2.1. Study Sites
 We studied five streams in southern Ontario, Canada (Figure 1). We sampled 2–4 sites per stream to help account for high spatial variability that has been reported in past studies [e.g., Reay et al., 2003]. Our sampling started in June 2006, and spans a 29-month period, but with reduced sampling in winter and at some sites. All samples were obtained during daylight. The shortest sampling period (June 2006 to November 2007) was in Stouffville Creek. This is a third order stream (Strahler) in a mixed urban-agricultural catchment. A flood control reservoir is located upstream of our sampling sites. The remaining four streams were sampled from June 2006 through the winter of 2007–2008. In a subset of sites, we extended our sampling until October 2008. The 2008 data, while not reflecting our full suite of sites, allow us to contrast between conditions in unusually dry years (2006, 2007) and a year of record precipitation (2008).
Figure 1. Study catchments in Ontario, Canada (area of detailed map is shown as inset). Clockwise from bottom catchments are Stouffville Creek, Black River, Layton Creek (smaller adjacent to Mariposa), Mariposa Brook (larger adjacent to Layton), and Jackson Creek. Sampling sites are shown as white dots with the most upstream site as 1, and increasing numbers downstream. The approximate overall direction of flow is indicated with an arrow.
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 In addition to the urban-agricultural stream which has a mixture of sand and rocky substrates and a mean depth of 0.2 m, our study sites include Layton Creek (stream-wetland complex with a highly organic substrate, second to third order at our sampling sites, depth = 0.4 m), the Black River (sandy substrate, fourth to fifth order, depth = 0.3 m), Mariposa Brook (silt-rocky substrate fourth order, depth = 0.4 m) and Jackson Creek (sandy substrate upstream, rocky mid and downstream, third to fourth order, depth = 0.4 m). The Jackson Creek sites include one site upstream of a major wetland complex, and two that are located at different distances downstream of the wetland.
2.2. Physicochemical Parameters
 We measured a variety of chemical parameters including ammonium (NH4+), organic N, dissolved organic carbon (DOC) and sulphate (SO42−) concentrations (Table 2). In all cases, we have a measurement of NO3− + nitrite (NO2−) which we abbreviate as NO2+3−. Starting in May 2007 we also measured NO2− separately. N2O samples were obtained in serum bottles sealed with a butyl-rubber stopper, and preserved with mercuric chloride (Table 2). Concentrations were determined using GC-ECD on a Varian CP-3800 gas chromatograph following headspace equilibration. Headspace concentrations were standardized using a series of certified standards (100, 500, 1000 and 10,000 ppbv; Matheson Tri-gas, Praxair), then concentrations in water and percent saturation were determined using solubility equations [Weiss and Price, 1980]. During the ice-free season, discharge was measured using the velocity-area method and a Swoffer 2100 velocity meter. Periods of ice cover were based on direct observation, and are estimated to be accurate within one week.
Table 2. Analytical Methods
| ||Summary of Method||Sample Bottles, Treatment|
|NO2+3− (Nitrate + nitrite)||Reduction to nitrite (using heated hydrazine in an alkaline solution catalyzed by Cu2+) and subsequent analysis using the red azo dye method [Ministry of the Environment, 2001b]||Filtered (pre-ashed, B-pure leached GFFs) 500 mL PET bottles|
|Nitrite (NO2−)||As for NO2+3−, but without prior reduction.||As above|
|Nitrate (NO3−)||NO2+3− minus NO2−||As above|
|Ammonium (NH4+)||Indophenol blue method (in buffered alkaline solution, [Ministry of the Environment, 2001b]||As above|
|Organic nitrogen||Analysis as total Kjeldahl nitrogen (TKN) minus ammonium nitrogen. TKN involves high temperature digestion with sulphuric acid, hydrochloric acid and potassium sulphate followed by neutralization and analysis using the phenate-hypochlorite method [Ministry of the Environment, 2001a]||As above|
|Dissolved organic carbon (DOC)||Oxidative combustion-infrared analysis (Shimadzu TOC-V analyzer)||As above|
|N2O||Triplicate equilibrations of subsamples in air-filled Exetainer vials (Labco Ltd., Buckinghamshire England) with known volumes. Samples were shaken for 90 min at 120 rpm (VWR orbital shaker), weighed, and the headspace was analyzed using GC (Varian CP-3800)-ECD following separation on a Hayesep D column.||125 mL serum bottles sealed with pre-baked butyl rubber stoppers, preserved with 0.4mL saturated mercuric chloride solution|
|Sulphate (SO42−)||Ion chromatography (Dionex)||Unfiltered, 500 mL PET bottles|
|Chloride (Cl−)||Ion chromatography (Dionex)||Unfiltered, 500 mL PET bottles|
|Total phosphorus (TP)||Ammonium-molybdate-stannous chloride method [Ministry of the Environment, 1994]||Glass vials|
2.3. Dissolved Gas Fluxes
 We estimated gas fluxes using the two-layer model of diffusive gas exchange [Liss and Slater, 1974]. Positive numbers indicate a net flux from the stream to the atmosphere:
where k is the gas exchange velocity. This is equal to the gas transfer coefficient (K, in units of d−1) times stream depth. CS is saturation concentration of N2O, and CL is the measured N2O concentration.
