped-storage hydropower plants are considered to be the most efficient systems to store electric energy (Kobler et al., 2019) and may play an important role in the management of renewable energy. The number and size of hydroelectric power reservoirs, and especially of pumped-storage systems, have increased substantially during the last years (Barbour et al., 2016;Deane et al., 2010;Rehman et al., 2015;REN21, 2017) to satisfy the increasing demand of energy and energy storage and the requirement to reduce greenhouse gas (GHG) emissions linked to energy production (Barbour et al., 2016;Commission, 2011;Ibrahim et al., 2008;Kobler et al., 2019). Hydroelectric energy has traditionally been considered green energy because its production seems free of GHG emissions to the atmosphere (Hoffert et al., 1998;Victor, 1998), and hydropower is therefore promoted as a climate neutral alternative energy source to fossil energy.
However, inland waters and thus also reservoirs are important components of the regional and global carbon cycle (Battin et al., 2009;Tranvik et al., 2009) and have been identified as an important source of atmospheric GHGs in the global budgets Barros et al., 2011;Beaulieu et al., 2014;Hertwich, 2013;Luyssaert et al., 2012;Raymond et al., 2013). Reservoirs are known to accumulate large amounts of fine-grained sediments and organic material and potentially act as important storage of terrestrial carbon (Clow et al., 2015;Mendonça et al., 2017;Phyoe & Wang, 2019). Because methane (CH 4 ) and carbon dioxide are major products of the carbon metabolism, reservoirs and impounded river sections are known to be potential hot spots of GHG emission (Deemer et al., 2016;Harrison et al., 2017;Maeck et al., 2014;Varadharajan & Hemond, 2012) and may contribute a major fraction of the global anthropogenic GHG emissions (Deemer et al., 2016;Hertwich, 2013).
CH 4 is mainly produced in anoxic sediments, and most of the CH 4 is stored in anoxic pore water or in anoxic water bodies (Bastviken et al., 2008). In oxic waters, CH 4 is typically oxidized at the sediment surface and the diffusive transport of CH 4 from the sediments into the water column is then rather small (e.g., Bastviken et al., 2002). Compared to the diffusive CH 4 , flux from the sediments ebullition can be a much more efficient pathway for the transport of CH 4 from the sediments, as this process can bypass CH 4 oxidation at the sediment surface. CH 4 fluxes due to ebullition can contribute a large fraction of the overall CH 4 fluxes to the atmosphere from small-to medium-sized lakes (Bastviken et al., 2004Joyce & Jewell, 2003;McGinnis et al., 2006). According to DelSontro et al., 2010, Sobek et al., 2012, and Maeck et al., 2014 ebullition is in many cases the major emission pathway of CH 4 from reservoirs.
Water level declines in natural inland water bodies and in reservoirs are typically associated with enhanced ebullition and thus with enhanced CH 4 emissions (Deborde et al., 2010;Engle & Melack, 2000;Harrison et al., 2017;Maeck et al., 2014;Varadharajan & Hemond, 2012). The reason is that a decrease in water level results in a decrease in hydrostatic pressure at the sediment surface which increases the likelihood that the equilibrium pressure of the gas stored in the sediments exceeds the ambient pressure. The latter is a prerequisite for the formation of a gas phase in the sediments and thus for the occurrence of ebullition. Substantial water level changes are a typical consequence of reservoir operation and are therefore a characteristic feature of reservoirs that is uncommon in lakes (Hayes et al., 2017). Most studies on ebullition fluxes in reservoirs have focused on the consequence of substantial reservoir drawdown in fall demonstrating that the level changes during this time period cause strongly enhanced ebullition and associated CH 4 fluxes that are substantially larger than during the rest of the year (Harrison et al., 2017;Ostrovsky et al., 2008;Scandella et al., 2011;Varadharajan & Hemond, 2012;Zohary & Ostrovsky, 2011). However, not only large level changes during drawdown over several days and weeks can enhance ebullition fluxes of CH 4 but also short-term level fluctuations connected to, for example, ship-lock operation (Maeck et al., 2014) or daily water drawdowns in reservoirs with hydroelectric power production (Harrison et al., 2017).
Because pumped-storage hydropower is up to now the most efficient way to store electric energy at intermediate time scales, reservoirs with pumped-storage operation will remain an important component in an energy concept based on renewable energy from solar and wind energy. We, therefore, address here the question whether pumped-storage operation can be optimized to reduce the emissions of CH 4 by ebullition. Specifically, we investigate whether it is advantageous to operate pumped-storage systems using frequent subdaily pump-turbination cycles with small amplitudes or using long-term, large-amplitude pump-turbination cycles with several days of pumping followed by substantial drawdown over several days.
Our investigation is based on data on CH 4 fluxes due to ebullition from the sediment in a pumped-storage hydropower reservoir that were measured over a time period of 3 months at a high temporal resolution (1 min). The mode of operation of the reservoir changed during the 3 months of observation which enabled us to investigate the implications of reservoir operation on ebullition and associated CH 4 fluxes in hydropower reservoirs. Specifically, the change in reservoir management (operation modes) caused a change in water level dynamics. This allowed a comparison of CH 4 ebullition fluxes during time periods with different water level fluctuation patterns within the same reservoir. Based on these results, we compared the CH 4 ebullition flux during continuous pumped-storage operation with that during intensive turbination after long-term storage.
(see isolines in supporting information (SI) Figure S1), with minimum depths in the northwestern part, where the major natural inputs enter into the reservoir (Seebach and Schwarzenbach rivers), and maximum depth in the southeastern part, where the reservoir dam is located. Schwarzenbach reservoir is a pumped-storage hydropower system; that is, the water is pumped from Kirschbaumwasen reservoir during low energy demands and withdrawn through turbines located in Forbach to generate electric power (see SI Figure S1). During periods of turbination, the water level is drawn down whereas during pumping operation the water level increases. Water inlet and outlet for the pumped-storage operation is close to the dam in the deepest 5 m of the reservoir. Schwarzenbach reservoir receives additional water from a catchment area in the southwest of the reservoir by an artificial channel entering the reservoir at the southwestern shore. This water enters the reservoir at the water surface.
