Rapid Determination of Nitrate Nitrogen Isotope in Water Using Fourier Transform Infrared Attenuated Total Reflectance Spectroscopy (FTIR-ATR) Coupled with Deconvolution Algorithm

Nitrate is a prominent pollutant in water bodies around the world. The isotopes in nitrate provide an effective approach to trace the sources and transformations of nitrate in water bodies. However, determination of isotopic composition by conventional analytical techniques is time-consuming, laborious, and expensive, and alternative methods are urgently needed. In this study, the rapid determination of 15NO3− in water bodies using Fourier transform infrared attenuated total reflectance spectroscopy (FTIR-ATR) coupled with a deconvolution algorithm and a partial least squares regression (PLSR) model was explored. The results indicated that the characteristic peaks of 14NO3−/15NO3− mixtures with varied 14N/15N ratios were observed, and the proportion of 15NO3− was negatively correlated with the wavenumber of absorption peaks. The PLSR models for nitrate prediction of 14NO3−/15NO3− mixtures with different proportions were established based on deconvoluted spectra, which exhibited good performance with the ratio of prediction to deviation (RPD) values of more than 2.0 and the correlation coefficients (R2) of more than 0.84. Overall, the spectra pretreatment by the deconvolution algorithm dramatically improved the prediction models. Therefore, FTIR-ATR combined with deconvolution and PLSR provided a rapid, simple, and affordable method for determination of 15NO3− content in water bodies, which would facilitate and enhance the study of nitrate sources and water environment quality management.


Introduction
In recent years, with the gradual control of fixed source pollution, agricultural nonpoint source pollution has become the main factor affecting the water quality. According to the Bulletin of the Second National Survey of Pollution Sources in 2017, the total nitrogen discharge of water pollutants in China was 3.014 million tons and the total phosphorus discharge was 31.54 million tons, of which the total nitrogen discharge of agricultural water pollutants was 1.41 million tons, and the total phosphorus discharge was 21.2 million tons, accounting for 46.52% and 67.22% of the total, respectively [1]. The agricultural sources become the main contributors to total nitrogen and total phosphorus discharges. Compared with phosphorus, the form of nitrogen, including organic nitrogen and inorganic nitrogen, is much more complicated, Ammonium nitrogen (NH 4 + -N), nitrate nitrogen (NO 3 − -N) and nitrite nitrogen (NO 2 − -N) are the main forms of inorganic nitrogen in water. Nitrate nitrogen is an important form of active nitrogen that can cause deterioration of aquatic ecosystem health, i.e., eutrophication, and human health risks; the former included the items of decreased oxygen levels in water bodies, algal blooms, and reduced aquatic biodiversity, and the latter included the items of stomach cancer, diabetes, thyroid disease, and "blue baby" syndrome [2][3][4]. The nitrate contents in water bodies are regulated by the interaction between external sources of pollution (e.g., industrial wastewater, municipal sewage, nitrogen runoff, and atmospheric deposition) and nitrogen cycling processes (e.g., nitrification, denitrification, ammonia volatilization, and plant/microbial utilization) [5][6][7]. As one of the main means to evaluate the degree of impact of agricultural non-point source pollutants on water environment quality, identification and determination of the main sources and transformations of nitrate are the primary objectives to construct effective strategies to address nitrate pollution.
The nitrate isotope ( 15 N/ 18 O-NO 3 ) provides an effective method to determine the potential nitrate sources and transformations [8,9]. The advantages of the isotope method include direct identification, less auxiliary information, and high precision in identifying pollution sources. Therefore, rapid, accurate, and affordable detection techniques of isotopic composition are extremely important. Usually, an isotope ratio mass spectrometer (IRMS) is a necessary instrument for measuring stable isotopic composition [10]. However, the IRMS is limited for many organizations and institutions due to its high price and maintenance costs. In addition, sample pretreatments, including ion exchange, cadmium azide reduction, and bacterial denitrification, are time-and labor-consuming. Given these issues, stable isotopes of nitrogen tend to be limited in practical applications. Therefore, it is necessary to develop an economical and effective method for the isotopic content qualification of water bodies.
As a nondestructive, rapid, and efficient analysis method, Fourier transform infrared attenuated total reflectance spectroscopy (FTIR-ATR) has been widely used in various fields. Due to the characteristic absorption peaks of nitrate around 1360 cm −1 , the contents of nitrate in soil, vegetables, and water bodies have been quantitatively determined by FTIR-ATR [11][12][13][14][15]. In comparison to the spectral absorption of 14 NO 3 − , the absorption band of 15 NO 3 − significantly shifted to the direction of low wavenumber, which has already been used to determine nitrogen isotope-labelled nitrates in solution and soil using the PLSR model [16][17][18]. Since the absorption of nitrate spectra is prone to strong interference from water, the previous studies eliminated the interference by directly deducting water absorption, and the PLSR models based on water yielded a determination error of 6.7-9.2 mg/L [16]. However, such a water deduction algorithm resulted in poor prediction performance in low concentrations with different N-isotopically labeled nitrates due to the relatively large errors. Therefore, developing efficient pre-processing approaches for spectral data to obtain higher prediction accuracy is in great demand.
In the process of spectral acquisition, spectra often exhibit signal overlap and noise interference, thus resulting in a decrease in resolution. Therefore, a signal processing algorithm for extracting target information effectively could improve the prediction accuracy. As a mathematical operation process, deconvolution is a typical signal extraction and recovery method [19,20], which showed unique advantages in spectral processing. The deconvolution technology improved the resolution beyond the instrument's limit and significantly improved the signal-to-noise ratio [21,22]. To obtain an accurate and reliable signal, spectral deconvolution was associated with Gaussian fitting of the absorption spectrum to adjust the Gaussian mathematical curve and obtain corresponding characteristic absorption peaks from an overlapping spectrum.
In addition, the objective of this study was to pre-process the FTIR-ATR spectra of 14 NO 3 − / 15 NO 3 − mixture to obtain the characteristic absorption peaks by using a deconvolution algorithm, and a PLSR model based on the deconvoluted spectra was explored to predict nitrate nitrogen isotope, which could provide technical support for nitrate sources and water quality management.

