Surface Temperature Simulation of Lunar Dayside and Its Geological Applications: a Case in Sinus Iridum

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Article Surface Temperature Simulation of Lunar Dayside and Its Geological Applications: A Case in Sinus Iridum

Jidong Zhang 1,2, Jinsong Ping 2,3,*, Zhaofa Zeng 1, Yongzhang Yang 4 , Xiangyue Li 1 and Mingyuan Wang 2

1 College of Geoexploration Science and Technology, Jilin University, Changchun 130026, China; [email protected] (J.Z.); [email protected] (Z.Z.); [email protected] (X.L.) 2 Key Laboratory of Lunar and Deep-Space Exploration, Chinese Academy of Sciences, Beijing 100101, China; [email protected] 3 University of Chinese Academy of Sciences, No. 19(A) Yuquan Road, Shijingshan District, Beijing 100049, China 4 State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430070, China; [email protected] * Correspondence: [email protected]

Received: 14 October 2019; Accepted: 12 December 2019; Published: 15 December 2019

Abstract: Lunar surface temperature is one of the fundamental thermophysical parameters of the lunar regolith, which is of great significance to the interpretation of remote-sensing thermal data. In this study, a daytime surface temperature model is established focusing on the lunar superficial layer with high spatial-temporal resolution. The physical parameters at the time of interest are adopted, including effective solar irradiance, lunar libration, large-scale topographic shading, and surrounding diffuse reflection. Thereafter, the 1/64◦ temperature distributions at five local times are quantitatively generated and analyzed in Sinus Iridum. Also, combined with Chang’E-2 microwave radiometer (CELMS) data and Diviner thermal infrared (TIR) data, the spectral emissivity distributions are estimated as a potential geological application of the simulated surface temperature. The results are as follows: (1) daytime surface temperature in Sinus Iridum is significantly affected by the local topography and observation time, and the influence of diffuse reflection energy is obvious; (2) the emissivity distributions provide a new way to understand the thermophysical properties difference of lunar regolith at different depths; (3) the influence of lunar orbiting revolution and precession on surface temperature should be analyzed carefully, which shows the importance of using the parameters at the time of interest.

Keywords: lunar surface temperature; Sinus Iridum; geological application; remote-sensing data

1. Introduction Lunar surface temperature is one of the important and fundamental parameters to interpret the thermal characteristics of the regolith from remote-sensing thermal data, which will give clues for solving thermal models and understanding the evolution of the Moon [1–5]. In particular, the lunar superﬁcial layer temperature of the lunar regolith is not only regarded as a basic boundary condition for the thermal evolution models, but also represents the outermost thermal environment of the lunar surface, which changes a lot during a lunar day [6,7]. Thermophysical characteristics play important roles in understanding the lunar surface thermal environment and geological evolution [8–12]. Furthermore, remote-sensing thermal data is a key data source in geological interpretation. In order to eliminate the inﬂuence of observation time,

