Introduction

Nitrate (NO3−) pollution of surface water is a global concern, with nitrate contamination of drinking water sources having recently become a widespread problem owing to rapid population growth and the intensive development of agricultural and industrial activities during the 20th century. The concentration of NO3− in rivers in many parts of the world has exceeded the upper limit of 10 mg/L in drinking water prescribed by the World Health Organization1. For example, ~7.83% of river water in China has NO3− concentrations in excess of 10 mg/L in the context of China’s large nitrogen emissions2,3. Excessive NO3− can lead to issues such as eutrophication of water bodies, methemoglobinemia, diabetes, spontaneous abortion, thyroid disease, and stomach cancer1,4,5,6. The direct medical costs of all adverse health outcomes caused by nitrates in the US state of Wisconsin are estimated to be between $23 million and $80 million annually7. The hydraulic connection between surface water and underground aquifers exposes groundwater to a significant threat of nitrate pollution, which is particularly concerning given that groundwater accounts for ~30% of freshwater resources8. The global nitrogen cycle remains a contentious topic, with concerns that anthropogenic pressures are pushing it to the limits of Earth’s natural resilience9. The varied transfer of reactive nitrogen in aquatic ecosystems has complicated the effort to reveal specific instances of NO3− concentrations in rivers or their associated aquifers at any given moment (excluding instances of regulatory exceedances). Furthermore, quantitative understanding of the nitrogen cycling processes in terrestrial-aquatic environments remains insufficient10.

NO3− in surface waters primarily originates from point source inputs such as domestic sewage, agricultural or industrial effluent, and non-point source inputs such as manure and sewage (MS), soil organic nitrogen (SN), atmospheric deposition (AD), and synthetic fertilizers (SF)1,11. Previous studies have demonstrated that NO3− from sewage and livestock runoff generally contains heavier niteogen isotopes (hereafter denoted as δ15N-NO3−) than NO3− from AD, fertilizer nitrogen, and SN12. The majority of existing studies have relied on Bayesian isotope mixing models based on stable nitrate nitrogen (δ15N-NO3−) and oxygen (δ18O-NO3−) isotopes to generate probability distributions of contribution ratios from various potential sources. Nitrate source analysis in surface water is currently based on in-situ sampling combined with δ15N-NO3− and δ18O-NO3− mixing modeling, which is challenging in terms of large-scale, long-term continuous monitoring and analysis of historical NO3− sources in areas without data.

To address these challenges, it is essential to develop a monitoring method that can meet the flexible response requirements of the full-scale range, and a quantitative analysis of δ15N-NO3− and δ18O-NO3− and their pollutant sources in surface water in the field of remote sensing is a desideratum. Multi-source remote sensing technology has considerable potential for monitoring nitrate sources in surface water, and we believe that the potent capabilities of satellite remote sensing in large-scale regional monitoring and UAV technology can compensate for the lack of spatio-temporal resolution inherent in satellite remote sensing13,14,15. Studies have used machine learning algorithms to predict isotope levels in water bodies, such as the simulation of hydrogen and oxygen isotopes in rainfall and groundwater16,17,18. Most currently available water quality inversion or isotope inversion algorithms do not have well-defined physical mechanisms. Given that nitrogen has certain spectral characteristics in water bodies19, although these characteristics will be obscured by the complex optical characteristics in inland water bodies, we hope to solve complex nonlinear problems based on machine learning’s ability to deal with complex nonlinear relationships among environmental parameters. Therefore, we emphasize that, while the ML algorithms used in this study constituted a black box model, it is necessary to establish a physical connection between isotope and spectral information in future work.

In this study, we developed an inversion framework (Rs-Siarsolo) (Supplementary Fig. 1) that couples remote sensing and the siarsolomcmcv4 algorithm in a Bayesian isotope mixing model to quantify the spatio-temporal distribution of NO3− contributions from three reservoirs in South China with water diverted from the Xijiang river as experimental objects for the first time. The ML model was validated with data integrated from the Global Network of Isotopes in Rivers (GNIR) database, Chinese surface water isotope-related literature, and in-situ sampled δ15N-NO3− and δ18O-NO3− data with surface reflectance (SR) images of UAV multispectral, Sentinel-2A/B MSI, and Landsat 7 ETM+. We evaluated the performance of four ML models in inverting δ15N-NO3− and δ18O-NO3− and subsequently explored the historical characterization of δ15N-NO3− and δ18O-NO3− and NO3− sources in the study area waters based on the optimal ML model. Additionally, we compared the multi-points model (siarmcmcdirichletv4 algorithm in SIAR mixing model) to verify the reliability of the technical framework and analyzed the consistency of various sensor map products and NO3− sources.