Between 13 and 28 July 2016, five ebullition flux funnels (EFF) were deployed~1 m above the sediment along the thalweg at different water column depths (Stations e1-e5, Figure 1). After this initial experiment, the EFF located at Position e2 ( Figure 1) remained at the same position until the end of October. Additional funnels were installed at Stations s1, s3, and s4 (see SI Figure S2). However, these funnels failed several times such that we have a long-term time series covering all three modes of operation only at Station e2.
At each of the EFFs water temperature and absolute pressure were measured at a frequency of 30 s (Aquatec AquaLogger 520). The pressure data were averaged to 1-min time resolution, and the water column height, wl, above the EFFs was calculated using the surface pressure measured during monthly gas sampling and batteries exchange when the EFFs were lifted to the water surface. The wl was used to calculate the rate of change in water level wlc = dwl/dt.
The EFF are inverted squared funnels that collect bubbles released from the sediment and guide the bubbles into a cylindrical column in which the gas displaces the water (see SI Figure S3). The volume of the collected gas is determined from the cross-section A c = π r c 2 of the cylindrical column with radius r c and the column height h c occupied by the gas. The height of the gas column is proportional to the difference between the hydrostatic pressure in the ambient water and the pressure within the column at the same depth. Differential pressure was measured with a differential pressure sensor at a sampling interval of 16 Hz. The time series of differential pressure was averaged to a temporal resolution of 1 min that was used in further statistical analysis. The height of the gas column, h c , was estimated from these data using a linear calibration as presented in Maeck et al., 2014. The gas flux due to ebullition, ef, was calculated from the relation where A f is the area of the opening of the funnels parallel to the sediment, p and T are the hydrostatic pressure and temperature at the water depth of the funnel, and p s and T s are standard pressure (1 atm) and standard temperature (273.15 K). The ebullition fluxes ef calculated with Equation 1 provide the total volume of gas at standard conditions emitted by ebullition per unit area of sediment per unit time. For our funnels A f = 0.64 m 2 and r c = 1.5 cm.
During monthly campaigns, the batteries of the EFF were exchanged and gas samples were taken from the gas phase accumulated in the collecting columns. Water samples for analysis of dissolved CH 4 in the water column were taken regularly at 1-m water depth and on 12 July, 16 August, 13 September, and 13 October at different water depths at the Station p1 ( Figure 1).
The water samples were collected using a 2-L water sampler (Limnos, Rossinkatu 2 E17, Turku, Finland) and transferred into 122-ml serum bottles that contained salt and were vacuumed before sampling. For details on the sampling procedure see Hofmann et al. (2010). The CH 4 concentration in these water samples was measured using the headspace technique. The gas samples from the EFF and the gas extracted from the head space of the water samples were analyzed for CH 4 using a gas chromatograph with a flame ionization detector (Shimadzu GC-9A). The GC was calibrated using gas standards of 10, 50, and 100 ppm (Air Liquide). The measurements of triplicate samples varied on average by <5%. Parallel to the water sampling, vertical profiles of temperature and dissolved oxygen (DO) were measured with a multiparameter probe (CTD probe, RBR Ltd., Ottawa, Canada; fast oxygen optode 4330F, AANDERAA, Bergen, Norway) at a sampling frequency of 6 Hz.
The relation between ebullition flux and total hydrostatic pressure was assessed using the fluxes measured by the five EFFs deployed along the thalweg at different water column depths ( Figure 1).
The implications of different modes of operation of the reservoir on ebullition fluxes were investigated by comparing water level fluctuations and ebullition fluxes measured at Station e2 ( Figure 1) because this is the only station for which we have ebullition fluxes during all three modes of operation of the reservoir. Detailed analysis is based on three time periods each covering 5 days (Table 1): Section 1 (7-11 August), Section 2 (5-9 September), and Section 3 (13-18 October). These time periods were selected because they are characterized by (i) similar water levels (658.9 to 659.7 m a.s.l.) implying similar mean water column height above the sediment (~10.8 m at Station e2) and thus similar mean hydrostatic pressure, (ii) similar water temperatures (13.07 to 14.73°C) implying similar production and oxidation rates of CH 4 , and (iii) different reservoir operation modes (Table 1).
Temporal patterns in the time series of the rate of water level change and of ebullition fluxes were investigated using the autocorrelation of each of these time series. Cross correlation between these two time series was employed to investigate the relationship between the rate of change in water level and the ebullition flux at Station e2. Data series were detrended prior to the correlation analysis, and the MATLAB function corrcoef was used for the determination of correlation coefficients.
The Anderson-Darling test was used to evaluate whether the ebullition flux followed a normal distribution or not. The Kruskal-Wallis test was used to assess whether different data sets originated from the same distribution. Both tests were performed using the adtest and Kruskal-Wallis functions from MATLAB.
In addition to ebullition fluxes we determined diffusive CH 4 fluxes at the water surface of the reservoir from CH 4 concentrations and water temperatures measured at 1-m water depth and wind speed measurements at the dam of the reservoir. Diffusive CH 4 fluxes were estimated using the gas transfer velocity of Cole and Caraco (Cole & Caraco, 1998) and the Schmidt number dependence of the gas transfer velocity (Liss & Merlivat, 1986; for details see Encinas Fernandez et al., 2014).

