Lunar Reflectance Research Articles

Turning Night into Day: The Creation and Validation of Synthetic Nighttime Visible Imagery Using the Visible Infrared Imaging Radiometer Suite (VIIRS) Day–Night Band (DNB) and Machine Learning

Abstract Meteorological satellite imagery is a critical asset for observing and forecasting weather phenomena. The Joint Polar Satellite System (JPSS) Visible Infrared Imaging Radiometer Suite (VIIRS) Day–Night Band (DNB) sensor collects measurements from moonlight, airglow, and artificial lights. DNB radiances are then manipulated and scaled with a focus on digital display. DNB imagery performance is tied to the lunar cycle, with the best performance during the full moon and the worst with the new moon. We propose using feed-forward neural network models to transform brightness temperatures and wavelength differences in the infrared spectrum to a pseudo-lunar reflectance value based on lunar reflectance values derived from observed DNB radiances. JPSS NOAA-20 and Suomi National Polar-Orbiting Partnership (SNPP) satellite data over the North Pacific Ocean at night for full moon periods from December 2018 to November 2020 were used to design the models. The pseudo-lunar reflectance values are quantitatively compared to DNB lunar reflectance, providing the first-ever lunar reflectance baseline metrics. The resulting imagery product, Machine Learning Nighttime Visible Imagery (ML-NVI), is qualitatively compared to DNB lunar reflectance and infrared imagery across the lunar cycle. The imagery goal is not only to improve upon the consistent performance of DNB imagery products across the lunar cycle, but ultimately to lay the foundation for transitioning the algorithm to geostationary sensors, making global continuous nighttime imagery possible. ML-NVI demonstrates its ability to provide DNB-derived imagery with consistent contrast and representation of clouds across the full lunar cycle for nighttime cloud detection. Significance Statement This study explores the creation and evaluation of a feed-forward neural network to generate synthetic lunar reflectance values and imagery from VIIRS infrared channels. The model creates lunar reflectance values typical of full moon scenes, enabling quantifiable comparisons for nighttime imagery evaluations. Additionally, it creates imagery that highlights low clouds better than its infrared counterparts. Results indicate the ability to create visually consistent nighttime visible imagery across the full lunar cycle for the improved nighttime detection of low clouds. Wavelengths chosen are available on both polar and geostationary satellite sensors to support the utilization of the algorithm on multiple sensor platforms for improved temporal resolution and greater simultaneous geographic coverage over polar orbiters alone.

Disk-integrated and disk-resolved photometry of the Moon with GaoFen-4 space observations

The GaoFen-4 (GF-4) satellite obtained high-resolution images of the entire lunar disk in a single exposure without atmospheric disturbance. These data are favorable for the study of both disk-resolved and disk-integrated photometric properties of the Moon. Using the GF-4 observations, we modeled the lunar reflectance phase functions with the Hapke model and analyzed the lunar photometric properties. The results indicate that the lunar surface exhibits pronounced backscattering, and the maria appear to be smoother compared to the highlands. The disk-resolved and disk-integrated models produced different best-fit parameters for the whole Moon, with the disk-integrated model fitting the small phase angle data better, and the disk-resolved model showing a more favorable appearance at large phase angles. By calculating the disk-integrated phase function with a disk-resolved method, the study confirms the equivalence of the two models, albeit with a small discrepancy due to an imperfect approximation of the roughness function. This discrepancy is due to the different forms of the phase function used in the models. The geometric albedo of the Moon derived from the disk-resolved model is 0.137 and the spherical albedo is 0.063 for Band 3 of GF-4 at 560.6 nm. This study observed an arched phase curve of the ratio of reflectance in two wavelengths, indicating a phenomenon of phase reddening at small phase angles and bluing at large phase angles.