Results and discussion

Model performance

Leveraging SR images of ETM+, MSI, and UAV, the Mixture Density Network (MDN) model demonstrated superior performance,with coefficient of determination (R2) range from 0.50 to 0.99, root mean square error (RMSE) range from 0.05‰ to 2.31‰ and mean absolute error (MAE) range from 0.03‰ to 1.35‰ in inverting the δ15N-NO3− and δ18O-NO3− in each reservoir compared to other ML models (with the exception of slightly lower δ18O-NO3− accuracy of the overall dataset compared to the extreme gradient boosting model in simulated ETM+, and lower δ18O-NO3− accuracy of the NS reservoir compared to the support vector regression (SVR) model in MSI) (Fig. 1, Supplementary Figs. 4–7, Supplementary Tables 2–4) in which the UAV platform exhibited the highest accuracy (coefficient of determination range from 0.74 to 0.99, RMSE range from 0.05‰ to 2.31‰ and MAE range from 0.03‰ to 1.35‰), attributable to its high-resolution imaging capabilities. The MDN model can flexibly capture the nonlinear relationship between input and output so that many different probability distributions can be modeled to quantify the uncertainty of the outputs, which achieved an effective enhancement on the ETM+ data with only four bands20,21,22.

Fig. 1: Performance evaluation of isotopes estimation using the MDN model based on various sensors.
figure 1

a The estimation accuracy of δ15N-NO3− in ETM+. b The estimation accuracy of δ15N-NO3− in MSI. c The estimation accuracy of δ15N-NO3− in UAV. d The estimation accuracy of δ18O-NO3− in ETM+. e The estimation accuracy of δ18O-NO3− in MSI. f The estimation accuracy of δ18O-NO3− in UAV. In both (a, b, d, e), the blue dots represent all dataset, the red dots represent study area dataset. The solid blue lines in all figures represent the fit curves of the blue dots, the red area represents the 5% error interval.

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MDN still had underfitting conditions, such as δ18O-NO3− in NS based on MSI, and δ18O-NO3− in NS was mainly distributed in more than 10‰ (Supplementary Table 3), which accounted for less in the data sets used in ETM+ and MSI. By performing 1000 data cuts and iterated the optimal hyperparameters of MDN of δ18O-NO3− in MSI through the random seed method of Sklearn library, we found that various data cuts have the greatest impact on the evaluation of R2, and the fluctuation ranges of RMSE and MAE are relatively smaller (Supplementary Fig. 8). In comparison, δ15N-NO3− had the same sample size but higher precision (Supplementary Fig. 3, Table 1), which we speculate may be due to the sample cutting method and the MSI not capturing some key spectral information of δ18O-NO3−.

Table 1 Number of matchups between isotope and remote sensing data selected for algorithm development
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The relatively lower inversion accuracy of the ETM+ platform may be attributed to the fact that ETM+ data mainly originate from rivers, and the fast-flowing water body made the temporal consistency between satellite data and ground data worse (Table 1). Additionally, the lower spatial resolution of ETM+ resulted in a poorer spatial position match with the ground and was more susceptible to the effects of atmospheric conditions.

To ensure consistent historical inversion accuracy for δ15N-NO3− and δ18O-NO3−, the MDN model was used for δ15N-NO3− and δ18O-NO3− in all remote sensing platforms.

Historical isotope features

We simulated δ15N-NO3− and δ18O-NO3− data of ETM+ and MSI from 2006 to 2023 and 2019 to 2023, respectively, and plotted the distribution characteristics of the daily average δ15N-NO3− and δ18O-NO3− for each reservoir according to Kendall et al.’s method1. ETM+ revealed that δ15N-NO3− and δ18O-NO3− in the three reservoirs since 2006 ranged from 1.04‰ to 15.72‰ and from −2.13‰ to 13.57‰, respectively, with the majority distributing in the overlapping sections of NH4+ fertilizer (NF), SN and MS (57–73%), as well as MSI reflecting δ15N-NO3− and δ18O-NO3− distributions in the SN and MS overlapping areas, accounting for 67–79% (Fig. 2a, b). LJ and QW extracted water from the Xijiang river, resulting in the distribution of δ15N-NO3− and δ18O-NO3− mainly overlapping with NF, SN and MS, which was consistent with previous research on the Pearl river or Xijiang river12,23. Since the NS reservoir had no external water diversion except for atmospheric rainfall, the map product (Fig. 2a, b, Fig. 3) revealed that the contribution rate of nitrate sources was evenly distributed across the entire water area. We speculate that this may not be caused by nitrogen flushing input from the surrounding soil because the contribution rate of SN in the shore area was essentially identical to that in other water areas. We hypothesize that the distribution characteristics of nitrogen and oxygen isotopes in the NS may be derived from the non-point source release behavior of residual nitrogen in the sediment. ETM+ and MSI showed an elevated percentage of NF-SN and NF-SN-MS sources in three reservoirs during the rainy season, which could be attributed to the heavy rainfall action during the rainy season that caused residual fertilizers and organic nitrogen in the near-shore soils to wash into the reservoirs through runoff (Fig. 2e–j). It is noteworthy that the results of δ15N-NO3− and δ18O-NO3− under the long time series simulated by ETM+ and MSI were quite different during the dry and rainy seasons, with MSI showing heavier δ15N source inputs and lower δ18O abundance in LJ and QW reservoirs during the rainy season, while the NS reservoir had the opposite (Supplementary Fig. 12). Comparison of the long-term results of δ15N-NO3− and δ18O-NO3− simulated by ETM+ and MSI showed better agreement between the two during the overlap period (Supplementary Fig. 13), suggesting that the higher temporal resolution of MSI may have captured richer information and was quite different from the results of the related studies in the Pearl River Basin (PRB)3,24,25,26, which implies that MSI simulations may have reveled seasonal variations of nitrate nitrogen-oxygen isotopes in the reservoirs affected by the Pearl river water system.

