An Adaptive Nudging Scheme with Spatially Varying Gain for Improving the Ability of Ocean Temperature Assimilation in SPEEDY-NEMO

Nudging remains a cost-effective data assimilation technique in coupled climate models, yet conventional schemes with fixed spatial strengths struggle to represent heterogeneous ocean processes. This study introduces an adaptive nudging framework in which a spatially varying gain matrix dynamically balances model and observational errors, providing a more physically consistent determination of nudging coefficients. Implemented in the SPEEDY-NEMO coupled model, the method is systematically evaluated against a traditional latitude-dependent scheme. Results show substantial improvements in subsurface temperature assimilation across key regions, including the Niño3.4, tropical Indian Ocean, North Pacific, North Atlantic, and northeastern Pacific. The most pronounced gains occur above and within the thermocline, where strong stratification renders fixed nudging strengths inadequate, yielding a 20–30% reduction in RMSE and a 30–50% increase in correlation. In mid- to high-latitude regions, improvements extend to greater depths, consistent with deeper thermocline structures. The adaptive framework corrects both systematic bias and variance, enhancing not only the mean state but also variability representation. Additional benefits are found in salinity, currents, and sea surface height, demonstrating that spatially adaptive nudging provides a more effective and practical alternative for improving ocean state estimation in coupled models.