Is the kinematic boundary condition on the water surface enough to specify the potential function $\phi$ ?

Okay, now we have a kinematic boundary condition for the water surface, but there is a problem. We do not know before hand the position of the water surface, and we do not know the potential function $\phi$. We have only one equation, but two unknowns, $\phi(x,y,z)$ and $\eta(x,z,t)$. We need another boundary condition for the potential function $\phi(x,y,z)$ at the water surface.