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We derive a new constraint on the thermal and dielectric properties of the lunar regolith layer by reconciling data from the Lunar Reconnaissance Orbiter (LRO) Diviner infrared radiometer and Chang'E‐2 (CE‐2) microwave radiometer (MRM). The bolometric Bond albedo of the lunar surface, which characterizes the ability of the lunar surface to reflect...
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Passive microwave frequency (~300 MHz to 300 GHz) observations of the Moon have a long history and have been suggested as a plausible orbital instrument for the Moon and other bodies. However, global, orbital multifrequency measurements of lunar passive microwave emission have only recently been made by the Chinese Chang'E‐1 and ‐2 microwave radiom...
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... 1) Computing annual averaged (southern winter) subsurface temperatures with heat flows from 0 to 24 mW/m 2 . 2) Modeling T B based on the above temperature profiles (Wei et al., 2019;Feng et al., 2020;Siegler et al., 2020). 3) Match the modeled T B and CE-2 observations and search for the best-fit heat flow value. ...
New advances in lunar and related planetary studies
... The bolometric Bond albedo A θ is a function of solar incidence angle θ and describes the ratio of reflected solar radiation to incident solar radiation. It was derived by Feng et al. (2020) from Diviner noontime surface temperatures as a function of latitude. ...
... but used different values for the coefficients a and b. In this work, we applied the description by Feng et al. (2020), who used Diviner surface temperatures acquired at noon as a function of latitude to determine the angular ...
... dependence (see Section 3.5 and Equation 13). However, at high latitudes shadows are present due to roughness and therefore the albedo inferred by Feng et al. (2020) must include these shadowing effects and contains some degree of uncertainty. Figure 9 gives an overview on the functional behavior of these albedos. ...
The microphysical structure of the lunar regolith provides information on the geologic history of the Moon. We used remote sensing measurements of thermal emission and a thermophysical model to determine the microphysical properties of the lunar regolith. We expand upon previous investigations by developing a microphysical thermal model, which more directly simulates regolith properties, such as grain size and volume filling factor. The modeled temperatures are matched with surface temperatures measured by the Diviner Lunar Radiometer Experiment on board the Lunar Reconnaissance Orbiter. The maria and highlands are investigated separately and characterized in the model by a difference in albedo and grain density. We find similar regolith temperatures for both terrains, which can be well described by similar volume filling factor profiles and mean grain sizes obtained from returned Apollo samples. We also investigate a significantly lower thermal conductivity for highlands, which formally also gives a very good solution, but in a parameter range that is well outside the Apollo data. We then study the latitudinal dependence of regolith properties up to ±80° latitude. When assuming constant regolith properties, we find that a variation of the solar incidence‐dependent albedo can reduce the initially observed latitudinal gradient between model and Diviner measurements significantly. A better match between measurements and model can be achieved by a variation in intrinsic regolith properties with a decrease in bulk density with increasing latitude. We find that a variation in grain size alone cannot explain the Diviner measurements at higher latitudes.
... where K s (∂T)/(∂x) is the heat energy transmitted from the surface to the subsurface, T s , ε = 0.95, and σ B (W·m −2 ·K −4 ) are the surface temperature, the infrared emissivity of lunar regolith, and the Stefan-Boltzmann constant, Q s = (1 − A)F is the surface energy flux, which is equal to the solar heating rate, and F (W·m −2 ) is the incident solar flux, which can be written as [9,17,44,46,47] ...
... The loss tangent of materials has been discussed many times [20,33,47,52]. The dielectric loss tangent models of both the mare and highland lunar regolith employed here are derived from Siegler et al. [20]: ...
