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The Global Surface Temperatures of the Moon as Measured by the Diviner Lunar Radiometer Experiment

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The Diviner Lunar Radiometer Experiment onboard the Lunar Reconnaissance Orbiter (LRO) has been acquiring solar reflectance and mid-infrared radiance measurements nearly continuously since July of 2009. Diviner is providing the most comprehensive view of how regoliths on airless bodies store and exchange thermal energy with the space environment. Approximately a quarter trillion calibrated radiance measurements of the Moon, acquired over 5.5 years by Diviner, have been compiled into a 0.5° resolution global dataset with a 0.25-hour local time resolution. Maps generated with this dataset provide a global perspective of the surface energy balance of the Moon and reveal the complex and extreme nature of the lunar surface thermal environment. Our achievable map resolution, both spatially and temporally, will continue to improve with further data acquisition.
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Icarus 283 (2017) 300–325
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Icarus
journal homepage: www.elsevier.com/locate/icarus
The global surface temperatures of the moon as measured by the
diviner lunar radiometer experiment
J.-P. Williams
a , , D.A. Paige
a
, B.T. Greenhagen
b
, E. Sefton-Nash
c
a
Department Earth, Planetary and Space Sciences, University of California, Los Angeles, CA 90095, USA
b
Johns Hopkins University, Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723, USA
c
Department of Earth and Planetary Sciences, Birkbeck, University of London, Malet Street, London, WC1E 7HX, UK
a r t i c l e i n f o
Article history:
Received 12 August 2015
Revised 4 June 2016
Accepted 11 August 2016
Available online 13 August 2016
Keywo rds:
Moon
Surface
Regolith
Infrared observations
Temperature
Radiance
Remote sensing
a b s t r a c t
The Diviner Lunar Radiometer Experiment onboard the Lunar Reconnaissance Orbiter (LRO) has been ac-
quiring solar reflectance and mid-infrared radiance measurements nearly continuously since July of 2009.
Diviner is providing the most comprehensive view of how regoliths on airless bodies store and exchange
thermal energy with the space environment. Approximately a quarte r trillion calibrated radiance mea-
surements of the Moon, acquired over 5.5 years by Diviner, have been compiled into a 0.5 °resolution
global dataset with a 0.25 h local time resolution. Maps generated with this dataset provide a global per-
spective of the surface energy balance of the Moon and reveal the complex and extreme nature of the
lunar surface thermal environment. Our achievable map resolution, both spatially and temporally, will
continue to improve with further data acquisition.
Daytime maximum temperatures are sensitive to the albedo of the surface and are 387–397 K at the
equator, dropping to 95 K just before sunrise, though anomalously warm areas characterized by high
rock abundances can be > 50 K warmer than the zonal average nighttime temperatures. An asymmetry
is observed between the morning and afternoon temperatures due to the thermal inertia of the lunar
regolith with the dusk terminator 30 K warmer than the dawn terminator at the equator. An increase in
albedo with incidence angle is required to explain the observed decrease in temperatures with latitude.
At incidence angles exceeding 40 °, topography and surface roughness influence temperatures resulting
in increasing scatter in temperatures and anisothermality between Diviner channels.
Nighttime temperatures are sensitive to the thermophysical properties of the regolith. High thermal
inertia (TI) materials such as large rocks, remain warmer during the long lunar night and result in anoma-
lously warm nighttime temperatures and anisothermality in the Diviner channels. Anomalous maximum
and minimum temperatures are highlighted by subtracting the zonal mean temperatures from maps. Ter-
rains can be characterized as low or high reflectance and low or high TI. Low maximum temperatures
result from high reflectance surfaces while low minimum temperatures from low-TI material. Conversely,
high maximum temperatures result from dark surface, and high minimum temperatures from high-TI
materials.
Impact craters are found to modify regolith properties over large distances. The thermal signature of
Tycho is asymmetric, consistent with an oblique impact coming from the west. Some prominent crater
rays are visible in the thermal data and require material with a higher thermal inertial than nominal re-
golith. The influence of the formation of the Orientale basin on the regolith properties is observable over
a substantial portion of the western hemisphere despite its age ( 3.8 Gyr), and may have contributed
to mixing of highland and mare material on the southwest margin of Oceanus Procellarum where the
gradient in radiative properties at the mare-highland contact is broad ( 200 km).
©2016 The Authors. Published by Elsevier Inc.
This is an open access article under the CC BY-NC-ND license
( http://creativecommons.org/licenses/by-nc-nd/4.0/ ).
Corresponding author. Fax: 310 825 2279.
E-mail addresses: jpierre@mars.ucla.edu (J.-P. Williams), dap@moon.ucla.edu
(D.A. Paige), benjamin.greenhagen@jhuapl.edu (B.T. Greenhagen), e.sefton-
nash@uclmail.net (E. Sefton-Nash).
1. Introduction
The Diviner Lunar Radiometer Experiment (Diviner; Paige et al.,
2010a ) is one of seven instruments aboard NASA’s Lunar Recon-
http://dx.doi.org/10.1016/j.icarus.2016.08.012
0019-1035/© 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ).
