We calculate the gas transfer velocity using the dual tracer approach . For each experiment, we dissolved a mixture of 3He and SF6 in the water, both of which are normally present at very low ambient concentrations, and then measured the change in the ratio of the two gases as a function of time. Measuring two tracers enables correction for dilution and mixing, which reduces the excess concentrations of both gases (relative to air–water equilibrium) but does not change their ratio. Over time, the concentrations of both gases decay toward air–water equilibrium as gas is ventilated to the atmosphere through gas exchange. Because the molecular diffusivity of 3He is 8–9 times higher than SF6, 3He is lost to the atmosphere more rapidly than SF6, and therefore the 3He:SF6 ratio decreases with time. The ratio of the gas transfer velocity for the two gases is expressed as 1k3HekSF6=Sc3HeScSF6-n, where k is the gas transfer velocity (m d-1) and Sc is the Schmidt number (unitless), defined as the kinematic viscosity of water divided by the molecular diffusivity of the gas in water, and n is an empirical exponent, typically between 0.5 and 0.67 . Using a time series of measurements of the two gases, the gas transfer velocity for 3He is calculated as 2k3He=hddtln⁡3Heexc/SF6exc1-ScSF6/Sc3He-n. Here h is the mixed layer depth, [3He]exc=[3He]meas-[3He]eq where [3He]exc is the 3He-excess concentration, [3He]meas is the measured concentration, and [3He]eq is the equilibrium concentration (calculated as a function of temperature and salinity). [SF6]exc is defined analogously.

We can write the analytical solution to Eq. () as 3[3He]exc[SF6]exct=[3He]exc[SF6]exct-1exp⁡-k3HeΔth1-ScSF6Sc3He-n. Using this equation and a cost function, we can find the value of k3He that minimizes the error between the measured and modeled [3He]exc/[SF6]exc. Once k3He is known, we can calculate k for any other gas using Eq. () by substituting ScSF6 for the Schmidt number of the gas of interest. For example, for Sc=600 (the Schmidt number for CO2 at 20 ∘C in freshwater), 4k600=k3He600Sc3He-n. For this study, we use a Schmidt number dependence of n=0.5 which is appropriate for wavy, unbroken water surfaces (no bubble entrainment) . At Little Narrows, we observed that tidal currents generated surface waves, even at low wind speeds. These waves produce near-surface water turbulence which is the ultimate driver of air–water gas exchange .

The Schmidt number at a salinity of 4 PSS and temperature of 2 ∘C is 305 for 3He and 2684 for SF6. The initial ScSF6/Sc3He ratio was 8.7 for Injection 1 and 8.2 for Injection 2.

The gas transfer velocity was much lower for Injection 1, which was sampled while the basin was essentially full of ice (31 March–10 April), compared to Injection 2, which was sampled when the basin was nearly ice-free (20–23 April). We used Eq. () to model the measurements. We started the model at the time of the first measurement, initialized it with an initial excess concentration ratio and ran it through time for the duration of the injection. We selected the value of k3He yielding the smallest root mean square deviation (RMSD) between the measured ratio and modeled ratio for each injection. The model ran 1000 times using a Monte Carlo simulation where the measured excess concentration ratios, including the initial condition, are varied with a Gaussian distribution, with the standard deviation being the estimated measurement error in the ratio (7.3 %).

We assume a constant Sc3He/ScSF6 and mixed layer depth (h) for each injection. In actuality, during each injection Sc3He varies by ∼1 % and the ratio of the Schmidt numbers varies by less than 0.2 %, so this is a small source of error. For Injection 1, we assume a mixed layer depth (h) of 0.8(0.3) m. This depth is consistent with the salinity profiles at Little Narrows (Fig. a) between 31 March and 8 April (between 0.6 and 1.0 m depth), as well as measurements with a hand-held temperature probe at the site of Injection 1 which indicated that the mixed layer depth was between 0.75 and 1 m. The mixed layer depth may have increased slightly between 8 and 10 April, but was likely 1.3 m or less (Fig. ).

For Injection 1, the excess SF6 and 3He concentrations were reduced by 2 orders of magnitude by the time the tracer reached Little Narrows (7–11 d after injection). The tracer ratio did not display a consistent decrease over the 3 days we sampled it at Little Narrows, which may be due to the substantially lower gas transfer velocity, as well as the very low tracer concentrations potentially increasing measurement uncertainty. The best fit to all the measurements was k600=0.0457(0.0051) m d-1, in the presence of ice and a shallow mixed layer, with the uncertainty the standard deviation of the distribution of k600 from the Monte Carlo simulation (Fig. ).

