Contrasting Biophysical Controls on Carbon Dioxide and Methane Outgassing From Streams

Small headwater streams are recognized for intense outgassing to the atmosphere of climate‐relevant carbon dioxide (CO2) and methane (CH4). Though these headwaters are markedly oversaturated for both CO2 and CH4, the origins and controls over the fate of these two carbon‐gases are still poorly constrained, especially for the stronger greenhouse gas CH4. Here, by measuring stream‐based production of CO2 and CH4, concurrently with their rates of outgassing to the atmosphere, we identify distinct biophysical control mechanisms for each gas. We show that while CO2 is largely imported from the catchment in proportion to discharge, CO2 outgassing can be modulated by in‐stream metabolism to offset outgassing by up to 30% in spring and summer. In contrast, CH4 shows a non‐linear response to seasonal changes in discharge and is predominantly produced in the streambed in relation to sediment type. Further, once released from the streambed, outgassing of CH4 at the surface and flow‐driven dilution occur far more rapidly than biological methane oxidation and CH4 leaves the water largely unaltered by biology. Incorporating the intense carbon cycling of headwater streams into the global carbon cycle will require distinct parameterizations for each carbon gas in Earth system models.

The aim of this study was to characterize how discharge and in-stream carbon metabolism together exert biophysical controls on the sources and final fates of CO 2 and CH 4 in temperate, low-gradient headwater streams (maximum catchment area of ∼60 km 2 ) in our case study catchment of the lowland Hampshire River Avon, UK. Within the catchment, we performed a seasonal study on six streams with distinct geologies (two each on the clay, Greensand and Chalk) and over a wide spectrum of hydrological characteristics, e.g., flashy to stable hydrograph, hydrological connectivity to the land and in-stream carbon metabolism (see Heppell et al., 2017;Rovelli et al., 2017Rovelli et al., , 2018. To quantify how much outgassing of CO 2 and CH 4 could be accounted for by either in-stream production or input from the catchment, we combined: (a) traditional measurements of benthic metabolism via isolated benthic chambers (Trimmer et al., 2009) with; (b) integrated estimates of whole stream metabolism using the state-of-the-art and non-invasive aquatic eddy covariance technique (Rovelli et al., 2017(Rovelli et al., , 2018; and (c) direct quantification of CO 2 and CH 4 outgassing from anchored floating chambers (Podgrajsek et al., 2014) (see Figure 1). The seasonal study was complemented by measurements of CO 2 and CH 4 concentrations in riparian soils and streambeds and laboratory-based assessments of the potential for methane oxidation in the water column. Finally, we made high-temporal-resolution day and night measurements of CO 2 and CH 4 outgassing and modeled any diel changes as functions of our directly parameterized biological (e.g., net ecosystem metabolism, water column methane oxidation) and physical control mechanisms (e.g., dilution, reaeration, outgassing).

Study Site
This study was performed in six ∼150 m headwater reaches of the lowland catchment of the Hampshire River Avon (UK) (Figure 1a; Allen et al., 2014;Jarvie et al., 2005). The headwaters drain three dominant geologies: Chalk (River Ebble and River Wylye), (Upper) Greensand, i.e., fine-grained glauconitic sands and sandstones, (River Nadder and West Avon) and clay (River Sem and Priors), although some sub-catchments and reaches encompass a combination of those geologies, e.g., clay and Greensand on River Nadder, Chalk and Greensand on River Wylye (Figure 1a). Here, we regard these sub-catchments based on their dominant underlying geology, which has been shown to modulate the local hydrology and hydrological connectivity (Bristow et al., 1999). Parallel studies at these reaches have also directly linked hydrological regime and baseflow index (BFI) to the dynamics of key stream sediment processes such as nitrogen gas (N 2 ) production (Lansdown et al., 2016), and   . Integrated baseflow, as a proportion of total flow over a single day, has also been identified as a robust predictor of seasonal differences in stream metabolism dynamics across the different reaches (Rovelli et al., 2017). The water column of these lowland headwaters has been shown to contribute to about a quarter of their annual whole-stream respiration and primary production, with water column respiration in the turbid waters, for example River Sem on the clay, contributing, on average, 71.3% of the spring and summer whole-stream respiration (Rovelli et al., 2017(Rovelli et al., , 2018. Surface water sampling by Heppell and Binley (2016a) has shown that mean pH remained largely comparable across the sites ranging from 7.3 to 7.7, although with the clay streams tending toward lower values. In contrast, mean dissolved inorganic carbon (DIC) was, on average, highest in the Chalk streams and in the Greensand West Avon (3.9-4.8 mmol L −1 ) and lowest in Greensand Nadder and in the clay streams (3.0-3.1 mmol L −1 ). Estimates of total alkalinity based on pH and DIC (after Millero, 1979) were in the order of 2,650-2,900 μmol L −1 (clay streams and Nadder) and 3,600-4,520 μmol L −1 (chalk streams and West Avon), respectively.
For the purposes of this study, each reach was studied for a period of one to three days in spring, summer, autumn and winter from April, 2013, until February, 2014. Using a variety of techniques (Figure 1), we quantified fluxes of dissolved oxygen (O 2 ), carbon dioxide (CO 2 ) and methane (CH 4 ) using chambers (benthic and floating) and O 2 fluxes via aquatic eddy covariance (Rovelli et al., 2017(Rovelli et al., , 2018, along with stream morphological characteristics and local hydrological regime . We experienced from below average rainfall in both spring and summer, to a 100-year flood in the winter of 2013-2014 and while this allowed us to capture a wide range of stream discharges it was not possible to sample during the extreme flood (see Figures S1 and S2 in Supporting Information S1). We used piezometers to measure porewater concentrations of CH 4 and CO 2 in riparian soils and streambed sediments every two months . A high-resolution survey of day and night CO 2 and CH 4 outgassing was performed in spring, 2015, using an automated floating gas chamber connected to an Ultraportable Greenhouse Gas Analyzer (UPGGA; Los Gatos Research). Benthic mapping surveys were also performed in each reach for each season to characterize the areal coverage of vegetated and non-vegetated patches of clay, Greensand and Chalk gravel following the methods described in Gurnell et al. (1996). The patch type areas were drawn manually onto local geo-referenced stream maps, and were digitized using Adobe Photoshop® to extract relative areal coverage (in percentage) of each sediment patch-type.

