Modelling Nitrification Inhibitor Effects on N 2 O Emissions after 1 Fall and Spring-Applied Slurry by Reducing Nitrifier NH 4 + 2 Oxidation Rate 3

7 Reductions in N2O emissions from nitrification inhibitors (NI) are substantial, but remain 8 uncertain because measurements of N2O emissions are highly variable and discontinuous. 9 Mathematical modelling may offer an opportunity to estimate these reductions if the processes 10 causing variability in N2O emissions can be accurately simulated. In this study, the effect of NI 11 was simulated with a simple, time-dependent algorithm to slow NH4 + oxidation in the ecosystem 12 model ecosys. Slower nitrification modelled with NI caused increases in soil NH4 + 13 concentrations and reductions in soil NO3 concentrations and in N2O fluxes that were consistent 14 with those measured following fall and spring applications of slurry over two years from 2014 to 15 2016. The model was then used to estimate direct and indirect effects of NI on seasonal and 16 annual emissions. After spring slurry applications, NI reduced N2O emissions modelled and 17 measured during the drier spring of 2015 (35% and 45%) less than during the wetter spring of 18 2016 (53% and 72%). After fall slurry applications, NI reduced modelled N2O emissions by 58% 19 and 56% during late fall in 2014 and 2015, and by 8% and 33% during subsequent spring thaw in 2


Introduction
Nitrification inhibitors (NI) have frequently been found to reduce N 2 O emissions from fertilizer and slurry applications in agricultural fields. In a meta-analysis of field experiments conducted for 2008, Akiyama et al. (2010) found average reductions of 38 ± 6 % in N 2 O emissions from NI, with some variation attributed to land use type and emission rates. Similar average reductions of 35 %-40 % were reported in more recent meta-analyses by Ruser and Schulz (2015), Gilsanz et al. (2016), and Gao and Bian (2017). However the magnitudes of these reductions are uncertain because they vary with the rate and timing of fertilizer or slurry application, with land use and ecosystem type (Akiyama et al., 2010), and with application method (Zhu et al., 2016). These magnitudes are also uncertain because measurements of the N 2 O emissions on which they are based are highly variable temporally and spatially and difficult to sustain over the annual time periods needed to estimate NI reductions.
The effects of NI on N 2 O emissions are attributed to inhibition of ammonia monooxygenase, which slows the oxidation of NH + 4 to NO − 2 during nitrification (Subbarao et al., 2006) and hence slows the reduction of NO − 2 to N 2 O during nitrifier denitrification. The consequent slowing of NO − R. F. Grant et al.: Modelling nitrification inhibitor effects on N 2 O emissions summer (e.g. Akiyama et al., 2010). The effectiveness of NI with fall applications of fertilizer or slurry on cold soils has thus far received very limited attention (Ruser and Schulz, 2015), although in cold climates N 2 O emissions during the spring thaw following fall applications may exceed those during late spring and summer following spring applications (Lin et al., 2018). Emissions during spring thaw were attributed by Wagner-Riddle and Thurtell (1998) to soil NO 3 -N concentrations exceeding 20 mg kg −1 generated by fallapplied slurry that contributed to total N 2 O emissions exceeding 0.2 g N m −2 measured between January and April of the following year. Large N 2 O emissions measured in late winter were attributed by Dungan et al. (2017) to labile N not used by soil microorganisms during the previous fall and winter that was actively metabolized when the soils began to warm in early March. Interannual differences in spring thaw emission events after fall slurry applications were related by Kariyapperuma et al. (2012) to those in total soil mineral N content in the upper 15 cm of the soil profile during spring thaw. The effects of NI on N 2 O emissions during spring thaw will therefore depend on the persistence with which NI reduce nitrification in cold soils during fall and winter and thereby alter mineral N concentrations during the following spring.
Reductions in N 2 O emissions directly caused by slower nitrification with NI may be partially offset by increases in indirect N 2 O emissions from increasing NH 3 emissions caused by greater soil NH + 4 concentrations (Lam et al., 2017;Qiao et al., 2015). NI may also decrease indirect N 2 O emissions by reducing NO − 3 concentrations and hence leaching. Both direct and indirect effects of NI on N 2 O emissions must be considered when estimating effects of NI on total N 2 O emissions.
The Intergovernmental Panel on Climate Change (IPCC) Tier 3 methodology for estimating N 2 O emissions under diverse climates, soils, fertilizers and land uses includes the use of comprehensive, process-based mathematical models of terrestrial C, N, and water and energy cycling (IPCC, 2019). Although NI effects on nitrification have been added to some existing process models (Cui et al., 2014;Del Grosso et al., 2009;Li et al., 2020), testing of modelled NI effects on N 2 O emissions against measurements remains limited to brief periods following soil N amendments (e.g. Giltrap et al., 2011). The mathematical model ecosys explicitly represents the key processes in nitrification (Grant, 1994), denitrification (Grant, 1991) and associated N 2 O emissions (Grant, 1995) and has been tested against measurements of N 2 O emissions using micrometeorological methods and manual and automated chambers Pattey, 1999, 2008;Grant et al., 2006Grant et al., , 2016Metivier et al., 2009). In this study, we propose that applying a time-dependent reduction of NH + 4 oxidation rates during nitrification will enable ecosys to simulate the time course of reductions in N 2 O emissions with NI measured after fall and spring applications of dairy slurry in a field experiment. The model is then used to estimate the di- rect and indirect effects of NI on annual N 2 O emissions with fall and spring slurry applications as required for IPCC Tier 3 methodology and how these effects would change with alternative tillage practices and timings of slurry application.
2 Model development

General overview
The hypotheses for oxidation-reduction reactions involving N 2 O, and the aqueous and gaseous transport of their substrates and products, are represented in Fig. 1 and described in further detail below. These hypotheses function within a comprehensive model of soil C, N and P transformations, which is coupled to models of soil water, heat and solute transport in surface litter and soil layers. These models function within the comprehensive ecosystem model ecosys. Key transformations that drive N 2 O emissions are described in Sect. 2.2 to 2.8 below, and modifications of these transformations to simulate nitrification inhibition are described in Sect. 2.9. References to equations and definitions in Sect. 2.2 to 2.8 and given in Supplement S1, S3, S4, S5 and S8 (Table 1) are provided for those interested in model methodology but are not needed for a general understanding of model behaviour.

