Lunar equatorial surface temperatures and regolith properties
The Diviner Lunar Radiometer Experiment onboard the Lunar Reconnaissance Orbiter has measured solar reflectance and mid-infrared radiance globally, over four diurnal cycles, at unprecedented spatial and temporal resolution.
These data are used to infer the radiative and bulk thermophysical properties of the near-surface regolith layer at all longitudes around the equator. Normal albedos are estimated from solar reflectance measurements. Normal spectral emissivities relative to the 8-μm Christiansen Feature are computed from brightness temperatures and used along with albedos as inputs to a numerical thermal model.
Model fits to daytime temperatures require that the albedo increase with solar incidence angle. Measured nighttime cooling is remarkably similar across longitude and major geologic units, consistent with the scarcity of rock exposures and with the widespread presence of a near-surface layer whose physical structure and thermal response are determined by pulverization through micrometeoroid impacts.
Nighttime temperatures are best fit using a graded regolith model, with a ∼40% increase in bulk density and an eightfold increase in thermal conductivity (adjusted for temperature) occurring within several centimeters of the surface.
The Moon experiences extremes in surface temperature due to its slow rotation, lack of atmosphere, and the near-ubiquitous presence of a highly insulating regolith layer. Equatorial daytime temperatures reach 400 K, while nighttime temperatures fall below 100 K. Because the subsolar point remains within ∼1.59° of the equator over the lunar year and nodal precession cycle, surfaces at high latitudes experience persistently large solar incidence angles and cold temperatures.
Some regions near the poles are permanently obscured from direct illumination by topography and have annual maximum surface temperatures near 30 K, with implications for trapping and retaining water ice and other volatiles [Vasavada et al., 1999; Paige et al., 2010b]. Details of the regolith’s thermal response to solar forcing provide information about the radiative and thermophysical properties, structure, and rock abundance of the near-surface layer.
These properties, as well as surface temperature and volatile stability, are of interest both scientifically and for planning lunar robotic and human exploration.
[3] Lunar surface temperatures have been measured for several decades using Earth-based infrared and radio telescopes, instruments aboard lunar orbiters, and in situ experiments at the Surveyor and Apollo sites [see Paige et al., 2010a, and references therein]. Returned samples have helped constrain regolith properties such as albedo, particle size distribution, bulk density, thermal conductivity, and heat capacity.
Together these data sets provide a basic understanding of the lunar regolith. A more detailed, contextual understanding requires a data set with systematic and comprehensive geographic, temporal, and spectral (visible and thermal infrared) coverage, high spatial resolution, sensitivity to all lunar temperatures, and correspondingly detailed topographic data.
The collection of such data has been a primary goal of the Lunar Reconnaissance Orbiter (LRO) mission [Vondrak et al., 2010]. Its measurements allow, for example, the assessment of spatial variations in regolith properties, the effects of surface roughness and slopes, and the correlations between thermal data and compositional or geological characteristics.
[4] The LRO launched on 18 June 2009 and entered lunar orbit five days later. On 15 September, after a commissioning period, the LRO transitioned to a low-altitude (∼50 km), circular, polar orbit fixed in inertial space [Tooley et al., 2010]. This orbit was designed to allow repetitive, high spatial resolution coverage of polar latitudes as local time and season (i.e., solar declination) varied over the one-year prime mission.
The Diviner Lunar Radiometer Experiment began systematically measuring the visible and thermal radiance from the Moon during the commissioning period and has since operated nearly continuously. The Diviner investigation is unique in the quality of its data, its spatial and temporal coverage, and its high spatial resolution.
[5] This paper describes the contributions of Diviner to understanding the thermophysical properties and structure of the near-surface layer. A companion paper looks specifically at the influence of rocks [Bandfield et al., 2011]. We constrain our analysis to a narrow band around the lunar equator in order to reduce the effects of latitude (i.e., the combined effects of incidence angle, roughness, and topography), while still sampling a swath of terrain that globally represents the lunar surface layer. Throughout the paper, we use east longitude and the following notation:
-
- A
- albedo, as defined in the text.
- εi
- spectral emissivity of Diviner channel i.
- θ
- solar incidence angle, degrees.
- k
- regolith bulk thermal conductivity, W/m/K.
- λ
- wavelength, μm.
- μ0
- cosine of the solar incidence angle.
- ρ
- regolith bulk density, kg/m3.