Sensors 2019, 19, 5545; doi:10.3390/s19245545 www.mdpi.com/journal/sensors Sensors 2019, 19, 5545 2 of 23 the brightness temperature (TB) maps of the region of interest are usually generated at the same local time within a short time span [13,14]. The lunar orbital explorers, such as the microwave radiometer (CELMS) instrument onboard Chang’E (CE)-1/2 and Diviner instrument onboard the Lunar Reconnaissance Orbiter (LRO), have successfully measured the thermal emissions of the lunar surface. However, the orbital explorers’ measurements are limited by the instantaneous field of view of the detector at the observation time [15,16], thus, the remote-sensing data from different orbital explorers may not have the temperature information at corresponding observation time. Moreover, it may take a long time to obtain the same local time thermal distribution of the region of interest with high spatial-temporal resolution. Because the measurements from the orbital explorer are acquired in a very short time, the acquisition of lunar superficial layer temperature at the time of interest is not only indispensable in the in-situ lunar exploration but of great significance for the remote-sensing thermal data. Great efforts have been made to obtain the lunar surface temperature for several decades [3,10,13,15, 17–20]. The earliest method of lunar surface temperature detection was to observe the lunar surface by using ground-based infrared and radio telescopes [17,18]. Thereafter, orbital remotely-sensed observations and in-situ measurements enriched the ways and have obtained a lot of surface temperature information [3,10,13,15,19,20]. However, the ground-based observations can only measure the lunar near-side temperatures, and the spatial resolution is low. The cost of in situ measurements is too expensive to select many landing sites. In-orbiter measurements are limited by the satellite orbit and lack timeliness. Hence, how to overcome these problems becomes key in current lunar study. Fortunately, with the help of thermal and physical properties of the lunar regolith acquired, the numerical simulation based on the theoretical model and regolith parameters emerges to meet the requirement. Because there is no atmospheric protection, the Moon is directly exposed to outer space. Compared with the night surface temperature, the daytime surface temperature is primarily influenced by the solar irradiance, surrounding thermal emissions, albedo and emissivity of the lunar regolith, which attracts more attention due to its complexity. Various lunar surface temperature models have been established in previous studies [2–5,7,21–27]. In the early time, the temperature models mainly employed the simplified variations of solar irradiance [21–24], which assumed that the temperature changed in a simple cosine function or Fourier series, and these simulations were not accurate enough because of the lack of topography and time-varying analysis. Thereafter, the scattering model within simple craters was preliminarily adopted based on the 1-D thermal model to acquire the temperatures in the lunar polar regions [25]. Based on the orbital parameters of the Moon and the Sun, the time-varying effective solar irradiance was gradually used to improve the lunar surface temperature model by means of analyzing the solar incidence angle and Sun-Moon distance [26,27]. In recent years, following with the acquisition of more detailed multi-source remote-sensing data, such as the Clementine Ultraviolet/Visible (UVVIS) data and Lunar Orbiter Laser Altimeter (LOLA) data, the solar albedo and large-scale topographic effect can be further introduced to simulate a more accurate surface temperature distribution [2–5,7]. Although these surface temperature models are constantly improved, these results are not combined with the physical parameters at the time of interest, and the effects of complex surrounding thermal environment and lunar libration are not mentioned. Surface roughness is a main factor affecting the lunar thermal environment. It can cause a partial re-absorption of scattered or emitted radiation, and the surface temperature will increase with the self heating [28]. A significant limb brightening and unusually slow cooling of certain craters during lunar eclipse had been confirmed to be caused by surface roughness [29]. Moreover, most of the studies on the influence of surface roughness on surface temperature focused on the lunar polar regions to explore the water ice, which also showed the importance on the surface temperature [25,30]. In addition, because of the aspherical distribution of lunar mass, the rotational dynamics are not uniform [31]. Consequently, the influences of complex surface thermal environment and lunar libration on surface temperature need to be further considered. Sensors 2019, 19, 5545 3 of 23

In this paper, a surface energy balance is established to simulate the superficial layer temperature of the lunar regolith. Based on the 1/64◦ LOLA data and DE430 ephemeris, we improve the effective solar irradiance model and the diffuse reflection model, and the dayside surface temperature is simulated according to the physical parameters at the time of interest, which are different from previous works. Also, combined with the CELMS data and Diviner thermal infrared (TIR) data, the thermophysical feature difference in Sinus Iridum is investigated. This paper is organized as follows. At the first step, a lunar surface temperature model is established and the physical parameters are discussed. Then, taking Sinus Iridum as the study area, five local-time temperature maps within 15 days are simulated and analyzed, and the uncertainty analysis is also included. After that, combined with CELMS data and Diviner TIR data, the spectral emissivity maps are estimated to reveal the thermophysical feature difference in Sinus Iridum, and the influence of observation time on the highest simulated temperature in 40 years is presented. Finally, the conclusions are given.

2. Methodology The primary goal of this section is to predict the superﬁcial layer temperature of the lunar dayside, therefore, we focus on the lunar surface boundary and solve this problem based on the surface energy balance.

2.1. A Physical Temperature Model Taking an arbitrary lunar superﬁcial layer as the boundary, there exists an instantaneous process of energy balance. From outside to inside, the energy includes direct solar radiation, Earth radiation, multiple scattering of solar radiation, surrounding infrared emissions, and the energy from the surface to the subsurface. From inside to outside, the energy includes the energy radiated from the lunar surface, and the heat ﬂow inside the Moon. The thermal energy in both directions follows the energy conservation law. Based on the Stefan–Boltzmann rule, above relationship can be described by the following equation [7,32]:

4 (1 α)(Is + Ie + I ) + εF + Qout = εσT + Ks(∂T/∂x) (1) − re f where α is the lunar surface albedo, Is is the direct effective solar irradiance, Ie is the Earth irradiance, Iref is the multiple scattering of solar radiation, ε is the infrared surface emissivity, F is the thermal energy of surrounding infrared emission, Qout is the heat flow energy from the interior of the Moon to the surface. σ is the Stefan–Boltzmann constant, T is the superficial layer temperature, Ks(∂T/∂x) is energy from the surface to the subsurface, Ks is the surface conductivity. Because the influences of Ie and Qout on the surface temperature are both very small during the daytime [33], we neglect their contributions. Besides, it is reported that Ks is very low [1,9,34], thus, the energy from the surface to the subsurface is almost 0 in a short time. Hence, we thoroughly analyze the other parameters to simulate the surface temperature with a better accuracy.

2.2. Parameter Identification For the physical temperature model to simulate the lunar superficial layer temperature accurately, parameter identification must be discussed, including Is, Iref, F, and illumination conditions. These factors are all acquired at the time of interest.