The rock strongly affects the surface and subsurface temperature due to its different thermophysical properties compared to the lunar regolith. The brightness temperature (TB) data observed by Chang’E-1 (CE-1) and Chang’E-2 (CE-2) microwave radiometers (MRM) give us a chance to retrieve the lunar subsurface rock abundance (RA). In this paper, a thermal conductivity model with an undetermined parameter β of the mixture has been employed to estimate the physical temperature profile of the mixed layer (rock and regolith). Parameter β and the physical temperature profile of the mixed layer are constrained by the Diviner Channel 7 observations. Then, the subsurface RA on the 16 large (Diameter > 20 km) Copernican-age craters of the Moon is extracted from the average nighttime TB of the CE-2 37 GHz channel based on our previous rocky TB model. Two conclusions can be derived from the results: (1) the subsurface RA values are usually greater than the surface RA values retrieved from Diviner observations of the studied craters; (2) the spatial distribution of subsurface RA extracted from CE-2 MRM data is not necessarily consistent with the surface RA detected by Diviner data. For example, there are similar RA spatial distributions on both the surface and subsurface in Giordano Bruno, Necho, and Aristarchus craters. However, the distribution of subsurface RA is obviously different from that of surface RA for Copernicus, Ohm, Sharonov, and Tycho craters.
... Two types of methods have been employed to produce gridded TB maps. The first type is the interpolation-based method, which performs two-dimensional (2D, along longitude and latitude) interpolation using the original MRM data points within a specific local time span that covers the space range [1], [2], [5], [16]- [22]. However, due to the limited amount of dataset, the original MRM data points cannot cover an extensive spatial range within a short time span. ...
... However, due to the limited amount of dataset, the original MRM data points cannot cover an extensive spatial range within a short time span. Particularly when generating the TB maps for the entire Moon, the length of the time span is typically no less than two local hours (~59 hours on Earth) when using the CE-1 MRM data [1], [2], [16], [17] or CE-2 MRM data [5], [18]- [21] and sometimes the span can extend up to four hours [22]. Given the apparent changes in TB over time [18], the interpolated maps produced by this method are not ideal for accurately evaluating the regolith's thermophysical parameters. ...
... In previous studies, global TB maps were traditionally generated using 2D interpolation methods using the original MRM data points obtained within at least two local hours [1], [2], [5], [16]- [22]. To evaluate the spatial rationality of the TB maps generated in this work, TB maps using the traditional method and the original MRM data points within two local hours were also generated for daytime ( Fig. 8(a), MRM data points from 12:00 to 14:00) and nighttime (Fig. 8(b), MRM data points from 23:00 to 1:00 the next lunation). ...
The Chang’e-1/2 satellites carried microwave radiometers (MRM), which supplied unique passive microwave data, supplementing visible, thermal infrared, and radar data in current lunar studies. However, the application of MRM data is constrained by the limited amount of the original dataset, which cannot express spatial variations at given local times. In this study, we present a novel approach to constructing a local-time brightness temperature (TB) model using barycentric interpolation based on Delaunay tetrahedralization. This model enables the generation of a complete TB dataset, producing TB maps that are both continuous and self-consistent in both spatial and temporal domains. Compared to the traditional methods, those generated in this work avoid a ~7-K bias on a global scale. Furthermore, the interpolated maps offer superior representations of the TB over time for various lunar surfaces. The preliminary evaluations on global and regional scales hint important application of MRM data in studying the geological features of the Moon.
... For the calibration issue of the CE-2 MRM data, it was widely reported by Feng et al. [24], Hu and Keihm [25], Hu et al. [26], and Siegler et al. [27]. Advantageously, in the comparative aspect, the MRM data show good correspondence with the lunar surface materials in the global scale, which was thoroughly evaluated by Chan et al. [5], Zheng et al. [1], Cai and Lan [7], Zhu et al. [4], Feng et al. [24], Siegler et al. [27], and Wei et al. [28]. ...
... For the calibration issue of the CE-2 MRM data, it was widely reported by Feng et al. [24], Hu and Keihm [25], Hu et al. [26], and Siegler et al. [27]. Advantageously, in the comparative aspect, the MRM data show good correspondence with the lunar surface materials in the global scale, which was thoroughly evaluated by Chan et al. [5], Zheng et al. [1], Cai and Lan [7], Zhu et al. [4], Feng et al. [24], Siegler et al. [27], and Wei et al. [28]. Even on the local scale, the great correlation between the basaltic units and the TB performance results was verified in the Maria Imbrium, Moscoviense, and Rumker regions [21,29]. ...