Mineralization and immobilization of ammonium by microbial functional types
Heterotrophic microbial functional types (MFTs) m (obligately aerobic bacteria, obligately aerobic fungi, facultatively anaerobic denitrifiers, anaerobic fermenters, acetotrophic methanogens, and obligately aerobic and anaerobic non-symbiotic diazotrophs) are associated with each organic 1. NH + 4 uptake by roots and mycorrhizae under nonlimiting O 2 is calculated from mass flow and radial diffusion between adjacent roots and mycorrhizae [C23a] coupled with active uptake at root and mycorrhizal surfaces [C23b]. Active uptake is subject to product inhibition by root nonstructural N : C ratios [C23g], where nonstructural N is the active uptake product, and nonstructural C is the CO 2 fixation product transferred to roots and mycorrhizae from the canopy.

Nitrification inhibition
For this study, NI were assumed to reduce specific rates of NH + 4 oxidation by nitrifiers in step 1 in Sect. 2.5, thereby simulating inhibition of ammonia monooxygenase (Subbarao et al., 2006). This reduction was represented by a timedependent scalar I : where t is the current time step (h), t − 1 is the previous time step (h), I is the inhibition (initialized to 1.0 at t = 0 at the time of application), R I is the rate constant for decline of I representing NI degradation (set to 2.0 × 10 −4 h −1 for more persistent NI such as 3,4-dimethylpyrazole phosphate -DMPP -and to 1.0 × 10 −3 h −1 for less persistent NI such as nitrapyrin; Ruser and Schulz, 2015), f T s is an Arrhenius function of soil temperature (T s ) used to simulate T s effects on microbial activity ([A6] in step 1, Sect. 2.3), and l is the soil layer in which NI are present. The values of R I and f T s for DMPP were selected to give time and temperature dependencies of DMPP activity following application inferred from incubation studies by Guardia et al. (2018). Model results for NI presented below are those using the smaller R I for DMPP unless stated as those using the larger R I for nitrapyrin. Specific rates of NH + 4 oxidation (step 1, Sect. 2.5) with NI was calculated as where X NH 4 and X NH 4 are specific NH + 4 oxidation rates with and without NI (g N g nitrifier C −1 h −1 ), [NH + 4 ] is the aqueous NH + 4 concentration (g N m −3 in dynamic equilibrium with [NH 3 ]), and K iNH 4 is an inhibition constant set at 7000 g N m −3 to reduce inhibition at very large [NH + 4 ] as suggested in Janke et al. (2019). These rates were used to calculate nitrification rates [H11]: where X NH 4 t is the nitrification rate (g N m −2 h −1 ), M n is the nitrifier biomass (g C m −2 ), and K NH 4 and K CO 2 are halfsaturation constants for aqueous NH + 4 and CO 2 (g N and C m −3 ). The NI in Eq. (1) slows X NH 4 t in Eq. (2) and thereby X NH 4 t in Eq. (3) and hence slows NO − 2 production from nitrification (step 4, Sect. 2.5) and thereby N 2 O production from nitrification (step 2, Sect. 2.7) and denitrification (step 3, Sect. 2.4). By slowing X NH 4 t in Eq. (3), NI also reduce nitrification energy yield and hence M n growth, biomass [A25] and O 2 uptake [H13], thereby further reducing N 2 O production. spring application of dairy slurry; split plot: control vs. NI treatments) on plots 2.4 m in width and 6.1 m in length with three replicates. The NI products ENTEC (EuroChem Agro, Mannheim, Germany) and the eNtrench nitrogen stabilizer (Dow Chemical Company, Dow AgroSciences, Calgary, AB, Canada) were mixed with the slurry immediately before application to provide 0.4 kg ha −1 of the active ingredient with slurry injection of 56.17 m 3 ha −1 at 12.7 to 15.2 cm (average 14 cm) depth and 28 cm spacing. Measured concentrations of NH + 4 and of organic N and C in each slurry application were used to calculate rates of NH + 4 , organic N and organic C amendments (Table 3). Soil NH + 4 concentrations were measured from 0 to 10 cm every 2-3 weeks between spring thaw and autumn freezing in 2014, 2015 and 2016. Further details of this field experiment are given in Lin et al. (2018).
Weather data (radiation, air temperature -T a , humidity, wind speed and precipitation) were recorded hourly from 2012 to 2016 at the South Campus Farm. During the first experimental year (16 September 2014 to 15 September 2015) T a remained 1-2 • C higher than historical (1981-2010) averages (Lin et al., 2018; Table 4). Precipitation was slightly higher than historical averages during autumn and winter but  Organic was about one-half those during spring and summer. During the second experimental year (16 September 2015 to 15 September 2016), T a was higher than that of the first year during winter and early spring and similar during late spring and summer. However precipitation during the second year was lower from autumn to early spring and much higher during late spring and summer.

