Exchange rates of gases over the air–water interface in rivers, streams, reservoirs, lakes, and estuaries are key parameters for estimating a number of important ecosystem variables (Cole et al., 2010). Gas exchange rates are used to estimate metabolism of aquatic systems (Hanson et al., 2004; Van de Bogert et al., 2007, 2012), emission of greenhouse gases like CO2 and CH4 to the atmosphere (Cole et al., 2010), and the role of inland and near-shore waters in regional (Billett and Moore, 2008) and global (Cole et al., 2007; Bastviken et al., 2011) carbon cycling. As a result, over several decades, a tremendous effort among aquatic scientists has focused on understanding and quantifying gas exchange processes at the air–water interface and their controls under naturally occurring field conditions (Whitman, 1923; Butman and Raymond, 2011; Raymond et al., 2013).

Multiple state variables and complex physical processes on both sides of the air–water interface control gas exchange (MacIntyre et al., 1995, 2010). Despite this complexity, the widely used expression for gas exchange rates was formulated based on a conceptually simple model assuming that gas is transported by molecular diffusion across intact boundary layers, or thin films, found on each side of the interface (Whitman, 1923; Liss and Slater, 1974): Jair–water=kCwater-Cair, where Jair–water is the exchange rate, or vertical flux, of the gas (positive upward), Cwater is the gas bulk concentration below the film on the water side, Cair is the concentration above the film on the air side, and k is the gas exchange coefficient, often also referred to as the “gas transfer velocity” or “piston velocity”. For most gases, Cwater and Cair are straight forward to measure with modern sensors (Koopmans and Berg, 2015; Fritzsche et al., 2017), or calculate from known functions, but the complexity of gas exchange and its many controlling variables is contained in k (MacIntyre et al., 1995; McKenna and McGillis, 2004; Cole et al., 2010).

For sparingly soluble gases such as O2, CO2, and CH4, the ratio between the molecular diffusivity in air and water is on the order of 104. Consequently, the resistance to gas diffusion is associated with the film on the water side, even if a substantially thicker film is found on the air-side of the air–water interface. This means that in the case of O2, Cair is simply the saturation concentration of O2 in water, which is a well-described function of the water temperature and salinity (Garcia and Gordon, 1992) and the atmospheric pressure.

Turbulence, or turbulent-like motions, that affects or controls the thickness of the film on the water side, and thus the diffusive resistance to gas transport, can be driven by conditions both below and above the air–water interface. In shallow streams and rivers, this turbulence is typically generated by the water flow over an uneven or rough bottom. Substantial heat loss from the water can similarly result in density-driven water motion that erodes the film (Bannerjee and MacIntyre, 2004). On the contrary, in reservoirs, lakes, and estuaries, the turbulence on the water side of the interface is typically generated by wind, which makes wind speed the dominant controlling variable for k for such systems (Marino and Howarth, 1993). Despite the fact that typical conditions such as rough weather, surface waves, and rain can rupture the film on the water side, the simple expression for gas exchange (Eq. 1) is still applied with k values that are adjusted accordingly (Watson et al., 1991). Keeping these multivariable, highly dynamic, and complex controls in mind, it is evident that determination of representative k values for specific sites is a challenging task.

A number of approaches have been used to study and determine values for k. For smaller rivers and streams, they include targeted parallel up- and across-stream additions of volatile tracers (e.g., propane) and hydrologic tracers (e.g., dissolved chloride), where the latter is added to correct for dilution of propane due to hyporheic mixing (Genereux and Hemond, 1992; Koopmans and Berg, 2015). A common approach for smaller reservoirs and lakes relies on additions of inert tracers, e.g., SF6 (Wanninkhof, 1985; Cole et al., 2010), whereas floating chambers are often deployed in larger rivers, reservoirs, lakes, and estuaries (Marino and Howarth, 1993). In a limited number of studies of large reservoirs and lakes, tower-mounted atmospheric eddy covariance systems have been used to measure air–water exchange, and from that, k values were derived (Anderson et al., 1999; Jonsson et al., 2008; Mammarella et al., 2015). Partly motivated by the substantial and often methodologically challenging effort required to measure k at specific sites with any of these approaches, many studies have simply relied on general empirical correlations for k produced by fitting k values measured for other similar aquatic systems (Raymond and Cole, 2001; Borges et al., 2004; Cole et al., 2010). With the exception of atmospheric eddy covariance measurements, none of these approaches represent a direct way of determining k values because they rely on assumptions that often are difficult to assess, or simply not fulfilled. As a result, gas exchange is viewed among aquatic scientists as the primary source of uncertainty in many standard estimates for aquatic systems such as gross primary production, respiration, and net ecosystem metabolism (Wanninkhof et al., 1990; Raymond and Cole, 2001; Raymond et al., 2012).

