Field investigations and the collection of hydrochemical and isotopic samples were conducted in the study area from 2022 to 2023. The temporal resolution for groundwater sampling was designed as seasonal snapshots, with campaigns occurring in October 2022 (normal season), April 2023 (dry season), and August 2023 (wet season), representing a temporal interval of approximately 4–6 months between surveys. A total of 66, 65, and 50 groundwater samples were collected in October 2022, April 2023, and August 2023, respectively. All groundwater samples were obtained from existing agricultural irrigation wells within the study area. In-situ physicochemical parameters (T, pH, TDS, DO, EC, and ORP) were measured using a Hach HQ400 multi-parameter meter (Li et al., 2022), and major ions, nitrogen species, and stable isotopes (δ2H, δ18O, δ15N-NO3-, δ18O-NO3-) were analyzed in the laboratory following standard protocols. Detailed sampling procedures, quality control measures, and analytical methods are provided in the Supplement (Sects. S1 and S2).

To compare with predictions based on in-situ field sampling data and to validate the accuracy of remote sensing-based nitrate prediction, this study incorporates the Google AlphaEarth Foundation (AEF) dataset. AEF provides a 64-dimensional surface semantic embedding vector (A00–A63) at 10 m spatial and annual temporal resolution, generated by pre-training on multi-source satellite imagery (e.g., Sentinel-2, Landsat). These embeddings implicitly encode environmental semantics such as land cover, vegetation dynamics, soil moisture, and human activity intensity (Alvarez et al., 2025; Tollefson, 2025). The 64-dimensional AEF vectors were extracted at each sampling point via the Google Earth Engine platform, and Principal Component Analysis (PCA) was applied to retain the minimum number of components explaining at least 95 % of the cumulative variance. The PCA-reduced features served as model inputs. Details of the AEF data processing workflow are provided in the Supplement (Sect. S3).

MixSIAR incorporates prior information on end-member values and their errors and distributions, and estimates the proportional contribution of each source via Markov Chain Monte Carlo (MCMC) iteration (Stock et al., 2018). In this study, it was applied to apportion five potential NO3- sources: precipitation (NP), soil organic nitrogen (SON), synthetic NH4+ fertilizer (NHF), synthetic NO3- fertilizer (NOF), and domestic sewage and manure (DSM), with the source end-member values listed in Table 2 (Mao et al., 2023; Gao et al., 2023; Torres-Martínez et al., 2021).

Pearson correlation coefficients (r) were calculated to quantify the linear relationships between nitrate concentrations and individual hydrochemical parameters (Su et al., 2025). We performed a two-tailed significance test for each correlation coefficient to determine whether the linear correlation was statistically significant. The significance criteria were set as: p<0.001 (highly significant), 0.001 ≤ p<0.01 (very significant), 0.01 ≤ p<0.05 (significant), and p≥0.05 (not significant) (Ma et al., 2025).

Bayesian linear regression was used to infer parameter posterior distributions, providing uncertainty quantification and reducing overfitting under small-sample conditions. z-score standardized nitrate concentration was regressed on the standardized predictors, with residuals assumed normal (mean 0, variance σ2). Weakly informative priors were used (Charizanos and Demirhan, 2023): a Student-t prior for the intercept, standard normal priors for the coefficients, and an exponential prior for the residual standard deviation. Posterior inference was performed via Markov Chain Monte Carlo (MCMC) sampling in the brms package in R (Addy et al., 2024). The probability of direction (pd), the proportion of each coefficient's posterior on the same side of 0 (Weller et al., 2022), quantified directional effects (0.5–1; higher values indicate stronger evidence).

To mitigate overfitting and poor generalization caused by data sparsity and skewed distributions in small-sample modeling, we propose a three-stage virtual sample generation strategy: t-SNE-Gaussian Mixture Sampling with KNN inverse mapping, which preserves the non-linear manifold structure and multi-modal distribution of the original high-dimensional feature space while generating physically plausible and statistically consistent virtual samples. Virtual samples are generated independently for each hydrological season (normal, dry, wet) within the hydrochemical feature space, i.e., the space spanned by the in-situ water-quality parameters and nitrate concentration, without temporal extrapolation or cross-season fusion, thereby augmenting sample density within each season while preserving the inherent seasonal hydrochemical heterogeneity. The workflow is as follows:

Data standardization.

All input features are z-score standardized to eliminate scale differences and stabilize the subsequent dimensionality reduction (Jamshidi et al., 2022). Notably, the target variable (NO3-) is standardized alongside the predictors (pH, T, EC, DO, ORP, Salt, TDS) to preserve the joint predictor-target distribution during generation.

Kolmogorov-Smirnov (KS) Test.