Spectral Characterization
The mixed solutions of 14  and 1800-1500 cm −1 that were attributed to the characteristic absorption of water were observed. Although the characteristic peak of nitrate was at approximately 1500-1200 cm −1 , the signal of the absorption peak was weak and was strongly interfered with by water, thus resulting in difficulty in direct observation.

Spectral Characterization
The mixed solutions of 14 NO3 − and 15 NO3 − with different proportions showed spectral characteristics (Figure 1). A total of two strong absorption peaks at 3800-30 and 1800-1500 cm −1 that were attributed to the characteristic absorption of wate observed. Although the characteristic peak of nitrate was at approximately 150 cm −1 , the signal of the absorption peak was weak and was strongly interfered w water, thus resulting in difficulty in direct observation.

Spectral Processing
The second derivative spectra of the of 14 NO3 − and 15 NO3 − mixtures with diffe tios did not show prominent characteristic peaks in the range of 1500-1200 cm −1 2a). The characteristic spectra of nitrate after directly deducting water exhibited a ular trend (Figure 2b). One reason might be that the infrared-characteristic absorp NO3 − was also strongly interfered with by water. Another factor could be attributed low concentration of NO3 − in the sample, resulting in a low characteristic peak in Therefore, it is necessary to further process the spectra of the 1500-1200 cm −1 band tain target spectral information from the overlapping band.
The peak-fit 4.12 software was used to deconvolve the spectra of the 1500-12 band: the goodness of fitting (R 2 ) obtained was all above 0.97, and the sum of s errors (SSE) was all less than 0.108, exhibiting excellent deconvolution effects. Th acteristic peak position and the overall intensity of 14 NO3 − and 15 NO3 − mixtures w ferent proportions were obviously different (Figure 2c). With the increase in the p tion of 15 NO3 − in mixtures, the characteristic peak of nitrate gradually shifted in th tion of a low wavenumber. The nitrate absorption peaks were 1365.7, 1362.1, 1354.8, 1344.1, 1340.4, and 1336.8 cm −1 when the 14 N/ 15 N ratios were 1:0, 3:1, 2:1, 1 1:3, and 0:1, respectively. Additionally, the overall spectral intensity decreased w increase in the proportion of 15 NO3 − , the main reason probably was that when the a tion peak of 14 NO3 − and 15 NO3 − mixture was close to the characteristic absorption o (1800-1500 cm −1 ) stronger interference could be observed. As shown in Figure 2d, t portion of 15 NO3 − showed a good negative correlation with the wavenumber of the absorption peaks. Therefore, the proportion of 15 NO3 − was calculated based on the teristic peak positions of the 14 NO3 − and 15 NO3 − mixtures. However, for different

