The concentration of N₂O dissolved in tile drainage water was measured by collecting grab samples at the outlet of the drainage tiles during flow events in 2002, 2003 and 2004 (see supplementary for details on sample collection process). Samples were collected on a weekly basis or when drainage events were occurring. The diurnal pattern of N₂O emissions was examined by collecting samples every 4 hours over a 3-day flow event on April 27–29, 2004.

The NO₃ ⁻ and NH₄ ⁺ content and temperature of tile water discharge was determined from water samples collected as part of a parallel study using ISCO 6712 automatic samplers (Teledyne ISCO Inc., Lincoln, NB) (Jiang et al., 2011) (see supplementary for details on sample collection process).

During the 2002 to 2004 observation period the frequency of sampling depended upon tile flow. During flow events samples were collected between 0800 and 0900 h. The flow rate for each tile drain was calculated by multiplying the total number of tips of the tipping bucket by the amount of water each bucket holds. The tipping buckets were wired to a data logger (Campbell Scientific, Logan, UT). Tile drainage water N₂O emissions were calculated by accounting for individual plot flow rate on each sampling date. Cumulative N₂O emissions were calculated by linear interpolation of N₂O concentrations over the sampling dates for each flow event and these concentrations applied to daily water flow as measured by the tipping bucket flow meters.

There is uncertainty as to the degree of degassing of N₂O that occurs as water runs along the tile drainage pipes. The influence of tile length on N₂O concentration was evaluated by sampling the three in-field tile drainage systems at plot #8, which was in addition to the 12 experimental plots where the agronomic treatments were replicated. Plot eight received the treatment of 120 kg N ha⁻¹ NH₄NO₃. The total length of each tile drain in this plot was 81.5 m (see supplementary for details on sample collection process).

On 28 May 2004, water samples were collected from streams and springs to compare their dissolved N₂O concentration with that of subsurface drainage water. The stream was situated adjacent to the research site, with subsurface drainage water flowing into it. Spring samples were also collected at a nearby location. Stream and spring water samples were collected by 5 mL disposable syringe (Luer-lok tip, latex free, Becton-Dickinson, Franklin Lakes, NJ), injected immediately in an exetainer (12 mL) with sodium azide and sealed with silica sealant.

Vials containing water samples for N₂O analysis were equilibrated at room temperature (25°C) before being analyzed for headspace N₂O concentration. N₂O analysis was performed using a Varian Star 3,800 Ga Chromatograph (Varian, Mississauga, ON) fitted with an electron capture detector with a Combi-PAL autosampler (CTC Analytics, Zwingen, Switzerland). The autosampler removes a 2.5 mL volume from the sample tube and injects this into a sample valve that delivers 0.1 mL to the ECD. The ECD was operated at 300°C, 90% Ar, 10% CH₄ carrier gas at 20 mL min⁻¹, Haysep N 80/100 pre-column (0.32 cm diameter x 50 cm length) and Haysep D 80/100 mesh analytical columns (0.32 cm diameter x 200 cm length) in a column oven operated at 70°C. Pre-column was used in combination with a four-port valve to remove water from the sample. Operational conditions and data handling was performed with Varian Star software. In each analytical run of 147 samples a single replicate of three concentrations of standard gas mixtures were included for standardization of the instrument. The lab temperature was recorded during the analysis of dissolved N₂O concentration. Total N₂O dissolved in the water sample is the sum of N₂O in the headspace and N₂O dissolved in water. The molar mass of N₂O in the headspace was calculated from the Ideal gas law (Equation 1). M N 2 O g = P N 2 O * 10 − 6 × V N 2 O R × T (1)

Where: M_N2Og = moles of N₂O in vial headspace (mol); P_N2O = partial pressure of gas in the headspace (atm); V_HS = Volume of headspace (L); R = Gas constant (0.08214 atm/mol k); and T = lab temperature (^oK).

Henry’s law (Equation 2) describes the partitioning of a compound between a dilute aqueous and the gas phase: C N 2 O = H N 2 O × P N 2 O (2)

Where: C_N2O = Nitrous oxide concentration in the aqueous solution (moles/L); H_N2O = Henry’s law constant for nitrous oxide (2.5 × 10⁻² M/atm), and P_N2O = partial pressure of gas in the headspace (atm).