Water Column Dynamics
Between July and September 2016, the reservoir was stably stratified as is indicated by the decrease of the water temperature with increasing depth (Figure 2a). On 11 October, the water temperature was almost constant in the entire column ( Figure 2a) suggesting that at least partial mixing of the water column had occurred. During the entire measuring period, dissolved O 2 concentrations were highest in the upper 2 m and decreased with increasing depth. The values just above the sediment were DO~7 mg L −1 in July and Note. Data are based on measurements at Station e2 ( Figure 1).

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ENCINAS FERNÁNDEZ ET AL.
August and DO~2 mg L −1 in September and October, indicating oxic conditions throughout the water column during the entire measuring period ( Figure 2b). In all profiles dissolved CH 4 concentrations were below 6 μg L −1 throughout the water column except for the deepest sampling points in July and in September, where the CH 4 concentration was increased near the sediment ( Figure 2c). The near surface concentrations of CH 4 between April and November 2016 measured at Station p1 at 1-m water depth ranged between 1 and 3 μg L −1 and the diffusive fluxes of CH 4 ranged between 0.6 and 1.8 mg CH 4 m −2 day −1 (see SI Figure S4).

Spatial Variability of Ebullition Along the Thalweg
During the initial deployment of the EFFs (Figure 1), the average ebullition flux decreased along the thalweg of the reservoir from the backwater in the northwest to the dam in the southeast ( Figure 3). Ebullition fluxes were highest at shallowest sites and small at larger water depths ( Figure 3). The 15-day average of ef at Station e1 (water column depth 5 m) was~86 ml m −2 day −1 whereas the 15-day average ef at Station e2 (water column depth 10.5 m) was only~54 mL m −2 day −1 . The gas collected in the funnels contained 56% CH 4 at Station e1 and 44% CH 4 at Station e2. Hence, the ebullition flux was 48 ml CH 4 m −2 day −1 at e1 and 24 ml CH 4 m −2 day −1 at e2. At standard conditions the molar gas volume is 22.41 L mol −1 , and 1 ml CH 4 therefore corresponds to 4.46 × 10 −5 mol CH 4 or 0.716 mg CH 4 . The ebullition flux of CH 4 therefore is~35 mg CH 4 m −2 day −1 at e1 and 17 mg CH 4 m −2 day −1 at e2. At all other stations, at which the water column depth exceeded 15 m, essentially no ebullition fluxes were observed ( Figure 3).

