The study area extends from 30° W to 37° E in latitude and from 30 to 65° N in longitude, covering the Mediterranean Sea (MED) and a portion of the northeastern Atlantic (NEA). This area is considered to be coastal in the pan-European domain, as shown in Fig. . It represents a critical zone for biogeochemical studies due to its extensive BGC-Argo observations and its unique position as one of the most data-rich coastal-proximate areas, where some of the continental shelf seas within this domain exhibit disproportionately high primary productivity and play a fundamental role in regulating oceanic biogeochemical cycles .

Nutrients from the open ocean and river runoff create a general and rapid biogeochemical cycle in the NEA , in contrast to the MED, which is distinguished by its semi-enclosed and oligotrophy conditions. This study aims to develop a robust and generalizable modeling framework by exploring the relationships between multiple variables and validating its effectiveness in different marine regions.

Figure depicts the process of estimating nitrate and related research in this paper. The SSEVs and spatiotemporal coordinates undergo data preprocessing and resampling (Sect. 2.3.1) to serve as the feature set for the two-step training of the MLP model. The simulated and BGC-Argo nitrate concentrations provide the constructed MLP model (Sect. 2.3.2) with labels for two-stage continual-learning (Sect. 2.3.3) training. So far, the MLP has completed the modeling of the relationship between the surface environment and the internal ocean nitrate. After undergoing four kinds of 3D performance validations, the model reconstructed the 3D nitrate field by inputting iterated spatiotemporal coordinates and the corresponding SSEV datasets. The feature contributions and the potential mechanisms for estimation were evaluated based on the training datasets and the model (Sect. 2.3.5).

In the five-fold profile-based cross-validation, all of the data are used once in the test set. As illustrated in Fig. , the model performance is evaluated by comparing estimated values with BGC-Argo observations. The model demonstrates high accuracy in estimating nitrate concentration, with estimated values generally aligning along the 1:1 line. Importantly, to ensure a comprehensive dataset and to enhance the stability of the reconstruction process, we retained all of the measured labels, including negative values. Furthermore, a Softplus activation function was applied to the model's output layer to guarantee non-negative predictions, albeit at the expense of some degradation in statistical performance metrics. Considering the significant differences between the two regions of the study area, Fig. b and c show the test results for the MED and NEA. Compared to the NEA, the MED exhibits a smaller range of nitrate variations and stronger estimation performance. The MED records account for 86 % of the total dataset, whereas the NEA contributes only 14 %. This data imbalance likely contributes to the more consistent performance in the MED compared to the NEA.

While the model has shown satisfactory overall performance, it is critical that the accuracy remains consistently desirable in the vertical dimension. Only then can the model fulfill its intended purpose of estimating and reconstructing the entire 3D ocean nitrate field. Figure  illustrates the vertical distribution of the primary statistical metrics and their comparison with simulated nitrate. The model maintains robust performance in the vertical dimension, with no significant fluctuations in RMSE and MBE, which is vital for accurately estimating nitrate profiles. The model exhibits slightly superior performance in the MED compared to the NEA at most depths. The RMSE in both the MED and NEA is higher between 0 and 150 m, with a notable peak at 60 m depth, reaching about 0.8 and 1.4 µmol kg⁻¹, respectively. Furthermore, the RMSE of the MED remains at a low level and slowly decreases as depth increases. In contrast, the RMSE of the NEA varies drastically, accompanied by a larger overall error, particularly in the 400–700 m depth range. As shown in Fig. b, MBE values are negative for most depth ranges in the NEA, suggesting a slight overall underestimation of nitrate concentrations, while a slight overestimation occurs in the upper-ocean layers of both subregions.

The model excels in the deep ocean layers beyond 800 m depth, where nitrates are characterized by low variability and minimal feedback from the sea surface environment. Nonetheless, through the use of temporal and spatial coordinates and a dual training process, the model accurately estimates nitrate concentrations. The model's relatively weak performance is observed at the upper 100 m depths, which could be attributed to the sensitivity of the surface layer to external nitrate inputs , thus leading to deviations from the model-fitted relationship between nitrate and SSEVs. Furthermore, the ocean at these depths is usually influenced by both the euphotic layer and mixed layers, where complex interactions between ecosystem and ocean dynamics occur, such as water transport, plankton consumption, and decomposition. Hence, predicting parameters at this depth has usually presented the biggest challenge in vertical dimension estimation .