M_N2Ol (Equation 3) is caclulated from C_N2O present in V (5 mL) of the aqueous solution (1 mL of sodium azide and 4 mL of water sample). M N 2 O l = C N 2 O × V (3)

Where: M_N2Ol = Moles of the nitrous oxide in dissolved in water (moles); V = Volume of the aqueous solution in the vial (L).

Therefore, the total number of moles of nitrous oxide in the vial (Equation 4), less the estimated contribution of nitrogen by sodium azide (5.3 × 10⁻⁸ mol) is, T N 2 O = M N 2 O g + M N 2 O l − 5.3 × 10 − 8 (4)

Where: T_N2O = Total moles of nitrous oxide in head space and aqueous solution (moles).

The flux of dissolved N₂O (g N ha⁻¹ d⁻¹) was calculated by multiplying the dissolved N₂O concentration by the volume of tile drainage discharge per unit area (L ha⁻¹) as measured by the tipping bucket gauges and the area of the plot drained by the tile system.

Nitrate and ammonium concentration of the water samples were determined colorimetrically using a TRAACS 800 analyzer (Milburn et al., 1997). Dissolved organic carbon was analyzed by Formacs TOC analyzer (Hasegawa et al., 2000).

Dissolved N₂O concentrations in tile water discharge exhibited significant differences between sampling dates (p = 0.001) but were not significantly affected by nitrogen source (NH₄NO₃, solid manure and liquid manure) or timing (spring and fall application) of N application to the potato rotation (Table 3A; Table 3B; Figure 2). There are several possible explanations for this. In their meta-analysis examining the impact of manure applications on surface N₂O emissions in agricultural soils, Xia et al. (2020) found that the application of manure and synthetic fertilizers induced similar magnitude N₂O emissions when applied at the same N rate. While the overall emission factor following manure application (1.11%) is slightly lower than that of synthetic N fertilizer (1.25%), manure N₂O emissions were also impacted by factors such as C:N ratio and C content (Xia et al., 2020), which resulted in similar levels of emissions produced. It is reasonable to assume that this would also apply to dissolved N₂O below the soil surface. Additionally, while N fertilizer application has been found to be associated with elevated concentrations of dissolved N₂O and NO₃ ⁻ in water draining from agricultural fields (Hasegawa et al., 2000), since the processes responsible for producing dissolved N₂O in drainage water are spatially and temporally complex, the relationship between dissolved N₂O and N application rate may not be straightforward (Reay et al., 2004; Quesnel et al., 2019). For example, fertilizers and manures are applied and measured at or near the soil surface and can subsequently be transported by leaching and surface runoff. In contrast, N₂O can be produced throughout the soil profile; therefore, even after NO₃ ⁻ has been depleted from the soil surface, N₂O can still be being produced in the soil, resulting in a temporal disconnect in the presence of these substances due to spatial differences in where they are measured and/or produced. It is possible that these same processes could make it difficult to detect differences in N source treatments. Failure to detect differences in treatments may have also resulted from differences in the length of drainage pipe from the plot to the collection station. We noted an inverse relationship between the lengths of the tile lines and averaged observed dissolved N₂O concentrations (Figure 3). To confirm this observation air and water sampling access ports were inserted at three locations along the perforated portion of the tile line and at one location just outside the plot on an adjacent site. Average dissolved N₂O concentrations over ten sampling events were observed to decrease from 1.1 mg N₂O-N L⁻¹ to 0.3 mg N₂O-N L⁻¹ (Figure 4). These observations suggest that degassing of N₂O was occurring in the tile line and that concentrations measured at the sampling hut may underestimate total N₂O leaving the field. Normalizing all results for length of tile line did not, however, reveal significant N treatment effects. For the remainder of the discussion, we will consider trends observed across all 12 experimental units independent of N treatment.