Spectral Processing
The second derivative spectra of the of 14 NO 3 − and 15 NO 3 − mixtures with different ratios did not show prominent characteristic peaks in the range of 1500-1200 cm −1 (Figure 2a). The characteristic spectra of nitrate after directly deducting water exhibited an irregular trend (Figure 2b). One reason might be that the infrared-characteristic absorption of NO 3 − was also strongly interfered with by water. Another factor could be attributed to the low concentration of NO 3 − in the sample, resulting in a low characteristic peak intensity. Therefore, it is necessary to further process the spectra of the 1500-1200 cm −1 band to obtain target spectral information from the overlapping band.
The peak-fit 4.12 software was used to deconvolve the spectra of the 1500-1200 cm −1 band: the goodness of fitting (R 2 ) obtained was all above 0.97, and the sum of squared errors (SSE) was all less than 0.108, exhibiting excellent deconvolution effects. The characteristic peak position and the overall intensity of 14 NO 3 − and 15 NO 3 − mixtures with different proportions were obviously different (Figure 2c). With the increase in the proportion of 15 NO 3 − in mixtures, the characteristic peak of nitrate gradually shifted in the direction of a low wavenumber. The nitrate absorption peaks were 1365.7, 1362.1, 1358.5, 1354.8, 1344.1, 1340.4, and 1336.8 cm −1 when the 14 N/ 15 N ratios were 1:0, 3:1, 2:1, 1:1, 1:2, 1:3, and 0:1, respectively. Additionally, the overall spectral intensity decreased with the increase in the proportion of 15 NO 3 − , the main reason probably was that when the absorption peak of 14 NO 3 − and 15 NO 3 − mixture was close to the characteristic absorption of water (1800-1500 cm −1 ) stronger interference could be observed. As shown in Figure 2d, the proportion of 15 NO 3 − showed a good negative correlation with the wavenumber of the nitrate absorption peaks. Therefore, the proportion of 15 NO 3 − was calculated based on the characteristic peak positions of the 14 NO 3 − and 15 NO 3 − mixtures. However, for different 14 N/ 15 N ratios, the characteristic peak intensity of nitrate was proportional to the nitrate concentration; therefore, the absorption peaks could be used for the quantitative analysis of nitrate in solutions. ratios, the characteristic peak intensity of nitrate was proportional to the nitrate conce tration; therefore, the absorption peaks could be used for the quantitative analysis of trate in solutions.

Principal Component Analysis
The principal component analysis (PCA) based on the spectra range of 1500-12 cm −1 was performed ( Figure 3). In the water deduction algorithm and deconvolution gorithm, the first two principal components both accounted for more than 96% of t whole spectral variance. Therefore, PC1 and PC2 were used to represent the spectral v iation. However, the score plot showed an irregular pattern with the water deduction gorithm ( Figure 3a). Instead, it was found that the scores of these two principal comp nents showed a regular and consistent distribution with the deconvolution algorithm (F ure 3b). The plot shifted to negative values of PC1 as the ratio of 15 NO3 − increased, and t PC2 scores of all seven 14 N/ 15 N combinations shifted from negative values to positive v ues with the increase of total N concentrations, which further proved that FTIR-ATR co pled with deconvolution could be used to determine 15

Principal Component Analysis
The principal component analysis (PCA) based on the spectra range of 1500-1200 cm −1 was performed ( Figure 3). In the water deduction algorithm and deconvolution algorithm, the first two principal components both accounted for more than 96% of the whole spectral variance. Therefore, PC1 and PC2 were used to represent the spectral variation. However, the score plot showed an irregular pattern with the water deduction algorithm (Figure 3a). Instead, it was found that the scores of these two principal components showed a regular and consistent distribution with the deconvolution algorithm ( Figure 3b). The plot shifted to negative values of PC1 as the ratio of 15 NO 3 − increased, and the PC2 scores of all seven 14 N/ 15 N combinations shifted from negative values to positive values with the increase of total N concentrations, which further proved that FTIR-ATR coupled with deconvolution could be used to determine 15

