Deep learning-driven 3D marine nitrate estimation: uncertainty mitigation through underwater signal exploitation and label augmentation

Nitrate is a critical limiting nutrient that significantly influences marine primary productivity and carbon sequestration. However, three-dimensional observation and reconstruction of oceanic nitrate remain constrained by the scarcity of in-situ data and limited spatial coverage. To address the challenge of limited observational labels hindering the development of global deep learning models for marine three-dimensional estimation, this study proposes a novel deep learning framework that utilizes underwater signals for label augmentation, thereby reducing the uncertainty in three-dimensional nitrate estimation. Initially, we employ a Bayesian neural network, utilizing multiple subsurface parameters from Biogeochemical-Argo (BGC-Argo) measurements to generate virtual nitrate labels with quantified uncertainty. These augmented labels are then assimilated into a U-Net-based model, greatly expanding the training dataset and further integrating sea surface environmental variables for comprehensive three-dimensional reconstruction. The proposed uncertainty-weighted loss function refines model training, balancing the quality and training impact of both observed and augmented labels. Quantitative evaluations using BGC-Argo and cruise measurement data demonstrate notable improvements in spatial and temporal generalization, with RMSE reductions of approximately 15% and 28%, respectively, particularly in under-sampled areas and complex upper ocean regions. This research framework offers a promising solution for oceanic three-dimensional data reconstruction in the absence of supervised data and has the potential to be coupled with various marine parameters and reconstruction models, providing deeper insights into the spatiotemporal variations of marine environments.