In the Tianwen-1 Mars exploration mission, ultrawideband radar is carried by the Zhurong Martian rover. The exponential attenuation at the center frequency was applied to invert the loss tangent of Mars regolith in previous studies. Ignoring the frequency-dependent absorption in the ultrawideband might cause a large error in the inversion results. Considering the transmitted linear frequency-modulated (LFM) waves, in this letter, an analytical formula for the attenuation of ultrawideband waves to invert the loss tangents of Martian regolith is derived with the accumulation of the frequency-dependent attenuated spectrum. The newly inverted loss tangent is much larger than the inverted values with the center frequency. In addition, the inversion of the loss tangent from the ultrawideband radar data obtained in the Chang’e-5 lunar program is discussed. This letter presents a corrected inversion method for the loss tangent of regolith from ultrawideband radar echoes.

Finding a flat area is critical for choosing the landing site, especially in the permanently shadowed region (PSR) without reference of optical images. The digital elevation model (DEM) data are not enough to describe the complex lunar topography in the landing mission. High-resolution polarimetric synthetic aperture radar (pol-SAR) can acquire the polarized scattering map of lunar surface. In this letter, Chandrayaan-2 pol-SAR images of flat and rocky regions at non-PSR are selected with the assistance of optical image. The statistics of the Stokes parameters can tell the difference between flat and rocky surfaces. Enhanced backscattering with a large variance from rough surfaces with rocks can be distinguished from the smooth and flat areas. Large value of the first Stokes parameter$I_{1}$with extendedly distributed probability distribution function is related with the scatterings from rough surface and rocks. A statistics rule of the Stokes parameters is established and is applied to identify the flat regions in the PSR of the crater Shoemaker.

The circular polarization ratio (CPR) was defined in compact-polarization (pol) mode as an indicator of water-ice in lunar PSR (permanently shadowed region). CPR is a composite pol-parameter described by co-pol and cross-pol scattering components, which caused by surface roughness and rocky objects on surface. In this paper, CPR is derived with linear-pol and circular-pol scattering components. Radar echoes from different rough surfaces are numerically simulated with the bidirectional analytic ray tracing (BART) method. The CPR, degree of polarization$(m)$and the relative phase$(\delta)$are numerically presented. As an example, Mini-RF radar images of the PSR crater Hermite-Band no- PSR crater Byrgius C are analyzed to illustrate how the roughness lead to different CPRs inside and outside the intermediately degraded craters.

Direct sampling has never been performed in the permanently shadowed regions (PSRs) of lunar poles up to now. In the Chinese Chang’e-7 (CE-7) mission, a mini-flyer will fly from the lander in a solar illuminated region at the lunar south polar region to the nearby PSRs to collect samples for analysis. In this letter, four potential craters of the lunar south pole, including Shackleton, Shoemaker, de Gerlache, and Slater are discussed for this proposal. Design principles of the landing site, sampling site, and flight route are presented. The local surface slopes are calculated using a digital elevation model (DEM) to select a flat area as a potential landing site, which should allow ample time for solar illumination to support the rover from the lander and allow the flyer to reach the neighboring PSRs. Mini-RF data are applied for further validation of the flat landing and sampling sites, particularly for some rocky rough surfaces that are not identified in DEM and optical images of PSRs. The craters de Gerlache and Slater are found to be suitable for further analysis when high-resolution synthetic aperture radar (SAR) data are acquired by the new polarimetric SAR carried by CE-7.

