All the experiments were conducted using chemical-grade ammonium sulfate ((NH₄)₂SO₄, 7783-20-2, Junsei, Japan), potassium nitrate (KNO₃,7757-79-1, Junsei, Japan), and urea (CO(NH)₂, 57-13-6, Junsei, Japan) as reference materials for both concentration and δ¹⁵N of NH₄ ⁺, NO₃ ⁻, and DON, respectively, throughout the experiments. Though nitrite (NO₂ ⁻) may be also be contained in rainwater, NO₂ ⁻ was not considered as the concentration of NO₂ ⁻ is reported to be as low as < 1% of NO₃ ⁻ (Sa et al., 2022). The δ¹⁵N of the compounds were analyzed using a stable isotope ratio mass spectrometer linked to an elemental analyzer (EA-IRMS) (VisION, Isoprime Ltd., Cheadle Hulme, United Kingdom), and reported as δ ( ‰ ) = [ ( R sample / R standard ) − 1 ] × 1000 where R is the atom % of ¹⁵N/(¹⁴N + ¹⁵N), and the standard was atmospheric N₂ (R = 0.3663%). Accuracy of the measurement by the EA-IRMS tested using IAEA-N1 and N2 (both ammonium sulfate, +0.4‰ and +20.3‰, respectively) was <0.2‰. The δ¹⁵N of the reference materials was calibrated against the IAEA-N1 and N2. The mean and standard errors of the δ¹⁵N of (NH₄)₂SO₄, KNO₃, and CO(NH)₂ measured in 10 replicates were ‒4.0 ± 0.03‰, ‒4.2 ± 0.03‰, and ‒5.4 ± 0.04‰, respectively.

To set pH and select evaporation method to obtain (NH₄)₂SO₄ salt from distillates for measurement of δ¹⁵N using the EA-IRMS, the effects of pH adjustment (pH < 3.5 and 5.4) and evaporation methods (oven at 60°C, oven at 100°C, infra-red chamber, and freeze-drying) were investigated using (NH₄)₂SO₄ as reference material. (NH₄)₂SO₄ solutions with two different concentrations (2 and 4 mg N L⁻¹ for low and high N, respectively) were prepared. Solution (100 ml) of (NH₄)₂SO₄ (0.2 and 0.4 mg N for low and high N contents, respectively) was transferred to a 250-ml beaker, and 10 mg sodium sulfate (Na₂SO₄) (1 ml of 10 g Na₂SO₄ L⁻¹ solution) was added to the beaker as a bulking agent to make sure sufficient amount of salt recovered after evaporation. Therefore, the N solutions are comprised of NH₄ ⁺, Na⁺, and SO₄ ²⁻, which are the ion compositions of the solutions when the distilled NH₄ ⁺ is collected in H₂SO₄ and back-titrated with NaOH (Hauck, 1982). The pH of the solution measured with a pH meter (Orion 3 Star, Thermo Fisher Scientific Inc., United States) was 5.4 ± 0.1. Another set of the N solution was acidified to pH < 3.5 by adding 0.2 ml of 0.1 N H₂SO₄.

To select evaporation methods, the beakers containing (NH₄)₂SO₄ solution were placed into a drying oven (WOF-155, Daihan Scientific, Korea), a house-made infra-red chamber, and a freeze drier (FD5508, Ilshin, Korea). The infra-red chamber (56 × 58 × 53 m³) was equipped with two infra-red lamps (Dr. Fischer 177.5 mm and 500 W). Each experiment was repeated four times for 2 N concentration levels, pH adjustment, and evaporation methods. The N solution was evaporated to dryness for 48 h. The dried salts were crushed to fine powder using a spatula. Powder containing approximately 0.1 mg N (²⁸N₂ beam area: 2.0E-07) was wrapped into a tin capsule and analyzed for δ¹⁵N using the EA-IRMS.