J.-P. Williams et al. / Icarus 283 (2017) 30 0–325 301
Fig. 1. Diviner’s nine spectral passbands.
naissance Orbiter (LRO) ( Chin et al., 2007; Tooley et al., 2010;
Vondrak et al., 2010 ). Diviner has been systematically mapping
the Moon since July 5, 2009 acquiring 250 billion calibrated
radiometric measurements (as of April 2015) at solar and infrared
wavelengths covering a full range of latitudes, longitudes, local
times and seasons. These are the first such comprehensive mea-
surements of the Moon, or any other airless body, providing the
ability to characterize the global lunar thermal environment, one
of the most extreme of any planetary body in the solar system
( Paige et al., 2010b ).
The Moon is an important airless body to study not only
because of its accessibility, but because it’s ancient surface records
events that occurred during the earliest phases of the formation
of the Earth and the inner solar system. The Moon also exhibits
a wide range of important planetary processes, such as impact
cratering, volcanism, volatile cold-trapping and space weathering
that relate directly to similar processes that are observed on both
large and small bodies elsewhere in the solar system.
Early Diviner observations have been used to infer the average
radiative and bulk thermophysical properties of the near-surface
regolith at the equator ( Vasavada et al., 2012 ). With continued
operations, the current density of Diviner observations both
spatially and in local time is high enough that diurnal tempera-
tures can be adequately resolved globally at 0.5 deg pix
1 spatial
resolution to create global gridded map datasets. This provides
insight into the radiative and thermophysical properties of the
lunar regolith globally. In this paper, we present an empirical
view of the Moon as seen from Diviner, utilizing all acquired
nadir-pointing observations without the aid of detailed physical
models or laboratory data. We first discuss the Diviner instrument
and its mapping history followed by the description of the data
gridding and map production. We next present the maps in global,
cylindrical projection and discuss and characterize the lunar global
temperatures. This is followed by a discussion of processes that
have resulted in widespread regolith modification that influence
surface temperatures as observed by Diviner.
2. The diviner instrument
2.1. Instrument description
Diviner is a 9-channel radiometer that maps solar reflectance
and infrared emission over a wavelength range of 0.3 to 400 μm
( Paige et al., 2010a ). The spectral response of Diviner’s channels
is shown in Fig. 1 . Channels 1 and 2, with identical spectral
passbands of 0.35–2.8 μm, measure reflected solar radiation from
the lunar surface at two different sensitivities. The remaining
channels (3–9) observe emitted infrared radiation from which
brightness temperatures of the lunar surface are derived. The
three narrow spectral passband filters of channels 3–5 are used
to map the wavelength of the mid-infrared thermal emission
maximum, a spectral feature called the Christiansen Feature (CF)
near 8 μm ( Conel, 1996 ) which is diagnostic of the bulk silicate
mineralogy (e.g. Greenhagen et al., 2010; Glotch et al., 2010 ,
2011 ). The remaining channels (6–9) are broad channels intended
to characterize the surface thermal emission over a wide range
of temperatures with separate filters covering 13–23, 25–41,
50–100, and 10 0–40 0 μm (full width half max).
The ground-projected surface footprint of Diviner is dependent
on spacecraft altitude which varies between 40 and 170 km in its
current elliptical orbit configuration, but is 170 m cross-track and
500 m in-track, accounting for spacecraft motion which results
in elongation in the in-track direction, at the nominal altitude of
50 km during the mapping mission phase ( Williams et al., 2016 ).
Each channel consists of an array of 21 detectors that are nomi-
nally nadir-pointing collecting data in a pushbroom configuration
with an integration period of 0.128 s. The characteristics of the
Diviner instrument are described in further detail in Paige et al.
(2010a) .
2.2. Mapping history
LRO launched on 18 June 2009 and the spacecraft commission-
ing phase was initiated on 27 June 2009. Diviner began acquiring
data eight days later on 5 July 2009 ( Fig. 2 ). The initial commis-
sioning orbits were quasi-frozen 30 ×200 km polar orbits with
periapsis near the lunar south pole. On 15 September 2009, LRO
transitioned into a near-circular, 2 h period mapping orbit with
an average altitude 50 km (referenced to a 1737. 4 km sphere) to
start the Nominal Mission ( Mazarico et al., 2011a ). After the initial
1 year nominal mission, LRO began its two year Science Mission,
during which it transitioned back into an elliptical quasi-frozen
orbit on 11 December 2011. LRO is currently conducting its second
extende d science mission.
The time evolution of the LRO orbit geometry during the mis-
sion phases is shown in Fig. 2 , encompassing the period of time
that data used in the maps was acquired. The LRO orbit plane is
inclined approximately 90 °from the equator and is nearly fixed
in inertial space. The Moon rotates 360 °relative to the LRO orbit
plane every 27.3 day sidereal rotation period, during which the
sub-spacecraft longitude migrates 360 °of longitude. This defines
the length of one Diviner mapping cycle in the level 2 Global Data
Records (GDR), which have been archived at the NASA Planetary
Geosciences Node (LRO-L-DLRE-5-GDR-V1.0) ( Paige et al., 2011 ).
