To construct the observational targets and training features for the global nutrient reconstruction, we compile a database of historical in situ observations spanning from 1965 to 2023. The target variables – specifically dissolved inorganic nitrate, phosphate, and silicate – are harmonized from quality-controlled public archives, primarily the World Ocean Database 2018 (WOD18; Boyer et al., 2018), the Global Ocean Data Analysis Project version 2 (GLODAPv2.2022; Lauvset et al., 2022), the CLIVAR and Carbon Hydrographic Data Office (CCHDO; Sloyan et al., 2019), and the Biogeochemical-Argo (BGC-Argo) program (Claustre et al., 2020). For BGC-Argo nitrate, we use the officially adjusted profiles with calibration information to reduce sensor-drift and calibration-related biases. The corresponding hydrographic predictors are sourced from the World Ocean Database 2023 (WOD23; Mishonov et al., 2024; Garcia et al., 2026) and collocated with these nutrient samples. Because our reconstruction model relies on the physical identification of water masses, we select only data containing concurrent temperature and salinity (T/S) measurements. To avoid data redundancy across these archives, duplicate profiles are identified and removed based on their spatiotemporal coordinates and cruise identifiers. Following data harmonization, deduplication, collocation, and quality control, the final dataset comprises 5 735 819 collocated T/S profiles. These physical features are paired with target nutrient observations, yielding a total of 4 225 374 nitrate, 3 578 340 phosphate, and 2 931 998 silicate measurements aggregated across the four archives. The detailed distribution of these observations per database is summarized in Table 1. The numbers in Table 1 represent the complete quality-controlled observational archive, while observations reserved for independent station and cruise-section validations are excluded from the training subset as described in Sect. 2.5.4.

To provide the machine learning model with a consistent biogeochemical and physical mean state, we incorporate climatological fields from the World Ocean Atlas (WOA). We utilize a combination of the most recent available versions for different variables to ensure the highest data quality. These fields define the spatial reference grid for our study, featuring a 1°×1° horizontal resolution and 67 standard vertical levels (0–2000 m).

We select a total of six variables to characterize the background environment. Specifically, dissolved oxygen, oxygen saturation, and apparent oxygen utilization are obtained from the World Ocean Atlas 2023 (Garcia et al., 2024b). Climatologies for density and conductivity are sourced from the World Ocean Atlas 2018 (Locarnini et al., 2019; Reagan et al., 2019), while the mixed layer depth is derived from the WOA18 temperature and salinity fields (Locarnini et al., 2018; Zweng et al., 2018). These climatological inputs provide the mean state of the global ocean, serving as static “background” features for the machine learning model.

For the global inference phase, we require continuous, time-varying, and historically consistent hydrographic inputs. We utilize the EN4.2.2 objective analysis dataset (Good et al., 2013), which provides monthly potential temperature and salinity fields from 1965 to 2023 at a 1°×1° resolution.

We select EN4 as the hydrographic predictors because of its systematic bias correction. EN4 integrates quality-controlled profiles from the World Ocean Database (WOD), the Global Telecommunication System (GTSPP), and the Argo array, while applying bias correction schemes (e.g., Gouretski and Reseghetti, 2010) to historical mechanical bathythermograph (MBT) and expendable bathythermograph (XBT) records. This processing reduces time-dependent instrumental biases, ensuring that the decadal trends in the input features represent physical variability rather than measurement artifacts.

Furthermore, the objective analysis framework of EN4 effectively bridges observational gaps, providing the spatiotemporally complete fields strictly required to drive global machine learning inferences. Because of its high fidelity in representing historical hydrographic environments, EN4 has been extensively validated as a foundational benchmark for capturing historical ocean heat storage and multi-decadal transport (Cheng et al., 2017; Zanna et al., 2019). Consequently, it is routinely employed as a highly reliable physical forcing dataset to drive large-scale data-driven biogeochemical mappings and carbon cycle reconstructions (Landschützer et al., 2016).