Fig. 2: Distribution of historical daily isotope values in reservoirs.
figure 2

Daily mean values of δ15N-NO3− and δ18O-NO3− on each reservoir simulated by ETM+ (from 2006 to 2023) and MSI (from 2019 to 2023) and in-situ measured value. a Simulation results of ETM+ in dry season. b Simulation results of ETM+ in rainy season. c Simulation results of MSI in dry season. d Simulation results of MSI in rainy season. e Statistics of LJ reservoir simulated by ETM+. f Statistics of NS reservoir simulated by ETM+. g Statistics of QW reservoir simulated by ETM+. h Statistics of LJ reservoir simulated by MSI. i Statistics of NS reservoir simulated by MSI. j Statistics of QW reservoir simulated by MSI. In both (a, b, c, d), solid blue dots represent the simulation value of LJ reservoir, the hollow blue dot represents the measured value of LJ reservoir, the solid red squares represent the simulation value of NS reservoir, the hollow red squares represent the measured value of NS reservoir, the solid yellow triangle represent the simulation value of QW reservoir, the hollow yellow triangle represent the measured value of QW reservoir. In both (e, f, g, h, i, j), the light blue part represents the distribution of isotopes in the MS source, the dark blue represents isotopic distribution in NF-SN mixed source, the light yellow part represents the distribution of isotopes in the NF-SN-MS mixed source, the dark yellow part represents the distribution of isotopes in the SN-MS mixed source, where the inner ring is the dry season and the outer ring is the rainy season.

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Fig. 3: Spatio-temporal distribution of nitrate source proportion simulated by each sensor on each reservoir.
figure 3

The grid fill represents areas of invalid data.

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Characteristics of historical NO3 − sources proportion

The ETM+ results revealed that the primary nitrate sources in the LJ, NS, and QW reservoirs have been predominantly attributed to MS, with mean contributions of 40%, 30%, and 35%, respectively, since 2006. SN followed closely behind, making a mean contribution of 26%, 28%, and 27% in the respective reservoirs (Fig. 4). The results of MSI showed that the mean contribution of MS, SN and SF in LJ reservoir were about 30%, MS contribution in NS reservoir was 35%, SN and SF contribution was about 23%, and QW was close to NS results from 2019 to 2023, which was consistent with a related study that focused on the Pearl river3,24. Nevertheless, MSI and ETM+ exhibited completely distinct phenomena in terms of seasonal characteristics, and we suggested that the high temporal resolution of MSI may captured richer dynamic information, which in comparison with the existing studies may have reveled the seasonal characteristics of nitrate sources in reservoirs subjected to the Xijiang River diversion3,24,25,26. Moreover, no significant trend was evident in the contributions of various nitrate sources from each reservoir over the long time series, but it is worth noting that the contribution of MS in LJ and QW increased significantly between 2009 and 2011, peaking in 2010 at 56% and 41%, respectively (Fig. 4, Fig. 5).

Fig. 4: Daily mean values of nitrate source proportion on each reservoir simulated by ETM+ long-term series data and statistics in dry season and rainy season.
figure 4

a–d Proportion of nitrate sources in LJ. e–h Proportion of nitrate sources in NS. i–l Proportion of nitrate sources in QW. m Proportion of nitate sources in LJ during dry season and rainy season from 2006 to 2023. n Proportion of nitate sources in NS during dry season and rainy season from 2006 to 2023. o Proportion of nitate sources in QW during dry season and rainy season from 2006 to 2023. In both (a–i), the blue bar represents the daily rainfall, the gray part represents the simulated maximum and minimum range, the red dashed line represents the MK test trend line, the solid color line represents the simulated mean value, and the black dashed line represents the mean of the simulated means over the entire time series. In both (m, n, o), the red box represents the dry season and the blue box represents the rainy season.