In contrast, simulated nitrate exhibits instability in describing the vertical distribution of nitrate concentration. Firstly, simulated nitrate produces significant errors at the ocean surface, possibly due to the limitations of biogeochemical models in simulating complex boundary interactions. However, the estimation error here has been significantly ameliorated by the MLP owing to the strong correlation between SSEVs and SSN. Secondly, the characterization of nitrate vertical changes by simulated nitrate is not precise enough. The vertical inaccuracy may result in disparities in the characterization of the changes, thus placing a limitation on small-scale biogeochemical research. An evident instance can be observed in the mesopelagic zone (MZ), ranging from 200 to 1000 m in the NEA. Simulated nitrate faced challenges in accurately describing the vertical rate of nitrate variations in this range, resulting in a notable overestimation of nitrate concentrations (Fig. b). This is also reflected in the distinct step-like pattern observed at nitrate concentrations of 10–15 µmol kg⁻¹ (Fig. a) and the overestimation in the vertical pattern (Fig. e). Furthermore, the MLP and simulated nitrate present similarities in the vertical profiles of the RMSE, while the MLP consistently outperforms simulated nitrate. This also demonstrates that the MLP has improved performance from incorporating prior knowledge from simulated nitrate through CL.

Due to the limited monitoring range of BGC-Argo, the spatial generalization ability of the model is crucial for accurately reconstructing the complete nitrate concentration field. Therefore, this section adopts a more rigorous validation procedure by partitioning the BGC-Argo dataset according to device sites and performing the five-fold cross-validation as outlined in Sect. . Under these circumstances, the spatial disparity between the training and test sets grows significantly, aiding in the assessment of the model's predictive performance across unknown marine regions and amplifying the comparative impact of CL on spatial generalization.

Figure e illustrates the accuracy of simulated nitrate concentrations by interpolating gridded simulated nitrate data across longitude, latitude, depth, and time to match the spatiotemporal coordinates of BGC-Argo observations, thereby approximating and validating the simulated values. The results indicate that simulated nitrate tends to form stepwise clusters due to its inertia and lack of variability in representing localized nitrate fluctuations (Fig. ), leading to similar y values within subsets that should correspond to x-direction gradients. Nevertheless, the overall agreement between the two datasets remains strong. The simulated nitrate achieves an acceptable accuracy (R2=0.826, RMSE = 1.882 µmol kg⁻¹), making it a valuable prior dataset. This compatibility is crucial, and given that simulated nitrate can provide data of comparable accuracy across the entire ocean, its shows great potential as a complement to BGC-Argo data. Simulated nitrate aids in understanding the large-scale distribution of nitrate, offering extensive insights that serve as a beneficial foundation for enhancing fitting relationships during subsequent CL training phases.

Figure a illustrates the spatial generalization test performance of the model, demonstrating that CL leads to enhanced test performance, as marked by an increase in R2 of 0.051 and a decrease in RMSE of 0.343 µmol kg⁻¹, compared to the non-CL results shown in Fig. c. Specifically, the MLP model without CL significantly underestimates high nitrate concentration samples, primarily due to its limited generalization ability in unfamiliar regions of the NEA during site-specific cross-validation. The introduction of CL effectively mitigates this limitation, allowing the model to maintain stable generalized estimates, even for high nitrate concentration samples. Furthermore, the majority of the samples exhibit a more consistent fit to the 1:1 line, significantly reducing the episodic uncertainty associated with simulated nitrate and the generalization error of the non-CL MLP model. Notably, coupling with CL retains the influence of prior knowledge from simulated nitrate, resulting in localized variability differences. For instance, the densely packed high-concentration samples in warm colors transitioned from symmetric fitting (Fig. c) to step-like clustering (Fig. a) while achieving a closer fit and overall improved performance. The extent of this transformation is influenced by the EWC parameter λ.