The aquatic eddy covariance technique for O2 flux measurements under undisturbed in situ conditions was originally developed for the benthic environment (Berg et al., 2003). The approach has several significant advantages over other flux methods, including its non-invasive nature (Lorrai et al., 2010), high temporal resolution (Rheuban and Berg, 2013), and its ability to integrate over a large benthic surface (Berg et al., 2007). As a result, it has been used to measure whole-system fluxes for substrates such as river bottoms (Lorke et al., 2012; Berg et al., 2013), seagrass meadows (Hume et al., 2011; Rheuban et al., 2014), and coral reefs (Long et al., 2013; Rovelli et al., 2015).

Here, we applied the aquatic eddy covariance technique “upside down” right below the air–water interface to measure O2 fluxes. From these fluxes, we derived exchange coefficients for O2, and then standard gas exchange coefficients (k600). All measurements were done from a floating platform, and because we used a newly developed fast-responding dual O2–temperature sensor (Berg et al., 2016), we were able to derive parallel fluxes of O2 and thermal energy, or sensible heat. We conducted proof-of-concept tests that were up to 40 h long at three river sites.

All measurements were made from a 1.2 m × 0.9 m floating platform with a catamaran-shaped hull (Fig. 1) that was kept at a fixed position at the river sites by two upstream anchors. The modular design and the catamaran-shaped hull allow the platform to be collapsed for storage and easy shipment in a standard sturdy polymer case (Pelican Products, USA).

The 3-D velocity field was measured with an acoustic Doppler velocimeter (ADV) with a cabled sensor head (cabled Vector, Nortek AS, Norway). This type of ADV allowed the sensor head to be positioned facing upwards (Fig. 1) while recording the velocity field right below the air–water interface (typically ∼ 4 cm). This distance was determined from standard ADV output. Data were collected continuously at a rate of 64 Hz and represent water velocity values averaged over the ADV's cylindrical measuring volume (h ∼ 1.4 cm, Ø ∼ 1.4 cm) located 15.7 cm above the sensor head (Fig. 1).

The O2 concentration was measured with a new fast-responding dual O2–temperature sensor (RINKO EC, JFE Advantech, Japan) developed specifically for eddy covariance measurements (Berg et al., 2016). This sensor allows for deriving simultaneous fluxes of O2 and heat. It also allows instantaneous temperature correction of the O2 concentration. The sensor was designed to interface with our standard ADVs (Vector, Nortek AS, Norway) through a single cable supplying power to the sensor and also transmitting its two outputs, one for O2 and one for temperature, to the ADV's data logger to be recorded along with velocities to ensure perfect time alignment of all data. The O2 measuring part of this new sensor is a small 6 mm diameter planar optode and concentrations are determined from fluorescence life-time measurements (Klimant et al., 1995; Holst et al., 1997, 1998). The tip of the sensor, which contains both the temperature thermistor and the O2 sensing foil, has a diameter of 8.0 mm, which makes it far more robust than O2 microsensors typically used for aquatic eddy covariance measurements. Yet because the sensor's tip is still only half the size of the ADV's measuring volume, it will not limit the eddy size that can be measured by the system. The sensor's response times (t90%) were measured to be 0.51 ± 0.01 s (SE, n=7) for O2 and 0.34 ± 0.01 s (SE, n=9) for temperature (Berg et al., 2016). The same response time for O2 was consistently found when the O2 sensing foil was replaced (an easy user performed operation typically needed after ∼ 10 days of continuous use). The edge of the sensor tip was positioned ∼ 2.0 cm downstream of the edge of the ADV's measuring volume so that water passed through this volume before sweeping over the angled O2 sensing tip (Fig. 1a). This setup ensured undisturbed measurements of the natural current flow. Power was supplied from an external battery (Fig. 1a) with a capacity that allowed 64 Hz data to be collected continuously for at least 48 h. Because all instrument components were designed for underwater use they were not affected by rain or humid conditions.