Annual cumulative dissolved N₂O emissions ranged from 0.01 to 5.69 kg N ha⁻¹ (mean 0.83 kg N ha⁻¹) which were slightly higher than annual cumulative N₂O emissions occurring from the soil surface of 0.09–1.16 kg N ha⁻¹ (mean 0.33 kg N ha⁻¹) (Table 3A). The dissolved N₂O-N loss through subsurface drainage water was an order of magnitude less than NO₃ ⁻-N, which ranged from 0.26 to 29.3 kg N ha⁻¹ (mean 8.7 kg N ha⁻¹; Table 3A). The dissolved N₂O results in our study are higher than other values of dissolved N₂O in tile drains reported in the literature, which ranged from 0.03–0.38 kg N₂O-N ha⁻¹yr⁻¹ (Dowdell et al., 1979; Hack and Kaupenjohann, 2002; Reay et al., 2004; 2009; Quesnel et al., 2019). Similarly, Reay et al. (2009), observed annual dissolved losses of N₂O in agricultural drainage that were higher than the amount being emitted at the soil surface. In contrast, Bruun et al. (2017) found that the main export pathway was dissolved N₂O, with negligible N₂O produced at the soil surface, and both Dowdell et al. (1979) and Hack & Kaupenjohann, (2002) concluded that N₂O loss in agricultural drainage water was a minor component of the soil N balance. However, Quesnel et al. (2019) found that cumulative annual soil surface N₂O emissions (13.8 kg N₂O-N ha⁻¹) were much higher than dissolved N₂O losses (0.03 kg N₂O-N ha⁻¹) in tile drainage systems. Hama-Aziz et al. (2016) observed concentrations of dissolved N₂O in agricultural tile drainage systems were comparable to NO₃ concentrations. Our results indicate that dissolved N₂O emissions from potato cropping systems can be a major source of agricultural N₂O emissions in PEI–comparable or higher than surface N₂O emissions. This is likely because the majority of precipitation occurs in the non-cropping season in PEI, when conditions at the soil surface may be less favorable for denitrification and may prevent the release of N₂O produced in deeper soil layers to the atmosphere. However, large amounts of NO₃ ⁻ are still lost from these tile drainage systems.

N₂O loss in tile drainage water was strongly influenced by season with up to 62% of N₂O emissions occurred during the non-growing season (Figure 2A). One or two high N₂O emission events can contribute a significant amount for that particular year (Figure 2B). Dissolved N₂O concentrations exhibited high temporal variability and were independent of the volume of tile flow (data not shown). For instance, in 2003, the highest and lowest dissolved N₂O concentrations (3.8 mg N L⁻¹, 0.01 mg N L⁻¹) were observed within a timespan of several days during the same flow event. A study of dissolved N₂O emissions over a 36-h monitoring period observed a mean concentration of 0.48 mg N L⁻¹, a coefficient of variation of 46%, with values ranging from 0.13 to 0.81 mg N L⁻¹. Reay et al. (2003) have observed similar variation in dissolved N₂O in agricultural drainage waters. Peak dissolved N₂O concentrations (4.2 mg N L⁻¹) recorded in this study were higher than those reported by others (Dowdell et al., 1979; Hack and Kaupenjohann, 2002; Hasegawa et al., 2000; Minami and Fukushi, 1984; Minami and Oshawa, 1990; Reay et al., 2003; Sawamoto et al., 2002; Sawamoto et al., 2003).

Over the monitoring period dissolved N₂O concentrations of water collected from tile lines ranged from less than 0.01 mg N L⁻¹–4.2 mg N L⁻¹ (Figure 2B). The highest dissolved N₂O concentrations occurred during winter 2003 (Figure 2B). A continuous frozen layer was present from 27 November 2002 to 29 April 2003, which may have prevented gas phase transport of N₂O to the soil surface and resulted in an accumulation of N₂O in the atmosphere of subsurface layers (Burton and Beauchamp, 1994). Elevated N₂O concentrations in the soil atmosphere would result in greater N₂O dissolution in soil water and a supersaturated soil solution. As N₂O is highly soluble in cold water, there is a high probability that the water draining through the soil profile at this time would contain a high concentration of dissolved N₂O (Goodroad and Keeney, 1984). In the tile flow of 2001–2002 and 2003–2004, N₂O emissions were much lower than 2002–2003. The winter pattern is similar for both years, with the soil at 5 cm depth freezing only for a few days at a time. Furthermore, there was precipitation at regular intervals from November to March in both 2001–2002 and 2003–2004 (Figures 1A, C). The lack of a continuous frozen layer and regular precipitation would favor more rapid NO₃ ⁻ leaching, reducing the opportunity for N₂O production and accumulation in the subsurface. The relative contribution of surface and sub-surface pathways appears to site-specific and may vary significantly from year to year.