Benthic Metabolism and Sediment CH 4 Release
Measurements of in situ O 2 -based benthic metabolism, along with release of CH 4 , were performed at the patch scale (<1 m 2 ) using benthic chambers (Figure 1b;Trimmer et al., 2009). These consisted of transparent Perspex chambers (0.5 L enclosed volume, 73 cm 2 surface area) mounted on a steel-ring, which were used to measure net benthic O 2 production and CH 4 release in the light (n = 12, daytime), and equally sized black, plastic chambers to measure benthic O 2 consumption and CH 4 release in the dark (n = 12, night-time). Potassium chloride was added as a tracer to quantify potential exchange of water from the chamber in the permeable sand and gravel-Chalk beds. The chamber incubations covered the range of sediment patch types identified during the initial stream habitat mapping. Each chamber deployment lasted ∼2 hr, and four chambers were deployed each day/night over three successive days. The chambers were continuously stirred using a magnetic stirrer. Changes in O 2 concentration within the benthic chamber were monitored at one-minute intervals using Clark-type oxygen microelectrodes connected to an Under-Water Meter (Unisense, Denmark) (Trimmer et al., 2010). Water samples for CH 4 analysis were taken from the chamber at the beginning and end of each deployment using a syringe connected to a valve on top of the chambers (Figure 1b).
Samples for CH 4 were transferred gently to 12 mL gas-tight vials (Exetainers, Labco), overfilled to ensure no air was introduced, and preserved within two hours of being taken by adding 100 μl zinc chloride solution (7M; see Dalsgaard et al., 2000). CH 4 was measured after headspace equilibration using a gas chromatograph fitted with a flame ionization detector (Agilent Technologies) and concentrations calculated using solubility coefficients (Yamamoto et al., 1976) following established protocols (e.g., Sanders et al., 2007). Rates of O 2 consumption or production over time were calculated using linear-regression and scaled to an areal flux (in mmol m −2 h −1 ) using the chamber inner dimensions. Similarly, CH 4 consumption or production rates were calculated using the concentration at the start and end of each deployment. Final rates of benthic gas exchange were scaled-up to the reach using our benthic mapping of each sediment patch type (vegetated, clay, Greensand and Chalk gravel), by weighting the respective patch-averaged rates by the relative areal coverage (in percentage) of each sediment patch-type within the reach. Benthic O 2 exchange was used to estimate reach-scale benthic ecosystem respiration (ER, as mmol CO 2 produced per m −2 h −1 ), benthic gross primary production (GPP, as mmol CO 2 consumed per m −2 h −1 ) and net benthic ecosystem metabolism (in mmol CO 2 m −2 h −1 ) assuming a 1 to 1 ratio for O 2 to CO 2 (Glud, 2008). It is well established that this ratio may vary over the diel cycle, across seasons as well as spatially, within a commonly reported rage of 0.8-1.2 (e.g., Glud, 2008;Therkildsen & Lomstein, 1993). As changes in the ratio will proportionally affect our rates, these are to be considered conservative estimates. Throughout the manuscript, positive CO 2 net benthic metabolism will be used to indicate a release of CO 2 from the benthic compartment into the water column, i.e., a net source of CO 2 . The mean benthic gas exchange from each sediment patch type across all sites was estimated by data clustering following a signed logarithmic transform (see Section 2.7).

Seasonal Outgassing of CO 2 and CH 4
Outgassing of CO 2 and CH 4 was quantified using anchored floating chambers (8.6 L volume and 674 cm 2 surface area; Figure 1c) which were deployed in parallel to the benthic chambers (Podgrajsek et al., 2014). The floating chambers consisted of an inverted plastic bowl covered in reflective aluminum tape, fitted with a polyurethane tubing sample port to allow for gas-sampling via a three-way luer-lock valve and a CO 2 sensor (SenseAir) (Bastviken et al., 2015). Typical chamber deployments lasted two hours and were performed in the morning, with the CO 2 sensor set to measure at 5-minute intervals. For CH 4 , discrete gas samples were taken at regular intervals from the sample port using a gas-tight syringe (SGE International Pty Ltd) and stored for later analysis by displacing de-gassed, de-ionized water from 3 mL gas-tight vials (Exetainers, Labco). Gas samples were analyzed by GC-FID for CH 4 as described above. For each chamber deployment the initial period of linear rise in gas was identified and the change in concentration over this period was converted into outgassing rates using linear regression and the chamber's dimensions. Positive outgassing rates indicate an upward exchange from the streams into the atmosphere, i.e., a net atmospheric source, while negative rates indicate a downward exchange from the atmosphere into the stream system, i.e., a net atmospheric sink. It should be also noted that anchored floating chambers, compared to freely drifting chambers, might enhance near-surface turbulence and thus bias outgassing rates . Although such bias can be substantial in fast flowing, high-gradient streams, flows in our low-gradient streams (Rovelli et al., 2017(Rovelli et al., , 2018 fell below this threshold (see Lorke et al., 2015).

High-Temporal-Resolution Diel Measurements of CO 2 and CH 4 Outgassing (Spring 2015)
The seasonal outgassing measurements were complemented by an intensive campaign in spring 2015, to characterize short-term outgassing dynamics in each stream. A LiCor Long-Term Chamber (Model 8100-101; LiCor, with a volume of 4.093 L and a surface area of 318 cm 2 ) was modified to float on the streams by mounting it on a plastic cylinder (collar) and life-ring ( Figure 1c) and with a total volume (chamber + collar) of 6.29 L. The chamber was connected to a CR800-Series Datalogger (Cambell Scientific Inc) to control the motorized chamber. During the deployment, the chamber was set to alternately open and close every 10 min to flush the chamber and prevent it from equilibrating with the underlying water. Concentrations of CO 2 , CH 4 and water vapor were measured at 10 s intervals with an Ultraportable Greenhouse Gas Analyzer (Los Gatos Research), attached to the chamber by a closed-loop ( Figure 1d). Gas fluxes, corrected for water vapor dilution, that accounted for the opening and closing of the chamber, were computed for each of the consecutive 10 min closed-chamber intervals using self-written R (R Core Team, 2014) and Matlab® scripts. An r 2 value of 0.9 was used as quality cut-off to flag weak regressions.
We also characterized methane ebullition events by analyzing the distribution of the rates of change in CH 4 (in ppm s −1 ) during all 1,416 measurements. Here we ascribed any sharp episodic increase in CH 4 concentration (i.e., sharp peaks increases, see Figure S9 in Supporting Information S1) that lasted for at least two or more consecutive data points to an ebullition event and delineated those from steady, diffusional increases in CH 4 ( Figure S9 in Supporting Information S1). We found that a 5-fold peak increase in the rate of change over the diffusional rate of increase, was the optimal threshold to identify ebullition events. Once identified, these events were subsequently cross-checked against the parallel CO 2 readings to discriminate between ebullition and other non-steady state fluxes or deployment issues (e.g., inadequate sealing, suboptimal flushing of the chamber), which would also result in clear deviation from a linear change in CO 2 . The significance of ebullition was quantified in terms of numbers of ebullition events, as well as the overall contribution from ebullition to CH 4 outgassing (single measurements and mean). The latter was estimated as the total rate of CH 4 outgassing (diffusion + ebullition), by computing a point-to-point slope from the first point at the beginning of the (diffusive) linear slope, before an ebullition event, and the last point of the linear slope after an ebullition event (see Figure S9 in Supporting Information S1).