The two-sample KS test was employed to quantify the maximum vertical distance between empirical cumulative distribution functions (ECDFs) of observed and virtual samples (Li and Yu, 2026). For each hydrochemical parameter, the test statistic DKS is defined as: 2DKS=supx|Fn(x)-Fm(x)| where Fn and Fm represent the ECDFs of observed (n samples) and virtual (m samples) datasets, respectively. The P-value tests the null hypothesis that both samples derive from the same underlying distribution. Following established criteria for environmental data synthesis (Farnia et al., 2023; Tung et al., 2023), DKS<0.15 was adopted as the strict threshold for high fidelity and DKS<0.20 as the acceptable limit for parameters with inherent geochemical heterogeneity (Michalek et al., 2023; Li et al., 2023).

The SHapley Additive exPlanations (SHAP) method was used for local and global explainability analysis (Merabet et al., 2025). Three visualizations were employed: the summary plot, revealing the overall ranking and distribution of feature importance across all samples (global perspective); the dependence plot, revealing nonlinear relationships and interaction effects between individual predictors and predicted nitrate concentration (conditional dependence); and the waterfall plot, revealing the contribution decomposition of each feature for a representative sample (local attribution) (Alam et al., 2025b; Li et al., 2024; Hollmann et al., 2025).

Given the limited sample size in each hydrological season, model performance was evaluated using Leave-One-Out Cross-Validation (LOOCV) (Ren et al., 2021). Prior to LOOCV, hyperparameters were tuned via 5-fold cross-validation grid search (n_estimators [100, 150], max_depth [5, 6, 7], min_samples_split [4, 6]) and then fixed for the LOOCV evaluation. To assess prediction uncertainty, 90 % prediction intervals were estimated using quantile regression forests, with coverage probability calculated to validate their reliability; in addition, bootstrap resampling (1000 iterations) was used to derive 95 % confidence intervals for all evaluation metrics, which are reported alongside the LOOCV metrics. Model accuracy was quantified by R2, RMSE, and MAE (Gul et al., 2025).

To evaluate the response of predicted nitrate concentrations to input perturbations and verify the robustness of the feature importance ranking, a multi-dimensional sensitivity analysis was conducted, including a SHAP-based global sensitivity index, one-at-a-time (OAT) perturbation tests, and elasticity coefficient calculations (Di Santo et al., 2025). First, from the SHAP values obtained via TreeExplainer, the first-order and total-order sensitivity indices were calculated to measure the independent and interactive contributions of each feature (Huang et al., 2021). The first-order sensitivity index for feature i is defined as the normalized mean absolute SHAP value: 8Si=1n∑j=1n|ϕi(j)|∑k=1p1n∑j=1n|ϕk(j)| where ϕi(j) is the SHAP value of feature i for sample j, n is the number of samples, and p is the number of features. The total-order sensitivity index STi, capturing both main and interaction effects, was approximated using the diagonal elements of the SHAP interaction values:

Second, an OAT perturbation test was conducted to assess local model stability, by varying each target feature within ±30 % of its measured range while fixing the other inputs; perturbation sensitivity was quantified as the relative change rate of the model's R2 across perturbation levels (Anderson and Lucas, 2018). Finally, the elasticity coefficient, defined as the ratio of the percentage change in the predicted output to the percentage change in the input, was used to quantify the directional response of the predictions to per-unit changes in each parameter. An absolute value greater (less) than 1 indicates an elastic (inelastic) response. Monte Carlo simulation was specifically used to analyze the propagation of input measurement errors to the final predictions (Dega et al., 2023).

To systematically evaluate how data inputs, virtual sample generation, and modeling strategy jointly affect seasonal nitrate prediction, we established a standardized, fully reproducible pipeline (Fig. 3), in which the output of each step serves as the direct input of the next: (1) Data inputs and preprocessing. Two complementary input feature sets were prepared from the seasonally partitioned observations (66, 65, and 50 samples for the normal, dry, and wet seasons, respectively): (i) in-situ field water-quality parameters and (ii) AlphaEarth Foundation (AEF) embeddings compressed by PCA. Both sets were z-score standardized independently per season; the raw observations were used without interpolation or smoothing to preserve intrinsic variability. These standardized features, together with the measured NO3- concentrations, constitute the sole data basis for all subsequent steps. (2) Virtual sample generation and validation. Each standardized seasonal dataset was fed into the t-SNE–GMM–KNN generator to produce virtual samples at generation factors of 1–10×. Only virtual datasets whose distribution consistency and physical plausibility passed the validation tests were allowed to enter model training, thereby explicitly linking generation quality to downstream evaluation. (3) Model training. Classical Random Forest (RF) and quantum-enhanced RF were trained under unified hyperparameters on two tracks of training sets built from the validated samples: the original samples alone, and the original samples combined with 1–10× virtual samples. For the quantum-enhanced RF, input features were encoded via parameterized quantum circuits to generate 〈Z〉 quantum features, which were concatenated with the original features (2n inputs in total). (4) Model evaluation. Every trained model was evaluated using leave-one-out cross-validation on the measured samples. (5) Interpretability analysis. SHAP-based multi-scale interpretation (summary, dependence, and waterfall plots) was conducted and cross-verified against Bayesian modeling and Pearson correlation analysis.