During the observation period, dissolved NO₃ ⁻ emissions from tile lines fluctuated between 0.09 and 39 mg N L⁻¹ (Figure 2B). In general, the NO₃ ⁻ concentrations observed in this study are comparable to previous studies conducted at this site (Milburn et al., 1997) and to values reported by others (Dowdell et al., 1979; Hack and Kaupenjohann, 2002; Hasegawa et al., 2000; Minami and Fukushi, 1984; Minami and Oshawa, 1990; Quesnel et al., 2019; Reay et al., 2003; Sawamoto et al., 2002; Sawamoto et al., 2003). The timing of manure and fertilizer applications to the potato crop (fall 2000, spring 2001, fall 2003, spring 2004) influenced the magnitude of NO₃ ⁻ loss in tile water. After the potato harvest in 2001, the research plots were left fallow. The NO₃ ⁻ not utilized by the potato crop and accumulating in the soil increased the loss of NO₃ ⁻ in the tile flow during 2001–2002 non-growing period (Figure 2B). Low rates of nitrogen fertilizer (40 kg N ha⁻¹) were applied to barley crop across all N treatments in 2002, reducing fall NO₃ ⁻ accumulation in the soil and the loss of NO₃ ⁻ via tile drainage flow during the 2002–2003 non-growing period (Figure 2B).

There was a significant (p < 0.01) negative correlation between dissolved N₂O-N and NO₃ ⁻-N concentration for individual observations, but this accounted for less than 10% of the total variation in the data (R ² = 0.05; Figure 5A). These results are similar to Sawamoto et al. (2003) and Reay et al. (2004), who both found little or no relation between N₂O-N and NO₃ ⁻-N concentration in agricultural drainage water. In contrast others have observed a positive relationship between dissolved N₂O-N and NO₃ ⁻-N in agricultural drainage waters (Hack and Kaupenjohann, 2002; Minami and Oshawa, 1990; Reay et al., 2003). Dowdell et al. (1979) and Hack and Kaupenjohann (2002) have noted NO₃ ⁻ concentrations are typically one to three orders of magnitude higher than N₂O concentrations. In our study N₂O and NO₃ ⁻ concentration were one to two orders of magnitude greater than dissolved N₂O concentrations, depending on season (Table 3A).

The strength of the relationship between dissolved N₂O-N and NO₃ ⁻-N was much greater when cumulative losses were examined. A significant (p < 0.001) positive relationship existed between cumulative annual N₂O-N and NO₃ ⁻-N losses (Figure 5B). The slope of this relationship was significantly greater in 2003 than in the other 2 years of study. The relationships within individual years accounted for a much greater percentage of the total variation ranging from 36% to 89% of the total variation (Figure 5B).

The difference in the relationship between N₂O and NO₃ ⁻ concentrations in drainage water for individual sampling events (Figure 5A) vs. cumulative annual N losses (Figure 5B) provides an interesting contrast. The rather weak negative relationship in the weekly samples indicates that the processes resulting in these losses are independent at this time scale or that these processes are occurring at different location and are thus exposed to different environmental conditions. However, the positive relationship between N₂O and NO₃ ⁻ for each year of observation indicates that over this longer timeframe both processes appear to be responding to similar controls. In essence the leakiness of the system with respect to nitrogen is similarly expressed in terms of both of NO₃ ⁻ and N₂O losses. These losses simply are not observed at the same time at the end of the tile drain. These results are similar to Quesnel et al. (2019), who observed a significant positive relationship between mean dissolved N₂O-N and NO₃ ⁻-N concentrations during the growing season, however they found that the relationship became weaker in the non growing season. They attributed this to the greater complexity of N₂O production and transport in the non-growing season. Overall, our results indicate that a positive relationship exists between NO₃ ⁻ and N₂O, but that these processes are spatially and/or temporally separate.

Currently the IPCC coefficients for N₂O emissions from agricultural drainage is calculated as a fixed fraction of the NO₃ ⁻-N estimated to be lost from the soil profile (EF₅ = 0.0075 kg N₂O-N kg⁻¹ N leached). Here, on an annual basis the ratio of kg N₂O-N lost per kg NO₃ ⁻-N leached ranged from 0.035 to 0.62 kg N₂O-N kg⁻¹ N leached. These values are significantly higher than the IPCC coefficient for this site in these years and therefore would underestimate the actual N₂O emissions at this site.