Methane in the Danube Delta: The importance of spatial patterns and diel cycles for atmospheric emission estimates

Methane (CH4) is one of the substantial greenhouse gases in our atmosphere and its concentration has increased by ∼ 4 % over the last decade. Although sources driving these increases are not well constrained, one potential contribution comes from wetlands, which are usually intertwined with rivers, channels and lakes, creating a considerable need to acquire higher resolution data to facilitate modelling and predictions. Here we took a fully contained sensor set-up to obtain measurements of CO2, 5 CH4, O2 and auxiliary parameters, installed on a houseboat for accessibility, to assess and analyse surface water concentrations within the Danube Delta, Romania. Over 3 seasons, we transected a∼ 400 km route with concentration mapping and additional stations for monitoring diel cycles. Overall, the delta was a source for CH4 throughout all seasons, with concentrations ranging between 0.113–15.6 μmol L−1. The dataset was split into three different subsystems; lakes, rivers and channels, with channels showing the highest variability. We found large to extreme diel cycles in both the lakes and channels, with concentrations 10 varying by an order of magnitude between these two systems. The observed strong diel cycle within the lake suggests daily vertical stratification allowing for macrophytes to create a temporal oxycline due to lack of light and movement between the stems as previously suggested. While throughout the day, there was a consistent overall surface concentration of CH4 at around 0.4 μmol L−1, there was a clear linear trend with an O2:CH4 molar ratio of -50:1 during the phase of nocturnal convection with the two water stratified bodies mixing during the night. Daily spot sampling techniques and neglecting such diel cycles 15 reducing the estimated average methane concentrations by 25 % and increase by 3.3 % for channels and lakes, respectively. On an individual lake basis, spot sampling can potentially incur an uncertainty range of a factor of 4.5. Analyses also included a ‘hot spot’, with a 10-fold stronger methane increase (4–15.6 μmol L−1) overnight compared to the lake, with an almost immediate and extreme decrease in CH4 following sunrise. Calculated diffusive CH4 fluxes for the overall delta yielded an average of 49 ± 61 μmol m−2 h−1 corresponding to an extrapolated annual flux of 0.43 ± 0.53 mol m−2 yr−1. Our data 20 illustrate the importance of collecting information on diel cycles in different habitats to improve the emission estimates from wetland systems. 1 https://doi.org/10.5194/bg-2020-353 Preprint. Discussion started: 17 October 2020 c © Author(s) 2020. CC BY 4.0 License.