LRO obtains “daytime” coverage (defined here to be 6 am to
6 pm local solar time) during half of each orbit, and “nighttime”
coverage (6 pm to 6 am local time) during the other half. As the
Earth/Moon system orbits the sun, the local time of the of the LRO
orbit shifts 1.8 h earlier during each mapping cycle, providing full
local time coverage over the course of half of an Earth Ye a r. The
302 J.-P. Williams et al. / Icarus 283 (2017) 30 0–325
Fig. 2. Variations in orbital and celestial parameters within the data set used in rendering the Diviner maps. (a) The longitude and (b) local solar time beneath the space-
craft’s two ground tracks (i.e. the ascending and descending nodes of the orbit) at the equator. (c) The sub-solar latitude responsible for seasonal variation s in insolation. (d)
The distance between the centers of the Sun and Moon. (e) The spacecraft altitude relative to a spherical Moon with radius of 1737. 4 km with the mission phases labeled.
Vertical dashed lines denote the transitions between mission phases. The nominal mapping orbits ( 50 km average altitude) are the near-circular orbits that start with the
Nominal Mission phase and extends into the Science Mission phase, after which LRO transitioned into an elliptical orbit.
lunar spin axis is inclined by 1.54 °relative to the ecliptic, which
results in seasonal variations in insolation over the course of the
346.62 day Draconic Year ( Paige et al., 2010b ).
Diviner has operated nearly continuously in pushbroom nadir
mapping mode to acquire a consistent global dataset with max-
imum coverage. Diviner’s nadir mapping is routinely interrupted
for space/blackbody calibrations and space/solar target calibrations,
and intermittently by special off-nadir observations and campaigns
as well as calibration sequences for other LRO instruments and
planned and unplanned spacecraft operations activities.
3. Global maps
We have compiled all nadir observations (defined here to be
emission angles < 10 °relative to a sphere) from July 5, 2009
to April 1, 2015 (over 25,0 0 0 orbits) into bins of 0.5 °latitude
and longitude and 0.25 h of local time. This was found to be an
optimal local time resolution that adequately resolves the diurnal
temperatures while providing sufficient spatial coverage at 0.5 °
resolution. Several quality constraints present in the Diviner Re-
duced Data Records (RDR’s) available at the Planetary Data System
(PDS) repository were used as well (quality flag for calibration
0; quality flag for miscellaneous –0; noise quality flag –0 to 1)
( Sullivan et al., 2013 ).
Diviner’s solar channels measure the reflectance of the surface
relative to the reflectance of a normally illuminated Lambertian
surface ( Greenhagen, 2009 ). An opposition surge is observed at
low phase angles and at high incidence angles scattering results
from topography. To minimize these effects, we generate a global
visual brightness map from Diviner’s channel 1 ( Fig. 3 ) restricted
to local time hours 9–10 (i.e. incidence angles 30 °–45 °at the
equator).
For the seven Diviner infrared spectral channels, the radiance
is binned into 0.25 h of local time from which brightness tem-
peratures are derived. The bolometric brightness temperature,
T
bol
, is then determined from the brightness temperatures of the
individual Diviner spectral channels for each 0.5 °bin and 0.25 h
local time, providing a diurnal temperature curve for each 0.5 °of
the lunar surface. T
bol
is a measure of the spectrally integrated
flux of infrared radiation emerging from the surface ( Paige et al.,
2010b ). For the purposes of quantifying the overall heat balance of
the surface and comparing with available models, the bolometric
brightness temperature is the most fundamental and interpretable
measurable quantity. With this data set, we generate global maps
J.-P. Williams et al. / Icarus 283 (2017) 30 0–325 303
Fig. 3. (a) Diviner channel 1 visual brightness for local time 9–10 and (b) with a photometric normalization applied by dividing each pixel by the cosine of the latitude.
of mean hourly bolometric surface temperatures ( Fig. 4 ) and
instantaneous bolometric surface temperatures for any arbitrary
subsolar longitude ( Fig. 5 ).
To render the instantaneous global temperatures for a subsolor
longitude, φss
, the local time is determined for each 0.5 °bin and
the temperatures are interpolated from each 0.25 h binned local
time diurnal curve. Some artifacts are observed resulting from gaps
or undersampling in the local time coverage. This is particularly
apparent near the dawn and dusk terminators where tempera-
tures change abruptly resulting in sharp inflections in the diurnal
curve. Unpopulated local time bins near this inflection in surface
temperatures results in poorer approximations of interpolated
temperatures. Further, the ground track locations from individual
orbits within a bin area can vary resulting in differences in mea-
sured radiances unrelated to changing local time. The width of a
ground track swath at the nominal mapping altitude of 50 km is
3.4 km, 0.1 °of longitude at the equator, which represents only
20% of the surface area within a bin ( Williams et al., 2016 ). The lo-
cal time resolution of 0.25 °h was chosen to optimize resolution of
the diurnal temperatures while minimizing empty or single orbit
local time bins. Artifacts such as these result in vertical striping
aligned with the near-polar LRO orbit at equatorial and mid-
latitudes. Though interpolation might be improved using modeled
diurnal curves fit to the data, we have not included any modeling
in the gridding procedure to avoid any model dependence on the
results. The continued acquisition of data will improve the spatial
and local time resolution of the Diviner data set globally and
enhance future Diviner data products and science return.