N 2 O flux measurements
N 2 O fluxes were measured at 3 h intervals from as soon as field conditions allowed after spring thaw to late summer during both experimental years with automated chambers (height of 26 cm, area of 0.216 m 2 ) connected by 0.5 cm i.d. tubes to a FTIR gas analyser (GASMET model CX4025, Temet Instruments, Finland) through which air flow was maintained at 5.1 L min −1 . During each 20 min measurement period, the chambers remained open for the first 5 min to re-store ambient N 2 O concentrations in the gas analyser, after which chambers were closed and N 2 O concentrations were measured at 10 Hz and averages recorded at 1 min intervals. Concentrations during the first minute after closure were discarded, and those during the following 14 min were used to calculate fluxes using linear regression with an acceptance criterion of R 2 ≥ 0.85. Based on the analytical precision of the gas analyser, the N 2 O flux detection limit was determined to be ±0.03 mg N m −2 h −1 .
N 2 O emissions were also measured once or twice per week from spring thaw to autumn freezing during both experimental years with manually operated chambers as described in Lin et al. (2018). The time required for installation of the automated chambers after snowmelt limited their ability to measure N 2 O emissions during spring thaw so that measurements from the manually operated chambers were used to evaluate emissions during these periods.

Model runs
The spin-up run was extended from 1 January 2014 to 31 December 2016 under weather data recorded from 2014 to 2016 with the land use schedules and practices from the field site (Table 3). Each modelled slurry application was added to the soil layer, the depth of which corresponded to that of slurry injection in the field experiment (14 cm). Modelled applications were accompanied by addition of water corresponding to the volume and depth of the application (5.6 mm from 56.17 m 3 ha −1 at 14 cm in Sect. 3.1), and by tillage using a coefficient for surface litter incorporation and soil mixing of 0.2 to the depth of application (14 cm), based on field observations. A control run was also conducted in which no slurry applications were modelled. For all silage harvests, cutting height and harvest efficiency were set to 0.15 m and 0.9 so that 0.9 of all plant material above 0.15 m was removed as yield. Concentrations of NH + 4 and NO − 3 , and N 2 O emissions modelled during key emission events, were compared with measured values (Sect. 3.1 and 3.2), and modelled emissions were then aggregated into seasonal and annual values.
There is some flexibility in the timing of fall slurry application between crop harvest in late summer and soil freezing in early November. To examine how timing of fall slurry application would affect subsequent N 2 O emissions with and without NI, fall slurry application dates were advanced or delayed by 2 weeks from those in Table 3, and effects on spring  ) and annual N 2 O emissions were evaluated. To examine how increased tillage during slurry application would affect subsequent N 2 O emissions with and without NI, coefficients for surface litter incorporation and soil mixing to the depth of slurry application were raised from 0.2 to 0.5 and 0.8 for fall and spring applications. In the model, NI slowed NH + 4 oxidation (Sect. 2.9, Eq. 3) so that declines in NH + 4 concentrations modelled and mea-sured after fall and spring slurry applications with NI were slower than those without NI (Fig. 2a), particularly during winter, when declines in inhibition were slowed by low T s (Sect. 2.9, Eq. 1) following the onset of soil freezing modelled at the depth of slurry injection (DOY 313 in 2014 and DOY 318 in 2015 in Fig. 2a). Overwinter declines in NH + 4 concentrations were slower during the winter of 2015-2016, with lower T s modelled under less winter precipitation and hence shallower snowpack (Table 4). These slower declines caused larger NH + 4 concentrations to be modelled during the following spring, consistent with measurements (Fig. 2a). The slower declines in NH + 4 concentrations modelled with NI caused slower rises in NO − 3 concentrations following fall slurry applications (Fig. 2c). However slower rises with NI were not always apparent in the measured NO − 3 concentrations.

Spring slurry applications
Declines in NH + 4 concentrations modelled after slurry applications with NI in spring 2015 and 2016 were also slower than after those without NI (Fig. 2b), consistent with higher NH + 4 concentrations measured after spring application with DMPP in both years (Fig. 2b). These slower declines caused slower rises in NO − 3 concentrations to be modelled following spring slurry applications with NI (Fig. 2d).

Fall slurry applications
In the model, soil ice impeded drainage during spring snowmelt and soil thaw, raising θ w and lowering θ g , thereby slowing gas transfers in gaseous phases and gas exchanges between gaseous and aqueous phases (Sect. 2.3, step 3; Fig. 1). Freeze-thaw effects on N 2 O emissions modelled during early spring are further described in Grant and Pattey (1999). Slower O 2 transfers relative to O 2 uptake (Sect. 2.3, 2.5 and 2.6) forced reductions in aqueous O 2 concentrations (O 2s ) to be modelled during early spring in 2015 (Fig. 3a (Table 4). Earlier and more persistent declines in O 2s were modelled in 2016 because greater θ i modelled with less thermal insulation under a shallower snowpack reduced or eliminated θ g during much of the winter. Drainage of meltwater after snowmelt eventually lowered θ w and raised θ g , allowing O 2s to return to atmospheric equivalent concentrations.
Declines in O 2s in slurry-amended treatments drove increases in aqueous N 2 O concentrations (N 2 O s ; Fig. 3b, d) during winter and early spring (Sect. 2.7, step 1). These rises were similar with and without NI in spite of higher NH + 4 concentrations without NI (Fig. 2a). Rises in θ g following spring drainage allowed volatilization of N 2 O from aqueous to gaseous phases, reducing N 2 O s and driving N 2 O emissions modelled during spring thaw.

Spring slurry applications
Declines in O 2s modelled after spring slurry application were small during the drier spring of 2015 (Table 4; Fig. 3e) but were greater with lower θ g during the wetter spring of 2016 (Fig. 3g). During both years, these declines were more rapid with slurry than without but less rapid with NI-amended slurry than with unamended slurry. Greater declines in O 2s modelled in 2016 vs. 2015 drove greater increases in N 2 O s (Sect. 2.7), particularly without NI, and hence greater emissions of N 2 O during subsequent declines in N 2 O s .