Temporal Variability of Ebullition at the Station e2
During the study period from July to October, the water level showed different patterns of water level change ( Figure 4a). Between 13 July and 22 August, water level fluctuations were characterized by reoccurring short-term decreases and increases of the water level by~20 cm at subdaily time scales (Figure 4a). The water level changes are caused by diurnal pumping and turbination (Operation Mode 1) typical in reservoirs used for hydropower generation; that is, water level drawdowns occurred in the evenings and at some days in the morning too due to turbination of water for energy production, and level rises occurred during the nights due to pumping of water into the reservoir, here from Kirschbaumwasen reservoir (see SI Figure S1). During this time period of diurnal pumped-storage operation, the average ebullition flux from the sediment was 65 ml m −2 day −1 .
From 22 to 28 August, the reservoir operation was characterized by turbination of water once a day causing a drawdown in water level by~18 cm day −1 (Figure 4a). The ebullition flux was only measured from 26 to 28 August. During these 3 days, the ebullition flux was~513 ml m −2 day −1 . After 28 August, the management changed to no pumping and no turbination (Operation Mode 2). This management resulted in an essentially constant rise of the water level at an average rate of~4.6 cm day −1 (Figure 4a). The ebullition flux was onlỹ 11 ml m −2 day −1 during this time period. The highest water level was reached on 5 October when turbination was restarted. From 5 to 20 October reservoir management aimed at hydroelectric power production from the water stored during the previous period when the turbines were not operational. Similar to the last period in August, the reservoir operation was characterized by turbination of water typically once a day that was not followed by pumping water back into the reservoir (Operation Mode 3). As a consequence, the water level decreased over this time period by~8.6 cm day −1 whereby the long-term decrease resulted from short periods of rapid drawdown followed by a rather constant level after the drawdown. Between 5 and 20 October, the ebullition flux was on average~303 ml m −2 day −1 .
The implications of different reservoir operation modes on the CH 4 flux (Figures 5b1-5b3 and 5c) due to ebullition were investigated in detail by focusing on three time periods (Sections 1-3, Figure 5) representing the different patterns of water level changes (Figures 5a1-5a3) associated with the three modes of reservoir operation: (1) diurnal pumped-storage operation, (2) no pumping and no turbination, and (3) diurnal turbination but no pumping (Figures 5b1-5b3).
During Section 1, that is, between 7 and 11 August, the water level typically showed maxima during the day and minima during the night (Figure 5a1). The absolute change in water level averaged over a day was close to zero, but within a day the water level increased and decreased several times (Figure 5a1). During Section 1, cycle with 6-hr duration. The average ef during Section 1 was~54 ml m −2 day −1 total gas (Figure 5c). The gas collected in the funnels contained 42% CH 4 . Hence, the ebullition flux of CH 4 was~16 mg CH 4 m −2 day −1 . Ebullition occurred mainly during negative wlc (Figure 6b1). This observation is supported by the cross correlation of ef and wlc indicating a significant negative correlation coefficient at a time lag of −1 hr (R = −0.41, p < 0.001, Figure 7c1). This significant negative correlation occurs periodically with a time period of 24 hr indicating a daily reoccurrence of ebullition events 1 hr after water level decreases. The cross-correlation analysis shows also a significant positive correlation (R = 0.4, p < 0.001, Figure 7c1) between ef and wlc at a time lag of 7 hr, that is, 6 hr after the negative correlation.
From 5 to 9 September (Section 2 and Figure 5a2) the water level increased on average by~5 cm day −1 (Figure 6a2) without diurnal fluctuations. This pattern of water level change is reflected in the wlc autocorrelation showing no significant periodic cycling (Figure 7a2). The ebullition flux was on average ef~0 ml m −2 day −1 total gas, thus substantially smaller than the ebullition flux during Time Period 1 (Figure 5c). Due to the low ebullition flux during Time Period 2 (Section 2), it was not possible to measure the proportion of CH 4 in the gas collected in the funnels. The ef and wlc during this period were not significantly correlated (Figure 7c2).
During Section 3 (13-18 October), the water level decreased (Figure 5a3) on average at a rate of about −11 cm day −1 (Figure 6a3). The long-term decrease in water level was mainly caused by several short-lasting drawdowns in water level. The autocorrelation of wlc did not show a daily pattern (Figure 7a3) indicating that the short-term events during Section 3 did not occur at a consistent diurnal pattern. As during Section 1 ebullition during Section 3 was strongly linked to the sporadic events of water level drawdown, as is indicated by the significant negative cross correlation between ef and wlc (R = −0.6, p < 0.001; Figure 7c3). However, the correlation coefficients in the cross correlation are only high at a time lag of 1 hr but not at time lags of 7 and 25 hr as were observed during Section 1. The average ef during Section 3 was~324 ml m −2 day −1 total gas (Figure 5c), which is much larger than the average ef during Sections 1 and 2. Furthermore, not only the ebullition flux but also the fraction of CH 4 in the collected gas (85%) during Section 3 was larger than during Section 1. Hence, the average flux of CH 4 due to ebullition was~197 mg CH 4 m −2 day −1 during Section 3 and thus~12 times larger than during Section 1.
According to the Anderson-Darling test, the ebullition fluxes within each of the three sections are not normally distributed (for each section the null hypothesis that the data originate from a population with a normal distribution was rejected: p < 0.05). Therefore, the nonparametric Kruskal-Wallis test was applied to assess whether the ebullition fluxes in the three sections differ. The null hypothesis that the ebullition fluxes originate from the same distribution was rejected (p < 0.05).
The results from the additional funnels deployed at Stations s1-s4 (see SI Figure S2) confirm the pattern between level fluctuations and ebullition fluxes observed for the different modes of operation at Station e2. Similar to the ebullition fluxes at Station e2, ebullition fluxes at Station s1 were large until 28 August and substantially lower thereafter ( Figure S5s1). The ebullition fluxes at Station s3 (see SI Figure S2) show a similar pattern as the ebullition fluxes at Station e2 during modes of Operations 2 and 3, that is, ebullition fluxes were lower during September and beginning of October and large after 5 October ( Figure S5s3). At Station s4 (see SI Figure S2) essentially no ebullition fluxes were observed during the entire measuring period ( Figure S5s4). The water depth at Station s4 was~31 m, and the lack of ebullition fluxes is therefore consistent with observations from July when ebullition fluxes at water column depths ≥15 m were very low (Figure 3).