4. Global temperatures
4.1. Bolometric temperatures and incidence angle
The highly insulating nature of the surface, the lack of an
appreciable atmosphere to buffer surface temperatures, and slow
rotation of the Moon allow daytime temperatures to nearly equi-
librate with the solar flux. Therefore daytime temperatures are
influenced by topographic effects and albedo with maximum
noontime temperatures at the equator in the range 387–397 K
( Fig. 6 ). Temperatures were not corrected for variations in the
Moon-sun distance prior to binning, therefore maximum tem-
peratures are for all orbital configurations. The zonal mean noon
temperatures ( Fig. 7 ) decrease with latitude, θ, consistent with
the cos
1/4
( θ) shape observed for daytime temperatures by the
Clementine long wave infrared (LWIR) camera ( Lawson et al.,
20 0 0 ). The lunar regolith is highly insulating due to its low den-
sity and thermal conductivity ( Linsky, 1966 ; Cremers and Birkebak,
1971 ; Keihm and Langseth; 1973 ) and therefore heat flow into
304 J.-P. Williams et al. / Icarus 283 (2017) 300–325
Fig. 4. Mean global bolometric temperatures for one hour of local time centered on (a) noon and (b) midnight.
the subsurface during the day is small compared to the incident
solar flux ( Vasavada et al., 1999 , 2012 ). Daytime temperatures can
therefore be approximated from the balance of incoming solar flux
and outgoing thermal emission:
T
(
θ)
=
[
S
(
1 A
)
cos
(
θ)
/εσ]
1 / 4 (1)
where S is the solar constant, A is albedo, ε is emissivity, and σ
the Stefan-Boltzmann constant. Similar to Vasavada et al. (2012) ,
we find that temperatures require the albedo to increase with
latitude ( Fig. 7 ). Using the albedo from Vasavada et al. (2012) :
A
(
θ)
= A
o
+ a
(
θ/ 45
)
3
+ b
(
θ/ 90
)
8
where a = 0.045 and b = 0.14 and assuming A
o
°= 0.08, S = 1370 ,
and ε = 0.95 provides similar temperatures to the observed mean
zonal temperatures and is similar to the analytic function derived
by Hurley et al. (2015) . The standard deviation of the mean T
bol
also increases with latitude. While T
bol
variations near the subsolar
point will be largely due to variations in albedo and emissivity
( Fig. 6 ), at higher incidence angles, the influence of topography
and surface roughness on temperatures will dominate resulting in
increasing variations in temperatures for a given local time.
Temperatures are observed to decrease with latitude at all local
times ( Fig. 8 ) with the largest amplitude in diurnal temperatures
occurring at the equator ( Fig. 9 ). Temperatures between noon and
midnight at the equator vary 290 K while at 85 °latitude, the
temperature variation is reduced to 120 K. Changes in tempera-
tures occur particularly rapidly in the early morning and late af-
ternoon local times. Temperatures increase > 15 0 K from hour 6 to
7 at the equator. The standard deviation of the mean temperatures
is also relatively large during these hours as slopes and shadows
will have the largest influence on temperatures ( Figs. 8 b and 9 b).
Nighttime temperatures by comparison are much more uniform
( Fig. 8 c-d). Nighttime temperatures are characterized by cold tem-
peratures with the sensible heat stored in the subsurface during
the day being the only heat source to balance the loss of thermal
radiation to space during the long lunar night. As a result, surface
temperatures are sensitive to the thermophysical properties of the
near-surface regolith. Rocky, coherent surfaces and blocks with
higher thermal inertia provide larger reservoirs of heat and remain
warmer than the pulverized, fine-grained regolith ( Bandfield et al.,
2011; Williams et al., 2016 ). Temperatures decrease throughout
the night with the mean temperatures at the equator decreasing
from 117 K to 95 K between the hours 19 and 5 ( Fig. 8 c). The
rate of cooling declines as surface temperatures decrease and heat
is conducted to the surface from increasing depth through the
night. From hours 19 to 20, equatorial temperatures cool 5.4 K
compared with 1.0 K between the morning hours 4 and 5 prior to
sunrise. Modeling by Vasavada et al. (2012) has shown that the
J.-P. Williams et al. / Icarus 283 (2017) 30 0–325 305
Fig. 5. Global instantaneous temperatures of the Moon in (a) cylindrical equidistant projection ( φss
= 180 °) and (b) orthographic projection (
φss
= 180 °, 120 °, and 0 °).
Fig. 6. Maximum bolometric temperatures at the equator (within ±5 °latitude) and
the corresponding relative surface reflectance from Diviner channel 1 ( Fig. 3 b).
equatorial nighttime temperatures are consistent with an expo-
nential increase in density and thermal conductivity with depth.
An asymmetry is observed between morning and afternoon
daytime temperatures. This is observed as an offset in tem-
peratures between morning and afternoon temperatures with
equivalent solar incidence angles ( Fig. 6 a). This asymmetry in-
creases with increasing incidence angle. For example equatorial
Fig. 7. (a) Zonal mean noontime bolometric temperatures. Error bars are standard
deviations plotted in (b). Curves are temperatures assuming radiative balance for
a constant albedo (dashed) and incidence angle dependent albedo (dash-dot) of
Vasavada et al. (2012) , and the analytic function (dot) from Hurley et al. (2015) .