Because our dataset originates from diverse observational platforms and encompasses highly varied temporal and geographic scales, establishing a strict, multi-tiered quality control (QC) pipeline is critical to eliminate inaccurate records. Guided by the fundamental principles outlined in the World Ocean Database (WOD) documentation (Boyer et al., 2018), we implemented a three-stage hierarchical strategy on the merged global archive. This framework systematically filters hydrographic and nutrient variables at the measurement, station, and cruise levels.

The first level of our hierarchical QC protocol targets individual measurements, employing a sequence of seven specific checks to identify and remove potentially erroneous records from the combined datasets. (1) Initially, we apply a depth-specific boundary constraint optimized for our target 0–2000 m water column. By defining physically realistic domains for every variable across designated water strata, any observation exceeding these established boundaries is consequently rejected. This restriction covers temperature, salinity, and the three target nutrient parameters: nitrate (NO3-), phosphate (PO43-), and silicate (Si(OH)4). (2) We evaluate the biogeochemical consistency of the data by checking empirical relationships between paired variables. We validate observations against accepted theoretical spaces for both physical pairings (T–S) and physical-biogeochemical combinations (e.g., T–N, T–P, T–Si, S–N, S–P, S–Si) to guarantee alignment with recognized water mass signatures. (3) To capture extreme statistical anomalies, we compute the local mean and standard deviation for each standard depth horizon. Any value shifting beyond six standard deviations from its respective mean is tagged as an outlier. (4) We assess vertical continuity by calculating the vertical gradient for each parameter. Any measurement showing a vertical rate of change that exceeds the mean gradient by more than five standard deviations is marked as questionable. (5) A density inversion assessment targets physically improbable vertical structures. Since parameters such as temperature and nutrients typically exhibit monotonic relationships with depth or potential density (σθ) in stratified waters, measurements violating preset thresholds for relationships (e.g., Depth–T, Depth–Nutrient, or σθ–Nutrient) are flagged. (6) We identify vertical spikes by comparing each measurement directly against its immediate upper and lower neighbors. If this difference exceeds a preset limit, the observation is flagged as a spike. (7) Finally, we rely on the original quality flags provided by the source databases. We only retain measurements explicitly labeled as “good” and discard any records marked as questionable or bad.

Following the assessment of individual measurements, regarding to the second level, we extend the quality control framework to the station and cruise levels to address systematic inconsistencies. To ensure vertical profile reliability, any station containing more than 30 % of data points flagged during the initial screening is deemed unreliable and entirely discarded. Similarly, at the expedition level, cruises exhibiting an aggregate flag rate exceeding 40 % are excluded to prevent the propagation of systematic instrumental errors or calibration drifts. The final selection process integrates flags across this hierarchy, permanently removing any data identified as erroneous at the individual, station, or cruise stage.

The final level of our quality control protocol is specifically designed to align with the input-output structure of the multi-task learning framework. Since the reconstruction relies on physical predictors to infer biogeochemical fields, complete availability of temperature and salinity is mandatory. Therefore, we apply a strict filter to ensure that every retained nutrient observation is strictly collocated with valid, high-quality physical measurements (T and S). However, unlike single-task models that might require simultaneous observations of all target variables, our multi-task architecture allows for valid training with partial targets. To maximize data utilization, we do not require the concurrent presence of all three nutrients. Instead, any data point containing valid physical predictors and at least one valid nutrient measurement is retained. This flexible inclusion strategy allows the model to leverage a significantly larger volume of historical data – where specific nutrients might be missing – thereby enhancing the distinct feature extraction capability for each element. This inclusion strategy maximizes the volume of historical data available for training. The resulting high-quality dataset exhibits extensive global coverage spanning the period 1965–2023, with the specific spatiotemporal distribution patterns illustrated in Fig. 1.