Discussion
The main aim of this study is to investigate the effect of different reservoir operation modes on the ebullition flux of CH 4 . We had the unique opportunity to assess the CH 4 ebullition flux over 4 months in a pumped-storage reservoir in which the mode of operation was changed due to maintenance work and technical modifications of the electric generation system. Initially, the reservoir was managed using a diurnal pumped-storage operation (Operation Mode 1) typical for this and many other pumped-storage systems. Later on, pumping and turbination were stopped (Operation Mode 2) and water slowly accumulated in the reservoir without substantial drawdowns. Finally, the management used the accumulated water for production of hydroelectric power by proceeding with turbination without pumping (Operation Mode 3). The ebullition flux measurements at Position e2 captured all these changes in the mode of operation at a high temporal resolution resolving subdaily time scales which allows linking diurnal and long-term changes in drawdown and water accumulation with ebullition fluxes over the 4 months of interest (Figures 4, 5, and 7). Although the additional flux measurements at other positions did not provide time series covering all modes of operation, the general findings from Station e2 are supported by these measurements ( Figure S5).
Ebullition fluxes from the sediments depend on the organic material and the microbial community within the sediment, the water level affecting ambient pressure in the sediment, and on the sediment temperature effecting CH 4 production and the equilibrium gas pressure. Seasonal changes in water level and/or in water temperature may therefore cause seasonal changes in ebullition fluxes (e.g., DelSontro et al., 2010;Soja et al., 2014;Tuṧer et al., 2017). However, in our comparison of the ebullition fluxes during the three sections with different operation modes (Figure 4), we compare ebullition fluxes at essentially the same sediment temperature and the same daily average water level (Table 1). Ebullition fluxes between the three sections are therefore expected to be independent of seasonal effects but dominated by the consequences of the different patterns of short-term water level fluctuations associated with the different modes of operation.
The focus on a time series of ebullition flux measurements with high temporal resolution from the same station, that is, Station e2, and on time periods with the same sediment temperature and similar average water 10.1029/2020WR027221

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level (selection of Sections 1-3, Figure 5) has the advantage that conclusions on the link between patterns of water level fluctuations and ebullition fluxes are neither effected by seasonal changes in abiotic conditions nor by spatial heterogeneities in microbial community or organic material within the sediment. Thus, the selected data provide an excellent basis for the investigation of the consequences of the mode of operation in pumped-storage systems for emissions by CH 4 ebullition.
The data from the different Stations s1-s4 reliably confirm our results on the link between drawdown and CH 4 ebullition fluxes during the different modes of operation. However, because the spatial distribution of ebullition fluxes of CH 4 can be very heterogeneous (Hilgert et al., 2019;Liu et al., 2020;Tuṧer et al., 2017), the limited spatial resolution of our ebullition flux measurements only allows for a crude estimate of the basin-wide CH 4 emissions due to ebullition. Basin-wide CH 4 emissions due to ebullition during the different modes of operation were estimated combining the information on the spatial differences in the ebullition flux from the first measurement campaign in July with the time series measured at Station e2.
In the following, we first discuss the spatial variability of ebullition fluxes and then estimate basin-wide CH 4 emissions due to ebullition. These estimates are compared to diffusive CH 4 emissions and to CH 4 emissions due to degassing during turbination and to CH 4 emissions due to ebullition observed in other studies. Thereafter, we discuss the temporal variability of the ebullition fluxes and the impact of different modes of operations on the CH 4 ebullition fluxes.

Spatial Variability of Ebullition
Ebullition fluxes decreased with increasing water column depth (Figure 3), which is consistent with previous studies (Bastviken et al., 2004;Harrison et al., 2017). At water column depths of ≥15 m, no ebullition was observed. The generation of a gas phase in the sediment requires that the equilibrium pressure of the dissolved gases in the pore water is larger than the total ambient pressure. Because hydrostatic pressure increases with water depth the generation of gas bubbles requires more net production of gas at larger than at shallower depth. Further, water and thus sediment temperature is typically higher at shallow than at large depths ( Figure S6). At higher temperatures equilibrium concentrations are shifted toward the gas phase and CH 4 production is typically enhanced, both effects resulting in an increase in ebullition fluxes with increasing temperature . Hence, the likelihood to generate ebullition from sediments is smaller at large than at shallow depth. Consistently, the ebullition flux of CH 4 in Schwarzenbach reservoir is larger from sediments at shallow than at large depths ( Figure 3).

Basin-Wide CH 4 Emissions Are Dominated by Ebullition Fluxes of CH 4
Basin-wide emissions of CH 4 due to ebullition were estimated by assuming that the average ebullition flux of CH 4 measured at Station e2 can be taken as estimate of the average CH 4 emission due ebullition from areas in which the water depth is shallower than 15 m (~0.21 × 10 6 m 2 ) and that no CH 4 emissions due to ebullition fluxes occur in areas with water depths larger 15 m. These assumptions are motivated by the results from the experiment in July (see section 4.1 and Figure 3) and additionally assume that the ebullition flux of CH 4 at depths less than 15 m is essentially the same as at the lake surface, which is supported by numerical analysis of CH 4 -bubble fluxes (McGinnis et al., 2006). Because ebullition fluxes of CH 4 from areas with water depth <5 m are more than 2 times larger than those at e2 (see section 3.1), our estimate of the basin-wide emission of CH 4 due to ebullition must be considered as lower bound of the true basin-wide ebullition flux of CH 4 . During continuous diurnal pumped-storage operation, the reservoir emitted~3.4 × 10 6 mg CH 4 day −1 via ebullition, whereas it emitted~4.1 × 10 7 mg CH 4 day −1 via ebullition during diurnal turbination. These ebullition fluxes are substantially larger than the diffusive emissions of CH 4 from the reservoir, that is, 4.3 × 10 5 , 5.3 × 10 5 , 4.8 × 10 5 , and 1.4 × 10 6 mg day −1 determined for 14 April, 12 May, 23 June, and 18 August, respectively (Peeters et al., 2019). The diffusive CH 4 surface emissions were determined from spatial distributions of CH 4 concentrations measured at 1-m depth. Each of the four distributions was based on~45 samples measured at different locations.
In systems, in which large amounts of CH 4 are stored in anoxic deep water, redistribution of the stored CH 4 during overturn can lead to substantial diffusive emissions of CH 4 at the water surface ("storage emission") that may contribute a major fraction of the annual diffusive emissions (Encinas Fernandez et al., 2014). However, in Schwarzenbach reservoir the deep water remained oxic throughout the year (Figure 2b) and 10.1029/2020WR027221

