The study was carried out at the National Field Observation and Research Station of Shenyang Agro-ecosystems of the Chinese Academy of Sciences, located in the Liaoning Province, Northeast China (41° 31′ N, 123° 22′ E). The mean annual temperature (MAT) is 7.5°C, and the mean annual precipitation (MAP) is 680 mm, with more than 80% precipitation during the crop-growing season (from May to September, Dong et al., 2018). The soil type is silt loam, with 24.1% clay, 59.6% silt, and 16.3% sand. The soil was acidic (pH 5.6 and 0–10 cm). The soil had a total carbon content of 11.3 g kg⁻¹ and total N content of 1.31 g kg⁻¹.

This study was performed over two consecutive years, from April 28, 2017 to March 31, 2019, at a rainfed maize (Zea mays L.) field. The soil was plowed on May 5, 2017 (year 1) and April 25, 2018 (year 2), and seeds were planted in the intra-row on May 7, 2017 and April 28, 2018. Maize plants were harvested on October 7, 2017 and September 24, 2018, respectively, and the maize residues were taken away in both years. In year 1, we reseeded on May 24 due to the failure of germination caused by severe drought. The experimental field received a fertilizer mix of urea and diammonium phosphate (at a 2:1 ratio), which was simultaneously applied within 2 cm of seeds on the intra-row (based on local agricultural management), at a rate of 150 kg N ha⁻¹. The same plot was used for both years and received the same fertilizer treatment.

N₂O concentrations were continuously and automatically measured using a static chamber-based method between April 28, 2017 and March 31, 2019. The system used seven opaque chambers (20 cm diameter × 10 cm height), with three chambers placed in the intra-rows, three placed in the inter-rows, and one reference chamber (gas-tight bottom made of Teflon). During the measurement, each chamber was closed twice to measure NO and N₂O emissions, respectively. For each chamber, first 6 min was for NO analyzing; gas samples were continuously transported at a flow rate of 0.4 L/min, and concentration of NO was measured at 10 s intervals by a chemiluminescence NO-NO₂-NO_x analyzer (42i, Thermo Electron Corporation, Waltham, MA, United States). After the NO analysis was finished, the chamber was opened for evacuation for 5 min, to remove any residual gas within the chamber and tubes. Then the same chamber was programmed to close for 20 min to determine the N₂O flux. The gas was automatically sampled at three time points (i.e., 0, 10, and 20 min after the chamber closure). The N₂O concentration was measured using a gas chromatograph (GC 2014; Shimadzu, Japan) equipped with an electron capture detector. The NO-NO₂-NO_x analyzer and GC were installed in a temporary cabin next to the study field. Although our automated system simultaneously measured nitric oxide (NO), herein, we only reported N₂O data; NO data was presented in another unpublished manuscript. Both N₂O and NO measurements for each chamber lasted 36 min. Therefore, the seven-chamber device allowed 40 flux measurements per day or 5 to 6 fluxes per day for each of the seven chambers.

The fluxes of N₂O (F_N2O, ng N m⁻² s⁻¹) were calculated using the following equation: F N 2 O  =  d C d t V A P P 0 T 0 T where d C / d t is the rate of N₂O concentration change over time determined by the linear regression, V is the internal chamber volume, and A is the chamber surface area. P 0 (1,013 hPa) and T 0 (273 K) are the atmospheric pressure and absolute temperature under standard conditions, respectively. P and T are the actual air pressure and chamber air temperature, respectively.

Daily fluxes were calculated as the arithmetic means of the 15 or 18 fluxes obtained from the three replicate chambers (5 or 6 fluxes per chamber per day) for the intra-row and inter-row locations. Estimates of field scale daily emissions were calculated using a weighted average of the spatial distribution of intra-row and inter-row areas. Annual cumulative N₂O emissions were calculated using linear interpolation to fill periods with missing data. The ratio of N₂O emissions to the fertilizer amount was calculated by the annual cumulative N₂O emissions directly divided by N fertilizer amount (150 kg N ha⁻¹).

In addition to the gas-flux measurements, soil temperature (°C) and moisture (%; volumetric water content, VWC) were monitored at 0–6 cm soil depth using six sensors (Campbell Scientific CS650, North Logan, UT, United States): three in the intra-row and three in the inter-row. The VWCs of the intra-row and inter-row soils were converted into water-filled pore space (WFPS), using the respective bulk density (BD) of 1.17 and 1.25 g cm⁻³, and a theoretical particle density of 2.65 g cm⁻³ ( WFPS =  ( 100 × VWC ) / ( 1 − BD / 2 .65 ) ). Daily precipitation and air temperatures at the study site was monitored by an on-site meteorological station (50 m away).

