The hydrology of the Danube River, which drives water exchange with the delta, has a pronounced seasonality. Receiving meltwater from the Alps and Carpathians, the Danube shows peak discharge in spring from April to June (Fig. 2), whereas the discharge minimum occurs in autumn from September through November. December and January often show a small peak in discharge. The discharge provided by the Danube River drives the seasonal and annual hydrological changes in the delta. From 2000 to 2014, the Danube's average annual discharge was 6760 m3 s-1 (ICPDR, 2018), which is a 3 % increase compared to the period from 1930 to 2000 (Oosterberg et al., 2000). In the delta region, the discharge splits into the different main branches as follows: Chilia – 53 %; Sulina – 27 %; St George – 20 % (ICPDR, 2018). Approximately 10 % of the Danube's total discharge (620 m3 s-1; averaged over 1981–1990) flows through the delta, of which about 20 % (120 m3 s-1) is lost via evapotranspiration (Oosterberg et al., 2000).

To assess the hydrological conditions during the time of observation with respect to the long-term average, we compared water level observations from Isaccea, Romania (INHGA; Feodorov, 2017), to the discharge data set from Reni, Ukraine (ICPDR, 2018). Reni is located about 30 km upstream of Isaccea, without any major tributary joining in between. Water level data from Isaccea were converted to discharge using rating curves created from paired water level and discharge data from the National Institute of Hydrology and Water Management (INHGA). The comparison shows that 2016 was quite an average year in terms of discharge (Fig. 2), while, contrastingly, the Danube had very low discharge in 2017, especially during the period between March and October. Average discharge in 2017 was 5237 m3 s-1 or 23 % below the average flow calculated from the International Commission for the Protection of the Danube River (ICPDR) data set; hence, we refer to it as a dry year. Water temperature and conductivity of our sampling period were also, in general, comparable with data from the ICPDR's long-term monitoring (see the Supplement). Although water temperature measured during summer months in both 2016 and 2017 was up to 3 ∘C warmer than the long-term mean, these values did not exceed the maximum temperatures measured in the last 20 years.

We categorized our sampling stations into three groups based on geomorphological characteristics, namely main river branches, lakes and channels. River branch stations are all located along the three main branches of the Danube River, exhibiting velocities of about 0.75 m s-1 (Danube Commission, 2018), large hydraulic cross sections and frequent embankments. The category of lake refers to shallow (2–3.5 m) open-water bodies within reed bed areas, and five out of six sampling stations showed abundant macrophytes in summer. Natural and artificial channels represent the third category. They provide a surface water connection between the lakes and the river branches. We included old meanders of the Danube and small channels within the delta. Both of these features show a low flow velocity of up to 0.3 m s-1, yet span quite a range in terms of surface area and depth. Accessibility by motor boat determined the sampling stations in lakes and channels and restricted our monitoring to deeper lakes and larger channels. Both lakes and channels are connected to adjacent reed beds and marsh areas. Very shallow or isolated lakes, which are not represented in our data set, may receive a significant part of their water from adjacent reed beds (Coops et al., 2008) and have a higher residence time of up to 300 d compared to the investigated lakes, which have an estimated residence time of 10–30 d (Oosterberg et al., 2000).

We used mostly field-based methods for the analysis of dissolved CH4, CO2 and O2. In 2016, samples for CH4 analysis were taken for laboratory-based analysis by gas chromatography. Bubble-free water was filled into 120 mL septa vials by allowing an overflow of approximately three times the sample volume before preserving the sample by adding CuCl2. Depending on the expected concentrations, a headspace of 15–25 mL was created in the lab using pure N2. Samples were equilibrated overnight at 23 ∘C on a shaker, and the headspace was analysed using gas chromatography with a flame ionization detector (GC-FID; Agilent Technologies, USA). In 2017, we used 1 L Schott bottles to prepare headspace equilibration directly in the field, using air. Samples were transferred to gasbags and analysed in the field for CH4 using an Ultraportable CH4 / N2O analyser (Los Gatos Research – LGR). We corrected for atmospheric contamination during the processing by subtracting the amount of CH4 introduced with the air during equilibration. As tests showed that there was no significant difference between the lab- and field-based methods (see the Supplement), we pooled the data in our analysis.