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surface concentrations and surface fluxes of CH 4 did not increase substantially during overturn ( Figure S4). At Station p1 the largest diffusive flux of CH 4 during the season was observed on 13 September when the reservoir was still stratified. The diffusive CH 4 flux decreased from 1.8 mg CH 4 m −2 day −1 on 13 September to 1.6 mg CH 4 m −2 day −1 on 29 of September to 0.7 mg CH 4 m −2 day −1 on 11 October when the water column was mixed ( Figure S4). The maximum diffusive CH 4 flux was about 1 order of magnitude smaller than the ebullition flux during period 1 (16 mg CH 4 m −2 day −1 ) and 2 orders of magnitude smaller than the ebullition flux during Period 3 (197 mg CH 4 m −2 day −1 ), indicating that in Schwarzenbach reservoir emissions due to ebullition are substantially larger than storage emissions. Several studies have proposed that degassing of CH 4 rich water during turbination is the most important source of CH 4 emissions from reservoirs Bambace et al., 2007;Kemenes et al., 2007). We estimated the CH 4 potentially released by degassing during turbination in Schwarzenbach reservoir from the volume of turbinated water, which was determined from the level decline during drawdown obtained from the pressure data and the average dissolved CH 4 concentration in the last 5 m of the water column (Figure 2) minus the CH 4 equilibrium concentration. The average CH 4 emissions due to degassing during turbination were estimated to bẽ 2.3 × 10 5 mg CH 4 day −1 for Section 1 and~1.5 × 10 5 mg CH 4 day −1 for Section 3. These emissions are substantially lower than the emissions of CH 4 due to ebullition.
The analysis of the CH 4 emissions due to different processes indicates that ebullition is the dominant CH 4 emission pathway in the Schwarzenbach reservoir. In tropical reservoirs, where degassing of CH 4 during turbination was the main source of CH 4 emissions to the atmosphere Bambace et al., 2007;Kemenes et al., 2007), the turbinated water was in two cases anoxic Kemenes et al., 2007) and the CH 4 concentration in the turbinated water was in all cases much higher than in Schwarzenbach reservoir. The dominance of CH 4 emissions by ebullition observed in Schwarzenbach reservoirs agrees well with observations from other temperate reservoirs where ebullition is also the main pathway of CH 4 emissions to the atmosphere (DelSontro et al., 2010).

Comparisons of the CH 4 Emission by Ebullition With Observations in Other Systems
According to a recent synthesis of GHG emissions from reservoirs (Deemer et al., 2020), the average emission via ebullition of reservoirs with hydropower capacity is~98 mg CH 4 m −2 day −1 (~0.43 tõ 591.62 mg CH 4 m −2 day −1 ). The estimates of the basin-wide emissions from Schwarzenbach reservoir were~3.4 × 10 6 mg CH 4 day −1 during continuous diurnal pumped-storage operations (Section 1) and 4.1 × 10 7 mg CH 4 day −1 during diurnal turbination (Section 3). The corresponding basin-wide emissions per unit surface area are~5.6 and 62 mg CH 4 m −2 day −1 , respectively, for these two modes of operation. Hence, the emissions due to ebullition from Schwarzenbach reservoir are at the lower end of those for the hydropower reservoirs compiled by Deemer et al. (2020). The comparatively low ebullition fluxes may be related to the rather shallow sediments in the reservoir, the recent complete drainage of the reservoir in 1997, or the low alkalinity of the water (0.2 mmol L −1 ).
Our observation that ebullition fluxes increase substantially when drawdown occurs after a time period without drawdowns (Operation Modes 2 and 3 in Figure 4) is consistent with observations in several reservoirs which were operated with a single major annual drawdown in fall (Harrison et al. (2017). Also in natural systems, for example, the Amazon floodplains, CH 4 ebullition fluxes become large when the water level drops after an extended time period of water level rise (Engle & Melack, 2000). The average ebullition flux of CH 4 for all reservoirs studied by Harrison et al. (2017) was 42 mg CH 4 m −2 day −1 (range 0.0-192.6 mg CH 4 m −2 day −1 ) during predrawdown time periods and increased by a factor of 5 to 223 mg CH 4 m −2 day −1 (range 0.09-719 mg CH 4 m −2 day −1 ) during drawdown periods and thus to values larger than the average CH 4 ebullition flux for hydropower reservoirs reported by Deemer et al. (2020).
The study by Harrison et al., 2017 includes 5 days of observations from J.C. Boyle reservoir during which daily drawdowns occurred. As in Schwarzenbach reservoir daily drawdowns were associated with pulsed release of CH 4 -rich bubbles from the sediment (Harrison et al., 2017). During the~5 days evaluated, the reservoir emitted~720 (±398) mg CH 4 m −2 day −1 , more than an order of magnitude more CH 4 than Schwarzenbach reservoir. The very high ebullition fluxes of CH 4 from J.C. Boyle reservoir are probably related to high CH 4 production in the sediments, as the temperature of the bottom water is~19.71°C and the ebullition flux of CH 4 during no-drawdown periods is~193 ± 107 mg CH 4 m −2 day −1 and thus larger than in the other six reservoirs investigated by Harrison et al. (2017) and also 2 times larger than the average CH 4 ebullition flux from the hydropower reservoirs considered by Deemer et al. (2020). The duration of daily drawdown in the J.C. Boyle reservoir was~10 hr and thus much longer than in the Schwarzenbach reservoir which has contributed to the very high CH 4 ebullition fluxes during drawdown periods.