The mineral N concentrations (ammonium and nitrate) of the topsoil (0–10 cm) were separately sampled from intra-row and inter-row soils once a week after fertilization last one month, and bi-weekly to monthly during the remaining sample period. The soil was sieved (2 mm mesh), and 10 g of sieved soil was extracted with 50 ml of 2 M KCl solution. Extracts were frozen at −18°C and later analyzed by a discrete chemistry analyzer (Smartchem 200, Westco Scientific Instruments, Inc., Italy). The obtained values (mg N L⁻¹) were converted to soil dry weight basis (mg N kg⁻¹ soil).

Statistical analyses were implemented using R, version 3.6.3 (R Core Team, 2019) and RStudio (version February 1, 5033). Graphics were implemented using both RStudio and Origin 9. The differences in the soil temperature, moisture, temperature and mineral N concentration between inter-rows and intra-rows were tested using a one-way ANOVA. A nonlinear or linear regression analysis was used to explore the relationship between soil N₂O fluxes and environmental factors (e.g., soil temperature, moisture, and mineral N concentration). A significance level of P < 0.05 was used for all data analyses.

The annual precipitation was 439 and 642 mm in the first and second measurement years, respectively. This difference was largely due to the rainfall in the first 30 days following fertilization, with 13 mm in year 1 and 150 mm in year 2 (Figure 1A). The mean WFPS in the intra-rows during the growing season was 28 ± 12% WFPS in year 1, significantly lower than that in year 2 (31 ± 15% WFPS). The temporal pattern of soil moisture in the inter-rows was similar to the intra-rows but was significantly wetter (Figure 1B). The mean annual soil temperatures for the intra-rows were 9.7°C in year 1 and 9.1°C in year 2. There was no significant temperature difference between the rows and inter-rows (Figure 1C).

Soil NH₄ ⁺–N concentration in the intra-row increased markedly following fertilization on May 7, 2017 and April 28, 2018 (Figure 1D). In year 1, the NH₄ ⁺–N concentration increased to 333 mg N kg⁻¹ immediately following fertilizer application and remained at that level for approximately a month. After precipitation in early June, the NH₄ ⁺–N concentration started to decrease, but still averaged 232 and 113 mg N kg⁻¹ in June and July, respectively. In year 2, the NH₄ ⁺–N concentration also increased following fertilization but reached a considerably lower level (120 mg N kg⁻¹) compared to year 1. Then, it decreased gradually to only 2 mg N kg⁻¹ in mid-July and remained at that level in the remaining months (Figure 1D). The NO₃ ⁻–N concentration increased following the decrease in NH₄ ⁺–N (Figure 1D–E). The peak concentration of NO₃ ⁻–N concentration in both years was significantly lower than NH₄ ⁺–N concentrations (234 mg N kg⁻¹ on July 5, 2017 and 80 mg N kg⁻¹ on May 24, 2018). In the inter-row, where no fertilizer had been applied, the mineral N concentrations were considerably lower than those in the intra-rows. In year 1, the mineral N concentrations showed a small pulse following fertilization, with NH₄ ⁺–N concentration increasing to 25 mg N kg⁻¹ and NO₃ ⁻–N concentration increasing to 70 mg N kg⁻¹ in the inter-row soils before immediately decreasing below 10 mg N kg⁻¹ (Figure 1D–E).

We observed pronounced seasonal variations in N₂O emissions during both measurement years (Figure 2), being highest after fertilizer application in summer and lowest in winter. Daily N₂O fluxes from the intra-rows also exhibited large interannual variation (Figure 2), despite the application of the same amount of fertilizer. Mean daily N₂O fluxes (ng N m⁻² s⁻¹) ranged from 1.4 to 122.1 (averaged 23.8 ± 3.2) in year 1, and −3.8 to 53.1 (averaged 10.0 ± 1.6) in year 2. In year 1, the peak N₂O emission in the intra-row (122.1 ng N m⁻² s⁻¹, Figure 2) occurred on July 16, approximately two months following the fertilization, and the highest flux (35 ng N m⁻² s⁻¹) in year 2 appeared on May 30, approximately one month following fertilization (Figure 2). The high emission period in the intra-row following N application lasted approximately three months (from June to August) in year 1 and two months (May to June) in year 2. The average N₂O fluxes from the inter-rows were 10.5 ± 1.6 ng N m⁻² s⁻¹ in year 1 and 7.3 ± 1.1 ng N m⁻² s⁻¹ in year 2; both were significantly lower than those from the intra-rows. In both years, we found no increase in N₂O fluxes during the spring freeze–thaw period (Supplementary Figure S1).