- Ti
- brightness temperature of Diviner channel i, K.
- TB
- brightness temperature, K.
- z
- depth below the surface, m.
2. Diviner Data Set and Its Characteristics
[16] The Diviner experiment is a nadir-pointed, pushbroom scanning radiometer with two spectral channels for reflected solar radiation, each 0.35 to 2.8 μm, and seven channels for infrared emission, spanning 7.55 to 400 μm [Paige et al., 2010a]. It is designed to globally map surface albedo and temperature over the lunar diurnal and seasonal cycles, including regions of extremely low temperature at the poles.
Three of the infrared channels also assess composition by accurately locating the silicate mid-infrared emissivity peak (Christiansen Feature) near 8 μm [Conel, 1969]. At an orbital altitude of 50 km, Diviner’s spatial resolution is approximately 320 m along track, set by signal timing, and 160 m across track, set by the fields of view of the twenty-one detectors in each of nine linear arrays. Nadir data are acquired nearly continuously along a north-south orbit track with an image swath of 3.4 km.
Regular interruptions in coverage allow for Diviner space and blackbody calibrations. Irregular interruptions occur when the spacecraft rolls to enable targeted observations by other LRO instruments.
[17] Because LRO’s polar orbit is fixed in inertial space, the local time beneath the spacecraft varies slowly over the year until two complete diurnal cycles (one each from the ascending and descending orbit tracks) are captured by Diviner. Each orbit track is aligned north-south and is nearly constant in local time. The Moon also rotates on its axis each month, spreading the local time coverage over all longitudes.
Each period of full longitudinal coverage is referred to as one mapping cycle. Diviner’s spatial and local time coverage far exceeds what was available before, but certain limitations are present. Irregular spacing of successive orbit tracks results in duplicate spatial coverage at some longitudes and gaps at others, especially at lower latitudes. The temporal sampling of any particular low-latitude location is typically no better than about every two hours of local time.
However, finer temporal resolution can be obtained by using data from a wider swath of longitudes. At polar latitudes the observation pattern is similar, but features of a given physical size receive many more observations than at the equator due to the convergence of orbit tracks.
2.1. Measurement Effects on Diviner Brightness Temperatures
[18] Each Diviner measurement ideally could be converted to a physical surface temperature. However, the scene viewed by each of Diviner’s detectors contains a distribution of physical temperatures due to small-scale slopes, shadows, rocks, and spatially variable photometric and thermophysical properties. Diviner measures infrared radiance within seven spectral bands that sample different portions of the emitted thermal radiation.
When sub-detector scale anisothermality is present, the derived brightness temperatures in each infrared spectral channel differ from one another. Shorter-wavelength channels have higher brightness temperatures due to the nonlinearity of the Planck function; they are more sensitive to the warmer portions of the scene.
The anisothermality effect increases when large illumination or viewing angles enhance the influence of roughness, topography, and shadowing. It can also affect un-illuminated surfaces, e.g., when local variations in thermophysical properties (such as the presence of rocks) result in persistent temperature contrasts at night, as discussed in a companion paper [Bandfield et al., 2011].
2.2. Equatorial Data Set
[20] We created an equatorial data set (EDS) by extracting all Diviner observations between −0.2° and 0.2° latitude that were acquired in nadir mapping mode between 6 July 2009 and 31 August 2011. There are approximately 21 million separate measurements per channel. The data set captures 29 mapping cycles and more than four diurnal cycles (two on each node of Diviner’s orbit).
[21] Figure 1 shows how selected orbital parameters vary with time in the EDS. High orbit altitudes prior to 15 September 2009 and the generally elliptical orbit shape result in significant variability in footprint size, but we find no systematic effect on measured brightness temperature. The latitude and longitude of each Diviner footprint are initially calculated on a sphere with no topography. Because the observations are slightly off-nadir due to Diviner’s ∼4° total field of view, lunar topography will affect where a ray traced from the instrument intersects the surface.
We use the UCLA Digital Moon topographic model, created by fitting a triangular mesh with a resolution of 0.5 km to the Lunar Orbiter Laser Altimeter (LOLA) data set [Smith et al., 2010], to estimate the local surface slope and refine each footprint’s location and orientation [Paige et al., 2010b]. Solar and lunar geometries are derived using ephemerides publicly available from the Navigation and Ancillary Information Facility (NAIF) at the Jet Propulsion Laboratory.
