This paper presents a composite interaction formula based on the discrete-interaction operator of wave-wave nonlinear interaction for deriving its adjoint source function in the wave assimilation model. Assimilation experiments were performed using the significant wave heights observed by the TOPES/POSEIDON satellite, and the gradient distribution in the physical space was also analyzed preliminarily. This paper presents a composite interaction formula based on the discrete-interaction operator of wave-wave nonlinear interaction for deriving its adjoint source experiments in the wave assimilation model. The Assimilation experiments were performed using the significant wave heights observed by the TOPES / POSEIDON satellite, and the gradient distribution in the physical space was also analyzed preliminarily.