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The one of the greatest contributions of Professor Adrian K. Fung to the microwave remote sensing is the development of the integral equation model that has significantly improved and advanced our ability in modeling microwave surface emission and scattering signals. The surface emission and scattering model is one of the essential components in many applications of the microwave remote sensing of geophysical properties in the complex earth terrain. It is a direct component in monitoring soil moisture in the bare surfaces. The surface emission and scattering model serves as the boundary condition in studying snow, vegetation, and atmospheric properties. It has been found that the underground surface emission and scattering signals have a great impact on snow water equivalence and vegetation properties retrieval. How the multi-frequency and polarization measurements to be used correctly in deriving the surface geophysical and atmospheric properties is an important research issue in microwave remote sensing. It is heavily depending upon our understanding on the ability of modeling surface emission and scattering signals. In honor of Professor Adrian K. Fung, this paper demonstrates how the integral equation model has been used in the developing the retrieval algorithms for several geophysical parameters, including soil moisture and vegetation properties.