Fall slurry applications
Smaller rises and subsequent declines in N 2 O s modelled with NI than without (Fig. 3b) drove smaller N 2 O emission events modelled during spring thaw in 2015 (Fig. 4a) following slurry application in fall 2014 (Fig. 4b). These events were driven by increases in θ g during mid-afternoon thawing of near-surface soil but were terminated by loss of θ g during nighttime refreezing. These events preceded the start of the automated chamber measurements on DOY 102 and so could not be corroborated by them. However measurements with manual chambers earlier in spring 2015 by Lin et al. (2018) indicated that N 2 O emission events occurred from DOY 85 to 100 that were similar in magnitude although not always in timing with those modelled (Fig. 4b). These measured emissions were smaller with NI than without, consistent with modelled emissions.
The smaller rises and subsequent declines in N 2 O s modelled with NI than without in the winter of 2016 (Fig. 3d) drove smaller emission events during thawing and refreezing of near-surface soil in spring 2016 (Fig. 5a) following slurry application in fall 2015 (Fig. 5b). These modelled events preceded the start of automated chamber measurements on DOY 91, but earlier measurements with manual chambers indicated that N 2 O emission events occurred from DOY 74 to 93. The smaller emission events modelled with NI were consistent with those measured using the manual chambers, although some larger emissions measured with DMPP using the automated chambers from DOY 91 to 102 were not modelled (Fig. 5b). In both years, emissions modelled and measured without slurry remained very small, consistent with low N 2 O s (Fig. 3b, f).

Spring slurry applications
Modelled N 2 O emissions closely followed measured values during a brief emission event following slurry application in the drier spring of 2015 (Fig. 6a, b), driven by small rises and declines in N 2 O s (Fig. 3f). The smaller rise and decline in N 2 O s modelled with NI than without drove smaller N 2 O emissions which declined more rapidly after application than emissions measured with DMPP (Fig. 6b).
Emissions modelled without NI in the wetter spring of 2016 were larger than those in the drier spring of 2015 (Fig. 7a, b), driven by a larger rise and decline in N 2 O s with lower θ g (Fig. 3h). These emissions were suppressed by low θ g with soil wetting during heavy rainfall on DOY 141-143 shortly after slurry application (Fig. 7a,b) but resumed when θ g rose with soil drainage thereafter (Fig. 7b). Emissions modelled without NI remained greater than those measured until DOY 150, after which modelled values declined with soil drying while the measured value rose (Fig. 7b). Greater reductions in N 2 O s (Fig. 3h) and hence in N 2 O emissions were modelled with NI after slurry application in the wetter spring of 2016 (Fig. 7b) than in the drier spring of 2015 (Fig. 6b). In both years, emissions modelled and measured without slurry remained very small, consistent with low N 2 O s (Fig. 3f, h).

Spring slurry applications
Reductions in annual N 2 O emissions modelled from spring slurry applications with DMPP and nitrapyrin occurred almost entirely during late spring and summer (1 May-15 September in Table 6). These reductions were 22 % and 40 % from those modelled without NI in 2014-2015 and 2014-2016 respectively ( Table 6). The reduction modelled with NI in 2014-2015 was greater than that of 0 % for DMPP estimated from manual chamber measurements from 1 October 2014 to 30 September 2015 by Lin et al. (2018), although the reduction modelled in 2014-2016 was similar to that of 38 %, estimated from manual chamber measurements from 1 October 2015 to 30 September 2016.

Effects of management on seasonal and annual N 2 O emissions modelled after fall and spring slurry applications
Advancing fall slurry application by 2 weeks increased N 2 O emissions modelled with and without NI during autumn but reduced those during subsequent spring thaw (F−2 in Table 6) so that annual emissions modelled with and without NI were similar to those in F with the application dates in the experiment (Table 3). Delaying fall slurry application by 2 weeks reduced N 2 O emissions modelled with and without NI only slightly during autumn but greatly increased emissions modelled during subsequent spring thaw (F+2 in Table 6), particularly with the later fall application in 2016 (Table 3). Consequently delaying fall slurry application by 2 weeks caused substantial increases in annual N 2 O emissions. However reductions in N 2 O emissions modelled with NI in F+2 in 2015 and 2016 (34 % and 47 %) were greater than those in F (26 % and 38 %) because inhibition declined more slowly in colder soil (Eq. 1), particularly with later application in 2016. Increasing surface litter incorporation and soil mixing during fall slurry application raised N 2 O emissions modelled without NI only slightly during 2014-2015 but substantially during 2014-2016, particularly during spring thaw (F0.5 and F0.8 vs. F in Table 6). Increasing surface litter incorporation and soil mixing during spring slurry application had limited effects on emissions (S0.5 and S0.8 vs. S in Table 6). Greater mixing caused reductions in N 2 O emissions modelled with NI to be smaller relative to those without NI.

NI effects on annual mineral N losses and NH 3 emissions
Injecting the slurry to 14 cm in the model suppressed NH 3 emissions with limited soil mixing and caused only very small emissions with greater mixing (Table 7). Higher NH + 4 concentrations modelled with NI ( Fig. 2a, b) increased net NH 3 emissions, particularly if fall slurry application was delayed or soil mixing was increased in 2014-2015.
The subhumid climate at Edmonton (Table 4) caused modelled NO − 3 losses to remain small. For both fall and spring applications, lower NO − 3 concentrations modelled with NI (Fig. 2c, d) caused small reductions in NO − 3 losses.