2.2.1. Improving Is Model

The Is model is the most important factor to predict the surface temperature of lunar dayside as a function of Sun-Moon distance (Dsm) and incident angle of solar irradiance. When considering the Sensors 2019, 19, 5545 4 of 23

2 perihelionSensors 2019, 19 and, x FOR aphelion PEER REVIEW distances, the solar irradiance changes from 1326 to 1418 W/m [24]. The4 ofIs 22is expressed as follows [6]: 2 Is = I (AU/Dsm)2 cos(z0) (2) I s  ·I (AU/D sm ) cos( z0 ) (2) 2 where I is the solar constant and set to the average value of 1368 W/m 2, AU is astronomical unit, z is where I is the solar constant and set to the average value of 1368 W/m , AU is astronomical unit, z00 is the solar zenith angle in degree. However, this model neglected the surface inclination, that is, z should be revised according However, this model neglected the surface inclination, that is, z0 should0 be revised according to theto the relationship relationship between between position position of the of theSun Sun and and the thesurface surface topographic topographic features. features. Fortunately, Fortunately, the positionthe position of the of the Moon Moon and and the the Sun Sun and and lunar lunar libration libration infor informationmation at at the the time time of of interest interest can can be z inferred from the ephemeris.ephemeris. Hence, a ann improved geometric model about z0 isis proposed based on topography data. Slope and aspect are typically parameters to describe the relief and structure of the land surface based on on raster raster data. data. In this In this paper, paper, the vector-based the vector-based surface surface geomorphic geomorphic generation generation algorithm algorithm proposed proposedin [35] is adopted, in [35] is which adopted, is a widelywhich is used a widely second-order, used second finite-di-order,fference finite algorithm-difference using algorithm the elevation using valuesthe elevation of the fourvalues immediately of the four adjacentimmediately pixels adjacent [36,37]. pixels [36,37]. Y Y Y Y As shown in FigureFigure1 1,, five five pixels pixels are are labeled labeled Y00 throughthrough Y44.. Y0 isis the target site, andand Y1 through Y4 areare the the four four neighboring neighboring lunar lunar unit unit surfaces surfaces of Y 0 of, respectively. Y0, respectively. The dashed The dashed lines labeled lines d labeled1 through d1 d through4 give the d4 magnitudegive the magnitude of the pixel of elevations,the pixel elevations, rising from rising the pixel from centers. the pixel The centers. geocentric The rectangulargeocentric rectangularcoordinate ( Yxcoordinatei, Yyi, Yz i(,Yxi =i, 1,Yy 2,i, 3,Yz 4)i, iof = the1, 2, four 3, 4) pixels of the can four be pixels obtained can frombe obtained longitude, from latitude, longitude, and Y Y latitude,elevation. and Also, elevation. a vector Also, with itsa vector tail at with the center its tail of at pixel the center1, and of its pixel point Y1 at, and the its center point of at3 theisshown, center n whichof Y3 is is shown, denoted which by eis( Yxdenoted3-Yx1, byYy 3n-eYy (Yx1, 3Yz-Yx3-1Yz, Yy1),3- andYy1, givesYz3-Yz an1), “east–westand gives an tilt” “east for–Ywest0; similarly, tilt” for theY0; vectorsimilarly,ns ( Yxthe2 -vectorYx4, Yy n2s- Yy(Yx4,2Yz-Yx24-,Yz Yy4)2- fromYy4, YYz4 2to-YzY42) givesfrom theY4 to “north–south Y2 gives the tilt” “north for Y–0south. The twotilt” vectorsfor Y0. Thecross two each vectors other, cross forming each a planeother, thatforming is equivalent a plane that to the is planeequivalent of Y0 to(the the yellow plane planeof Y0 in(the Figure yellow1). The normal vector Nslp produced by the cross product ns ne is orthogonal to the plane of Y , which plane in Figure 1). The normal vector Nslp produced by the× cross product ns × ne is orthogonal0 to the planecan be of used Y0, which to describe can be the used surface to describe slope and the aspect. surface slope and aspect.

Figure 1. SchematicSchematic figure ﬁgure showing the relationship of the ﬁvefive pixel labeled labeled YY00 throughthrough YY44 and geometric model of z.