The cumulative annual N₂O emissions in year 1 were 2.8 kg N ha⁻¹, which was approximately 1.6 times higher than that in year 2 (1.8 kg N ha⁻¹), accounting for 1.9 and 1.2% of the applied N fertilizer (150 kg N ha⁻¹ yr⁻¹). Approximately 70% of the difference in annual N₂O emissions can be attributed to the different accumulated emissions from July and August (Supplementary Figure S2), when soils produced 1.5 kg N ha⁻¹ in year 1 and 0.8 kg N ha⁻¹ in year 2. N₂O emissions during the non-growing season (November to March) contributed to 23.2% of the annual N₂O emissions in year 1 and 9.7% in year 2.

For the diurnal cycles of N₂O flux, we only observed clear diurnal patterns from intra-rows during the growing season, which correlated well with the changes in soil temperature (Figure 3). We found that sampling at LST (local standard time) 9:00–10:00 or 18:00–19:00 best represented the daily average N₂O emissions in this area.

We simultaneously measured NO flux; detailed analysis is provided in another unpublished manuscript; however, herein, we only present the daily molar ratio of NO and N₂O fluxes (Figure 4). In the intra-rows (with high mineral N concentration and low soil moisture), the NO/N₂O ratio >1 prevailed for 97 and 56% of the measured fluxes during the growing season in year 1 and year 2, respectively, (Figure 4). The NO emission was over 10 times greater than N₂O emissions during the peak emission period, especially in year 1 (May to August), and the ratio began to decline when the NH₄ ⁺–N concentration approached 0 mg N kg⁻¹. The ratios in the inter-rows (with high soil moisture and low mineral N concentration) were usually less than one (Figure 4), with NO/N₂O < 1 accounting for 60% of the measurements in year 1 and 84% in year 2. However, from April 28 to mid-June in year 1, when the inter-row soil moisture was very low (from 15 to 30% WFPS), the NO/N₂O ratios were >1 (Figure 4).

Figure 5 shows the relationship between N₂O and NO fluxes from intra-rows and inter-rows during the growing and non-growing seasons. We found that there was a significant linear correlation between N₂O and NO fluxes from intra-rows during the growing season, and the R ² reached 0.88. No significant relationships were found in the non-growing season (Figure 5).

In this study, we divided the entire observation period into three periods: the growing season (May to September), non-growing season (October to February), and freeze–thaw period (March), to analyze the correlation between soil N₂O flux and soil temperature or moisture (Figure 6, Supplementary Figure S3). The results showed that for the intra-rows, soil N₂O fluxes were significantly and exponentially correlated with soil temperature during the growing seasons in both years and during the non-growing season in year 2 (Figure 6). For the inter-rows, the N₂O fluxes are significantly correlated with the soil temperature during the growing season in year 1 and the non-growing season in year 2 (Figure 6). There were no significant relationships between N₂O fluxes and soil temperature during the two-year freeze–thaw periods. No significant correlation between N₂O flux and soil moisture were observed (Supplementary Figure S3), and the optimum moistures for N₂O production were 25–30% WFPS in the intra-rows and 50–60% WFPS in the inter-rows during growing season in both measurement years (Supplementary Figure S3).

For soil available N, a positive and significant linear relationship with N₂O fluxes was only found against NO₃ ⁻–N in the intra-rows, and no significant correlation was found with NH₄ ⁺–N for both intra-rows and inter-rows (Figure 7).

We monitored soil N₂O fluxes based on an automatic and continuous method over two years for a rainfed maize field in Northeast China. The cumulative N₂O emission in year 1 and year 2 was 2.8 and 1.8 kg N ha⁻¹, respectively, which were comparable to another multiyear measurement obtained at the same field station (ranging from 0.3 to 2.5 kg N ha⁻¹, Dong et al., 2018). However, it is higher than the N₂O emission (0.1–0.6 kg N ha⁻¹) reported by Ni et al. (2012) from another maize field in Northeast China, which may be attributed to their short-term monitoring (only measured the growing season). Shang et al. (2020) summarized more than 20 studies which monitored N₂O emissions in-situ and found that ignoring N₂O emissions in the non-growing season would lead to an underestimation of annual N₂O emissions by 10–30%. Therefore, the measurement of N₂O emissions over an entire year is essential to accurately estimate annual N₂O emissions. In addition, our annual N₂O emissions were considerably lower than those in the report of Gagnon et al. (2011), from a maize field in Canada (ranging from 4.6 to 22.8 kg N ha⁻¹), which used the same type and amount of nitrogen fertilizer as in this study. Notably, the soil in Gagnon’s report was poorly drained, and the soil organic matter (SOC = 4.6%) was significantly higher than that in our study (1.1%), which may easily form an anaerobic environment and provide sufficient carbon to promote denitrification and produce more N₂O (Stehfest and Bouwman, 2006; Dong et al., 2018).

