Recently there has been growing interest in the application of polarimetry to active microwave remote sensing of geophysical terrain. However, for passive microwave remote sensing, the third and fourth Stokes parameters were usually neglected in the past. In this paper, we make theoretical calculations of brightness temperatures of the third and fourth Stokes parameters for geophysical terrain. The calculations are based on vector radiative transfer theory with emission vector for random discrete scatterers. We also derive the reciprocal relations between emission of third and fourth Stokes parameters and the bistatic scattering coefficients for rough surface problems. Numerical results are illustrated. It is shown that brightness temperatures for third and fourth Stokes parameters can be as large as ±60°K for certain statistical asymmetrical configurations of scatterers.