Measurement of supporting environmental variables during each deployment allowed verification of recorded data and assisted in the interpretation of the derived eddy fluxes. These variables included mean O2 concentration and temperature at the measuring depth recorded every 1 min with one or two stable independent dual O2–temperature sensors (miniDOT, PME, USA; referred to as the independent sensor below). In most deployments, photosynthetically active radiation (PAR) was recorded at the measuring depth every 5 min using an independent submersible PAR sensor (Odyssey, Dataflow Systems, New Zealand). For one deployment, light data were used from nearby meteorological weather stations.

The new approach for determining air–water gas exchange rates and associated exchange coefficients from underwater eddy covariance measurements was tested at three river sites, all in Virginia (US); one in the Hardware River, one in the Mechums River, and one in the Moormans River. All sites had a fairly linear run with a water depth between ∼ 0.3 and ∼ 1 m and smooth and quietly flowing water without standing riffles or waves. As a result of this, the two-point anchoring system, and the current's constant pull on the hull, the platform was stationary during measurements. Typical surface flow velocities ranged from 6 to 30 cm s-1. The ADV and the fast-responding O2–temperature sensor were adjusted to record data ∼ 4 cm below the air–water interface. Four deployments lasting up to 40 h were initiated on 22 November 2015 and 14 September 2016 in the Hardware River, on 21 December 2016 in the Mechums River, and on 18 January 2017 in the Moormans River. Using a level and by placing dive weights on the platform (Fig. 1b) care was taken to ensure that the platform was horizontal within the tolerance of the level to minimize post-processing rotations of the velocity field to correct for sensor tilt.

Fluxes of O2 were extracted from the raw eddy covariance data following the multi-step process briefly described below.

Using the two simultaneously measured outputs from the fast-responding dual O2–temperature sensor, one for O2 and one for temperature, the O2 concentration was calculated from the calibration equation provided by the manufacturer. Because this equation contains both outputs, this calculation includes instantaneous temperature correction of the O2 concentration evaluated in detail below. If needed, the O2 concentration was calibrated against the independent sensor data. All 64 Hz data were then reduced to 8 Hz data, which reduces noise while providing sufficient resolution to contain the full frequency spectrum carrying the detectable flux signal (Berg et al., 2009). This assumption was validated by comparing fluxes calculated from both 8 and 64 Hz data for a subset of the data.

O2 fluxes, one for each 15 min data segment, were extracted from the 8 Hz data using the software package EddyFlux version 3.1 (P. Berg, unpublished data). If needed, this software rotates the flow velocity field for each data segment to correct for any sensor tilt (Lee et al., 2004; Lorrai et al., 2010; Lorke et al., 2013) bringing the transverse and vertical mean velocities to zero. The vertical eddy flux was then calculated as (defined positive upward) Jeddy=w′C′‾, where the overbar symbolizes averaging over the 15 min data segment, and w′ and C′ are the fluctuating vertical velocity and the fluctuating O2 concentration, respectively. These fluctuating components were calculated as w-w‾ and C-C‾ where w and C are measured values (at 8 Hz), and w‾ and C‾ are mean values defined as least square linear fits to all w and C values within the 15 min time segment, a procedure usually referred to as linear de-trending (Lee et al., 2004; Berg et al., 2009).

Due to the response time of the dual O2–temperature sensor and its position downstream from the ADV's measuring volume, a time shift correction was applied. This was done by repeating the outlined flux calculation, while shifting the 8 Hz O2 concentration data back in time, 0.125 s (1/8 s) at a time, until the numerically largest flux was found.

Estimating the gas exchange coefficient requires the O2 flux over the air–water interface to be known. However, the eddy flux, Jeddy (Eq. 2), is measured ∼ 4 cm below the interface. By using the linear fit to the measured O2 concentrations in each 15 min data segment, defined as C‾ above, Jeddy is corrected for storage of O2 in the ∼ 4 cm column of water to give the flux at the air–water interface: Jeddy, air–water=Jeddy-∫0hdC‾dtdz, where h is the ∼ 4 cm tall water column, and the integral represents the change in time of O2 stored in this column. For further details on this flux extraction protocol included in EddyFlux version 3.1, see Lorrai et al. (2010), Hume et al. (2011), and Rheuban et al. (2014). For presentation, the 15 min fluxes were lumped in groups of four to give hourly values.

To examine the eddy frequencies that carried the flux signal, cumulative co-spectra of the O2 concentration and the vertical velocity were calculated for representative periods in each deployment using the software package Spectra version 1.2 (P. Berg, unpublished data). This software essentially performs the identical flux calculation in the frequency domain after fast Fourier transforming the de-trended data as EddyFlux does in the time domain. Both software packages rely on the same methods for de-trending and time shifting data.