High circular polarization ratio (CPR) characteristics were found in permanently shaded regions (PSRs) near the lunar poles. High CPR was regarded as a water ice index. The compact-polarimetric (CP) miniature radio frequency (Mini-RF) radar transmits left-circularly polarized signals and receives horizontally polarized ($S_{\text {HL}}$) and vertically-polarized ($S_{\text {VL}}$) echoes from the lunar surface. Statistics of the CPR data show its relations with the relative phase ($\delta$) between$S_{\text {HL}} $and$S_{\text {VL}} $and the degree of polarization ($m$) but few interpretations were provided. The average CPR data reach the maximum and minimum at$\delta =\pm 90^{\circ }$, respectively. As$m$becomes very small, the CPR approaches 1. It has been found that CPR is also affected by surface roughness and incidence angle of radar waves. The CPR is now expressed in CP mode to explain the Mini-RF observation. Full-polarimetric radar echoes and CP parameters of the lunar surface are numerically simulated using the bidirectional analytic ray-tracing method. Single-bounce and multiple-bounce scattering components are included in the simulation. Radar images of the lunar crater are simulated with the digital elevation model (DEM) data. The$H-\alpha $decomposition derived from the full-polarimetric simulation is presented to analyze$\delta $and$m$. Simulated radar images with different surface roughness are analyzed statistically to study the functional dependences of$\delta $,${m}$, and CPR on incidence angle and roughness. Relationships among$\delta $,$m$, and CPR are used to analyze the effects of incidence angle, roughness, TiO2, and rock abundance on the scattering components. The CPR,$m$, and$\delta $of PSR craters of different ages are compared with those of nonpolar craters. The results indicate that the CPR,$m$, and$\delta $are unlikely to be unambiguous evidence of water ice.

The Moon’s surface shows long-term stability and may be a suitable candidate of thermal calibration source. When the field of view (FOV) of an Earth radiometer, e.g., the high-resolution infrared radiation sounder (HIRS), occasionally scans across the Moon, it measures the average brightness temperature (TB) of the entire nearside of the Moon. The lunar surface roughness causes changes in the surface emissivity and anisothermality. Analysis of the infrared TB (IR TB) of the lunar surface from the nadir observations of the Diviner IR radiometer showed that the IR TB difference (TB-D) between the Diviner channels is largest near sunrise and sunset, when the anisothermality is most significant. In this article, the nearside of the lunar surface is divided into$30\times 30$subregions, where a rough surface is constructed using small triangular meshes. The ray-tracing method is used to determine the shaded meshes. Heat conduction equations are solved for the temperatures of all meshes. The simulated IR TB and TB-D are compared with the Diviner data. The thermal emissions of Gaussian rough surfaces with different height variances, the cratered surface with digital elevation model, and two-scale rough surface are simulated to discuss the influence of topographies. Under nonnadir observation conditions, the ray-tracing method is used to determine the visibility of each mesh in the detector’s FOV. The IR TB characteristics are asymmetric with respect to the emission angle. The average IR TB of the nearside of the Moon at the wavelength of$14~\mu \text{m}$is obtained and compared with the IR TB derived from HIRS data. The rough surface model can more feasibly describe the average IR TB data than flat surface model and is favorable for HIRS calibration/validation.

Calibration of satellite-borne radiometer is a key issue for quantitative remote sensing. Its accuracy depends on the stability of the calibration source. Because of no atmosphere and biological activity, the Moon surface keeps stable in the long term and may be a good candidate for thermal calibration. Observation of microwave humidity sounder (MHS) onboard the NOAA-18 made measurements of the disk-integrated brightness temperature (TB) of the Moon for the phase angle between -800 and 500. The measurement of NOAA-18 has been studied to validate the TB model of lunar surface. In this article, the near side of the Moon surface is divided into 900 subregions with a span of 60 x 60 in longitude and latitude. By solving 1-D heat conductive equation with the thermophysical parameters validated by the Diviner data of the Lunar Reconnaissance Orbiter (LRO), the temperature profiles of the regolith media in all 900 subregions are obtained. The loss tangents are inversed from the Chang'e-2 (CE-2) 37-GHz microwave TB data at noontime. Employing the fluctuation-dissipation theorem and the Wentzel-Kramer-Brillouin (WKB) approach, the microwave and millimeter-wave TBs of each subregion are simulated. Then, the weighted average TB can be disk-integrated from 900 TBs of all subregions versus the phase angle. These simulations well demonstrate diurnal TB variation and its dependence upon the frequency channels. It is found that the disk-integrated TB of the Moon in MHS channels is sensitive to the full-width at half-maximum (FWHM) of the deep space view (DSV), which is corrected in our simulation, where the Moon is now taken as an extended target, instead of a point-like object. Simulated integrated TBs are compared with the corrected MHS TB data at 89, 157, and 183 GHz. The simulated TB is well consistent with these MHS TB data at 89 and 183 GHz at various phase angles. But the maximum TB of MHS data at 157 GHz is unusually lower than that of 89 GHz. The influence of the loss tangent, emissivity, and the pointing error is analyzed. Some more careful design to observe the Moon TB and technical parameters, especially the FWHM should be well determined. Our model and numerical simulation provides a tool for TB calibration and validation.