The mixed layer appeared to deepen between the CTD profiles on 8 April 16:08 UTC and 12 April 19:13 UTC (Fig. ), and it is possible that the mixed layer depth on 9–10 April may have been slightly deeper than the estimate of 0.8(0.3) m. However, if mixed layer deepening had a significant influence on our gas transfer velocity estimate, we would expect k600 (calculated assuming a constant mixed layer depth) to be lowest when calculated over the longest time period, using the sample collected on 10 April. Instead, the gas transfer velocity was actually the lowest when integrated to 9 April (the excess tracer ratio appears above the best-fit line) and second lowest on 8 April. Since the gas transfer velocities for Injection 1 integrate over 7–10 d, any change in mixed layer depth during the last 1–2 d will have a small effect on the calculated k.

For Injection 2, we use a mixed layer depth of 2.7(0.3) m based on CTD profiles at Little Narrows on 20 and 23 April, which had mixed layer depths of 2.4 and 3.0 m, respectively (Fig. a). Calculation of the gas transfer velocity for Injection 2 was relatively straightforward as the ratio of excess 3He/SF6 steadily decreased over the five measurements (Table ). The best fit to all four measurements was k600=0.71(0.13) m d-1 for open water (Fig. ).

Using the published He solubility from instead of the unpublished data of Dempsey E. Lott III and William J. Jenkins (personal communication, 2015) results in a gas transfer velocity that is 8 % lower in the presence of ice (for Injection 1) and 0.4 % lower in open water (for Injection 2).

The gas transfer velocity calculated for Injection 1 is the effective gas transfer velocity (keff); it averages the gas transfer velocity through ice (kice), weighted by the time the tracer spent under ice, and the gas transfer velocity for open water (k), weighted by the time the tracer spent in open water . In partially ice-covered waters, the effective gas transfer velocity is sometimes calculated as 5keff=(f)k+(1-f)kice, where f is the fraction of open water . If kice is negligible, then keff=(f)k . For Injection 2, we determined k, the value for open water. We expect kice to be lower than k because the ice acts as a physical barrier to gas exchange. The rate of gas molecular diffusion in water is higher than gas diffusion through ice . However, the exact rate of gas diffusion through saltwater ice (and by extension the value of kice) is not well constrained and likely varies based on the physical properties of the ice such as brine volume and temperature .

To evaluate these results within the framework of Eq. (), we must estimate the fractional ice cover during Injection 1. Visual surveys along the shoreline of Whycocomagh Bay and satellite data indicated that the bay was nearly fully covered with a continuous sheet of ice from 31 March to 10 April, except for an opening close to Little Narrows (Fig. a–b). Beginning between 7 and 12 April, a small region of water appeared to open up along the shoreline northwest of the site of Injection 1; however, by this time the tracer patch had moved eastward close to Little Narrows and likely was not significantly affected by this open water (Fig. c). We mapped out the location of the ice edge closest to Little Narrows by boat on 26 March and 7 and 12 April (Fig. a). Using these surveys and shoreline data, we calculate that for the surface area of the bay between the injection site and Little Narrows, f=0.01 on 26 March, 0.05 on 7 April, and 0.08 on 12 April. The f experienced by the tracer patch during Injection 1 is likely between 0.02 and 0.08 because the tracer was injected on 30–31 March and flowed through the open water near Little Narrows between 6 and 11 April. If k for open water is the same for both injections (k=0.71 m d-1), then the results yield keff=(f)k with f=0.064, which is consistent with the fraction of open water we estimate for Injection 1. Thus we conclude that kice was negligible, compared to k. For example, if kice was even 10 % of k for open water, then keff for Injection 1 would have been ∼0.11 m d-1, more than double the observed value of 0.0457(0.0051) m d-1. One source of uncertainty in estimating the correct value of f is that the transit speed between the injection site and Little Narrows was non-constant. The mean current velocity at Little Narrows channel was 3.4 km d-1, but the tracer took approximately 8 d to flow 7 km from the injection site to Little Narrows.

In calculating GOP and NOP by oxygen mass balance, we apply the tracer-based gas transfer velocities estimated by dual tracer release throughout the time series, since there is no consensus on the best treatment of gas transfer in lakes and estuaries , nor on the parameterization of gas transfer in the presence of ice . Additionally, if bottom-derived turbulence (e.g., from tidal flow) is a significant contributor to air–water gas exchange, a parameterization based on wind speed alone may not be appropriate. This method of calculating one average k600 for each injection does not enable the development of a wind speed-dependent parameterization for the gas transfer velocity.

Because the k600 values for Injection 1 and Injection 2 are very different, the treatment of the gas transfer velocity in between the two injections strongly affects the productivity estimates for this period. We use k600=0.0457(0.0051) m d-1 from the beginning of the time series until the end of 15 April. Figure d, collected on 16 April, is the first satellite image showing substantial open water within Whycocomagh Bay, but the open water is primarily in the western half of the bay, far from Little Narrows. We use k600=0.71(0.13) m d-1 from 21 April until the end of the time series on 28 April. Surveys by boat on 19 and 20 April indicated <10 % ice cover on these days, and we collected the first tracer measurements following Injection 2 on 20 April 23:30 UTC. Between 16 and 20 April, we apply a linear interpolation of the k600 for Injection 1 and Injection 2 as a function of time. The gas transfer velocity is most uncertain during the period when the ice cover rapidly decreased because we do not have any measurements of gas transfer at intermediate ice cover. However, because the ice cover retreated rapidly, only 4 days of the productivity estimates (out of a 33 d time series) are affected by the uncertainties in gas transfer at intermediate ice cover.