CO2 concentrations were measured in the field using a syringe headspace equilibration of 30 mL sampling water with 30 mL air. The syringes were shaken for 2 min and allowed to equilibrate before the transfer of the headspace into a dry syringe and analysis in an infrared gas analyser (EGM-4; PP Systems). The method is explained in more detail in Teodoru et al. (2015).

Dissolved O2 concentration was measured in situ using a YSI ODO probe. The sensor was calibrated daily using water-saturated air and cross-checked with oxygen readings from a YSI Pro Plus multimeter sensor. We measured local in-stream respiration rates to evaluate if community respiration could sustain our measured CO2 fluxes. The respiration rate was measured as O2 drawdown over a 24 h period. For the measurement, six biological oxygen demand (BOD) bottles were filled with water samples, and three were measured immediately afterwards at t=0. The other three bottles were stored in the dark at approximately in situ temperatures, and the O2 concentration was measured after 24 h. The O2 consumption rate was derived from the time and concentration difference, assuming a linear decrease over time. We used this respiration rate to estimate the local CO2 production rate by assuming a 1:1 aerobic respiration relation of O2:CO2. Ward et al. (2018) argue that respiration rate measurements in BOD bottles underestimate the respiration rate because microbial processes are limited by both the bottle size and the lack of turbulence, and they suggest a correction factor of 2.7 to correct BOD-derived respiration rates for size effects only or a factor of 3.7 for size and low turbulence effects. Applying these correction factors did not change the main point of our comparison between fluxes and CO2 production rates.

CO2 and CH4 fluxes were measured using a floating chamber. The chamber had an internal area of 829.6 cm2 and an internal volume of 10 080 cm3, leading to a volume/area ratio of 12.15 cm. An aluminium foil coating minimized heating during deployment. CO2 was routinely measured in the field over a 30 min period by coupling an infrared gas analyser (EGM-4; PP Systems) to the chamber in a closed loop. In 2016, CH4 was sampled from the chamber by syringe and transferred overhead into 60 mL septa vials that had been pre-filled with a saturated NaCl solution until the liquid was replaced by gaseous sample. These discrete samples for lab analysis were taken at time t=0, 10, 20 and 30 min and analysed by GC-FID. In 2017, this laborious procedure was replaced by attaching the LGR analyser directly to the floating chamber.

Flux chamber measurements were conducted, unless conditions were too windy or boat traffic was too frequent in the main channel. In total, we took 265 flux measurements for CO2 and 122 for CH4. Of the latter, 91 measurements seemed to be without any significant influence of ebullition (i.e. R2 of linear regression > 0.96; for more detail, see the Supplement) and are henceforth referred to as diffusive CH4 fluxes. In the high-resolution LGR analyser time series, the influence of gas bubbles could easily be identified. We calculated the diffusive flux by fitting a linear regression to periods where data showed no influence of ebullition. In this case, the flux is calculated from the slope and the height of the gas volume in the chamber. In the discrete time series, it was hard to distinguish between diffusive flux and ebullition. When the linear regression of the discretely measured samples had an R2<0.96, we considered the flux measurement to be influenced by bubbles. In this case, we calculated the total flux by dividing the total concentration increase by the observation time, as we did to calculate the total flux of the LGR analyser measurements. A total of three cases with R2>0.96 showed fluxes >20 mmol m-2 d-1 and were thus also classified as total flux. Discrete time series showing a non-monotonous course (n=12) were excluded from further processing. Missing monotony can have several explanations, including sampling captured a bubble or a sample mix up.

We used our CO2 flux measurements to calculate the gas transfer coefficient k600 as follows: 1kCO2=FCO2(pCO2,water-pCO2,air)⋅KH,CO22k600=kCO2(ScCO2/600)-12, where FCO2 is the flux of CO2, pCO2 is the measured partial pressure of CO2 in water and air, respectively, and KH,CO2 is the solubility coefficient for CO2 according to Weiss (1974). ScCO2 is the Schmidt number for CO2, calculated based on temperature (Wanninkhof, 1992). We estimated missing flux measurements using the median k600 of the respective water type and the measured CO2 concentrations.