Effect of Different Modes of Operation on CH 4 Ebullition
Despite several investigations providing information of CH 4 ebullition fluxes from reservoirs, the consequences of different modes of operation in a pumped-storage hydropower reservoir on CH 4 ebullition fluxes have, to our knowledge, not yet been studied in detail. Our investigation in Schwarzenbach reservoir includes three time periods that resemble conditions during three different types of reservoir operation (Figures 5a1-5a3). During Section 1, the reservoir is operated in a diurnal pump-turbination mode which is typical for pumped-storage hydropower generation. This mode of operation causes diurnal increases and decreases in water level (Figure 5a1). A similar pumped-storage operation was performed every day, as is indicated by the positive wlc autocorrelation at a time lag of 24 hr (Figure 7a1). The negative wlc autocorrelation at a time lag of 6 hr ( Figure 7a1) suggests that pumping starts 6 hr after turbination, that is. the water is discharged via the turbines and pumped back from Kirschbaumwasen after 6 hr. The ebullition fluxes from the sediment during Section 1 predominantly occurred during periods of water level drawdown (Figure 6b1). The time lag of the negative cross correlation between the ef and the wlc of about −1 hr ( Figure 7b1) suggests that the ebullition flux is maximal shortly after the maximum rate of water level decrease. The data show also a diurnal cycle in ebullition fluxes from the sediment (Figure 7b1) that agrees with the diurnal change in water level (Figure 7c1). The~7-hr lag in the positive cross correlation between ef and wlc ( Figure 7c1) results from the 6-hr difference between maximum rate of water level decrease due to turbination and the maximum water level increase due to pumping. Because ef occurs mainly during the decrease in water level, the 6-hr lag leads to negative autocorrelations in wlc (negative wlc versus positive wlc) but positive cross correlation (positive wlc versus positive ef) at~7-hr lag. Section 2 is characterized by a constant increase in the water level (Figure 5a2) caused by the mode of operation during this period which did not include turbination and therefore no water level drawdowns. Thus, during Section 2 the ebullition flux was negligible (Figure 5c), that is,~200 times smaller than during Section 1 (diurnal pumping and turbination operation).
During Section 3, reservoir management aimed at production of hydropower from the water stored during the previous section and therefore performed intensive turbination. Thus, drawdowns dominated the changes in water level (Figure 5a3). Unlike during Section 1 (Figure 7a1), the wlc during Section 3 did not show a significant positive autocorrelation at any time lag (apart of the 0-hr lag; Figure 7c1), which indicates that turbination was not conducted periodically. As in Section 1, the ebullition fluxes from sediments showed a significant negative cross correlation with the rate of change in water level (Figure 7c3), which is consistent with the conclusion that the water drawdown caused by the turbination triggers ebullition fluxes. During Section 3, ebullition fluxes from sediments did not occur periodically (Figures 7c2 and 7c3) which is consistent with nonperiodic changes in water level and thus the reservoir management.
Turbination causes a drawdown in water level, and the associated decrease in hydrostatic pressure at the sediment is the main mechanism that triggers ebullition. This is supported by the correlation analysis ( Figure 7) and by the observation that ebullition fluxes were substantially larger (Figure 5c) during modes of operation with turbination (Sections 1 and 3) than without turbination (Section 2; significant differences between the three sections based on the Kruskal-Wallis test, p value <0.05). However, CH 4 ebullition fluxes varied substantially between the different modes of operation that included turbination. During continuous diurnal pumped-storage operation (Section 1) CH 4 ebullition fluxes were~12 times smaller than during diurnal turbination (Section 3) that followed a time period of no pumping and no turbination (Section 2). The amount of gas emitted as bubbles and also the CH 4 concentration within this gas are larger during Section 3 than during the other two sections (1 and 2) indicating that the management of the reservoir has an effect on the ebullition flux and the associated CH 4 emissions. Between 28 August and 5 October, ebullition was minimal because turbination was stopped and water level did not show diurnal fluctuations but increased over time (Figure 4; see also Section 2 in Figure 5). During this time period, CH 4 was not regularly removed from the sediment by ebullition as it was the case for example, during Section 1. Hence, from 10.1029/2020WR027221