varying by an order of magnitude between these two systems. The observed strong diel cycle within the lake suggests daily vertical stratification allowing for macrophytes to create a temporal oxycline due to lack of light and movement between the stems as previously suggested. While throughout the day, there was a consistent overall surface concentration of CH 4 at around 0.4 µmol L −1 , there was a clear linear trend with an O 2 :CH 4 molar ratio of -50:1 during the phase of nocturnal convection with the two water stratified bodies mixing during the night. Daily spot sampling techniques and neglecting such diel cycles 15 reducing the estimated average methane concentrations by 25 % and increase by 3.3 % for channels and lakes, respectively.
On an individual lake basis, spot sampling can potentially incur an uncertainty range of a factor of 4.5. Analyses also included a 'hot spot', with a 10-fold stronger methane increase (4-15.6 µmol L −1 ) overnight compared to the lake, with an almost immediate and extreme decrease in CH 4 following sunrise. Calculated diffusive CH 4 fluxes for the overall delta yielded an average of 49 ± 61 µmol m −2 h −1 corresponding to an extrapolated annual flux of 0.43 ± 0.53 mol m −2 yr −1 . Our data 20 illustrate the importance of collecting information on diel cycles in different habitats to improve the emission estimates from wetland systems. Diel cycles of dissolved gases within inland waters are driven by multiple processes including temporal variability of biological processes such as photosynthesis and respiration, transportation, vertical stratification or temperature dependent solubility 55 (Nimick et al. 2011;Maher et al. 2015;Zhang et al. 2018;Sieczko et al. 2020). Although potentially substantial, these are rarely considered in studies of CH 4 fluxes due to general lack of data. Just as with overall data coverage of CH 4 , both spatially and temporally, there is also need for refined understanding of the contributions and the controls of CH 4 production and sources (Bogard et al. 2014;Abril and Borges 2019).
With climate warming, CH 4 production is set to increase from lakes as well as through eutrophication (Marotta et al. 2014;60 Del Sontro et al. 2019, Sepulveda-Jauregui et al. 2018. Bartosiewicz et al. (2019) suggest that increased warming and browning of the lakes will increase the warming of surface waters causing increasing stratification. This may lead to an increase the CH 4 production in bottom waters potentially leading to +8% of the current global lake emissions from shallow (< 5 m) lakes.
Therefore, analyzing the spatial and temporal (i.e. at least seasonal and diel) variability of methane emissions is important for future predictions and modelling efforts. Given the complexity of inland water systems, especially wetlands, monitoring approaches tend to stay within one system. Here we deployed an on-site monitoring device throughout the Danube delta, which measured gas concentrations continuously from a moving platform. The acquired high spatial and temporal resolution of methane concentrations and corresponding emissions formed the observational data basis to assess the importance of different systems (lakes, rivers and channels) and of diel cyles for the overall methane emissions in such a complex system.
The Danube River Delta, as most river deltas, is known to be an important natural source of CH 4 (Cuna et al. 2008;Durisch-70 Kaiser et al. 2008;Pavel et al. 2009). Recently, Maier et al. (2020) investigated the seasonal emission rates of CO 2 and CH 4 in parts of the Danube Delta, focusing on a set of stations that were analyzed at monthly intervals. Here, we take a complementary approach focusing on extremely high-resolution data in space and at the diel time-scale, with focus on three field studies.
The objectives of this study are split into two main aspects: 1) to assess the differences between regions within the Danube delta in regards to CH 4 concentrations and fluxes, and 2) to use high-resolution data to assess the importance of diel cycles 75 both on a local and global scale in such systems.

Set up
A portable and versatile flow-through sensor set-up was placed on-board a small houseboat for continuous mapping throughout the Danube Delta. Campaigns took place over three seasons: May (17-26), Aug (3-12), and Oct (13-23) 2017. The set-up 80 consisted of the HydroC ® CO 2 FT (CO 2 partial pressure, pCO 2 , -4H-JENA engineering GmbH, Jena), HydroC ® CH 4 FT (CH 4 partial pressure, pCH 4 , -4H-JENA), HydroFlash ® O 2 (dissolved oxygen, O 2 , -4H-JENA) and a SBE 45 thermosalinograph (Sea-Bird Electronics, Bellevue, USA) to measure temperature and conductivity. All sensors ran simultaneously at a speed of up to 1 Hz on the same continuous water flow (submersible pump deployed over the side at a depth of approx. 40 cm). The HydroC ® CO 2 FT and the HydroC ® CH 4 FT use non-dispersive infrared (NDIR) and tunable diode laser absorption 85 spectroscopy (TDLAS) technology respectively, while the HydroFlash ® O 2 Optode sensor uses the principle of dynamic florescence quenching (Bittig et al. 2018). Further details on the setup, its calibration and validation can be found in Canning et al. (2020).