Heat fluxes and associated co-spectra were extracted from the raw eddy covariance data following the same multi-step process.

The saturation concentration of O2 (Cair in Eq. 1) was calculated from Garcia and Gordon (1992) as a function of salinity (here 0 ‰) and surface water temperature measured with the fast-responding dual O2–temperature sensor ∼ 4 cm below the air–water interface and then corrected for actual atmospheric pressure (average sea-level pressure of 1013.25 mbar corrected for elevation). The water column O2 bulk concentration (Cwater in Eq. 1) was measured with the same sensor. By substituting Jair–water (Eq. 1) with the 15 min values for Jeddy, air–water (Eq. 3), a gas exchange coefficient for O2 was calculated from Eq. (1) and converted to the standard exchange coefficient, k600, for CO2 at 20 ∘C (Cole et al., 2010). For presentation, the 15 min k600 values were lumped in groups of four to give hourly values.

For a 40 h long deployment initiated on 18 January 2017 in the Moormans River, the 15 min mean current velocity (Fig. 2a) was relatively constant (averaging 20.5 cm s-1). The O2 concentration measured with the fast-responding dual O2–temperature sensor (Fig. 2b) agreed closely with the concentration recorded with the independent sensor and showed a distinct diurnal pattern. During most of the first night of the deployment, the O2 concentration increased linearly (h 19 to h 32), whereas a smaller and non-linear increase that tapered off was measured during the second night (h 45 to h 56). A diurnal pattern was also seen in the calculated O2 saturation concentration (Fig. 2b) reflecting variation in water temperature. The cumulative O2 flux (Fig. 2c), with each data segment covering a 15 min time interval, had clear linear trends indicating a strong eddy flux signal in the data. The hourly O2 flux (Fig. 2d), representing means of four successive 15 min flux estimates, also exhibited a clear diurnal pattern with a nighttime average uptake by the river of 16.4 mmol m-2 d-1 for the first night, 9.1 mmol m-2 d-1 for the second night, and an average daytime release of 11.1 mmol m-2 d-1. As observed for the O2 concentration (Fig. 2b), the hourly O2 flux differed during the two nighttime periods with a near-constant flux during the first night and a flux that tapered off during the second night. The hourly standard gas exchange coefficient (k600; Fig. 2e) derived from the 15 min O2 flux and the O2 concentration difference over the air–water interface (Fig. 2b) was almost constant over the first night of the deployment with an average of 3.9 m d-1. After that, k600 diminished almost 3-fold to a value of 1.4 m d-1 during the daytime. During the second night, k600 tapered off markedly from a level found for the first night to almost 0.89 m d-1 during the last 4 h of the deployment. This pattern was unexpected given the almost constant mean current velocity (Fig. 2a) and insignificant winds and the similar O2 concentration difference (Fig. 2b) for the two nighttime periods. The pattern suggests that gas exchange was controlled by at least one driver apart from the river current velocity or winds (see Discussion section below).

The parallel temperature data measured with the fast-responding dual O2–temperature sensor agreed perfectly with the temperature recorded with the independent sensor (Fig. 3b) and had, as with the O2 concentration, a distinct diurnal pattern. A near-linear decrease occurred during the first night (h 18 to h 32), whereas a smaller and non-linear decrease that tapered off was recorded during the second night (h 45 to h 56). During the daytime the temperature increased. Unfortunately, we do not have reliable on-site measurements of the air temperature, but we infer that it, together with short-wave (sunlight during day) and long-wave (nighttime) thermal radiation, controlled the recorded water temperature variations (Fig. 3b). The cumulative heat flux (Fig. 3c) had, as for O2, clear linear trends indicating a strong flux signal in the data. The hourly heat flux (Fig. 3d) also exhibited a clear diurnal pattern with a nighttime average release of heat of 60.6 W m-2 for the first night and 27.5 W m-2 for the second night. As was observed for the temperature (Fig. 3b), the hourly heat flux showed different trends for the two nights with a near-constant flux during the first night and a flux that tapered off during the second night.

Ignoring differences in the sign, representative cumulative co-spectra for the O2 and heat fluxes (Fig. 4) during the first night (Figs. 2, 3) were similar in the 0.1 to 1 Hz frequency band with all substantial flux contributions for both the O2 and heat fluxes having frequencies lower than ∼ 0.9 Hz.