All computations were performed on an Apple M2 Pro (10-core CPU, 16 GB RAM) using Python 3.9, with scikit-learn 1.7.2, qiskit 1.4.5, shap 0.49.1, pandas 2.3.3, numpy 2.2.6, scipy 1.15.3, joblib 1.5.2, and matplotlib 3.9.0. All random operations were seeded (random_state = 42) to ensure deterministic results. The complete source code, covering quantum 〈Z〉 feature extraction, model training, LOOCV evaluation, bootstrap uncertainty quantification, and sensitivity analysis, is publicly available at GitHub.

Groundwater pH was weakly alkaline in the normal water period with minimal variation and near-neutral in the dry and wet seasons, with a minimum of 5.77 in the wet season indicating occasional acidic water (Table S1 in the Supplement). Temperature varied markedly among seasons but remained stable within each (CV ≈ 0.06). EC, salinity, and TDS followed consistent seasonal patterns, peaking in the dry season and reaching minima in the wet season. Redox indicators were highly variable: DO was slightly higher in the wet season, whereas ORP remained low across all seasons with large standard deviations. Among major ions, Ca²⁺, Mg²⁺, Na⁺, Cl⁻, and SO42- all peaked in the dry season, while HCO3- was highest in the wet season and K⁺ remained low. NO3- concentrations were highest in the dry season and lowest in the wet season, far exceeding those of NO2- and NH4+. Most variables were right-skewed, with notable extreme values for NO3- in the dry season (maximum = 358.58, mean = 42.93 mg L⁻¹), Cl⁻ in the dry season (maximum = 241.36, mean = 24.90 mg L⁻¹), and F⁻ in the normal period (maximum = 13.17, mean = 3.70 mg L⁻¹). The Piper diagram (Fig. 4) shows that dry-season samples cluster tightly in the Ca-HCO3- facies, indicating dominant control by carbonate dissolution. In the wet season, the Ca-Mg-HCO3- type remains dominant but some samples shift toward sulfate and chloride types, reflecting leaching inputs of surface pollutants via rainfall infiltration. In the normal season, the hydrochemical types are most dispersed, showing mixed HCO3--Cl facies. Overall, the groundwater hydrochemistry in the study area is jointly controlled by precipitation-evaporation dynamics and carbonate weathering.

The Gibbs diagram shows that the groundwater in the study area is primarily controlled by rock weathering during the normal, dry, and wet seasons, indicating the dominance of water-rock interaction (Fig. 5). The ratio of γ(Na++ K⁺) to γCl⁻ (Fig. 6a) shows that the vast majority of sample points plot above the 1:1 line, indicating that Na⁺ and K⁺ are primarily sourced from the dissolution of evaporite rocks. In the relationships between γ(Ca2++ Mg²⁺) and γHCO3-, and between γ(Ca2++ Mg²⁺) and γ(HCO3-+ SO42-) (Fig. 6b–c), samples from all periods plot above the 1:1 line, confirming that Ca²⁺ and Mg²⁺ mainly originate from the dissolution of carbonate minerals. Furthermore, the γCa²⁺-γMg²⁺ relationship (Fig. 6d) helps identify the types of mineral dissolution. Samples from the dry season are concentrated below the 1:2 line, indicating a dominance of magnesium-poor mineral dissolution, with cation exchange causing a relative depletion of Ca²⁺. Samples from the normal and wet seasons are stably distributed between the 1:1 and 1:2 lines, reflecting that dolomite dissolution has reached equilibrium while calcite remains in a state of non-equilibrium dissolution, continuously supplying Ca²⁺. In the relationship between γ(SO42-+ Cl⁻) and γHCO3- (Fig. 6e), the distribution of sample points on both sides of the 1:1 line suggests that groundwater ions have dual contributions from both evaporite and carbonate rocks. Conversely, in the γCa²⁺ versus γSO42- relationship (Fig. 6f), samples generally plot above the 1:1 line, which excludes gypsum as a primary source of Ca²⁺ and indicates that Ca²⁺ is mainly derived from the dissolution of carbonate minerals. Therefore, the chemical composition of groundwater in the study area is primarily controlled by the dissolution of carbonate minerals, and is also influenced by hydrological seasonal variations and cation exchange processes.

