The field experiment was set up at Reinshof research farm (51.49°N, 9.93°E, 150 m asl) of the Department of Crop Sciences of the University of Göttingen in Germany. The climate is continental with a long-term (1961–1990) average precipitation of 645 mm and a mean temperature of 8.7°C (Deutscher Wetterdienst, 2019). The soil was classified as a luvisol, according to the soil classification scheme proposed by the IUSS Working Group WRB (IUSS, 2015), with a silty loam texture (12.2% sand, 72.7% silt and 15.1% clay). It represents a typical agricultural soil used for oilseed rape cropping. The soil properties were characterized by a bulk density of 1.29 g cm⁻³, pH 7.1, C content 1.3%, N content 0.12% and thus a measured C/N ratio of 10.5 in the topsoil (0–10 cm). Soil at Reinshof study site has high nutrient conditions, previous data from the site showed a GLA of c.a. 83, where GLA stands for German Land Appraisal, a soil fertility index varying on a scale from 0, (minimum soil fertility) to 100 (maximum soil fertility) (Ghaouti et al., 2008). The high soil nutrient was also shown by our measured high mineral N content and low soil C/N ratio data.

The field experiment was carried out in a fully randomized block design during the autumn and winter of 2013/2014 and 2014/2015. The plot size was 7.5 m × 6 m and all N fertilizer treatments were done with three replicates. The treatments of this first factor included three levels of calcium ammonium nitrate (CAN) mineral fertilizer (No-fert: 0 kg N ha⁻¹; Fert-90: 90 kg N ha⁻¹; and Fert-180: 180 kg N ha⁻¹). Fertilizer application was done in spring, according to common farming practice, with 67% of the total amount being applied as first dressing on 22 April in 2013 and 19 March in 2014. The remaining 33% of N was applied on 7 May in 2013 and 7 April in 2014 (Fert-90, Fert-180). Plant protection was done in line with local recommendations. Winter oilseed rape (Brassica napus L., cv. Visby) was harvested on August 1, 2013 and July 23, 2014. Following common agricultural practice, the uppermost soil layer (0–10 cm) was rototilled 1 day later.

After harvest, straw was removed whereas stubble and roots remained in the field. All fertilizer plots were subdivided into two subplots. These were treated with straw incorporation (+str) by using the respective residual straw from the 0, 90 or 180 kg N ha⁻¹ fertilizer treatments. The second subplot was kept without straw, i.e. all straw was removed (−str). The measured C/N ratio of incorporated straw with different fertilization treatments ranged from 38 to 71 (Table 1). For all subplots, the amount of straw added was determined according to residue biomass in all treatments of the respective years; on average, residue biomass was 7.17 t fresh matter ha⁻¹. In October, following typical regional crop rotations, winter wheat was sown in both years. N₂O and other parameters were sampled from harvest until the first fertilizer application for winter wheat was done in early spring.

Apparent N (ARN) recovery of oilseed rape was calculated as ARN   ( % ) =   N uptake ( fertilized ) − N uptake ∗ ( unfertilized ) Amount   o f   N   a p p l i e d × 100 (1) Where N_uptake including N content of the seed and straw.

Soil mineral N contents (N_MIN) were measured in 50 g samples from the top 0–15 cm soil layers. Samples were extracted with 0.0125 M CaCl₂ solution (1:5 w/v), then filtered with 615 ¼ filter paper (Macherey – Nagel GmbH & Co. KG, Düren, Germany) and stored frozen at −20°C (VDLUFA 2002). The extracts were subject to colorimetric analysis to determine the concentrations of NO₃ ⁻ and NH₄ ⁺ using an automated continuous flow N analyzer (San++; Skalar Analytical B.V., Breda, Netherlands).

N₂O gas fluxes were assessed using the manual chamber approach (Hutchinson and Mosier, 1981). In each of the 36 subplots, a round basal collar (PVC, diameter: 0.6 m, height 0.15 m) was driven into the soil to 5 cm depth and kept there permanently. For gas flux measurements these collars were covered by a closed chamber top of 0.3 m height. The outside of both collars and chambers were covered with aluminum foil to reflect solar radiation. The collar and chamber joints were sealed with a butyl rubber band of 10 cm width. Gas samples were taken 0, 20 and 40 min after chamber closure using a 30 ml gastight syringe and filled into pre-evacuated 12 ml vials (Labco, Lampeter, United Kingdom). Gas sampling was conducted during the post-harvest period until the first fertilizer application for winter wheat in early spring. The gas measurements thus covered the periods from August 8, 2013 to February 17, 2014 and from July 29, 2014 to March 3, 2015. Overall, the number of sampling days for 2013 and for 2014 were 28 and 30, respectively.