To compare the gas exchange estimates with other published studies, we use wind speed data measured at 10 m height (u10) at Eskasoni Reserve, 27 km northeast of Little Narrows (Fig. b) and archived by the Government of Canada (http://climate.weather.gc.ca, last access: 27 August 2019). The archived data are 2 min averages measured once per hour. During the period that samples with tracer from Injection 2 were collected (between 20 April 23:00 and 23 April 11:00), the average wind speed was 2.6(1.4) m s-1 and the median was 2.2 m s-1. The calculated k600 over this time period from dual tracer data is 0.71(0.13) m d-1. found k600=0.636(0.029) m d-1 (95 % confidence interval) and their estimate is independent of wind speed in a lake with daily wind speeds of 1.39(0.06) m s-1 (95 % confidence interval); this k600 is consistent within uncertainty with the Injection 2 result. Standard open ocean parameterizations that use a quadratic dependence on wind speed predict k600 ≃ 0.5–0.6 m d-1 with uncertainties of ∼20 % or ∼0.10 m d-1 .

found that in a lake gas exchange can be estimated nearly equally well using three different parameterizations. Using their parameterizations with the wind speed record during our time series, we calculate transfer velocities of 0.32–0.66 m d-1, and the velocity is most similar to our result when we use a constant gas transfer velocity k600=0.24 m d-1 for u10<3.7 m s-1 and k600=1.23u10-4.30 for u10≥3.7 m s-1. However, parameterized the gas transfer using instantaneous (e.g., 1 min averaged) winds measured throughout the time series, not once per hour, and emphasize the importance of including the variability in short-term winds when quantifying gas exchange at low wind speeds. If gas transfer velocity has a nonlinear dependence on wind speed, then short-term wind speed measurements will more accurately represent the gas transfer than wind speed values averaged over longer periods . Since we only have 2 min averages measured once per hour (for a total of 60 measurements during Injection 2), the wind record we use may not fully represent the variability in winds during the Injection 2 measurement period.

A source of error in comparisons with published results is that the wind speed data come from a different location than the study area. Although Eskasoni Reserve is adjacent to the Bras d'Or Lake, the local topography and bathymetry are different near the reserve and in Whycocomagh Bay. Thus, it is likely that the wind speed and momentum stress at the air–water interface differ at Whycocomagh Bay compared to Eskasoni Reserve .

The measurements are in agreement with other studies showing that gas transfer velocity is significantly reduced under near-complete ice cover and contrast with studies showing enhanced gas transfer under >85 % ice cover . We find that keff=(f)k for >90 % ice cover, but we cannot evaluate whether the same equation holds at intermediate ice cover because there was no injection at a lower fractional ice cover. In this study, the ice cover was near-continuous across the entire bay during Injection 1 and likely did not contain the ice leads that are common in Arctic and Antarctic sea ice; differences in gas transfer behaviour are expected based on the nature of the ice pack.

The triple oxygen isotopic composition of O2 is an effective tracer of gross photosynthetic O2 production . Due to reactions in the upper atmosphere that impart a small mass-independent isotopic signature on atmospheric oxygen, dissolved O2 derived from air–water exchange has a unique triple isotopic signature compared to O2 generated by photosynthesis and O2 consumed by respiration. We characterize the oxygen isotopic composition using 6δ18O=X18/Xstd18-1, and express the δ18O in ‰ by multiplying by 1000. Here X18=r(18O/16O) is the measured ratio and Xstd18=r(18O/16O)std is the ratio of the isotopes in the standard. We calculate δ17O analogously. For GOP studies, O2 in air is the standard for isotopic measurements of O2 and isotopes of H2O are referenced to the VSMOW-SLAP scale. For clarity, we distinguish between the isotopic composition of the two substrates (O2 and H2O) as δ18O-O2 and δ18O-H2O.

The term 17Δ quantifies the triple isotopic composition of dissolved O2: 717Δ=ln⁡(δ17O-O2+1)-λln⁡(δ18O-O2+1). We report 17Δ with λ=0.5179, the ratio of the fractionation factors for respiratory O2 consumption in 17O relative to 18O (i.e., λ=17ϵ/18ϵ, where ϵ is the isotopic fractionation of O2 due to respiratory consumption) . This value for λ is selected so that 17Δ is nearly unaffected by respiratory O2 consumption and reflects the proportion of O2 that is derived from photosynthesis relative to air–water gas exchange . We report 17Δ in per meg (1 per meg = 0.001 ‰) due to the small range of values in natural waters, typically 8–242 per meg .