The reconstruction performance is quantitatively evaluated using two standard statistical metrics: the Coefficient of Determination (R2) and Root Mean Square Error (RMSE). Let N denote the total number of matched samples, while yobs,i and ypred,i represent the observed and predicted values for the ith sample, respectively, and y¯obs is the mean of the observed values. These metrics are calculated as follows: 3R2=1-∑i=1N(yobs,i-ypred,i)2∑i=1N(yobs,i-y¯obs)2,4RMSE=1N∑i=1N(yobs,i-ypred,i)2, To evaluate the model's performance and the effects of the proposed architecture, we design a rigorous training and comparative framework. We adopt a strict time-based K-fold cross-validation strategy to prevent temporal data leakage. In this study, K=6, and the 59-year dataset is divided into six chronological folds: 1965–1975, 1976–1985, 1986–1995, 1996–2005, 2006–2015, and 2016–2023. By partitioning the 59-year dataset into chronological blocks rather than random subsets, distinct time periods are rigorously isolated as test sets, providing an objective assessment of the model's generalization. Within this cross-validation framework, we further establish a comparative baseline by training independent Single-Task Learning (STL) models for each nutrient. Comparing the proposed multi-task framework against these single-element counterparts under identical conditions allows us to verify the mutual enhancement effects driven by shared feature learning.

Beyond statistical benchmarks, a multi-dimensional verification scheme is implemented to assess the physical and biogeochemical representation of the reconstruction. This comprehensive evaluation includes: (1) Climatological Patterns and Seasonal Cycles, which examines the reproduction of large-scale seasonal variations and long-term trends; (2) Temporal Dynamics through Station Validation, where representative stations are selected to evaluate the time-series dynamics and vertical profiles; (3) Spatial Variability through Cruise Verification, utilizing independent cruise data to assess the spatial representation of nutrient distributions across ocean basins; and (4) Spatiotemporal Uncertainty Analysis, which quantifies the model variance and uncertainties of the reconstructed product across different oceanic regions and historical periods.

To ensure independent station and cruise-section validations, all HOT, KERFIX, P16N (2015), P16S (2014), and P06E (2017) observations are excluded from the training data before model development, including duplicate or overlapping records in the source archives. These reserved observations are identified using station information, cruise identifiers, and spatiotemporal coordinates, and are used only for the validations described in Sect. 3.3 and 3.4. Detailed results and analyses from these validation modules are presented in Sect. 3.

The reconstruction performance of the proposed Multi-Task Learning (MTL) and Single-Task Learning (STL) models is evaluated using aggregated predictions from the validation sets of the time-based K-fold cross-validation. Figure 3 presents the density scatter plots comparing the reconstructed nutrient concentrations against the in situ observations across the full study period (1965–2023) for both architectures. By utilizing chronological blocking rather than random partitioning, the evaluation mitigates the influence of short-term temporal persistence, providing an objective assessment of the models' generalization capabilities. The scatter distributions for both the MTL and STL models generally align with the 1:1 reference line across the concentration spectrum, indicating that the models can reproduce the concentration limits without systematic bias. Furthermore, a comparison of the scatter distributions reveals that the MTL model shows tighter alignment with the reference line than the STL model, demonstrating improved reconstruction performance for all three nutrients.

Table 3 summarizes the quantitative metrics (R2 and RMSE) to further assess the specific effects of the multi-task architecture compared to the single-task baselines. On average, the MTL framework yields R2 values of 0.9911, 0.9691, and 0.9902 for nitrate, phosphate, and silicate, respectively, with corresponding mean RMSE values of 1.2951, 0.1627, and 4.1085. As shown in Table 3, the joint learning framework consistently yields lower RMSE and higher R2 values compared to the single-element models across all chronological folds. Overall, the MTL approach reduces the fold-averaged RMSE by approximately 39.3 % for nitrate, 47.1 % for phosphate, and 41.1 % for silicate compared with their STL counterparts. This improvement can be attributed to the shared representation mechanism of the MTL architecture. By processing the elements jointly, the model is guided to learn their concurrent biogeochemical variations, which contributes to the observed improvements in numerical accuracy compared to the isolated single-task models.