Figure b presents the horizontal distribution of the RMSE. The predictions exhibit the highest accuracy in the central MED, while larger RMSE values are observed in the NEA and peripheral regions of the MED. The substantial variability in nitrate concentrations in the NEA is largely attributable to the active exchange of eutrophic seawater. Furthermore, the sparse distribution of BGC-Argo measurements in the NEA results in significant deviations from the training data, posing substantial challenges to accurate cross-validation in this region. Overall, high error rates are frequently observed in coastal locations, particularly in the western Strait of Gibraltar and the southern parts of the MED. These areas are more susceptible to anthropogenic influences and complex land–sea interactions, which complicate prediction efforts. Additionally, the shallower topography of these regions contributes to increased errors in the vertical water column, particularly in the error-prone ocean surface layer (Fig. a).

Notably, regional disparities introduced by CL are evident in Fig. d. When the peripheral regions are used as test sets, the discrepancies between training and test data distributions become more pronounced. This sparsity of BGC-Argo data poses a considerable challenge for model estimation in regions lacking sufficient global training on similar datasets, leading to reduced performance metrics. However, CL significantly enhances the model's estimation capabilities in sparsely observed regions, particularly in areas with high RMSE values near the boundaries of BGC-Argo coverage. This suggests that CL helps reduce model instability when generalizing to unfamiliar regions by incorporating prior knowledge from simulated nitrate. For instance, in the western Strait of Gibraltar, complex environmental interactions and similarities in spatial coordinates to the MED present significant estimation challenges. Nevertheless, the model demonstrates substantial improvements in both accuracy and generalization stability compared to the MLP without CL. Moreover, the model achieves more accurate estimates by fitting BGC-Argo data, showing a comprehensive improvement over simulated nitrate (Fig. f), which is critical for reconstructing the 3D nitrate field. Interestingly, in data-dense regions such as parts of the Mediterranean, the incorporation of CL results in a slight increase in the RMSE. This phenomenon occurs because, in well-sampled regions, prior knowledge may interfere with the MLP's fitting process. However, the influence of this prior knowledge can be optimized by regionally adjusting the EWC parameter λ. Currently, this parameter is selected to achieve an overall optimal performance.

In conclusion, it is reasonable to infer that CL enhances the overall model performance and generalization capability in regions not covered by BGC-Argo by incorporating relevant knowledge and patterns from simulated nitrate. This process is influenced by data distribution and weighting parameters.

To further ensure a more stable assessment of the model's generalization ability in data-sparse regions while avoiding potential autocorrelation within the BGC-Argo dataset, the GLODAPv2 database was employed for independent validation, which was not part of the training. Fifteen cruises measuring nitrate concentrations at depths ranging from 0 to 2000 m in the study area were selected, and their measurements were compared against model estimates and simulated nitrate. Figure c illustrates that a significant portion of the GLODAPv2 data is located in the NEA, thereby allowing for an effective assessment of the model's performance in undersampled regions. The results indicate a strong correlation with the GLODAPv2 nitrate concentrations, as evidenced by an R2 value of 0.94 (Fig. a).

Figure c also depicts the regional distribution of errors, revealing that model performance varies significantly across different regions. The lowest errors are observed in the western MED and the southern NEA, whereas larger errors are concentrated in areas with sparse BGC-Argo observations. This distribution pattern and its underlying causes align with the spatial performance in site-based cross-validation, as shown in Fig. b. Factors such as enhanced water exchange dynamics , intricate land–sea interactions, and shallow topography contribute additional complexities. Moreover, several expeditions north of 50° N took place in 2010–2012 and 2015, while most BGC-Argo observations in the same region were made after 2020. The pronounced variability of nitrate concentrations in the NEA, coupled with limited observations and temporal discrepancies, diminishes the data representativeness, leading to an increased RMSE. Overall, the error margins are deemed acceptable and still outperform the validation accuracy of the simulated nitrate (Fig. b).

To thoroughly examine and contrast the seasonal vertical patterns of BGC-Argo, modeled, and simulated nitrate, two representative regions depicted in Fig.  were selected to facilitate a comprehensive evaluation of the model's efficacy. The box NEA, located at 14–19° W and 46–53° N, and the box MED, located at 26–30° E and 32–36° N, were chosen due to their frequent BGC-Argo sampling, which ensures great consistency between measured data and observed vertical patterns. The vertical distribution of nitrate is depicted in Fig.  for these two regions, where the MLP model, simulated nitrate, and BGC-Argo observations are juxtaposed for comparison.