Prediction of Nitrate Nitrogen with a Water Deduction Algorithm
The PLSR was used to model the spectra of the 1500-1200 cm −1 region based on the water deduction algorithm ( Figure 4). Firstly, the cross-validation method was performed to obtain the optimal number of principal components in the seven mixed solutions of 14 NO3 − and 15 NO3 − . The optimal number of principal components were 6, 1, 3, 1, 1, 1 and 1 when the 14 N/ 15 N ratios were 1:0, 3:1, 2:1, 1:1, 1:2, 1:3, and 0:1, respectively, corresponding to the minimum value of the RMSECV (Figure 4a,c,e,g,i,k,m). Therefore, the optimal principal components were used to construct the PLSR model. The R 2 between the measured and predicted values in the validation set were 0.722, 0.862, 0.772, 0.628, 0.923, 0.747, and 0.394, respectively, and the RPD values were 1.86, 2.15, 1.83, 1.53, 2.60, 1.93, and 1.28, respectively, which were higher than the minimum standard of 1.4 required for quantitative determination except for the RPD of 15 NO3 − solution ( 14 N/ 15 N = 0:1). However, the LODs of seven models were 8.75, 7.36, 9.21, 16.56, 5.32, 9.17, and 17.71 mg/L, respectively, which exhibited poor performance for the determination of low nitrate nitrogen concentration.
A bias value close to zero indicates a low systematic error between the measured and predicted values. The biases of the models were shown in Table 1. According to the absolute value, the low systematic errors of seven models were 0.302, 0.232, 0.192, 0.269, 0.163, 0.156, and 0.298, respectively.

Prediction of Nitrate Nitrogen with a Water Deduction Algorithm
The PLSR was used to model the spectra of the 1500-1200 cm −1 region based on the water deduction algorithm ( Figure 4). Firstly, the cross-validation method was performed to obtain the optimal number of principal components in the seven mixed solutions of 14 NO 3 − and 15 NO 3 − . The optimal number of principal components were 6, 1, 3, 1, 1, 1 and 1 when the 14 N/ 15 N ratios were 1:0, 3:1, 2:1, 1:1, 1:2, 1:3, and 0:1, respectively, corresponding to the minimum value of the RMSECV (Figure 4a,c,e,g,i,k,m). Therefore, the optimal principal components were used to construct the PLSR model. The R 2 between the measured and predicted values in the validation set were 0.722, 0.862, 0.772, 0.628, 0.923, 0.747, and 0.394, respectively, and the RPD values were 1.86, 2.15, 1.83, 1.53, 2.60, 1.93, and 1.28, respectively, which were higher than the minimum standard of 1.4 required for quantitative determination except for the RPD of 15 NO 3 − solution ( 14 N/ 15 N = 0:1). However, the LODs of seven models were 8.75, 7.36, 9.21, 16.56, 5.32, 9.17, and 17.71 mg/L, respectively, which exhibited poor performance for the determination of low nitrate nitrogen concentration.

Prediction of Nitrate Nitrogen with a Water Deduction Algorithm
The PLSR was used to model the spectra of the 1500-1200 cm −1 region based on the water deduction algorithm (Figure 4). Firstly, the cross-validation method was performed to obtain the optimal number of principal components in the seven mixed solutions of 14 NO3 − and 15 NO3 − . The optimal number of principal components were 6, 1, 3, 1, 1, 1 and 1 when the 14 N/ 15 N ratios were 1:0, 3:1, 2:1, 1:1, 1:2, 1:3, and 0:1, respectively, corresponding to the minimum value of the RMSECV (Figure 4a,c,e,g,i,k,m). Therefore, the optimal principal components were used to construct the PLSR model. The R 2 between the measured and predicted values in the validation set were 0.722, 0.862, 0.772, 0.628, 0.923, 0.747, and 0.394, respectively, and the RPD values were 1.86, 2.15, 1.83, 1.53, 2.60, 1.93, and 1.28, respectively, which were higher than the minimum standard of 1.4 required for quantitative determination except for the RPD of 15 NO3 − solution ( 14 N/ 15 N = 0:1). However, the LODs of seven models were 8.75, 7.36, 9.21, 16.56, 5.32, 9.17, and 17.71 mg/L, respectively, which exhibited poor performance for the determination of low nitrate nitrogen concentration.
A bias value close to zero indicates a low systematic error between the measured and predicted values. The biases of the models were shown in Table 1. According to the absolute value, the low systematic errors of seven models were 0.302, 0.232, 0.192, 0.269, 0.163, 0.156, and 0.298, respectively.