Whole Stream Carbon Metabolism
An integrative assessment of whole-stream benthic metabolism in each stream was obtained seasonally using the non-invasive aquatic eddy covariance technique (Berg et al., 2003). Aquatic eddy covariance measurements in rivers and streams quantify the dynamics and driving forces of benthic stream metabolism and riverine O 2 gas exchange (Berg et al., 2003;Berg & Pace, 2017;Koopmans & Berg, 2015;Murniati et al., 2015;Rovelli et al., 2017Rovelli et al., , 2018. In essence, the technique relies on the simultaneous acquisition of high-resolution time series (64 Hz) of both vertical flow velocity and dissolved O 2 concentrations at the same point in the water above the sediment from which turbulence-driven fluctuations in both vertical velocity and O 2 can be extracted. With the appropriate setup and procedures (see Berg et al., 2003;Lorrai et al., 2010;Rovelli et al., 2017Rovelli et al., , 2018, the co-variance of those fluctuations provides instantaneous O 2 flux estimates that are then averaged over time (e.g., hours or days) to provide a net estimate of O 2 uptake or release from the sediment. Model validations of the aquatic eddy covariance have shown that the obtained O 2 flux integrates contributions from a theoretically constrained area of the sediment, termed the footprint area, whose extent depends on: (a) the distance from the sediment in which the measurements are collected; and (b) specific characteristics of the sediment surface roughness (i.e., bottom roughness length scale) (see Berg et al., 2007). The aquatic eddy covariance technique may capture benthic O 2 fluxes over much larger areas of the streambed (tens of m 2 footprint) and was, therefore, complimentary to the patch-scale measurements made with the benthic chambers (described above).
Our aquatic eddy covariance system consisted of an acoustic Doppler velocimeter (Vector, Nortek A/S, Rud), Clark-type O 2 microelectrodes (Revsbech, 1989) and submersible amplifiers (McGinnis et al., 2011) and was operated as described in McGinnis et al. (2016) (Figure 1e). Aquatic eddy covariance was used to quantify benthic GPP, ER and net benthic metabolism, while light and dark incubations of discrete water samples (Rovelli et al., 2017(Rovelli et al., , 2018 captured the same parameters in the water to enable us to quantify net, whole stream metabolism (NWM) within each stream reach. This includes contributions from the sediments, water column and aquatic plants to integrate in-stream metabolism at the reach scale (20-70 m 2 ). Measurements were made over at least two and half of the three day sampling period at each site. A comprehensive description of the seasonal aquatic eddy covariance work performed within River Sem, River Nadder and River Wylye, as well as Ebble and West Avon in spring, is presented elsewhere (Rovelli et al., 2016(Rovelli et al., , 2017(Rovelli et al., , 2018. Within the remit of this study, we only report the O 2 -based net whole-stream metabolism (in mmol m −2 h −1 or mmol m −2 d −1 ) as CO 2 , assuming a 1 to 1 ratio of O 2 to CO 2 for metabolic activity (see Section 2.2.). As for the benthic chambers, positive net whole-stream metabolism indicates a net release of CO 2 from the benthic compartment into the water column, while negative values indicate a net benthic uptake of CO 2 .

Water Column Oxidation and Dilution of Streambed CH 4
Estimates of water column methane oxidation rate potentials were obtained for each stream from laboratory-based measurements of methane oxidation rate potentials of suspended particulate matter (SPM, in mg L −1 ), scaled to in situ suspended particulate matter and CH 4 concentrations, following Shelley et al. (2014Shelley et al. ( , 2015. For each site, methane oxidation was measured at a standard CH 4 concentration of 8 μmol L −1 with 100%, 62.5%, 37.5% and 0% of the original suspended particulate matter concentration. Gas samples were taken from the headspace at five time points over the incubation period (0 , 26.5 , 49 , 122.5 , and 168 hr, respectively) and measured as above and an empirical relationship between suspended particulate matter and methane oxidation derived ( Figure S4 in Supporting Information S1). Rates of methane oxidation (in nmol CH 4 g −1 SPM h −1 ) were obtained via linear regression and subsequently scaled from the standard laboratory concentration (C stand = 8 μmol CH 4 L −1 ) to in situ CH 4 concentrations (C in situ ) using our previously, laboratory established empirical Michaelis-Menten kinetic relationship between methane oxidation rate (MO) and CH 4 concentration (∼0.01-22 μmol L −1 ) for fine sediment (Shelley et al., 2015): with the maximum rate (V max ) equal to 586 nmol CH 4 g −1 h −1 and the Michaelis constant (K m ) being 3.7 μmol L −1 for C stand between ∼0.01 to 22 μmol CH 4 L −1 . Background CH 4 concentrations for each stream were obtained from the initial measurements at the beginning of each benthic chamber incubation (t 0 ). The potential for methane oxidation associated with stream-water suspended particulate matter to alter CH 4 concentrations in the water column was calculated using the methane oxidation rates and the in situ ratio of CH 4 concentration to suspended particulate matter for each stream. The resulting parameter, here termed Rk CH4 (in h −1 ), represents a measure of the turnover time for CH 4 in the water column due to biological activity. The residence time of CH 4 due to outgassing, here quantified as the reaeration constant for K CH4 (in h −1 ), was obtained from standardized gas transfer velocities (k 600 , in m d −1 ) estimated for each stream using hydraulic equations (see Section 2.7), accounting for mean water depths and the Schmidt number for CH 4 at in situ stream temperatures (Raymond et al., 2012). Flow driven dilution of CH 4 , here termed K flow , was defined as the residence time of water (in h −1 ) within any stream reach driven by local discharge. A comparison of the ratios between these parameters enables an assessment of their relative importance in modulating water column CH 4 dynamics. For instance, a ratio of Rk CH4 to K CH4 or K flow close to 1 would indicate that microbial, methane oxidation is a major driver of changes in water column CH 4 concentrations.