The reconstructed vertical nitrate profiles derived from the MLP model demonstrate greater consistency and robustness compared to the BGC-Argo data, whereas the profiles from simulated nitrate still exhibit significant discrepancies in capturing seasonal variations. The MLP model has shown a remarkable ability to capture medium-scale features, such as the seasonal increase during winter and decrease during summer, aligning well with the BGC-Argo data and effectively depicting seasonal variations in the upper ocean. Furthermore, the MLP model is consistent with BGC-Argo in representing depth-dependent variability within the MZ while bridging gaps left by the intermittent nature of BGC-Argo measurements. In contrast, simulated nitrate tends to underestimate concentrations in the upper ocean (Fig. b) and shows relatively sluggish seasonal variations, including the absence of a pronounced increase during winter in the box NEA and insufficient representation of seasonal changes in the upper layers of the box MED.

As discussed previously, the model's estimation results demonstrate satisfactory accuracy and strong performance in the test dataset. Additionally, the model's predictions have been analyzed comprehensively across the vertical, horizontal, and temporal dimensions, all indicating high performance. To ensure robust generalization across diverse oceanic environments, the joint model was employed to estimate nitrate concentrations in both the MED and NEA, despite facing specific challenges. Given the complexity of the marine environment and the fact that the NEA represents only 14 % of the dataset, a higher error rate in this region is acceptable. Despite increased errors in some challenging cases, the model generally proves to be reliable for reconstructing the 3D nitrate concentration field.

The reconstruction of the 3D nitrate field from 2010 to 2023 was done using the MLP model combined with the SSEV for the corresponding period. The reconstructed field features a monthly temporal resolution, a horizontal spatial resolution of 0.25°, and 63 depth levels, with vertical intervals ranging from 5 to 50 m. Figure  illustrates the spatial distributions of the reconstructed nitrate at various depths across the pan-European region, with representative profiles selected at depths of 0, 50, 100, 150, and 500 m.

The reconstructed nitrate field reveals substantial spatial variability, with a clear increasing trend in nitrate concentrations with depth. The MED was identified as an oligotrophic region and generally exhibits nitrate concentrations below 5 µmol kg⁻¹ at depths between 0 and 150 m. Unlike the NEA, the MED nitrate concentrations are less influenced by seasonal dynamics, primarily due to the region's enclosed nature and restricted seawater exchange. The oligotrophic characteristics of the MED intensify from west to east, with more pronounced differences evident in the deeper ocean layers . In contrast, the NEA is characterized by higher nitrate concentrations and pronounced seasonal variability, which is largely driven by the influx of nutrient-rich water masses from the open ocean . The highest nitrate concentrations are found in the NEA seawaters, which form a typical eutrophic region. The spatial pattern of the reconstructed results overall aligns well with that of the simulated nitrate dataset (Fig. S1 in the Supplement), including extensive regions not covered by BGC-Argo, such as the coastal waters of the UK and Norway. Meanwhile, discrepancies are observed in certain small-scale 3D structures between the reconstruction and the simulated nitrate field. These differences have the potential to provide valuable data foundations and insights for further ecological research.

Figure  presents the time–depth profiles of nitrate concentration as a function of the month in both the MED and NEA, allowing for a more detailed examination of their temporal patterns. The seasonal variability of nitrate in the MED is relatively subtle. During winter, upwelling of nutrient-rich cold water elevates nitrate concentrations in the upper ocean, with a marked increase observed from October to February of the following year. After reaching this peak, nitrate levels decline due to phytoplankton uptake during spring, followed by a secondary rise in fall as phytoplankton biomass decays . Conversely, the NEA exhibits a pronounced temporal pattern in nitrate concentration that is primarily governed by ocean dynamics. In the mixed layer, from the surface to a depth of approximately 100 m, nitrate levels increase from October to March and subsequently decrease from April to August. The temporal pattern in the NEA resembles the winter increase observed in the MED but lacks a distinct secondary peak, instead showing a more sustained high-nutrient period.

