Gases evade water bodies through the diffusive, ebullitive and advective pathways [1] [2] . Diffusive emissions of greenhouse gases (GHG) such as carbon dioxide (CO₂), methane (CH₄), and nitrous oxide can be directly measured using the concentration increase rate of these gases in the headspace of floating static chambers. The thin boundary layer method is also used [3] . However, floating static chambers are not used to sample diffusive emissions of our subject dinitrogen gas above environmental concentration (N₂aec)―such as denitrified N₂―because of the high concentration of atmospheric N₂ (78%) in the headspace and the difficulty to distinguish N₂aec from environmental N₂ [4] . As for bubble emissions of GHG, they are sampled carrying out a different procedure in which equipment similar to inverted funnels [5] [6] is used, thus allowing ebullitive emission sampling to be done independently of the diffusive one. While the difficulty to distinguish environmental N₂ from N₂aec in diffusively emitted gas samples exists for bubble-gas samples too, this can be dealt with by using argon (Ar) as a tracer of environmental N₂ in bubble-gas―a path here taken.

The ebullitive:diffusive water-air emission partition ratio for a certain gas can be explained in part by its solubility in water and atmospheric concentration. For instance, ebullitive water-air emission of CO₂ tends to be very small. Typically, there is less than 1% CO₂ in the gas composition of bubbles escaping tropical reservoirs [7] . On the other hand, CO₂ water-air emission occurs via the diffusive pathway mainly for two reasons. First, it is highly soluble in water (88 ml/100 ml H₂O at 20˚C) [8] . Second, water bodies tend to be under saturated with dissolved CO₂ because of the small―although increasing―concentration of CO₂ in Earth’s atmosphere (485 ppm in year 2015) [9] . (Dissolved CO₂ saturated water bodies exist under a 100% CO₂ atmosphere. Under this scenario, further generation of CO₂ would increasingly super saturate water bodies with dissolved CO₂. Then, concentration of CO₂ in emitted bubbles would tend to increase with CO₂ production, simply because streams, rivers and reservoirs could not dissolve CO₂ indefinitely and therefore diffusively emitted CO₂ could not increase indefinitely).

Solubility of CH₄ (3.5 ml/100 ml H₂O at 17˚C) [8] is much smaller compared to that of CO₂. Because of the small concentration of CH₄ in air (1.84 ppm in year 2015) [9] water bodies are also under saturated with dissolved CH₄ concerning contact with the atmosphere. However, dissolved CH₄ from decomposition of organic matter can super saturate water to an extent that the ebullitive pathway can periodically overwhelm the diffusive one [7] . Compared to CO₂ and CH₄ and due to the overlying 78% N₂ atmosphere, N₂aec emission is potentially more straightforward to model. Solubility of N₂ ranges between 18.42 ml/l (in water at 0˚C with 0‰ salinity) to 6.95 ml/l (40˚C, 40‰) under one atmosphere total pressure [10] . As one mol of N₂ (28 g) occupies 22.4 liters, the solubility range can be expressed in molarity: 310 µmol/l - 822 µmol/l, and the saturation concentration range is 397 µmol/l - 1054 µmol/l. For higher altitudes, for instance, at pressure 0.9 atm the solubility range is 279 µmol/l - 740 µmol/l and the saturation concentration range is 357 µmol/l - 949 µmol/l. Due to contact with the 78% N₂ atmosphere, the solubility ranges shown above are actually the background concentrations of dissolved N₂ in environmental water bodies. They are close to saturation. Difference between background and saturation are within the range 87 µmol/l - 232 µmol/l under one atmosphere and smaller at higher altitudes, in theory. A higher difference (250 µmol/l) has been measured in practice [11] possibly caused by sudden temperature and/or pressure gradients. Therefore, an inflexion in the diffusive emission of N₂aec is expected when dissolved N concentration in water is as high as ~87 to 250 µmol/l. If a source of N₂ (such as denitrification) exists in the water, it will become increasingly unlikely that the N₂ thus produced will escape diffusively to the atmosphere and more probable that it will escape ebullitively. A “cat leap” realization led us to infer that, not only does the expected transition in the N₂aec diffusive flux in N-saturated waters exist [12] but that, the N₂aec diffusive emission is modeled fairly well [12] by either of two equations:

y = ( 640 x ) / ( 180 + x ) (1)