Microwave radiometer (MRM) is one of the important payloads on the Chang’e-2 (CE-2) Lunar satellite. In the Chang’e satellite’s observation of the microwave radiation brightness temperature (TB) on the lunar surface, there are some “cold spots” of microwave thermal radiation at night containing the Jackson crater. In order to compare the diurnal radiation TB differences of “cold spots” on the lunar surface, two typical craters at similar latitudes on the northern hemisphere on the lunar farside were selected: Jackson, which represents the new craters with a large number of discrete rocks on their surfaces; and Morse, which no longer has a large number of rocks after long-term meteorite impact and lunar evolution. In this paper, the diurnal variation of CE-2 MRM data in the two craters is presented, and a comparative analysis is made with the (FeO + TiO2) abundance (FTA) obtained by Clementine UV-VIS data and the rock abundance (RA) data of LRO Diviner. We find that the variation of the "cold spots" of lunar surface thermal radiation is closely related to the RA distribution in the newly formed craters on the lunar surface, and also has a certain correlation with the FTA.
... Microwave radiometry provides a means to peer below the surface to measure the integrated subsurface physical temperature. The measurement frequency and the dielectric properties (summarized by the loss tangent, which is the ratio between the real and imaginary dielectric constants) 18,19 controls the depth over which materials add to the emitted radiance. Lower frequencies (longer wavelengths) and lower loss tangents will sense heat from greater depths. ...
... Although this enhancement's location coincides with the increased surface Th observed at the CBVC 7 of lunar granitic samples 18 . A heat flux of 180 mW m −2 would require a layer of roughly 45 km of such material, neglecting any lateral heat conduction, implying the material below the surface exceeds concentrations estimated at the surface. ...
... As discussed in refs. 18,19, there appear to be substantial offsets in the absolute temperature calibration of the Chang'e data, but the relative calibration (comparing location to location or diurnal amplitudes) appears robust and in alignment with model expectations. All work in this paper relies on relative calibration (for example, how hot Compton-Belkovich is compared with its surroundings at a given frequency). ...
Granites are nearly absent in the Solar System outside of Earth. Achieving granitic compositions in magmatic systems requires multi-stage melting and fractionation, which also increases the concentration of radiogenic elements¹. Abundant water and plate tectonics facilitate these processes on Earth, aiding in remelting. Although these drivers are absent on the Moon, small granite samples have been found, but details of their origin and the scale of systems they represent are unknown². Here we report microwave-wavelength measurements of an anomalously hot geothermal source that is best explained by the presence of an approximately 50-kilometre-diameter granitic system below the thorium-rich farside feature known as Compton–Belkovich. Passive microwave radiometry is sensitive to the integrated thermal gradient to several wavelengths depth. The 3–37-gigahertz antenna temperatures of the Chang’e-1 and Chang’e-2 microwave instruments allow us to measure a peak heat flux of about 180 milliwatts per square metre, which is about 20 times higher than that of the average lunar highlands3,4. The surprising magnitude and geographic extent of this feature imply an Earth-like, evolved granitic system larger than believed possible on the Moon, especially outside of the Procellarum region⁵. Furthermore, these methods are generalizable: similar uses of passive radiometric data could vastly expand our knowledge of geothermal processes on the Moon and other planetary bodies.
... GHz,and 7.8 GHz and ≈25 km at 3 GHz (Wang et al. 2010). Microwave T B data at the low-frequency channels of CE-2 suffer from a calibration issue (Hu & Keihm 2021), but the data at 37 and 19 GHz are reliable (Feng et al. 2020). With the temperature profiles derived from the one-dimensional heat conductive equation, where the albedo is derived from Clementine reflectance data (Vasavada et al. 2012), Liu et al. (2019) calculated the loss tangents along the equator using CE-2 microwave T B data at 37 GHz and found them in the range of the measured values of lunar samples. ...