The Chloro-Alkaline Index (CAI) was used to assess cation exchange and adsorption between groundwater and sediments, where negative values indicate exchange and more negative values reflect stronger intensity. This was further examined through the relationship between [γ(Ca2+)+ γ(Mg2+)-γ(HCO3-)-γ(SO42-)] and [γ(Na+)-γ(Cl⁻)] (Fig. 7). Samples from the normal and wet seasons plotted near the slope =-1 line (slopes of -1.52 and -1.36, respectively), confirming active cation exchange consistent with the CAI results; exchange was most pronounced in the rainy season (R2= 0.41), leading to Na⁺ enrichment. In contrast, the dry-season slope of 0.55 indicates negligible cation exchange during this period.

The spatial distribution of groundwater depth reflects the regional hydraulic gradient and groundwater flow direction, whereas the spatial variability of nitrate concentration is closely associated with flow paths, pollution source inputs, and hydrological processes (Fig. 8). During the normal season, the groundwater depth distribution is relatively uniform. The eastern region of the farm, characterized by shallower depths, serves as a recharge zone, with groundwater flowing towards the deeper western region. At this time, nitrate concentration are relatively dispersed, with high-concentration zones located in the southeastern part of the farm. In the dry season, the groundwater depth becomes deeper, and the flow direction shifts from the eastern and western sides towards the central area. During this period, nitrate concentration reach their annual peak (mean: 42.93 mg L⁻¹). The distribution of nitrate exhibits a higher degree of spatial coincidence with the groundwater flow direction, indicating that enhanced evaporative concentration during the dry season leads to the further accumulation of flow-transported pollutants in the discharge zone. In the wet season, the groundwater depth further becomes shallower, and groundwater flows from the southeastern region towards the northwestern region. nitrate concentration drop to their annual minimum (mean: 27.14 mg L⁻¹). High-concentration areas are distributed in the northwest, overlapping with regions of deeper groundwater depth. It is inferred that precipitation infiltration during the rainy season dilutes the groundwater nitrate; as dilution is the dominant process during infiltration, the nitrate concentration exhibits a decreasing trend along the groundwater flow direction.

During the normal season, the mean values of groundwater δD and δ18O were -61.31 ‰ and -7.31 ‰, with ranges of -73.40 ‰ to -53.52 ‰ and -10.25 ‰ to -2.82 ‰, respectively. The d-excess values ranged from -38.07 ‰ to 17.30 ‰, with a mean of -2.80 ‰. In the dry season, the mean groundwater δD and δ18O values were -71.05 ‰ and -9.74 ‰, with ranges of -76.93 ‰ to -60.55 ‰ and -10.75 ‰ to -7.86 ‰, respectively. The δ17O values ranged from -5.60 ‰ to -2.79 ‰, averaging -5.01 ‰, while the d-excess varied from 0.01 ‰ to 13.69 ‰, with a mean of 6.89 ‰. During the wet season, the mean groundwater δD and δ18O were -74.43 ‰ and -9.99 ‰, with ranges of -76.84 ‰ to -70.91 ‰ and -10.70 ‰ to -8.73 ‰, respectively. The δ17O values were between -5.72 ‰ and -4.72 ‰, with a mean of -5.28 ‰, and the d-excess ranged from -3.67 ‰ to 9.80 ‰, averaging 5.50 ‰. The d-excess during the dry season was the highest among the three periods, while it was the lowest during the normal period, indicating significant variations in d-excess across different seasons. The δ17O values in the dry season were higher than those in the wet and normal periods, which is a direct reflection of the impact of precipitation variations on the isotopic composition of the water body.

The isotopic values of precipitation δD and δ18O ranged from -97.78 ‰ to -20.22 ‰ and from -13.48 ‰ to -1.96 ‰, with mean values of -55.36 ‰ and -7.60 ‰, respectively. Overall, the δ18O and δD values of precipitation in the study area fall within the global ranges of -50 ‰ to 10 ‰ and -350 ‰ to 50 ‰. The Local Meteoric Water Line (LMWL) for the study area is defined by the equation: δD = 6.2 δ18O-8.2 (Fig. 9). Specifically, the equations for the normal, dry, and wet seasons are: δD = 1.07 δ18O-53.50, δD = 4.20 δ18O-30.09, and δD = 1.95 δ18O-54.97, respectively. The slope of the annual LMWL is lower than that of the Global Meteoric Water Line (GMWL) proposed by Craig in 1964 (δD = 8 δ18O+10), as well as lower than the China Meteoric Water Line (CMWL) (δD = 7.9 δ18O+8.2). The stable hydrogen and oxygen isotopic characteristics of groundwater samples from the three periods all exhibit a discrete, linear distribution and plot below both GMWL and LMWL. This phenomenon reveals that the water isotopes have undergone strong fractionation during evaporation in the normal, wet, and dry seasons. Furthermore, the stable hydrogen and oxygen isotope data for the dry and normal seasons are mainly concentrated in the lower-left region of the plot, indicating relative isotopic depletion during these two periods. During the normal period, the δD and δ18O values exhibit a high degree of dispersion and are widely distributed in the upper-central part of the scatter plot. This reflects that the stable hydrogen and oxygen isotopes are relatively enriched and have a wide range of variation during the normal season.