Figure 1 – Variations in orbital and celestial parameters within the Equatorial Data Set. Quantities are plotted against Julian Date (2455000 is 17 June 2009). (a and b) The longitude and local solar time at the equator below the spacecraft’s two ground tracks (i.e., the ascending and descending nodes of the orbit). (c) The sub-solar latitude, which varied between −1.58° and 1.56° over this time period. (d)
The spacecraft’s orbital altitude, calculated relative to a spherical moon with a radius of 1737.4 km. The altitude in the early part of the mission varied between 102 and 125 km. The spacecraft then transitioned to a lower orbit with altitude varying between 36 and 67 km, except in the final month. (e) The distance between the centers of the Sun and Moon. Gaps in the data set show up as gaps in the curves.
[22] Figures 2a and 2b show local time coverage and slope distribution versus longitude. The temporal coverage at any given longitude is every ∼2 h and local time and longitude remain correlated in this data set. Mare and highland surfaces clearly differ in their surface slope characteristics, with the former having slopes less than 2° in our digital elevation model (with some exceptions), and the latter having a broad distribution of slopes up to 20°–30°.
Figure 2 – Local time coverage, local slope distribution, albedo, and spectral emissivity from the equatorial data set. (a) Local time of each Diviner data point. (b) The angular difference between the normal vector of a non-sloped surface and the local normal vector of each Diviner point taken from the UCLA Digital Moon mesh. The data are truncated at 30°. (c) Average Diviner albedo in each 0.05° × 0.05° bin (points), the profile smoothed as described in the text (black line), and the DLAM-1 model (gray line). (d) Channel 7 spectral emissivity averaged in each bin and its smoothed profile (black line).
3. Diviner-Derived Albedo and Emissivity
[23] The following sections describe our process for estimating the solar albedo and infrared emissivity of the lunar surface versus longitude at the equator, necessary as inputs to our thermal model. Our estimates of Diviner albedo and emissivity are strictly a means of improving the accuracy when deriving surface thermophysical properties.
We intentionally constrain our analyses (e.g., by significantly filtering the input Diviner measurements) to simplify the treatment of spectral and angular effects. A full understanding of lunar photometry and emission from Diviner awaits future studies. The error associated with these methods is described in section 6.
3.1. Albedo
[24] The albedo of the lunar surface can be derived from Diviner’s broadband solar channels. Channels 1 and 2 both measure scattered sunlight between 0.3 and 3 μm, but channel 2 has a neutral density filter that reduces its sensitivity [Paige et al., 2010a]. Here we use calculated values of relative surface reflectance (a Diviner data product archived in the Planetary Data System) derived from channel 1. It is the ratio of the radiance from the lunar surface to that of a perfectly reflective, normally illuminated, Lambert surface at the location of the spacecraft.
[25] The measured relative reflectance has an opposition surge at low phase angles, then decreases with increasing solar phase angle (primarily due to illumination, not to be confused with any angular dependence of albedo). To exclude the surge and reduce scatter from topographic effects, we restrict local time to 8–10 and 14–16 h (i.e., incidence angles of 30°–60° and equivalent phase angles given the nadir observational geometry) and remove points with a local slope >2°.
Within this constrained data set, we find that for darker surfaces, the dependence of reflectance on phase angle can be removed by dividing by μ01.3. This is a slightly stronger dependence than for a Lambertian surface (i.e., dividing by μ0). It is difficult to assess its appropriateness for brighter surfaces due to (unresolved) surface slopes that cause higher levels of scatter in the data.
[26] We use the derived dependence to remove the illumination effect from all data points. We take the resulting quantity (the reflectance of the lunar surface at zero phase angle with the opposition surge removed) to represent the fraction of insolation that is not absorbed, hereafter called normal albedo, or albedo. Figure 2c includes a profile of normal albedo versus longitude, smoothed by a moving average of all data within 2° of longitude, every 0.05° of longitude.
After accounting for the low spatial resolution of the DLAM-1 model (harmonic expansion with a wavelength of 24°), the curves are generally in good agreement, but are offset by as much as 0.03 at some longitudes.
3.2. T7 Spectral Emissivity
[28] Having chosen T7 as our surface temperature data set, we would like to understand the emissivity of the lunar surface in its spectral range. A decrease in ε in the mid-infrared is expected as an inherent property of lunar surface materials and a decrease in the apparent emissivity is predicted due to the anisothermality effects described above.
