Scale-transformation Based Inversion Of Lunar FeO Abundance

The Moon, as the nearest satellite of the Earth, has been the outpost of human’sdeep space exploration and one of the mainstream detecting Targets. After enteringthe second period of lunar exploration in1990s, with the launching of manycountries’ satellites, people focus on the lunar high spectrum exploration. Their aim isto study the composition and distribution of lunar elements and minerals, and toexpand our understanding of the origin, history, formation and elevation of the Moon.After the comparison of BRDF models for arbitrary terrain, the BRDFconceptual model is selected, which is based on the principle of reflectivity and hassimple form and a clear physical meaning. The model is built on the basis of lunarsurface incoming and emergent radiation, which would simulate the reflectance usingthe radiance and DEM data. Because there is no atmosphere on the Moon, the effectof sky diffuse irradiance is ignored. Based on the lambert assumption, the totalincoming radiation is divided into two parts, as the solar direct irradiance and adjacentterrain-reflected irradiance. The former is the reflectance weaken caused by thetopographic relief, the latter is increases the irradiance entering the Target pixel, dueto the reflection from adjacent pixels. In this paper, a flat region is selected as thestudy area. And the slope, aspect and terrain-view factor are derived from the LOLADEM. And based on the three terrain parameters and solar spectrum, other parametersare calculated, as the incidence angle, emergence angle, direct component ofirradiance on a horizontal surface, total irradiance on a horizontal surface and binarycoefficient to control cast shadow. And at the same time, the effect of topographicfactors is taken into account. Then the M3L2reflectivity products are simulated usingthe L1B radiance data, which are compared with the real data.Our study is on the fundamental of geological mechanism and computationalgeometry, which would make sure the scale transformation has a clear physicalmeaning. By the interpolation method, LOLA DEM data with different spatialresolution, as140m、1km、5km and10km, are obtained, and the topographicparameters under different scales can be calculated. On the premise of invariable solarzenith angle、solar azimuth angle、sensor zenith and sensor azimuth, on the basis of principle of reflectivitynd the selected eight characteristic bands, the reflectance datawith70m spatial resolution is respectively scaled up to140m、1km、5km and10km.And the real Global model M3data is used for the method validation.The method for lunar surface FeO inversion includes graphical method,1-μmabsorption band method and multiple regression method. And the multiple regressionmethod is selected for the FeO inversion of Apollo17landing site. Based on thelatitude and longitude of Apollo and Luna sampling points and the lunar ground-truthFeO abundance provided by Lucey, the sampling points except Apollo17are foundusing M3data, and the reflectance of characteristic bands are extracted. Tworegression models, as liner model and band ratio model, are respectively established.Based on the least square method, and make sure the RMSE is minimal, the modelcoefficients of the two models are solved. The appropriate model is selected bycomparing the correlation coefficient and standard deviation.At present, the method for lunar FeO inversion is almost based on theClementine UV/VIS data and Lucey’s empirical formula. But Clementine has onlyfive bands, and the spectrum is discontinuous. What’s more, when inversion of lunarFeO abundance, the topography and scale effect are not taken into account. Based onthis, the M3data obtained by Chandrayaan-1is selected for the research of scaletransformation lunar FeO inversion, which has two kinds of spatial resolution, as70mand140m, and higher spectral resolution. And when the scale transformation iscarried on, the lunar surface topography is considered.Based on the up-scaling method and multiple regression model, the M3Globaldata is respectively resampled and scaled up to15km spatial resolution, and the FeOabundance of Apollo17landing site is calculated. In order to analyse the scale andtopographic effect, the inversed FeO abundance is compared with the measured valueof LP and LSCC data. The result shows that the scale and topography would affect theinversed FeO abundance, but not for its distribution. Before the FeO abundanceinversion, the scale and topography should be taken into account. The FeO inversionresult would be closer to the true value if the M3data is scaled up to the LP resolution.What’s more, it is necessary to carry on the scale transformation before the FeOabundance is inversed.