The initialization and forcing of embedded coastal ocean models is shown to raise several serious difficulties, however, surprisingly enough, very little attention is paid by coastal modelers to resulting dynamical discrepancies introduced over both short and long time scales. A modular and "Knowledge accumulating" approach for coastal ocean embedded modeling is proposed based on a variational approach. The extrapolation situations mostly associated to bathymetry constraints are discussed and are shown to be of great importance for any embedded coastal model. A well adapted extrapolation scheme is proposed. Two variational constraints are more particularly shown to lead to important improvements of the downscaling: the mass balance is satisfied in a dynamically coherent way based on Green's theorem and an optimal scheme is presented to extrapolate both the temperature and the salinity in the deepest regions where no data is available.