A neural network topographic correction method for the Lunar Reconnaissance Orbiter Diviner Christiansen feature map

Topographic correction for lunar optical and thermal infrared remote sensing images is a challenging task. Although geometrical, photometrical or albedo-dependent correction methods have been used in an attempt to eliminate topographic effects in the initial lunar reflectance and emissivity images, these methods did not perform well on lunar steep slopes, large crater interiors or walls. In this paper, a novel neural network topographic correction (NNTC) model that was trained based on the relationships between flat (< 0.1° slope angle) and rugged pixels with similar Kaguya FeO abundance and optical maturity parameters (OMATs) (relative ratio < 0.1%) was applied to the Lunar Reconnaissance Orbiter (LRO) Diviner standard Christiansen feature (CF) image. The topographic correction accuracy is 0.03 μm, and no outliers are produced. Visual comparisons with the previous topographic corrected reflectance and emissivity images indicate that the topographic effects on various slope and aspect pixels were effectively corrected. The excavated anorthosite materials in the highland crater (such as the Jackson, Giordano Bruno and Tycho) interiors, surroundings, ejecta, and ray deposits have very similar NNTC CF values. The crater structures in maria or cryptomaria are identified more clearly. In addition, the NNTC method has the potential to be a universal topographic correction method for lunar optical and thermal infrared images, and it provides reliable data sources and a new method for space weathering correction.

NASA CERES Spurious Calibration Drifts Corrected by Lunar Scans to Show the Sun Is not Increasing Global Warming and Allow Immediate CRF Detection

AbstractOrbital Earth Radiation Budget measurement comparisons to models, are critical for climate prediction confidence. Satellite systems must reduce calibration drifts for this purpose. NASA Clouds and the Earth's Radiant Energy System (CERES) measures Earth albedo reductions that if correct, would increase solar forcing and suggest greater sunlight absorption is driving much of recent temperature increases. Such results are presented, alongside those from the Moon and Earth Radiation Budget Experiment (MERBE). MERBE uses constant lunar reflectivity for tracking and compensation of instrument telescope degradation, undetectable by CERES. MERBE finds Earth albedo constant compared to that of the Moon, because Arctic solar warming effects are balanced by solar cooling elsewhere, likely due to negative feedbacks. Contrary to NASA, this shows the Sun is not increasing warming and that CERES results are not as stable as claimed and assumed. Furthermore, MERBE can actually resolve Cloud Radiative Forcing (CRF) signals from the existing record, rather than in decades with official observations.

Searching for Galactic micro-FRB with lunar scattering

ABSTRACT Does the Galaxy contain sources of micro-fast radio burst (FRB), lower energy events resembling the known FRB but detectable only at Galactic distances? The answer to this question is essential to determining the nature of FRB sources. At typical (10 kpc) Galactic distances a burst would be about 117 dB brighter than at a ‘cosmological’ (z = 1) distance. The radiation of Galactic micro-FRB, if they exist, could be detected after Lunar reflection, or an upper bound on their rate set, by a modest (20 m at 1.4 GHz) radio telescope staring at the Moon. It would have all-sky sensitivity. The delay between detection of direct (by STARE2 or dipoles) and Lunar-scattered radiation would restrict a burst’s position to a narrow arc.

Global classification of lunar reflectance spectra obtained by Kaguya (SELENE): Implication for hidden basaltic materials