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Fig. 5: Daily mean values of nitrate source proportion on each reservoir simulated by MSI long-term series data and statistics in dry season and rainy season.
figure 5

a–d Proportion of nitrate sources in LJ. e–h Proportion of nitrate sources in NS. i–l Proportion of nitrate sources in QW. m Proportion of nitate sources in LJ during dry season and rainy season from 2006 to 2023. n Proportion of nitate sources in NS during dry season and rainy season from 2006 to 2023. o Proportion of nitate sources in QW during dry season and rainy season from 2006 to 2023. In both (a–i), the gray part represents the simulated maximum and minimum range, the red dashed line represents the MK test trend line, the solid color line represents the simulated mean value, and the black dashed line represents the mean of the simulated means over the entire time series. In both (m, n, o), the red box represents the dry season and the blue box represents the rainy season.

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Map assessment

We evaluated the spatio-temporal distribution of δ15N-NO3− and δ18O-NO3− and NO3− sources contribution at pixel scale on the in-situ sampling days and found that all results exhibited robust consistency in reflecting the overall characteristics of the study area, particularly MSI and UAV (Fig. 3, Supplementary Fig. 9). All the remote sensing inversion results showed that δ15N-NO3− and δ18O-NO3− in LJ and NS reservoirs were mainly distributed in the NF or the mixed region of NF and SN (>60%), and more than 43% of δ15N-NO3− and δ18O-NO3− in QW reservoirs were located in the SN and MS overlapping region (Supplementary Fig. 9). Additionally, at least 30% of nitrate was contributed by MS in LJ reservoir during dry season, at least 32% of nitrate was contributed by SF in NS reservoir during both periods, and the nitrate in QW reservoir during both periods was mainly contributed by MS (more than 39%) (Fig. 6). It is worth noting that the relatively low signal-to-noise ratio of ETM+ may generate more obvious salt-and-pepper noise in the map and that its detailed performance is inferior to that of other sensors27.

Fig. 6: Comparison results of Rs-Siarsolo framework and in-situ on each reservoir.
figure 6

a LJ in dry season. b NS in dry season. c QW in dry season. d NS in rainy season. e QW in rainy season. The pink box represents the simulation value of UAV, the blue box represents the simulation value of MSI, the red box represents the simulation value of ETM+, and the green box represents the simulation value of in situ.

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Reliability analysis of the Rs-Siarsolo framework

Compared with the simulation results of the siarmcmcdirichletv4 algorithm based on in-situ sampling data, the overall characteristics of the Rs-Siarsolo nitrate source contribution rate results in all reservoirs remain wholly consistent, with a mean value absolute error range of −9.6 to 27.3% (Fig. 6). We discovered that a greater coverage of the entire water area by in-situ sampling points improved the accuracy and representability of siarmcmcdirichletv4’s results, which led to closer results between Rs-Siarsolo and siarmcmcdirichletv4, contributing to the narrower difference in their outcomes in the QW reservoir.

Consistency analysis of satellite remote sensing

To ascertain the reliability of ETM+ and MSI in delineating the historical contribution of nitrate sources, the scatter plots of the corresponding bands of ETM+ and MSI during the overlap period demonstrated that the two have strong band agreement firsty (Supplementary Fig. 14). In addition, there was no strong fluctuation in the band data of both under the long time series, which means that the probability of extreme inversion results is low (Supplementary Fig. 14). Moreover, the nitrate isotope dynamic of ETM+ and MSI simulations during 2019–2023 were highly consistent, indicating that ETM+ and MSI were in excellent agreement in reflecting the long-term reservoir nitrate source (Supplementary Fig. 13). Finally, we examined congruity in the mapping outcomes across two time series within a ±48 h window. The overall MAE for the contribution rates across the four sources remained below 10%, highlighting the strong agreement between the datasets. This was further supported by boxplot illustration (Fig. 7), which showed that ETM+ and MSI exhibited strong alignment in both ranking and quantitative values of nitrate source contributions, with maximum absolute error contained to 5%, and which suggested that ETM+ and MSI remain in great alignment in the short-term time window.

Fig. 7: Daily mean proportion of nitrate sources on each reservoir during the 48 h window of ETM+ and MSI.
figure 7

a Comparison of MS proportion. b Comparison of SN proportion. c Comparison of AD proportion. d Comparison of SF proportion. e Overall comparison of long time series of sources proportion on LJ. f Overall comparison of long time series of sources proportion on NS. g Overall comparison of long time series of sources proportion on QW. In both (a, b, c, d), the blue areas represent the maximum and minimum ranges of the simulated value of ETM+, the red areas represent the maximum and minimum ranges of the simulated value of MSI, the solid blue line represents the daily mean of the simulation of ETM+, the solid red line represents the daily mean of the simulation of MSI, the black dashed line represents the difference between ETM+ and MSI’s daily simulated mean value. In both (e), (f) and (g), the red boxes and dots represent the simulation result of ETM+, the blue boxes and dots represent the simulation result of MSI.