The N₂O emission factors (EF, in %) is defined as the N₂O emission from fertilized treatment minus the emission from unfertilized control treatment expressed as a percentage of the N applied (Eggleston et al., 2006). However, our study had no unfertilized control treatments, neglecting background N₂O emissions, the annual N₂O emissions accounted for 1.9 and 1.2% of the fertilizer amount (150 kg N ha⁻¹) in years 1 and 2, respectively. We assume that the N₂O emissions from inter-rows (without fertilization) can be used as background N₂O emissions, and their annual emissions for the two years were 1.9 and 0.9 kg N ha⁻¹, respectively. Thus, the estimated EF–N₂O for both years was 0.6%, which corresponds with other studies from rainfed maize fields in Northeast China (0.3–1.1%, Ni et al., 2012; Guo et al., 2013; Chen et al., 2014; Dong et al., 2018). However, this estimation might be conservative, due to the relatively high soil moisture of the inter-rows. The EF–N₂O values of these rainfed agricultural soils were lower than those of irrigated agricultural soils. For example, McSwiney and Robertson (2005) monitored N₂O emissions from irrigated maize fields for three years, and the EF–N₂O values ranged from 2 to 7%. Liu et al. (2011) also reported an EF–N₂O value of 2% from an irrigated maize field. A review by Aguilera et al. (2013) found that N₂O emissions from rainfed agriculture were one order of magnitude lower than those from conventional irrigated fields in the Mediterranean climate cropping system. One of the main reasons is that the low precipitation and soil moisture in rainfed agricultural soil suppresses N₂O production (Ni et al., 2012; Dong et al., 2018).

The cumulative annual N₂O emission in year 1 (2.8 kg N ha⁻¹) was considerably higher than in year 2 (1.8 kg N ha⁻¹). Although the precipitation in the second year (634 mm) was more than that in the first year (439 mm). However, the severe drought before and after fertilization in the first year reduced the plants N uptake (maize emergence and extension was notably delayed in year 1), resulting in substantial levels of nitrogen remaining in soil, and the soil mineral N concentration (NH₄ ⁺–N + NO₃ ⁻–N) reached 460 mg N kg⁻¹ in mid-May to early June in year 1, approximately three times higher than the highest soil N concentration in year 2 (Figures 1D–E). After the precipitation in early June, the mineral N concentration started to decrease but remained above 30 mg N kg⁻¹ until late September. An extended period of high soil N concentrations in year 1 extended the window of N₂O emissions (Figure 2), resulting in higher N₂O emissions in year 1 than in year 2.

We suggest that N₂O emissions from the intra-rows were mainly attributed to nitrification, and the inter-row process was more complicated. First, the soil moisture of intra-rows was lower than 60% WFPS during the growing season (averaged 30 ± 10%, range from 12 to 53% WFPS), suggesting that nitrification would be dominant (Davidson, 1993; Bateman and Baggs, 2005; Pilegaard, 2013); the soil moisture of the inter-rows exhibited a wide range (from 10 to 75% WFPS), suggesting that both nitrification and denitrification processes may occur. Second, the molar ratio of NO/N₂O has been used as a useful indicator for evaluating the contribution of nitrification (NO/N₂O > 1) and denitrification (NO/N₂O < 1; Anderson and Levine, 1986; Skiba et al., 1993; Davidson et al., 2000; Zhang et al., 2011). In the intra-rows, during the high emission period in year 1 (June to September) and year 2 (May to June), over 90% of the NO/N₂O ratios were higher than one (Figure 4), suggesting that nitrification was dominant, and the soil NO/N₂O ratio of the inter-rows was mostly less than 1 (80%), indicating that denitrification was dominant (Figure 4).