Mass-Balance of Diel CO 2 and CH 4 Dynamics
The obtained fluxes and field measurements were combined into a simple mass-balance model to further investigate potential controls on diel changes in dissolved CO 2 and CH 4 concentration dynamics at the reach scale.
Here, concentration changes of CO 2 and CH 4 over time ( ∕ , in mmol m −3 h −1 ) were modeled based on: (a) the amount of dissolved gas coming into the reach from upstream, including from the catchment (F in ); (b) the net gas release or uptake across the entire streambed surface area of the reach (F streambed ); (c) net biology-mediated gas production or consumption within the water column as it moves through the reach (F water column ); (d) the net amount of outgassing to the atmosphere occurring across the entire water surface area of the reach (F outgassing ); and (e) the amount of dissolved gas being discharged downstream at the lower end of the reach (F out ) as: In Equation 2, F in (in mmol m −3 h −1 ) is quantified as the dissolved gas concentration upstream of the reach (C upstream, in mmol m −3 ) multiplied by water discharge (m 3 h −1 ) at the upper end of the reach, which were both assumed constant throughout the model run. Similarly, F out (in mmol m −3 h −1 ) was computed at each time step as the final modeled stream concentration from Equation 2, for the previous time step, multiplied by the discharge out of the reach, starting from C background (t = 0, in mmol m −3 ). The model was run for up to 6 hr with time steps of 5 s and a control volume (V) of mean stream width x 150 m length (along the flow direction) x mean stream depth (in m), assuming a constant stage (i.e., water level). The model focuses on the difference in CO 2 and CH 4 dynamics between day and night and we assume a constant rate of supply or loss of these gases from each pathway over the model run. The modeled mass balance does not include lateral and vertical groundwater recharge and discharge, respectively, which we know to be comparatively minor on the modeled time scales (e.g., Rovelli et al., 2018). Water column gas concentrations in the reach come from field measurements during summer, 2013, and were used for both the initial (t = 0) concentration within the reach (C background , in mmol m −3 ) and C upstream . For CO 2 , F streambed (in mmol m −3 h −1 ) is the day and night aquatic eddy covariance O 2 -flux (in mmol m −2 h −1 ) multiplied by the area-to-volume (A/V) ratio of the control volume, while F water column (in mmol m −3 h −1 ) is the O 2 -flux in bottle incubations with both expressed as CO 2 equivalents using a 1 to 1 molar ratio as above (Rovelli et al., 2017). These were chosen over invasive chamber-based fluxes as they are, overall, expected to provide more accurate estimates of daytime primary production, and more constrained benthic uptake rates in permeable sediments (e.g., Attard et al., 2015). For CH 4 , F streambed is the measured sediment CH 4 release, obtained from the light or dark benthic chambers (in mmol m −2 h −1 ) multiplied by A/V, while the suspended particulate matter-scaled methane oxidation rates, in mmol m −3 h −1 , were used for F water column . Positive values of F water column and F streambed indicate a source of CO 2 and CH 4 within the water column or a net gas exchange from the benthic compartment into the water column, respectively. Reach-scale outgassing (in mmol m −2 h −1 ) for both CO 2 and CH 4 was quantified as: from gas concentrations in the streams (C) and equilibrial atmospheric concentrations (C sat ) (Weiss, 1974;Wiesenburg & Guinasso, 1979), with positive values indicating a net atmospheric source, i.e., a net gas exchange from the stream into the atmosphere. Gas transfer velocities (k, m h −1 ) were obtained from k 600 values scaled by the respective Schmidt numbers for each gas at in situ water temperature (Raymond et al., 2012). Values of k 600 were quantified from stream discharge and site-specific hydraulic parameters, based on the average output from the seven model parametrizations provided by Raymond et al. (2012), which were validated previously for two of the investigated streams (see Rovelli et al., 2018). Temperature time series were obtained from Heppell and Parker (2018).
The model requires meaningful estimates of the average day and night benthic CH 4 fluxes for the dominant streambed patches e.g., vegetated and non-vegetated sand and Chalk gravel, as well as for clay. Due to the limited amount of data and the inherent heterogeneity of benthic CH 4 flux measurements, values tended to span several orders of magnitude and were often characterized by a strong skewness toward higher values (Figure 2). To minimize the risk of biasing our mean estimates, the data were transformed as = sign( ) × ln(| | + 1) to ensure that the original sign of the flux would be maintained. The transformed data were then averaged into clusters in full digit increments (e.g., −1 to 0, 0 to 1, …) to give each cluster equal weighting. The resulting monotonic data set was subsequently averaged, and the obtained averaged value (ln_average ) converted back a mean flux as mean ≈ sign(ln_average) × |ln_average| . Note that the flux data set for the gravel patch type were found to be more constrained than for the other patch types, with 75% of the data falling within the −0.9 to 1.3 μmol m −2 h −1 range, and the outliers deviating by a factor of 3 to more than 600. Given the reduced magnitude of the flux range, the data were averaged arithmetically.
The model was first used to reproduce the CO 2 dynamics, matching the observed daytime outgassing by fine-tuning both the stream discharge and background CO 2 and CH 4 concentrations to within the range provided by the field observations, e.g., mean, median for the month (Heppell & Binley, 2016a, 2016bRovelli et al., 2017). Model performance was evaluated by comparing the resulting modeled night-time outgassing rates, with the mean values obtained during our high-resolution sampling campaign. The same hydrological parameters, once validated for CO 2 , were then applied to CH 4 , where the fine-tuning of the model was only performed on the background concentrations. The model was also used to investigate the relevance of different physical and biology-mediated parameters in driving diel changes in CO 2 and CH 4 outgassing, via a measurements-oriented sensitivity analysis. This included discharge dynamics and diel temperature changes (Heppell & Parker, 2018) that were evaluated for both gases, as well as gas specific parameters, such as the respiratory quotient to covert O 2 fluxes to CO 2 equivalents and suspended particulate matter concentrations (Heppell & Binley, 2016b), used as a descriptor for methane oxidation in the water column. While k is parametrized in the model as described above, and thus coupled to stream discharge, k values associated the lower and upper end of the observed discharge were also applied to the base model to assess the sensitivity of the diel outgassing dynamics to changes in gas transfer velocity.

Statistical Analysis
We used linear mixed effects models with the lme4 package in R (Bates et al., 2015;Pinheiro & Bates, 2000;R Core Team, 2014) to estimate the overall main effect of light, season, patch type (gravel, sand, clay and vegetated sediment) or individual stream on measured benthic O 2 and CH 4 exchange. For example, to isolate the overall main effect of light we pooled the data for each stream and each seasonal campaign and fitted models that included season and stream as random effects on the intercepts (see Tables S1-S3 in Supporting Information S1). Note, that the effect of patch type was not tested in the turbid clay streams as the beds were homogenous, i.e., there were no vegetated patches. Similarly, we modeled the overall main relationship between outgassing and discharge for CO 2 or CH 4 by pooling the data from each seasonal campaign and fitting slopes and intercepts as random effects to the data for each stream. In each case, nested models of varying complexity, e.g., models with random slopes and intercepts versus random intercepts only, were compared using the Akaike Information Criterion (AICc for small samples sizes) with the "MuMin" package (Barton, 2009) and final parameter estimates for the most parsimonious models derived using the "emmeans" package (Lenth, 2019). Where appropriate, the overall relationship in the data is visualized by plotting the partial residuals from the mixed-effects model. Data with a high degree of skewness were cube-root ( 3 √ ) transformed to improve normality and to maintain the original positive and negative value structure in the data (Miles et al., 2013;Zuur et al., 2009). Further details are given in the Supporting Information.

