A Microwave Brightness Temperature Model For The Lunar Regolith With A Rough Surface

The Chang'E-1 Lunar Orbiter(CE-1) took Microwave radiometer of four channels(3.0,7.8,19.35,37GHz). One important task of CE-1 is for detecting the thickness of the lunar regolith though the measured brightness temperature from the CE-1 microwave radiometer. To reserve the lunar regolith from the brightness temperatures of the multichannels microwave radiometer at 3.0, 7.8, 19.35, and 37GHz aboard on CE-1, an accurate forward model for the brightness temperature of the lunar surface is needed.In the existing emission models for lunar regolith, many factors which influence the brightness temperature (TB) are considered, such as the regolith layer thickness, temperature distribution, the lunar soil bulk density and the dielectric permittivity profiles. And, of most models, the assumptions are flat surfaces of the lunar regolith. However, as we know, there are undulating terrains in the range of 35–50 km, spatial resolutions of multichannels microwave radiometer, especially for the highest frequency channel. Moreover, even for areas with flat terrains, for an example, Mare, the surface is still rough for high microwave frequencies. Therefore it is necessary to study the influence of the surface roughness on the TB of lunar regolith.To build the rough lunar surface radiative transfer model, exact scatterring model and radiative transfer model are needed. The passage introduced random rough surface scattering theory firstly, and verified kirchhoff's approximate method and the perturbation method of energy conservation. Secondly the paper introduced radiative transfer theory , and calculated the four frequencies of microwave brightness temperature using the first-order multi-layer model of Burke ,then calculated the rough interface semi-infinite medium of microwave radiation brightness temperature. Lastly combining the random rough surface scattering theory and radiative transfer theory, established the model of rough surface microwave radiation transmission, and calculated the brightness temperature of lunar surface in different roughness condition and the different regions of lunar and analysted the brightness temperature of each channel with the measured data of Chang'E-1.The result is shown that a rough surface will increase the microwave radiative brightness temperature of lunar surface, and the increment will become bigger along with the increase of roughness. That, to some extent, explained why the brightness temperatures calculated by the radiative transfer model for a plane stratified medium are always smaller than the observed data by microwave radiometers at high frequencies.