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Originating in Germany, the Danube River travels across 2,857 km, with a drainage basin of 817,000 km 2 (Panin 2003). The delta is a complex system of wetlands, lakes, rivers and channels, both manmade and natural, with the largest compact reedbed zone in the world (Oosterberg et al. 2000;Panin 2003). The fluvio-marine delta system accounts for 51% of the total area (Pavel et al. 2009) in which it sees salt intrusions and through-flow from the Black Sea into the delta. Since the 1970s, the Danube Delta has been subject to eutrophication, with its peak during 1987during -1988during (Cristofor et al. 1993Galatchi and Tudor 2006;95 Enache et al. 2019). After a decrease of nutrient loads in the 1990's, due to socioeconomic changes in Eastern Europe, a slow 4 https://doi.org/10.5194/bg-2020-353 Preprint. Discussion started: 17 October 2020 c Author(s) 2020. CC BY 4.0 License. decline of nutrient levels was observed (Rîşnoveanu et al. 2004;Pavel et al. 2009), however, more recent levels comparable to those in 1988 were reported (Tudor et al. 2016;Spiridon et al. 2018). and Isac (c.vi). Blue circles indicate the sites of the two diel cycles at Lake Roşu (b1) and the 'hot spot' channel (b2), both during the August campaign.
The delta is within the temperate climate system, but experiences extreme temperature ranges with air temperature from below freezing (0 • C) to +30 • C (ICDP 2004). Deltas are continuously changing landscapes, with moving lake systems and 100 floating islands. The overall Danube delta is roughly 4423 km 2 with a 67-81% coverage in either aquatic ecosystems (rivers, lakes and channels) or wetlands (Cristofor et al. 1993). Using the small houseboat, the set-up was fixed, and a thorough transect throughout the delta was carried out with extensive lake transects completed in all three seasons for comparability (Fig 2). This study also featured two stationary diel cycle measurements (Fig 2b: blue circles), one in Lake Roşu and the other in the channel where we witnessed a major biogeochemical 'hot spot'.

Computations of saturation and fluxes
The average global atmospheric CH 4 concentration (ppb) was taken from NOAA/ESRL Global Monitoring Division program (Dlugokencky 2020) for May, Aug and Oct 2017 (1847, 1844.7 and 1858.1 ppb respectively). As the delta is practically sea level, barometric pressure as well as wind speed measured at the Gorgova station were used. Schmidt numbers (Sc) were calculated for temperature dependence following (Wanninkhof 1992) for freshwater. The corrected Schmidt numbers varied 110 between 296 and 824 in this study, consistent with the large temperature variance. Using CH 4 solubility (Wiesenburg and 5 https://doi.org/10.5194/bg-2020-353 Preprint. Discussion started: 17 October 2020 c Author(s) 2020. CC BY 4.0 License.
Guinasso 1979), CH 4 equilibrium concentrations in water were calculated and employed in the flux calculation. Fluxes were calculated following Peeters et al. (2019;supplementary material S3.2). Given slow stream velocities, we used the parameterisation from Cole and Caraco (1998) with constant gas-transfer velocity of ∼2 cm h −1 in the absence of wind where U is wind speed at 10 m height in m s −1 , and k 600 is the gas transfer velocity normalised to a Schmidt number of 600, i.e. CO 2 in freshwater at 20 • C (Jähne et al. 1987;Crusius and Wanninkhof (2003): where k CH4 is the transfer velocity at Sc CH4 , which is the Schmidt number of CH 4 at a given temperature, and the exponential n reflects two wind speed regimes (Jähne et al. 1987). For rivers, due to differencing fetch and dynamics we used n = -0.5 throughout, consistent with multiple river studies (Borges et al. 2004;Guérin et al. 2007;Bange et al. 2019). The flux was then calculated using the CH 4 concentration in the water and air: Flux=k CH4 · (CH 4,water −CH 4,air ) mol m −2 s −1 Given that the effect of spatial variability of k CH4 is relatively small in lakes with surface areas of 5x10 5 m 2 or larger, we disregarded size effects of lakes on emission fluxes noted by Schilder et al. (2013). In the following analyses, both day and night data will be shown unless stated otherwise for CH 4 .
3 Results and discussion Our high spatiotemporal resolution CH 4 data showed constant supersaturation (CH 4 concentration range 113 to 15600 nmol L −1 ), throughout the delta. Both significant systemical and seasonal variability was observed, with channels having the highest concentrations of up to 15600 nmol L −1 (Table 1)  High spatial variability was found across systems and water type boundaries (such as channels to lakes), which was also observed clearly by Crawford et al. (2017). More confined areas in closer proximity to the wetlands, were found to have the highest concentrations. These boundary crossovers were due to seasonal changes in concentrations and change of flow direction varying throughout the delta. May and Aug show similar median CH 4 concentrations at 627 nmol L −1 and 951 nmol L −1 , 140 respectively, Oct CH 4 median level however, had increased to 1440 nmol L −1 (Fig. 3). In each season, 3 specific locations stood out with extreme CH 4 concentrations: the two channels joining Lake Puiu (Crisan channel to the north and one from the south), and the 'hot spot' channel anomaly (blue circle (b2) on channel in Fig. 2). Rivers and channels (including the anomaly)

