The exploration of the Moon has never ceased. One of the most significant challenges is determining the thickness of the lunar regolith. This paper employs the relative microwave brightness temperature (TB) to invert the thickness of the lunar regolith. A multi-layer parallel stratified model serves as the forward model. In the inversion process, the simulated microwave TB is derived by calculating the sum of the TB contributions from each layer. Based on the forward model, areas where the simulated TB is sensitive to lunar regolith thickness can be identified. Subsequently, the simulated TB is compared with the measured TB by the Chang'E-2 Microwave Radiometer (MRM) at 3 GHz at midnight (24:00) of the lunar local time. The discrepancy between the observed and modeled TB at a specified location such as the Apollo 12 landing site (A12) is regarded as a correction for the simulated TBs at other locations with the same latitude. Ultimately, the thickness of the regolith is inverted according to the corrected simulated TB. This paper compares the inverted result with the regolith thickness obtained by DEM data. It found that regions where the model inverted results closely align with the DEM data tend to have higher FeO/TiO2content. The uncertainty of the inversion is also discussed, which indicates that the method presented in this paper is feasible.

We present new model predictions of the earth-directed microwave brightness temperatures (TB) of the moon with dependence on phase angle over the wavelength range of 1 mm – 10 cm. Both disk average and global maps are included. The models are based on detailed thermophysical property retrievals provided by Apollo in situ measurements, Diviner and Chang E’2 (CE2) global measurements, and high quality pre-Apollo earth-based observations. Of particular importance are the advances in electrical property (loss tangent) determinations provided by the CE2 lunation amplitude data. A detailed error analyses is included to provide estimates of the TB model error bounds due to realistic assessments of the uncertainties of the contributing thermophysical properties. Disk average TB uncertainty levels of ~ +/- 4 K are found for wavelengths in the 1-10 cm range and ~ +/-8 K for ~ 1-5 mm wavelengths. Analyses are presented indicating that neither surface roughness nor potential correlation of the thermal parameter uncertainties significantly impact the model total error budget. The new models are proposed as stable absolute calibration references for earth-based microwave radiometers, in particular the vast array of earth-orbiting instruments now monitoring weather and climate properties globally.

Basic radiative transfer theory reveals that the physical temperature gradients related to heat flow (HF) within the lunar regolith below the diurnal varying layer can be constrained by measurements of brightness temperature (TB) variations over a selected wavelength range, coupled with knowledge of the regolith electrical loss properties. We present a methodology illustrating the processing using recalibrated data from the Chang’E-2 (CE2) 10 and 3.85 cm wavelength microwave radiometer (MRM) data (channels 1 and 2). The utilized data are contained in latitude bins of 1 degree width centered at latitudes of 0, 5,..., 60, north and south. Results, presented as retrieved HF gradients (dT/dz in K/m) vs longitude for each of the 25 latitude bins, provide useful constraints on the overall variability of the heat flow gradient within the 60S-60N latitude range. In particular, no evidence is found that HF variations exceeding twice the Apollo value occur widely in the extensive highland regions of low electrical loss. Limitations related primarily to signal-to-noise (SNR) issues in regions of elevated electrical loss severely reduce thermal gradient retrieval accuracy needed for correlation with enhanced thorium concentrations observed in the frontside mare. Analyses of the CE2 data reveals a noise uncertainty of ~ 0.5 K in the TB10-TB3.85 measurements, equivalent to ~ 0.7 - 1.4 (loss tangent dependent) times the Apollo measured mean HF value of 1.8e-6w/cm2. The limitations preclude meaningful identification of regional variations within a precision less than one Apollo heat flow unit. An analyses is presented demonstrating that a threefold increase in SNR would be attained by addition of a 30 cm wavelength channel to the CE2 MRM’s design, providing sufficient resolution to map regional HF variations to ~ 0.5e-6w/cm2precision, ~ 30% of the averaged Apollo sites’ measured HF value.

Lunar thermal conductivity is significantly important for understanding the geological processes of the Moon. The Apollo in situ heat flow experiments and diviner remote sensing data provide us with good constraints on the thermophysical properties of the lunar regolith fines layer. As the first farside in situ experiments, Chang’E-4 (CE-4) temperature sensors will further extend our understanding. In this study, a 1-D thermal model with updated bulk densities by the CE-4 lunar penetrating radar (LPR) data is used. Then, the nighttime surface temperatures from the sensors of the CE-4 lander are applied to retrieve the surface thermal conductivity at the CE-4 landing site. After minimizing the differences between the predicted temperature and CE-4 measurements, the range of surface layer contact conductivity ($k_{s}$) within the upper 1 cm is about (0.95–2.26)$\times 10^{-3}\,\,\text {Wm}^{-1}\cdot \text {K}^{-1}$for T1, (1.04–2.44)$\times 10^{-3}\,\,\text {Wm}^{-1}\cdot \text {K}^{-1}$for T2, (0.60–1.40)$\times 10^{-3}\,\,\text {Wm}^{-1}\cdot \text {K}^{-1}$for T3, and (0.60–1.39)$\times 10^{-3}\,\,\text {Wm}^{-1}\cdot \text {K}^{-1}$for T4, respectively. In addition, the factors that may affect the inversion or the measurements were discussed, such as the shadowing effect, the rock abundance (RA), the lateral conduction from the rover transfer mechanism, and the densification effect during the measurements.

