In polar and mid- to high-latitude regions, snow accumulates every year which covers the Earth's surface. In order to carry out geophysical work in such regions, prior knowledge of snow thickness is essential. In the present paper, the emitted brightness temperature based on an incoherent approach has been calculated for various two-layered snowpack models representative of the snow-covered terrains. The effect of snow surface roughness caused by local winds and snow melting on passive microwave remote-sensing response has also been studied. The comparison of theoretically calculated brightness temperature with the measured data shows good agreement. The results presented in this paper will be useful in the analysis and interpretation of microwave remote-sensing data of snow-covered terrains.