During the normal water period, the nitrogen and oxygen isotopic compositions in groundwater exhibit a wide range of variation. The δ15N-NO3- values range from 5.6 ‰ to 24.52 ‰ (average: 18.22 ‰), while the δ18O-NO3- values range from -6.33 ‰ to 6.23 ‰ (average: 0.22 ‰). In the low water period, the range of δ15N-NO3- values expands to 3.2 ‰–21.96 ‰ (average: 12.19 ‰), and the δ18O-NO3- values range from -9.58 ‰ to 8.04 ‰ (average: 0.65 ‰). Previous studies have established characteristic δ18O-NO3- ranges for different nitrate sources: atmospheric deposition (23 ‰–75 ‰), nitrate fertilizers (18 ‰–24 ‰), and products of nitrification (-10 ‰–10 ‰). The data points are predominantly concentrated within the zone of animal manure and domestic wastewater, indicating that nitrate is primarily derived from these sources, with soil nitrogen as a secondary contributor.

The MixSIAR model was employed to quantitatively apportion the sources of groundwater nitrate nitrogen. According to the average contributions from each source, the five pollution sources in the study area were ranked as follows: DSM (74.1 %) > SON (20.9 %) > NHF (4.2 %) > NOF (0.6 %) > NP (0.2 %) (Fig. 10). This indicates that the primary contributor to groundwater NO3--N in the study area was manure and sewage, followed by soil nitrogen. The influences of atmospheric precipitation and chemical fertilizers on groundwater nitrate were negligible. The quantitative results from the MixSIAR analysis are consistent with the qualitative findings, confirming that manure and sewage, along with soil nitrogen, are the dominant sources of nitrate pollution in the study area.

To address the modeling bias arising from limited measured samples, this study constructed virtual datasets at 1–10 times the original scale based on a strategy combining t-SNE dimensionality reduction, GMM clustering sampling, and KNN inverse mapping, to enhance the robustness of model training. Taking the 10× virtual dataset as an example, the statistical characteristics (Table 3) show that the virtual samples effectively reproduced the central tendency and dispersion of the original data. For the normal season, the mean NO3- concentration was 30.41 mg L⁻¹ (vs. observed mean of 33.67), with a standard deviation of 28.78 (vs. 35.83) and a coefficient of variation (CV) of 0.95 (vs. 1.06). In the dry season, the maximum value of the virtual samples reached 178.09 mg L⁻¹, while this did not fully replicate the extreme high values (observed maximum of 358.58 mg L⁻¹), it effectively expanded the range of the heavy-tailed distribution. For the wet season, although the CV for all indicators was slightly lower than the measured values, their ranges (8.47–80.37 vs. 4.15–98.36 mg L⁻¹) still showed a high degree of overlap, indicating that no systematic distortion was introduced.

Standardized multivariate boxplots (Fig. 12) visually confirm that the median, interquartile range (IQR), whisker length, and outlier distribution of the virtual data for each period were highly similar to the measured data, demonstrating that the central tendency and dispersion characteristics were well-preserved. Hydrological seasonal characteristics, such as high EC, TDS, Cl⁻, and NO3- in the dry season and low, concentrated NO3- in the wet season, were also accurately preserved. Although the number of some newly added outliers slightly increased, they all fell within physically reasonable ranges, with no non-physical solutions, such as negative concentrations or out-of-bounds pH values, occurring. Figure 13 presents a comparison of nitrate concentration frequency distributions between the original and virtual datasets across normal, dry, and wet periods. The distributional comparison indicates that the proposed t-SNE + GMM + KNN inverse mapping virtual sample generation strategy maintains the core features of the NO3- distribution for each hydrological period, while simultaneously improving sample representation in sparse areas and intervals of high variability. Therefore, the t-SNE + GMM method effectively captured the non-linear structure and extreme value information of the original data, and can provide reliable data support for subsequent model training.