A global classification map of lunar absorption spectra is developed under unified classification criteria by applying the K-means and ISODATA unsupervised classification methods. The spectra were obtained by the Spectral Profiler (SP) onboard the Kaguya (SELENE) lunar orbiter spacecraft. The spectra are mostly categorized into seven spectral groups by the K-means method: K1, K2, K3, K4, K5, K6, and K7. Then, each K-means group is divided into 66 total classes by the ISODATA method. The K1 and K3 groups are classified into 21 and 14 classes, respectively, for which the average spectra are high-calcium pyroxene (HCP)-abundant compared to the other groups. Both groups are mainly located on maria and pyroclastic deposits. However, while the K1 group can be found primarily near the center of large maria, the K3 group can be found mainly at small maria and the margins of large maria. The K2 group contains eight classes and shows average spectra, such as low-calcium pyroxene (LCP), in abundance, which are found mainly on the South Pole-Aitken (SPA) basin and on the coast of Mare Frigoris. The K5 (eight classes), K6 (two classes) and K7 (three classes) groups indicate average spectra with shallower absorption (between 0.9 µm and 1.2 µm wavelength) than those of the K1, K2, and K3 groups. These groups are located in highland regions, and the K5 group is located in high-albedo regions, such as fresh craters. The K6 group is found on nearside highland areas and the K7 group is found on farside highland areas. The K4 group with nine classes shows average spectra, such as mixtures of K1/K2/K3 and K5/K6/K7, and these classes are located around boundaries between mare/SPA and highland. In addition, one class is independently defined without using K-means and ISODATA because its spectra are unsuitable for automatic unsupervised classification. However, this class is still geologically meaningful.The average spectra of the ISODATA classes show not only the characteristics of the major host material belonging to a spectral group, but they also show the small influence of materials from other groups in nearby regions on that host material. This influence is considered to be caused by horizontal material mixing of materials in that location with the ejecta from nearby regions. However, occasionally the ISODATA classes of the K4, K5, and K6 groups influenced by the K1/K3 groups are clustered geographically in regions far from the K1/K3 regions. Some locations of the clusters correspond to locations of the well-known cryptomaria and small pyroclastic deposits. On the other hand, some locations of them also contain candidates of hidden subterranean basaltic materials, such as undiscovered cryptomare, dike, and sill estimated based on recent lunar gravitational anomalies. This agreement suggests to be appeared hidden basaltic materials by the material mixing occurring vertically. The total area of the clusters except for known cryptomaria is approximately two times larger than that of the known cryptomaria, and this area reaches approximately 20% of the total area of exposed maria. The total volume of hidden basaltic materials, except for the known cryptomaria, is estimated to be 104 to 106 km3, depending on assumptions of the relative abundance between cryptomare and dike/sill. This volume is comparable to that of the known cryptomaria and approximately 10% of that of the exposed mare.

Lunar reconnaissance orbiter wide angle camera algorithm for TiO2 abundances on the lunar surface, including the highlands and low-ti maria

A new algorithm is proposed for estimating TiO2 abundance on the moon using lunar reflectance values measured by the Wide Angle Camera on the Lunar Reconnaissance Orbiter spacecraft. The algorithm provides useful values for mature regoliths on the entire lunar surface including highlands and low titanium maria. However, it underestimates the abundances of immature regoliths, so that the algorithm returns a lower limit for such features as young craters and rays.

Development of an application scheme for the SELENE/SP lunar reflectance model for radiometric calibration of hyperspectral and multispectral sensors

We have developed an application scheme for conducting lunar calibration, one of the radiometric calibration methods for optical instruments onboard Earth-orbiting satellites and planetary explorers, with a newly developed hyperspectral lunar reflectance model based on SELENE/SP data. Because the model considers photometric properties (lunar surface reflectance and its dependences on incident, emission, and phase angles) with high spectral and spatial resolution (6–8nm wavelength intervals and 0.5° grid meshes in lunar latitude and longitude), it enables us to simulate disk-resolved Moon radiance observed by not only multispectral but also hyperspectral sensors in space. Simulations of Moon observations conducted by ASTER with its three visible and near infrared bands, produced brightness profiles of simulated Moon images that show high correlation (more than 0.99) with the observed images in all bands, and the relative brightness of each pixel can be evaluated with 5% uncertainty. Consistency of dependence on phase angle and the libration effect between the SP model and another lunar reflectance model, ROLO, was also confirmed. The SP model will therefore be useful for evaluating the relative degradation of sensors in space.