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ML model feature interpretation

Figure 8 sorted features by the sum of SHAP values over all samples in three sensors bansed on MDN. The blue band (B1 in ETM+, B1 and B2 in MSI) in ETM+ and MSI had a positive effect on the prediction of δ15N-NO3−, while the red band (B3 in ETM+, B4 in MSI) had a negative correlation with the prediction of δ15N-NO3−. The blue band (B1) in ETM+ and B2 in UAV had a positive effect on δ15N-NO3− predictions, while the green band (B2) in ETM+ and B4 in UAV had a negative effect on δ15N-NO3− predictions. The blue band (B2) in ETM+ and the B4 in UAV simultaneously showed a clear positive correlation with the prediction of δ18O-NO3−. The blue band (B2) in MSI and UAV exhibited a positive correlation with both δ15N-NO3− and δ18O-NO3− predictions. Moreover, the spectral information at 739 nm had poor correlation with the predictions of δ15N-NO3− and δ18O-NO3− in both MSI and UAV. It was worth mentioning that some features were less important to the whole dataset, but showed higher importance in the estimation of a partial sample. For example, B1 in MSI had the lowest global importance for δ18O-NO3− estimates, while it had a larger influence on model output at specific sample points, indicating that it had high local importance.

Fig. 8: SHAP values for δ15N-NO3− and δ18O-NO3− in various sensors based on MDN.
figure 8

a δ15N-NO3− in ETM+. b δ18O-NO3− in ETM+. c δ15N-NO3− in MSI. d δ18O-NO3− in MSI. e δ15N-NO3− in UAV. f δ18O-NO3− in UAV. Where each dot corresponds to an individual sample in the study, the multiple point arrangements in the vertical direction of the same feature represent a large number of sample aggregations. The dispersion of the samples on each feature represents the magnitude of the feature influence, and the color of dots reveals the direction of the impact of each feature on the prediction values.

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It was worthing note that δ15N-NO3− and δ18O-NO3− were significantly correlated with nitrate concentrations, which was understandable because nitrate concentration changes were closely related to isotopic fractionation processes, and the spectral bands that were significantly correlated with nitrate are essentially the same as those for δ15N-NO3−, implying that δ15N-NO3− and nitrate may share the same spectral signature or that the spectra of nitrate may indirectly reflect information about the abundance of δ15N-NO3− (Supplementary Fig. 10a–c). Additionally, δ15N-NO3− and δ18O-NO3− were strongly correlated with conductivity in the reservoirs in the study area, suggesting that higher concentrations of ions may be potentially associated with nitrate in waters primarily influenced by manure effluent (Supplementary Fig. 10c). Moreover, although we attempted to construct characteristic spectral indices to improve model accuracy and interpretability by constructing a band combination model in this study but failed to identify significant spectral indices (Supplementary Table 6). we found that δ15N-NO3− and δ18O-NO3− and the relative concentrations and slopes of colored dissolved organic matter (CDOM) in the 220 nm band were significantly correlated (Supplementary Fig. 10d, e), and we believe that the 220 nm band optical information was commonly used in determining nitrate concentrations, and it may contain the information of the spectral of δ15N-NO3− and δ18O-NO3−. Nevertheless, the current remote sensing sensors not equipped with the 220 nm band, so we can consider adding aCDOM(220), nitrate concentration and conductivity parameters to the model to provide the inversion accuracy and interpretability of the model in future research.

Nitrate source analysis

In the context of nitrate in the PRB being influenced by human activities, rainfall-induced surface runoff, and land-use changes, anthropogenic sources of nitrate pollution (MS and SF) in LJ and QW were more closely related to wastewater discharge and agricultural fertilizer application in the exogenous water system, whereas the high AD contribution of NS was more significantly influenced by intense rainfall (Fig. 4). Although China achieved its goal of zero growth in fertilizer use by 2020, it is noteworthy that over 20% of the nitrate still originates from SF (Fig. 4). For a populous country like China, with a population exceeding 1.4 billion, implementing a more effective fertilizer use strategy without compromising food security presents a formidable challenge. In Guangdong Province, both the amount of wastewater discharged into rivers and the total nitrogen content of this wastewater have been on the rise since 2004 (Supplementary Fig. 15, 16), which undoubtedly exerted a significant impact on nitrate in surface water, especially in drinking water. We contend that current efforts to ensure the safety of nitrate in drinking water should focus on developing strategies for wastewater management, such as enhancing wastewater treatment processes to improve treatment plants’ nitrogen removal efficiency, reinforcing wastewater discharge regulation, and promoting the effective recycling of manure. Such measures are crucial for mitigating the potential risks associated with nitrate contamination. It is worth noting that this study assumed that the fractionation factor was zero, considering that denitrification was not present in all reservoirs. If this method is extended to other regions in which denitrification is particularly evident, the fractionation value must be set appropriately. Moreover, given the variations in δ15N-NO3− and δ18O-NO3− distribution from nitrate sources across different regions, establishing a reference value for nitrate sources within the SIAR model necessitates careful consideration of local background values.