Analogously, diffusive CH4 fluxes were estimated from the individually calculated k600, using the solubility coefficient from Wiesenburg and Guinasso Jr. (1979), the mean global atmospheric CH4 mole fraction of 1.84 parts per million (ppm; Nisbet et al., 2019) and the Schmidt number for CH4 from Wanninkhof (1992). We attributed the difference between this estimate and the total measured flux to ebullition.

During the entire monitoring period, CH4 in water samples of the delta was always oversaturated with respect to atmospheric equilibrium concentrations of 0.0046 to 0.0023 µM at T=0 to 30 ∘C (Fig. 4c, d). Median concentrations in the river samples were thus ∼ 100 times oversaturated (0.33 µM). The channels exhibited a more than 3 times higher median concentration than the main river (1.1 µM), with the highest concentrations in July to September 2016 (up to 59 µM). In contrast, the median concentration in the lakes exceeded the value of the main river only slightly (0.43 µM) yet with a much larger range. In all three subsystems, concentrations increased from February 2016 to maximum values in July to October 2016. In 2017, concentrations were lower in the channels compared to 2016.

Similarly to CH4, we found CO2 concentrations to be constantly supersaturated with respect to the atmosphere in the main branches of the Danube, ranging from 26 to 140 µM (Fig. 4e, f). The median concentration of 59 µM was more than 3 times as high as the equilibrium concentration of CO2 at 15 ∘C (18.2 µM). Channels showed a much higher range (2.4 to 790 µM), with a significantly higher median of 140 µM. During the entire monitored period, we encountered undersaturated conditions in this class at only two stations (17 and 18) in August 2017. Lakes, however, were undersaturated on 11 occasions in 2016 and 32 occasions in 2017. Dissolved concentrations in this category ranged from 0 to 95 µM, with a median of 28 µM.

In 2016, CO2 concentration showed a pronounced seasonality in all three subsystems. In the main river, median CO2 nearly doubled from January 2016 to April 2016 and subsequently decreased to reach levels around 60 µM. In 2017, no clear seasonal pattern emerged. That year, median values mostly ranged around 60 µM, with the lowest median concentration recorded in June (44 µM) followed by the maximum in July (81 µM).

Channels showed the largest increase in CO2 during the warm season. Median concentrations increased more than 4 times, from 66 µM in February 2016 to 290 µM in July 2016. In terms of inter-annual CO2 variability, 2017 showed a later and less pronounced increase in concentration (72 µM in March to 187 µM in May), followed by an earlier decline than 2016. From August 2017 to November 2017, median monthly concentrations ranged around 50 µM and were lower than the concentrations in the main river during this period. In general, CO2 concentrations in the channels in 2017 were 18 % to 75 % below the values observed in 2016. We found the highest concentrations in the eastern part of the delta (station 10; Fig. 1), where concentrations reached around 360 µM in winter and up to 785 µM in summer 2016.

Compared to rivers and channels, lakes generally had the lowest CO2 concentrations and showed a distinctly different seasonal pattern. Most of the observed lakes (stations 7, 8, 13 and 14) were undersaturated in the period from May to November 2016. CO2 undersaturation in these lakes (including station 20) occurred 3 times more often and over a longer period, from March to December, in the drier year of 2017. In 2016, lakes showed highest median CO2 concentrations in April (74.4 µM) and the lowest concentrations in July and August (20.5 and 14.6 µM, respectively). With the concentration increase in early spring, the decrease in summer and the following increase in autumn, the seasonal signal in 2016 recalls a sinusoidal curve. The pattern in the drier year, 2017, however, showed less variation with lower concentrations which were ranging from 0 to 71 µM.

O2 saturation, as one might expect, often showed a mirror image to the CO2 time series in all three systems (Fig. 4g, h). The main river was generally slightly undersaturated, with a median O2 saturation of 93 %. O2 saturation in river water ranged between 75 % and 109 % during the whole observation period. Median saturation in the channels was 14 % lower (79.5 %) and – as for CO2 – covered a much broader range than in the main river. The lowest values observed were as low as 5 % O2 saturation (0.4 mg L-1) in July 2016, while maximum saturation reached nearly 150 % in August 2017. In winter, O2 saturation in the channels was comparable with the river stations. Station 10 showed an exceptional behaviour and never exceeded a saturation of 72 % or 9 mg L-1. O2 saturation in the channels strongly decreased in the spring and summer months, resulting in concentrations of less than 2 mg L-1 at station 9 in July 2016 and at station 10 from July to September 2016 and in June, July and October 2017. Contrastingly, most lakes showed a strong oversaturation of up to 180 % from April to October, resulting in a median saturation that slightly exceeded 100 %.