Lunar absolute reflectance as observed by Chang’E-1 Imaging Interferometer

Lunar absolute reflectance, which describes the fraction of solar radiation reflected by the Moon, is fundamental for the Chang’E-1 Imaging Interferometer (IIM) to map lunar mineralogical and elemental distributions. Recent observations made by the Spectral Irradiance Monitor (SIM) onboard the Solar Radiation and Climate Experiment (SORCE) spacecraft indicate that temporal variation in the solar radiation might have non-negligible influence on reflectance calculation, and the SIM measurements are different from the two previously used solar irradiances, i.e., ATLAS3 and Newkur. To provide reliable science results, we examined solar irradiance variability with the SIM daily observations, derived lunar absolute reflectances from the IIM 2A radiance with the SIM, ATLAS3 and Newkur data, and compared them with the Chandrayaan-1 Moon Mineralogy Mapper (M3), the Robotic Lunar Observatory (ROLO) and the Kaguya Multispectral Imager (MI) results. The temporal variability of the SIM solar irradiance is 0.25%–1.1% in the IIM spectral range, and less than 0.2% during the IIM observations. Nevertheless, the differences between the SIM measurements and the ATLAS3 and Newkur data can respectively rise up to 8% and 5% at particular IIM bands, resulting in discrepancy between which might affect compositional mapping. The IIM absolute reflectance we derived for the Moon using the SIM data, except for the last two bands, is consistent with the ROLO and the MI observations, although it is lower.

SHORT-DURATION RADIO BURSTS WITH APPARENT EXTRAGALACTIC DISPERSION

We present the results of the longest yet undertaken search for apparently extragalactic radio bursts at the Bleien Radio Observatory covering 21000 hours (898 days). The data were searched for events of less than 50 ms FWHM duration showing a $\nu^{-2}$ drift in the spectrogram characteristic of the delay of radio waves in plasma. We have found five cases suggesting dispersion measures between 350 and 400 cm$^{-3}$ pc while searching in the range of 50 -- 2000 cm$^{-3}$ pc. Four of the five events occurred between 10.27 and 11.24 a.m. local civil time. The only exception occurred at night with the full moon in the beam. It was an event that poorly fits plasma dispersion, but had the characteristics of a solar type III burst. However, we were not able to confirm that it was a lunar reflection. All events were observed with a log-periodic dipole within 6800 hours but none with a more directional horn antenna observing the rest of the time. These properties suggest a terrestrial origin of the "peryton" type reported before. However, the cause of these events remains ambiguous.

Sandmeier model based topographic correction to lunar spectral profiler (SP) data from KAGUYA satellite.

The Moon may be considered as the frontier base for the deep space exploration. The spectral analysis is one of the key techniques to determine the lunar surface rock and mineral compositions. But the lunar topographic relief is more remarkable than that of the Earth. It is necessary to conduct the topographic correction for lunar spectral data before they are used to retrieve the compositions. In the present paper, a lunar Sandmeier model was proposed by considering the radiance effect from the macro and ambient topographic relief. And the reflectance correction model was also reduced based on the Sandmeier model. The Spectral Profile (SP) data from KAGUYA satellite in the Sinus Iridum quadrangle was taken as an example. And the digital elevation data from Lunar Orbiter Laser Altimeter are used to calculate the slope, aspect, incidence and emergence angles, and terrain-viewing factor for the topographic correction Thus, the lunar surface reflectance from the SP data was corrected by the proposed model after the direct component of irradiance on a horizontal surface was derived. As a result, the high spectral reflectance facing the sun is decreased and low spectral reflectance back to the sun is compensated. The statistical histogram of reflectance-corrected pixel numbers presents Gaussian distribution Therefore, the model is robust to correct lunar topographic effect and estimate lunar surface reflectance.