NI effects on barley silage yields
Silage yields modelled with fall slurry application were smaller than those measured in the drier year 2015, but those modelled with both applications were greater than those measured in the wetter year 2016, likely because of lodging observed in the field plots following the second year of heavy manure use (Table 8). Modelled yields were unaffected by NI for fall and spring applications in both years, although measured yields were raised by NI with spring application in 2015. Modelled yields were affected by the cutting height and harvest efficiency set in the model runs (Sect. 4.2).  (Fig. 1) (Nguyen et al., 2017;Owens et al., 2017). These O 2 deficits were modelled using a K m for O 2m of 10 µM by nitrifiers (Sect. 2.5, step 3) and 2 µM by denitrifiers (Sect. 2.3, step 3) derived from biochemical studies by Focht and Verstraete (1977). These K m values are less than 5 % and 1 % of atmospheric equivalent concentration, indicating the importance of explicitly simulating gaseous and aqueous transport processes when modelling N 2 O emissions. O 2 deficits were modelled in spring thaw 2015 (Fig. 3a), when diffusion was sharply reduced by soil saturation because drainage from snowmelt and soil thaw was impeded by underlying ice layers. These declines drove N 2 O generation (Fig. 3b) and emission (Fig. 4b) almost entirely from NO − 2 reduced during spring thaw. O 2 deficits were also modelled during winter 2016, when increased θ i from soil freezing with lower T s under a shallower snowpack caused nearsurface soil porosity to be fully occupied by ice and water. Consequent loss of θ g greatly reduced surface gas exchange and hence gradually reduced soil O 2 concentrations, particularly with increased O 2 demand from fall slurry application (Fig. 3c). The extended period of low O 2s prolonged overwinter accumulation of N 2 O s after fall slurry application (Fig. 3d). Transient increases in θ g during soil freezethaw cycles caused several N 2 O emission events to be modelled during spring thaw in 2016, mostly from degassing through volatilization of overwinter N 2 O s (Fig. 5b). De- Table 7. Annual NO − 3 discharge and NH 3 emissions modelled from 16 September to 15 September in 2014-2015 and 2014-2016 without slurry (C) or with slurry applied in fall (F) or spring (S) without NI and with DMPP on dates in the field study (Table 3), in fall on dates 2 weeks before (F−2) or after (F+2) those in the field study, and with soil mixing during slurry application (M) increased to 0.5 and 0.8 from 0.2 in the field study. For NH 3 positive values indicate deposition, and negative values indicate emission.  Table 8. Barley silage yields modelled and measured without slurry (C) or with slurry applied in fall (F) or spring (S) with and without NI applied on dates in the field study (Table 3).
Mes. a Mod.
Mes. a,b Treat. Amend. g C m −2 g C m −2 g C m −2 g C m −2 gassing events in the model were consistent with field observations by Chantigny et al. (2017) that passive degassing of accumulated gases made a significant contribution to spring thaw emissions, during which two or more consecutive emission peaks were often observed. In the model, the contribution by degassing of overwinter N 2 O s to spring thaw emissions increased with intensity and duration of soil freezing during the previous winter. N 2 O emissions simulated during spring thaw were thus driven by concurrent NO − 2 reduction during spring thaw (2015) and by earlier NO − 2 reduction accumulated over the previous winter (2015-2016), as has been proposed from experimental observations (Teepe et al., 2004).
O 2 deficits were also caused by rapid increases in O 2 active uptake with addition of labile C in slurry, the rapid decomposition and oxidation of which (Sect. 2.3, step 1) caused transient declines in O 2s with soil wetting from slurry application and precipitation (Fig. 3e, g). After slurry application in the wetter spring of 2016, modelled O 2g declined to around one-half of atmospheric concentration, driving the sharp declines in O 2s shown in Fig. 3g. The modelled declines in O 2g were consistent with results from an incubation of wetted soil amended with cattle slurry by Nguyen et al. (2017), in which O 2g declined below one-half of atmospheric concentration within 1 d of slurry application and gradually rose again after 2 d, while no decline occurred in an unamended soil. The period of low O 2s in this incubation study coincided with peak emissions of CO 2 and N 2 O from the amended soil, as was modelled here in Figs. 3f, h, 6b and 7b. This coincidence indicated that NH + 4 and DOC oxidation drove O 2 deficits from demand for O 2 from oxidation vs. supply of O 2 through convection-dispersion, which caused NO − 2 reduction as represented in the model, again demonstrating the importance of simulating aqueous and gaseous O 2 transfers when modelling N 2 O emissions.
6.2 Process modelling of NI effects on N 2 O emissions 6.2.1 Fall slurry application NH + 4 oxidation in the model (Sect. 2.5, step 4) proceeded rapidly after fall slurry application without NI, as indicated by rapid declines in NH + 4 (Fig. 2a), consistent with observations in other studies that soil NH + 4 concentrations returned to background levels 30 d after fall slurry application (Rochette et al., 2004). Slower NH + 4 oxidation modelled with NI (Eq. 3) during fall caused slower declines of soil NH + 4 before and during freezing and hence larger NH + 4 concentrations during spring thaw (Fig. 2a). These slower declines were modelled from slower decline of I t with low f T s in cold soils (Eq. 1), which slowed NH + 4 oxidation and thereby reduced N 2 O emissions simulated during late autumn and spring thaw (Figs. 4b and 5b), despite increased NH + 4 concentrations (Fig. 2). These reductions were consistent with those from chamber measurements at the Edmonton South Campus Farm (Lin et al., 2018) and with those from a limited number of studies elsewhere, in which persistent effects of NI in reducing overwinter N 2 O emissions have been found (e.g. Pfab et al., 2012), indicating the importance of f T s in Eq. (1).
The slower decline of I t from low f T s enabled ecosys to simulate larger reductions in N 2 O emissions with NI after fall slurry applications in cooler soil vs. spring slurry applications in warmer soil during both years (F during autumn vs. S during late spring-summer in Table 6). Reductions in N 2 O emissions modelled with NI after fall slurry applications became greater when fall applications were delayed (F+2 in Table 6), further reducing T s and f T s during subsequent nitrification. The greater reductions modelled with fall applications were consistent with experimental observations by Merino et al. (2005), who attributed larger reductions in N 2 O emissions measured with NI from fall-applied vs. spring-applied cattle slurry to slower NI degradation in cooler soil. These modelled and experimental results indicated that NI effectiveness in reducing N 2 O emissions varies with the effect of fall slurry timing on f T s . The greater reductions in N 2 O emissions modelled from delayed fall applications with NI were associated with much greater N 2 O emissions modelled from delayed fall applications without NI (F+2 in Table 6). These greater emissions were attributed to less NH + 4 oxidation before freezeup in fall, resulting in more NH + 4 remaining to drive NH + These model findings were consistent with field results from Chantigny et al. (2017) in Quebec and Kariyapperuma et al. (2012) in Ontario, where greater spring N 2 O emissions were measured when fall slurry was applied in late November than in early November. These greater spring thaw N 2 O emissions were attributed by Kariyapperuma et al. (2012) to greater mineral N concentrations during spring thaw caused by less nitrification before freeze-up during the previous fall, as modelled here. The greater N 2 O emissions modelled with later slurry application were also driven by more rapid DOC oxidation from more labile manure C remaining during spring thaw. This more labile manure C reduced [O 2s ] below that simulated after earlier fall applications (Fig. 3d). NI may therefore be particularly effective in reducing N 2 O emissions during spring thaw following late fall slurry applications. The decreases in N 2 O emissions modelled with NI from greater soil mixing (F0.5 and F0.8 vs. F in Table 6) were affected by how the redistribution of NI activity with soil mixing was modelled. Simulating this redistribution during tillage requires further consideration and corroboration from observations. These decreases in N 2 O emissions with NI were associated with greater N 2 O emissions modelled from greater soil mixing without NI in 2016 (F0.5 and F0.8 in Table 6). These greater emissions were attributed in the model to longer periods with high θ i and low θ g in the upper soil profile caused by greater heat loss through reduced insulation from less surface litter under a shallow snowpack [D12, D13]. This longer period further reduced overwinter [O 2s ] from that modelled in F (Fig. 3c), causing greater accumulation of N 2 O s and hence greater emissions during thaw. These model findings were consistent with field observations by Congreves et al. (2017) and Wagner-Riddle et al. (2010) that overwinter N 2 O emissions increased with greater freezing under conventional tillage vs. no tillage, particularly with surface residue removal. Model findings were also consistent with observations by Teepe et al. (2004) that N 2 O emissions during soil thawing rose sharply with increased duration of soil freezing. Consequent changes in T s with freezing may alter NI effectiveness with tillage.