All analyses of N₂O concentrations were done on a Bruker gas chromatograph (456-GC, Bruker, Billerica, United States) equipped with an electron capture detector and controlled by CompassCDS Software. Sample introduction was done with a Gilson GX281 autosampler operated with Trilution Software (Gilson, Inc., Middleton, WI, United States). For calculation of N₂O fluxes, linear regression was performed for the three samplings after chamber closure, and linear interpolation between measurement days was done to obtain cumulative gas fluxes.

The CoupModel (coupled heat and mass transfer model for soil-plant-atmosphere systems) is an updated version of the earlier SOIL and SOILN models (Jansson and Moon, 2001). The main model structure is a one-dimensional, layered soil depth profile, in which water, heat, and C and N dynamics are simulated based on detailed descriptions of soil physical and biogeochemical processes. C and N dynamics are simulated both in the soil and in the plant, driven by canopy-intercepted radiation, and regulated by multiplicative response functions of air temperature and plant availability of water and N (He et al., 2016a; He et al., 2016b). The model is available at http://www.coupmodel.com/. A detailed description of the model, its model structure, parameterization and setup is given in He et al. (2016a), He et al. (2016b) and Jansson and Karlberg (2011).

The model simulates ecosystem variables at daily intervals and is driven by measured meteorological variables from a nearby weather station, including precipitation, air temperature, wind speed, relative humidity and global radiation. The general model parameterization was based on previous model applications on similar soil types (Johnsson et al., 1987; Nylinder et al., 2011). The soil physical characteristics – i.e., water retention curve and hydraulic properties – were estimated from the measured soil texture by using the model’s pedotransfer functions. When straw was applied, it was assumed to be added to both the soil litter C and N pools and to be uniformly mixed into the soil to a depth of 0.05 m. The application of mineral fertilizer was assumed to directly add NH₄ and NO₃ to the soil surface N pool. The model was evaluated mainly against the measured N₂O flux data from the Reinshof site. Due to the strong coupling of N dynamics with the C cycle and abiotic environmental factors, we further evaluated the model output against observed soil respiration flux, water filled pore space (WFPS) and soil temperature data. Overall, the evaluation was conducted in a stepwise manner, where the model was first evaluated with WFPS and soil temperature data, then with the measured seed yield and residue biomass data and soil respiration data. A few plant and soil parameters were calibrated to fit the simulated plant growth and soil respiration since these two processes regulate the two major N fluxes, i.e., plant N uptake and soil net N mineralization, both being important for N₂O production. Finally, the model was evaluated with the measured soil mineral N contents and N₂O fluxes. Its need to be noted that we did not calibrate the model for best fit to the measured N₂O emission data, but instead to describe a complete carbon and nitrogen budget of the system. The evaluation was conducted using time series and goodness of fit quantified by the linear regression coefficient of determination (R²) and mean error (ME) and root mean square error (RMSE). The harvests in 2013 and 2014 were assumed to remove 100% of the grain and 10% of both leaf and stem. The initial conditions of the oilseed rape crop were defined by measured plant biomass data. Initial plant and soil conditions were set according to the measured data. The model was run for 5 years for initialization with a duplicated climate before the studied period.

Soil NO₃ ⁻, NH₄ ⁺ and N₂O emissions are shown as arithmetic means ± SE. Cumulative N₂O emissions were obtained by linear interpolation between sampling dates and integration of area under the interpolated fluxes. The cumulative data of the 7-months period following harvest were tested for homogeneity of variance (Levene’s test) and normal distribution (Shapiro-Wilk test). Then the differences among fertilizer levels were assessed by performing one-way ANOVA with Tukey’s test, and differences among years were assessed by performing a t-test. Statistical significance was considered as p < 0.05. For the correlation of non-parametric N₂O fluxes with soil NH₄ ⁺, NO₃ ⁻, WFPS and air temperature, Spearman correlations were calculated with * standing for p < 0.05 and ** for p < 0.001.

For statistical analysis of the split-plot design of the field experiment, a mixed model with repeated measurements with heterogeneous autoregressive structure was set up to test for significant differences in fertilizer rate and residue application for each period (2013/2014 and 2014/2015). Significant differences among treatments were based on Tukey’s tests. For computing, the software SAS v. 9.3 (SAS Institute Inc., Cary, North Carolina, United States) was used.

