Assimilation of Satellite Altimeter Observations in a Free-Surface Ocean Model Using a 4DVAR Analysis System

Ocean models rely on the assimilation of satellite observations of sea surface height (SSH) from altimeters in order to constrain circulation features in the simulation (i.e. ocean eddies, currents, etc.). This is especially difficult to do with ocean models that have a free-surface as direct assimilation of SSH observations tend to generate gravity waves when the free-surface is adjusted. To date, this problem has been circumvented by deriving synthetic profiles of temperature and salinity from the steric component of the SSH observations, then assimilating these profiles in order to adjust the model free-surface. Techniques such as the Cooper-Haines method (Cooper and Haines, 1996), the Modular Ocean Data Assimilation System (MODAS; Fox et al. (2002)) and the Improved Synthetic Ocean Profiles (ISOP; Helber et al. 2013) have been applied with good success. There are drawbacks to using synthetic profiles, for example the sheer number of profiles that are generated tend to overwhelm the assimilation process and make it more difficult to fit real in-situ profiles of temperature and salinity. Ngodock et al. (2016) introduced a method of direct SSH assimilation with a free-surface model that greatly reduced the gravity wave contamination using a four-dimensional variational (4DVAR) assimilation system. This method, while very useful, can still introduce gravity wave contamination through the baroclinic fields obtained from the adjoint. A new method, demonstrated here, relies on a steric height observation operator built for a 4DVAR assimilation system. This method maps model temperature and salinity to steric height in order to calculate the model-observation innovation. This innovation is then used to force the adjoint of the ocean model via the adjoint of the observation operator. This demonstration is done using the Navy Coupled Ocean Data Assimilation 4DVAR (NCODA-4DVAR) using an Observing System Simulation Experiment (OSSE) in the Gulf of Mexico in May through June, 2018. These results indicate that the assimilation of SSH observations using this steric height observation operator is able to accurately capture the nature run SSH field while at the same time avoiding the generation of gravity waves that can act to degrade the solution.