 Saturation N2O concentrations were calculated using the solubility equations of Weiss and Price , assuming constant atmospheric mixing ratios of 320 ppbv. N2O is well mixed in the atmosphere due to its long lifetime [Stein and Yung, 2003]. The use of a single CL is dependent upon the assumption that the streams are well mixed, and variation in N2O concentrations across the stream channel is negligible. At low flow, variation in N2O concentrations across our study channels (6%) was approximately equal to analytical error (5%).
 We measured rates of gas transfer via the addition of a gas tracer (sulphur hexafluoride; analysis by GC-ECD as for N2O) and conservative tracer [Kilpatrick et al., 1987], as well as diel oxygen (O2) curves [Venkiteswaran et al., 2007, 2008]. Briefly the O2 method uses an O2 mass balance model, and iteratively fits the data (in Matlab©) using a defined range of possible rates of photosynthesis, respiration (both 0–5000 mg O2 m−2 h−1) and gas exchange velocities (0.01–0.50 m h−1) to obtain the lowest sums of squares between measured and modeled data. The model was re-run 15 times with different randomly selected starting points for each diel time series. Model results wherer2 between modeled and observed data was >0.80 were averaged to obtain the k value. These multiple results varied by an average of 0.006% (coefficient of variation (CV); maximum CV was 0.02%). Model results constrained by O2 isotopes, and where the model was run without these data varied by <1% to ∼4%. Rates of gas transfer were normalized to stream temperature [Thomann and Mueller, 1987] and N2O using Schmidt number scaling [Wanninkhof, 1992] assuming an exponent of 2/3 which reflects smooth surfaces.
 We have at least one measurement of gas transfer velocity per site, with the exception of the downstream site on the Black River, which we assume (based on similar substrate, depth and velocity relationships) to parallel the upstream site. The downstream site on Jackson Creek has different substrate and is shallower than either of the other study sites, so lacking a reliable estimate of gas transfer velocity we exclude this site from flux estimates.
 Seasonal changes in stream depth and velocity can contribute to variability in gas exchange. Numerous approaches to address this issue have been used. Beaulieu et al.  developed a gas transfer model in one stream, and applied this model across several streams with similar slope and substrate. In a group of Mexican streams, a measurement of gas transfer velocity in one stream was applied across several streams, and comparisons were made with chamber methods [Harrison and Matson, 2003]. In this study we calibrate gas transfer models to our study streams using an approach based on the ratio of measured to model-predicted gas transfer coefficients [Moog and Jirka, 1998]. The calculation is presented in its original form (equation (2)) using the gas transfer coefficient (K, which is equal to gas exchange velocity divided by depth) [Moog and Jirka, 1998]:
where KPC is the calibrated prediction, Km is the measured gas transfer coefficient, Kp is the predicted gas transfer coefficient under measurement conditions and n reflects the number of measurements. We selected the models of O'Connor and Dobbins , Owens et al. , and Bennett and Rathburn , which were developed for conditions similar to those of our study streams [Cox, 2003]. Our flux estimates are based on equation (1), using the three estimated KPC values based on these three models, and 1–4 measurements of gas transfer velocity per stream (Figure 2).
Figure 2. Solute concentrations, flow and KPC. Sites are shown from (left) the most upstream site to (right) the most downstream site in a stream. Box shows median ice-free season data bounded by 25th and 75th percentiles. Whiskers show the 10th and 90th percentiles. Dots indicate outliers. White triangles show concentrations from periods of complete or partial ice cover. Data plotted are (a) N2O % saturation (the horizontal dashed line indicates 100% saturation), (b) discharge, (c) N2O concentration, (d) KPC (mean of 3 models, values for N2O at stream temperature); white circles on KPC plot show measured KN2O values (at 20°C), (e–k) nutrients and other solutes. The Mariposa Brook data are truncated in the plot of % saturation. Outliers at the most upstream site (1700% saturation) and most downstream site (1630% saturation) are not shown.