Based on the orbital parameters of the Moon and Sun at the time of interest interest,, the vector L with its tail at the center of Y0 and its point at the center of the Sun is introduced. Furthermore, the included angle ( (zz)) between between vector vectorL andL and vector vectorNslp Ncanslp can improve improvez0 respected z0 respected to the to horizontal the horizontal plane and plane regard and regardit as the it solar as the incidence solar incidence angle. Theangle. cosine The c valueosine ofvaluez is theof z verticalis the vertical component component of L respecting of L respecting to the planeto the ofplaneY0, of which Y0, which can better can better eliminate eliminate the inﬂuence the influence of surface of surface slope slope on I son. It Is can. It can be calculatedbe calculated by byEquation Equation (3): (3):

z = arccos(Nslp L/( Nslp L )) (3) z  arccos(N slp· L /( N slp ·L| )|) (3) Note that if z is greater than 90◦, the direct solar illumination does not aﬀect temperature, and cos(zNote) should that be if setz is to greater 0. Actually, than I90°,s is inﬂuencedthe direct solar by the illumination Sun-Y0 distance does ( Rnotsm), affect andit temperature can be improved, and cos(as follows:z) should be set to 0. Actually, Is is influenced by the Sun-Y0 distance (Rsm), and it can be 2 improved as follows: Is = I(AU/Rsm) cos(z) (4) · 2 Is  I(AU / Rsm ) cos(z) (4)

2.2.2. Acquisition of Illumination Condition

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2.2.2. Acquisition of Illumination Condition SensorsThe 2019 illumination, 19, x FOR PEER condition REVIEW is another decisive factor to be further considered. The shadow5areas of 22 can be determined by the solar illumination model [38,39], whether a target site can be illuminated dependsThe on illumination the value of conditiony by using is Equation another decisive(5): factor to be further considered. The shadow areas can be determined by the solar illumination model [38,39], whether a target site can be

illuminated depends on the value of y byy = usinghsun +Equθ ationh (5): (5) 0 − hormax y  hsun 0  hhormax (5) where y is regarded as the Sun’s apparent angle, hsun is the elevation of the Sun; θ0 is the solar apparent radius;where yh hormaxis regardedis the maximum as the Sun value’s apparent of the horizon angle, elevation hsun is the between elevation the oftarget the site Sun; and θ0 frontis the sites solar in solarapparent azimuth radius; direction. hhormax is The the target maximum site is value illuminated of the byhorizon the Sun elevation only when betweeny is greater the target than site 0. and frontFurthermore, sites in solar azimuth when the direction. target site The is target illuminated site is illuminated by part of the by Sun,the Sun the only solar when energy y is received greater willthan be 0. greatly reduced. As shown in Figure2, Y0 is the target site, Yn is the front site with the hhormax. WhenFurthermore, 2 θ > y > 0,whenY is the only target illuminated site is illuminated by part of theby Sun.part Thisof the introduced Sun, the solar error energy on temperature received × 0 0 shouldwill be notgreatly be neglected reduced. especiallyAs shown near in Fig theure lunar 2, Y poles.0 is theTherefore, target site, the Yn visibleis the front fraction site of with the the Sun h (horP)max is. introduced,When 2 × θ0 which> y > 0, indicates Y0 is only the illuminated solar energy by receivedpart of the as aSun. percentage This introduced of the total error energy on temperature emitted by theshould Sun. not It canbe neglected be expressed especially according near to the the lunar area fractionpoles. Therefore, of the solar the disk: visible fraction of the Sun (P) is introduced, which indicates the solar energy received as a percentage of the total energy emitted P = 1 y > 2 θ by the Sun. It can be expressed accordingq to the area fraction of the solar disk: × 0 2 2 P = 1 [arccosP  1 (y / θ 0 1) 2y/θ0 y /θ0 (y θ0)/ θ 0 y]/π22 θ0 y θ0 − − q− − × − 0 × ≥ ≥ (6) 2 2 2 2 P = [arccosP(11[arccos(y/θ0)y /0 21)y/θ20y /y0 /yθ/00 ((θy00y) /)/0θ]/0]/π 20  θy0 >0 y 0 − − − × − ≥ (6) 2 2 P = 0 P  [arccos(1 y /0 )  2y /0  y /0  (0  y) /0 ]/ 0  y y0 < 0 P  0 y  0 Speciﬁcally, P = 1, Y0 is illuminated by full of the Sun; P = 0, Y0 is in shadow; and in other cases, 0 0 Y0 isSpecifically, illuminated byP = part 1, Y of is the illuminated Sun. Finally, by fullIs is of updated the Sun; as P follows: = 0, Y is in shadow; and in other cases, Y0 is illuminated by part of the Sun. Finally, Is is updated as follows: 2 Is = I(AU/Rsm)2 cos(z)P (7) Is  I(AU / Rsm ) cos(z)P (7)

Figure 2. The target site Y0 illuminated by part of the Sun. Figure 2. The target site Y0 illuminated by part of the Sun.