Concentrations distribution and estimated fluxes
showed the highest variability during Aug and May, consistent with the directional flow regime bringing in the water from the surrounding wetlands after the flood waters. The highest median was during Oct for rivers, lakes and channels (median: 559, 145 693 and 1500 nmol L −1 respectively), which coincides with the degradation of the macrophytes.
Oxygen (O 2 ) was mostly undersaturated, however measurements were not distributed proportionally throughout the delta potentially leading to the lower median in May from more measurements collected in the 'hot spot'. During Aug and Oct, O 2 saturation (%) was generally above 60% with Aug showing the larges variability above 100% coinciding with both temperature and production. These values included the 'hot spot', given it is a natural feature and most likely not the only one within the 150 Danube delta. Concentrations almost translate to the water-air fluxes (Fig. 3), with some variability ultimately due to temperature and wind.
Using the estimated area from Maier et al. (2020) for total area of rivers, channels and lakes (164, 33, 258 km 2 respectively) we estimated the delta's total emissions. Taking   * Excluding Stinky channel ('hot spot') and connecting channels, due to this location experiencing extremely high concentrations as an 'anomaly' within our full transect ** Higher range in lakes due to influence of channels From our meteorological data, we found little correlation with external factors such as wind, however, given these were not measured in situ, this cannot be fully quantified. We therefore suggest the observed distribution patterns over the entire delta are mostly more driven by both biological and physical processes affecting water-side CH 4 concentrations instead of effected

Seasonality
Seasonally, the delta changes significantly owing to a range of processes. High concentrations and therefore fluxes during May, have previously been explained due to growth, temperature and biomass peak, linking plant biomass to CH 4 emissions 180 during growing season (Milberg et al. 2017). This can be further linked to the previous flood period just before the transect in May. The Danube delta is known to have high levels of nutrients (Panin 2003;Durisch-Kaiser et al. 2008;Spiridon et al. 2018) arriving from the Danube river. This could account for higher concentrations, and saturation due to enhanced plankton growth being a source of additional labile organic matter fuelling CH 4 productivity in the sediments, which then outfluxes (Mendonça et al. 2012;Ward et al. 2017). Aug showed the largest CH 4 range among the seasons, however with the lowest 185 median coinciding with the theory that there is decreased CH 4 concentrations and emissions during lower water levels (Melack et al. 2004;Marín-Muñiz et al. 2015;McGinnis et al. 2016).
During Aug and Oct, the process of macrophyte degradation within the delta, mainly the lakes, was linked with elevated CH 4 concentrations in specific locations. This sharp increase of biodegradable organic matter triggered anoxic decomposition of organic carbon which released CH 4 (Segers 1998).

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The channels are highly influenced by the surrounding reed beds, which are known to produce high levels of CH 4 (Bastviken et al. 2011), and have influence on the surrounding systems they flow into (e.g. lakes). This both explains the high variability ( Fig. 3) and higher overall concentrations and fluxes (Table 1). They are also influenced by the lakes, which are sources of labile organic carbon that fuels methanogenesis. However, given methanogenesis was not measured, we can only make assumptions about this. Channels are the links between the rivers and the lakes, surrounded by wetlands form which the collect water and 195 therefore generally have the highest concentrations of CH 4 and lowest in O 2 . Delta systems are highly diverse, and therefore each region has been split to give a more descriptive assessment of the dynamics in the Danube delta.