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 We assessed whether tile drains present in the catchments of three of our study streams (Layton Creek, Black River, and Mariposa Brook) were likely to affect gas concentrations using a first-order gas loss equation [Chapra and di Toro, 1991] to define the length of reach over which 95% of the gases input by a tile drain will be dissipated:
where v is stream velocity, KPC is the calibrated gas transfer coefficient, Dist5% is the distance at which 5% of the gases will remain in solution.
 Based on this relationship, tile drains in Layton Creek and the Black River are sufficiently far from our sampling sites that they will not affect gas dynamics. Mariposa Brook has numerous tile drains which affect our measured fluxes at all sites. Gas dynamics at the most upstream sampling site of Stouffville Creek are affected by an upstream flood control reservoir. Impacts are also consistently evident at the second site downstream, but not at the two sites located further downstream.
 Distance between sampling sites varied, but on average sites were separated by 5 km. Based on criteria described in equation (3), the distance between sites was sufficiently long that the vast majority (>95%) of gases were emitted prior to passage to adjacent downstream sites. However, in Stouffville Creek, gas concentrations at the second site were periodically influenced by the adjacent upstream site.
 We estimated time-weighted yearly fluxes for each site and each year. Time-weighted fluxes were calculated by averaging the instantaneous flux at the start and end of a sampling interval, multiplying this measurement by the duration of the sampling interval, then summing results for a 365 day period. 13–22 flux measurements were used in each annual flux estimate. We assumed no emissions occurred during periods of complete ice cover [Macdonald et al., 1991].
 We then calculated the mean flux for a stream across years and sites. Annual fluxes were calculated as described for 365 day periods ranging from June 2006–2007, June 2007–2008 and October 2006–2007 and October 2007–2008 for all sites where we had data. Recognizing the overlap in some annual estimates, we took the mean of any overlapping annual periods, and then the mean within a site (across years), then finally, the mean of sites within a stream.
 We excluded the third site on Mariposa Brook from our mean stream flux estimates because of concern that high fluxes of N2O are not indicative of the study reach. Due to access limitations at this site we measured gas transfer velocity downstream of our sampling site. While this reflects a real flux, it appears to reflect N2O accumulated in a deeper, slow-flowing upstream section, then degassed as it passes through this more turbulent downstream riffle.
2.4. Statistical Analyses
 We used best-subset multiple linear regression (SYSTAT 13.0) to develop models of annual N2O flux based on stream chemistry (NO2+3−, NH4+, total phosphorus [TP], DOC), accepting models where ΔAIC was ≤2 (from the minimum AIC).
 Next, we compiled N2O flux and NO3− concentration data from all published studies of streams where annual values were reported. Although discharge, depth, velocity and stream order were not reported, all of the streams assessed were small streams. Discharge in these systems (where reported) was typically <2 m3 s−1 [Baulch, 2009]. Where necessary, N2O flux and NO3− concentration data were digitized from figures (using Engauge Digitizer 3.0). Literature data were combined with the results of this study and simple linear regression was used to determine whether N2O fluxes were related to concentrations of NO3−. Data were log-transformed if necessary to meet the assumptions of statistical analyses.
 In addition to assessing predictors on an annual scale, we report simple correlations between daily fluxes and each variable across study period within our five study streams. As well, to identify predictors of under-ice N2O concentrations, we used best subset multiple linear regression, (Systat 13.0; using NO2+3−, NH4+, TP, organic N, SO42− and DOC data) and thresholds noted previously (ΔAIC ≤ 2). Data were restricted to periods where upstream ice coverage was 90–100% complete (average cover was 99%) to restrict the data to periods where gas exchange was zero, or extremely low.
 To further explore the issue of N2O consumption in Jackson Creek, we used a regression tree to analyze predictors of N2O % saturation among sites and over time. A regression tree is similar to stepwise regression procedures, but is a nonparametric method that does not assume linear relationships and is well-suited to analyses where interaction effects are anticipated, or relationships may vary through sample space. Data are repeatedly partitioned into two groups, with each split based on the explanatory variable which makes the resulting groups as homogenous as possible [De'ath and Fabricius, 2000]. The analysis results in a graph which can be interpreted in a similar fashion to a dichotomous key. We applied k-fold cross validation (k= 10), and based the selection of tree size on minimum cost criteria (lowest cross-validated relative error), regardless of tree size. We report two metrics of model fit, the cross validated relative error, where 0 indicates perfect fit, and 1 is equivalent to random guessing, and, the re-substitution relative error, which is akin to the coefficient of non-determination (i.e., 1 −r2). The predictive variables available for entry into the model were: NO2+3−, NH4+, organic N, DOC, SO42−, and temperature. Statistical analyses were performed using JMP 7.0.2, CART Pro V6.0, Systat 8.0 or Systat 13.0. A level of significance of α = 0.10 was applied.