Methods

Study area

The experimental areas for this study were the Qianwu (QW, 22°10'57.18”–22°12'24.57”, 113°12'4.44”–113°12'24.23”), Longjing (LJ, 22°11'41.82”–22°12'24.2”, 113°15'21.59”–113°16'5.46”), and Nanshan reservoirs (NS, 22°10'7.13”–22°10'40.70”, 113°11'14.13”–113°11'53.37”) (Fig. 9). The LJ and QW reservoirs draw water from the Xijiang river, while the NS reservoir relies solely on atmospheric precipitation for recharge. The total nitrogen (TN) concentrations of all reservoirs were within the II to V water standards (0.5–2.0 mg/L) (China’s Surface Water Environmental Quality Standards, GB3838-2002), with NO3−-N accounting for 12–70% of the TN content.

Fig. 9: Location of the study area and dataset positions.
figure 9

a The matching point of each data set with the satellite and study area location. The yellow triangle represents the study area used to construct the long time series and UAV sampling. b The location of the sampling points on the LJ reservoir. c The location of the sampling points on the QW reservoir. d The location of the sampling points on the NS reservoir. In both (b, c, d), the blue dots represent ground sampling sites on October 26, 2021 (dry season), the yellow dots represent ground sampling sites on July 13, 2022 (rainy season). e RedEdge-MX Blue Dual 10 channels multispectral camera. f DJI M300 RTK unmanned aerial vehicle platform. g Radiation calibration panel.

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In-situ water samples

Surface water samples of 50 cm (1.5 L) were collected on October 26, 2021 (dry season) and July 13, 2022 (rainy season) were used for δ15N-NO3− and δ18O-NO3− analysis (Fig. 9, Table 1).

Laboratory analysis of in-situ stable isotope

Denitrifying bacteria were utilized to convert NO3− to N2O, and the purified N2O was extracted using a PreCon system (Thermo Fisher) before being analyzed for δ15N-NO3− and δ18O-NO3− using an isotope ratio mass spectrometer (Delta Advantage V, Thermo Fisher). The samples were compared with three international references (IAEA-NO-3, USGS34, and USG35), to correct their isotope values. The analytical accuracies for δ15N-NO3− and δ18O-NO3− were ±0.4‰ and ±0.5‰, respectively28,29. δ15N-NO3− and δ18O-NO3− in LJ reservoir during rainy season were not detected.

Unmanned aerial vehicle multispectral image

Images were acquired using a RedEdge-MX Blue Dual 10 channels multispectral camera (MicaSense, Seattle, WA, USA) in conjunction with a DJI M300 RTK fixed quadcopter flight platform in sunny weather, which covers coastal blue to near infrared (NIR) bands (Supplementary Table 1). We try to select clear weather and light wind to perform drone flight missions, but inevitably there was a sudden change of wind speed during the flight which caused serious flare on the water surface in some areas, so we manually eliminated those areas.

The GNIR and China surface water isotope datasets

In order to obtain more data for training and validation of algorithms to improve the generalization ability of inversion models, we collected δ15N-NO3− and δ18O-NO3− isotope data of surface rivers and lakes from the Global Network of Isotopes in Rivers (GNIR, https://nucleus.iaea.org/sites/ihn/Pages/GNIR.aspx) database and related literature (Fig. 9, Table 1). The GNIR is a global environmental isotope observation program that began in 2007, focusing on seasonal water collection from Earth’s large rivers and making these isotope data available in an online database. Samples were primarily analyzed at the International Atomic Energy Agency (IAEA) Isotope Hydrology Laboratory in Vienna, with some measurements conducted at collaborating laboratories. We also gathered as much δ15N-NO3− and δ18O-NO3− data from rivers and lakes as possible, from literature sources.

Satellite data

Considering the length of observation time, spatio-temporal resolution, and the free availability of data, this study mainly used Sentinel-2A/B MSI and Landsat 7 ETM+ data. We downloaded the Collection 2 Level 1 SR images (time series 2006–2023) of Landsat ETM+ from USGS in earthexplorer and used Acolite software (Windows version 20210802.0) for atmospheric correction processing, which widely used in inland water bodies and the dark spectrum fittin method in the software largely avoids the amplification of scintillation and neighboring effects30. Given the ease of use of Google Earth Engine (GEE) data, MSI used the GEE-integrated Sen2Cor atmospheric correction algorithm, and while the Sen2Cor algorithm was not as effective as other algorithms such as Polymer in inland waters, its accuracy was still usable31,32. It is worth noting that no atmospheric algorithm is perfectly applicable to inland waters, and the poorer corrections of Acolite and Sen2Cor in the near-infrared band (NIR) may have an impact on the inversion accuracy of the model. Sentinel-2 L2A SR products from 2018 to 2023 were screened using GEE. MSI images were declouded in GEE and saved locally, and then oversampled to full-band 10 m using SNAP software. The band information used by the satellite is shown in the Supplementary Table 1. The location of the data points and study area is shown in Fig. 9, and the number of matchups between the isotope and remote sensing data selected for algorithm development is show in Supplementary Table 2. Moreover, considering that the coordinate information of the sampling points in the database was not wholly accurate and that most of them were near the land, we relocate the sampling point to the first pixel unit closer to the center of the water than the original sampling point perpendicular to the shore to avoid the adjacency effects caused by the land and retaining the original information as much as possible, although this may have affected the original SR value at the point to some extent, resulting in the deterioration of satellite inversion performance. However, we believe that the above treatment is meaningful compared to the significant effect of the proximity effect.