The Chang’E-1 and E-2 (CE-1 and CE-2) orbital sounders provided high-resolution global maps of lunar microwave brightness temperatures (TBs) at wavelengths of 0.8, 1.55, 3.85, and 10 cm covering approximately two years of data over the 2007–2010 time frame. The four-channel microwave radiometers (MRMs) effectively sampled the upper ~2 m of the lunar regolith and are diagnostic of thermal and electrical properties, including mineralogy, rock abundance, and, potentially, interior heat flow. Early comparisons of colocated data between the two instruments revealed ~10–20 K offsets between the CE-1 and CE-2 measurements that required in- flight recalibration efforts. These have included comparisons with model predictions at Apollo sites as well as adjustments of the cold sky horn reference temperatures to include contamination from lunar surface emissions. This article proposes an in- flight recalibration methodology that focuses on correction of the preflight transfer coefficients that determine the relative importance of component losses along the radiometer hardware paths connecting the antennas to the detectors. It is shown that for each channel, a single parameter, representing the ratio of the cold sky and main antenna transfer coefficients, can be constrained by knowledge of the stable regolith physical temperatures below the diurnal-varying layer and is sufficient to establish values for the complete set of hardware transfer coefficients. The in- flight comparisons proposed for recalibration are based on backside highland models of regolith thermal properties. Potential remaining offsets of the recalibrated MRM data are evaluated in terms of parameter uncertainties of our chosen nominal thermal model.

The two microwave radiometers (MRMs) onboard the Chinese Lunar explorers Chang’E-1 (CE-1) and Chang’E-2 (CE-2) are considered to be identical instruments, yet the results differ, with lunar brightness temperatures obtained by CE-2 generally lower than those of CE-1 in all four frequency channels. The differences can reach over 10 K in the same local time. We propose a recalibration model that takes into account the brightness temperature constant shift of the MRM equipment and the possibility that the Chang’E calibration antennas may have inadvertently picked up some thermal radiation from the lunar surface due to its field of view cutting into the lunar surface. These effects may have negatively influenced the accuracy of the simple two-point calibration procedure and led to the difference between the available MRM level 2C data from CE-1 and CE-2. Our recalibration model determines the correction parameters through a statistical analysis that minimizes the mismatch between the two datasets. Recalibration of the level 2C data based on our recalibration model successfully realigns the microwave brightness temperatures measured by CE-1 and CE-2.

Near-surface temperatures of permanently shadowed regions (PSRs) on the Moon provide fundamental information for water ice exploration. Seasonal temperature variations of PSRs are found in both Chang’E-2 microwave radiometer data and Diviner Lunar radiometer observations. Furthermore, unusual microwave brightness temperature variations between February 2011 and May 2011 of double-shaded PSRs are shown in the Chang’E-2 observational data, i.e., that the minimum microwave brightness temperature occurs before the time when the infrared brightness temperature reaches the minimum in double-shaded PSRs. To interpret this phenomenon, the 1-D thermal model and the microwave radiation transfer model are used. In the thermal model, the reradiation energy from the illuminated area is estimated by effective solar irradiance, which is an analytic solution for the radiative equilibrium temperature in the shadowed area of a spherical bowl-shaped crater. In the simulation, an assumed internal 0.4 W/m2heat flow beneath the lunar surface made a plausible fit to the unusual variations during some lunations. However, this is a huge value compared with the well-known heat flow value of about 0.018 W/m2. Furthermore, it is difficult to obtain this extra heat energy by lateral conduction below the surface in a large impact crater due to the small thermal conductivity of the lunar regolith. Finally, the unusual microwave brightness temperature (TB) changes are concluded to be caused by a calibration problem after excluding other possible reasons. In addition, a statistical correction method is applied to revise the problematic TB data to obtain the proper variation trend of the brightness temperature.