... On the basis of this relationship, Liu et al. (2019) could then establish an analogous relationship between TiO 2 and the loss tangents. A similar method was employed by Feng et al. (2020) to determine the loss tangents of the lunar surface: They derived the Bond albedo by using Lunar Orbiter Laser Altimeter reflectance data, and they calculated the real part of the permittivity by using an empirical model based on measurements of lunar samples. ...
We describe the measurement of the brightness temperature of the Moon from space during a total lunar eclipse by using a microwave sounder aboard a weather satellite. Previous observations of lunar eclipses were inconsistent and did not cover the frequency range between 100 and 200 GHz. In this work, we seek to establish a reliable relationship between frequency and drop in brightness temperature during a total eclipse for millimeter wavelengths. For this purpose, we chose the eclipse on 2004 October 28, because it coincided with appearances of the Moon in the deep space view of the Advanced Microwave Sounding Unit-B on NOAA-15. It was therefore possible to measure its disk-integrated radiance at 89, 150, and 183 GHz at 100 minutes intervals. Our observations are, to the best of our knowledge, the only ones between 100 and 200 GHz, and demonstrate the nearly linear dependency on frequency of the maximum relative drop in effective temperature during an eclipse. The slope of this function is m = 0.00114 ± 0.00017 GHz ⁻¹ in the range 88–300 GHz. The good agreement between the variations of the effective lunar temperature and a new radiative-transfer model suggests that the Moon is suitable as a flux standard for microwave observations with beam sizes larger than 0.5°.
... 1) Computing annual averaged (southern winter) subsurface temperatures with heat flows from 0 to 24 mW/m 2 . 2) Modeling T B based on the above temperature profiles (Wei et al., 2019;Feng et al., 2020;Siegler et al., 2020). 3) Match the modeled T B and CE-2 observations and search for the best-fit heat flow value. ...
The internal heat flow related to the Moon’s composition, interior structure, and evolution history is not well-constrained and understood on a global scale. Up to now, only two in situ heat flow experiments, Apollo 15 and 17 were deployed nearly 50 years ago. The measured high values of heat flow might be influenced by lateral heat at highland/mare boundaries and enhanced by heat production from radioactive elements enriched unit, and may also be disturbed by astronauts’ activities. In this study, we proposed a new method to retrieve heat flows at two permanently shadowed craters, Haworth and Shoemaker of the Moon’s south pole, from Chang’E-2 microwave radiometer data and Diviner observations. Our results show that the average heat flow is 4.9 ± 0.2 mW/m ² . This provides a constraint for the bulk concentration of Thorium within the lunar south polar crust 656 ± 54 ppb, which helps us understand the Moon’s thermal evolution and differentiation.
... The sensitivity of MRM data to the thermal emission features of the regolith at the penetration depth has been proven; the data provide a good description of the surface deposits in the vertical direction [21][22][23]. Combining the data from the Lunar Reconnaissance Orbiter (LRO) Diviner data and the Lunar Orbiter Laser Altimeter data, Siegler et al., [24] and Feng et al., [25] also suggested that the CE-2 MRM data are sensitive to the loss tangent of the regolith, which is positively correlated with the ilmenite content of the substrate materials on the lunar surface [26]. Thus, MRM data provide a new way to assess the distribution and dielectric properties of cryptomare deposits, which was the motivation for this study. ...
... In the B-K region, the thickness of the surface impact ejecta in the cryptomare region is at least 33 m [7], which is beyond the penetration depth of the microwave used by the MRM instrument. Thus, a one-layer model with infinite depth is employed to construct the radiative transfer model, which is an extension of the two-layer model ( Figure 1a) [24,25,30]. An expression for the model is as follows [30]: ...
... Moreover, the nighttime TB in the cryptomare region with mixed mare deposits and highland debris should be lower than that in highland debris but higher than that in pure mare deposits and vice versa at daytime. The higher TB of mare deposit at noon and lower TB during the night compared with the highland debris agree well with the calculated thermal properties by Feng et al., [25], who proposed that the loss tangent of the dielectric constant of the surface deposits is higher in the maria than in the highlands. ...