Alternatively:

y = ( 700 x ) / ( 320 + x ) (2)

Actually, Equations (1) and (2) represent diffusively emitted denitrified N₂ (y, µmol∙N∙m⁻²∙h⁻¹) as a function of above-background dissolved N in water (x, µmol∙N∙l⁻¹). Plots of saturation Equations (1) and (2) show how the rate of increase of diffusive denitrified N₂ emission with concentration undergoes an inflexion around roughly x = 87 to x = 232 µmol∙N∙l⁻¹ [12] . These concentrations added to background concentration (310 to 822) are the saturation concentrations (397 and 1054 µmol∙N₂∙l⁻¹) of dissolved N₂, discussed above. Equations (1) and (2) also show that at limit_×→∞, diffusive emissions of denitrified N₂ can, in theory, increase no more than about 640 - 700 µmol N∙m⁻²∙h⁻¹. In practice, one order of magnitude higher diffusive emission rates have been measured [12] .

Given that diffusive emissions are limited to these maximum values one can expect an increasingly significant ebullitive pathway, especially if there is a source of N₂ (e.g. denitrification) in dissolved-N saturated waters. The penalty for disregarding N₂aec (e.g. denitrified N₂) emitted in bubbles is that the fate of anthropogenic N will appear to be uncertain [13] [14] because nitrogen will seem to be “missing”, in other words, not enough N output will be found to balance riverine N inputs and outputs. Several studies observed such imbalances [1] [11] [15] - [22] .

The purpose of this work is to model our findings of excess N₂ in ebullitive emissions, complement it with the existing diffusive denitrified N₂ models described above, and predict denitrified N₂ emissions from inland waters with available data on total dissolved N.

All six sampled rivers were sources of ebullitive N₂aec (Table A1, Appendix). Two out of the 131 collected samples lacked data (e.g. bubble emission volume data) to calculate emission; even so, those 2 samples were chromatographically analyzed (Table A1(b) and Table A1(d)). From the 129 ebullitive emission samples which provided N₂ emission rates, 19 had insufficient volume (<1.6 ml) for transfer-tube purging and chromatographic analyses and were labeled “zero emission” (Table A1(a) and Table A1(b)). Thirty-eight samples had sub-environmental N₂ concentrations (Tables A1(a)-(d)). These 38 samples resulted in negative emission rates of N₂aec. They were also considered “zero emission”, for the purpose of N₂aec emission quantification. Therefore, less than half (44%) of the 129 samples yielded zero N₂aec ebullitive emission either because of too small sample volume or due to a negative emission result. Table 2 summarizes bubble emission measurement results.

The following five case studies use the findings here reported to estimate N₂aec emission across aquatic environments.

To the best of our knowledge, this is the first work to report N₂aec in ebullitive emission samples using Ar as a tracer of environmental N₂. Furthermore, this approach can be used to quantify ebullitive N₂aec in bubbles sampled elsewhere (Table 8 and Table 9).

Using a different analytical approach―headspace equilibration―gaseous N₂:Ar in the collected bubbles at sites from South Platte River within 81 km of Denver (Colorado, USA) were quantified [35] . The collected bubbles were injected into a vial containing 40 ml of N₂-saturated water and shaken for 1 minute. Dissolved N₂ and Ar concentrations in the liquid fraction, measured via MIMS [36] [37] , were used to back-calculate gas concentrations in the collected bubbles. The N₂aec―possibly denitrified N₂ in fact―in those bubbles ranged from 0% to 13.9% (Table 9).