Figure  illustrates the interannual anomalies of nitrate concentrations across the study area, derived by subtracting the annual mean nitrate value for each year from the monthly nitrate concentrations. In most instances, nitrate anomalies exhibit consistency throughout the vertical profile, with this uniformity being more pronounced in the MED. Additionally, episodic discontinuities are often detected at depths around 100 and ≈500 m, corresponding to the mixing layer and certain pycnoclines. In the NEA, where seawater exchange is more dynamic, discontinuities in nitrate concentration are more prevalent. Compared with existing data sources, although BGC-Argo and simulated nitrate represent some of the most advanced nitrate data available from current observational and numerical models, they still face significant challenges in depicting interannual trends (Fig. S2). Due to the varying geographical locations of BGC-Argo observations over time, regional differences in nutrient levels introduce considerable interference and fluctuations into the calculation of interannual trends. Consequently, the trends presented by BGC-Argo appear to be more radical and may even be reversed if the sampling locations encompass both high- and low-nutrient regions. As for CMEMS nitrate, its response to mesoscale nitrate variations is relatively sluggish, leading to an overly homogeneous trend that is likely more conservative than the actual scenario. Nevertheless, its overall trend can serve as a reference for multiyear scale variations, such as the increasing nitrate levels in the MED and the intensified downward deposition of upper-ocean nitrate in the NEA (Fig. S2).

This study identifies three significant temporal trends. Firstly, there is a discernible overall increase in nitrate concentrations that is characterized by more frequent positive anomalies, particularly since 2021. This trend indicates an increasing fluctuation in nitrate levels and an escalation in eutrophication within the study area. The reconstruction outcomes align closely with trends observed in various case studies and extend these observations by providing results on a broader scale with more detailed quantification.

The MED exhibits a notably regular upward trend. BGC-Argo sequence analyses from the Sicily Channel revealed a slightly negative nitrate trend from 2011 to 2016, shifting to a positive trajectory thereafter until 2020 . In simulations employing physical–biogeochemical models under Representative Concentration Pathway (RCP) 4.5 and 8.5 scenarios for the northwestern MED, nutrients displayed a general ascending pattern that was notably more pronounced in deeper ocean layers than in surface waters . Remarkably, an anomalous nutrient surge after 2022 could potentially be linked to the severe winter storm Carmel in 2021. A detailed time series analysis over 4 years at the Levantine basin site demonstrated substantial replenishment of marine nitrates during the 2021 winter storm, reversing a declining trend that began in 2018 . By contrast, interannual anomalies in the NEA are significantly more volatile. Although certain hypotheses suggest that intensified ocean stratification due to climate warming could limit nutrient availability in the upper-ocean layers, recent findings indicate that this limitation primarily affects phosphates, whereas nitrates continue to exhibit frequent and pronounced local fluctuations. The reconstruction results provide meticulous trend characterizations consistent with documented positive anomalies observed in the NEA's upper-ocean layers between 2010 and 2014 , together with the identified growth patterns within the Iberian upwelling system .

Secondly, while vertical consistency of nitrate anomalies is stronger in the MED compared to the NEA, a decline in upper-ocean nitrate concentrations is evident in the NEA. Ocean warming has hindered the upward transport of nutrient-rich cold water, modifying the vertical nitrate distribution in the NEA. Moreover, no consistent overall trend of anomalies is apparent in surface nitrate concentrations in the NEA, which may be driven by complex ocean–atmosphere interactions and anthropogenic influences. Thirdly, the transition period of nitrate anomalies appears to be lengthening. The duration of individual positive or negative anomalies has extended from a few months at the beginning of the study period to several months or even over 1 year. This lengthening may indicate irreversible shifts in the marine environment or a decline in the ocean's self-regulatory capacity.