306 J.-P. Williams et al. / Icarus 283 (2017) 300–325
Fig. 8. (a) Zonal mean hourly daytime bolometric temperatures and (b) standard
deviation. (c) Zonal mean hourly nighttime bolometric temperatures and (b) stan-
dard deviation. Higher nighttime temperatures and standard deviations at latitudes
above ±80 °in (c-d) result from the occurrence of low-angle illumination of sur-
faces, especially during polar summers. Nighttime is defined here by local time, not
sun elevation.
temperatures at hour 6 (dawn terminator) is 133 K and hour 18
(dusk terminator) is 163 K, a difference of 30 K. Temperatures at
hours 7 and 17 are 263 K and 267 K respectively, a difference of
4 K and temperatures at hours 8 and 16 are 317 K and 318 K.
The offset also appears to be larger at higher latitudes. Bandfield
et al. (2015) found that non-radiative-equilibrium conditions are
Fig. 9. (a) Zonal mean bolometric temperatures and (b) standard deviation versus
local time for latitude bands 0 °, 30 °, 45 °60 °, 70 °, 80 °, and 85 °.
prevalent at local times approaching sunrise and sunset and high
latitudes where illumination conditions are changing rapidly and
sunlit and shaded surfaces can be cooler or warmer respectively
than predicted by models assuming equilibrium conditions.
The effects of thermal inertia can also be observed when com-
paring morning and afternoon temperatures with incidence angle
globally ( Fig. 10 ). We generate instantaneous surface temperatures
as described in Section 3 ( Fig. 5 ) for every 15 °of subsolar longi-
tude. The 24 global temperature maps represent 24 h of the luna-
tion cycle. These maps are then shifted in longitude so the subsolar
longitudes co-align providing an average of the temperatures in
relation to the subsolar point ( Fig. 10 a). The daytime temperatures
are split into am (hours 6–12) and pm (hours 12–18) local times
and binned into 5 °increments of incidence angle ( Fig. 10 b). Mean
temperatures are increasingly higher in the pm hours than the am
hour at increasing incidence angle with a difference of 10 K at 85 °.
4.2. Anisothermality
4.2.1. Daytime
Brightness temperatures in Diviner’s individual infrared chan-
nels may vary depending on the distribution of sub-footprint-scale
temperatures, spectral emissivities, and photometric properties.
In general, Diviner’s surface footprint contains small scale slopes,
shadows, or rocks, resulting in a mixture of temperatures within
the field-of-view. Due to the non-linear nature of Planck radiance
J.-P. Williams et al. / Icarus 283 (2017) 30 0–325 307
Fig. 10. (a) Average of 24 T
bol
maps generated with 15 °increments of subsolar longitude normalized to the subsolar point (0 °, 0 °). (b) Mean daytime T
bol
from (a) for morning
hours 6–12 (grey) and afternoon hours 12–18 (black) as a function of incidence angle binned at 5 °intervals. Error bars are the standard deviation.
with respect to wavelength, the warmer temperatures have an
increased proportional influence on brightness temperatures in
the shorter wavelength channels. Therefore the brightness tem-
peratures cannot be interpreted in terms of a unique surface
temperature. The bolometric temperature, by integrating the full
spectrum, is more directly related to the heat balance of the
surface. However, the anisothermality in the individual Diviner
channels provides information about surface roughness ( Bandfield
et al., 2015 ) and heterogeneities in thermophysical properties
( Bandfield et al., 2011 ).
At high incidence angles, sunlit slopes and shadows result in
a variety of temperatures depending on slope orientations with
respect to the sun. Large lateral temperature gradients are possible
due to the highly insulating nature of the top few cm of the
regolith with surfaces separated by distances a few mm able to re-
main thermally isolated in the lunar environment ( Bandfield et al.,
2015 ). The mixture of sunlit and shaded slopes in the early morn-
ing and late afternoon hours results in elevated anisothermality
observable by differencing the brightness temperatures of individ-
ual Diviner channels. Fig. 11 shows a difference map of Diviner
channels 4 (8.10–8.40 μm) and 7 (25–41 μm) daytime temperatures
with the subsolar longitude and latitude at 0 °. The channel 4
passband is near the observed mean CF emission peak (8.15 for
highlands, 8.30 for mare; Greenhagen et al., 2010 ) and observed
temperatures are consistently 5–7 K warmer than channel 7 for
incidences angles < 30 °( Fig. 12 ). The T
4
T
7
an isothermility in-
crease with incidence angle results from surface roughness where
shadowing and slope effects lead to mixtures of temperatures
within the field-of-view and are maximized at incidence of 90 °
representing the poles and the terminators where illumination
is at grazing angles. Channel 4 loses sensitivity below 190 K
resulting in some anomalous low, or negative anisothermality
values near the poles and the nighttime hours.