Median CO2 fluxes were largest in channels (93 mmol m-2 d-1; see Table 2) where we also observed the highest overall flux of 880 mmol m-2 d-1. Lakes were the only locations that showed significant negative fluxes, i.e. CO2 uptake during summer, when O2 was strongly oversaturated.

The highest median diffusive fluxes of CH4 were observed in the channels with 1.1 mmol m-2 d-1. Diffusive efflux from the river was generally lowest, while the lakes showed the largest variability, with a minimum of 0.03 and a maximum of 6.7 mmol m-2 d-1. Considerable ebullition occurred only in the delta lakes and channels, which accounted for ∼ 70 % of the total CH4 flux.

The gas transfer coefficient, k600, was calculated from the measured CO2 fluxes. Median k600 was lowest in the river branches and in the channels at 0.69 and 0.74 m d-1, respectively (see Table S1). As lakes were more exposed to wind, median k600 was considerably higher (1.2 m d-1), and we observed the maximum k600 of 8.6 m d-1 in this category.

We find respiration rates ranging between 0.8–390 mmol m-2 d-1 for rivers, while in the channels and lakes they ranged from 2.3–560 mmol m-2 d-1 and 1.0–350 mmol m-2 d-1, respectively (Figs. 5 and S7–S9). Median respiration rate is highest in rivers (54 mmol m-2 d-1), followed by lakes (48 mmol m-2 d-1) and channels (45 mmol m-2 d-1). Many stations showed a pronounced seasonality, with the highest respiration rates occurring mostly between July and October. Respiration rates, i.e. CO2 production rates, generally exceed CO2 fluxes in river and lake stations throughout the year (Fig. 5), which implies that local instream CO2 production sustained the observed fluxes. At the channel stations, we frequently observed fluxes exceeding the local production, even if we account for the potential underestimation of the CO2 production, which implies the presence of other CO2 sources. This was most striking at station 10, the CO2 hot spot, where CO2 outgassing exceeded local respiration on average by a factor of 40. At the other channel stations (also see Fig. S8), there seems to be a seasonally occurring pattern. CO2 fluxes exceed local production in the first half of the year, while they fall below local production for the remainder of the year. While this pattern is very distinct in 2016, it is less pronounced in the drier year of 2017, which suggests that the additional CO2 source is linked to hydrology.

The main river branches of the Danube are mostly influenced by the hydrology and chemistry of the catchment, as shown by the comparison between the concentrations at the delta apex with concentrations in the three main branches close to the Black Sea. There is comparably little variation between the stations with respect to DIC, DOC and POC. At all sites, O2 is slightly undersaturated most of the time, but we do not see a strong influence of the delta close to the Black Sea.

Carbon dynamics in the channels are strongly affected by the water source. The channels are connecting the river branches to the delta lakes. The direction of this connection depends primarily on hydrologic gradients between the delta and the main branches, which means that flow direction can reverse in individual channels and, thus, alter their chemical signature due to a change in the main inflow. Seasonally, the channels transport dissolved carbon into the delta and provide nutrients to the reed stands during the high-water season. During times of receding water levels in the main branches, the channels act as the delta's drainage pipes. The comparison between CO2 fluxes and local CO2 production rates (Fig. 5) shows that the high CO2 fluxes in the channels are often not sustained by in-stream respiration alone, in contrast to what we observed in the river and lakes. While this discrepancy mainly occurs during high discharge in spring, it is most evident at station 10, where it occurs throughout the year of 2016. Station 10 is located in Canalul Vatafu-Împutita, Romania, at the border of a core protection zone of the biosphere reserve. During this study, it stood out as a CO2 hot spot, responsible for the highest CO2 concentrations (Fig. 4f). Additional CO2-rich water inflows from adjacent wetlands could explain the large CO2 fluxes, which exceed CO2 production. The water at station 10 was always exceptionally clean, low in oxygen content and had a low pH, supporting the hypothesis of a pronounced input from the reed beds. During times of unusually low water levels, such as in August and September 2017, the lateral influx from the reed seems to cease (Fig. 5). The, at first glance, contradictory timing of the increased lateral inflow during increasing water levels at the other channel stations could be explained by a pressure wave. Water flooding the vegetated area in the west will push out old water with a long residence time in the vegetated area at the other edges further east. In general, channel water in the Danube Delta is therefore a mixture of three main sources, namely Danube river water, lake water and water infiltrating from the wetland. The importance of the individual water source depends on the location of the channel sampling sites and on the water levels, which trigger flooding or draining conditions.

