Gases evade water bodies through the diffusive, ebullitive and advective pathways   . 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  . 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  . As for bubble emissions of GHG, they are sampled carrying out a different procedure in which equipment similar to inverted funnels   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  . 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)  . 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)  . (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)  is much smaller compared to that of CO2. Because of the small concentration of CH4 in air (1.84 ppm in year 2015)  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  . 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  . 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  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  but that, the N2aec diffusive emission is modeled fairly well  by either of two equations:
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  . 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  .
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   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    -  .
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.
2. Materials and Methods
2.1. Studied Sites and Rivers
Between years 2008 and 2012, we investigated 131 sites distributed among four tropical and two sub-tropical rivers, all in Brazil (Figure 1).
The geographic coordinates, depth, quantity of bubble-samplers (funnels) collectively deployed per site; surface water temperature and atmospheric pressure are in Table A1. Land cover surrounding the surveyed river reaches range
Figure 1. Catchments and sampled sites of the six Brazilian surveyed rivers.
from tropical rainforest typically subjected to periodic floods, to heavily urbanized land.
The purpose was to measure CH4 and CO2 emissions. We studied stretches of the tropical rivers: Xingu (surrounded mainly by tropical rainforest), Tocantins (forest and grassland), Madeira (forest and grassland) and São Marcos (grassland and agricultural land). Also of highly impacted sub-tropical stretches of rivers Tietê and Pinheiros, both surrounded by São Paulo city. Physical and chemical parameters of the investigated reaches are in Table 1.
We surveyed tropical rivers Xingu, Tocantins and Madeira along stretches located in the Brazilian Amazon, near Altamira, Marabá and Porto Velho cities,
Table 1. Median (1rst quartile; 3rd quartile) (number of measurements) of physical and chemical parameters of the surveyed areas. Parameter measurements are contemporary with the ebullitive emission measurements reported in this work except for Tocantins River, where we measured bubble emissions in year 2008 but found parameter data only for year 2011.
aSmaller than (unspecified in original report) detection limit. bNo existing data. cMonth and year this table’s parameters were measured. dBALCAR Carbon Balance Project private databank and Furnas Reports. Published with permission from Furnas.
respectively. Due to agriculture, only 30% of tropical river São Marcos catchment’s original cerrado (a savanna-type biome) remains. Tietê and Pinheiros rivers are both located in the upper Tietê River basin; their studied sites are on a sub-tropical reach within São Paulo, a city with 11 million inhabitants. São Paulo city’s municipal disposal service collects 97% of total sewage generated and 75% is treated, but this treatment does not remove N compounds such as organic N, ammonium, nitrite and nitrate from the effluents discharged into the rivers  . Dredged sediment volume from the studied areas in May 2012 for desilting, was 84383 m3 from the 24.5 km extension (3444 m3∙km−1) of Tietê River canal. And 50387 m3 from the 10.1 km extension (4988 m3∙km−1) of Pinheiros River canal (2016 email from Waters and Electrical Energy Department of São Paulo City to us).
References  and  discuss the design of the measurement campaigns.
2.2. Bubble Sampling
Bubble emissions were sampled using submerged inverted funnels (70 cm Ø × 70 cm height) using established sampling procedures     . Engaged to the narrower opening of the funnel is a bubble-gas collecting vial (typically 500 ml volume). The narrower opening of a deployed funnel is typically about 15 cm below the water surface. We deployed more than one funnel per site at sites closer to river shores and fewer funnels per site at sites closer to river thalwegs, because shallower sites tend to be more ebullitive  . Funnels collected ebullitive emissions for about 24 h, unattended, and then were retrieved. At funnel retrieval, transference of the collected ebullitive gas per site into one graduated vial permits total bubble-gas volume measurement. It was not of interest at the time to measure variability of bubble emission among the simultaneously deployed funnels within a same site. After volume measurement, an aliquot was transferred to a 37 ml glass ampoule (made by Construmaq São Carlos) and screw-capped. Bubble-gas sample harvest, total volume measurement and transference into glass ampoules were always done underwater (leaning over the boat), with no exposure of the bubble-gas samples to the atmosphere. Bubble-gas samples < 1.6 ml were discarded because, although sufficient for chromatographic analyses, they were insufficient for purging and transference. When sampling was done for the day and the boat returned to shore, the glass ampoules containing the samples were immediately taken to our field portable-laboratory for chromatographic analysis.