Machine learning methods

This study utilized four novel machine learning algorithms, namely mixed density network (MDN), extreme gradient boosting (XGBoost), deep neural network (DNN) and SVR. Instead of outputting the target variables directly, the MDN algorithm generates a set of three variables (mean, standard deviation and mixing coefficients) for each Gaussian function, which forms the final output estimate by combining probability or maximum likelihood Gaussian distributions, where the number of Gaussians is a tuning parameter MDN aims to solve the inverse problem of multiple y outcomes with a single x by modeling conditional probability distributions over a range of target variables21,22,27. The hyperparameters of the model via grid search include the number of mixtures used in the gaussian mixture model (n_mix: 2–20, step = 1), number of hidden layers (n_hidden: 2–20, step = 1), and number of neurons per layer (n_nerous: 10–250, step = 10). XGBoost is an integrated learning algorithm based on decision trees33, which uses the regression tree from the classification and regression tree method as the base classifier for the optimized gradient boosting tree algorithm34,35, and uses augmentation and regularization techniques to reduce the model variation36. DNN are artificial neural networks with multiple hidden layers between the input and output layers37. Each layer of a DNN contains several neurons that are fully connected between the layers. A grid search was used to obtain the best hyperparameters, including n_estimators (range: 100–600, step = 50) learning_rate (range: 0.01–0.5, step = 0.05), max_depth (range: 2–10, step = 1), min_child_weight (range: 0–3, step = 0.1), gamma (range: 0–1.2, step = 0.1), subsample (range: 0–1.2, step = 0.1), and reg_alpha (range: 0–2, step = 0.1). In this study, the number of hidden layers (range: 2–8, step = 1) and the number of neurons (range: 10–300, step = 10) in each hidden layer were obtained using a grid search. SVR is a technique derived from support vector machines2,38. The key attribute of SVR lies in its capacity for nonlinear mapping of the original data as well as the analysis of linear regression problems within a high-dimensional feature space. Through its kernel function, SVR can effectively perform a nonlinear mapping of the original finite-dimensional space into a higher dimensional space, facilitating the subsequent analysis and resolution of linear regression problems within this expanded feature space. In this study, the kernel function was selected as “rbf”, and the optimal value of the kernel function’s coefficient (gamma, range: 2−10 to 210, step = 1) and the penalty factor (c, range: 2−10 to 210, step = 1) of the error term were found through a grid search.

This study employs Shapley Additive explanations (SHAP) to explore the mechanism of ensemble ML models for water quality estimation. SHAP is an explanatory method for ML algorithms that can calculate both global and local feature importance. The marginal contribution of a feature is defined as the change in model prediction upon adding the feature39. SHAP values attribute each feature to the expected change in model prediction when adjusting that feature. Detailed information about SHAP values can be found in Lundberg and Lee40. In this research, SHAP values are computed using the Shapely library (v1.8.4) in Python, using the KernelExplainer interpreter.

The training and validation data for each algorithm were divided in a 2:1 ratio. The number of bands for the UAV, ETM+, and MSI input models were 10, 4, and 10 respectively (refer to Supplementary Table 1). All machine learning algorithms were implemented using Python 3.7. The MDN algorithm was obtained from Nima Pahlevan’s open source code (https://github.com/BrandonSmithJ/MDN), via TensorFlow 2.5 machine learning repository implementation. Additionally, the XGBoost model was built using the XGBoost machine learning library. The DNN model was implemented utilizing the Keras machine learning library in TensorFlow. Lastly, the SVR model was constructed using the scikit-learn machine learning library.