The global albedo of the Moon at 1064 nm from LOLA

The Lunar Orbiter Laser Altimeter (LOLA) measures the backscattered energy of the returning altimetric laser pulse at its wavelength of 1064 nm, and these data are used to map the reflectivity of the Moon at zero-phase angle with a photometrically uniform data set. Global maps have been produced at 4 pixels per degree (about 8 kilometers at the equator) and 2 kilometers resolution within 20 deg latitude of each pole. The zero-phase geometry is insensitive to lunar topography, so these data enable characterization of subtle variations in lunar albedo, even at high latitudes where such measurements are not possible with the Sun as the illumination source. The geometric albedo of the Moon at 1064 nm was estimated from these data with absolute calibration derived from the Kaguya Multiband Imager and extrapolated to visual wavelengths. The LOLA estimates are within 2 sigma of historical measurements of geometric albedo. No consistent latitude-dependent variations in reflectance are observed, suggesting that solar wind does not dominate space weathering processes that modify lunar reflectance. The average normal albedo of the Moon is found to be much higher than that of Mercury consistent with prior measurements, but the normal albedo of the lunar maria is similar to that of Mercury suggesting a similar abundance of space weathering products. Regions within permanent shadow in the polar regions are found to be more reflective than polar surfaces that are sometimes illuminated. Limiting analysis to data with slopes less than 10 deg eliminates variations in reflectance due to mass wasting and shows a similar increased reflectivity within permanent polar shadow. Steep slopes within permanent shadow are also more reflective than similar slopes that experience at least some illumination. Water frost and a reduction in effectiveness of space weathering are offered as possible explanations for the increased reflectivity of permanent shadow; porosity is largely ruled out as the sole explanation. The south polar crater Shackleton is found to be among the most reflective craters in its size range globally but is not the most reflective, so mass wasting cannot be ruled out as a cause for the crater's anomalous reflectance. Models of the abundance of ice needed to account for the reflectance anomaly range from 3 to 14% by weight or area depending on assumptions regarding the effects of porosity on reflectance and whether ice is present as patches or is well mixed in the regolith. If differences in nanophase iron abundances are responsible for the anomaly, the permanently shadowed regions have between 50 and 80% the abundance of nanophase iron in mature lunar soil.

The expected performance of cloud optical and microphysical properties derived from Suomi NPP VIIRS day/night band lunar reflectance

AbstractThe day/night band channel of the Visible Infrared Imaging Radiometer Suite (VIIRS) instrument on board Suomi‐National Polar Partnership (S‐NPP) is a visible/near‐infrared sensor (500–900 nm band pass) capable of measuring extremely low magnitudes of light, down to the levels of reflected moonlight and beyond. Whereas similar measurement capabilities have existed on predecessor sensors (principally, the Defense Meteorological Satellite Program), the day/night band offers the first calibrated radiance measurements, and as a result, it is the first opportunity to apply moonlight measurements to the problem of retrieving nocturnal cloud optical properties. Daytime retrievals of cloud properties such as top height, optical thickness, cloud top particle size, and water content, have been conducted routinely from an assortment of operational and research grade optical sensors for decades. These observations are providing a satellite‐based global data record of increasing relevance to climate change monitoring (where clouds are thought to play an integral feedback role). The lack of a complete diurnal record of such key parameters presents an important shortfall of these records. Here we present the adaption of the daytime cloud optical and microphysical properties algorithm, which derives cloud optical thickness and effective radius from reflected sunlight to lunar reflectance. The new algorithm is referred to nighttime lunar cloud optical and microphysical properties. Day/night consistency of optical depth is shown through global analysis for one complete day of VIIRS data. Limitations of the retrieval of effective radius are discussed.

Lunar terrain and mineral's abundance automatic analysis

The image is the important data in the lunar exploration. The main objective of this work is to detection lunar craters with the multi-information fuzzy logic method, and to quantify the image's terrain and the abundance of lunar surface minerals based on crater distribution law and soil characterization consortium data set with lunar surface reflectance. We implement image processing to recognize lunar crater and analysis lunar terrain; use lunar reflectance model to solve mineral reflectance question; joint commonly used look-up lunar reflectance tables and least squares to solve lunar surface reflectance questions; and calculate the minerals reflectance, region reflectance, and then estimate abundance of lunar surface soil minerals. An actual lunar image (Apollo 15 landsite, Clementine mission) of Mare region as an example, this method analysis results of the terrain and mineral's abundance are basically same with published literature. In the future, this method can be simple rapid in-time implemented in real-time lunar exploration.

