ABSTRACT
Satellite altimetry provides an essential constraint for all uses of data assimilation, including climate applications such as ocean reanalysis and operational oceanography. This chapter introduces elements of ocean modeling and Ocean data assimilation, both with a focus on sea level and presents some exposure to ocean fluid dynamics, though the material is reasonably self-contained. It describes the dynamical framework for ocean circulation models and discusses various theoretical frameworks to use for understanding sea level evolution and spatial structure. The chapter summarizes elements of data assimilation, with an emphasis on ocean climate studies and presents examples of ocean modeling and data assimilation in the context of satellite altimetry. To formulate the discrete equations of an ocean model, it is useful to transform the material parcel equations into Eulerian flux-form equations. The oceanic Boussinesq approximation is based on the observation that dynamically relevant density changes are quite small in the ocean, thus motivating an asymptotic expansion around a global mean density.