CO 2 Fluxes, Outgassing Versus Discharge and Porewater Concentrations
Rates of CO 2 outgassing (in mmol m −2 h −1 ) from the streams, quantified with floating chambers, were strongly seasonal, ranging from 3.95 ± 0.63 (4.12) (mean ± standard error (median)) in spring, to 16.66 ± 2.67 (13.07) during winter (Figure 2a), while chamber-based net benthic metabolism (in mmol m −2 h −1 ) ranged from −0.10 ± 0.51 (−0.34) on average, in spring, to 0.69 ± 0.21 (0.87) in autumn (Figure 2a). Contributions of net benthic metabolism to CO 2 outgassing varied among seasons, ranging from ∼69% in summer, to ∼22% in spring and autumn, to ∼8% during the winter, but represented only about a third of the estimated mean annual CO 2 outgassing (Table 1). Assessments of net whole-stream metabolism (in mmol m −2 h −1 ) using aquatic eddy covariance showed that half the reaches acted as CO 2 sinks (negative net whole-stream metabolism) in spring and summer. Overall, seasonal averages were negative and/or carbon neutral (−0.53 and −0.02; Figure 2a), being −20% and −30% of the CO 2 outgassing rates, respectively, on average. In contrast, in autumn and winter the net wholestream metabolism was positive, but comprised only 25% (2.42 mmol m −2 h −1 ) and 17% (1.81 mmol m −2 h −1 ) of seasonal total outgassing of all streams, respectively. Outgassing of CO 2 was not correlated with the observed rates of net benthic or whole-stream metabolism, but was almost linearly proportional to stream discharge and baseflow (discharge normalized by the respective sub-catchment areas, power-law exponent 0.84 vs. 1; Figure 2b, Table S1 in Supporting Information S1). Outgassing was maximal in autumn and winter under high discharge and lowest in summer. Porewater concentrations of CO 2 in the streambed and riparian soils of gaining reaches were comparable ( Figure 2e). Overall, on the clay, the net benthic metabolism could account for 70% of the outgassed CO 2 in spring and all of CO 2 outgassing in summer (average of Priors and Sem sites in Table 1). In contrast, on the Chalk and Greensand, net benthic metabolism in spring and summer could only account on average for 8%-10% of CO 2 outgassing at these sites, respectively (Table 1).

CH 4 Fluxes, Outgassing Versus Discharge and Porewater Concentrations
Outgassing of CH 4 (in mmol m −2 h −1 ; mean ± standard error (median)) to the atmosphere ranged from 0.04 ± 0.02 (0.03) during summer, to 0.07 ± 0.03 (0.05) during autumn (Figure 2c). Chamber-based release of CH 4 from the sediments ranged from 0.37 ± 0.13 (0.23) in autumn, to 0.82 ± 0.24 (0.65) in winter ( Figure 2c) and was up to 50 times higher than CH 4 outgassing ( Figure 2c). The release of CH 4 from the streambed was also not correlated with CH 4 outgassing and revealed a non-linear relationship to normalized stream discharge (Figure 2d, Table S2 in Supporting Information S1). Porewater concentrations within the streambed and in bankside riparian soils in gaining reaches, were highly variable, but, overall, riparian CH 4 concentrations were four-fold lower (median to median) than in the streambed (Figure 2e). The release of CH 4 from the streambed (in μmol m −2 h −1 ) showed large variation both across streams and seasons, but, overall, streambed sediments in the dark released significantly (P < 0.001, see Table S3 in Supporting Information S1) more CH 4 (median 23.8) than streambed sediments in the light (median 2.11, Figure 3). The only exception being the River Nadder on the Greensand, where the CH 4 release in the light was 7% higher than in the dark ( Figure S3 in Supporting Information S1). Generally, mean sediment CH 4 release, quantified from on our data clustering approach, was highest on clay (up to 8.18, on average at night) and on sand streams (up to 18.5), with very little contribution from the Chalk gravels (up 0.04) (Figure 3). In contrast, vegetated patches of both Greensand and Chalk streambeds were found to be hotspots of CH 4 release (58.8). Note. The percentages are based on flux comparisons by season and stream, and would only equal 100% if the amount of CO 2 outgassing is matched by that of local metabolism, i.e., NBM or NWM. Note that negative values indicate net sinks for CO 2 , e.g., in the Nadder in spring, net benthic metabolism represents the potential to reduce CO 2 outgassing by 17%. a site not accessible due to flooding.

High-Resolution Diel CO 2 and CH 4 Outgassing in Spring
We used high-resolution automated floating chambers to characterize diel dynamics of CO 2 and CH 4 outgassing. For CO 2 , mean daytime outgassing (in mmol m −2 h −1 ) ranged from 0.54 ± 0.02 (mean ± standard error) to 13.52 ± 0.35 across the six streams, while at night, outgassing was 30% higher, on average (P = 0.036, Figure 4a). Only 3.5% of the data set (49 values) failed our quality check (r 2 < 0.9). Mean outgassing of CH 4 remained largely constant across the day, with no significant daytime to nighttime variability (P = 0.455; Figure 4b). Averaged daytime CH 4 outgassing (in μmol m −2 h −1 ) ranged from 2.10 ± 0.05 to 56.82 ± 1,15. Increases in CO 2 outgassing at night tended to be greatest in streams on the Greensand and Chalk, where GPP tends to be the highest (e.g., average reach-scale estimates determined in 2013-14; Rovelli et al., 2017) despite its intrinsic temporal variability (see Hall, 2016; and references therein), and lowest on the more turbid clay streams, where GPP also tends to be the lowest (Figure 4c). Discharge values (51 measurements, 3.5% of total) were mostly concomitant with those for CO 2 .
Out of the total 1,416 high-resolution chamber measurements, we only observed 21 ebullition events (i.e., 1.5%), and almost all exclusively at Priors (18 events, 86% of all events) on the clay. During these events, contributions from ebullition to total CH 4 outgassing (ebullition + diffusion), expressed as a percentage, was 13.5%, on average, ranging from no measured increase (33% of ebullition events) to 43% (1 event) and 73% (1 event) at River Ebble and West Avon, respectively. At River Nadder and Priors, the increase was found to be only 3% (1 event) and 9% (average of 18 events), respectively ( Figure S9 in Supporting Information S1). Overall, ebullition had a very marginal effect on mean day and night CH 4 outgassing, with 0.7% at Priors, 0.5% at the Ebble, 0.3% at West Avon and a negligible 0.03% at the Nadder.