Automatic Analysis of Mineral’s Abundance

The mineral is the important data in the Lunar Exploration. The main objective of this work is to segmentation lunar craters with the C-V Model, and to quantify the images terrain and the abundance of lunar surface minerals based on Crater distribution law and Soil Characterization Consortium data set with Hapke model and lunar surface reflectance. Actual lunar images of mare region as an example, this method analysis result of the minerals abundance are basically same with published literature. This method can be simple rapid in-time implemented in real-time lunar exploration.

Photometric correction and in-flight calibration of Chang’ E-1 Interference Imaging Spectrometer (IIM) data

The main objective of this study is to develop a new photometric correction that is suitable for global Chang’ E-1 (CE-1) Interference Imaging Spectrometer (IIM) data. We considered two improvements in the accuracy of the photometric correction: (1) classifying the whole Moon’s surface into four classes (very bright rays, mature highlands, low FeO basalts, and high FeO basalts) based on the FeO contents; (2) decoupling the combined effects of the solar photometry and the detector responsivity along the cross-track. The results showed that our decoupling method could correct the non-uniformity of detector response but retain the cross-track photometry. Based on these in-flight calibrated data, spectrally continuous photometric functions of the four classes were obtained. By eliminating the contamination from highlands ejecta and low FeO basalts, the opposition surge of the high FeO maria was evident for the first time. The amplitude and width of the opposition surge presents wavelength dependence, which suggests that shadow hiding is the mechanism responsible for the opposition surge. A global lunar reflectance map whose boundaries between adjacent orbits are invisible was generated using the new four-type photometric functions. The quality of the global mosaic and the consistency of the reflectance spectra of the same area obtained in different orbits indicate the effectiveness of our photometric correction method. Although our method was specifically applied to the IIM data, the photometric correction method and the parameter values derived in this study is expected to be suitable for other optical instruments.

Lunar photometric properties at wavelengths 0.5–1.6 μm acquired by SELENE Spectral Profiler and their dependency on local albedo and latitudinal zones

The lunar photometric function, which describes the dependency of the observed radiance on the observation geometry, is used for photometric correction of lunar visible/near-infrared data. A precise photometric correction parameter set is crucial for many applications including mineral identification and reflectance map mosaics. We present, for the first time, spectrally continuous photometric correction parameters for both sides of the Moon for wavelengths in the range 0.5–1.6 μm and solar phase angles between 5° and 85°, derived from Kaguya (SELENE) Spectral Profiler (SP) data. Since the measured radiance also depends on the surface albedo, we developed a statistical method for selecting areas with relatively uniform albedos from a nearly 7000-orbit SP data set. Using the selected data set, we obtained empirical photometric correction parameter sets for three albedo groups (high, medium, and low). We did this because the photometric function depends on the albedo, especially at phase angles below about 20° for which the shadow hiding opposition effect is appreciable. We determined the parameters in 160 bands and discovered a small variation in the opposition effect due to the albedo variation of mafic mineral absorption. The consistency of the photometric correction was checked by comparing observations made at different times of the same area on the lunar surface. Variations in the spectra obtained were lower than 2%, except for the large phase angle data in mare. Lastly, we developed a correction method for low solar elevation data, which is required for high latitude regions. By investigating low solar elevation data, we introduced an additional correction method. We used the new photometric correction to generate a 1° mesh global lunar reflectance map cube in a wavelength range of 0.5–1.6 μm. Surprisingly, these maps reveal that high latitude (≳75°) regions in both the north and south have much lower spectral continuum slopes (color ratio r 1547.7nm/ r 752.8nm ≲ 1.8) than the low and medium latitude regions, which implies lower degrees of space weathering.

