Solving calibration and reanalysis challenges of ocean biogeochemical dynamics with neural schemes: a 1D vertical model case-study

Numerous studies in climate and ocean sciences have highlighted the crucial role of ocean biogeochemical (BGC) models in studying and monitoring the global carbon cycle. Despite major advances due to both modelling and observation efforts, the quantification and reduction of the uncertainties in ocean BGC processes remain a key challenge. These difficulties arise primarily from the scarcity of observational datasets and the considerable uncertainties in ocean physics. Current ocean physics reanalyses still struggle to accurately represent the ocean's complex dynamics, particularly at small scales, which play a critical role in driving biogeochemical cycles. Consequently, the performance of operational ocean Data Assimilation (DA) systems remains limited when applied to BGC dynamics, using both BGC observations and physical reanalyses. This stands for model calibration and reanalysis applications. Here, we explore machine learning approaches to address these challenges. To this end, we develop an Observing System Simulation Experiment (OSSE) framework for 1D ocean BGC dynamics, designed for both training and benchmarking purposes. We rely on a differentiable programming code of a 1D Nitrate-Ammonium-Phytoplankton-Zooplankton-Detritus (NNPZD) ocean BGC model forced by solar irradiance and vertical mixing. The proposed OSSE incorporates location-dependent uncertainties in physical forcings and considers realistic configurations of in situ observing systems. Based on these OSSEs, we design numerical experiments addressing both the calibration of BGC model parameters, the reconstruction of 1D ocean BGC state variables from sparse observations and the reduction of the uncertainties in the physical forcings. For calibration and inversion, we investigate a model-based variational DA scheme, an end-to-end deep learning scheme and their hybrid combination. Our results demonstrate the potential of learning-based schemes to substantially reduce calibration uncertainties and improve physical forcing estimates. When coupled with a variational DA scheme, the learning-based approach yields enhanced reconstructions of ocean BGC state variables. Sensitivity analyses with respect to forcing uncertainties and observing system configurations provide insights into how these findings could be extended to real-world ocean BGC modelling and monitoring.