Methane Oxidation Potential and In-Stream CH 4 Turnover
Concentrations of suspended particulate matter ranged from 11 to 16 mg L −1 in Greensand streams in summer, up to 501 mg L −1 on the clay in autumn ( Figure S5c in Supporting Information S1). On average, suspended particulate matter was lowest on the Chalk (River Ebble; 88 ± 20 mg L −1 , mean ± standard error), intermediate on the Greensand (126 ± 58 and 129 ± 72 mg L −1 for River Nadder and West Avon, respectively) and highest on the clay (River Sem; 287 ± 91 mg L −1 ). Laboratory-determined rates of potential methane oxidation ranged from 1.35 nmol L −1 h −1 for negligible (∼0 mg L −1 ) suspended particulate matter in the Greensand West Avon, to 32.22 nmol L −1 h −1 in the clay-based River Sem for 52 mg L −1 suspended particulate matter, with an overall robust correlation between methane oxidation and suspended particulate matter across all streams (P < 0.001, Figure S5 in Supporting Information S1). Rates of methane oxidation normalized to suspended particulate matter (in nmol mg −1 h −1 ) were 0.98 ± 0.44, on average, and highest for Greensand streams (1.38-2.52) and lowest for the Chalk River Wylye (0.19). For the clay streams, methane oxidation activity was in between, although at the lower end (0.37-0.45). Concentrations of CH 4 , normalized to suspended particulate matter, ranged from 3.82 to 53.64 nmol mg −1 , with no clear trend across geologies. Turnover of CH 4 in the water column via biological methane oxidation, quantified as R kCH4 , ranged from <0.01 to 0.22 hr −1 and was 0.04 ± 0.01 (0.01) (mean ± standard error (median)), on average (Figure 4d). In contrast, turnover of CH 4 driven by gas transfer out of the streams (K CH4 ) and flow driven dilution (K flow ), were both substantially higher at 0.26 ± 0.02 (0.25) and 3.98 ± 0.57 (4.00) h −1 , respectively (Figure 4d).

Mean Benthic CH 4 Fluxes
The model was run with the mean benthic CH 4 fluxes from our logarithmic transformation and clustering approach. Mean estimates for average night and day fluxes (in μmol m −2 h −1 ) were highest for the vegetated patches (night 58.78 and day 19.51) and lower, but still elevated, for the sandy patches (18.49 and 7.43) and for the clay Figure 3. Sediment methane sources. In situ rates of CH 4 release from streambeds were greater in the dark (n = 140) than in the light (n = 141) and were also significantly different between the dominant streambed patch-types (gravel, sand, vegetated. n = 39, 72, 55, respectively). Note that the different patch-types were only a characteristic of the sand and Chalk-gravel streambeds and were not measured in the clay (n = 107). See Figures S4 and S8 in Supporting Information S1 and Table S3 in Supporting Information S1 for statistical analysis. streambed (8.18 and 4.32), respectively. For the gravel patch type, fluxes were strongly reduced at night (average 0.04) and turned negative, that is becoming sinks for CH 4 during the day (average −0.25).

Modeled Reaches
Our model was applied to three of the reaches, representing the Chalk (River Wylye), Greensand (River Nadder) and clay (River Sem) during the summer. These sites were selected because they have been more extensively investigated with regards to O 2 fluxes (see Rovelli et al., 2017) which are used here to drive in-stream CO 2 dynamics. The model was run until day and night CO 2 and CH 4 concentrations reached steady-state and constant outgassing rates were achieved, which is illustrated in Figure 5b for the River Wylye. Overall, the model was able to reproduce the magnitude of observed CO 2 and CH 4 night outgassing rates at all three sites (Figure 5c). In terms of actual deviation from the observed day and night difference in outgassing, the model matched the dynamics in the Chalk and clay reaches (<3% deviation), but was found to underestimate diel outgassing in the Greensand reach by 20% (Figure 5d). In contrast, for CH 4 , the Greensand model showed good agreement with the observations with only 4% deviation. On the Chalk, the model could not initially reproduce the observed diel trends when contributions from the vegetated patches were scaled to their spatial coverage (51.5% of the reach), but was found to match the observations when a smaller fraction of this area (25%) was considered as a hotspot for CH 4 release. For the clay site, the model suggested a 4% difference between day and night outgassing of CH 4 Figure 4. Contrasting diel changes in CO 2 and CH 4 outgassing. Outgassing of CO 2 was 30% greater at night than during the day (a), but consistent throughout for CH 4 (b). Each point in (a and b) is the average rate (in mmol m −2 h −1 ± standard error) derived from three to four days of continuous measurements in each of the six streams in spring, 2015, with typically 230 flux estimates for each stream (see Figure S3 in Supporting Information S1; Rovelli et al. (2021a)). The black lines in (a and b), give the overall gradient and the gray line a 1:1 relationship. Note that the linear regressions were performed using the reciprocal of the standard error as weighting, to give robust average outgassing rates, with small standard errors more weight over those with larger standard errors. (c) the difference (Δ) between night and day outgassing rates for CO 2 (a) could partly be explained by reach-scale gross primary production (GPP w , in mmol m −2 h −1 ) in each stream (see Methods; Rovelli et al., 2017Rovelli et al., , 2018. (d) In contrast, the potential for biology to reduce CH 4 concentrations in the water column (methane oxidation on suspended particulate matter, Rk CH4 ) before being either outgassed (here as a reaeration constant, K CH4 ) or diluted by the flow (K flow ) was negligible.

10.1029/2021JG006328
13 of 19 which was at odds with the observed 21%. Due to the disproportionally high standard error around the measured nighttime outgassing rate, this 21% difference was found to be not significant.
Modeling showed that, within the observed range of discharge, diel differences in CO 2 outgassing varied by up to 17% during the extremes of low flow and high flow (Table S4 in Supporting Information S1). Discharge, however, had a weaker effect (∼6% offset) on CH 4 than CO 2 at all sites. Temperature changes, exemplified by a 10% shift in mean temperature toward both lower nighttime and higher daytime averages, were found to change modeled outgassing for both gases by 6%-9%. Changing the respiratory quotient from 0.8:1 to 1.2:1 (O 2 :CO 2 equivalents), had only a minor effect (<7%). Small changes in suspended particulate matter (10%-20%) also had very little effect (<1%) on modeled CH 4 outgassing, while peak (seasonal or annual) suspended particulate matter concentrations drove changes comparable in magnitude to those associated with changes in discharge. For the more turbid water of the clay and Greensand sites (River Sem and Nadder respectively) we also found that, under low flows, concentrations of suspended particulate matter ∼240 mg L −1 , well below peak values, could potentially drive methane oxidation rates comparable in magnitude to the overall outgassing and effectively reducing daytime outgassing to 0 (Table S4 in Supporting Information S1). Values of k showed reduced variability across all three modeled reaches, increasing by about 50% between low discharge and high discharge conditions. When decoupled from discharge, such changes drove increases or decreases in outgassing that were on average 14%-16%, for CH 4 and CO 2 across the sites. As the magnitude of both day and night outgassing are proportionally affected, the initial day-to-night ratio remained unchanged (Table S4 in Supporting Information S1).