Thermal removal from near-infrared imaging spectroscopy data of the Moon

[1] In the near-infrared from about 2 μm to beyond 3 μm, the light from the Moon is a combination of reflected sunlight and emitted thermal emission. There are multiple complexities in separating the two signals, including knowledge of the local solar incidence angle due to topography, phase angle dependencies, emissivity, and instrument calibration. Thermal emission adds to apparent reflectance, and because the emission's contribution increases over the reflected sunlight with increasing wavelength, absorption bands in the lunar reflectance spectra can be modified. In particular, the shape of the 2 μm pyroxene band can be distorted by thermal emission, changing spectrally determined pyroxene composition and abundance. Because of the thermal emission contribution, water and hydroxyl absorptions are reduced in strength, lowering apparent abundances. It is important to quantify and remove the thermal emission for these reasons. We developed a method for deriving the temperature and emissivity from spectra of the lunar surface and removing the thermal emission in the near infrared. The method is fast enough that it can be applied to imaging spectroscopy data on the Moon.

Sources and physical processes responsible for OH/H2O in the lunar soil as revealed by the Moon Mineralogy Mapper (M3)

[1] Analysis of two absorption features near 3 μm in the lunar reflectance spectrum, observed by the orbiting M3 spectrometer and interpreted as being due to OH and H2O, is presented, and the results are used to discuss the processes producing these molecules. This analysis focuses on the dependence of the absorptions on lunar physical properties, including composition, illumination, latitude, and temperature. Solar wind proton-induced hydroxylation is proposed as the creation process, and its products could be a source for other reported types of hydrogen-rich material and water. The irregular and damaged fine-grained lunar soil seems especially adapted for trapping solar wind protons and forming OH owing to abundant dangling oxygen bonds. The M3 data reveal that the strengths of the two absorptions are correlated and widespread, and both are correlated with lunar composition but in different ways. Feldspathic material seems richer in OH. These results seem to rule out water from the lunar interior and cometary infall as major sources. There appear to be correlations of apparent band strengths with time of day and lighting conditions. However, thermal emission from the Moon reduces the apparent strengths of the M3 absorptions, and its removal is not yet completely successful. Further, many of the lunar physical properties are themselves intercorrelated, and so separating these dependencies on the absorptions is difficult, due to the incomplete M3 data set. This process should also operate on other airless silicate surfaces, such as Mercury and Vesta, which will be visited by the Dawn spacecraft in mid-2011.

Calibration against the Moon I: A disk-resolved lunar model for absolute reflectance calibration

We present a model of the absolute radiance of the disk-resolved Moon at visible to near infrared wavelengths. It has been developed in order to use the Moon as a calibration reference, particularly by space-based sensors observing the Earth. We begin with the development of Hillier et al. (Hillier, J., Buratti, B., Hill, K. [1999]. Icarus 141, 205–225) for the reflectance as a function of phase angle and base the lunar reflectance on the Clementine 0.750 μm basemap. We adopt Hapke’s (Hapke, B. [2002]. Icarus 157, 523–534) expression for the multiple scattering term, including the more accurate approximation to the Chandrasekhar H function. The geometry is based on the Jet Propulsion Laboratory Lunar Ephemeris DE 421, and the topographic slope is from the Kaguya-LALT laser altimetry ( Araki, H., and 10 colleagues [2009]. Science 323, 897–900). We define three types of terrain by combining the reflectance from the Clementine basemap and the topographic model to specify maria, highlands, and crater regions, and allow mixed types between each class. Parameters of the model are solved for as a function of surface type and wavelength by comparison against data “chips” from the Robotic Lunar Observatory (ROLO; Kieffer, H.H., Stone, T.C. [2005]. Astron. J. 129, 2887–2901). The reflectance in any waveband may be computed by spectral interpolation of the model predictions relative to the scaled Apollo 16 soil spectrum. The accuracy of the model, evaluated against ROLO imagery, was found to be 2–4%.