Lunar cryptomare records both early-stage mare volcanisms and large-scale impact cratering, which can provide important information about the thermal evolution of the Moon. We built a mixing dielectric constant model to represent the cryptomare deposits mixed by highland debris and mare deposits, and the proper radiative transfer simulation was constructed to evaluate the thermal emission features of surface deposits in the cryptomare region. The microwave radiometer (MRM) data in the Balmer-Kapteyn region were extracted, and the linear interpolation method was used to generate brightness temperature (TB) maps at noon and at night. To enhance the correlation between cryptomare deposits and TB performances, normalized TB (nTB) and TB difference (dTB) maps were also generated. Combined with the datasets, including Lunar Reconnaissance Orbiter Wide Angle Camera, Lunar Orbiter Laser Altimeter, and Diviner and Clementine UV–VIS, the main findings are as follows: (1) The mare-like cryptomare deposits were discovered and identified according to the nTB and dTB performances. Combined with the surface compositions, at least two kinds of buried mare deposits were identified in the B-K region, which erupted during different episodes. (2) A construct-like volcanic feature was suggested by the nTB and dTB performances. (3) The results of our analysis indicated the presence of materials with low dTB anomalies in the northern and southwestern parts of the cryptomare region and in the mare unit within the Vendelinus crater, which illustrates the heterogeneity of the lunar crust in the vertical direction.
... Although the bolometric brightness temperature (which is the integrated infrared flux across channels 3-9) is generally used to address this anisothermality effect, we use Diviner channel 7 (T7, 25-41 mm) to represent a physical surface temperature. Various studies have used this channel, including Vasavada et al. (2012) and Feng et al. (2020), due to its high signal-to-noise ratio and insensitivity to small and hot rocks. We filter any measurements with more than 1% rock abundance through a derived rock abundance map available on the Global Data Records (GDR) accessible through PDS (Paige, 2017). ...
... The final thermal conductivity model is then used to compare diurnal surface and subsurface temperature results between a standard lunar thermal model and the updated thermal model for various latitudes. Both thermal models include the bolometric Bond albedo model developed by Feng et al. (2020), which provides an updated angular dependence between Bond albedo and solar incidence angle. In addition, the 1,064-nm normal albedo map produced by LOLA (Lucey et al., 2014) is used as an input parameter into the albedo model based on the respective longitude, latitude, and whether we are observing lunar highlands or maria. ...
... We first build the thermal conductivity model to match the conventional model at 0° latitude and subsequently analyze how it affects model results in cooler polar regions. The standard model we will use to compare results is described in Appendix A of Hayne et al. (2017), though we introduce a couple of minor modifications (the resulting model is most similar to the model described in Feng et al., 2020). One-dimensional heat transfer through a solid medium is investigated by implementing a numeric model that solves the heat flow equation (Equation 2) such that diurnal temperature variations T at time t are determined at the surface and depth z. ...
Although some of the coldest surface temperatures in the entire Solar System are found near the poles of our own Moon, the thermophysical properties of lunar regolith at these ultracold temperatures (i.e., below ∼150 K) are not well understood. Standard lunar thermal models generally match the surface temperatures observed by global orbital remote sensing data but are inconsistent with infrared data collected from ultracold polar terrain. We build upon previous theoretical work on the low‐temperature physics of lunar regolith to introduce a global thermal conductivity model consistent with the temperature trends observed by the Diviner Lunar Radiometer Experiment (Diviner). This updated thermophysical model primarily affects nighttime surface temperatures, subsurface temperatures at high latitudes, and permanently shadowed regions (PSRs). An additional outcome of this thermophysical model is the ability to accommodate the surface temperature trends observed by Diviner both in warm low latitudes and cold high latitudes. Subsurface temperatures in near‐polar craters are ∼5–10 K warmer than previous thermal models, and cooler nighttime surface temperatures are observed globally. Model results of PSRs reveal larger surface temperature amplitudes (as observed by Diviner) and steeper geothermal gradients. A comprehensive understanding of lunar regolith's low‐temperature thermal behavior is an essential step in modeling the potential location and quantity of cold trapped volatiles in the lunar south pole. Here, we hope to provide theoretical support and motivation for more complete low‐temperature thermal conductivity laboratory measurements.
