This study presents the development and sensitivity analysis of the sea level operator within the OceanVar software which implements an oceanographic incremental three-dimensional variational data assimilation scheme. In OceanVar, the background error covariance matrix is decomposed into a sequence of physically based linear operators, allowing for individual analysis of specific error matrix components. The key development of OceanVar2.0 is the full integration of both dynamic height and barotropic model formulations as a flexible option for handling sea level covariance. The comparison of the two formulations of the sea level operator which provides correlations between Sea Level Anomaly, temperature and salinity increments is presented. The sensitivity experiments were performed in the Mediterranean Sea and the quality of the analysis assessed by comparing background estimates with observations for the period January–December 2021. The results confirm the methodological advantage of the barotropic model operator, which successfully overcomes the physical and operational limitations associated with choosing an appropriate level-of-no-motion for the dynamic height formulation. Furthermore, we present a method to assimilate along-track satellite altimetry considering a forecasting model with tides. © 2026 Paolo Oddo et al.

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