Diviner’s three narrow-band channels near 8 μm provide the ability to locate the Christiansen Feature (CF), a spectral peak in ε for particulate silicate materials [Conel, 1969]. Once it is found, the relative emissivity at other wavelengths can be calculated. We derive ε7 relative to εCF using the method of Greenhagen et al. [2010] as follows.
[29] We first estimate the peak in TB(λ) corresponding to the CF by fitting a parabolic curve to T3,4,5 to predict the wavelength of the maximum brightness temperature. The predicted brightness temperature at this wavelength is taken as the kinetic temperature of the surface, i.e., εCF = 1. Then ε3, ε4, and ε5 are calculated as the ratio of the observed radiance within each bandpass to that predicted assuming blackbody emission at the kinetic temperature.
We fit a parabolic curve to ε3, ε4, and ε5 to find the magnitude and spectral location of the peak. Because our initial guess of maximum TB had some error, the magnitude of the derived emissivity peak is not exactly equal to unity. We re-normalize the derived Diviner channel emissivities to the derived peak (a small correction) and adjust the derived surface temperature.
Finally, ε7 is computed as the ratio of its radiance to that of a blackbody at the derived surface temperature. We only use T3,4,5 measurements above 250 K to avoid large solar incidence angles and to maintain high signal-to-noise ratios. These channels are not sensitive to nighttime temperatures.
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Joseph Olson
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The Moon gets the exact same amount of solar radiation as Earth. Lunar poles get no direct sunlight and are near constant 40°K. The equator varies from -300°F to +260°F and reaches these two conditions rapidly due to “radiative balance”. Solar warming never goes below 0.4 meter per figure 8 in article.
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Jerry Krause
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Hi Joseph and PSI Readers,
I recently emphasized that a PSI reader should not only read what Galileo wrote in his well known but seldom read book; but also to read, in the preface, what the publisher wrote to the reader of Galileo’s book. For in the midst of the preface Louis Elzevir wrote (as translated by Crew and de Salvio 1914): “For, according to the common saying, sight can teach more and with greater certainty in a single day than can precept even though repeated a thousand times; or, as another says, intuitive [without thinking or reasoning] knowledge keeps pace with accurate definition.”
It is the latter saying to which I refer in being critical of what the authors of the article and Joseph independently wrote.
In the article I read: “The Moon experiences extremes in surface temperature due to its slow rotation, lack of atmosphere, and the near-ubiquitous presence of a highly insulating regolith layer.” Which is very good except I have to infer what is the definition of the word REGOLITH. Which is not a word with which Iam familiar and I doubt if regolith is familiar with many PSI Readers. Regolith: “Geol. The mantle of loose material consisting of soils, sediments, broken rock, etc, overlying the solid rock of the earth [moon in this case].” (Websters)
Only you a reader can decide if this definition helps you better understand what the authors of the article have written.
Joseph, are you certain that “The Moon gets the exact same amount of solar radiation as Earth.”? And when you wrote “The equator varies from -300°F to +260°F and reaches these two conditions RAPIDLY due to “radiative balance”.” are you possibly confusing a read who has recently read “The Moon experiences extremes in surface temperature due to its slow rotation”? And what is this “radiative balance”?
I have read and heard that SCIENTISTS are often JUDGED to be poor writers. Which I consider might be a fact because GOOD SCIENTISTS should accurately define the uncommon words they must use to accurately define the ideas (information) about which they are writing.
Yes, I know I make a lot of undebatable mistakes as I write and I know I am sometimes wrong about that which I right. But we need to have discus to correct these possible errors about which we both agree. In SCIENCE this activity is termed Peer (Sp?) review.
Have a good day, Jerry
Have a good day, Jerry
Have a good day, Jerry
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Zoe Phin
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I provide some simple summaries here:
http://phzoe.com/2020/02/12/average-moon-temperature/
http://phzoe.com/2021/02/15/average-moon-day-night-temperature/
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Joseph Olson
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Earth has an elliptical solar orbit which varies from 91 to 93 million miles. Lunar orbit is 240,000 miles, a minor distance, equal at half Moon, more at full Moon, less at new Moon. Over it’s 28 day rotation cycle, the Earth and Moon get exactly the same solar radiation. Earth’s magnetosphere does reduce gamma rays.