Two key constraints in the calculation of GOP from measurements of the triple isotopic composition of O2 are the isotopic composition of O2 derived from air–water exchange and the isotopic composition of photosynthetic O2. The composition of photosynthetic O2 is dependent on the triple oxygen isotopic composition of H2O, the substrate for photosynthetic O2, and the isotopic fractionation associated with photosynthetic O2 production. In oceanic studies, a common assumption is that the H2O isotopic composition is equivalent to VSMOW (standard mean ocean water), but in brackish systems it is necessary to estimate the isotopic composition of water and incorporate this into the GOP calculation .

Because we did not measure the triple oxygen isotopic composition of H2O, we use previously published measurements of δ18O-H2O and published relationships between δ17O-H2O and δ18O-H2O to estimate the values of δ18O-H2O and δ17O-H2O during the time series, as described in . We assume that the waters in the estuary represent a mixture of two endmembers: seawater and meteoric (precipitation-derived). We define the salinity and δ18O-H2O for the two endmembers and then calculate δ18O-H2O for each water sample collected during the time series as a linear function of salinity. A similar approach is applied for δ17O-H2O.

For the seawater endmember, we use compilations of δ18O-H2O and salinity available from an online database . We included all 19 near-surface samples (<5 m depth) between 44–48∘ N and 58–64∘ W in the database. For these samples, the average δ18O-H2O = -1.68(0.26) ‰ and salinity = 31.25(0.30) PSS.

For the meteoric water endmember, we use an 8-year time series of δ18O-H2O measured in Truro, Nova Scotia (200 km southwest of our study area and at 40 m elevation), and archived in the Global Network of Isotopes in Precipitation (GNIP) database . The amount-weighted value of δ18O-H2O over the time series was -9.3(3.1) ‰ versus VSMOW, using precipitation measurements from Truro, NS, over the same time period from the Government of Canada historical weather database (http://climate.weather.gc.ca, last access: 27 August 2019). Also, measured δ18O-H2O = -8.8(0.1) ‰ on a water sample collected in July 2009 from the Skye River, within the Whycocomagh Bay watershed , consistent with the average Truro, NS, value.

Using the two endmembers, S=0 PSS, δ18O-H2O = -9.3 ‰ (local meteoric water) and S=31.25 PSS, δ18O-H2O = -1.68 ‰ (local seawater), we derive the equation δ18O-H2O = 0.2439S-9.30 (Fig. ). This equation is consistent with published δ18O-H2O measurements from within the estuary (Fig. ). collected water samples from the Bras d'Or Lake in November 1985 and found a salinity of S = 26.42 (1.12) PSS and δ18O = -2.99 (0.32) ‰ for samples at 17 different stations (albeit none within Whycocomagh Bay). Notably, VSMOW (S=34.5 PSS) plots 0.9 ‰ above the local mixing line, which demonstrates the importance of accurately defining both the freshwater and seawater endmembers.

Then, for the two endmember values of δ18O-H2O, we estimate δ17O-H2O using the following equation: 817O-excess=ln⁡δ17O-H2O+1-λwln⁡δ18O-H2O+1, with λw=0.528 and all isotopic compositions referenced to VSMOW-SLAP. Equations (7) and () have a similar form; however, researchers in the H2O isotope community have traditionally used the 17O-excess terminology, whereas researchers in the O2 isotope community have used the 17Δ notation . The value of λw=0.528 is well established for meteoric waters and seawater . Spatial variability in the 17O-excess of natural waters is less well understood due to the currently limited observations at sufficient accuracy to resolve the small excess . To calculate the freshwater and seawater endmembers for δ17O-H2O, we use the average values of 17O-excess of 33 per meg for meteoric water and -5 per meg for seawater . The endmembers are δ17O-H2O = -4.888 ‰ and -0.908 ‰ for meteoric water and seawater, respectively, and the linear regression is δ17O-H2O = 0.1274S-4.89. These δ values for H2O, referenced to VSMOW, are subsequently referenced to atmospheric O2 using results from . In this study, the choice of δ18O-H2O is more important than the 17O-excess because 17O-excess varies by less than 0.1 ‰ between samples, whereas the freshwater δ18O-H2O differs from VSMOW by 9.1 ‰. We discuss the sensitivity of the GOP calculations to the assumed 17O-excess and δ18O-H2O below, and the effect of other processes on the isotopic composition of H2O in Sect. .

We calculate GOP using Eq. (7) from , which is equivalent to Eq. (S8) from , 9GOP=kO2[O2]eqX17-Xeq17X17-λX18-Xeq18X18Xp17-X17X17-λXp18-X18X18+h[O2]∂17Δ∂tXp17-X17X17-λXp18-X18X18.