To determine the recovery of NH₄ ⁺ after evaporation, another set of four replicates was processed following the same procedures described above. The dried salts were re-dissolved by adding 50-ml of deionized water, and N content was determined using the indophenol method (Mulvaney, 1996) to calculate the loss of N during evaporation. The overall pattern of temperature change during evaporation was monitored using 1 L of deionized water contained in a 1 L beaker. Tip of temperature sensors (TR-52, T&D Cooperation, Japan) was installed at 3.5 cm above the bottom and 3.5 cm below the water surface, and the temperature was monitored for 10 h. After 10 h, it was not possible to measure temperature at the position due to decreased sample volume.

Nitrogen mixture solutions containing NH₄ ⁺, NO₃ ⁻, and CO(NH₂)₂ (0.5, 1, 1.5, 2, and 2.5 mg N for each N species) were prepared by dissolving the reference (NH₄)₂SO₄, KNO₃, and CO(NH₂)₂ in 1 L deionized water. The concentrations of reference N were set to include the range of N concentration of rainfall (<0.1 to >1.0 mg N L⁻¹) reported in the literature (Lee et al., 2012; Zeng et al., 2020; Chen et al., 2022). Distillation was performed following the standard distillation procedures of Mulvaney (1996) with some modifications to distillate a large quantity of samples. Briefly, 200 ml of the solution (containing 0.1, 0.2, 0.3, 0.4, and 0.5 mg N for each N species) was transferred to 500-ml distillation flasks, and the flasks were placed on a heating mantle (GLHMP-F100, Global Lab, Korea). NH₄ ⁺ was liberated by distillation with addition 0.5 g of carbonate-free MgO (1309-48-4, Junsei, Japan) for 4–5 min to collect 30–40 ml of distillates. Carbonate-free MgO was prepared by heating MgO at 700°C for 2 h and used following the suggestion of Mulvaney (1996). In a preliminary experiment, 4–5 min distillation was sufficient to recover NH₄ ⁺ (>99%). The liberated NH₃ was collected in a 250 ml beaker containing 10 ml of 0.01 N H₂SO₄. The (NH₄)₂SO₄ solution was titrated to pH 5.4 using 0.01 N NaOH and further acidified to pH < 3.5 by adding approximately 0.2 ml of 0.01 N H₂SO₄ and dried to salt under the infra-red lamps.

The distillation flasks were cooled down to room temperature, and the distillation apparatus was washed by distilling 30 ml of 90% ethanol for 5 min using another set of distilling flasks. For distillation of NO₃ ⁻, 50 ml of deionized water was added to the flasks to restore sample volume. To convert NO₃ ⁻ to NH₃, 0.3 g of Devarda’s alloy (8049-11-4, Kanto Chemical, Japan) was added and distilled again following the procedure for NH₄ ⁺. The (NH₄)₂SO₄ solution was acidified to pH < 3.5 following the procedure described above. The acidified solution was dried through evaporation under infra-red lamps as it was found that oven drying at 60°C, freeze-drying, and drying under infra-red lamps were all suitable (see the results). The δ¹⁵N of dried powder was analyzed using the EA-IRMS. The experiments were replicated four times.

The same N mixture solutions containing NH₄ ⁺, NO₃ ⁻, and CO(NH₂)₂, which were used for the distillation experiment were prepared. The theoretical values of δ¹⁵N-TDN calculated from NH₄ ⁺, NO₃ ⁻, and CO(NH₂)₂ was ‒4.5 ± 0.03‰. An aliquot (200 ml) of the standard samples were transferred to 250-ml beaker, and 10 mg Na₂SO₄ (1 ml of 10 g Na₂SO₄ L⁻¹ solution) was added to the beaker as a bulking agent followed by addition of 0.2 ml of 0.1 N H₂SO₄ to adjust the pH of the solution <3.5. The mixture was dried under infra-red lamps, and the dried powder was analyzed for δ¹⁵N of TDN using the EA-IRMS. All experiments were replicated four times.