The rate of increase of total N₂aec emission weakens with dissolved N concentration: from 3 µmol N₂aec-N∙m⁻²∙h⁻¹/µmol∙N∙l⁻¹ (Table 3) to 1.797 (Table 3) to 0.4315 (Table 3). The denitrification (a source of N₂aec) model from co-workers also points to a decrease in denitrification capability of streams with increasing nitrate loads: “higher loading rates stimulate NO 3 − uptake and denitrification, but yield an associate disproportionate increase in downstream NO 3 − export to receiving waters” [38] .

While it is possible that the N₂ gas in bubbles is due to “excess air” from groundwater recharge, the fact that the ratio N:Ar in this “excess air” is close to that in the atmosphere [39] excludes the N₂ of this source to be accounted as denitrified N₂. This suggests denitrification is the source of excess N₂ in the bubbles here reported.

Possible causes for negative emission rates are: N consumption, N fixation in excess of production, excess O₂ (possibly from photosynthesis), and/or Ar gas seeping into the bubble faster than O₂ or N₂. If the cause was N consumption or N fixation in excess of production, then inclusion of the negative rates in median calculation would yield net N₂ “production”. However, median emission results for each one of the eleven surveys would not be impacted by this inclusion except for São Marcos’ River June 2011 survey 2/3 (median would be

^ahttp://www.fgg-elbe.de. ^bQuantity of measurements. ^cTotal N is multiplied by 71.4 (1 mg N = 71.4 µmol N). The appropriate equation is selected from “Total emission” column in Table 3. The result is divided by 71.4.

^†5% of (O₂ + Ar).

−3.27 mg∙N₂-N∙m⁻²∙d⁻¹, rather than zero) as shown in Table A1, indicating that in the six rivers here studied N production would exceed N fixation. Excess N₂ was also found in most bubble samples collected in the White Oak River estuary USA (Table 8) and South Platte River USA (Table 9).

Synthetically stirred bubbles from bubble-enriched sediment sites [27] showed higher median concentration (24.1 % N₂aec-N, n = 14, Table 8) of N₂aec than ours (5.75 % N₂aec-N, n = 112, data from Table A1) and, than the median (7.51 % N₂aec-N, n = 8, Table 9) for naturally emerging bubbles from a high nutrient segment of South Platte River. The relatively small median (5.75%) obtained here could be due to partial bubble dissolution during the diel harvest, or greater variety of sampled aquatic environments.

The significant rates of ebullitive gas water-air emission from the heavily urbanized stretches of Pinheiros and Tietê rivers here observed support the finding that urban streams and rivers should be included in river nitrogen cycling models [40] .

Bubble occurrence in the eyes and inwards of fish [41] is a condition known as “gas bubble disease” also referred to as “gas bubble trauma”. This can possibly be explained by super saturation levels of dissolved N concentration (>~250 µmol∙l⁻¹) because this favors excessive bubble formation while promoting the ebullitive escape discussed here.

In waters with small concentrations of dissolved N (<10 µmol∙N∙l⁻¹) ebullitive N₂aec water-air emissions are practically insignificant and diffusive N₂aec emissions predominate. Ebullitive and diffusive N₂aec emissions increase with dissolved N concentration but diffusive N₂aec emissions saturate at ~700 µmol∙N∙m⁻²∙h⁻¹ in waters with > ~1000 µmol∙N∙l⁻¹, while ebullitive continue to grow.

While the chromatographic analyses of N₂ and O₂ (although CH₄ and CO₂ were the main gases of interest at the time) were carefully done, the Ar concentration in the ebullitive emission sample hinges on a statement, i.e. that 5% of the “O₂” peak is Ar. Here, there is margin for refinement because the Ar concentration in each ebullitive emission sample can easily be done chromatographically, using O₂ as a carrier gas, with the precision required for this work.