2.2.3. Diffuse Diffuse ReflectionReflection Energy The didiffuseffuse reflectionreflection energyenergy fromfrom surroundingsurrounding lunar surfacesurface mainly includes the secondary reflectionreflection of directdirect solarsolar radiation radiation and and thermal thermal infrared infrared radiationradiation [[32]32].. Evaluation of the didiffuseffuse reflectionreflection energy at the target site requires knowledge of the total fluxflux scattered from or emitted by the surrounding lunar surfaces, as well as the fraction fraction of of this this flux flux that that actually actually reaches reaches the the targe targett site. site. The fraction of energy that lunar unit surface emitted to the target site can be described mathematically by the view factor βj for a given surface topography [25], that is:

1 cos cos S    0 j j j 2 (8)  R j

where γ0 and γj are the angles between the surface normals of the target site Y0 and the lunar surface j and the line connecting their centers, Rj is the distance between their centers, and the Sj is the surface area of lunar surface j. Note that if γ0 ≥ 90° or γj ≥ 90°, βj = 0. Moreover, there is a risk that

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The fraction of energy that lunar unit surface emitted to the target site can be described mathematically by the view factor βj for a given surface topography [25], that is:

1 cos γ0 cos γjSj β = (8) j 2 π · Rj where γ0 and γj are the angles between the surface normals of the target site Y0 and the lunar surface j and the line connecting their centers, Rj is the distance between their centers, and the Sj is the surface area of lunar surface j. Note that if γ 90 or γ 90 , β = 0. Moreover, there is a risk that surrounding 0 ≥ ◦ j ≥ ◦ j surfaces is inﬁnite, therefore, a limitation of βj is necessary. Here, the calculated radius is set to 5 km. This model is easily calculated at simple landforms, such as the bowl-shaped craters, because all of the surrounding surfaces can transfer their energy to the target site. However, there is a crucial problem for complex terrain areas, that is, the line of sight between the target site and surrounding surfaces may be intercepted by topography. Therefore, the visibility must be analyzed. In the direction of line of sight, the target site will receive the surrounding energy only when the following relationship is satisﬁed: n hj < hj n = 1, 2, 3, ... (9) n where hj is the elevation between the target site to lunar surface j, hj is the elevation of front sites between the target site to lunar surface j, n depends on the number of front sites.

XN Ire f = βjαjIsjkj (10) j=1   N  = P 4  F εσ βjT0 j kj  j=1 (11)   T = [(1 α )I /(εσ)]1/4 0 j − j sj where N is the total of surrounding lunar surfaces; Isj and αj are the eﬀective solar irradiance and albedo of lunar surface j, respectively; kj = 1 represents visible, otherwise, kj = 0.

2.2.4. Lunar Surface Albedo Albedo α is related to the absorbed energy, and varies with the surface materials photometric properties. This parameter is considered as an empirical function as follows [40]:

3 8 α(z) = α0 + a(z/45) + b(z/90) (12) where α0 is the normalized albedo, z is solar incidence angle, a and b are two empirical coeﬃcients. The Clementine UVVIS mosaic is a single 5-band image, which has been calibrated for the global Moon by radiometry, geometrical control, and photometry [41]. Furthermore, the 750-nm data are single-wavelength measurements, and a multiplicative factor of 1.31 is introduced to adjust the solar wavelength range [42]. This data has been considered in good agreement with the Diviner albedo and widely used in the surface temperature calculation [3,5,7]. In this paper, the albedo data derived from Clementine UVVIS 750 nm warped image mosaic is employed. The normalized albedo α0 can be converted from the image as below:

α = (DN 0.000137)/1.31 (13) 0 × where DN = 16-bit pixel value of UVVIS image array. For the regions without data, the linear interpolation method is used to predict these values. In addition, based on the global Diviner infrared data, the better estimated constant a = 0.06 and b = 0.25 in [4] are adopted here. Sensors 2019, 19, 5545 7 of 23

2.2.5. Infrared Emissivity The lunar surface temperature corresponds to black-body spectrum peaks in the middle to middle-far infrared range, thus, the emissivity varies with the wavelength. According to the sample measurements of Logan et al. [43] from Apollo 14 and 15 in the mid infrared and Perry et al. [44] from Apollo 11, 12, 14 and 15 in the far infrared, the emissivity is found to be generally higher than 0.9. Moreover,Sensors 2019,such 19, x FOR studies PEER are REVIEW alsoestimated by Diviner TIR measurements and consistent with previous7 of 22 conclusions [1,45]. AmongAmong thethe studiesstudies ofof infraredinfrared emissivity,emissivity, BandﬁeldBandfield etet al.al. [[45]45] acquired acquired anan apparentapparent broadbandbroadband hemisphericalhemispherical emissivity emissivity of of 0.95 0.95 for thefor average the average daytime daytime based based on the onDiviner the Diviner emission emission phase function phase observations,function observations, which characterized which characterized the radiative the radiative behavior withbehavior wavelength with wavelength and phase and angle phase in detail. angle Moreover,in detail. Moreover, this value isthis widely value used is widely in the used study inof the surface study temperatureof surface temperature [3–5,32]. Therefore, [3–5,32]. εTherefore,= 0.95 is adopted = 0.95 in isthis adopted study. in this study.