Bandfield et al. (2015) showed that surface roughness had little
effect on anisothermality for incidence angles less than 30 °and
the observed difference in brightness temperatures at these angles
is predominantly due to differences in emissivity for the two
channel’s passband wavelengths. These emissivity differences are
highlighted by subtracting the zonal mean anisothermality from
maps with local times constrained to ±2 h of local time around
308 J.-P. Williams et al. / Icarus 283 (2017) 30 0–325
Fig. 11. Daytime brightness temperature difference between Diviner channels 4 and
7 for subsolar longitude and latitude 0 °. Grey areas are where channel 4 loses sen-
sitivity below 19 0 K.
noon (
Fig. 13 ). The observed variations in emissivity of T
3
T
7
and T
4
T
7
are shown in Fig. 13 . Channel 4 is typically near the
peak in the Christiansen feature and less susceptible to emissivity
variations than channel 3. This is apparent in Fig. 13 where the
T
3
T
7
map displays larger emissivity variations than T
4
T
7
. This
demonstrates that emissivity varies to a greater extent near 8 μm
than at the channel 7 passband (26–41 μm) and the variation in
anisothermality observed in the maps result from shifts in the CF
wavelength position ( Greenhagen et al., 2010 ). The maria and re-
gions containing extensive pyroclastic deposits such as Aristarchus
Plateau, Sulpicius Gallus, Mare Vaporium, Rimae Bode, exhibit
typically smaller emissivity differences while highly reflective sur-
faces, such as the immature materials excavated by young impacts,
including rays in some cases (e.g. Tycho and Jackson craters), show
larger emissivity differences. These variations correspond to the
variation in CF mapped by Greenhagen et al. (2010) .
4.2.2. Nighttime
Anisothermality in nighttime temperatures is indicative of
materials with differing thermophysical properties within Diviner’s
field-of-view. Bandfield et al. (2011) modeled anisothermality
in Diviner channels 6–8 to derive rock abundances and regolith
fines temperature. We have created a global nighttime average
anisothermality map using the mean brightness temperatures for
the local time range 20–4 from Diviner channels 6 (13–23 μm)
and 8 (50–100 μm) which provide the largest nighttime anisother-
mal contrast ( Fig. 14 ). The signal-to-noise ratio for the shorter
wavelength channels is not adequate for the relatively cold lunar
nighttime temperatures and channel 9 has relatively large drifts in
brightness temperature following calibration sequences that result
in striping artifacts in channel difference maps.
The nighttime T
6
T
8
map reveals broad global variations in
regolith thermophysical properties within the top 30 cm, the
approximate penetration depth of the diurnal thermal wave
( Vasavada et al., 2012 ). High T
6
T
8
values represent locations
where temperature contrasts occur within Diviner’s field-of-view
during the lunar night, for example areas with various fractions of
rocks and regolith fines with highly contrasting thermal inertias
( Bandfield et al., 2011 ). The largest values correspond to young
Copernican-age impact craters that have excavated large blocks
such as Tycho crater (43.4 °S, 11.3 °E). The age of Tycho is 100 Ma
Fig. 12. (a) Scatter plot and (b) binned values of Diviner channel 4–7 brightness
temperatures versus incidence angle for subsolar longitude and latitude 0 °. Error
bars are standard deviation.
( Stöffler and Ryder, 2001 ) and likely the youngest crater of its size
( D = 86 km). The pattern of anisothermality also reflects the distri-
bution of maria and regolith that has been disturbed or modified
by impact events such as the emplacement of rays or impact melts.
Rocks and coherent blocks on the surface of the Moon will
be mechanically broken down into fine-grained regolith by mi-
crometeorite bombardment, the dominant surface geologic process
operating on the Moon. Ghent et al. (2014) found a strong inverse
correlation between the 95th percentile value of Diviner derived
rock abundance for the ejecta of Copernican-age craters and their
published model crater-retention ages. The implied rate of break-
down of large ejecta blocks is qualitatively consistent with the
estimated survival times of meter-sized boulders from LRO Camera
(LROC) images. Basilevsky et al. (2013) find that for boulders 2 m
in diameter, 50% of the original rock population will be destroyed
after 40–80 Ma. These implied survival times are about a factor
of 5 shorter than pre-LRO estimates ( Horz et al., 1975 ). Vasavada
et al. (2012) noted a general thermophysical homogeneity implied
by Diviner observations near the equator due to the ubiquitous
bombardment of the lunar surface that has pulverized material
into fine grains. However, as the T
6
T
8
map shows, differences in
the bulk properties of the surface and near-surface do persist.
J.-P. Williams et al. / Icarus 283 (2017) 30 0–325 309
Fig. 13. Zonal mean (a) T
3
T
7
and (b) T
4
T
7
averaged over a 4 h local time window centered on noon (hours 10–14) corresponding to incidence angles 30 °at the equator.
Black arrows are large pyroclastic deposits with below average anisothermality and white arrows are examples of immature, high-reflectance surfaces with above average
anisothermality associated with the Copernican-age craters
Jackson and Tycho.
Fig. 14. Mean nighttime (local time hours 20–4) brightness temperature difference between Diviner channels 6 and 8. Grey areas near the poles are where channel 6 loses
sensitivity below 95 K.
310 J.-P. Williams et al. / Icarus 283 (2017) 300–325
Fig. 15. (a) Early nighttime temperatures (hours 20–0) and (b) late nighttime temperatures (hours 0–4). (c) Early nighttime temperature anomalies and (d) late nighttime
temperature anomalies. The circles are the locations of the five coldest temperature anomalies within ±45 °latitude. Black circles are cold spots and grey circles are poleward
facing slopes.