In the lakes, residence times of 10–30 d allow primary production and local decomposition of organic matter to become important factors driving carbon cycling. We observed abundant macrophytes like Ceratophyllum demersum and Elodea canadensis growing in spring and early summer, which, depending on lake depth, even reached the lake water surface. A change in the abundance of submerged vegetation to vegetation with floating leaves might be linked to changes in the CO2 and CH4 fluxes (Grasset et al., 2016). Around July, algal blooms coincided with a significant reduction in macrophyte abundance. This pattern seems to be reoccurring due to the eutrophic state of the delta lakes (Tudorancea and Tudorancea, 2006; Coops et al., 2008, 1999). During our observations, both macrophytes and algal blooms caused a drawdown of CO2 and supersaturation in O2 (Fig. 4f, h). The algal blooms also partly explain the peak in measured POC from July to November, which extended to most of the delta's channels (Fig. 3f). The degradation of the macrophyte biomass coincided with locally elevated CH4 concentrations from July to October (Fig. 4d).

In constructed wetlands, macrophytes were found to influence the composition of methanogenic communities by affecting dissolved O2 and nitrogen in the rhizosphere, which had a direct impact on the amount of CH4 released to the atmosphere (Zhang et al., 2018). Potamogeton crispus, for example, which is also found in the delta lakes and channels, seasonally sustained CH4 fluxes that were up to 3 times higher than CH4 fluxes from Ceratophyllum demersum (Zhang et al., 2018). Studies showed that the plant community composition in the delta lakes shifted since the 1980s due to increasing eutrophication, which also led to an increase in Potamogeton species recorded in the delta (Sarbu, 2006). It remains unresolved whether this change in vegetation also affected the CH4 release in the Danube Delta.

In a hydrologically complex system like the Danube Delta, upscaling CO2 and CH4 is prone to several sources of uncertainties, most of them linked to the delta's small channels and lakes. First, the channel category showed a large range, not only in DOC and POC concentrations but also in dissolved gases and their fluxes. We attribute this primarily to the varying contribution from the three different water sources, with lateral influx from the reed stands drastically increasing the local CO2 concentration and fluxes. One could thus argue that this group is too broad and should be refined. However, in a complex system like the Danube Delta, this is a laborious task since individual channels are known to reverse the flow direction (Irimus, 2006), and potentially, the amount of lateral inflow also depends on the hydrologic conditions in the main branches. The existing 1D hydrological model, SOBEK (DANUBS, 2005), could assist in delineating periods of reversed flow, but a detailed model for the exchange with the wetlands would have to be developed.

Second, the surface area of the channels is estimated based on the channel length, given in Oosterberg et al. (2000), and an assumed channel width of 19 m, which leads to an estimated surface area that we consider quite conservative. More exact mapping or better spatial data, which might exist with local authorities but was not at our disposal, could improve this estimate. A larger or smaller surface area attributed to the channel would influence the flux estimates from this category accordingly.

Third, we identified station 10 as a CO2 hot spot, with concentrations reaching up to 22 000 ppm, during our study. The hot spot channel had an east to west orientation and was draining a core protection zone. Considering channels with these two criteria indicates that potential hot spots could account for up to 2 % of the channel length (see the Supplement) and contribute up to 20 % of the CO2 and CH4 fluxes of the channel category. The overall emissions from the channels (including hot spot channels) was decreased by 10 % to 30 % in this scenario, since considering the high fluxes separately lowered the median value used for the calculation of the channel fluxes. A first step to improve the upscaling would thus be to map the spatial distribution of dissolved gases in the delta. This would give insight on important questions linked to the hot spots – how many hot spots did we miss with our discrete sampling approach? What is their lateral extent? And how steep are the concentration gradients between hot spots and nearby sites?