2.3.2.3. TemperatureTemperature afterafter ShadingShading ForFor thethe complexitycomplexity ofof topography,topography, thethe lunarlunar surfacesurface couldcould bebe ininshadow shadow becausebecause ofof thethe terrainterrain maskingmasking butbut notnot onon regularregular sunsetsunset time.time. TheThe surfacesurface temperaturetemperature withoutwithout thethe solarsolar illuminationillumination cancan bebe regardedregarded simplysimply asas aa coolingcooling process.process. ConsideringConsidering thethe accuracyaccuracy andand complexity,complexity, thethe relationshiprelationship betweenbetween thethe ApolloApollo 1515 heat-ﬂowheat-flow experimentexperiment (HFE)(HFE) measurementsmeasurements andand coolingcooling timetime isis empiricallyempirically analyzed,analyzed, andand thenthen itsitsglobal global applicationapplication is isdiscussed. discussed.

2.3.1.2.3.1. ApolloApollo 1515 Heat-FlowHeat-Flow ExperimentExperiment (HFE)(HFE) DataData versusversus CoolingCooling TimeTime TheThe Apollo Apollo 15 15 HFE HFE was was conducted conducted from from 31 31 July July 1971 1971 to to 31 31 December December 1974. 1974. TheThe experimentexperiment consistedconsisted ofof twotwo probesprobes toto measuremeasure thethe temperaturetemperature profileprofile withinwithin thethe lunarlunar regolith.regolith. Fortunately,Fortunately, thethe firstfirst thermocouplethermocouple ofof probeprobe 2,2, labeledlabeled TC1,TC1, isis thethe nearestnearest toto thethe lunarlunar surface,surface, andand thethe measuredmeasured temperaturestemperatures can can be be considered considered as as the the surface surface temperature temperature [27 [27].]. Thus, Thus, the the probe probe 2 2 night-time night-time measurementmeasurement isis usedused toto simulatesimulatethe thesurface surfacetemperature temperature variations variations in in shadow. shadow. ByBy analyzinganalyzing the the illumination illumination condition, condition, Apollo Apollo 15 15 HFE HFE data data from from the timethe time just afterjust after sunset sunset to 6:00 to are6:00 selected. are select Aftered. preliminary After preliminary data processing, data processing, 14,387 data 14,387 are used data to are predict used the to surface predict temperature the surface intemperature cooling period, in cooling where period, the cooling where time the ( xcooling) is defined time as:(x) is defined as:

x x=tte tts (14)(14) e− s where te is the observation time, ts is the time to start fitting, the unit of x is lunar hour. where te is the observation time, ts is the time to start fitting, the unit of x is lunar hour. TheThe ApolloApollo 1515 measurementsmeasurements areare thethe greengreen dotsdots shownshown inin FigureFigure3 .3. According According to to the the surface surface temperaturetemperature distribution distribution characteristics, characteristics, the the cooling cooling period period is roughly is roughly divided divided into twointo parts, two theparts, one the is theone first is the stage first from stage 140 from K in which140 K i temperaturen which temperature drops rapidly drops with rapidly time; thewith other time is; the a slow other descending is a slow stagedescending with a smallstage with cooling a small rate. cooling Thus, two rate. fitting Thus, models two fitting are established. models are established.

FigureFigure 3. 3.Apollo Apollo 15 15 heat-ﬂow heat-flow experiment experiment (HFE) (HFE TC1) TC1 data data (green (green dots) dots) versus versus cooling cooling time. The time. linear The andlinear the and polynomial the polynomial ﬁtting modelsfitting models are in blue are in and blue black, and respectively. black, respectively.

From Figure 3, a linear fitting model is reasonable for the first stage, whereas how to divide the two parts is a key problem. We selected the Apollo 15 measurements greater than 105.5 K to calculate the cooling rate of the ﬁrst stage due to the slope of the ﬁing model is the largest, −90.12 K per lunar hour. In the slow descending stage, the temperature varies about 20 K, while the cooling time is close to 11.5 lunar hours. Therefore, a 4th-degree polynomial fitting model is acceptable to describe the temperature variation. In order to acquire a better connection between two models, when the temperature is greater than 102 K and less than 140 K, the linear model is adopted (blue line in Figure 3), where the fitting model is as below:

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From Figure3, a linear fitting model is reasonable for the first stage, whereas how to divide the two parts is a key problem. We selected the Apollo 15 measurements greater than 105.5 K to calculate the cooling rate of the first stage due to the slope of the fitting model is the largest, 90.12 K per − lunar hour. In the slow descending stage, the temperature varies about 20 K, while the cooling time is close to 11.5 lunar hours. Therefore, a 4th-degree polynomial fitting model is acceptable to describe the temperature variation. In order to acquire a better connection between two models, when the temperature is greater than 102 K and less than 140 K, the linear model is adopted (blue line in Figure3), where the fitting model is as below: T = 140 90.12x (15) − As shown in the black curve of Figure3, when the temperature is lower than 102 K, the fitting model is as follows:

T = 0.003081x 4 0.09005x 3 + 0.9917x 2 5.79x + 101.5 (16) 1 − 1 1 − 1 where x1 is the cooling time of temperature below 102 K, it can be expressed as Equation (17):

x = x 38/90.12 (17) 1 − 2.3.2. Global Application of Apollo 15 HFE Data Due to the HFE only being conducted at one location, its global application should be further discussed. Previous works have shown that latitude dependence is an important typical feature of lunar surface temperature distribution [2,7,10]. To study the latitude variations of the simulated temperature, a ﬁtting equation of the mean surface temperature was proposed and applied in [3]:

0.32 T = Tsur0 cos (φ) (18) where T is the surface temperature, Tsur0 is the surface temperature at the lunar equator, φ is the selenographic latitude. This model is based on 1D heat transfer equation and measured CE-2 CELMS data, and reveals latitude effect on the surface temperature. Therefore, this fitting equation is also adopted in this paper. Moreover, a relevant reasonable condition is that the simulated temperature variation in shadow can be adopted as the similar variation of Apollo 15 landing site entering the night. Thus, combined with the two fitting models, the approximate surface temperature in shadow at different latitudes can be acquired from the following equation:

T = T cos (φ )0.32/ cos (φ )0.32 (19) lat 15 × lat 15 where Tlat is the surface temperature at the target latitude, T15 is the surface temperature from Equations (15) and (16), φlat is selenographic latitude of target site, φ15 is the selenographic latitude of Apollo 15 landing site. In addition, the initial ﬁtting temperature also follows this rule.

3. Data Processing and Analyzing Using the lunar surface temperature model, the same local time surface temperature maps are generated and analyzed in Sinus Iridum where is a typical region with abundant geomorphic features and complex evolutionary history. The LOLA dataset provides a variety of spatial resolution DEMs for the global Moon [46]. In this paper, the spatial resolution of the used LOLA data is 1/64◦, which is high enough to simulate the surface topography and evaluate the geological applications of the simulated temperature. Sensors 2019, 19, 5545 9 of 23

3.1. Sinus Iridum

Sinus Iridum, centered at (45.01◦ N, 31.67◦ W), is about 249 km in diameter, which is an important bay in the northwest of the Mare Imbrium. As shown in Figure4, the elevations in most area within Sinus Iridum are between 3000 and 2500 m and increase from the northwest to southeast in the − − ﬂoor. The geomorphologic features are abundant. It is surrounded from the northeast to the southwest by the Montes Jura range. Mare Imbrium is to the southeast of there through the Heraclides Cape and Laplace Cape. Also, there are extensive lava landforms in and around Sinus Iridum, there is Sensorsreported 2019 to, 19 have, x FOR a PEER number REVIEW of wrinkle ridges, but this topography is not obvious in the elevation9 map.of 22 In particular, the bay includes three important satellite craters: Maupertuis crater in the northeast, easternBianchini edge crater. There in the are north, also and many Laplace small A craters crater scatteredalong the easternat the inner edge. Sinus There Iridum, are also such many as small the Bianchinicraters scattered G crater. at the inner Sinus Iridum, such as the Bianchini G crater.

FigureFigure 4. 4. ElevationElevation map map of of Sinus Sinus Iridum Iridum..