The δ¹⁵N of DON was calculated using the following isotope mass balance equation (Karamanos and Rennie, 1981): δ 15 N DON = [ ( δ 15 N TDN × C TDN ) − ( δ 15 N NH 4 × C NH 4 + δ 15 N NO 3 × C NO 3 ) ] / [ C TDN − ( C NH 4 + C NO 3 ) ] where C_DON, C_TDN, C_NH4, and C_NO3 are contents of DON, TDN, NH₄ ⁺, and NO₃ ⁻, respectively, and δ¹⁵N_DON, δ¹⁵N_TDN, δ¹⁵N_NH4, and δ¹⁵N_NO3 are their respective δ¹⁵N. The standard deviation (SD) of δ¹⁵N_DON (SD _δDON) was calculated by using the following equation (Cao et al., 2021): SD δDON = [ ( ( C TDN / C DON ) × SD δTDN ) 2 + ( ( C NO 3 / C DON ) × SD δNO 3 ) 2 + ( ( C NH 4 / C DON ) × SD δNH 4 ) 2 ] 1 / 2 where SD_δTDN, SD_δNO3, and SD_δNH4 are the standard deviations of δ¹⁵N of TDN, NO₃ ⁻, and NH₄ ⁺, respectively.

The methods for the determination of δ¹⁵N of NH₄ ⁺, NO₃ ⁻, DON, and TDN using distillation and evaporation developed in the present study were validated using reference solutions. The reference solutions were prepared by dissolving the reference (NH₄)₂SO₄, KNO₃, and CO(NH₂)₂ in distilled water at two levels of N concentrations (2 and 3 mg N L⁻¹ for each N species). 200 ml of the solution (containing each 0.4 or 0.6 mg N of NH₄ ⁺, NO₃ ⁻, and DON) was distilled for the analysis of the δ¹⁵N of NH₄ ⁺ and NO₃ ⁻, and another 200 ml of the solution was directly dried for the analysis of δ¹⁵N of TDN under infra-red following the procedures described above. All experiments were replicated four times. The δ¹⁵N of DON was calculated using the isotope mass balance equation.

All statistical analyses were performed using IBM SPSS Statistics 23 (IBM Corp., Armonk, New York, United States) at a significance level of 0.05. Data were tested for normality of distribution and homogeneity of variance with Shapiro-Wilk test and Levene’s test, respectively. Data transformation was not needed as no heterogeneity was detected and the distribution was normal. In each experiment, the changes in the δ¹⁵N among the treatments (e.g., N content, pH adjustment, and evaporating method) were assessed by the analysis of variance (ANOVA). The precision of the δ¹⁵N measurement was assessed by calculating the standard deviation for the replicated treatments. The accuracy of the δ¹⁵N measurement was evaluated by calculating isotope enrichment, the differences between δ¹⁵N obtained from distillation-evaporation methods and that of reference materials determined with the direct combustion method. A t-test was performed to examine the difference in δ¹⁵N between distillation-evaporation and direct combustion methods.

The temperature of the solutions quickly increased to the maximum temperature within 1 h, and was maintained at the temperature thereafter (Figure 1). The maximum temperatures of the top and bottom sides of the solution were 50.1 and 49.0°C for oven drying at 60°C, 87.0 and 69.3°C for oven drying at 100°C, and 53.0 and 53.2°C for infra-red chamber, respectively. The δ¹⁵N of (NH₄)₂SO₄ measured after evaporation was affected by N content and pH of the solutions and evaporation method (Table 1). Though the effects of these three factors on δ¹⁵N were complicated as inferred from the significant interactions among the experimental factors, evaporation at pH < 3.5 produced more reliable δ¹⁵N than pH 5.4 across the N contents and evaporation methods. Among the evaporation methods, oven at 60°C, infra-red chamber, and freeze drier, but not oven at 100°C resulted in the δ¹⁵N comparable to the initial δ¹⁵N (‒4.0‰) at pH < 3.5 regardless of N contents. Evaporating the solutions at pH 5.4 resulted in significant errors (1.4–21.8‰) regardless of N contents and evaporation methods including freeze-drying due to N loss as inferred from the low N recoveries (30–89%) (Table 1).