Fourth, our study neglected small, hardly accessible and remote lakes. A study of lakes of various sizes in northern Quebec, Canada, revealed a strong, negative relation between lake CO2 concentration (and fluxes to the atmosphere) and lake area, suggesting a higher CO2 emission potential of smaller lakes compared to lakes with a large area (Marchand et al., 2009). Previous studies of lakes with a small area in the Danube Delta characterize them as very clear-water lakes (Coops et al., 1999) that have little or no surface water connection to the main branches (Coops et al., 2008), with increased water residence times and O2 concentrations below 5 mg L-1 during midday (Oosterberg et al., 2000). This indicated that these lakes, like the hot spot channel in this study, receive the majority of their water from the reed stands (Oosterberg et al., 2000). In contrast to the channels, which are wind sheltered by 2–4 m high reed stands, these small lakes provide a larger surface area and, thus, a larger wind fetch. Depending on the primary productivity in these lakes, better wind fetch, in combination with water contributions from the reeds, could result in higher fluxes to the atmosphere – at least compared to the larger lakes measured in this study. Based on the research in the literature, we estimate the area of potentially isolated lakes to be 99 km2. Attributing these isolated lakes with channel-like flux properties would raise the total CO2 and CH4 emissions of the lakes several times and turn them from a potential CO2 sink into a CO2 source in 2017 (see the Supplement). The scenario, as such, represents an extreme case, but it highlights the potentially large contribution from small, thus far overlooked, lakes in the delta.

Seasonal data coverage is often not sufficient to address the seasonality of the fluxes, which might bias the estimates towards either higher or lower emissions. However, not only the under-representation of certain seasons or events but also the pooling of the data during the upscaling process influences the resulting estimates. In the following, we look at the effects of data pooling for our 2 year data set by comparing different upscaling approaches. In addition to the approach presented in Eq. (4), where we discriminate by year, month and waterscape (case “c”), we also calculated the yearly fluxes in more simple ways by either pooling all data (pooled), discriminating between years only (case “a”), and by discriminating according to year and waterscape (case “b”). In case “c”, where we considered individual months, data coverage of CH4 did not allow the calculation for 2017. In all approaches, we treated the reed stands in the wetlands as a terrestrial part of the system, i.e. excluding them from the analysis.

For the Danube Delta, CO2 flux estimates decreased when considering spatial heterogeneity and seasonality because the channel data, which showed the most pronounced seasonality and the highest fluxes, are treated independently and assigned to a comparably small area. Independent consideration of data from different years allows the exploration of the inter-annual variability, which is quite pronounced for CO2 (Fig. 7a). CH4 emissions tend to be higher in 2017, but the trend is not as clear, especially considering total fluxes (Fig. 7c; case “b”). The lower CO2 flux in 2017 can be explained by the weaker connection of the wetland to the freshwater system of the Danube. We expect that, in 2017, most of the water exchange, especially during low-discharge conditions, between the river and the inner delta was along the channels as surface water connections, with comparably little water bypassing laterally through the wetland. While the CO2 fluxes from the river were only marginally smaller than in 2016, channels emitted less than 50 %, and the lakes even turned into a net CO2 sink in 2017 (Fig. 6a, b). The importance of the flooded vegetated area on CO2 concentration in rivers was also found in the Congo and Amazon river basins (Borges et al., 2015, 2019; Amaral et al., 2019), where larger inundated areas correlated with higher pCO2 values. In the case of the lakes, reduced lateral inputs from adjacent wetlands reveal their large CO2 uptake potential. However, this might result in higher CH4 emissions, as calculations according to case “b” indicate. Neglecting seasonality, diffusive CH4 fluxes from the lakes were 0.3 GgC yr-1 higher in 2017 (1.0 GgC yr-1; data not shown).

Durisch-Kaiser et al. (2008) found Danube lakes to be sources of CO2 and CH4 to the atmosphere in both May and September 2006. Their measured fluxes fall well within the range of our observations. The comparison of data for corresponding months shows, however, that their CO2 concentrations in May are, on average, twice as high as the ones we measured in 2016, while September concentrations are, on average, 18 % smaller. The higher fluxes in May could have been due to the aftermath of the severe flood, which reached Romania in the second half of April 2006 and inundated large parts of the delta, thereby promoting lateral exchanges.