Beyond the performance differences between the two architectures, a common characteristic observed in both the MTL and STL results is a progressive improvement in predictive performance from the 1960s to the 2020s. For instance, the MTL RMSE for nitrate decreases from 1.8306 in the 1965–1975 fold to 0.9273 in the 2016–2023 fold. This temporal trend corresponds with the historical evolution of global ocean observing systems; the relatively higher errors in earlier decades relate to the spatial sparsity of historical bottle measurements, whereas recent accuracy gains reflect the availability of high-density hydrographic observations that provide additional physical constraints for the models.

To evaluate whether the Jingwei-Nutrients data product captures the fundamental biogeochemical structure of the global ocean, we compare the model-derived climatologies with the standard World Ocean Atlas 2023 (WOA23). This comparison assesses whether the Jingwei-Nutrients model captures large-scale spatial patterns rather than overfitting to local observations. Figures 4 to 6 display the comparison of spatial distributions for nitrate, phosphate, and silicate across three representative depth layers: the surface (0 m), the intermediate layer (500 m), and the deep layer (2000 m). Overall, the reconstructed fields show spatial agreement with WOA23, reproducing the major global nutrient regimes across these selected depths.

The spatial patterns at each evaluated stratum reflect distinct physical-biogeochemical dynamics. As illustrated in Fig. 4, at the surface layer (0 m), the model reproduces the global nutrient regimes governed by biological uptake and physical stratification, identifying the nutrient-depleted oligotrophic subtropical gyres alongside the High-Nutrient Low-Chlorophyll (HNLC) outcropping in the Southern Ocean (Moore et al., 2013). At the intermediate layer (500 m) in Fig. 5, the spatial patterns transition to reflect organic matter remineralization and main thermocline ventilation, mapping the accumulation of regenerated nutrients in the North Pacific and Indian Ocean oxygen minimum zones (OMZs) (Paulmier and Ruiz-Pino, 2009; Sarmiento and Gruber, 2006). In the deep layer (2000 m), as shown in Fig. 6, the reconstruction captures the large-scale horizontal gradients associated with the global thermohaline circulation. The spatial distribution aligns with the general nutrient accumulation pattern (Broecker, 1991), transitioning from the relatively nutrient-poor North Atlantic Deep Water (NADW) to the older, nutrient-rich Pacific Deep Water (PDW) (Sarmiento and Gruber, 2006).

The difference maps between the reconstructed fields and WOA23 provide further insight into the spatial distribution of residuals. While the anomalies are generally small across open-ocean basins, their spatial and vertical distributions exhibit structured patterns. Spatially, larger deviations are primarily located in high-latitude regions (e.g., the Southern Ocean) and certain coastal margins. Vertically, the differences in the shallow euphotic layers tend to be larger than those in the deep ocean. This spatial-vertical contrast aligns with established oceanographic processes: surface waters and high-latitude regimes are modulated by seasonal biological uptake, atmospheric forcing, and mesoscale dynamics (Benitez-Nelson et al., 2007; Moore et al., 2013), introducing greater natural variability. In contrast, the deep ocean is characterized by relatively stable, slow-moving water masses driven by large-scale circulation. Overall, these regional variations are consistent with known oceanographic processes, and the comparison indicates that the Jingwei-Nutrients product provides a consistent representation of global biogeochemical distributions.

The vertical representation of the reconstructed fields is examined by comparing meridional sections across distinct ocean basins. Figures 7 and 8 present the vertical distributions of nitrate, phosphate, and silicate along two representative lines: 25° W in the Atlantic Ocean and 90° E in the Indian Ocean. The reconstructed fields capture the basin-scale fractionation patterns associated with the global thermohaline circulation. As illustrated in Fig. 7, the Atlantic sector exhibits relatively lower nutrient concentrations, showing the southward-intruding tongue of the ventilated, nutrient-poor North Atlantic Deep Water (NADW) in the mid-to-deep layers. Conversely, Fig. 8 displays the transition to higher deep-water concentrations in the Indian Ocean interior, reflecting the accumulation of remineralized organic matter along the aging path of the deep circulation (Broecker, 1991; Sarmiento and Gruber, 2006). Across both basins, the characteristic vertical gradient – rapid nutrient depletion in the euphotic zone followed by an increase across the thermocline to a deep maximum – is evident, indicating that the reconstruction captures the vertical coupling associated with the biological pump and subsequent subsurface remineralization (Sigman and Hain, 2012).