Due to careful leveling of the platform prior to data collection (Fig. 1b), rotation of the velocity field to correct for sensor tilt was minimal with an average of only 1.3∘ from horizontal. This rotation had an insignificant effect on the flux calculation. The applied time shift averaged 1.3 and 1.2 s for the O2 and heat flux calculations, respectively, whereas the average storage correction (Eq. 3) amounted to 11 % for the O2 flux and 15 % for the heat flux.

The three other test deployments were shorter than the one presented in Figs. 2 and 3 but results were of comparable quality. Average values for selected parameters covering periods of time with several successive 15 min time intervals from all four deployments are given in Table 1. These periods were identified by containing consecutive time intervals with consistent standard gas exchange coefficient values, k600, that had little variation and appeared to represent a particular field condition. The longest period (n=51) covers the first full night of the deployment shown in Fig. 2 (h 19 to h 32). Overall, the average current velocity varied from 8.3 to 28.4 cm s-1 while k600 ranged from 0.4 to 5.1 m d-1, or more than a factor of 12.

There was no significant relationship (R=0.37, p=0.22) between river current velocity and k600 values (Fig. 5) for all of the data in Table 1. Substantial variations in k600 values were found for some individual deployments even though the current velocity did not change markedly. Most prominently in the Moormans River deployment (Figs. 2, 3), where the k600 values varied more than a factor of 5. As we discuss below, this suggest that, at least for some sites and under some field conditions, other drivers of air–water gas exchange than river flow and winds are more important.

In the benthic environment the vertical turbulent heat flux is usually small relative to the O2 flux due to slowly and modestly varying mean temperatures in the bottom water. At the air–water interface, however, the heat flux is typically larger due to substantial variations in air temperature and short- and long-wave thermal radiation, and the associated turbulent temperature fluctuations can represent a challenge in O2 flux measurements by eddy covariance.

All highly sensitive fast-responding O2 sensors that can be used for aquatic eddy covariance measurements are to the best of our knowledge inherently sensitive to temperature changes, and thus give variable O2 readings at the same molar O2 concentration if the temperature varies. Typical temperature coefficients (% change in O2 concentration reading caused by a temperature change of 1 ∘C) for Clark-type microelectrodes, the most common sensor type used for aquatic eddy covariance, have values of ∼ 3 % (Gundersen et al., 1998). Lab measurements in which the O2 concentration was held constant but temperature varied showed that the fast-responding dual O2–temperature sensor used in this study has a temperature coefficient of 2.9 % if temperature correction was omitted. This characteristic of fast-responding O2 sensors implies that rapid temperature fluctuations associated with any turbulent heat flux will mistakenly be recorded as fluctuations in O2 concentration and bias the O2 flux calculation unless an instantaneous temperature correction of the signal is performed. In this study, this correction was done using the fast-responding dual O2–temperature sensor's temperature reading from within a few millimeters of the O2 sensing foil. Below, we exemplify the nature and magnitude of this potential bias using data measured during the first night (h 18 to h 32) of the deployment shown in Figs. 2 and 3.

The turbulent temperature fluctuations for a 3 min period shown in Fig. 6a are associated with a vertical heat flux of ∼ 60 W m-2 (Fig. 3d) and amount to ± ∼ 0.015 ∘C. Based on a temperature coefficient of ∼ 3 %, this translates into fluctuations in O2 concentration readings of ± ∼ 0.2 µmol L-1 (Fig. 6a; right axis). Using such “simulated” O2 data, derived from the 8 Hz nighttime temperature data (Fig. 3; h 18 to h 32), representing solely temperature sensitivity effects and no true O2 reading, produced an O2 release, or flux bias, of 11.9 mmol m-2 d-1 (blue bar; Fig. 6b). Using the instantaneous temperature corrected O2 data, as was done for all other calculations we present, gives an oppositely directed O2 uptake of 16.9 mmol m-2 d-1 (red bar; Fig. 6b). Using the sensor's O2 readings, but without the instantaneous temperature correction, gives an update of only 4.4 mmol m-2 d-1 (green bar; Fig. 6b).

The magnitude of this O2 flux bias, if temperature correction is omitted, scales with the heat flux and is proportional to the O2 sensor's temperature coefficient and the actual O2 concentration. Given the millimeter-close proximity of the temperature thermistor and the O2 sensing foil, and the relatively small difference between the fast-responding dual O2–temperature sensor's response times (0.51 for O2 and 0.34 s for temperature; Berg et al., 2016), we conclude that the effects of temperature sensitivity were removed from our O2 flux calculations. This point is supported by the high-frequency end (∼ 0.9 Hz) of the co-spectra for the O2 and heat fluxes (Fig. 4).