The measured annual mean air temperature was 8.9°C in 2013 and 10.6°C in 2014. Annual precipitation in 2013 was 641 mm, which was greater than the total of 609 mm in 2014 (Figure 1). In 2014, the period from June to August had high rainfall of 278 mm, whereas in 2013 these months accounted for only 128 mm. In line with the rainfall data, WFPS values were lower in 2013 (dropping from 42% WFPS at the beginning of August to 26% WFPS in September) than in 2014 (remaining at ca. 50% WFPS throughout the experimental period) (Figure 6).

The oilseed rape in No-fert control subplots had a seed yield of 3.7 ± 0.2 and 3.6 ± 0.2 tons dry matter per hectare per year (t DM ha⁻¹) in 2013 and 2014, respectively. With N fertilizer input, seed yield showed consistent but insignificant increases in both years (Table 2). The measured straw biomasses in the No-fert control subplots were 5.3 ± 0.2 and 5.1 ± 0.1 t DM ha⁻¹ in 2013 and 2014. The effect of N fertilization on straw biomass was also insignificant, but there was a consistent positive trend, increasing applied N rates led to decreasing measured C/N ratios of straw in both years (Table 1). The amount of N returned to soil with the residue biomass was higher in the fertilized plots than in the unfertilized treatment in 2014, but not in 2013, and there was no effect on the straw biomass production and seed yield when the N- fertilizer rate was further increased from 90 to 180 kg N ha⁻¹.

N₂O emission rates varied significantly (p < 0.001) between years, and the maximum N₂O peaks were significantly higher (ca. tenfold) in 2014 compared with 2013 (Figure 2). In both years, the highest N₂O emission peaks were detected shortly after post-harvest tillage. In 2013, the highest measured daily N₂O emission rate was 0.04 ± 0.0 kg N₂O-N ha⁻¹ d⁻¹ (in the Fert-180 treatment with straw amendment), whereas it was 0.33 ± 0.08 kg N₂O-N ha⁻¹ d⁻¹ (in the Fert-180 treatment with straw) in 2014, thus almost ten times higher. Winter N₂O emissions were generally low, being consistently below 0.02 kg N₂O-N ha⁻¹ d⁻¹ from November to March in all treatments and years. The N doses applied in spring did not affect post-harvest N₂O emissions in either year, despite higher residual soil NO₃ ⁻ -N in Fert-180 treatments at oilseed rape harvest time. Similarly, straw amendment did not affect N₂O fluxes in 2014, but caused a slight (p < 0.05) decrease in 2013 for the Fert-90 treatment. Overall, cumulative post-harvest N₂O emissions were very substantially higher in 2014 than those measured in 2013 (Figure 3).

Soil NH₄ ⁺ concentrations in the uppermost 0.15 m soil layer were below 5 kg N ha⁻¹ in both years and were not significantly affected by any treatments (Figure 4). In contrast, soil NO₃ ⁻ concentrations measured shortly after harvest were 12.3 ± 0.6 and 13.0 ± 2.4 kg N ha⁻¹ in the control treatments in August 2013 and August 2014. Fertilizer application in spring resulted in substantially higher residual NO₃ ⁻ in the uppermost soil layer in August, amounting to 28.2 ± 3.6 and 28.3 ± 1.6 kg N ha⁻¹ in the Fert-180 treatments in 2013 and 2014, respectively. Soil NO₃ ⁻ concentration remained more or less constant throughout the experiment in 2013, whereas in 2014 it decreased gradually over time to almost zero during winter. The data clearly showed that straw amendment decreased soil NO₃ ⁻ content significantly (p < 0.05) in all treatments and years. The decrease in soil NO₃ ⁻ concentration due to straw amendment was more pronounced in 2013.

In general, significant correlations were found between N₂O fluxes and environmental factors such as soil moisture WFPS and air temperature. Furthermore, soil NH₄ ⁺ concentrations showed moderate but significant correlation with post-harvest N₂O fluxes (Table 3). In treatment Fert-180, air temperature showed the highest correlation with post-harvest N₂O emissions (Spearman R = 0.91, p < 0.001). Figure 5 clearly shows an exponential relationship between air temperature and N₂O emissions. High emissions occurred when air temperature was above 15°C. It is also interesting to note that N₂O emissions show higher correlation with soil NH₄ ⁺ than with NO₃ ⁻ even though soil NH₄ ⁺ contents were much lower than NO₃ ⁻ contents.

The measured soil N and abiotic data were used to test the CoupModel ecosystem model. Overall, the simulation was in good agreement with measured soil temperatures, as indicated by an R² of 0.93, but it showed less accuracy in simulating the WFPS (Figure 6). The fit of modeled N₂O emission rate was best in the Fert-180 treatment (R² = 0.5, ME = 0.02, RMSE = 0.5). However, the model seemed to overestimate N₂O fluxes in the Fert-90 and Fert-180 treatments, as shown in Figure 2. The simulated emission peaks show time shifts with the measured data. The model yielded higher denitrification rate estimates for Fert-180 soils compared with the No-fert treatment.