The Kolmogorov-Smirnov (KS) test results indicate that the dry season exhibited the lowest mean KS statistic (0.1214 ± 0.0387), with 80.0 % of the features falling below the strict threshold of 0.15 (Fig. S2 in the Supplement). This demonstrates that the virtual samples during this period highly reproduced the distribution characteristics of the observed data. The normal season followed, with a mean KS statistic of 0.1278 ± 0.0356, where 72.5 % of the features had KS values below 0.15. The distribution similarity during the wet season was relatively lower, characterized by a mean KS statistic of 0.1657 ± 0.0542; although 37.5 % of the features had KS values below 0.15, 70.0 % still satisfied the acceptable criterion of KS < 0.20. The P-values from the KS test provided a quantitative assessment of the statistical significance regarding distributional differences. When P > 0.05, the null hypothesis could not be rejected, indicating no significant difference between the distributions of the virtual and observed samples (Figs. S2 and 14). Jensen-Shannon (JS) divergence analysis further corroborated these findings (Fig. 15). The mean JS divergence across all three hydrological periods remained below the threshold of 0.05, demonstrating high consistency with the original distributions. These low JS divergence values indicate that the probability distributions of the synthetic samples closely approximated the observed data, with no significant distributional shift observed. Notably, the JS divergence values for Salt and NO3- were relatively higher across all hydrological periods. Evaluation results using the Maximum Mean Discrepancy (MMD) showed that MMD values approaching zero and remaining within the confidence interval indicate no significant distributional differences between the synthetic and observed data in the Reproducing Kernel Hilbert Space (RKHS), confirming that the virtual samples introduced no systematic bias (Fig. 16).

Analysis of the impact of sample generation multipliers revealed that a multiplier of 7 to 10 times yielded the optimal performance across all hydrological periods. Within this range, both KS statistics and JS divergence remained at low levels with minimal fluctuation, indicating the most stable distribution similarity. In contrast, sample generation with multipliers of 1 to 3 times exhibited larger fluctuations in some indicators, demonstrating insufficient stability. Based on a comprehensive evaluation, this study recommends adopting a sample generation multiplier of at least 7 to ensure the quality of virtual samples. Feature-level analysis revealed the response characteristics of different water quality parameters to the data augmentation strategy. The KS statistics for ORP, Temperature, and EC were generally low (mean < 0.12), indicating excellent performance in virtual sample generation for these features. In contrast, Salt, NO3-, and TDS exhibited relatively higher KS statistics (mean > 0.18). Nevertheless, the MMD values for all features remained within the confidence interval, suggesting that even for features with high KS values, the virtual samples did not introduce significant distributional bias. These diagnostics confirm that the t-SNE-GMM-KNN strategy effectively mitigates small sample bias without introducing systematic distributional distortion.

In the normal season, baseline and quantum enhanced RF models achieved R2 of 0.6727 and 0.6602, respectively, with wide bootstrap 95 % CIs reflecting the limited sample size (Table S2). Augmenting virtual samples from 1× to 10× the original size steadily raised R2 above 0.958 (quantum enhanced RF reaching 0.9622, 95 % CI: [0.9744, 0.9881]), with gains plateauing beyond approximately 500 virtual samples. The dry season showed the poorest baseline performance (R2= 0.2841, 95 % CI: [0.2884, 0.7276]; Tables S2–S3), attributable to high NO3- variability and outlier sensitivity under data sparsity. Virtual sampling markedly improved accuracy: R2 reached 0.527 at 1× generation and 0.854 (95 % CI: [0.8431, 0.9221]) at 8×. Although the quantum enhanced model slightly lagged at 2× generation or less, both models converged to high accuracy, confirming that virtual samples effectively mitigated data sparsity and skewed distributions. The wet season yielded the best baseline performance (R2= 0.7331, 95 % CI: [0.6715, 0.8926]; Table S4), owing to lower NO3- concentrations and smaller spatial variability. Augmentation further raised accuracy to R2= 0.962 at 4× generation and a stable 0.977 at 10× (RMSE as low as 3.03 mg L⁻¹; 95 % CI: [0.9787, 0.9875]). Quantum enhanced and classical RF performed nearly identically, indicating limited marginal benefit from quantum feature encoding when data quality is high and relationships are more linear.

In the normal season (Fig. 17A1–A2), both models trained on the 66 original samples showed marked deviations between predicted and observed values, with highly dispersed predictions and medians far from the observed median, consistent with the low R2 of small sample modeling. As virtual samples increased, predicted distributions gradually converged toward the observed values and the boxplot IQR and whiskers narrowed, indicating substantially improved stability and accuracy. At 10× generation (660 virtual samples), predicted and observed boxplots nearly overlapped, with RMSE reduced to 6.02 mg L⁻¹; the quantum enhanced model slightly outperformed classical RF (R2= 0.9622, bootstrap 95 % CI: [0.9744, 0.9881]), confirming robust accuracy despite the small original sample. In the dry season (Fig. 17B1–B2), both models systematically overestimated NO3- on the original data owing to its extremely high and skewed concentrations, placing predicted boxplots entirely above the observed values (R2= 0.28, 95 % CI: [0.2884, 0.7276]). Virtual sampling brought substantial improvement: predicted medians and ranges began converging from 1× generation, and at 8× or higher the models captured the high concentration intervals, with RF reaching R2= 0.8542 (95 % CI: [0.8431, 0.9221]) at 9×. Classical RF slightly outperformed the quantum enhanced model at low generation levels, but their performance converged as sample size grew, demonstrating that virtual sample generation effectively alleviates challenges from data sparsity and extreme values. In the wet season (Fig. 17C1–C2), predictions already agreed well with observations on the original data, and virtual samples further narrowed the IQR and concentrated predictions within the observed distribution. At 10× generation, agreement was exceptionally high (R2= 0.977, RMSE = 3.03 mg L⁻¹), demonstrating excellent predictive performance.

