Guoping Hu

Chang’E (CE) microwave radiometer (MRM) measurements provide a unique opportunity to detect the heat flow (temperature gradients) across the global Moon. However, rocks influence the brightness temperature (TB) and consequently impact the precision of the inferred temperature gradients derived from the antenna temperature (TA) sensed by the CE MRM. Hence, we propose an improved rock method to simulate the TA using assumed antenna patterns corresponding to the main beam width and efficiency as specified by the MRM manufacturer. In order to quantify the rock effect, the CE MRM’s footprint is segmented into square grids matching the Diviner’s footprint resolution (128 pixels per degree). The rock abundance (RA) derived from Diviner infrared measurements is used to determine the antenna weight for each discrete cell within the MRM footprint. The cumulative weight for rocks is then obtained by summing the weights of all rock-containing cells. Conversely, the weights without rocks are calculated by subtracting the rock weights from one. For the TB of both the regolith and rocks within each cell, we compute these values based on our established TB and thermal heat models. Subsequently, we utilize the highland diurnal TAs observed at the same latitudes with a 0.01° bandwidth to estimate the loss tangent outside the crater. The diurnal agreements between the simulated and observed TAs over four selected fresh craters demonstrate that our method works well and the rock effect was slightly exaggerated in our earlier rock model. Furthermore, based on our validated model, the estimated average diurnal TB difference induced by rocks between the 10 cm (3 GHz) and 3.85 cm (7.8 GHz) channels is approximately 0.33 K. This magnitude suggests that the rock effect should be accounted for in future MRM-based heat flow retrievals, particularly over rocky terrains like fresh craters.

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/TiO₂ content. The uncertainty of the inversion is also discussed, which indicates that the method presented in this paper is feasible.

The stratigraphic structure of the lunar regolith was essential for studying the formation and evolution of the lunar shallow layer within the lunar crust, which was constrained by previous lunar missions through spectral remote sensing, laboratory analyses, and in situ radar such as the Lunar Penetrating Radar (LPR) on Chang'e missions. However, the stratigraphy of the vertical shallow 3-5 meters layer remains unclear to date. In this work, we proposed a method to stratify the shallow lunar regolith (∼ 5 m) using the microwave radiometer (MRM) onboard China's Chang'e-2 (CE-2). The averaged subsurface rock abundance (RA) at depths (∼ 0.5–5 m) was extracted from CE-2 microwave brightness temperature (TB) at four channels: 3.0, 7.8, 19.35, and 37 GHz. Variations of RA with depth were estimated based on the differing penetration depths of the MRM. The near-surface regolith at the Chang'e-3 (CE3) and Chang'e-4 (CE-4) landing sites is divided into three layers: layer I, strongly weathered regolith with RA < 0.20; layer II, weakly weathered ejecta with RA > 0.50; layer III, moderately weathered paleoregolith with RA between 0.20–0.50. We speculated that impact events during the late Copernican period (approximately 50 million years ago) created a crater (approximately 450 m diameter). The ejecta layer exhibits high RA detectable by 7.8 GHz but not by 19.35 GHz.

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 ^-6 w/cm ² . 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 ^-6 w/cm ² precision, ~ 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 one-dimensional 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) × 10 ^-3 Wm ^-1 K ^-1 for T1, (1.04 ~ 2.44) × 10 ^-3 Wm ^-1 K ^-1 for T2, (0.60 ~ 1.40) × 10 ^-3 Wm ^-1 K ^-1 for T3, and (0.60~1.39) × 10 ^-3 Wm ^-1 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, the lateral conduction from the rover transfer mechanism, and the densification effect during the measurements.

This paper studies the two-dimensional DOA estimation of coherent targets. Subspace algorithm is usually used to solve this problem. Compared with subspace algorithm, tensor decomposition has significant advantages in estimation accuracy and has been widely used in the field of signal processing. However, the research on tensor decomposition algorithm mainly focuses on incoherent targets. Therefore, we study how to use the advantages of tensor decomposition to improve the estimation accuracy of coherent targets. Firstly, we construct the echo signal model corresponding to the “Sum array” of MIMO radar, and then use the spatial smoothing to process the data to solve the problem of covariance rank deficiency. Then a third-order tensor is constructed according to the position relationship of the data. Finally, the DOA can be estimated from the decomposed tensor according to the position relationship of the data. Simulation results show that proposed algorithm has significant advantages in estimation accuracy.

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/m ² heat 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/m ² . 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.

The two microwave radiometers on board 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 which takes into account the brightness temperature constant shift of the microwave radiometer 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 microwave radiometer level 2C data from CE-1 and CE-2. Our recalibration model determines the correction parameters through a statistical analysis that minimize the miss-match between the two data sets. Recalibration of the level 2C data based on our recalibration model successfully realigns the microwave brightness temperatures measured by CE-1 and CE-2.