In this study, soil NO₃ ⁻ concentrations at harvest were found to be strongly governed by the N fertilizer level in spring and were higher with higher fertilizer rates (Figure 4). Similarly, in a¹⁵N labeling study of oilseed rape, Malagoli et al. (2005) showed that about 45 kg N ha⁻¹ entered the soil before harvest via withered leaves. In the period from harvest to autumn (September–October), the incorporation of oilseed rape straw reduced soil NO₃ ⁻ concentration (no straw (−str) vs. straw amendment (+str) of soil) (Figure 4). This is probably because the high C/N of straw led to a higher incorporation of soil N into soil microbial biomass (Spohn, 2015). Our applied straw C/N ratio, ranging from 38 to 71, was well above the soil C/N ratio of 10.5. Thus, the increased microbial soil respiration likely created a immobilization of mineral N, thus reducing the soil NO₃ ⁻. A net mobilization of NO₃ ⁻ in bare soil about 6 weeks after harvest was also found in a study conducted by Engström and Lindén (2012). This might also explain the substantial drop in NO₃ ⁻ concentration in all treatments in the first 4 weeks after harvest in 2013. However, a build-up of NO₃ ⁻ could also have resulted from the cessation of plant uptake with ongoing mineralization.

The NO₃ ⁻ concentration dropped substantially in 2013, in the first week following harvest and in particular in the first 30 days. There are several possible explanations for this. On the one hand, Engström and Lindén (2012) observed a similar fluctuation in the soil mineral N pool. They conducted an in-situ incubation study in a field experiment with treatments that included the addition of oilseed rape straw after harvest and measurements of mineralization and immobilization of soil mineral N. The net N immobilization was 11 kg N ha⁻¹ in the 6-week period right after harvest. Our field experiment confirmed a net immobilization of 19 kg N ha⁻¹ in the Fert-180 treatment with straw amendment (+str) from 2 August to September 3, 2013. On the other hand, the decline of soil NO₃ ⁻ could be ascribed to the uptake of N by volunteer oilseed rape, that new oilseed rape emerged by fallen seeds in autumn. Volunteer oilseed rape results from grain loss during harvest and it has been reported to take up upto 28 kg N ha⁻¹ (Justes et al., 1999). Moreover, high NO₃ ⁻ concentrations in the soil N pool after harvest increase rates of loss from nitrate leaching into deeper soil layers (Engström and Lindén 2012).

After harvest and incorporation of oilseed rape straw, a short pulse in N₂O emission activity was found in both years. However, the magnitude of fluctuation differed considerably for the two post-harvest periods. In the approach towards winter, N₂O emissions declined to very low rates. In the two experimental periods of 2013/2014 and 2014/2015, the variations in residue incorporation into the soil and N fertilizer level revealed that both factors had only minor effects. Most studies have documented that N₂O emissions were exponentially increased by increasing fertilizer levels (Shcherbak et al., 2014; Song et al., 2018; Yao et al., 2018). However, in our study, 180 kg N ha⁻¹ did not greatly increase N₂O emissions in the post-harvest period, and the calculated apparent recovery of nitrogen ARN of Fert-180 was only between 20–30%, which indicates that in the Fert-180 treatment a substantial amount of N was leached out during the growing season or emitted to the atmosphere. It can be expected that these losses were also related to the high soil fertility of the site which was probably derived from repeated long-term return of crop residues, intercrops and occasional application of organic manures in the past decades. Regarding the C/N ratio of straw in 180 kg N ha⁻¹ fertilized fields being much lower than the No-fert C/N ratio, it was suggested that oilseed rape was adapted to assimilate more N in plant tissue in soils with a higher N fertilizer level.

In our study, straw incorporation also has minor effects on N₂O emissions, although it has been widely debated whether straw incorporation could increase or reduce N₂O emissions (Hu et al., 2019; Xia et al., 2014; Schmatz et al., 2020; Surey et al., 2020; Xu et al., 2019). In a meta-analysis, Hu et al. (2019) demonstrated that residue returned with plough tillage (as in our study) showed lower N₂O emissions than reduced tillage/no tillage, and that the C/N ratio of straw residues was negatively correlated with N₂O emissions (Chen et al., 2021), while straw incorporation with a C/N ratio between 40 and 80 showed minor changes in soil N₂O emissions. However, even with straw-removed treatments, there was still a large amount of C inputs to the soil from leaf litter, stubble and roots. These residues may regulate soil C/N ratios. Our previous study also demonstrated that, although straw incorporation increased CO₂ emission, the increase of N₂O emission was minor when no additional N was applied in autumn (Köbke et al., 2018). The Köbke et al. study thus indicates that increased soil respiration by straw respiration did not necessarily convene high soil N₂O emissions, as confirmed again in our current study.