To explore the potential of remote sensing semantic embedding features in predicting groundwater nitrate concentrations, this section employs the 64-dimensional surface semantic vectors derived from the Google AlphaEarth Foundation (AEF) dataset as model input variables. We reduced the variables through principal component analysis to preserve ≥ 95 % variance.

In the normal season, models trained on the original samples performed poorly, with R2 of 0.167 (RF) and 0.119 (quantum enhanced RF) and RMSE as high as 32.89 and 33.82 mg L⁻¹, respectively (Table S5), indicating that AEF embedding features alone cannot adequately capture the hydrological processes of this period under limited sample size. Virtual sampling markedly improved performance: at 10× generation, RF reached R2= 0.860 with RMSE reduced to 10.73 mg L⁻¹ and a narrowed bootstrap 95 % CI of [0.8792, 0.9326], while the quantum enhanced RF achieved R2= 0.844 with a consistent trend, confirming statistically stable performance even with indirect remote sensing inputs. Boxplot comparison (Fig. 18A) shows that initial predictions severely overestimated low to medium concentrations while underestimating high value tails; as sample size expanded, predicted distributions progressively converged toward the observed values, with much improved agreement in median and IQR. This confirms that virtual samples effectively enhanced the capability of AEF features to represent nonlinear patterns.

In the dry season, the original dataset yielded a negative R2, reflecting the weak generalization of AEF features under high variability and heavy tailed distributions (Table S6). Performance improved steadily with virtual sampling: R2 rose to 0.039 at 1×, 0.641 at 8× (RMSE = 21.05 mg L⁻¹, bootstrap 95 % CI: [0.6385, 0.8638]), and 0.674 at 10× (RMSE = 19.86 mg L⁻¹). The quantum enhanced RF slightly outperformed standard RF at high expansion levels, suggesting that quantum encoding helps mitigate the influence of extreme values and enhances robustness (Fig. 18B). Prediction distributions show that the initial model entirely failed to capture the high concentration clustering of dry season NO3-, whereas after data generation the predicted boxplots progressively covered the true high value intervals, with tail behavior aligning with observations. In the wet season, although baseline R2 was also negative, improvement was the most rapid (Table S7): R2 reached 0.5 at only 2× expansion, 0.685 at 5×, and stabilized at 0.784 (RF, RMSE = 8.27 mg L⁻¹) and 0.781 (quantum enhanced RF) at 10×. Boxplots confirm that the initially dispersed and systematically biased predictions rapidly converged to the dense intervals of observed values, with final IQR and whisker ranges showing high overlap.

Compared to modeling results based on in-situ observation data, the predictive performance based on AlphaEarth Foundation embedding features was generally lower. Under the same virtual sample generation multiplier, the maximum R2 for the normal, dry, and wet seasons were approximately 10.27 %, 17.37 %, and 19.33 % lower, respectively. This indicates that measured water quality parameters more directly reflect the key processes of nitrogen migration and transformation. However, given that AEF can be obtained globally without the need for field sampling, it offers a feasible alternative for the rapid screening of groundwater nitrate risks in large-scale unmonitored areas.

In the normal season, the total order Sobol indices of the classical RF consistently ranked TDS (0.2882 to 0.2933), EC (0.2701 to 0.2839), and Salt (0.2411 to 0.2612) as the three most sensitive parameters across all generation gradients (Fig. 22), in close agreement with the Gini and SHAP importance rankings. The first order index of TDS remained above 0.29 in the original data and stabilized at 0.2938 after 10× generation, indicating a stable and dominant independent contribution to nitrate prediction. In contrast, pH, T, DO, and ORP showed total order indices below 0.08, reflecting limited influence. The quantum enhanced RF yielded the same overall ranking, with the sensitivity of TDS, EC, and Salt further stabilized at 10× generation (0.2586, 0.2516, and 0.2416, respectively). Notably, the total order sensitivity of ORP rose from 0.0313 (original) to 0.0608 (10×), suggesting that quantum feature encoding strengthens the model's perception of redox contributions to nitrate dynamics and that virtual sampling improves the stability of sensitivity estimates for low contribution parameters.

