Dynamic Constraints in Local Ensemble Transform Kalman Filter (LETKF) for the Coastal Ocean

The state of ocean in numerical models is constrained by several relationships, such as the equation of state, temperature-salinity relation and geostrophic and thermal current balances. During data assimilation (DA), analysis may not sustain the reasonable dynamic balances as model background, because of the no guarantee of dynamic consistence between various types of observations. Hence, dynamic constraints are applied in DA schemes to address this issue. In multivariate DA, this application has usually been done in variational schemes. In this study, dynamic constraints with the help of variable localization has been employed into an advanced ensemble Kalman filter, Local Ensemble Transform Kalman Filter (LETKF) within the framework the Regional Ocean Modeling System (ROMS). The LETKF with dynamic constraints and variable localization is formulated. The ROMS-LETKF has been applied off the California coast to test its performance through the observing system simulation experiments (OSSEs) in idealized California current system. The role of dynamic constraints in the ROMS-LETKF is verified by a set of single observation experiments. The experiments assimilating a variety of observations present the ability of ROMS-LETKF with dynamic constraints to reproduce the complex meso-scale variations and processes in California coast, such as upwelling. This study indicates the possibility and effectiveness of the application of dynamic constraints in ensemble DA schemes.