Isotope enrichment during evaporation, which was calculated as the difference between the δ¹⁵N measured after evaporation and the initial δ¹⁵N of solid (NH₄)₂SO₄ before dissolving and evaporation (Table 1), was negatively correlated with N recovery (Figure 2A). The relationship between N recovery and δ¹⁵N followed the Rayleigh isotope enrichment model (Mariotti et al., 1981): δ 15 N s = δ 15 N i − ε ⁡ ln ( 1 − f ) where δ¹⁵N_s is δ¹⁵N of the remaining substrate (i.e., N in dried salts), δ¹⁵N_i is the initial δ¹⁵N (‒4.0‰) of the substrate, ε is the isotope enrichment factor (the difference in δ¹⁵N between the substrate and its instantaneous product), and f is the fraction of the substrate that is consumed in the reaction (i.e., the fraction of N lost during evaporation). The slope of the regression equation indicated that ε is 23.0‰ and thus isotope fractionation factor is 1.023 (Figure 2B). This value is within the isotope fractionation factors (1.005–1.031) reported for NH₃ volatilization (Cejudo and Schiff, 2018).

Acidification (pH 3–4) of the distillate solution containing NH₄ ⁺ is conventionally recommended for evaporation using an oven or infra-red chamber (Buresh et al., 1982; Feast and Dennis, 1996; Lee et al., 2012). Our results provide quantitative data on ¹⁵N enrichment of the samples caused by NH₃ volatilization. Notably, it was found that acidification did not completely prevent NH₃ from volatilization under oven drying at 100°C, resulting in ¹⁵N enrichments (0.5–0.9‰). This result is interesting as it is believed that acidulated (NH₄)₂SO₄ solution is stable at high temperature up to 235°C (Hauck, 1982). It is also notable that freeze-drying at pH 5.4 resulted in significant ¹⁵N enrichments (1.4–2.6‰), suggesting that freeze-drying does not prevent NH₃ from volatilization and thus that acidification is still necessary even when the samples are evaporated using a freeze drier (Stock et al., 2019). Therefore, our results suggest that evaporation using an oven at 100°C should be avoided and that acidification of NH₄ ⁺ solution is essential regardless of evaporation methods (including freeze-drying).

The δ¹⁵N-NH₄ ⁺ measured using the distillation method varied (p = 0.022) with N content (Figure 3A). When N content was ≤0.3 mg, δ¹⁵N-NH₄ ⁺ was underestimated by 1.0–2.1‰ (Figure 3A); meanwhile, when N contents were 0.4 and 0.5 mg, δ¹⁵N-NH₄ ⁺ (‒4.0 ± 0.5‰ for both) was comparable to the reference δ¹⁵N. The poor accuracy for low-NH₄ ⁺ samples could be attributed to the sample size effect on EA-IRMS measurement and/or inevitable background N contamination (Stark and Hart, 1996). However, in the present study, a similar amount of N (ca. 0.1 mg N) was used for the δ¹⁵N analysis on EA-IRMS for all the samples, and thus the sample size effect might be negligible. Therefore, background contamination arose from impurities of reagents and unintended trapping of NH₃ from laboratory air during evaporation might be more critical (Stark and Hart, 1996; Jensen, 1991; Sakata, 2001). In the present study, air NH₃ contamination was not detected in the evaporation experiment (Table 1), and thus the background contamination should be ascribed to impurities in the reagents. The underestimated δ¹⁵N-NH₄ ⁺ together with the positive correlation between N contents and δ¹⁵N-NH₄ ⁺ (Figure 3B) indicates potential contamination by NH₄ ⁺ impurity of which δ¹⁵N is lower than the sample NH₄ ⁺ (‒4.0‰). The δ¹⁵N of background NH₄ ⁺ contaminants could be estimated using a regression equation between N content and δ¹⁵N of NH₄ ⁺ (Figure 3B). The regression equation indicated that the δ¹⁵N of background NH₄ ⁺ was ‒6.3‰ (y-intercept; i.e., the δ¹⁵N value when no sample NH₄ ⁺ was added). Theoretically, background correction can be made using isotope dilution of a known ¹⁵N-enriched standard (Stark and Hart, 1996; Chen and Dittert, 2008; Cao et al., 2018) though this was not possible in the present study. As the magnitude of background contamination may vary with the experimental batch, we suggest that a laboratory-specific minimum N requirement (0.4 mg in the present study) needs to be determined prior to sample analyses for reliable measurement of δ¹⁵N of NH₄ ⁺ using distillation. For samples containing a low NH₄ ⁺ concentration, therefore, either increasing sample volume or sample concentration is necessary for distillation though this process may require an additional time. However, it is necessary to notice that other method for the determination of the δ¹⁵N of NH₄ ⁺, such as diffusion methods, also takes several days (up to 7 days) for complete diffusion (Cao et al., 2018).