The comparison of N₂O fluxes of the post-harvest periods in both years shows marked differences. Here, rather than the fertilization treatment or the removal of straw, the different climatic variations had a great influence with a tenfold difference for the presented years. Ruser et al. (2001) conducted a field experiment covering several years and crops. In their study, NO₃ ⁻ concentrations had a significant effect and also water-filled pore space showed quite high positive correlations with N₂O emissions. These factors accounted for 52% of the variability of N₂O emissions. In a study under controlled conditions (Harrison-Kirk et al., 2013), repeated rewetting of the soil showed the highest cumulative N₂O emissions compared with either continuously dry or wet soil. In our experiment, there were more rainfall events and higher amounts of precipitation post-harvest in 2014, which led to measured WFPS of nearly 60%, compared with only 50% in 2013. Soil samples were oftren taken a day or two after rainfall events, hence top soil WFPS might have been even higher immediately after rainfall. In addition, soil NO₃ ⁻ contents were more consistent during the 2014 post-harvest period. Thus there was sufficient mineral N, higher water supply and high O₂ consumption by respiration which probably triggered N₂O emissions from denitrification (Wu et al., 2018). Thus, these factors are seen as explanatory for a great share of the higher N₂O emissions in 2014. In addition, the fact that, following our sampling schedule, gas samples were often taken a day or two after rainfall events, may have led to a certain overestimation of N₂O emissions in 2014. Another major factor for the substantial difference in N₂O emissions between the 2 years was temperature, which is known to be a strong control of soil microbial activity and N mineralization from soil organic matter. Billings and Tiemann (2014) showed in an incubation experiment that warm June soils have a high capability to produce N₂O, displayed in the N₂O production which was underlined by the high amount of cnorB genes. In those soils, the nosZ genes were lower than cnorB genes, which was in line with high rates of N₂O production but low N₂ production. We have not been able to measure this in our experimental approach but it nonetheless underlines the potential of soils to produce N₂O by incomplete denitrification, and annual mean temperature in 2014 was 1.7°C higher than that in 2013. These results also warn of the risk of high N₂O emissions as a consequence of global warming (Dobbie and Smith, 2001; Butterbach-Bahl and Dannenmann, 2011).

Finally, the share of N₂O released from the soil mineral N pool (NH₄ ⁺ and NO₃ ⁻) seems to follow a pattern. Since soil mineral N concentrations ranged at equal levels in both years, the ratio of released N₂O in relation to the soil mineral N concentration on a specific date was less than or equal to 0.12%, even for the dates shortly after harvest in 2013. In contrast, in 2014 the ratio of N₂O being released in relation to the soil mineral N pool was well above 1% right after harvest, and it did not drop to the level of 2013 before beginning of October. This indicates that in 2014 there were greater rates of N₂O-producing processes rather than greater pool sizes from which N₂O was produced. A possible explanation might be that high WFPS, low oxygen partial pressure and the high temperature in 2014 induced anaerobic conditions more rapidly, which then increased the ratio of N₂O emissions to the pool size of soil mineral N, which is indicative of the dominance of denitrification. Nevertheless, a large C source presented by root biomass and straw may also lead to production of N₂ as a denitrification end product, which could explain the same levels of N₂O emissions in different treatments.

The CoupModel reproduced the measured high N₂O emissions in 2014 and, according to the model, these were primarily produced by denitrification as the year’s temperature and soil moisture were favorable for this process. However, it should be noted that, for 2014, the model overestimated not only soil moisture (WFPS) but also straw biomass and seed yield. Therefore, the modeled high emissions might partly be due to a bias resulting from combined high residual mineral N and anaerobiosis in the model. There is a number of potential reasons for the higher number of peaks simulated by CoupModel, which was not observed in the field. First, the simulated WFPS which is used for denitrification calculation showed more pronounced responses to precipitation in the model than in measured data (Figure 6). Also, the model simulated a slightly higher mineral N availability compared to the measured data. Both have probably contributed to more and higher emission events in the model. Nevertheless, the modeled soil respiration agreed well with the measured data (Supplementary Figure S1), and therefore it is likely that organic matter decomposition and also mineralization were reasonably well described by the model. For the fertilized soil, model results indicate higher denitrification rates.