2.3. Bubble-Gas Sample Transference into a Syringe
In the laboratory, bubble-gas was transferred from the glass ampoule into a syringe (BD Ultra-fineTM 12.5 mm needle-length, purchased over the counter) using a 0.6 ml volume transfer equipment. This equipment consisted of 50 cm length tubing and a glass bulb, previously purged with sample. Tubing consisted of stainless steel tube 1.5 mm outside diameter (OD) × 1.0 mm inner diameter (ID) × 30 cm length, and PVC tubing 2.0 mm OD × 1.3 mm ID × 20 cm length. Connected to the PVC tubing was a small glass bulb, sealed with a small plug made with stationery-shop-purchased white vinyl eraser. (Sample transferring setup image is available at http://www.construmaq.ind.br/produtos/bulbo-de-vidro-selado-com-rolha-de-borracha-e-inserido-em-mangueira-flexivel/)
2.4. Chromatographic Analyses
Samples were chromatographically analyzed for CH4 and CO2, within the first 24 hours after being harvested. Oxygen and N2 peaks elute from the Molecular Sieve chromatographic column prior to methane’s (peak area is proportional to gas concentration). The O2 peak is in fact an O2+Ar peak because these two gases elute together; chromatograms showed them as one combined peak. We used a Molecular Sieve 5A filled stainless steel chromatographic column of 3.2 mm (OD) × 1.6 mm (ID) × 1.95 m length and a thermal conductivity detector (TCD) chromatograph manufactured by Construmaq São Carlos. Carrier gas was hydrogen (H2). Injector, column and detector operated at room temperature. Samples were injected by hand using the BD syringe mentioned above. Injected gas volumes were 0.1 milliliter (100 µl). Variability (average ratio of standard deviation divided by average peak area of 3 peaks) was ± 1.5% O2 and ± 1.2% N2. Detection limits were 0.5% O2 and 1% N2. Oxygen and Ar elute together from the Molecular Sieve 5A column as one combined peak, followed by the N2 peak and CH4 peak. Reference  briefly mentions that 5% of the O2+Ar peak is Ar.
2.5. N2aec Bubble-Emission Calculation Method
Consider data from the third line of data in Table A1(a). After a period of 22.33 sampling hours, four funnels at 5.5 m depth Xingu River site 3.3118˚S 52.1960˚W, collectively collected 520 ml of gas. Chromatographic analysis of an aliquot of the collected volume resulted 4.89% O2+Ar and 26.5% N2. The bubble sample had 0.2445% Ar (5% of the O2+Ar mixture). Environmental N2, in the bubble sample was 0.2445% Ar × 78.1% N2/0.93% Ar = 20.5%. Emitted N2aec concentration, in bubble sample was 26.5% − 20.5% = 6.0%. Emitted N2aec volume, in the bubble sample was:
Emitted N2aec-N mass, in bubble sample was:
Funnel area was 0.3848 m2. Rate of emitted N2aec-N from site 3.3118˚S 52.1960˚W was:
Variability is 1.9% . Had the collected volume been 1.6 ml rather than 520 ml, then, the minimum detectable ebullitive N2aec emission in this case would have been 74.2 µg N2aec-N∙m−2∙d−1.
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.
3.1. Ebullitive N2aec Emission Model
Table 2. Ebullitive N2aec-N medians given in both emission rate units used in this work, and dissolved N concentration in the studied rivers.
aTocantins River data are not used to model dinitrogen emission because ebullitive emission (measured in 2008) and dissolved N concentration (measured in 2011) are not contemporary.