The difference maps in the rightmost columns of Figs. 7 and 8 provide further details on the distribution of residuals within the ocean interior. Anomalies are generally small across the majority of the water column. However, larger deviations are primarily localized along the boundaries of major water masses and in regions characterized by sharp spatial gradients. For instance, higher differences are observed around the edges of the NADW nutrient tongue and across the stratified main thermocline. This distribution of differences is physically interpretable, as these transition zones feature intense mixing and dynamic frontogenesis, introducing greater natural variability. Furthermore, the observed differences at these complex physical-biogeochemical interfaces may partially arise from distinct methodological approaches. While traditional objective analysis relies on spatial autocorrelation, the data-driven model infers nutrient concentrations through non-linear relationships with varying physical drivers. Overall, these comparisons indicate that the Jingwei-Nutrients data product provides a structurally consistent representation of three-dimensional biogeochemical distributions.

Beyond static spatial patterns, the temporal evolution of nutrient fields is critical for understanding ecosystem dynamics and phenology (Longhurst, 2007). Figure 9 compares the reconstructed seasonal anomaly cycles with WOA23 data across the Northern and Southern Hemispheres at four representative depths (0, 50, 300, and 800 m). The Jingwei-Nutrients reconstruction (solid lines) aligns with the WOA23 reference (dashed lines), capturing both the phase and amplitude of the seasonal variations. The model reproduces the out-of-phase seasonal dynamics between the two hemispheres. In the biologically active shallow layers (0 and 50 m), a pronounced seasonal amplitude is evident: the Northern Hemisphere shows winter/spring replenishment (January–March) mediated by convective mixing, followed by a distinct summer/autumn drawdown (July–October) driven by phytoplankton blooms (Behrenfeld et al., 2006; Keppler et al., 2020), while the Southern Hemisphere mirrors this pattern to reflect austral seasonality. Furthermore, the reconstruction captures the vertical attenuation of seasonal variability. While the euphotic zone experiences significant temporal fluctuations, the seasonal anomalies at deeper layers (300 and 800 m) are thermodynamically and biologically dampened, maintaining stable, near-zero baseline fluctuations throughout the year (Talley, 2013). This temporal agreement indicates that the Jingwei-Nutrients data product captures the phenological timing of global biogeochemical cycles.

To assess the reproduction of localized biogeochemical variability, we perform independent validations using in situ observations from two globally representative, long-term ecological time-series stations. These observatories encompass distinct marine biogeochemical regimes: the Hawaii Ocean Time-series (HOT; Karl and Lukas, 1996), which represents the highly stratified, oligotrophic subtropical gyre of the North Pacific; conversely, the KERFIX station (Jeandel et al., 1998) in the Southern Ocean represents a dynamic, high-latitude regime dominated by deep convective winter mixing and intense seasonal blooms. The HOT and KERFIX observations used in this evaluation are excluded from the training data and retained only for independent station validation.

Figure 10 presents the evaluations for the HOT station. The Jingwei-Nutrients data product shows consistent agreement with observations. As shown in the scatter plots, the predicted concentrations at the HOT station (Fig. 10) tightly cluster around the 1:1 reference line, yielding high localized correlation coefficients (R2≥0.993) and low RMSE (1.34, 0.11, and 3.32 µmol kg⁻¹ for nitrate, phosphate, and silicate, respectively). The vertical profile comparisons reveal that the product delineates the depth-dependent biogeochemical gradients, capturing the stably depleted surface layers and the depth of the deep nutricline at this location. Furthermore, for the interannual time-series comparisons, we select depth layers characterized by abundant historical observations and high biogeochemical representativeness – specifically, the 300 m layer for HOT. The temporal trajectories at this specific depth demonstrate that the reconstructed fields maintain long-term stable baselines. Notably, while the historical discrete observations occasionally exhibit localized high-frequency noise or sampling-induced spikes, the continuous reconstruction smooths these short-term variations while preserving the primary physical and biological signals.