Furthermore, interannual anomaly trends must be interpreted cautiously due to their dependence on SSEVs and specific weights of the model, and their reliability requires further research. For instance, the reconstructed results may overestimate anomalies in the bathypelagic zone (>1000 m). At these depths, nitrate concentrations are relatively stable (Fig. ) and are not effectively represented by SSEVs. Nonetheless, the model's estimates are inevitably influenced by the SSEV signal. The accuracy of these anomalies is significantly influenced by both the generalization capacity of the model and the stability of the input features. Despite the model's proven reliability, particularly with the MEB performance most relevant to anomaly calculations consistently maintaining an excellent level of ±0.04 µmol kg⁻¹ across multiple validations, small-scale findings still require further corroboration through targeted case studies. Overall, compared to the limitations posed by the discontinuous discrete observations from BGC-Argo and the inadequacies of simulated nitrate in capturing fine-scale variability, the reconstructed dataset offers an encouraging and comprehensive perspective for trend analysis.

The current model is established based on all available features in the dataset, but given the redundancy among these features, the model may require fewer of the most efficient features. There are two benefits to entering all of the mentioned features. The ability of the MLP to automatically extract features ensures that the model will be enhanced and minimally affected by feature redundancy. In particular, the utilization of large-scale simulated nitrate data has significantly contributed to the model's ability to capture nonlinear relationships between multiple features, thus enabling it to effectively monitor nitrate concentration across a wide range of SSEV scenarios. On the other hand, analyzing the importance of each feature based on the model with all of the input features is crucial for further studies of nitrate estimation.

Figure  depicts the Pearson correlation coefficients among the features. Nitrate has been found to be positively correlated with depth and Chl and negatively correlated with SST . Furthermore, nitrate is positively correlated with features such as colored dissolved material (CDM), normalized fluorescence line height (NFLH), and 10 m wind speed (S10) and negatively correlated with features such as bottom euphotic layer depth (ZEU), heated layer depth (ZHL), and Secchi disk depth (ZSD). The spatial distribution is characterized by a positive correlation with latitude and a negative correlation with longitude, since nitrate concentrations in the NEA are generally higher than in the MED. Diverse relationships between the input features suggest the potential for feature redundancy, as exemplified by the marked positive correlation between SST and ZHL and the negative correlation between ZSD and Chl. The correlation coefficient can only capture linear relationships between variables, while MLP is a model to fit nonlinear relationships. Therefore, the contribution of features to the results cannot be determined solely based on correlation coefficients. The contributions of features based on SHAP values are discussed next.

Given the high computational cost of SHAP and the sufficient representativeness of a smaller sample , we randomly selected 200 000 samples to estimate feature contributions. Figure  illustrates the probability distribution of the SHAP values for each feature, with the features ranked according to their average ASV. Given the different mechanisms by which the features affect the ocean at various depths, it is divided into two layers in the contribution discussion. Bounded by 200 m depth, the upper layer is the epipelagic zone (EZ), and the deeper layer of 200–2000 m is the mesopelagic zone and part of the bathypelagic zone.

The input spatial features include depth, longitude, and latitude. Of these, depth is consistently identified as the strongest feature extracted by the model, which corresponds to the pattern of variations in the vertical distribution of nitrate, as depth uniquely facilitates the mapping of nitrate profiles (Fig. S3). Particularly in the EZ, the contribution of depth features is extremely significant, with IDepthEZ=2.36, surpassing that of other features and by far that of the contribution at depths of 200–2000 m. This is attributed to the fact that the increase in nitrate concentration with depth is most pronounced in the EZ. The nitrate concentration at 200 m depth may be several times higher than that at the sea surface. Although such a trend is also observed at depths of 200–2000 m, the magnitude of this change is relatively small. Hence, depth always remains the most crucial feature, especially in the EZ.

Furthermore, longitude is the second essential feature in the model. Nitrate concentration in the MED and NEA differs greatly, resulting in longitude being more vital than latitude. At 200–2000 m depths, the contribution proportion of spatiotemporal coordinates increases, while the contributions of other SSEV features decrease. On the one hand, nitrate concentration in the surface ocean is more susceptible to SSEVs. On the other hand, nitrate in the deep ocean exhibits low seasonal variability but stable regional characteristics, and its concentration is primarily related to its location. The estimation process in the deeper ocean mainly relies on spatiotemporal coordinates supplemented by subtle adjustments to environmental variables.

