Hydrodynamic models are important for the design, simulation and control of wave energy converters (WECs). Linear hydrodynamic models have formed the basis for this and have been well verified and validated over operating conditions for which small amplitude assumptions apply. At larger amplitudes a number of nonlinear effects may appear. One of these effects is due to the changing bouyancy force as the body moves in and out of the water. In this paper we look at identifying a nonlinear static block to be added the linear hydrodynamic model to account for this effect. The parameters for this nonlinear block are identified from WEC experiments simulated in a numerical wave tank (NWT). The parameters for the linear hydrodynamic model are also identified from NWT experiments. Here we explore the use of a discrete time linear hydrodynamic model which is well suited to the identification procedure