Radiative Balance occurs when the Moon reflects (albedo) and radiates (IR emission) the same rate as the Sun projects. The half million mile variation difference between New and Full have an imperceptible difference at the equator, less at higher latitudes. See the step-function plots in article, or in Slaying the Sky Dragon.
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Jerry Krause
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Hi Joseph, Zoe and PSI Readers,
Joseph, you just wrote: “Radiative Balance occurs when the Moon reflects (albedo) and radiates (IR emission) the same rate as the Sun projects.”
The moon’s surface cannot reflect radiation because it is not atomistically smooth as a mirror’s or an ocean’s liquid water surface is!!! I see I might have invented a new word–atomistically. The moon’s “mantle of loose material consisting of soils, sediments, broken rock, etc, overlying [its] solid rock is ROUGH!!! Hence, it scatters solar radiation. And it seems that the scattering of radiation is a phenomenon which you (and many others) do not recognize as existing.
You, Zoe, and I need to come to a common agreement as to this fundamental issue. Hopefully, you and Zoe and other PSI Readers will respond to this comment.
Have a good day, Jerry
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Zoe Phin
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Yes, there is a lot of scattering. But we measured it all around, and hence can compute and average.
Reply
Jerry Krause
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Hi Zoe and PSI Readers,
“intuitive [without reasoning] knowledge keeps pace with accurate definition.” (Louis Elzevir)
Zoe, you wrote: “But we measured it all around, and hence can compute and average.”
We measure the solar scattering by the atmosphere and its contents only during the day time but the contents (larger particles than gaseous molecules like condensation nuclei, smoke particles, dirt particles from wildfires and volcanic eruptions, cloud droplets, and ice crystals) scatter both solar radiation and the IR radiation being emitted from the earth’s surfaces according to these surfaces’ temperatures every 24 hours of a day.
Yes, averaging this radiation which occurs during a period of time is unavoidable. The NOAA Surface Radiation Project (SUFRAD) averages its measurements over a period of a minute. Which generates a lot, lot of numbers. The NOAA U.S. Climate Reference Network USCRN) averages its measurements over a period of a hour and reports this average plus the maximum and minimum measurements during that hour. Hence these maximum and minimum measurements are actual measurements and provides the important information of what actually occurred during that averaged hour.
The three fundamental measurements being measured and report in this fashion are the conventional atmospheric temperature at a distance of about 1.5 meter, the incident solar radiation, and the surface temperature. The velocity of the wind is averaged plus the speed of the maximum gust is reported. Which is important because we commonly know (observe without any instrument) that the wind is quite variable. As we know the incident solar radiation can be if there are observed scattered clouds.
From the SURFRAD project which averages the radiation fluxes for each minute, we see that Incident solar radiation can change very rapidly, which we understand is the result of scattered clouds, and that the upward IR emission from the surface also rapidly changes with the rapid changes of the solar radiation flux.
Zoe and readers I have to review all this because I have had to first inspect the data of these two NOAA projects and to have studied this data for hours, for days, for weeks and months to be able to confidently write what I know can be seen from the NOAA data and understood from the NOAA data.
Finally, I conclude with another of my understandings. Every time I read someone write (or state) that what they study is COMPLEX, I remember that Einstein stated: “If you can’t explain it simply, you don’t understand it well enough.”
Have a good day, Jerry
Reply
Jerry Krause
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Hi Zoe and PSI Readers,
I am discovering that I have read a lot. But considering all that I could have read, it is not much. So, I have stated that for some reason, which I subscribe to GOD, I have mainly read the GOOD STUFF of SCIENCE.
And I know that the NOAA SCIENTISTS AND ENGINEERS, who designed the two project which I have described, made two gross mistakes of their own admissions
First, in the case of the SURFRAD project they didn’t initially see the need of an instrument to measure the DIFFUSE DOWNWELLING SOLAR RADIATION.
Then, in the case of the USCRN project, they placed instruments to measure the wind velocity 1.5 meter above the Earth’s surface. But one cannot find any wind data being reported.
Why??? These scientists discovered that these wind measurements were chaotic!!! Hence this wind data made no sense and they decided to not report it.
However it makes no sense to average data over long periods of time which makes the Earth and seasons homogeneous whe we clearly can see that the natural environment is quite hetrogeneous.
The general diurnal temperature oscillation should never be overlooked.
Have a good day, Jerry
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