The permanent shaded regions (PSRs) at the lunar poles receive no direct solar illumination throughout the year, so their temperatures are extremely low. The PSR is mainly heated by the radiation heat flow and the scattered solar radiation from the sunlit crater wall. The temperature distribution in the PSR and its diurnal and seasonal variations have been calculated using the ray-tracing method, which determines the radiation heat flow and the scattered solar radiation. In this article, the radiation heat flows were calculated by anisotropic emissivity of the PSR, and the scattered solar radiation was calculated using the lunar Lambert model. To conform to the Diviner IR temperature data, the 1-D heat conduction equation was solved with modified heat conductivity (an important parameter of the regolith media). As an example, the daytime and nighttime temperatures in the Hermite-A crater at the North Pole during summer and winter were numerically simulated and were compared with the Diviner IR data. In addition, rocks near the central peak of the crater in the PSR may enhance the nighttime temperature. This was validated by the PSR images captured by the Lunar Reconnaissance Orbiter Camera (LROC), the Miniature Radio Frequency instrument data on the LRO, and the numerical simulations.

A small tilt in the spin axis of the moon over the ecliptic plane causes seasonal incidence variation of solar illumination and, especially, causes significant temperature difference at the polar region. In this article, following the position of the subsolar point, the real-time model of solar illumination incidence over the moon polar region is developed. Based on this model with solving the 1-D heat conduction equation, the seasonal temperature of the lunar surface is obtained and is in agreement with the Diviner infrared (IR) data. Meanwhile, using the fluctuation-dissipation theorem and the Wentzel-Kramers-Brillouin (WKB) approach for lunar regolith media, the seasonal microwave (MW) brightness temperature (TB) is also obtained and validated by Chang'e-2 (CE-2) 37-GHz TB data. These data also show that the lunar surface temperature and the MW TB even in the permanent shaded region (PSR) undergo seasonal variation as well. It might be due to the seasonal thermal radiation on the topographic PSR coming from the sunlit crater walls caused by seasonal temperature variation. The Diviner IR data show that the highest temperature in the Hermite-A crater at the north polar PSR can reach 109 K in summer.

Circular polarization ratio (CPR) was regarded as an important index for water ice existence in permanently shadowed region (PSR) of the Moon poles. However, some studies have intuitively described that the double bounce scattering caused by dihedral structure of stone facets may yield high CPR as well. In this paper, a numerical model of the Moon cratered rough surface with volumetric scatterers, e.g. rock-stones, is developed. The bidirectional analytic ray tracing (BART) method is applied to numerically solve high-order scattering of lunar rough surface and volumetric rock-stones. The lunar surface is modeled by Digital Elevation Model (DEM) data from Lunar Reconnaissance Orbiter (LRO) Lunar Orbiter Laser Altimeter (LOLA). It is the first numerical approach to quantitatively analyze how the cratered surface topography, discrete stones and radar local incidence etc. affect and enhance the CPR.

The Moon is a good calibration source for the millimeter-wave radiometer onboard the Feng Yun-4 Millimeter (FY-4M) satellite. The temperature profiles of the lunar surface can be obtained by solving the one-dimensional heat conduction equation with the thermo-physical properties of regolith. Then, the loss tangent is fitting using the Chinese Chang'e-2 (CE-2) 37GHz brightness temperatures (TB) data against TiO2 abundances, which is derived from Clementine five-bands multispectral data. The calculated surface temperatures and the TBs are validated by Diviner infrared data and CE-2 37GHz TB data. With the theoretical analysis of the radiative transfer, the TBs at FY-4M frequencies of lunar center area is obtained for calibration. In addition, the abnormal thermal emission at "cold spots" should be excluded for calibration.