Figure 11 illustrates the validation at the KERFIX station, which represents the complex dynamics of the Southern Ocean. The time-series trajectory at the surface (0 m) indicates that the product captures pronounced seasonal amplitudes driven by winter overturning and subsequent summer biological drawdowns. At this station, the model yields high R2 values for nitrate (R2=0.904) and silicate (R2=0.967), indicating that it captures the complex regional water mass mixing processes, such as the upwelling of Circumpolar Deep Water (CDW) (Talley, 2013). However, a relatively lower correlation is observed for phosphate (R2=0.749). This specific discrepancy can be attributed to two factors. First, the absolute background concentration of surface phosphate is naturally low, which reduces the signal-to-noise ratio in historical observations and mathematically amplifies the penalty of analytical errors on the R2 metric. Second, the intense iron limitation characteristic of the Southern Ocean (Boyd et al., 2007; Moore et al., 2013) often triggers localized decoupling of the classical N:P uptake ratio (Deutsch and Weber, 2012), a highly specific regional anomaly that poses a generalization challenge for global-scale reconstructions. Nevertheless, despite the lower R2, the absolute error for phosphate at KERFIX remains low (RMSE = 0.14 µmol kg⁻¹). This suggests that, even in dynamically complex and anomalous oceanic regimes, the Jingwei-Nutrients product provides a reliable basis for large-scale climatological and temporal analyses.

Complementing the temporal validations, capturing the three-dimensional spatial variability of the ocean interior is equally critical. To assess the spatial representation of the Jingwei-Nutrients product, we conduct independent validations using high-resolution, synoptic shipboard measurements from the U.S. GO-SHIP program (Sloyan et al., 2019). Unlike gridded climatologies that tend to smooth out transient features, continuous cruise sections provide a “snapshot” of the product's ability to reconstruct sharp frontal zones and mesoscale variabilities. As illustrated in Fig. 12, we select three representative expedition datasets encompassing different spatial domains: the P16S (2014) and P16N (2015) cruises, which together form a nearly complete meridional corridor across the Pacific Ocean, and the P06E (2017) cruise, which provides a zonal cross-section across the South Pacific. The P16N, P16S, and P06E observations used in this evaluation are excluded from the training data and retained only for independent cruise-section validation.

To facilitate a direct spatial assessment, the dense in situ measurements are objectively interpolated to construct continuous observational sections. These reference fields are then compared against the coincident cross-sections extracted from the Jingwei-Nutrients product. Figure 13 presents the comparative contour sections and the corresponding residual error distributions for the P16N cruise in the North Pacific. The reconstructed fields reproduce the large-scale accumulation of nutrients in the deep North Pacific, exhibiting high concentrations in the deep interior. The difference maps in the rightmost column reveal that deviations for nitrate and phosphate are predominantly concentrated in the 200–500 m depth range. This depth directly coincides with the stratified main nutricline, where concentrations change rapidly over short vertical distances. For silicate along this same section, larger residuals emerge deeper in the water column below 1000 m. This specific pattern is biogeochemically consistent with the complex accumulation of dissolved silica in the oldest North Pacific Deep Water, where slow biogenic dissolution processes (Tréguer et al., 2018) contribute to larger absolute variations.

Moving to the Southern Hemisphere, Fig. 14 presents the validation along the P16S section. Here, the reconstruction captures the nutrient outcropping near the Southern Ocean surface. However, the difference maps reveal a distinct error structure compared to the North Pacific. A vertical band of higher anomalies spanning from the surface to the deep ocean is visible around 45 to 50° S across all three nutrients. This localized feature corresponds to the Subantarctic Front within the Antarctic Circumpolar Current system. This dynamic region is characterized by energetic mesoscale eddies, intense deep vertical mixing, and steeply sloping isopycnals (Marshall and Speer, 2012), creating substantial synoptic variability in the cruise “snapshot” that naturally deviates from the temporally averaged representation of a global product.

