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

Nudging still is a cost-effective data assimilation technique in coupled climate models, but conventional schemes apply fixed spatial strengths and are less effective in representing heterogeneous ocean processes. An adaptive nudging framework based on a spatially varying gain matrix is proposed to dynamically balance model and observational errors. The method not only preserves the merits of the latitude-dependent nudging approach but also provides a more physically consistent determination of the spatial distribution of nudging coefficients. Implemented in the SPEEDY-NEMO coupled model, the framework is systematically evaluated against the traditional latitude-dependent scheme. Results show that the adaptive approach substantially improves subsurface temperature assimilation, particularly in the Niño3.4 region, the tropical Indian Ocean, North Pacific, North Atlantic, and the northeastern Pacific. In the tropics, the improvement is mainly achieved above and within the thermocline (roughly 100--200 m), where strong vertical stratification and sharp gradients make fixed nudging strengths inadequate:the RMSE decreases by 20% and the correlation with observations increases by 30% compared with the traditional latitude-dependent scheme. By dynamically adjusting the assimilation strength, the adaptive scheme better constrains the thermocline variability and surface-subsurface interactions. In mid- to high-latitude regions, the improvement extends to greater depths, consistent with a deeper thermocline, where oceanic processes dominated by the mixed layer dynamics and convection exhibit large regional biases that require spatially adaptive correction. In addition, compared with the latitude-dependent nudging scheme, the adaptive approach achieves simultaneous corrections of both the systematic bias term and the variance term of temperature deviations, thereby enhancing not only the mean state but also the model’s ability to capture variability. Generally, the root-mean-square errors decrease by 20-30% and the correlation with observations increases around 30-50% by the adaptive scheme. Beyond temperature, improvements are also evident in salinity, currents, and sea surface height anomalies, indicating the broader benefits of the adaptive scheme. These results indicate that spatially adaptive nudging provides a more effective and practical alternative to fixed schemes, offering a solid basis for improving ocean state estimation in coupled models.