In the dry season, characterized by highly skewed nitrate distributions and strong evaporative concentration, parameter sensitivity differed from the normal season (Fig. 23). For classical RF on the original data, the five most sensitive parameters were TDS (0.2713), Salt (0.1907), DO (0.1766), EC (0.1739), and pH (0.1146). The notably higher pH sensitivity than in other seasons indicates that the acid-base environment strongly controls nitrate accumulation under intense evaporation. With increasing virtual sample generation, the sensitivity of TDS, EC, and Salt gradually stabilized, while DO remained high (0.1596 to 0.2165), confirming its persistent control over nitrate as an indicator of nitrification intensity in the oxidizing dry season environment. After 10× generation, the quantum enhanced RF showed higher sensitivity for pH (0.1015) and DO (0.1665) than classical RF, suggesting the hybrid quantum-classical framework is more robust in capturing nonlinear hydrochemistry-nitrate relationships under the highly heterogeneous, small sample conditions of the dry season.

In the wet season dominated by precipitation dilution and infiltration, the parameter sensitivity pattern was more concentrated (Fig. 24). For the classical RF model, TDS (total-order index 0.2819–0.3179), Salt (0.2565–0.2810), and EC (0.2478–0.2492) maintained an absolute dominant position in global sensitivity across all generation gradients, with the sum of their total-order indices exceeding 75 % of the total sensitivity of all parameters. The total-order sensitivity of ORP ranked fourth (0.1153–0.1435), which was higher than that in the normal and dry seasons, reflecting that the redox potential change caused by rainfall infiltration is a key secondary factor affecting nitrate leaching and migration in the wet season. The sensitivity of pH, T, and DO was extremely low, with total-order indices all below 0.03, indicating that these parameters have limited independent influence on nitrate prediction under the dilution effect of heavy precipitation. The quantum-enhanced RF model showed a consistent sensitivity ranking with the classical RF, and the total-order sensitivity of ORP further increased to 0.1343 after 10x generation, verifying the reliability of ORP as a key driving parameter in the wet season.

The OAT perturbation test was performed by varying each target parameter within ±30 % of its measured range while fixing others, and elasticity coefficients were calculated to quantify the directional response of predicted nitrate per unit parameter change (|value| > 1 indicates an elastic response). The results corroborated the Sobol analysis. In the normal season, the perturbation sensitivity of TDS and EC remained highest (> 0.11) for both models after 10× generation. In the dry season, pH sensitivity rose sharply from 0.3033 to 2.0128 (classical RF) and from 0.6026 to 1.3757 (quantum enhanced RF), confirming the model's strong responsiveness to pH; correspondingly, pH elasticity coefficients reached 18.5446 and 24.2152 after 10× generation, an extremely strong positive elastic response identifying pH as the key control on dry season nitrate accumulation. In the wet season, the perturbation sensitivity of Salt and TDS stabilized at 0.1358 and 0.1616 (classical RF, 10×) as the highest responses. Elasticity analysis further showed that in the normal season T, pH, and EC had coefficients above 1 (positive elastic response), whereas ORP was inelastic (0.1037); in the wet season, the coefficients of TDS, EC, and Salt were all close to 1, indicating a near proportional linear response of nitrate to salinity indicators, consistent with the dominant dilution effect.

The t-SNE-GMM-KNN virtual sample generation markedly improved the stability and reliability of sensitivity estimation. For the dry season with the most severe data sparsity, the 95 % CI of the Sobol index for TDS narrowed by 87.9 % from original to 10× generation, and the coefficient of variation of perturbation sensitivity decreased by an average of 62.4 %, indicating that augmentation effectively reduces small sample variance and avoids ranking bias from insufficient representation. As generation multiples increased, the ranking of core parameters (TDS, EC, Salt) remained stable while estimates for secondary parameters (ORP, DO, pH) gradually converged, confirming that virtual sampling improves statistical robustness without altering the inherent hydrochemical driving mechanism. The quantum enhanced RF further showed smaller sensitivity fluctuations across generation gradients than classical RF, particularly on the original dry season data (21.7 % lower coefficient of variation in total order indices), demonstrating that quantum feature encoding enhances robustness under small sample conditions. Overall, the multi-dimensional sensitivity analysis consistently identified TDS, EC, and salinity as the most critical and stable parameters across all seasons, in close agreement with the correlation, Bayesian, and SHAP analyses, while dry season pH and DO and wet season ORP emerged as season specific drivers, revealing differentiated controls on nitrate dynamics under varying hydrological conditions. These results validate the model structure and feature selection and provide a quantitative basis for optimizing monitoring indicators and targeted control of groundwater nitrate pollution.