Prediction of Nitrate Nitrogen with a Deconvolution Algorithm
The deconvoluted spectra in the range of 1500-1200 cm −1 were involved in the PLSR modeling ( Figure 5). The optimal principal components were 2, 3, 2, 4, 3, 3, and 2 when the 14 N/ 15 N ratios were 1:0, 3:1, 2:1, 1:1, 1:2, 1:3, and 0:1, respectively (Figure 5a,c,e,g,i,k,m). Therefore, the PLSR model could be established with each optimal principal component. The results showed that the R 2 values between the measured and predicted values in the validation set were 0.935, 0.960, 0.976, 0.843, 0.908, 0.982, and 0.857, respectively, showing a good linear relationship (Figure 5b,d,f,h,j,l,n). The RPD values were respectively obtained at 2.93, 2.59, 6.27, 2.38, 3.19, 4.57, and 2.55, which were all higher than the minimum standard of 1.4 that was required for quantitative determination. The prediction capacity of all the above models reached a good level. In addition, the PLSR models in the calibration set also exhibited robust prediction performance (Table 2), and the LOD of seven models were 3.73, 4.67, 2.31, 4.86, 3.57, 2.79, and 5.62 mg/L, respectively, significantly lower than that of the LOD with the water deduction algorithm. Over the last several decades, a large number of sensing methods have been developed to detect nitrate nitrogen in water. Several have a high sensitivity with a good LOD but expensive instrumentation; A bias value close to zero indicates a low systematic error between the measured and predicted values. The biases of the models were shown in Table 1. According to the absolute value, the low systematic errors of seven models were 0.302, 0.232, 0.192, 0.269, 0.163, 0.156, and 0.298, respectively.