One of Chinese meteorological satellites, Feng Yun-4M (FY-4M), as one the of new generation of geosynchronous series satellites, is planning to upload multichannel millimeter-wave radiometers, e.g., from 50 to 430 GHz. Due to long-period stability and no atmospheric interference, brightness temperature (TB) of the lunar surface can be seen as a good candidate for thermal calibration of FY-4M radiometers. In this paper, the physical temperature profile of lunar regolith media is first derived by resolving 1-D heat transfer equation with validation of the measurements of the Diviner lunar radiometer experiment onboard the lunar reconnaissance orbiter. Then, the loss tangent is fit and validated using the TiO2 abundances, which is derived from Clementine five-band multispectral data and Chinese Chang'e-2 37-GHz TB data. Multichannel TB of a lunar surface region along the moon equator at certain lunar time (noon and midnight) is numerically derived for all FY-4M channels. TB of lunar equator center area (0°N, 0°E) is presented with variation of the lunar local time. These results can be well applied to calibration of FY-4M, with a sustainable error in the range of 1.8 (425 GHz) to 3.8 K (89 GHz).

The anomalous “hot spots” in infrared (IR) bands on lunar surfaces were discovered earlier in the 1960s. It was then found that those “hot” spots in IR turned out to be “cold” spots at night in microwave (MW) bands observations by Chinese CE-1, CE-2 (Chang'e) radiometers. It was intuitively explained by the thermal properties of a large number of rocks over the cratered surface. In this paper, a radiative transfer layering model of rocks over regolith is presented for the quantitative analysis of the anomalous IR “hot” and MW “cold” spots. First, the physical temperature profiles of the rock/regolith media are derived by solving the 1-D heat conduction equation. Brightness temperatures (TB) of these media in both IR and MW are obtained. Due to large inertia of rocks, its temperature is higher than regolith surface at night and causes IR “hot spots.” However, quickly cooled surface at night reverses the temperature profile of the regolith. Due to the MW penetration, warm regolith beneath the surface without rocks can contribute more TB in comparison of “cold spots” of the rocky surface. Based on the thermo-physical and dielectric parameters of layering rock and regolith media, the quantitative results of our radiative transfer model in both IR and MW bands well match the data of Diviner IR and CE-2 MW-37 GHz.

Searching for water–ice in the lunar media has been a key issue in the moon explorations. Missions of mini-SAR and mini-RF SAR made compact-pol (polarization) measurements on lunar polar permanent shadowed region (PSR). High circular polarization ratio (CPR) data and a two-layer model were applied to studying if water ice in PSR could be retrieved. However, it has been studied that high CPR is not simply due to the presence of water ice, and the Campbell model is a degenerated half-space model, which confused final inversion. In this letter, using the mini-RF data on the PSR of Hermite-A crater on the north pole, a two-layer model with the Kirchhoff and small perturbation approximations is presented. It takes account of the surface-layering topography, which makes changes of local incidence and polarimetric base rotation. Our results do not support Calla’s conclusions based on the half-space model, suggesting that the inversion of mini-RF is not so straightforward in proving water–ice existence in the PSR media. It points out that the double- and high-order scattering of random volumetric scatters on the lunar surface might play a role, and high-resolution measurements and more elaborate modeling are needed for further studies.

Radar range echoes of the UHF radar souder is presented to explore the lunar surface in the permanently shdaowed polar regions (PSR). Based on radiative transfer with the Euler-angles transformation, the temporal Mueller matrix to take account of all scattering mechanisms of undulated rough surface and underlying scatter media is derived. It is applied to invert the dielectric constant of PSR region for water ice detection.

Dielectric inversion of lunar permanently shadowed region (PSR) of moon poles has been studied for estimation of possible water-ice content. The Campbell model was directly applied to mini-SAR data for inversion on the Hermite-A crater region. However, this letter presents quantitative analysis that the lunar surface topography, i.e., surface roughness and slopes, and underlying dielectric media, and so on, can significantly affect this inversion. The model is actually degenerated into a half-space model without topographic account. This letter presents a two-layer model of Kirchhoff-approximation surface/small perturbation approximation subsurface to take account of all these topographic factors for PSR dielectric inversion.