Geographic-dependent variational parameter estimation: A case study with a 2D ocean temperature model

Using observational information to tune uncertain physical parameters in an ocean model via a robust data assimilation method has great potential to reduce model bias and improve the quality of sea temperature analysis and prediction. However, how observational information should be used to optimize geographic-dependent parameters through four-dimensional variational (4DVAR) data assimilation, which is one of the most prevail-ing assimilation methods, has not been fully studied. In this study, a two-step 4DVAR method is proposed to enhance parameter correction when the assimilation model contains biased geographic-dependent parameters within a biased model framework. Here, the biased parameters are set to an oceanic eddy diffusion coefficient, Kv, that plays an important role in modulating synoptic, seasonal and long-term changes in ocean heat content. Within a twin assimilation experiment framework, the temperature "observations" generated from sampling a "truth" model are assimilated into a biased model to investigate to what extent Kv can be estimated using the 4DVAR method when Kv remains geographic-dependent. The results show that the geographic-dependent Kv distribution can be optimally estimated to further improve the sea temperature analysis performance compared with the state estimation only method. In addition, the model prediction performance is also discussed with optimally estimated parameters under various conditions of noisy and/or sparse ocean observations. These re-sults provide some insights for the prediction of ocean temperature mixing and stratification in a 3D primitive ocean numerical model using 4DVAR data assimilation.