In this equation, kO2 is the gas transfer velocity for O2 (m d-1), [O2] is the O2 concentration (mol m-3), h is the mixed layer depth (m), X17=r(17O/16O), and λ=0.5179 (Eq. ). The subscripts eq and p refer to O2 at air–water equilibrium and produced by photosynthesis and terms without a subscript ([O2], X17, and 17Δ) are the measured mixed layer values. The first term on the right-hand side of Eq. () is the steady-state GOP term, and the second term is the non-steady-state GOP term. If the system is at steady state with respect to 17Δ (i.e., there is no change in 17Δ with time), then the second term on the right-hand side of Eq. () equals zero and can be eliminated.

This non-steady-state equation for GOP incorporates temporal variability in both O2 concentration and isotopic composition (see Eq. 5 in ). It does not account for time variability in mixed layer depth (e.g., entrainment of deeper waters into the mixed layer), nor does it account for vertical diffusion of O2 across the mixed layer. In order to account for vertical processes in the O2 mass balance, we would need to have triple oxygen isotope measurements below the mixed layer . Since we do not have these data, we cannot correct for vertical processes affecting the O2 budget.

We calculate Xeq18 based on and Xeq17 using 17Δeq=8 per meg , which is consistent with the daily measurements of distilled water equilibrated at room temperature that were analyzed along with the environmental samples (8.1 per meg with a standard error of 1.6 per meg, n=12), as well as prior measurements of distilled water equilibrated at <5 ∘C (Rachel H. R. Stanley, unpublished data). We calculate Xp18 and Xp17 using the salinity-dependent isotopic composition of H2O defined above and isotopic fractionation factors for photosynthetic O2 with respect to H2O based on data in for average phytoplankton (αp18=1.0033890 and αp17=1.0017781). The Matlab code used to calculate GOP and the triple oxygen isotopic composition of water (from two-endmember mixing of δ18O-H2O and salinity) is available online .

We calculate gross oxygen production using samples collected at Little Narrows from 25 March to 27 April (Fig. ). Visual inspection of the 17Δ data indicated that 17Δ changed during the time series, and therefore the calculation includes a non-steady-state GOP term. The non-steady-state term in Eq.  is h[O2]∂17Δ/∂t. To calculate the rate of change in 17Δ with time, we first averaged the data into 24 h bins (beginning and ending at 19:30, local sunset) to avoid over-weighting times when samples were collected at higher frequency. We calculated the average 17Δ and sampling time for all samples collected each day. Next, we separated the data into two periods: one period began on 25 March and ended 19 April 07:30, and the second period covered the remainder of the time series (ending 27 April). A linear regression of 17Δ versus time for the two time periods yielded a slope of 0.67 per meg d-1 (r2=0.47) for the first period and -2.99 per meg d-1 (r2 = 0.94) for the second period. The approximate timing for the change between periods was determined by visual inspection and then adjusted to maximize the r2 and so that the equations of the two lines gave very similar 17Δ values at 19 April 00:00 (within 1 per meg). Splitting the period from 25 March to 19 April into two separate regressions (or one period where 17Δ increased and one period where it was constant) yielded much lower r2 values and a discontinuous 17Δ record (different 17Δ values at the end of one period and the start of another), so a single regression was used for this period.

The other two variables in the non-steady-state GOP term are the mixed layer depth (h) and [O2]. We estimate [O2] as 10[O2]≃[O2]eqO2/ArO2/Areq. This estimate assumes that [Ar] = [Ar]eq. If [Ar] is, for example, 2 % supersaturated, then the estimated [O2] and non-steady-state GOP term will be 2 % too high .

Using Eq. (), GOP is estimated for each sample, using an isotopic composition for H2O based on the salinity of the sample, and a mixed layer depth, rate of change in 17Δ with time, and gas transfer velocity based on the sampling time (values shown in Fig. ), and then calculate the daily average GOP from all samples on a given day (beginning and ending at 19:30, local sunset). The mean number of samples per day was two, the maximum was four, and a few days had no measurements. The uncertainty in GOP on each day is calculated by propagating uncertainty in kO2 (11 % for Injection 1, 18 % for Injection 2), uncertainty in the mixed layer depth (from 10 % to 38 %, 0.3 m), uncertainty in the rate of change in 17Δ with time (22 % and 9 % where 17Δ is increasing and decreasing, respectively), and uncertainty in the photosynthetic endmember (discussed below). Measurement uncertainty in the isotopic composition of O2 is excluded from the error calculation because it is a random error, rather than a systematic error (meaning that by taking many measurements of 17Δ over several days, the measurements with high and low 17Δ will average out) and because the measurement error is smaller than most other sources of error. All uncertainties are expressed as the standard deviation.

The isotopic composition of H2O is one of the largest sources of error: if the 18O-H2O endmembers for meteoric water and local seawater are changed to the minimum values of -12.4 ‰ and -1.94 ‰ (1 standard deviation below the mean value) and then δ18O-H2O and δ17O-H2O are re-calculated for each sample, GOP is on average 48 % higher. If we shift the δ18O-H2O endmembers for meteoric water and local seawater to the maximum values of -6.2 ‰ and 1.42 ‰, respectively, GOP is on average 23 % lower. The calculated GOP increases nonlinearly as the isotopic composition of photosynthetic O2 becomes more different from the isotopic composition of equilibrated O2 . If the 17O-excess of H2O is increased or decreased by 20 per meg, GOP changes by an average of 10 %.