Figure 2. Data markers distant from clusters represent measured outliers. Table A1’s measured ebullitive N2aec emission rates (y) in unit µmol∙N2aec-N∙m−2∙h−1 (1 mg∙N2aec-N∙m−2∙d−1 ≅ 3 µmol∙N2aec-N∙m−2∙h−1), plotted against dissolved N (NH4-N + NO3-N + NO2-N + N2-N, x) median concentration (Table 1). Linear fit is curved “up” due to the log-X plot, and was calculated with median emission from Xingu (0 µmol∙N2aec-N∙m−2∙h−1), São Marcos (1.6), Madeira (121), Tietê (1057) and Pinheiros (2780), as functions of dissolved N concentration (2.79; 8.07; 53.7; 1150; 1257 µM N, respectively). Tocantins’ 23 rates (◊) median (8.7 µmol∙N2aec-N∙m−2∙h−1) was not used to calculate linear fit because it is unlikely that year 2011’s dissolved N, 40.2 µM N, was valid also back in year 2008, when N2aec bubble emission from Tocantins River was measured.
dependence of bubble emission on concentration is best (high R/small P) described by the first-order equation:
where y is N2aec bubble emission (µmol∙N2aec-N∙m−2∙h−1) and x is total dissolved (reactive + inert) N concentration in water (µmol∙N∙l−1). As bubble growth is a function of dissolved gas concentration in water  , it is pertinent to know (besides reactive N concentration) how much dissolved N2 is in the studied water.
If investigated N2 emissions from swine farms  hold for rivers too then, for dissolved N concentrations > 1200 µmol∙N∙l−1 ebullitive emissions increase at a smaller rate and, rather than by Equation (6), are better described by:
3.2. Total N2aec Emission Model
For a given total dissolved N concentration in water, the ebullitive emission (Equation (6) if dissolved N concentrations < 1200 µmol∙N∙l−1 and Equation (7) if concentrations > 1200 µmol∙N∙l−1) plus the diffusive emission (Equation (1) or (2)) results total N2aec emission (Figure 3).
Actually, diffusive emissions were originally  plotted against dissolved NO3-N, which, for lack of more data on dissolved N, we assume roughly represents total dissolved N. The ready-to-use version of our model (Table 3) will be used while working through the five case studies.
3.3. Partition between Ebullitive and Diffusive N2aec Emissions
The ebullitive:diffusive partition ratio changes radically with increasing dissolved N. In river water with small concentrations (<11 µmol∙N∙l−1) of dissolved N, N2aec ebullitive emissions are not significant and diffusive emissions predominate (Figure 3(a), Table 3 and Figure 4).
In waters with > 11 µmol∙N∙l−1 ebullitive N2aec emissions increase steadily, along with the diffusive ones. At concentrations between 140 - 240 µmol∙N∙l−1 ebullitive rate equal diffusive rate emissions (Figure 3(b) and Figure 4). At concentrations > 250 µmol∙N∙l−1, ebullitive will tend to be higher than diffusive emissions (Figure 3(b) and Figure 3(c), and Figure 4). In the concentration range 300 - 1200 µmol∙N∙l−1 water is supersaturated with dissolved N and bubble emissions continue to increase, while diffusive emissions eventually saturate at 640 - 700 µmol∙N2aec-N∙m−2∙h−1 (Figure 3(c) and Figure 4). In waters with dissolved N concentration > 1200 µmol∙N∙l−1 ebullitive emissions predominate (Figure 3(d) and Figure 4).
In addition, ebullitive N2aec emission correlates significantly with CH4 ebullitive emission (R = 0.96; P = 0.002; n = 11; data from Table A1; graph not shown) and CO2 ebullitive emission (R = 0.94; P = 0.005; n = 11; data from Table A1; graph not shown), suggesting that the production of N2aec is associated with decomposition of organic matter.
4. Case Study Application
The following five case studies use the findings here reported to estimate N2aec emission across aquatic environments.
4.1. Case Study 1: The “Missing” Nitrogen
Approximately 50% of the net anthropogenic N input was unaccounted for in a watershed N budget, which included diffusive but not ebullitive emission  .