Spring slurry application
Annual N 2 O emissions modelled without NI from spring applications were smaller than those from fall applications in 2014-2015, with a wetter early spring and drier late spring, and slightly greater in 2015-2016, with a drier early spring and wetter late spring (Table 4), except when fall application was delayed (e.g. F+2 in Table 6). These modelled differences in emissions were consistent with experimental findings that drier springs reduce N 2 O emissions from fall applications relative to those from spring (e.g. Cambareri et al., 2017). These model results indicate that effects of spring vs. fall slurry applications on annual N 2 O emissions may not be consistent but rather will depend on the timing of fall application relative to freeze-up and on precipitation during the following winter and spring. R. F. Grant et al.: Modelling nitrification inhibitor effects on N 2 O emissions 2035 Amendment of slurry with NI slowed declines in NH + 4 modelled after spring applications comparably to those measured (Fig. 2b). These slower declines were caused by slower NH + 4 oxidation that reduced nitrifier growth (Sect. 2.9, Eq. 3) and active O 2 uptake (Sect. 2.5, step 3). Consequently smaller nitrifier biomass and greater [O 2s ] were modelled with NI vs. without NI (Fig. 3e, g), particularly with rainfall after spring application in 2016 (Fig. 7a). The smaller nitrifier biomass modelled with NI was consistent with the findings of Dong et al. (2013) that DMPP reduced populations of ammonia oxidizing bacteria in soil incubations. Greater [O 2s ] modelled with NI was consistent with greater [O 2g ] measured in an incubation of wetted soil amended with cattle slurry with DMPP vs. without DMPP by Nguyen et al. (2017). Slower nitrifier growth and greater [O 2s ] both contributed to reductions in N 2 O emissions modelled with NI beyond those from the direct effects of I t on nitrification in Eq. (1), indicating additional effects of NI on N 2 O emissions that should be considered in NI models.
The reductions in N 2 O emissions modelled for 30 d after spring slurry applications with R I for DMPP and nitrapyrin in 2015 (35 % and 30 %) and 2016 (53 % and 41 %) were less than those measured with automated chambers (Table 5) but within the range of 31 % to 44 % in meta-analyses of NI research by Akiyama et al. (2010) and Ruser and Schultz (2015). The greater reductions modelled in 2016 vs. 2015 (Fig. 7 vs. Fig. 6) were consistent with findings in metaanalyses by Akiyama et al. (2010) and Gilsanz et al. (2016) that NI was more effective in reducing N 2 O emissions from a given land use when emissions were greater. These greater reductions were attributed in the model to heavy rainfall several days after application in 2016 (Fig. 7a) that extended the N 2 O emission period (Fig. 7b). During this extension I t remained high because [NH + 4 ] had declined from the large values modelled immediately after application (Eq. 3).
The effects of NI on N 2 O emissions modelled with greater soil mixing during spring applications (S0.5 and S0.8 vs. S in Table 6) were affected by how the redistribution of NI activity with soil mixing was modelled, as were those during fall applications. The effects of soil mixing on N 2 O emissions without NI modelled from slurry applications in spring were smaller than those in fall in the absence of soil freezing effects on O 2s . These smaller effects were modelled because tillage in this study involved mixing of injected manure rather than incorporation of surface-applied manure. These small effects were consistent with an observation by Van-derZaag et al. (2011) that tillage was less important than timing and placement for N 2 O emissions from slurry applications.
The reductions in annual N 2 O emissions modelled after spring slurry applications with R I for DMPP and nitrapyrin in 2015 (22 % and 17 %) and 2016 (40 % and 27 %; Table 6) were smaller than those modelled after 30 d (Table 5) due to gradual degradation of NI effectiveness modelled with time since application (Eq. 1), indicating the importance of year-round modelling and measurements to fully assess NI effects on N 2 O emission factors for IPCC Tier 3 methodology. However most of the datasets used in meta-analyses of these assessments did not include emissions during autumn, winter and spring thaw (Ruser and Schulz, 2015). which are particularly important for estimating emission factors for NI effects from fall slurry applications in cold climates (Table 6). An ecosystem modelled with well-tested simulation of NI effects may make a valuable contribution to these assessments.