Prediction of Nitrate Nitrogen with a Deconvolution Algorithm
The deconvoluted spectra in the range of 1500-1200 cm −1 were involved in the PLSR modeling ( Figure 5). The optimal principal components were 2, 3, 2, 4, 3, 3, and 2 when the 14 N/ 15 N ratios were 1:0, 3:1, 2:1, 1:1, 1:2, 1:3, and 0:1, respectively (Figure 5a,c,e,g,i,k,m). Therefore, the PLSR model could be established with each optimal principal component. The results showed that the R 2 values between the measured and predicted values in the validation set were 0.935, 0.960, 0.976, 0.843, 0.908, 0.982, and 0.857, respectively, showing a good linear relationship (Figure 5b,d,f,h,j,l,n). The RPD values were respectively obtained at 2.93, 2.59, 6.27, 2.38, 3.19, 4.57, and 2.55, which were all higher than the minimum standard of 1.4 that was required for quantitative determination. The prediction capacity of all the above models reached a good level. In addition, the PLSR models in the calibration set also exhibited robust prediction performance (Table 2), and the LOD of seven models were 3.73, 4.67, 2.31, 4.86, 3.57, 2.79, and 5.62 mg/L, respectively, significantly lower than that of the LOD with the water deduction algorithm. Over the last several decades, a large number of sensing methods have been developed to detect nitrate nitrogen in water. Several have a high sensitivity with a good LOD but expensive instrumentation; others have a reasonable sensitivity with reduced cost. It has been reported that an ion chromatography technique can be useful to determine nitrate nitrogen in water with a good LOD of 0.05 mg/L [23], while the LOD of some detection methods based on biosensors and voltammetry was higher than 5 mg/L [24,25]. Although our analytical methods did not show excellent LOD compared to some reference methods, the LOD were acceptable for determination. In fact, in spectral analysis, RPD could also be used to represent the sensitivity. In all seven 14 N/ 15 N combinations, the RPD of the PLSR prediction models based on deconvolution was more than 2, indicating that the models were at a good level. However, compared to the models with the water deduction algorithm, all seven models for nitrate prediction showed lower systematic errors ( Table 2).
In previous studies, the PLSR models, coupled with the deconvolution algorithm, showed good prediction performance for low concentrations of 14 NO 3 − (Table 3). For the sample with a high 15 NO 3 − concentration, the models based on the water deduction algorithm were acceptable for prediction, but for the sample with a low 15 NO 3 − concentration, the spectra with water deduction showed strong interference and irregular trends, and the models exhibited poor prediction capacity (Figure 4). In this experiment, a deconvolution algorithm was adopted to pre-process the spectra to obtain an effective small target signal and further achieve rapid determination for low concentrations of 14 NO 3 − and 15 NO 3 − . Overall, the above results indicated that this method could be used for the quantitative determination of nitrate in 14 NO 3 − and 15 NO 3 − mixtures with different proportions. In this study, as a theoretical investigation, standard samples were prepared and used in the investigation. However, the model developed in a different aquatic environment might be different due to varied background interference on the spectra. Our previous study confirmed that the presence of carbonate in the water impacted the nitrate determination [15]. Therefore, when this technology is applied to different aquatic environments (e.g., surface water and groundwater) in the future, the factors that may affect the prediction performance of the models need to be fully considered and investigated. Further, the parameters of the spectral deconvolution algorithm can also be optimized to further improve the sensitivity and applicability of the model. others have a reasonable sensitivity with reduced cost. It has been reported that an ion chromatography technique can be useful to determine nitrate nitrogen in water with a good LOD of 0.05 mg/L [23], while the LOD of some detection methods based on biosensors and voltammetry was higher than 5 mg/L [24,25]. Although our analytical methods did not show excellent LOD compared to some reference methods, the LOD were acceptable for determination. In fact, in spectral analysis, RPD could also be used to represent the sensitivity. In all seven 14 N/ 15 N combinations, the RPD of the PLSR prediction models based on deconvolution was more than 2, indicating that the models were at a good level. However, compared to the models with the water deduction algorithm, all seven models for nitrate prediction showed lower systematic errors ( Table 2).
In previous studies, the PLSR models, coupled with the deconvolution algorithm, showed good prediction performance for low concentrations of 14 NO3 − (Table 3). For the sample with a high 15 NO3 − concentration, the models based on the water deduction algorithm were acceptable for prediction, but for the sample with a low 15 NO3 − concentration, the spectra with water deduction showed strong interference and irregular trends, and the models exhibited poor prediction capacity (Figure 4). In this experiment, a deconvolution algorithm was adopted to pre-process the spectra to obtain an effective small target signal and further achieve rapid determination for low concentrations of 14 NO3 − and 15 NO3 − . Overall, the above results indicated that this method could be used for the quantitative determination of nitrate in 14 NO3 − and 15 NO3 − mixtures with different proportions.
In this study, as a theoretical investigation, standard samples were prepared and used in the investigation. However, the model developed in a different aquatic environment might be different due to varied background interference on the spectra. Our previous study confirmed that the presence of carbonate in the water impacted the nitrate determination [15]. Therefore, when this technology is applied to different aquatic environments (e.g., surface water and groundwater) in the future, the factors that may affect the prediction performance of the models need to be fully considered and investigated. Further, the parameters of the spectral deconvolution algorithm can also be optimized to further improve the sensitivity and applicability of the model. 1 (e,f); 1:1 (g,h); 1:2 (i,j); 1:3 (k,l); 0:1 (m,n)).   1 (e,f); 1:1 (g,h); 1:2 (i,j); 1:3 (k,l); 0:1 (m,n)).  Notes: RPD: the ratio of prediction to deviation; RMSE: the root mean square error.

Spectra Recording and Pre-Processing
A 4300 handheld FTIR spectrometer with an ATR spectra accessory (Thermo Fisher Scientific, Waltham, MA, USA) was used to record the spectra in the range of 4000 to 600 cm −1 , with a spectral resolution of 4 cm −1 , 32 scans. The atmospheric and instrumental noises were corrected by subtracting the background from each scan. An appropriate amount of each sample was placed in the sample tank for three measurements.
The FTIR-ATR spectra were prepossessed by the Savitzky-Golay smoothing filter to improve the signal-to-noise ratio by eliminating baseline floating and noise [26]. According to the absorption characteristics of nitrate, the spectrum in the 1500-1200 cm −1 region was subjected to smoothing, baseline correction, and Gaussian deconvolution with Peak-fit 4.12 software. The deconvolution process has been elaborated in detail in Figure 6. The deconvolution of the spectral curve assumed that several single-peak spectral bands superimpose the experimental spectrum Y(x). The purpose of fitting was to find the single-peak spectral band Fi(x) (i = 1, 2..., n) [27,28]. The principle was as follows: (1) Figure 6. The process of spectra deconvolution.
The deconvolution of the spectral curve assumed that several single-peak spectral bands superimpose the experimental spectrum Y(x). The purpose of fitting was to find the single-peak spectral band F i (x) (i = 1, 2 . . . , n) [27,28]. The principle was as follows: where Y is the spectrum, x is the wave number, i (1, 2, 3 . . . , n) is the number of independent peaks, and F is the kernel function of the expansion or deconvolution. The Gaussian function is taken as the kernel function: where a 0 , a 1, and a 2 represent peak amplitude, position, and width, respectively, while x and y represent wave number and absorption intensity.