Figure 5.
Simple reach-scale mass-balance modeling of diel changes in CO 2 and CH 4 . (a) Changes in water column CO 2 and CH 4 are products of benthic uptake or release (F streambed ); activity in the water column (F water column ), e.g., oxidation for CH 4 and net ecosystem metabolism (NEM) for CO 2 ; outgassing at the stream surface (F outgassing ); transport from upstream (F in ); and advective transport downstream (F out ). (b) Example of development of new steady-state concentrations for CO 2 and CH 4 after the switch from day to night for the Chalk River Wylye. Background is the initial (t = 0) concentration in the water column (C background ), which is assumed equal to the concentration in water transported from upstream (C upstream ). (c) Modeled night outgassing rates versus observed mean outgassing rates during our high-resolution 2015 field campaign at the River Wylye (Chalk; green circles), Nadder (Greensand; blue squares) and Sem (clay; red triangles) for CO 2 (filled symbols) and CH 4 (open symbols). (d) The resultant change in rate of day to night outgassing, in percentage, for each gas based on (c).

In-Stream Contributions to Seasonal Outgassing
The combined data set from our array of flux measurement techniques revealed a marked difference in the magnitude of CO 2 and CH 4 outgassing compared to what could be accounted for by in-stream metabolism (Figure 2, Table 1). Given that our flux techniques integrate contrasting footprint areas, from patch-scale to km-long stream stretches, these results must be considered within a spatial context, in term of representativeness of in-stream dynamics. In Rovelli et al. (2018) we have shown for two of the investigated streams that benthic and wholestream metabolism from based on aquatic eddy covariance were representative enough of in-stream dynamics to be combined with km-long assessments of O 2 water-air gas exchange (single station approach) to close the local O 2 budget regardless of their spatial differences. As the same considerations for site selections was applied to each site, here and in Rovelli et al. (2017Rovelli et al. ( , 2018, one could reasonably assume that in-stream dynamics were adequately represented within those measurements. Outgassing of CO 2 was strongly proportional to stream discharge ( Figure 2b) indicating that catchment processes in the form of groundwater and soil water inputs are an important overall controlling factor (Butman & Raymond, 2011;Marx et al., 2017). The relative contributions of each input have not been quantified in this study but soil-derived CO 2 inputs from shallow lateral subsurface flows are likely to be relatively more important at the clay sites compared to the groundwater-fed streams on the Chalk and Greensand. Given the high proportion of groundwater-derived baseflow throughout the year in the Chalk sites (90%, exemplified in Figure S1c of Supporting Information S1) it seems likely that, for these streams, CO 2 derived from deeper groundwater sources dominate inputs. The lack of a similar relationship for CH 4 outgassing suggests other factors contribute, including local streambed sources of CH 4 , that we know have a high potential to produce CH 4 (Bodmer et al., 2020;Romeijn et al., 2019;Sanders et al., 2007;Schindler & Krabbenhoft, 1998;Shelley et al., 2015) . Further inputs might arise also from proportional changes in the upstream contributions of CH 4 in different flow pathways (e.g., under baseflow and quickflow). Although CO 2 outgassing could be predicted much better by discharge than by net benthic metabolism, all the streambeds were typically net heterotrophic (with the exception, in spring, of the Ebble on the Chalk and the Nadder on the Greensand), acting as sources of both CO 2 and CH 4 to the streams (Figure 2). In spring and summer, half the reaches acted as CO 2 sinks (negative net whole-stream metabolism), illustrating the important control that photosynthetic activity exerts on carbon dynamics in these lowland, headwater streams ( Figure 2, Table 1). During autumn and winter, net whole-stream metabolism was positive, but still more than 80% of the CO 2 outgassing was attributable to transport in from the catchment. Thus, even though overall the streambeds act as CO 2 sources (yearly median 0.57 mmol m −2 d −1 ), the majority of CO 2 appears catchment-derived (see Hotchkiss et al., 2015), but seasonal dynamics in CO 2 outgassing are modulated by in-stream metabolism.

Modulation of Outgassing From Catchment Geology
In addition to the broad, overall patterns in CO 2 outgassing and discharge, i.e., averages across all six streams in Figure 2, there was also variation in sources and sinks in relation to underlying catchment geology. Elsewhere, we have shown that dynamics in net whole-stream metabolism were distinctive across these geologies, with clay reaches largely representing biological sources of CO 2 , Chalk reaches typically representing CO 2 sinks, and the Greensand shifting from sinks for CO 2 in spring, to sources throughout the rest of the year (Rovelli et al., 2017). On the clay, we found that a large portion of CO 2 outgassing in spring could be accounted by the net benthic metabolism, while in summer, the totality of outgassed CO 2 could be attributed to streambed metabolism. In contrast, streambed metabolism on the Chalk and Greensand could only account for up to 13% of the total outgassing (Table 1), indicating that while carbonate-rich groundwater inputs are significant sources of CO 2 to groundwater-fed streams on Chalk and Greensand (Gallois & Owen, 2018), such contribution is minimal in impermeable clay streams.