Water Resources Research
28 August onward until 5 October CH 4 production probably resulted in the accumulation of CH 4 and thus in an increase in the partial pressure of CH 4 within the sediments. When turbination was resumed on 5 October, CH 4 concentrations in the sediment most likely were substantially oversaturated supporting bubble formation and large ebullition fluxes at decreasing hydrostatic pressure associated with the mode of operation consisting of regular turbination without pumping for water storage.
The accumulation of CH 4 in the sediment during the time period of no turbination may explain why ebullition fluxes and CH 4 concentrations in the emitted gas were substantially larger during Section 3 than during Section 1. The continuous diurnal pump-turbination mode of operation during Section 1 caused diurnally short ebullition events regularly removing CH 4 from the sediments thus preventing a substantial accumulation of CH 4 in the pore water. Hence, the partial pressure of CH 4 in the pore water most likely was substantially larger during Section 2 than during Section 1. Increased partial pressure of CH 4 in the pore water prior to bubble release not only explains that a decline in hydrostatic pressure due to turbination triggered larger ebullition fluxes during Section 3 but also that the fraction of CH 4 in the gas bubbles was larger during Section 3 than during Section 1. Increased CH 4 concentration in the gas at larger ebullition fluxes was also observed in Lacamas Lake (Harrison et al., 2017). Harrison et al. (2017) reported a fraction of~61% CH 4 in the gas of bubbles released from the sediments during drawdowns but only~30% CH 4 during no-drawdown periods. Moreover, a positive log linear relationship was found between ebullition flux and bubble CH 4 concentrations (Harrison et al., 2017), suggesting an increased sediment-to-atmosphere transfer efficiency for CH 4 in bubbles emitted during drawdown due to larger bubble sizes and/or higher sediment or water column CH 4 concentrations.
The ebullition fluxes quantified for the three sections with the three different modes of operation suggest that a reservoir management using continuous diurnal pumped-storage operation over 100 days causes essentially the same CH 4 emissions due to ebullition (~1,600 mg m −2 CH 4 ) as a management that uses 92 days of no turbination followed by~8 days of diurnal turbination. The latter type of reservoir management, that is, no turbination over an extended time period followed by drawdowns over several days is typical for many reservoirs used for purposes such as flood prevention, recreational uses, water supply, or even hydroelectric power generation (Harrison et al., 2017).
The conclusion that a reservoir operation using no turbination over an extended time period followed by water drawdown over several days leads to a larger average CH 4 ebullition flux than continuous diurnal pumped-storage operation is based on the data from the three, 5-day long, selected sections ( Figure 5). However, a very similar conclusion is obtained if the analysis is based on the CH 4 ebullition fluxes measured during the 51-day long time period from 28 August until 18 October. During this time period, which combines the time period of CH 4 accumulation in the sediment between 28 August and 5 October with the drawdown period thereafter until 18 October, the average CH 4 emission from the sediment by ebullition was~36 mg CH 4 m −2 day −1 . This average CH 4 ebullition flux assumes that the molar fraction of CH 4 in the gas bubbles was 42% (as in Section 1) until 5 October and was 85% (as in Section 3) after 5 October. Note that the average CH 4 ebullition flux of~36 mg CH 4 m −2 day −1 is an underestimation because it does not include the time periods with missing data (Figure 4b). Assuming that during the data gaps from 18 to 24 September and from 14 to 17 October CH 4 fluxes correspond to the average CH 4 fluxes measured during Sections 2 and 3, respectively, the average CH 4 ebullition flux for the continuous time period from 28 August to 18 October increases to~46 mg CH 4 m −2 day −1 . This value is~2.8 times larger than the average CH 4 ebullition flux during Section 1 (~16 mg CH 4 m −2 day −1 ) that is characteristic for CH 4 ebullition fluxes during diurnal pumped-storage operation (Operation Mode 1).
The results from the analysis imply that during 51 days of continuous diurnal pumped-storage operation, the CH 4 flux due to ebullition is~831 mg CH 4 m −2 , which is only~35.7% of the CH 4 ebullition flux released by a 51-day reservoir operation that uses 38 days of no turbination followed by 13 days of diurnal turbination (~2,325 mg CH 4 m −2 ).
Hence, reservoir management aiming at a continuous diurnal pumped-storage operation supports a reduction of CH 4 ebullition fluxes compared to management strategies that use longer-term time periods of no turbination followed by intensive turbination over several days.

Water Resources Research
Our study shows that pumped-storage systems cause emissions of the potent GHG CH 4 by ebullition. The typical mode of operation in pumped-storage hydropower reservoirs, that is, turbination and pumping at subdiel time scales, is however a good means to keep CH 4 emissions due to ebullition at a comparatively low level. In reservoirs used for other purposes than hydropower generation that typically do not use a subdiel pumped-storage operation, regular smaller drawdowns instead of single massive draw down at the end of the season may be advantageous to reduce methane emissions.

Conclusions
Our results show that water level drawdown associated with turbination triggers CH 4 ebullition from the sediment and that the mode of operation of the reservoir has a substantial influence on the ebullition fluxes of CH 4 from the reservoir. The data suggest that continuous diurnal pumped-storage operation causing short drawdowns and water level restoration at a diel or subdiel cycle results in smaller CH 4 emissions by ebullition from the sediments than management strategies aiming at the accumulation of water over an extended time period followed by intensive turbination over several days. Because ebullition is in many cases the dominant pathways of overall CH 4 emissions from reservoirs to the atmosphere (DelSontro et al., 2010;Sobek et al., 2012) and CH 4 is a very potent GHG, adopting a management strategy of continuous diurnal pumped-storage operation will contribute to a reduction of GHG emissions from reservoirs.

Data Availability Statement
All data and information relevant to this article will be made available before publication.