The feature ranking in Fig.  aligns closely with that in Table S1 in the Supplement, though there are some minor differences. Both discuss the importance of features, but the SHAP values in Fig.  focus on the contributions of features, while the RMSE changes in Table S1 emphasize the irreplaceability of the features. For example, Z (total terrain depth), which provides a unique perspective, has a small contribution but significantly impacts the model when excluded. Furthermore, when excluding features, we combined Jday1 (the cosine function of the Julian day) and Jday2 (the sine function of the Julian day), which have a high contribution but a minimal impact on model performance when excluded. This is because Jday is a heuristic feature that, while useful for providing temporal information, can be inferred through the periodic variation of other variables. Figure  shows the correlation heatmap between nitrate and all of the input variables. The current feature combination is sufficient and potentially redundant; some highly correlated features can substitute one another to some extent, which is why the RMSE increase after excluding high-contribution features like photosynthetically available radiation (PAR) is relatively small. However, the comparison experiments in Table  confirm that the model can accommodate these correlated features and enhance their performance.

The residual features comprise environmental parameters, which encompass diverse facets of climate, biology, and ocean dynamics. Of these parameters, SSH exhibited a notably higher Ij value and demonstrated the most significant impact on model performance when excluded (Table S1). SSH reflects various dynamic effects of ocean circulation, mixing layers, and eddies, which together influence the horizontal and vertical transport of nitrates . SSH reflects the influence of ocean dynamic variability on nitrate concentrations, typically exhibiting opposing impacts between the EZ and the deeper ocean.

Another set of critical features comprises SST-related variables. SST exhibits strong correlations with ZHL, PAR, and ZSD (Fig. ), each concurrently presenting high Ij values and underscoring the dominant role that SST-related features play in nitrate estimation processes. Highly correlated features may dilute their individual contributions to the results, and SST may therefore play a more significant role than depicted in Fig. .

Previous studies have established SST as a principal environmental factor in nitrate retrieval, highlighting the fact that upwelling and winter convective mixing constitute two crucial physical processes that drive the transportation of cold, nitrate-rich waters into the euphotic layer, thereby boosting SSN and simultaneously reducing SST . Since SST and SSH provide information on vertical mixing, their contribution in the deep ocean remains significant compared to other SSEVs. Of these, ZEU, PAR, NLFH, and CF are indicative of the optical environment, which is probably related to the oxidation of nitrogen by light inhibition and the activity of phytoplankton . Furthermore, ocean dynamic parameters (e.g., MLD and S10) contribute to nitrate estimation by influencing nutrients in multiple ways .

Notably, Chl has previously been employed as another pivotal variable for SSN retrieval . However, in the EZ and the deeper layers, its average contribution remains relatively low, exhibiting instead a distribution characterized by a long tail of positive values. This phenomenon aligns closely with feature assessments of nitrate reconstruction in the Indian Ocean and dissolved organic nitrogen studies in the Atlantic Ocean . The predominant limiting factor is the confined spatiotemporal scope; although Chl is intrinsically linked to nitrate, its positive contributions are restricted primarily to vertical biologically productive upper layers and horizontally confined nutrient-rich regions, which only comprise a small portion of the oceanic 3D field. Consequently, regions minimally influenced by Chl dilute the average contribution of phytoplankton across broader oceanic estimations. Figure  illustrates the distribution of Chl contributions across specific samples. In the majority of cases, low chlorophyll concentrations yield negligible effects, while slight increases in Chl typically exert a negative influence, as phytoplankton growth consumes available nitrates . Conversely, exceedingly high chlorophyll levels significantly enhance nitrate estimation, potentially signaling eutrophication events. Furthermore, during training, the model seemingly captures more valuable Chl-related information from alternative features such as CDM, redistributing Chl's overall contribution to 3D nitrate estimations.

As described above, the SHAP approach can explain the effect of each feature on the MLP output from both holistic and individual perspectives. This approach enables comprehension of the role played by features in deep-learning black-box models. The ASV distribution of most features exhibits a long tail (Fig. ), suggesting that even features with a low Ij can have a significant impact on model estimation in extreme environments. Nevertheless, the SHAP contribution is solely based on mathematical models and data-driven interpretations, which may result in conclusions that deviate from physical processes. Although it has been confirmed experimentally that removing features with a lower Ij results in less decline in model accuracy, the evaluation of the features still requires caution.