Diel Dynamics
Our high-temporal-resolution measurements (spring 2015) showed a clear decrease in CO 2 outgassing during the day across all streams. Such a diel pattern is consistent with the modulation of CO 2 concentration from instream metabolism (i.e., streambed, water column and riparian zone) which offsets CO 2 concentrations toward higher values via respiration at night and toward lower values via net primary production during the day (Herreid et al., 2020;Hotchkiss et al., 2015;Lynch et al., 2010;Rocher-Ros et al., 2020). Our mean CO 2 outgassing rates were consistent with those reported by Attermeyer et al. (2021) for a collection of 34 European rivers (median up to 25.6 mmol m −2 h −1 ) including 13 headwaters (stream order 1-3; median up to 20.5 mmol m −2 h −1 ), where drifting flux chambers were used on a seasonal basis. Our results are also in line with their overall reported increase of 39% and 24% between midday and nighttime CO 2 outgassing (all seasons combined and summertime only respectively). Comparable findings were also reported from empirical models (e.g., Gómez-Gener et al., 2021), where the authors reported an overall 27% diel difference in outgassing based on long-term monitoring of over 66 streams worldwide.
For CH 4 , the magnitude of our chamber-based estimates of outgassing are representative of the global averages for headwaters presented by Stanley et al. (2016) based on a large (n = 205) database of headwater streams, which includes estimates for other lowland headwaters in temperate climates (e.g., Hlaváčová et al., 2006). In contrast to our observations for CO 2 , diel CH 4 outgassing remained constant ( Figure 4) and was thus at odds with the approximate doubling of CH 4 released from the sediments between dark and light chambers (Figure 3). This suggests that before being outgassed through re-aeration, CH 4 released from strong sources such as vegetated sediments could: (a) be diluted within the water column by water with a lower concentration of CH 4 (immediate surroundings and upstream); and/or (b) be oxidized in the water column, especially in the more turbid streams on the clay and Greensand (Rovelli et al., 2017;Sawakuchi et al., 2016). We tested these hypotheses by comparing the turnover time for CH 4 in the stream associated with outgassing (K CH4 ), with turnover due to methane oxidation in the water column (Rk CH4 ) and flow-driven dilution (K flow ). A ratio of Rk CH4 to K CH4 higher than 1, for example, would indicate that methane oxidation plays a major role modulating CH 4 concentration changes in the water column. As shown in Figure 5, however, the potential for CH 4 to be removed by methane oxidation in the water column is trivial compared to outgassing through re-aeration. Here the ratio was consistently <0.2 (median) and would only approach 1 when suspended particulate matter concentrations exceed 300-400 mg L −1 , which only occurred during brief periods of intense rainfall during our study (see Figures S1 and S5 in Supporting Information S1). The influence of methane oxidation in the water column would be even lower for CH 4 transported rapidly through the water column by ebullition (McGinnis et al., 2016). In this study, our analysis of the high-resolution outgassing data set showed very little evidence of ebullition events, and their effect on the overall outgassing rates was found to be minimal ( Figure S9 in Supporting Information S1). The likely reason for this is that porewater CH 4 concentrations in our streambed sediments were just too low for widespread development of CH 4 bubbles in the sediment (median CH 4 concentrations = 0.718 μmol L −1 , Figure 1e, in our streambeds c.f. 1000s μmol L −1 CH 4 reported by McGinnis et al. (2016) for a stream where ebullition was identified as the main driver of CH 4 outgassing). In the absence of strong ebullition, the turnover of CH 4 in the water column will likely be determined by the interplay of K CH4 and K flow . Across sites, the ratio of K flow to K CH4 was, on average, 15 to 1, indicating that dilution by stream flow likely impresses the dominant control on in-stream CH 4 concentrations and their temporal variability.
To further rationalize the differences that we observed between the day and night outgassing rates for CH 4 and CO 2 , we applied our mass-balance model to three reaches, ranging from a fast-flowing highly productive clear-water stream on the Chalk (River Wylye) to a slow-flowing turbid stream on the clay (River Sem), with the River Nadder on the Greensand representing an intermediate system. On the Chalk, despite large CO 2 import from the groundwater-fed catchment and enhanced dilution from high flow, we expected in-stream metabolism (i.e., net benthic and whole-stream metabolism) to exert a clear modulation on diel variability in CO 2 outgassing. On the Clay, conversely, we expected to have the best chance of detecting diel changes in CH 4 outgassing, as here we observed strong streambed CH 4 release in combination with the highest ratio of Rk CH4 to K flow of all sites.
Despite the recognized simplicity of our model (see Methods), we were mostly able to reproduce the contrasting diel patterns that we observed for CO 2 and CH 4 in the field (Figures 5c and 5d), thus further validating the representativeness of our assessment of in-stream metabolism. For CO 2 , the largest deviation from the observed outgassing rates was found on the Greensand; likely a result of under-representation of the heterogeneity of the sand patch type. Whilst the majority of CO 2 in the stream water is transported in from the catchment (Butman & Raymond, 2011;Hotchkiss et al., 2015), primary production, and respiration at the reach scale during the summer months, significantly split the resulting CO 2 outgassing between night and day (Figures 4 and 5). Later in the year, in autumn and/or winter, these streams turn into biological sources of CO 2 , i.e., positive net whole-stream metabolism (see Rovelli et al., 2017) likely making decreases in daytime CO 2 concentration from gross primary production less pronounced, thus dampening the overall diel CO 2 dynamics.
In contrast, CH 4 present in the stream water is predominantly produced in the streambed, with the magnitude of production depending on sediment type (Jones & Mulholland, 1998a;Shelley et al., 2015) (Figure 3a). Release of CH 4 from a streambed can be less during the day, most likely due to diel changes in microphytobenthic O 2 production on the immediate streambed (Fenchel & Glud, 2000) and deeper hyporheic, temperature-modulated microbial metabolism (e.g., Mächler et al., 2013). The main challenge when quantifying CH 4 benthic release at the reach scale remains the integration of the contributions from hotspots, for example fine sediment accumulated under vegetation (see Sanders et al., 2007). Such hotspots (such as Ranunculus patches in Chalk rivers) are heterogeneous in terms of both sediment depth and areal extent, and change in shape and volume with the seasonal growth and die-back of vegetation (Cotton et al., 2006;Sanders et al., 2007). On the Chalk River Wylye, we found that only 25% of the contributions from the observed vegetated patch area were needed to provide a good model fit to our observational data, with higher percentage contributions resulting in an over-estimate of reach-scale benthic CH 4 release. This suggests that these fine-sediment patches might be more heterogeneous in terms of CH 4 release than we were able to resolve with our patch-scale measurements.
In general, we found that once released into the water column, the overall sediment CH 4 signal is diluted and dispersed by stream flow, rather than by biologically mediated methane oxidation in the water column; and the resulting space and time integrated CH 4 outgassing rates to the atmosphere remain comparatively constant between day and night (Figures 4 and 5). It should also be noted that the highest R KCH4 values, driven by the highest methane oxidation activity, occurred during periods of intense rainfall, when suspended particulate matter concentrations were high and discharge elevated above baseflow. As a result, K flow and likely K CH4 would both be enhanced, with the overall effect of methane oxidation on CH 4 dynamics being even further dampened, as shown by our model (see Table S4 in Supporting Information S1). In contrast, regions of reduced flows within a stream (e.g., pools and marginal regions) or periods of strongly reduced flow (e.g., during summertime droughts) would enhance R KCH4 locally and thus increase the importance of methane oxidation to water column CH 4 dynamics. In terms of emissions, however, such conditions would also reduce re-aeration (K CH4 ), and the concentration of CH 4 in the water column, thus strongly limiting the overall outgassing of CH 4 from the reach, as illustrated in our model for the more turbid streams (clay and Greensand, Table S4 in Supporting Information S1).

Conclusions
Here we have characterized distinct biophysical controls on the final outgassing of CO 2 and CH 4 from headwater streams in lowland catchments. Outgassed CO 2 is principally controlled by hydrology-tempered by season and whole stream metabolism-stressing the importance of the connection between terrestrial and freshwater ecosystems with regard to carbon cycling. In contrast, outgassed CH 4 is principally stream borne and, once released from sediment, that CH 4 passes relatively unimpeded by biology in the water column, with dilution largely governing the final integrated magnitude of CH 4 outgassing. Our observations have characterized distinct biophysical controls on the two carbon gases and incorporating the intense carbon cycling of headwater streams into the global carbon cycle will require distinct parameterizations for each carbon gas in Earth system models.

Data Availability Statement
Data presented in this work are available from NERC Environmental Information Data Centre.