'Hot Spot'
The 'hot spot' was classified as a small channel system receiving partially anoxic water from the reed stands ( Fig. 2b (b1)).
The highest conductivity was observed around the 'hot spot' as 0.08 S m −1 (overall mean ± SD of 0.038 ± 0.005 S m −1 ),

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suggesting also the potential of ground water influences. Given the dramatic change within the concentrations and properties of the water, such as the water temperature dropping further into the 'hot spot', even within summer, this would further provide evidence from cooler ground waters or potential waters from the reed beds also suggested by Maier et al. (2020).
The 'hot spot' showed seasonality in concentrations and dynamics. In Aug, median fluxes measured 211 ± 86.3 µmol m −2 h −1 , however when compared to all months combined, the median from the 'hot sport' reduced to 54.9 ± 106 µmol m −2 205 h −1 . The influence of the 'hot spot' on the surrounding areas was significant, with high concentrations tending to diperse into the following channels (Canning et al. 2020). However, the influence of the 'hot spot' on the data as a whole system, is more dependant on the extension of this location. In the recent study by Maier et al. (2020), it was estimated that due to other similar environments within the delta, areas of little movement, could account for 2% of the total channel area, or 20 % of CO 2 and CH 4 fluxes from the channels. The fluvial delta (rivers and channels) works as the supply of incoming water into the main part of the delta, accounting for the base level of CH 4 concentrations being laterally transported. We found very little evidence that intrusions from the Black Sea may have reached into the delta and have an impact such as suggested before (Durisch-Kaiser et al. 2008;Pavel et al. 2009). This would be important to explain reduced methane production as sulfate reduction becomes the dominating anaerobic mineralization. Rivers had the lowest range of concentrations for CH 4 with the smallest variability out of all systems and the delta (Fig. 3) ranging from 154 to 1600 nmol L −1 (during Aug). In channels, when excluding the 'hot spot', medians were larger than rivers but fairly consistent throughout May and Aug yet higher during Oct (1170, 1300 and 2230 nmol L −1 respectively) within channels. However, channels experienced some of the highest concentrations when including the 'hot spot', ranging from 221 to 15600 nmol L −1 for May and Aug respectively. It also changed the dynamics during Aug, observing the highest 220 median of 5710 nmol L −1 , showing the significant influence one hot spot can have on a system. This provides evidence that most of the CH 4 production happens within the delta, not the river itself.
As stated before, CH 4 fluxes followed roughly the same trend as CH 4 concentration, only moderately modulated by variable wind speed. For rivers, such as with concentrations, Aug fluxes had the highest variability (Table 1 and  comparing within the fluvial system (rivers and channels separately), riverine CH 4 concentration during May and Aug had a median comparable to channels and therefore showed overall homogeneity, however channels appeared to have more extreme 235 values and ranges than rivers. This difference would be due to less biological and physical processes occurring within the rivers due to depth, proximity to the wetlands and the flow generally being faster. However, both rivers and channels concentrations varied, showing large dependence on both seasonal changes and sample location. Furthering evidence, just as with the 'hot spot', for significant spatiotemporal influence on CH 4 fluxes. The comparison to this earlier study indicates, that eutrophication and carbon turnover have not significantly changed during this period (Tudor et al. 2016;Spiridon et al. 2018). These concentrations ranged from the lowest 113 nmol L −1 to the highest 11300 nmol L −1 both in May (largest concentration close to a channel). The median however, stayed roughly the same for both May and Aug (465 and 466 nmol L −1 respectively), with Oct reaching 630 nmol L −1 . We expect less productivity and 245 more mineralization of macrophytes in Oct, leading to enhanced CH 4 production. Before entering each lake complex, the water had to travel through either the channels or the reed beds, increasing the concentrations coming into the lakes. The inflowing water however quickly dispersed, and was soon oxidized as seen before (Crawford et al. 2017). This inflow was only visible on the edges of the lakes and although had influence on the overall concentration, were seen as outliers as the CH 4 due to being quickly oxidised (Fig, 4). Morphology and seasonal changes were far clearer in the lakes than any of the other systems, due to noticeable influences from the channels showing larger productivity and macrophyte distributions. This led to higher concentrations during Oct as the macrophytes broke down as mentioned before, but also potential stratification (Milberg et al. 2017).

Situation of CH 4 in lakes
By averaging over the lakes, we obtained the total lake area fluxes of 2.9, 6.5 and 4.8 mol CH it is not possible to capture ebullition through dissolved CH 4 surface measurements, such as in this study, this can potentially lead to mild-significant underestimations (Maier et al. 2020). However, the benefits of this study, were being able to pick up local dynamics that is usually missed by just daily or intermediate sampling.