To determine the likelihood that the surface contamination effects can explain the offsets between Chang’E-1 (CE-1) and Chang’E-2 (CE-2) microwave radiometers’ (MRMs) calibrated antenna temperatures (TAs), we quantitatively estimate the effects of the lunar contamination of the CE MRMs’ cold sky horn antennas on TA. We calculated the lunar radiation contributions to the cold sky horn (${ {\Delta T}}_{\text {cosmic}}$) values from the Apollo model brightness temperatures (TBs) convolved with the CE-1 and CE-2 cold sky horn antenna patterns for the circular orbit geometries of CE-1 and CE-2. The calculations were done for all four channels and estimated 20°–40° range of the full width half maximum (FWHM) Gaussian beam sizes over a latitude range of 0°–64°. Small differences between the predawn and noon results illustrate that the local time effects are negligible. Most noteworthy is the result that the largest plausible “${ {\Delta T}}_{\text {cosmic}}$” are less than 10.8 K for CE-1 and less than 23.6 K for CE-2 at the largest assumed beam size. The latitude effect is small, although significant (~5–6 K difference), from the equator to 64°. Most importantly, the cold sky horn contamination effects are shown to produce target TA errors of only 2–5 K for CE-1 and 4–10 K for CE-2 with the largest errors occurring at the lowest TAs. These errors are inadequate to resolve much larger relative offsets reported in the CE-1 and CE-2 TA data. We thus propose an alternative recalibration scheme that focuses on the role of uncertainties in the preflight derivation of hardware loss coefficients.

Thermal anomaly spots (both hot and cold) have been found in the global 37-GHz brightness temperature (TB) map of the moon based on the Chang'E (CE) microwave radiometer measurements. To explain their origin, a rock model is proposed to simulate the TB variation against latitude along the profile of a fresh crater in a single track way, which is selected to highlight the topographic effect and avoid any modification to the data. A mixed upper layer made up of rock and soil (regolith and dust) was employed into our previous multilayer model. The thermal properties (thermal conductivity and heat capacity) of the mixture layer are presumed to be linear with the fraction of rocks. Given that high-frequency (37 GHz) measurements are chosen, only the meter size and larger rocks of the upper mixed layer are considered to avoid scattering effects. Several fresh craters poor/rich in ilmenite are selected as testing sites. Despite uncertainties in parameters such as rock abundance (RA), and iron and titanium abundances, three conclusions can be reached from these cases: 1) RA has a significant effect on both the TB value and TB variation trend against latitude; its contribution over some craters may be as high as 15 K; 2) the simulations based on our rock model fit the CE observations better than those when rocks are not included; and 3) the rock and ilmenite contributions could be the main cause for the cold and hot spots found in the CE microwave map.

Lunar surface temperature (LST) is important for both uncovering the thermal environment and evolution and planning lunar robotic and human exploration such as exploring water/ice. Therefore, an LST calculation method is proposed in this letter for the preparation of the LST database, with an improved effective solar irradiance model, including the topographic effect. As an example, the global LST map with the spatial resolution of 1° is shown, based on the topography and albedo data and retrieved parameters from in situ experiments. The topographic signatures can be identified in the map, including the boundaries between mare and highlands and the contours of craters. The good agreements of the global moon between the simulated temperature and the bolometric brightness temperature by the Diviner Lunar Radiometer Experiment (DLRE) demonstrate the validity of our model and the credibility of the simulated global LST map. The better fitness with the DLRE data produced by our physical model than that by the analytic model proves the advantage of our method.

To improve the retrieval accuracy of the lunar properties from microwave brightness temperature (TB) data sets of the lunar surface, TB measurements of the global moon need a calibration source to better estimate. In this letter, the standard for the calibration source is defined, and two possible calibration sources (the lunar center and Apollo 15) are proposed, which are based on a theoretical TB model. There is a difference of about 4 (3/37 GHz) and 11 K (7.8/19.35 GHz) between the simulated calibration source and Chang'E observation at the lunar center, and of about 7 K (3/7.8/19.35/37 GHz) at Apollo 15. The simulated calibration source (7.8/37 GHz) of the lunar center is within the range of the ground-based measurement. Note that the lunar center has been measured frequently by both ground-based and in-orbiter instruments, and the calibration source of the lunar center is the most possible and credible for the lunar surface. The uncertainty of the calibration source has been also analyzed.

The calibration quality of the Chang'E-2 (CE-2) microwave radiometer (MRM) and the accuracy of brightness temperature (TB) data should be adequately addressed. The quality of CE-2 MRM data can be demonstrated by the analysis and simulation of TB data with the microwave transfer model and by the relative comparison between the TB and other data sets. To calibrate the TB data in a relative way, we calculated the variation of TB with respect to the latitude over certain typical regions theoretically. Three types of areas in the Moon, including the old crater, the fresh crater, and the Apollo region, are chosen as examples. A detailed method incorporating the topographic effect is employed to compute the TB. The Lunar Reconnaissance Orbiter's Diviner infrared measurement is used to ensure the accuracy of the simulated physical temperature. The consistency of the TB undulation between simulations and observations along the profile of these regions verifies the reasonability of CE-2's TB data partly. Our simulation also confirms the topographic effect of sloping walls at the crater rims on the solar heat flux received per unit surface area and reproduces the TB undulation observed by CE-2. Rock abundance and topography data are used for qualitative comparison with the CE-2 TB data. General similarity between the diurnal TB difference and the altitude profile over most craters and the similarity between the diurnal TB difference and the rock abundance profile over fresh craters can prove the relative qualification of CE-2 MRM data to a certain degree.