Spectra Recording and Pre-Processing
The principal component analysis (PCA) is a dimensionality reduction chemometrics technique because it reduces redundant information in a data set. In this experiment, PCA was used to reduce the dimensions of the spectral data by providing new variables and to find the regularities among the different ratios of 14 N/ 15 N in the spectral subsection. The PCA treated the intense peak positions in each spectrum as vectors and formed linear combinations of the vectors by assigning a weight to each vector. The MATLAB software (MATLAB2018b, the MathWorks, Natick, MA, USA) was used for the data analysis.

Prediction Models
The partial least squares regression (PLSR) model is one of the most commonly used stoichiometry algorithms in spectral data analysis. It was a bilinear model where a matrix X, containing the variables (spectra wavenumber), and a matrix Y, a function of the variables in matrix X (nitrate contents), were used to predict the smallest number of latent variables. Cross-validation is a statistically sound method for choosing the number of components in the PLSR model. It avoids over-fitting data by not reusing the same data to both fit a model and estimate the prediction error. Thus, the estimate of the prediction error is not optimistically biased downward. PLSR has an option to estimate the root-mean-squarederror (RMSE) by cross-validation, and when the model reached the first lowest RMSE, the corresponding number of factors was optimal [29].

Calibration and Validation Datasets
The spectral data sets of each ratio of 14 NO 3 − / 15 NO 3 − mixture were randomly divided into a calibration data set containing 75% spectra and a validation data set containing the remaining 25% spectra.

Model Evaluation
The ratio of prediction to deviation (RPD), the correlation coefficient (R 2 ), and the root-mean-square error (RMSE) were used to evaluate the model's predictive performance. The parameters were evaluated by the following equations:

RPD = SD RMSE
(4) where y i andŷ i denote the measurement value and predicted value of nitrate in the e th sample, respectively; y is the mean value of the measured nitrate content; SD is the standard deviation. RMSE C and RMSE V represent the root mean square error (RMSE) in the calibration and validation dataset models. High R 2 , RPD, and low RMSE define the robustness and accuracy of the models. RPD value less than 1.4 is considered unsuitable for quantitative measurement; RPD value between 1.4 and 1.8 is acceptable; RPD value between 1.8 and 2.0 is good, in which case quantitative prediction could be made; RPD value between 2.0 and 2.5 is very good quantitative analysis; and an RPD higher than 2.5 indicates excellent model prediction performance [30].

Limit of Detection
In the process of linear multivariate analysis, the limit of detection (LOD) reflected the model's sensitivity. The LOD was calculated by 3σ/m, where σ was the standard deviation of the predicted concentration, which was denoted by RMSEP, and m was the fitting-curve slope of the model (using real value as the X-axis and predicted value as the Y-axis) [31].

Systematic Error Assessment
The systematic errors are derived from the inadequacy of calibration models. The bias is the sum of the differences between the estimated value y i and the measured value x i [32,33], and was calculated by Equation (6): where n is the number of samples. A bias value close to zero indicates a low systematic error between the measured and predicted values [34].

Conclusions
Combining the deconvolution algorithm and PLSR model, FTIR-ATR, was used to determine the N isotope in the 14 NO 3 − and 15 NO 3 − mixtures with different proportions. The wavenumber of nitrate absorption peaks exhibited a regular shift as the proportion of 15 NO 3 − . The PLSR models showed good prediction performance of nitrate content in the mixed solutions of 14 NO 3 − and 15 NO 3 − , which achieved the quantitative determination of 15 NO 3 − content. The above results implied that FTIR-ATR technique coupled with deconvolution algorithm was an effective and alternative option for estimating the isotopic composition of nitrate in water bodies, which provided a simple, rapid and affordable method for isotopic tracing of nitrate nitrogen, further generating a better understanding of nitrate sources and transformation processes.