A continual learning-based multilayer perceptron for improved reconstruction of three-dimensional nitrate concentration

Abstract. Nitrate plays a crucial role in marine ecosystems, as it influences primary productivity. Despite its ecological significance, accurately mapping its three-dimensional (3D) concentration on a large scale remains a considerable challenge due to the inherent limitations of existing methodologies. To address this issue, this study proposes a continual learning-based multilayer perceptron (MLP) model to reconstruct the 3D ocean nitrate concentrations above 2000 m depth over the pan-European coast. The continual learning strategy enhances the model generalization by integrating knowledge from CMEMS nitrate data, effectively overcoming the spatial limitations of BGC-Argo observations in comprehensive nitrate characterization. The proposed approach integrates the advantages of extensive spatial remote sensing observations, the precision of Biogeochemical Argo (BGC-Argo) measurements, and the broad knowledge from simulated nitrate datasets, exploiting the capacity of neural networks to model their nonlinear relationships between multi-source sea surface environmental variables and subsurface nitrates. The model achieves excellent performance in profile cross-validation (R² = 0.98, RMSE=0.522 µmol · kg⁻¹), and maintains robustness across diverse 3D validation scenarios, suggesting its effectiveness in filling observational gaps and reconstructing the 3D nitrate field. Then, the spatiotemporal distribution of the reconstructed 3D nitrate field from 2010 to 2023 reveals a spatial distribution pattern, an interannual upward trend, and the degree of consistency in vertical variation. The contributions of all 22 input features to the model's estimation were respectively quantified by using Shapley additive explanations values. This study reveals the potential of the proposed approach to overcoming observational limitations and enrich further insights into the 3D ocean condition. The reconstructed 3D nitrate dataset is freely available at https://doi.org/10.5281/zenodo.14010813 (Yu et al., 2024).