GOP calculated with the local isotopic composition of H2O is 46 %–97 % higher (mean 74 % higher) than GOP calculated assuming the water's isotopic composition is equivalent to VSMOW. Using the local isotopic composition of water instead of VSMOW is particularly important in this study because the system is not pure seawater. However, even in some oceanic regions such as the Arctic, the isotopic composition of H2O can be substantially different from VSMOW . The definition and importance of the photosynthetic endmember for GOP calculations in different environments warrant further review .

We calculate the mixed layer-integrated GOP (mmol O2 m-2 d-1) and the volumetric GOP (mmol O2 m-3 d-1), which is the mixed layer-integrated GOP divided by the mixed layer depth. For this time series GOP is only calculated for the mixed layer because there are no O2 measurements below the mixed layer. The average errors in the daily GOP are +77-49 % and +52-31 % for the volumetric and mixed layer-integrated GOP, respectively.

We do not present GOP estimates during the period where ice cover decreased most rapidly (16–19 April, grey shaded area in Fig. ) due to the large uncertainties in GOP at this time. We do not have an estimate of kO2 at intermediate or varying ice cover, nor do we have estimates of ice cover on 17 April or 19 April, because clouds obscured the satellite images on those days. Additionally, the exact timing of the change in the sign of the non-steady-state term is unclear. For example, on 18 April the calculated GOP assuming 17Δ is increasing at 0.67 per meg d-1 (the slope of the first best-fit line in Fig. b) is 58 mmol O2 m-2 d-1 and the calculated GOP assuming 17Δ is decreasing at 2.99 per meg d-1 (the slope of the second best-fit line in Fig. b)) is 27 mmol O2 m-2 d-1 on 18 April. The concentration of photosynthetic O2 is highest during this time (17Δ=48–54 per meg on 16, 18, and 19 April), despite the increasing gas transfer velocity. It is likely that GOP peaked during or soon after the end of the ice melt period and then declined to values similar to the beginning of the time series, but the uncertainties in GOP from 16 to 19 April are large.

Before interpreting the GOP results, we emphasize that the impact of changing mixed layer depth on the O2 mass balance is not accounted for in our calculations. The mixed layer deepened from 8 to 23 April and then appeared to shoal from 23 to 28 April. If the 17Δ value below the mixed layer were higher (lower) than 17Δ in the mixed layer, this would cause us to overestimate (underestimate) GOP as the mixed layer deepened.

Overall, the rate of volumetric mixed layer GOP was relatively constant throughout the time series at 5.7+3.1-1.9 mmol O2 m-3 d-1. The mixed layer-integrated GOP showed larger changes with time that are related to the influence of changes in the mixed layer depth on the non-steady-state term. From 25 March through 8 April, mixed layer-integrated GOP was 4.6+3.7-2.6 mmol O2 m-2 d-1. Beginning after 8 April, the mixed layer depth began to increase and the non-steady-state calculation showed a substantial increase in mixed layer-integrated GOP to 7.2+5.4-3.3 mmol O2 m-3 d-1 on 14 April, a 56 % increase. The non-steady-state GOP term is multiplied by the mixed layer depth, and therefore it increases linearly as the mixed layer deepens, causing the total mixed layer-integrated GOP to decrease. However, the non-steady-state GOP term is constant in volumetric units because the mixed layer depth cancels out of the equation. After the ice was gone, 17Δ began to decrease, and so did the mixed layer-integrated GOP. On the last 4 days of the time series, the mixed layer-integrated GOP was 8.7+3.6-6.3 mmol O2 m-2 d-1, 89 % higher than the average value prior to 9 April, but the mixed layer was also more than twice as deep at the end of the time series compared to the beginning.

The result that volumetric GOP was similar at the beginning and end of the time series indicates that ice-free conditions are not a pre-requisite for phytoplankton growth in this system. Currently, ecosystem dynamics within and below ice formed from fresh and brackish waters are not well understood . Other investigators have shown that photosynthetic microbes can inhabit the interior, upper surface, and lower surface of ice, and tend to be most concentrated on the bottom surface . Traditionally, investigators have argued that ice-associated communities are most prevalent in ice formed from seawater; as salinity increases, the volume of unfrozen brines within the ice that the microbes can inhabit increases, and the bottom surface of the ice becomes more uneven, increasing bottom algal settlement efficiency . However, more recently, investigators have also found algae growing within and on the bottom of freshwater ice in lakes and rivers, including locations in Canada such as the Great Lakes and the St. Lawrence River .