As dissolved N is a predictor of N₂aec emission, denitrified N₂ emission models would benefit from data of simultaneous measurements of total dissolved N concentration (NH₄-N + NO₃-N + NO₂-N + N₂-N) and denitrified N₂ ebullitive and diffusive emission (rather than not measuring total dissolved N along with the ebullitive and diffusive measurements).

Our N₂aec emission model predicted 13% - 15% (63 − 50 = 13 and 65 − 50 = 15) more ebullitive N losses than the actual “missing N”, in Case Study 1. Causes for this overestimation could probably be understood with more bubble emission measurements in other river systems, considering local variability such as slope, sediment types, N inputs and biochemistry. In Case Study 2, the nitrogen-removal range predicted by our model tends to be within the measured range by MIMS, except when nitrate concentrations are highest (840 and 1096 µmol N/l) then, our model overestimates the measured nitrogen-removal rates. This could be due to local conditions and/or underestimation by MIMS of the ebullitive nitrogen-removal pathway. In Case Studies 3, 4 and 5 the measured values by co-workers are predicted relatively well by our model.

We thank Professor John Prausnitz for acknowledging that our explanation for the observed bubble behavior is reasonable. We thank field survey colleagues and boatmen from the Carbon Budget Brazil projects; also F. S. David and W. C. Valenti for priming our interest in the nitrogen cycle and B. Matvienko for the insightful discussions on, given the amassed data how can we quantify denitrified N₂ bubble emission; D. Sikar and B. Matvienko for helping to survey the polluted rivers of the São Paulo city metropolitan area; I. and P. Matvienko-Sikar, L.R.C. Ribeiro and R. L. North for their comments; and ten anonymous reviews of earlier versions of this work. We thank Trimmer et al. 2012 [42] for leading us to discover where the excess nitrogen we found in bubbles, was being missed. For permission to use results of O₂, N₂, CH₄ and CO₂ in bubble samples, we thank: Prefeitura de São Paulo/Secretaria do Verde e Meio Ambiente, ANTP-Associação Nacional de Transportes Públicos (data from 2 rivers in the São Paulo city metropolitan area), Ministry of Mines and Energy-MME and Eletronorte (data from the other 4 rivers). “Take note of the O₂ and N₂ concentrations in bubbles, you might discover something” Professor Bohdan Matvienko (*1933†2013), to whom we dedicate this work.

The authors declare no conflict of interest, financial or otherwise.

Sikar, E., dos Santos, M.A. and dos Santos, E.O. (2019) An Empirical Model for Dinitrogen Gas Emission from Inland Waters. Atmospheric and Climate Sciences, 9, 1-25. https://doi.org/10.4236/acs.2019.91001

Table A1 Each of the six rivers’ surveyed sites. ^aSite depth. ^bVolume of collected bubble gas. ^cQuantity of 70 cm diameter funnels at sampled site. ^dSampling time interval. ^eSurface water temperature, at ~10 cm depth. ^fAtmospheric pressure in field laboratory. ^gO₂+Ar, N₂, CO₂ and CH₄ concentrations in bubble gas samples. ^hSee 2.5 N₂aec bubble-emission calculation method (main text). ⁱExcluded, river flow probably tilted the funnels and air entered bubble-gas vial. ^jNo existing data. ^kMedian temperature; temperature probe had faulty contact. ^lUnderestimated volume due to bubble-gas overflow. ^mNot analyzed. ⁿFirst and third quartiles are the nonparametric statistics’ numerical equivalents to the normal distribution’s two values in between which the central 50% of the area under the normal curve lies. First and third quartiles were calculated assuming: ebullitive N₂aec emission rate histograms of polluted rivers display normal distributions; ±1 standard deviation from the mean were 293 and 405 (Tietê River) and 858 and 1011 (Pinheiros River). ^†Negative emissions, and results of calculations using negative emissions, are italicized. This parallel calculation was done for the following reason: if the assumption that negative N₂ emission rates indicate N fixation is true, then their inclusion in median calculation would yield either net N₂ production (positive median) or net uptake of N i.e. consumption (negative median).