Modelling NI effects on NH 3 emissions and mineral N losses
The small NH 3 emissions modelled from slurry injection with limited soil mixing (Table 7) were consistent with observations of almost no NH 3 volatilization from closed-slot injection of slurry by Rodhe et al. (2006). In the model, NH 3 emissions with or without NI were sharply reduced by NH + 4 adsorption with diffusion of NH 3 and NH + 4 from the injection site. Greater soil mixing brought more NH + 4 closer to the surface, reducing NH + 4 adsorption and thereby increasing NH 3 emission, particularly from fall applications with NI (Table 7). Consequently only small net increases in NH 3 emissions (Table 7) were modelled with NI from increased volatilization of aqueous NH 3 in equilibrium with increased NH + 4 concentrations (Fig. 2). However these increases were large in relative terms, particularly following fall applications, consistent with increases of 33 %-67 % and 3 %-65 % relative to emissions without NI derived from meta-analyses of field experiments by Qiao et al. (2015) and Lam et al. (2017) respectively. Increases in NH 3 emissions with NI will thus depend on soil adsorptive properties and depth of slurry incorporation.
The small losses of NO − 3 , and consequently the small reductions in these losses with NI, modelled in the subhumid climate at the Edmonton South Campus Farm (Table 7) conform to the assumption by De Klein et al. (2006) that NO − 3 leaching is an insignificant source of indirect N 2 O emission from dryland cropping systems in subhumid climates. Consequently reductions in leaching have minimal impact on the overall effect of NI on N 2 O emission in these climates (Lam et al., 2017). Reductions in NO − 3 losses modelled with NI would be larger at sites with better drainage and more excess precipitation, although even under these conditions such reductions may be small and inconsistent (Smith et al., 2002).
The increases in NH 3 emissions modelled with NI were larger than reductions in NO − 3 leaching (Table 7), indicating that net increases in N 2 O emissions from indirect effects of NI will partially offset decreases in N 2 O emissions from direct effects. This offset must be included when estimating changes in N 2 O emission factors attributed to NI in IPCC Tier 3 methodology. The simulation of N 2 O emissions from nitrification and denitrification in ecosys is based on a comprehensive representation of biological and physical processes governing production and transport of N 2 O. Parameters used in these processes are well constrained from basic research so that the model may provide a robust means to predict emissions under diverse climates, soils and land use practices. These processes in ecosys were not changed when adding the algorithm for inhibiting NH + 4 oxidation by nitrifiers proposed in Eqs.
(2), with values of 1.0, 2.0×10 −4 h −1 and 7000 g N m −3 to simulate the time course of NI activity following slurry application. The first two parameters correspond to those in earlier models of NI for inhibition effectiveness (0.5-0.9) and duration (30-60 d; Cui et al., 2014;Del Grosso et al., 2009). These models have given reductions in N 2 O emissions with NI in agricultural crops of around 25 % (Cui et al., 2014), 10 % (Del Grosso et al., 2009) or less (Abalos et al., 2016), which are frequently smaller than reductions of 26 %-43 % and 24 %-46 % derived from meta-analyses of NI effects in agricultural crops by Akiyama et al. (2010) and Gilsanz et al. (2016) respectively. Direct effects on NI of soil water content and pH were not modelled here due to uncertainty in parameterization, although both affect nitrification and hence the magnitude of NI activity.
Each of the parameters used to model NI in ecosys requires further evaluation. A larger R I , such as that used for nitrapyrin vs. DMPP (Sect. 2.9), caused a more rapid decline of NI activity in soil and hence greater N 2 O emissions with time after slurry application that were consistent with measurements (Tables 5 and 6; Lin et al., 2018). This larger value might represent more rapid degradation of nitrapyrin through volatilization (Ruser and Schulz, 2015), although meta-analyses of N 2 O reductions with NI indicate that those with nitrapyrin are similar to those with DMPP. The value of R I used for NI in the model will thus likely be product specific. The effect of T s on R I might reasonably be represented by f T s , as is the effect of T s on all other biological reactions in the model. This function allowed modelled NI activity to persist over winter (Fig. 2) and hence reduce N 2 O emissions modelled during spring thaw (Figs. 6 and 7). However the effects of temperature on reductions in N 2 O emission with NI over time are sometimes unclear in controlled studies (Kelliher et al., 2008).
The value of I t=0 set the value of I t at the time of slurry application, after which I t underwent first-order decline over time according to Eq. (1) (Sect. 2.9). The current value of 1.0 indicates complete inhibition at the time of application but might be reduced if the amount of NI at application is less than that required for complete inhibition. However I t had to remain large enough to reduce N 2 O emissions from Table 9. Sensitivity of seasonal N 2 O emissions modelled during late spring in 2015 and 2016 to changes in initial inhibition (I t=0 in Eq. 1) and inhibition constant (K iNH 4 in Eq. 2) following spring slurry application on dates in the field study (Table 3) nitrification for several weeks after application (Figs. 6 and 7) even with higher soil NH + 4 concentrations (Fig. 2). Lowering I t=0 from 1.0 to 0.8, similar to that in earlier NI models in which I t decline was not simulated, increased N 2 O emissions modelled over 30 d after spring slurry applications by 7 % in 2015 and 25 % in 2016 (Table 9).
The value of K iNH 4 in Eq.