Diel CH 4 cycling
One advantage to measuring continuously at high-resolution, was the opportunity to observe diel cycles. These extractions of temporal variability (i.e. over nearly a full 24 h cycle (Fig. 4)) were successfully carried out at specific locations. For analyses and comparison, two diel cycles were recorded: one in Lake Roşu (Fig. 2b(ii)), and the other within the 'hot spot', both locations <3 m depth.

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Lake Roşu's diel cycle (Fig. 4 left) shows clear indications of strong temporal variability on the diel time scale. The nocturnal buildup in CH 4 is linearly correlated with the loss of oxygen (molar CH 4 :O 2 ratio 1:-50). CH 4 concentrations started from 400 nmol L −1 at sunset and reached 1400 nmol L −1 at sunrise. During the diurnal period, CH 4 concentrations quickly relaxed back to initial conditions. As the mapping transect in Lake Roşu started already around 9:00, some spatial variability is superimposed from then on to the dominant diel cycle causing CH 4 concentrations to vary over the range 200-500 nmol L −1 . Overall, the 270 CH 4 concentration shows a strong co-variation with oxygen. The diurnal relaxation of the CH 4 and O 2 concentrations to initial state has a more exponential shape. A possible explanation for this hysteresis: the water column stratifies during the day, and undergoes vertical mixing as the surface water is cooling during the night. This process progressively mixes the two formerly separated water bodies resulting in the observed linear mixing line (Milberg et al. 2017). Diurnal warming then quickly re-stratifies the water column so that the surface layer has no further entrainment from low-oxygen, high-methane 275 waters below and undergoes rapid CH 4 loss due gas exchange (Fig. 4). In contrast to oxygen, CH 4 does not reach equilibrium during the diurnal period. This could be due to continued supply from background sources of CH 4 (e.g. from macrophytes, lateral transport, diffusive flux across the thermocline or production via photoautotrophs (Bižić et al. 2020). Given the rate and extent of the CH 4 increase, this shows potentially significantly CH 4 production during the day in the bottom waters (Grasset et al. 2019), supporting the hypothesis of anoxic conditions close to the sediment and therefore intensified methanogenesis 280 (Crawford et al. 2014b;2017). This is more likely to lead to other effective transport of CH 4 such as ebullition which could supply CH 4 to the surface waters or the atmosphere. Oxygen, in contrast relaxes back to equilibrium during the day as both air-water fluxes and in-situ photosynthetic production of O 2 would drive the system towards equilibrium. The data (Fig. 4c) also show a clear hysteresis in the relationship between CO 2 and O 2 changes over a diel cycle. The CO 2 peak of about 8 µmol L −1 (corresponding to a pCO 2 of about 250 µatm) just after sunrise is around 65% saturated, only 285 during the transect do some values exceed 100%, reaching 130% (Fig. 4c few points over 15 µmol L −1 ). The data show a slight decoupling of metabolism of CO 2 and O 2 (Fig. 4d), such as CO 2 increasing significantly without the use of O 2 , which has also been observed by Peeters et al. (2016). These concentrations, however, coincide with the mapping; higher CO 2 rates when closer to the lake edges (similar to the CH 4 pattern in Fig. 5), due to incoming waters from the wetlands. During the day, Lake Roşu is undersaturated in CO 2 and supersaturated in O 2 , indicating high levels of productivity in the surface waters.