The zonal P06E section presented in Fig. 15 illustrates the east-west biogeochemical asymmetry across the South Pacific. The reconstructed cross-section captures the nutrient-rich upwelling signals, with concentration contours shoaling towards the South American eastern boundary, which is consistent with the cruise data. Moreover, the difference maps for this zonal section show low anomalies in the deep ocean interior, yielding minimal residuals below 1000 m across the entire basin. Deviations are primarily confined to the upper water column, driven by the coastal upwelling systems (Chavez and Messié, 2009).

In summary, the cruise verification supports the three-dimensional spatial representation of the Jingwei-Nutrients product. By reproducing the synoptic features of these oceanographic sections across diverse dynamical regimes, the product demonstrates its capacity to reconstruct the continuous, full-depth spatial structure of global marine nutrients. The representation of deep-basin accumulations indicates that Jingwei-Nutrients provides a physically consistent global product.

To systematically evaluate the reliability of the Jingwei-Nutrients product, it is essential to quantify its spatiotemporal uncertainty. Since mapping sparse data often introduces more uncertainty than inherent measurement errors (Ito et al., 2025), relying solely on analytical errors is inadequate. Instead, we estimate reconstruction uncertainty using the ensemble standard deviation (SD) across our six K-fold models (Gregor et al., 2019). As shown in Fig. 16, this ensemble spread remains remarkably low relative to absolute concentrations – particularly across vast open-ocean basins – confirming the high stability and reliability of the product.

The top panels of Fig. 16 illustrate the depth-averaged spatial uncertainty for nitrate, phosphate, and silicate. The global maps reveal that the ensemble standard deviations are generally low across the open-ocean gyres, indicating model consensus in these environments. However, the uncertainty distribution exhibits spatial heterogeneities. For all three nutrients, higher uncertainties are localized along coastal margins and high-latitude boundary regions. Higher uncertainty values are observed in the subpolar North Pacific – specifically within the Bering Sea and the Sea of Okhotsk. These marginal seas are characterized by shelf-basin water exchanges, riverine inputs, and seasonal phytoplankton blooms, introducing greater natural variability. Furthermore, for silicate, a band of elevated uncertainty is observed across the Southern Ocean. This is consistent with the upwelling of the Antarctic Circumpolar Current and the presence of diatom blooms, which drive biogenic silica cycling (Tréguer et al., 2018), contributing to larger absolute variations compared to nitrate and phosphate.

The bottom panels of Fig. 16 track the temporal evolution of the global mean uncertainty from 1965 to 2023. The time-series demonstrates a long-term declining trend, corresponding to the historical evolution of global ocean observing systems. A notable decrease in the global mean Std occurs around 1990. This reduction in uncertainty aligns with the onset of the World Ocean Circulation Experiment (WOCE) (Siedler et al., 2001) and the Joint Global Ocean Flux Study (JGOFS) (Fasham, 2003), which marked the transition from sparse historical sampling to systematic global hydrographic surveys.

Entering the 21st century, the global mean uncertainties for all three nutrients remain generally stable at lower levels compared to earlier decades. For nitrate, the deployment of the Biogeochemical-Argo (BGC-Argo) float array post-2010 (Roemmich et al., 2019; Claustre et al., 2020) provided additional autonomous profiles, contributing to the sustained low uncertainty. For phosphate and silicate, despite the gradual decline in traditional shipboard measurements in recent decades and the lack of Argo-based sensors for these elements, their mean uncertainties remain relatively low, though a slight upward trend is observable in the most recent years. Ultimately, this analysis indicates that the Jingwei-Nutrients product provides stable reconstructions, while also highlighting the regions and periods where data sparsity introduces greater variance.