(2) reduced I t with the very large NH + 4 concentrations modelled immediately after injecting slurry with large NH + 4 content (Table 3) into small bands (Sect. 3.1). The use of K iNH 4 was suggested by the findings of Janke et al. (2019) that NI may not have the expected impacts on N transformations and availability when applied in a concentrated band with large NH + 4 concentrations (up to 12 kg N Mg −1 ), similar to those modelled immediately after slurry application in this study. The modelled NH + 4 concentrations declined rapidly after application through diffusion, adsorption and nitrification (Sect. 2.5), and thus so did K iNH 4 effects on inhibition. The value of K iNH 4 in Eq.
(2) therefore governed NI effects modelled during the brief periods of rapid N 2 O emissions following application (around 3 d in Figs. 6 and 7) but had sharply diminishing impacts on NI effects modelled thereafter. An alternative hypothesis for reduced inhibition by NI immediately after application might be more rapid diffusion of NH + 4 than NI from the band, leading to spatial separation (Ruser and Schulz, 2015), although parameterization of this hypothesis is uncertain. Halving or doubling K iNH 4 from the value set in Sect. 2.9 raised or lowered N 2 O emissions modelled over 30 d after spring slurry applications by 7 %-8 % in 2015 and 2016 (Table 9), indicating some latitude in evaluating this parameter.
Reductions in N 2 O emissions modelled with all proposed values of I t=0 and K iNH 4 varied from 27 % to 41 % in 2015, and from 38 % to 57 % in 2016 (Table 9), close to the range of 42.6 % ± 5.5 % derived from meta-analyses of NI effects with cattle slurry by Gilsanz et al. (2016). Further evaluation of these parameters should be undertaken in future studies in which measurements are taken at higher frequencies (e.g. Figs. 6 and 7) required to assess N 2 O emissions and NI effects on them.
6.5 Modelling NI effects on N 2 O emissions: outstanding issues Several issues remain to be addressed in modelling N 2 O emissions and NI effects on these emissions. Accurately modelling emissions during spring thaw depended upon accurately modelling soil freezing and thawing following snowmelt and their effects on soil O 2 transfer. A small delay of 2-3 d in modelled thawing caused some small emission events measured in early spring of 2015 to be missed (Fig. 4b). However because modelled emissions were driven by overwinter accumulation of N 2 O (Fig. 3), seasonal emissions were less affected by such delays than emissions from individual events. Algorithms for modelling snowpack accumulation and ablation in ecosys are being further refined to improve simulation of soil freezing and thawing. Accurately modelling emissions later in spring depended upon accurately modelling soil wetting and drying following rainfall and their effects on soil O 2 transfer. Soil wetting from heavy precipitation typically drives N 2 O emission events following soil N additions, as modelled here during DOY 143-146 in 2016, although such events were not always measured (Fig. 7b). Such wetting caused sharp declines in O 2s when soil water content rose above a critical threshold, driving N 2 O generation and subsequent emission (Fig. 3). However modelling these thresholds depends on soil hydrological properties used in the model (Table 2) which may not be known with sufficient accuracy. Modelling NI effects on N 2 O emissions depended not only upon I t=0 (Eq. 1) and K iNH 4 (Eq. 2) as evaluated in Sect. 6.4 and Table 9 but also upon the time course for declining NI activity governed by the first-order rate constant R I and its temperature dependence f T s l (Eq. 1). NI activity modelled with R I and f T s l in this study reduced nitrification alone (Sect. 2.9), which enabled higher [NH + 4 ] and lower [NO − 3 ], and hence greater NH 3 emissions, to be simulated with NI after amendment, as has been found in field studies (Fig. 2). These higher [NH + 4 ] required a low value of R I so that NI activity would persist in reducing nitrification and hence N 2 O emissions after soil amendment. This model of NI activity contrasted with that in a more complex model in which NI reduced N 2 O emissions directly rather than through nitrification (Li et al., 2020). In such a model, NI would not directly affect [NH + 4 ] and [NO − 3 ] so that greater values of R I could be used to get similar reductions in N 2 O emissions. The val-ues of R I and f T s l used in our model caused N 2 O emissions modelled with NI to decline more rapidly than those measured following spring applications (Figs. 6b and 7b). These values need to be constrained by further studies with more frequent measurements of declines in NI activity following amendment to determine if alternative models for the time course of these declines might be considered.

Conclusions
Findings from this modelling study may be summarized as follows: d. Slower nitrification modelled with this algorithm caused increases in soil NH + 4 concentrations and reductions in soil NO − 3 concentrations and N 2 O fluxes that were consistent with those measured following fall and spring applications of slurry over 2 years. e. NI in the model remained effective in reducing N 2 O emissions modelled during spring thaw, particularly when these emissions were increased by delaying fall slurry applications or increasing fall tillage intensity.
f. NI in the model increased NH 3 emissions more than they reduced NO − 3 leaching, causing indirect effects on N 2 O emissions that partially offset direct effects.
g. NI had no significant effect on modelled or measured barley silage yields.
h. Some further work is needed to corroborate parameters in the NI algorithm under a wider range of site conditions.
i. The addition of NI to ecosys may allow emission factors for different NI products to be derived from annual N 2 O emissions modelled under diverse site, soil, land use and weather, as required in IPCC Tier 3 methodology.
Data availability. The model ecosys used in this study may be accessed at: https://ales-ssl.ales.ualberta.ca/htcomnet/Default.aspx? Standard= using the user ID and password provided by the corresponding author.