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Overnight we observe respiration with the CO 2 increasing towards equilibrium and O 2 moving away from equilibrium. This is an indication for high rates of primary production during the day with an intense drawdown of CO 2 which is not compensated during the night, as has been observed in eutrophic lakes (Balmer and Downing 2011). Our observed CO 2 concentrations were far lower than those reported by Pavel et al. (2009): 26 ± 27 µmol L −1 during September 2006.
The 'hot spot' (Fig. 4, right) also shows a clear co-variation of CH 4 with oxygen. Here CH 4 increases from roughly 4000 295 to 16000 nmol L −1 over the nocturnal period (sunset to sunrise), followed by a rapid return to values around 6000 nmol L −1 during the diurnal period (sunrise to sunset). O 2 decreases while CH 4 stays roughly the same until around 3:30 am when it appears to enter into hypoxic and even towards suboxic conditions as the ratio increases to about 1:3. This pronounced nonlinearity be indicative of mixing with more than two endmembers, e.g., surface layer, sub-surface layer and a distinct bottom layer. The initial mixing encompasses only surface and sub-surface layer (similar to the lake situation) whereas later during the 300 night, near-bottom waters are entrained that have extremely elevated CH 4 concentration (and no oxygen) as a consequence of anoxic methanogenesis in sediment pore waters. An alternative explanation would be groundwater or lateral injection of water from adjacent wetlands.
CO 2 reaches saturation levels of close to 4500% during the diel cycle in the 'hot spot', over the night with the lowest supersaturation of 1175% at the end of the diel cycle (∼150 to 550 µmol L −1 ). Dissolved CO 2 displays a mirror image with 305 temperature (Fig. 4f). The CO 2 :O 2 relationship has a molar ratio 2:1 (with indications of progressive steepening as observed more clearly for CH 4 ) during the night and such as with CH 4 , CO 2 shows a steep decrease following sunrise, with initially little change in O 2 . The diel hysteresis is far clearer with CO 2 than with CH 4 , showing a steady increase and decrease. This is ultimately due to different processes, and potential methanogenesis occurring in the bottom waters before mixing, as stated above.

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The diel changes in temperature are roughly the same for the two situations (± 2.5 • C: Fig. 4), showing influence on all variables and induced strong density variations. The observed strong density variations were potentially sourced by the mixing of the bottom waters over the course of the night (Fig. 4), when cooling of the warm surface layer mixed with the colder bottom waters. Although it could be argued that temperature could have had an effect within the diel variability as previously  To show the impact of these diel cycles, Table 2  The mapping route is representative of a high spatial resolution mapping routine (Fig. 5). The diel cycle was observed within the mapping transect and therefore we were able to extract this section (Fig. 5c). Fluxes from the transect during the day (DL) 325 and the full diel cycle (FD) were then scaled up to year averages showing an underestimation by just day night data alone.
For the 'hot spot',we used the day night data (after sunrise) for this comparison due to no mapping transect following the diel cycle. Excluding all full diel cycles from the entire data set, the mean CH 4 flux decreased from 49 ± 61 µmol m −2 h −1 to 34.9 ± 35.7 µmol m −2 h −1 , or a factor of 1.4. Therefore, scaling this by year changes the fluxes for the entire Danube delta from 340 0.4 ± 0.5 mol m −2 h −1 to 0.3 ± 0.3 mol m −2 h −1 . Aug showed the largest variability when extracting diel cycles, with an uncertainty range of a factor of 2.27 from 84 ± 38 to 37 ± 33 µmol m −2 h −1 . This greater variability can be linked to higher temperatures, greater stratification and increased production and organic matter degradation, all leading to potential increases in CH 4 (Duc et al. 2010;Fuchs et al. 2016). However, given diel cycles were not continuously measured throughout the entire system, these values may not express the exact change when including all data from both day light hours and at night. To note, upscaling these numbers is to give more of an awareness of the difference between including and excluding diel cycle data and between spot sampling. These values should not be taken at face value due to the major component of the Danube delta in terms of CH 4 influence (the wetland) was not measured and only diffusive fluxes calculated.
There have been multiple studies looking into diel cycles (Nimick et al. 2011;Zhang et al. 2018;van Bergen et al. 2019;Sieczko et al. 2020), yet they are usually undetected or unresolved therefore are often ignored, particularly in studies with 350 sampling during daylight hours. This can lead to substantial under-or overestimation of emissions, as has also been noticed in systems with high CH 4 concentrations (Natchimuthu et al. 2017). From our evidence of lake diel cycles, we conclude, in terms of discrete sampling techniques to fully capture the full variable cycle, sampling should be conducted during 3 periods: before sunrise, just after sunset and during the early afternoon. This way there is potential to capture the peak amplitude, low and average concentrations, providing a better overall estimate of concentrations. Although, the best sampling techniques would 355 be mapping with complete spatiotemporal coverage, however this is unfeasible in most cases.
Typically, delta systems tend to be either measured in specific regions (entrances or middle of lakes or channels), or with in situ measurements over time (e.g. Cuna et al. 2008;Wang et al. 2009;Olsson et al. 2015;Cunada et al. 2018). These measurements are then usually upscaled from single locations (e.g. Bouillon and Dehairs 2007;Borges et al. 2015;Joesoef et al. 2017), failing to include spatial variability, system specific impacts (such as the 'hot spot' we observed here), and monthly 360 changes. Here we can see that all of these impacts can have significant effects on the observed measurements. In Table 2 and