(a) (b)(c) (d)
Figure 3. (a), (b), (c) and (d) Graphical representations of ebullitive (bubble), diffusive, and total (bubble + diffusive) N2aec water-air emission as a function of total N concentration in water. Circles in Figure 3(d) are reference  ’s denitrified N2 bubble emission data from swine farms.
Figure 4. The “scissors-like” ebullitive:diffusive partition. N2aec emission percentage (%, y) as a function of dissolved total N in water (µmol∙N∙l−1, x).
Figure 4 shows that ratio 63% - 65% ebullitive/37% - 35% diffusive N emission is predicted for stream waters with 500 µmol∙N∙l−1 such as those studied. Albeit a higher ebullitive loss (63% to 65%) than what was actually missing (~50%), this still shows that the fate of the missing N can be explained by ebullitive losses. See “Conclusion”.
4.2. Case Study 2: Nitrogen-Removal Rates
Nitrogen-removal rates were measured  with the membrane inlet mass spectrometry (MIMS) technique. Using the nitrate concentration data from Sugar Creek and Iroquois River  and our model, we find:
Table 3. N2aec emission (µmol∙N2aec-N∙m−2∙h−1, y) as a function of dissolved N concentration (µmol∙N∙l−1, x) in water, within the 0 to 45,500 µmol∙N∙l−1 concentration range.
1) How denitrified N2-emission is partitioned between ebullition and diffusion. For example, we estimated 83 to 123 µmol∙N∙m−2∙h−1 diffusive emission (Table 4, line “Sugar Creek Sep 1999”, column “Diffusive estimated by us”); and 52 µmol∙N∙m−2∙h−1 ebullitive emission (column “Ebullitive estimated by us”);
2) Significant discrepancy between predicted and measured rates for the high dissolved [N] range. For example, in June 2001 Sugar Creek’s sampled waters had the relatively high dissolved N concentration 1096 µmol/l (Table 4). While a relatively small denitrification rate range 290 ± 151 µmol∙N∙m−2∙h−1 (Table 4) was found, we estimated eight times higher rates 2319 to 2327 µmol∙N∙m−2∙h−1 (Table 4).
4.3. Case Study 3: Nitrogen Budget
Estimation of total annual N2 emitted and N buried in a subtropical river reservoir (Xipi) in southeast China with 8.5 km channel length and mean width of 125 m. For Xipi an annual 80∙103 kg gaseous N total emission was estimated  , while we obtained 88∙103 kg∙N (“TOTAL” line, Table 5). However, assuming permanent carbon sedimentation median rate 78 mg∙C∙m−2∙d−1  and that the Redfield ratio 6.625 (106 C:16 N) roughly holds, we estimate sedimentation rate is:
In addition, annual buried N is:
It follows that the total annual retention (88.260 + 4.564) × 103≈ 93 × 103 kg estimated by us, is equal to 93 × 103 kg∙N annual retention of dissolved inorganic N, estimated by using a different approach  .
4.4. Case Study 4: N2 Emission Estimation
The Jiulong River is a large agricultural river in southeast China. We use N concentration data (Table 6) to estimate its N2 water-air emissions. These estimates are then compared to those of co-workers  :
1) The North River median area-weighted N2 flux range 812 - 873 µmol∙N∙m−2∙h−1 (estimated by us, Table 6) expressed in kg∙N∙ha−1∙yr−1 is:
Table 4. Source data (from reference  ) are shown in bold font.
aUsing Equations (2) and (1). E.g.: [(700 × A)/(320 + A)] and [(640 × A)/(180 + A)]. bUsing Equation (6). E.g.: [(1.638 × A) − 18.11]. cN (% d−1) is the percentage of water-column nitrate removed by denitrification. E.g.: ((135 to 176) × 14)/76 = (25 to 32)% N∙d−1.