4.3. Nighttime temperature anomalies
Anomalous nighttime temperatures are highlighted by subtract-
ing the zonal mean temperature from the global temperatures,
T
bol
= T
bol
T
zonal mean
. Surface temperatures are highly sensitive
to properties such as density and particle size distribution. Slight
modifications to the grain packing or concentration of rocks can
result in a temperature contrast relative to typical lunar regolith
that can be readily detected in Diviner observations (e.g., Bandfield
et al., 2011; Hayne et al., 2013; Vasavada et al., 2012; Yu and Fa,
2016 ). Similar to the nighttime T
6
T
8
map, these T
bol
maps reveal
areas of atypical thermophysical properties ( Fig. 15 ). Note that
J.-P. Williams et al. / Icarus 283 (2017) 30 0–325 311
Fig. 16. Histograms of (a) early (hours 20–0) and late (hours 0–4) nighttime tem-
peratures and (b) early and late nighttime temperature anomalies within ±45 °lat-
itude.
the T
6
T
8
values do not necessarily correlate with the anomalous
nighttime temperatures. A surface of uniform temperature within
Diviner’s field-of-view will not result in anisothermality regardless
of whether that surface is anomalously warm or cool for a given
latitude and local time as anisothermality results from a mixture
of temperatures within the instruments field of view.
We have split the temperatures into early nighttime (hours
20–0) and late nighttime (hours 0–4) to create mean global tem-
perature maps of the early and late nighttime and corresponding
early and late nighttime temperature anomaly maps ( Fig. 15 ).
Histograms of the temperatures within ±45 °latitude ( Fig. 16 )
show the relative cooling between the early and late hours with
the peaks of the histograms shifting from 105 K to 98 K. The
histograms of the temperature anomalies show a reduction in
temperature differences in the late nighttime implying a homog-
enization of temperatures over time. This could result from a
reduction in thermal contrast between sloped surfaces or high
and low thermal inertia materials, or a reduction in contrasting
thermophysical properties at deeper levels of the regolith as heat
is conducted from greater depths later in the night.
The five coldest temperature anomalies in the early nighttime
and the late nighttime maps within ±45 °latitude are marked
with circles in Fig. 15 c and d respectively. The black circles are
locations that contain cold spots: thermal features characterized
by small, fresh craters surrounded by extensive distal, highly
insulating surfaces ( Bandfield et al., 2014 ). Two of these cold spots
appear in both the early and late nighttime anomaly maps at map
pixels centered on 5.75 °S, 90.75 °E and 34.25 °N, 131.75 °E. Two
additional cold spot at 3.25 °S, 152.25 °E and 27.25 °S, 17 7. 2 5 °E
are among the coldest temperature anomalies in the late evening
map. These four cold spots persist as cold temperature anomalies
in the late nighttime with T
bol
values of 8.4, 6.9, 6.2 and
5.6 K. The other locations identified as having large T
bol
values
are associated with poleward facing slopes near the 45 °latitude
cutoff implying slopes begin to influence temperatures to a larger
extent near this latitude. All but one are identified in the early
map indicating that, unlike the cold spots, their thermal contrast
diminishes over time. The average temperatures of the cold spots
for each hour of local time between hours 20 and 4 is plotted in
Fig. 17 . The cold spots maintain their approximate T
bol
values
throughout the night without converging toward the mean tem-
peratures of the corresponding latitude explaining why cold spots
become more apparent as thermal anomales later in the night.
The hottest temperature anomalies are associated with the
young rayed Copernican-age craters Giordano Bruno, Tycho, and
Moore-F with average nighttime temperatures of 149.4, 141.3, and
135.4 K respectively for the warmest map pixels at each crater
which represent T
bol
values of 50.9, 45.0, and 36.3 K. These
craters are associated with high rock abundances and bright rays.
Unlike the cold spots, their thermal contrast diminishes over time
during the night ( Fig. 17 b). Localized surfaces likely have even
warmer nighttime temperatures. These temperature anomalies
are an average of the area represented by the 0.5 °binned data
and isolated regions at smaller spatial scales that are unresolved
at this resolution will be hotter. Areas such as these may be of
importance for exploration and long-duration surface missions
as the warmer nighttime temperatures reduce the temperature
extremes experienced by hardware deployed on or near the lu-
nar surface. Significant variations in temperature complicate the
design of habitats and other structures due to thermal expansion
and contraction and can lead to structural fatigue (e.g. Ruess et al.,
2006; Mottaghi and Benaroya, 2015; Malla and Brown, 2015 ).
4.4. Minimum and maximum temperatures
Daytime temperatures on the Moon are approximately in
radiative equilibrium. For slowly rotating bodies with low thermal
inertias like the Moon, heat diffusion models predict surface
temperatures at the equator within 1 K of radiative equilibrium
between local time hours 8 and 16 (i.e. incidence angles < 60 °)
( Vasavada et al., 2012; Bandfield et al., 2015 ). Maximum tempera-
tures therefore occur at noon and will depend on the albedo while
being sensitive to the orbital and celestial geometry. The mini-
mum temperatures will occur just prior to local sunrise and are
dependent on the thermophysical properties of the near-surface.