Performance evaluation metrics

To evaluate the accuracy of the models, the three most commonly used evaluation indexes were selected: coefficient of determination (R2), RMSE, and MAE.

$${R}^{2\,}=1-\frac{{\sum }_{i=1}^{n}{(\hat{{y}_{i}}-{y}_{i})}^{2}}{{\sum }_{i=1}^{n}{(\bar{{y}_{i}}-{y}_{i})}^{2}}$$
(1)
$${RMSE}=\sqrt{\frac{{\sum }_{i=1}^{n}{\left(\hat{{y}_{i}}-{y}_{i}\right)}^{2}}{n}}$$
(2)
$${MAE}=\frac{1}{n}\mathop{\sum}\limits_{i=1}^{n}\left|(\hat{{y}_{i}}-{y}_{i})\right|$$
(3)
$${Bias}=\frac{{\sum }_{i=1}^{n}({\hat{y}}_{i}-{y}_{i})}{n}$$
(4)

Bayesian stable isotope mixing model

Research suggests that potential major sources of NO3− in surface water may be MS, SN, AD, and synthetic nitrogen fertilizers (SF)1. To quantify the proportionate contribution of nitrate sources, we have employed the widely recognized Bayesian isotope mixing model, utilizing the SIAR package in the R language41. The siarsolomcmcv4 command is used when only one sample is available42, we utilized this command to reverse-engineer the contribution rate of pixel-level nitrate sources in the Rs-Siarsolo framework. Conversely, the siarmcmcdirichletv4 multi-script command was utilized to simulate the overall contribution rate of nitrate sources in the study area during two in-situ sampling periods and then compared with the inversion results of Rs-Siarsolo framework. According to previous studies3, denitrification does not play a significant role in river water within the study area, thus leading us to assume that fractionation factor of isotope value was equal to 0. Furthermore, Supplementary Table 5 presents the reference values of δ15N-NO3− and δ18O-NO3− from nitrate sources in this study. The SIAR mixing model can be expressed as follows:

$${X}_{{ij}}=\mathop{\sum}\limits_{k=1}^{k}{P}_{k}\left({S}_{{jk}}+{C}_{{jk}}\right)+{\varepsilon }_{{ij}}$$
(5)
$${S}_{{jk}} \sim {\rm{N}}\left({\mu }_{{jk}},{\omega }_{{jk}}^{2}\right)$$
(6)
$${C}_{{jk}} \sim {\rm{N}}({\lambda }_{{jk}},{\tau }_{{jk}}^{2})$$
(7)
$${\varepsilon }_{{ij}} \sim {\rm{N}}(0,{\sigma }_{j}^{2})$$
(8)

where Xij represents the isotopic value of j in mixture i (i = 1, 2, 3,…, I; j = 1, 2, 3, …J); Sjk represents the isotopic value j (k = 1, 2, 3,…, K), following a normal distribution with a mean of μjk and a standard deviation of ωjk; Pk represents the proportion of sources; Cjk represents the fractionation factor of isotope value j on pollutant k, which follows a normal distribution with mean μjk and standard deviation ωj. εij represents the residual error of j in mixture i, following a normal distribution with a mean of 0. A detailed description of SIAR model can be found in the literature41. The siarsolomcmcv4 command is used when only one sample is available42, we utilized this command to reverse-engineer the contribution rate of pixel-level nitrate sources in the Rs-Siarsolo framework. Conversely, the siarmcmcdirichletv4 multi-samples command was utilized to simulate the overall contribution rate of nitrate sources in the study area during two in situ sampling periods and then compared with the inversion results of Rs-Siarsolo framework. According to previous studies3, denitrification does not play a significant role in river water within the study area, thus leading us to assume that Cjk was equal to 0.

Modeling framework

The main technical procedures may be outlined as follows (or shown in Supplementary Fig. 1): (1) Assimilate the training data from three remote sensing platforms into four ML models and fine-tune the hyperparameters to achieve optimal performance. To enhance the efficacy of the models, all data underwent normalization through a maximum-minimum process prior to input; (2) The most optimal models for δ15N-NO3− and δ18O-NO3− were meticulously chosen based on the comprehensive evaluation indexes specific to each remote sensing platform; (3) The selected optimal model from the preceding step was utilized across each remote sensing platform to reverse engineer effectively the spatio-temporal distribution of long-term nitrogen and oxygen isotope values; (4) The contribution rate of the nitrate source was determined by integrating the isotope simulation results with the isotope mixing model. Prior to executing the siarsolomcmcv4 algorithm in R software, we transformed the spatial distribution diagram of δ15N-NO3− and δ18O-NO3− values from the previous step into an n × 3 matrix format (with “group”, “δ15N-NO3−” and “δ18O-NO3−” as column names). Following the completion of the simulation, siarsolomcmcv4 reconverted the output data into an image that was integrated with geographic information. To alleviate the computational burden resulting from excessive amounts of data, we selectively sampled reflectance information at original sampling point coordinates across various time frames, to simulate the percentage contribution rate of nitrate sources, thus depicting characteristics specific to that particular region at each given moment; (5) The reliability of the simulation results produced by the Rs-Siarsolo framework was verified. The inversion results of nitrate source contributions from remote sensing platforms during the in-situ sampling periods were compared with the simulation results of the siarmcmcdirichletv4 algorithm based on the in-situ sampling data, and the consistency of the source contribution characteristics between the two results was observed.