Table 5. Source data (from reference  ’s Figure 5) are shown in bold font.
aDissolved N2, in excess of environmental (background) dissolved N2. b3 × (A + B + C), see Table 3. c[(1.797 × (A + B + C)) + 360.6], see Table 3. d8500 m ×125 m × (396.0172 µmol∙N∙m−2∙h−1) × (24 h∙d−1) × (61 d) × (1 mmol/1000 µmol) × (1 mol/1000 mmol) × (14 g/mol) × (1 kg/1000 g) = 8624.066 kg N per 61 days.
or 9.96 - 10.7 kg∙N∙ha−1∙yr−1, and similar to 9.88 kg∙N∙ha−1∙yr−1 estimated by co-workers (in reference  ’s Table 3);
2) Likewise, West River median area-weighted N2 flux range 1100 - 1149 µmol∙N∙m−2∙h−1 (Table 6) or 13.49 - 14.09 kg∙N∙ha−1∙yr−1, is similar to 14.06 estimated by co-workers (in Reference  ’s Table 3).
4.5. Case Study 5: Comparison between Denitrification Rates (Median and Interquartile) Measured on the Elbe River with Rates Predicted by Our Model
Elbe River denitrification rates were obtained by measuring dissolved N2 “super-saturation” (measured dissolved N2 minus equilibrium dissolved N2) and
Table 6. Source data (from Reference  ’s Figure 3) are shown in bold font. Data from tributary sites’ (W1, W2 and W3) were not used here.
aDissolved N2, in excess of environmental (background) dissolved N2. b[(700 × (A + B))/(320 + (A + B))] and [(640 × (A + B))/(180 + (A + B))], see Table 3. c[(1.638 × (A + B)) − 18.11], see Table 3.
using varying reaeration-rate coefficient gas exchange equations  . Comparison shows:
1) The decreasing N2 emission tendency from upstream (Reach A) to downstream (Reach C) is observed in both works, here and  , (Table 7).
2) Median (and interquartile) total N in the Elbe River water between years 2011 and 2012 was 5.0 (4.0; 6.1) mg N/l based on 863 measurements (http://www.fgg-elbe.de) performed on the about 105 km2 studied river area. Using this data and the model here proposed we estimate a nitrogen removal of 12,910 (11,038; 14,728) t∙N∙yr−1. These rates are compatible with the ~10,000 t∙N∙yr−1 extrapolated annual estimate, based on annual temperature changes  .
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  . 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   , 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 uptake and denitrification, but yield an associate disproportionate increase in downstream export to receiving waters”  .
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  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
Table 7. Dissolved N and N2 emissions from Elbe River (source data  in bold).
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.
Table 8. Columns “Site”, “% O2+Ar” and “% N2” are from reference  . There it is stated that 5% of the O2+Ar mixture is Ar (calculated in the “% Ar” column). Assuming environmental concentrations 78% N2 and 0.93% Ar, we used Ar as a tracer of environmental N2 to calculate the concentration (%) of N2aec (possibly denitrified N2) in bubbles (results in “% N2aec-N” column). Example of calculation (using data from line 1, Site DC): 5.40 = 7.5 − (0.025%Ar × 78%N2/0.93%Ar). We assumed negative values indicated zero N2aec in bubbles (see Table A1 header). Median (24.12) was not changed by including negative (rather than zero) value observed in site CLB.
†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).
Table 9. Columns “Site”, “Distance” and “Gaseous N2:Ar” were copied form Reference  . Sites are situated on South Platte River downstream from the point of discharge from the largest wastewater treatment plant from Denver, serving 1.3 million people. Concentration of N2aec was calculated using environmental ratio 78% N2:0.93% Ar. Calculation example for the South Plate site: (79.93 × 0.93) − 78 = −3.67 (0). Median (7.51) was not changed by inclusion of negative value observed in South Platte site.
Synthetically stirred bubbles from bubble-enriched sediment sites  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  .
Bubble occurrence in the eyes and inwards of fish  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  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.
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).
Table A1. (a) Xingu River; (b) Tocantins River; (c) Madeira River; (d) São Marcos River; (e) Tietê River; (f) Pinheiros River.