Conclusions
To conclude, the overall Danube river delta surface waters were a source of CH 4 , at a mean concentration of 1700 ± 1930 nmol L −1 and calculated aquatic emission to the atmosphere of 0.43 ± 0.53 mol m −2 yr −1 . This is comparable to concentrations 365 and diffusive flux mean of other systems of this type and size (see Stanley et al. (2016) for literature comparison: 1350 ± 5160 nmol L −1 and 3 ± 9.3 mol m −2 yr −1 and Maier et al. (2020)). However, given that wetland systems (and therefore the reed beds) are known to be the significant in CH 4 fluxes of high variability (Segers 1998;Nisbet et al. 2019), our data only cover the water-air interface of channels, rivers and lakes and therefore may be underestimating the overall fluxes that include the vegetation cover of the wetlands. Being able to measure extensively within the lakes systems provided evidence 370 that the reed bed concentrations were far higher than that of the lakes themselves. Our data have shown significant need for increased recordings of diel cycles in all systems, with channels and lakes show significantly lower concentrations and fluxes when excluding these. Of our three water types, rivers had the smallest fluxes, showing that most of the CH 4 production must come from further within the wetlands. Most calculated CH 4 budgets, stem from extrapolations and data driven approaches due to lack of process-based models (Saunois et al. 2020), therefore investigations of the interactions between reed stands and 375 open water will be of high priority.
With our analysis of diel cycles both in the channels and the lakes we were able to further confirm the importance of adequate data collection, through 24-h coverage or specific correction for sampling bias, and implementation into models. The diel cycle within the lake was consistent with stratification over the day, where vast amounts of organic carbon from macrophytes created anoxic subsurface waters, which slowly and steadily mixed during the night. We showed that this cycle could have major 380 consequences for spot measurements of concentrations and fluxes. Far larger quantities of CH 4 are released during the night due to daily stratification and with most current sampling techniques, such variability would be missed. A similar diel cycle was also active at the 'hot spot' site in a channel, where concentration changes varied four-fold between 4000-16000 nmol L −1 indicating that the process of advective cooling during the night, should also be considered in shallow systems.
In summary, when comparing the overall peak-to-peak concentration ranges of observed diel cycles, there was a correspond-385 ing potential uncertainty of a factor of up to 4.5 within our measured lake (roughly 30%). Incurred by spot sampling without a dedicated sampling strategy taking diel variability into account. Using our measured examples with the diel cycles removed, accounted for an underestimation of up to 25% for channels, whereas an overestimation in lakes by 3.3% CH 4 concentration (nmol L −1 ) (no diel cycles were measured in rivers). Including our measured diel cycle measurements, accounted for roughly an increase of 20.4% in lakes and 4.2% decrease in channel fluxes. From this one study, this shows compelling evidence diel 390 cycles must be accounted for when measuring concentrations and calculating fluxes and further proves, that the conventional picture of methane dynamics in freshwaters ( Fig. 1) is too static. That further analysis of diel cycles must be included in the development of dynamic models of methane release from inland waters, especially with eutrophication predicted to. Given these cycles didn't just occur in lakes, a re-evaluation is needed on sampling techniques and data checks to include such cycles from all water systems.

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Data availability. All data presented in this paper are available from the corresponding author.