The δ¹⁵N-NO₃ ^- fluctuated from ‒4.4 ± 0.1‰ to ‒3.9 ± 0.5‰, but the values were not statistically different (p > 0.05) from the reference δ¹⁵N across the contents of NO₃ ⁻ (Figure 3A). This result indicates that any trace background NH₄ ⁺ was removed from the distillation system during the first distillation for sample NH₄ ⁺ under alkaline conditions using MgO. Therefore, δ¹⁵N of NO₃ ⁻ can be measured with a high accuracy using the distillation method across a wide range of N content.

The δ¹⁵N-TDN was consistent across N contents from 0.1 to 0.5 mg N, and the averaged δ¹⁵N-TDN (‒4.5 ± 0.1‰) (Figure 4A) was not different (p > 0.05) from the theoretical δ¹⁵N-TDN (‒4.5 ± 0.03‰). Some studies have investigated δ¹⁵N-TDN using alkaline-persulfate oxidation of TDN to produce NO₃ ⁻ followed by reduction to gases N₂O for δ¹⁵N measurement (Lachouani et al., 2010; Cao et al., 2021). Our results show that direct evaporation of water samples after acidification is also a feasible and simple method to determine δ¹⁵N-TDN. Though a small segment of CO₂ contained in water sample may be decomposed to CO (¹²C¹⁸O) to interfere with ³⁰N₂ in the IRMS (Russow et al., 2002), acidification of the sample could eliminate the potential interference as CO₂ is removed under acidic conditions.

δ¹⁵N-DON calculated using the isotope mass balance equation showed a high variability with errors of 1.2–2.0‰ when DON content was 0.1–0.3 mg N, suggesting that the accuracy of δ¹⁵N-DON is dependent on the DON content (Figure 4B). Cao et al. (2021) reported that accuracy of indirect determination of δ¹⁵N-DON by measuring δ¹⁵N-TDN through alkaline-persulfate digestion method depended on DON content as analytical errors for determination of δ¹⁵N-DON were as high as 0.7–1.4‰ for samples with a low DON content (<0.2 mg N). It is also obvious that δ¹⁵N-DON is dependent on δ¹⁵N of other N species used in the isotope mass balance equation (Cao et al., 2021). In the present study, among N species, the variability of δ¹⁵N-NH₄ ⁺ was highest for the samples containing 0.1–0.3 mg N (Figure 3A). Therefore, the accuracy of determination of δ¹⁵N-DON with the isotope mass balance equation using δ¹⁵N-NH₄ ⁺ and δ¹⁵N-NO₃ ^- (distillation) and δ¹⁵N-TDN (direct evaporation) is dependent on NH₄ ⁺ content. Therefore, indirect determination of δ¹⁵N-DON might be feasible for water samples with a high NH₄ ⁺ concentration.

