Effects Of Small-and Big-scale Roughness On Microwave Radiative Brightness Temperature Of Lunar Regolith

The lunar surface is rough surface with not only large-scale roughness liketopography but also small-scale roughness. On one hand, previous studies on theeffects of the small-scale rough lunar surface on microwave brightness temperature(hereafter TB) are based on geometric optics, which are valid only when microwavewavelength much smaller than the radius of curvature of the rough surface. The defectof the models is the absence of explicit wavelength dependence. In some area withflat terrain such as the maria, the surface of lunar soil can be regarded as a slightlyrough surface. In the paper, mare regolith is modeled as a multi-layer planar layeredmedia with slightly rough top surface. The temperature profile is gotten by solving theheat conduction equation. The noncoherent method is utilized to calculate theemission of the multi-layer media. To calculate the effect of the rough top surface onTBs, we use the bistatic transmission coefficients by applying the second-order SPM(small perturbation method). Then according to the presented TB model, themicrowave TBs of Apollo12area under different roughness conditions are calculated.The results show that a slightly rough lunar surface will decrease or increase themicrowave radiative TB of lunar surface and that the change is related to theroughness, incidence angle, frequency and polarization. Especially, for Chang’E-1and Chang’E-2microwave radiometer, where incidence angle is0°, the small-scaleroughness will increase TBs of lunar surface. On the other hand, there are few studieson the effects of the large-scale roughness on the TB of the lunar regolith radiationboth at home and abroad. In the paper, we first model a small region (like footprint onlunar surface of Chang’E-2Antenna) of lunar terrain as two parts, one is the tilt datumplane, the other is two-dimensional roughness on that datum plane, by using theglobal lunar topographic data from Lunar Orbiter Laser Altimeter (hereafter LOLA).Then we deduces the formula of effective solar irradiance according to the lunarterrain model, and substitute it to the heat conduction equation, improve the numericalsolution of the equation to get a more accurate temperature profile. Finally we use thetemperature profile and the stratified TB model to calculate TBs of three typical areas,Apollo15area, Aristoteles crater and Hercules crater, and compare them with Chang’E-2measured TBs. The result shows that the rule of the calculated TB oflarge-scale rough surface changing with the latitude keeps consistent with themeasured TB, which is much better than plane surface model. So the influence oflarge-scale roughness must be taken into account when calculating TB.