Maximum and minimum global surface temperature maps are
shown in Fig. 18 . The mean temperature at the equator is 215.5 K
with an average maximum of 392.3 K and average minimum of
94.3 K ( Fig. 19 ), representing an average change in temperature
of 300 K. Average maximum and minimum temperatures in the
polar regions (poleward of 85 °) are 202 K and 50 K respectively
with a mean average temperature 104 K. Mean maximum temper-
atures in the south polar region are 11 K warmer than the north
polar region, however the average minimum temperatures are the
same at both poles. This discrepancy is likely due to differences
in the distribution and configuration of the topography which is
the dominant control of polar temperatures on the Moon. The
south polar topography is more rugged, displaying a larger range
of elevations ( Smith et al., 2010 ). The maximum solar declination
of 1.5 4 °results in surfaces that are permanently shadowed down
to roughly 60 °latitude ( McGovern et al., 2013; Siegler et al., 2015 ).
Though a larger surface fraction of the south polar region is in
permanent shadow compared to the north polar region, the larger
topography range responsible for this results in generally more
favorable illumination conditions for equator facing slopes than in
the north ( Mazarico et al., 2011b ).
312 J.-P. Williams et al. / Icarus 283 (2017) 300–325
Fig. 17. Hourly average nighttime T
bol
for (a) three lowest temperature anomaly cold spots and (b) three hottest temperature anomaly bright-rayed Copernican craters along
with the average T
bol
for their corresponding latitudes.
The latitude effects on the maps are removed by subtracting
the zonal mean minimum and maximum temperatures ( Fig. 20 ),
as was done in Section 4.3 to highlight nighttime temperature
anomalies ( Fig. 15 ). Like the nighttime temperature anomalies,
minimum temperature anomalies are related to thermophysical
properties while maximum temperature anomalies are related
to albedo. Darker surfaces have higher maximum temperatures
relative to bright surfaces, while high thermal inertia (TI), or
rocky surfaces have high minimum temperatures relative to low-TI
surfaces ( Fig. 21 ).
The ratio of the maximum and minimum temperatures,
T
max
/ T
min
, highlights relative differences between the temperatures
while differencing the minimum and maximum temperatures,
T
max T
min
, shows the absolute difference, or amplitude, between
the two temperature extremes ( Fig. 20 ). While these are similar in
that they both convey information about variations between the
maximum and minimum temperatures, they do not necessarily
correspond; T
max
/ T
min
can remain the same between two loca-
tions while T
max T
min
does not, and vice versa. For example, if
T
min
= 80 K and T
max
= 250 K at location A ( T
max
T
min
= 170 K) and
T
min
= 112 K and T
max
= 350 K at location B ( T
max T
min
= 238 K),
then T
max
/ T
min
= 3.125 at both locations. Alternately if we compare
location B to a new location C with T
min
= 80 K and T
max
= 318 K,
T
max T
min
= 170 K at both locations, however T
max
/ T
min
= 3.975
at location C . In other words, for a given amplitude, shifting the
minimum and maximum temperatures downward increases the
ratio. As a result, T
max
/ T
min
is more sensitive to smaller amplitude
differences at colder temperatures relative to T
max T
min
. The cold
spots provide a good example of this as they have large positive
values in the ratio anomaly map, but are not as apparent in the
difference anomaly map ( Fig. 20 ). Being correspondingly larger at
lower temperatures, T
max
/ T
min
is also less sensitive to slope effects
at high latitudes as poleward and equator facing slopes at a given
latitude have similar relative T
max
/ T
min
values.
The absolute difference between the maria and highlands is
apparent in the T
max
T
min
anomaly map, however the relative dif-
ference between them is similar. This lack of distinction between
the two terrians in the T
max
/ T
min
map results from the diurnal
modulation of temperatures occurring at higher temperatures in
the maria. The region in the black box in Fig. 20 , for example, is a
region of fairly homogenous T
max
/ T
min
values though they include
both highland and mare units. The T
max
T
min
values however dif-
fer between maria and highlands reflecting a higher temperature
amplitude in the mare.
J.-P. Williams et al. / Icarus 283 (2017) 30 0–325 313
Fig. 18. (a) Maximum and (b) minimum global temperatures.
Fig. 19. Histograms of maximum, mean, and minimum global temperatures. The mean temperature at the equator ( ) is 215.5 K with an average maximum of 392.3 K and
average minimum of 94.3 K (arrows show range between average maximum and minimum T
bol
). The mean temperature of the polar regions poleward of 85 °( ) is 104 K
with an average maximum of 202 K and average minimum of 50 K (arrows show range between average maximum and minimum T
bol
).
5. Discussion
5.1. Copernican-age craters
Many young, Copernican-age craters are associated with bright,
high-reflectance surfaces within their interiors, blocky ejecta,
and rays as fresh excavated subsurface material is generally
brighter than surrounding surface materials. This modification
of the regolith by impacts is apparent in the thermal data as
the addition of blocky material and changes in albedo alter the
surface energy balance. The maturation of lunar soils results in
darkening due to micrometeorite bombardment and solar wind
and cosmic-ray exposure, causing the high-reflectance regions to
fade with time ( Lucey et al., 20 0 0; Grier et al., 2001 ). Consequently
bright, rayed craters are typically confined to the Copernican era
( Wilhelms, 1987 ).
314 J.-P. Williams et al. / Icarus 283 (2017) 300–325
Fig. 20. (a) Maximum and (b) Minimum temperatures with zonal mean subtracted. (c) Ratio of maximum and minimum temperatures with ratio of the zonal mean max-
imum and minimum temperatures subtracted.