Based on the results of this study, a procedure was suggested for determination of δ¹⁵N of multiple N species including NH₄ ⁺, NO₃ ⁻, DON, and TDN of rainwater samples using distillation for NH₄ ⁺ and NO₃ ⁻, direct evaporation for TDN, and indirect calculation using isotope mass balance equation for DON (Figure 5). Prior to δ¹⁵N measurement, it is necessary to determine N concentration of each N species to determine the sample volume to be used for distillation, particularly for NH₄ ⁺. The N concentrations of samples could be determined with the non-distillation method more accurately with colorimetry (Mulvaney, 1996) and ion chromatography (Mou et al., 1993). Though the concentrations of NH₄ ⁺ and NO₃ ⁻ could be determined through distillation and acid-base titration, it is known that the precision and accuracy of distillation for the determination of NH₄ ⁺ and NO₃ ⁻ are not reliable particularly when H₂SO₄ is used as an absorbent of NH₃ instead of boric acid (APHA-AWWA-WEF, 1998). The concentrations of NH₄ ⁺ and NO₃ ⁻ can be easily determined accurately with colorimetry (Mulvaney, 1996) and ion chromatography (Mou et al., 1993). The concentration of TDN can be easily determined using TN auto-analyzer or alkaline-persulfate oxidation followed by manual or automated determination of NO₃ ⁻ (Ebina et al., 1983). The concentrations of DON can be calculated as difference between TDN and inorganic N (NH₄ ⁺ + NO₃ ⁻).

The δ¹⁵N-NH₄ ⁺ and δ¹⁵N-NO₃ ^- could be determined through distillation and evaporation following the procedure described above. For δ¹⁵N-NH₄ ⁺, it is important to make sure that NH₄ ⁺ content of the samples subject to distillation should be at least 0.4 mg N. However, a minimum requirement of NH₄ ⁺ for reliable measurement of δ¹⁵N may differ with laboratory conditions, and thus it is necessary to determine the minimum NH₄ ⁺ requirement using a standard NH₄ ⁺ chemical for each laboratory following the procedure used in the present study. For samples containing a low NH₄ ⁺ concentration, a larger volume of samples needs to be used for distillation. As the concentrations of NH₄ ⁺ in rainwater are highly variable depending on the sites and seasons, ranging from <0.1 to >1.0 mg N L⁻¹ (Lee et al., 2012; Zeng et al., 2020; Chen et al., 2022), however, water samples with an extremely low NH₄ ⁺ may be concentrated to reduce the volume of water sample being added to distillation flasks, which have a confined volume capacity (e.g., 500 ml in the present study). Water samples containing a low N are often concentrated using a freeze-drier (Chen et al., 2022). In this context, our results further suggest that acidification of water samples is essential to prevent ¹⁴NH₃ loss even under freeze-drying. The δ¹⁵N-TDN can be directly determined using salts obtained from evaporation of the acidified samples to dryness. Finally, δ¹⁵N-DON is determined with an isotope mass balance equation using N concentration and δ¹⁵N of N species.

When the methods were tested using the reference solutions, the measured δ¹⁵N was not statistically (p > 0.05) different from the values determined by the direct combustion method using the EA-IRMS (Table 2). However, the δ¹⁵N of NH₄ ⁺ and NO₃ ⁻ were slightly lower than the reference δ¹⁵N, while the δ¹⁵N of DON was higher than the reference δ¹⁵N, probably due to the potential influence of hydrolysable DON (i.e., CO(NH₄)₂ in the present study) on the δ¹⁵N of NH₄ ⁺ and NO₃ ⁻. In the present study, pH was raised by using MgO rather than NaOH to minimize the interference of N liberated from DON under alkaline conditions (Mulvaney, 1996; Sakata, 2001). However, such variations in the δ¹⁵N of NH₄ ⁺ and NO₃ ⁻ suggest that CO(NH₂)₂ used as a DON reference might be partially subject to hydrolysis during distillation. As such interference of DON was not detected in the early experiment, it was suspected that alteration of the δ¹⁵N of NH₄ ⁺ and NO₃ ⁻ by hydrolyzable DON is not systematic but random. In the natural water environment, however, DON compounds present as more complex and recalcitrant compounds associated with lipids, proteins, amino sugars, lignins, and tannins (Lusk and Toor, 2016; Zhang et al., 2021), and thus the interference caused by DON during distillation of natural water samples might be less significant than the experimental conditions in the present study.