Surprisingly, we found a significant positive correlation between the NO and N₂O emission rates from the intra-rows during the growing season (Figure 5), indicating that NO and N₂O were produced by similar processes and controlled by similar environmental factors. In other words, when nitrification dominated NO and N₂O production, their fluxes were significantly positively correlated. Similar results were also revealed by Ding et al. (2007) from a lab incubation experiment. This finding will aid building models to predict NO emissions (which is a reactive nitrogen gas and less in-situ measurements) based on N₂O in-situ measurements (Dorich et al., 2020a). For the inter-rows, both nitrification and denitrification can occur, and there was no significant linear relationship between NO and N₂O emissions.

Many studies reported that soil freeze–thaw cycles promote N₂O emissions, contributing 17–85% of the annual N₂O emissions (Yanai et al., 2011; Abalos et al., 2016; Wagner-Riddle et al., 2017; Gao et al., 2018). Several hypotheses may explain the increase in N₂O emissions during this period: 1) enhanced available C and N substrates due to the physical cracking of soil aggregates and the nutrients from the microbial community that died during winter freeze (de et al., 2009; Wolf et al., 2010); 2) increased soil moisture which formed an anaerobic environment and increased denitrifier activities (Priemé and Christensen, 2001; Teepe et al., 2001; Congreves et al., 2018). Several studies have observed that clay soil with high organic carbon content more easily produces high N₂O emissions during the freeze–thaw period (Van et al., 2000; Müller et al., 2003; Groenevelt and Grant, 2013; Wang et al., 2014). Dong et al. (2018) found that the N₂O pulses during freeze–thaw cycles are also related to the precipitation and depth of snow cover during the non-growing season. However, in our study, we found that there was no significant increase in N₂O emissions during the freeze–thaw period in both years. The main reasons were 1) our study located in a temperate semi-humid continental monsoon climate with little snowfall episode in winter, leading to insufficient anaerobic conditions during the freeze-thaw period, which inhibits denitrification to occur; 2) the SOC is low (1.1 g C kg⁻¹) in our study site and cannot provide sufficient carbon substrate for denitrification; and 3) the soil clay content is low (24.1%). Chen et al. (2014) also found that the contribution of the soil freeze–thaw period to annual N₂O emissions from rainfed agriculture in Northeast China is negligible.

Most in-situ N₂O measurements are still carried out by manual sampling, repeated usually in the intervals of days to weeks, and are in turn integrated across time to calculate annual losses. Such low-frequency measurements over or underestimate annual emission budgets (Liu et al., 2010). Barton et al. (2015) suggested that automated chambers should be continuously used to build guidelines for manual sampling. Here, we assume that the temporal coverage of manual flux measurements is daily, weekly, biweekly, and monthly, to analyze the influence of sampling frequency on calculating cumulative N₂O emissions from May to October in 2017. The subset is the N₂O flux between 09:00 and 12:00 extracted from our hourly measurements (similar to previous studies, e.g., Zhao et al., 2015; Guardia et al., 2017; Dong et al., 2018, 2018; Yao et al., 2019). Figure 8 shows that, compared with the high-resolution continuous measurements (5 times a day), low sampling frequencies can overestimate N₂O emissions by 8–49% (Figure 8). Therefore, sampling between 09:00 and 12:00 with low-frequency manual measurements can lead to considerable uncertainties in quantifying annual emissions.

Previous studies reported that sampling at LST 08:15 (Laville et al., 2011) or 09:00 (Liu et al., 2010) best represented the daily average of N₂O emissions; however, the best sampling time requires investigation across a broader range of land uses and climates (Smith and Dobbie, 2001; Barton et al., 2015). Here, we intended to reveal the best sampling time during the day for rainfed agriculture in our study region of Northeast China. After aggregating the entire dataset, Figure 3 shows that sampling at LST 9:00 to 10:00 am or 18:00 to 17:00 pm best represents the daily mean N₂O flux. We then calculated the cumulative N₂O emission sampling from 9:00 to 10:00 at daily, weekly, biweekly, and monthly intervals. We found that the deviations ranged from +2% to +9% (“+” indicated overestimations), which was considerably smaller than the deviation when sampling was performed between 9:00 and 12:00 (Figure 8). Therefore, we suggest that sampling between 9:00 and 10:00 is the best empirical sampling time for the intermittent manual measurements of N₂O emissions in our study region. High-frequency flux measurements enabled us to identify the diurnal pattern and highlight the effect of sampling frequency and sampling time on N₂O flux balance and provide guidance for low-frequency manual sampling.