Thermal emission from a layered medium bounded by a slightly rough interface

The small perturbation method (SPM) is applied to study thermal emission from a layered medium bounded by a slightly rough interface. Brightness temperatures are calculated to second order in surface height, including both specular reflection coefficient corrections and incoherent Bragg scatter terms. Unlike the homogeneous medium case, in which the SPM applied for emission predictions produces an expansion in surface slope, the theory remains a small height expansion, and convergence of the series is shown to depend on properties of the layered medium. Results from this theory can be applied in studies of soil moisture, sea ice, or sea surface remote sensing and buried object detection with microwave radiometers.