Phytoplankton can also grow in the water column beneath ice, especially under thin first-year ice . Bare ice transmits more light to surface waters than snow-covered ice, and melt pond-covered ice transmits 4 times as much light as bare ice . First-year ice in the Arctic (0.5–1.5 m thick) transmits ∼47 %–75 % of incident light through melt pond-covered ice and ∼13 %–25 % of incident light through snow-free ice . The ice in the Bras d'Or Lake near the site of Injection 1 was ∼0.3 m thick on 29 March, and therefore likely similar or greater fractions of light were transmitted through the ice. Ice transmitting just 2 % of surface irradiance may support high rates of photosynthetic activity if the phytoplankton are acclimated to lower light levels . We observed melt ponds in Whycocomagh Bay during tracer injections on 31 March and frequently during visual surveys in April. The shallow mixed layer prior to ice melt (∼0.8 m from the beginning of the time series until 8 April) would have kept phytoplankton in the mixed layer close to the surface and therefore receiving light that penetrated through the ice.

Our O2 mass balance techniques will record GOP by free-floating phytoplankton in the water column below the ice, as well as GOP by ice-associated phytoplankton if the O2 they produce diffuses into the water rather than into the ice surface or atmosphere. Bottom-associated algae likely release much of their O2 into the water column, especially for filamentous forms such as the diatoms frequently observed in Lake Erie and the Arctic .

We believe that the O2 measurements at Little Narrows from the beginning of the time series through 16 April (the date when the fraction of open water in Whycocomagh Bay began to increase rapidly) are generally representative of the under-ice rates due to the rapid transport of water through Little Narrows channel. The mean current speed at Little Narrows channel at 0.5 m depth was 3.4 km d-1. The distance between the ice edge and the sampling intake ranged from ∼0.4 to 1 km between the beginning of the time series and 12 April. Assuming a gas transfer velocity for O2 of 0.5 m d-1 once the water mass encountered open water and a mixed layer depth between 0.8 and 2 m, the residence time of O2 in the mixed layer was 1.6–4 d. Assuming a current speed of 3.4 km in open water, the water mass would have only been exposed to open water for between 0.1 and 0.3 d (20 % or less of the residence time of O2). However, we recognize that the current speed near the ice edge may have been somewhat slower than the speed at the constriction at Little Narrows; therefore, the transit time in open water may have been somewhat longer than 0.1–0.3 d.

We quantify non-steady-state NOP, incorporating the observed changes in O2/Ar during the time series. We estimate NOP as 11NOP=kO2Δ(O2/Ar)[O2]eq+h∂Δ(O2/Ar)∂t[O2]eq, where kO2 is the real-time gas transfer velocity (m d-1), [O2]eq is the equilibrium O2 concentration (mol m-3), and h is the mixed layer depth (m) . The first term on the right-hand side of Eq. () is the steady-state NOP term, and the second term is the non-steady-state NOP term, which is dependent on the rate of change in Δ(O2/Ar) with time. To calculate the rate of change in Δ(O2/Ar) with time, we resampled the data to a fixed 5 s interval (each scan of all masses took 5–6 s) and filled in gaps with a linear interpolation. Then we applied a third-order lowpass Butterworth filter with a cutoff frequency of 0.3 d-1 to generate a smooth O2/Ar record (Fig. ). We selected the cutoff frequency to remove the short-term variability from tides and diel changes in photosynthesis and respiration, and to minimize the number of times the inflection of the curve changed while capturing the overall trends in O2/Ar. Below we discuss the sensitivity of the calculated NOP to the choice of cutoff frequency. Finally, we calculated the derivative of Δ(O2/Ar) with respect to time using the filtered record. We applied the same filtering method to the in situ salinity and thermocouple temperature data and used the filtered data to calculate the [O2]eq and kO2, to prevent short-term fluctuations in salinity and temperature from producing apparent changes in NOP. We calculate the daily NOP (from 19:30 to 19:29 local time) using the average ∂Δ (O2/Ar)/∂t based on the filtered record and the average Δ(O2/Ar) (using the raw, unfiltered data).

As for the GOP calculations, our NOP calculations do not account for the impact of changing mixed layer depth, nor the impact of vertical diffusion, on the O2 mass balance because we do not have any measurements of O2 below the mixed layer . We expect that the O2 concentration below the mixed layer was lower than the concentration within the mixed layer, based on past measurements showing undersaturated O2 in the subsurface waters of Whycocomagh Bay . Therefore, vertical processes would likely cause us to underestimate NOP. For example, a deepening of the mixed layer between 8 and 23 April may have entrained waters with a lower O2 concentration into the mixed layer, causing a decrease in O2 (and O2/Ar). Using Eq. (), we would interpret this decrease in O2 as a decrease in NOP.

To calculate the uncertainty in NOP, uncertainty in kO2 (11 % for Injection 1, 18 % for Injection 2), mixed layer depth (0.3 m, 10 %–38 %), and the non-steady-state term are propagated. Uncertainty in the non-steady-state term is based on the results using different filtering methods. A conservative 13 % error associated with the cutoff frequency choice is included in the estimates of daily NOP. Uncertainty in Δ(O2/Ar) (<0.1 %, based on the mean offset between the EIMS and the discrete samples) has a negligible impact on NOP, relative to the other sources of error. The average errors in the daily NOP are ±0.8 mmol O2 m-2 d-1 (34 %) and ±0.3 mmol O2 m-3 d-1 (23 %) for the mixed layer-integrated and volumetric NOP, respectively. All uncertainties are the standard deviation.

Finally, we calculate the ratio of NOP to GOP for each daily estimate (the export efficiency). This ratio is similar to an f-ratio or an e-ratio and provides information on the fraction of GOP that is available for export out of the mixed layer (Fig. f). The uncertainties in the NOP/GOP ratio on each day are quite large. In a steady-state NOP and GOP calculation, the gas transfer velocity kO2 cancels out of the equation for the NOP/GOP ratio, and therefore it is not a source of uncertainty; however, in the non-steady-state term the kO2 does not cancel out.

As for GOP, we do not present NOP estimates during 16–19 April due to the uncertainties associated with the rapid decrease in ice cover. There are additional uncertainties in NOP from 12 to 23 April due to the increasing mixed layer depth, which may have entrained lower-O2 waters into the mixed layer. Historical O2 data from Whycocomagh Bay showed that there is a strong decrease in O2 with depth below the mixed layer; however, to our knowledge, no prior measurements during ice melt have been published .

Based on the non-steady-state NOP estimates, the ecosystem was on average net autotrophic as the ice was melting, from the beginning of the time series through 15 April (mean volumetric NOP of 1.9(2.1) mmol O2 m-3 d-1, median 2.5 mmol O2 m-3 d-1). During the (nearly) ice-free period from 20 April through the end of the time series, the community was on average net heterotrophic but with a smaller magnitude than during the start of the time series (mean volumetric NOP of -0.7(0.9) mmol O2 m-3 d-1, median -0.7 mmol O2 m-3 d-1). When the bay was nearly full of ice cover (from the beginning of the time series until ∼16 April), NOP was dominated by the non-steady-state term, and this term was positive except for between 31 March and 3 April when it was negative but small in magnitude. As the ice cover retreated, the non-steady-state term decreased and became negative on 18 April. From 18 to 22 April the steady-state term was roughly equal in magnitude but opposite in sign to the non-steady-state NOP term. The NOP is more strongly negative from 23 to 25 April (volumetric NOP of -1.6(0.5) mmol O2 m-3 d-1) and then on the last 2 days of the time series Δ(O2/Ar) was close to 0, and so was the rate of change in Δ(O2/Ar) with time (volumetric NOP of -0.7 mmol O2 m-3 d-1). If the time series had continued for longer, it would have been possible to observe whether the NOP value eventually stabilized near 0 following the dynamic ice melt period or whether it continued to oscillate between periods of net autotrophy and net heterotrophy.

The ratio of NOP/GOP has large uncertainties but qualitatively follows the trends of NOP, since the mixed layer-integrated GOP was relatively constant throughout the time series, whereas the mixed layer-integrated NOP was far more variable. At the start of the time series, there are two dates where NOP/GOP > 1, which by definition is not possible. The high NOP/GOP values could be due to uncertainty in the isotopic composition of water, which enters into the GOP calculation but not the NOP calculation, and/or the non-steady-state terms for GOP and NOP. Vertical diffusion across the mixed layer is another possible cause of the estimated NOP/GOP ratios exceeding 1; because we do not have measurements below the mixed layer, we cannot compute a correction for vertical mixing. The gradients in 17Δ and Δ(O2/Ar) are likely different with depth, leading to different magnitudes of the vertical mixing correction for NOP and GOP, which could potentially lead to errors in the estimated NOP/GOP ratio (Sect. ). We recommend that researchers planning future studies using O2-based tracers include depth profiles of O2/Ar and 17Δ in their experimental design .

The GOP results demonstrate that GOP was similar when Whycocomagh Bay was full of ice and when it was ice-free (on a volumetric basis). On the other hand, the calculated volumetric NOP was generally positive when the bay was full of ice, but began to decrease toward negative values around 12 April. The mixed layer depth was ∼0.8 m from the beginning of the time series until 12 April, deepened from 12 to 23 April and then increased until the end of the time series. The apparent decrease in volumetric NOP beginning around 12 April could be due to a number of factors, including an increase in respiration and recycling of organic carbon by autotrophs and/or heterotrophs, and/or vertical processes that are not taken into account in our calculations. We note that the mixed layer NOP was actually lowest and ΔO2/Ar was decreasing between 23 and 27 April, a period where the mixed layer actually appeared to shoal. Therefore a deepening mixed layer cannot be the only driver of the decrease in NOP following ice melt.