Moreover,Moreover, Sinus Sinus Iridum Iridum experienced experienced several several episodes episodes of ofmagmatic magmatic activity, activity, indicating indicating those those of greatof great geological geological significance. significance. It has It has ever ever been been recommended recommended as as the the preliminary preliminary landing landing site site of of Chang’EChang’E-3-3 mission, mission, and and close close to to Luna Luna 17 17 landing site. Based Based on on the the orbital orbital image image data, data, Sc Schaberhaber [47] [47] distinguisheddistinguished three three different different basalts, which firstly firstly show showeded the multiple magmatic activities within SinusSinus Iridum Iridum.. Thereafter Thereafter,, Hiesinger Hiesinger et etal. al.[48] [48 divided] divided the thegeological geological units units and anddated dated the basalt the basalt ages usingages using Clementine Clementine UVVIS UVVIS data data,, which which again again proved proved the the complex complex and and multi multi-stage-stage evolutionary history.history. Chen Chen et et al. al. [49] [49] interpreted the the craters and stratigraphy of of Sinus Sinus Iridum Iridum,, show showinging the the great great differencesdifferences in in formation formation mechanism mechanism and ageand of age the Mareof the Imbrium. Mare Imbrium. Through analyzingThrough the analy topographic,zing the topograpcompositional,hic, compositional, stratigraphic, stratigraphic, and geological and features geological of Sinusfeatures Iridum, of Sinus Qiao Iridum, et al. [50Qiao] defined et al. [50] the definedmare units the andmare inferred units and their inferred geological their evolution geological history. evolution Additionally, history. Additionally, the geological the and geologic structuralal andmaps structural were studied maps by were Wu studied et al. [51 by] with Wu diverse et al. [51] remote-sensing with diverse datasets, remote-sensing the geology datasets, diversity the geologyfurther indicateddiversity thefurther great indicated importance the ofgreat Sinus importance Iridum in of understanding Sinus Iridum thein understanding lunar thermal evolution.the lunar thermalMoreover, evolution. using CE-2 Moreover, CELMS using data, aCE microwave-2 CELMS thermal data, a perspectivemicrowave inthermal Sinus Iridumperspective was givenin Sinus by IridumMeng et was al. [given11], which by Meng also et validated al. [11], which the complex also validated basaltic volcanismthe complex activities. basaltic volcanism activities. InIn summary, Sinus Sinus Iridum Iridum is isof ofgreat great significance significance in lunar in lunar geology geology research research and worthy and worthy of further of furtherstudy. Therefore,study. Therefore, the simulated the simulated temperature temperature distribution distribution maps are maps generated are generated and hopefully and hopeful enablely enableresearchers researchers to understand to understand these geological these geological findings findings better. better.

3.2. Simulation Results 3.2. Simulation Results BBasedased on on the the DE430 e ephemerisphemeris data data of of the the Jet Propulsion Laboratory (JPL) (JPL) and and the the US US Naval ObservatoryObservatory Vector Vector Astrometry Software (NOVAS), t thehe position of the Sun and the Moon and lunar lunar librationlibration cancan be be obtained obtained according according to the to time the of time interest. of interest We compiled. We compiled the corresponding the corresponding calculation calculationprograms with program the helps with of FORTRANthe help of FORTRAN programming programming language. language. AsAs shown shown in in Figure Figure5a–e, 5a– thee, thetemperature temperature of every of every lunar unit lunar surface unit insurface Sinus Iridumin Sinus are Iridum generated are generatedat 6:00, 9:00, at 6:00, 12:00, 9:00, 15:00 12:00, and 15:00 17:30, and corresponding 17:30, corresponding to the time to spanthe time from span 11 tofrom 25 August11 to 25 2019.August In 2019. In order to clearly show the mare temperature, the histogram equalization stretching method was used in the five maps. Generally, the thermal environment in Sinus Iridum is extreme, and the daytime temperature variation is displayed.

Sensors 2019, 19, 5545 10 of 23 order to clearly show the mare temperature, the histogram equalization stretching method was used in the ﬁve maps. Generally, the thermal environment in Sinus Iridum is extreme, and the daytime temperatureSensors 2019, 19, variation x FOR PEER is REVIEW displayed. 10 of 22

Figure 5. Surface temperature distributiondistribution mapsmaps ofof SinusSinus IridumIridum atat 6:006:00 ((aa),), 9:009:00 ((bb),), 12:0012:00 ( (cc),), 15:00 15:00 ( (dd)) and 17:3017:30 ((ee).).

Figure5 5aa isis thethe temperaturetemperature distributiondistribution atat sunrisesunrise whenwhen thethe elevationelevation ofof thethe SunSun isis thethe lowest,lowest, whichwhich clearlyclearly revealsreveals thethe greatgreat influenceinfluence ofof topography.topography. TheThe resultresult indicatesindicates thethe locationslocations facingfacing thethe Sun havehave obviousobvious higher higher temperatures, temperatures, especially especially at theat the the the eastern eastern part part of the of Montes the Montes Jura. TheJura. same The characteristicssame characteristics appear appear at the at west the craterwest crater walls, walls, such as such the as Bianchini the Bianchini crater andcrater Maupertuis and Maupertuis crater. Thecrater. highest The highest temperature temperature of 221.2 of K occurs221.2 K at occurs (35.96875 at (35.96875°◦ W, 41.875 W,◦ N), 41.875° where N), is thewhere eastern is the boundary eastern ofboundary the Montes of the Jura. Montes There Jura. are large There areas are oflarge the areas lowest of temperature the lowest temperature on the west sideon the of thewest Montes side of Jura, the theMontes west Jura, side ofthe the west Laplace side Cape,of the and Laplace the floors Cape, of and Bianchini the floors crater of and Bianchini Maupertuis crater crater, and whichMaupertuis enjoy longercrater, nights.which Interestingly,enjoy longer the nights. wrinkle Interestingly, ridges greatly the alter wrinkle the surface ridges temperature greatly distributionsalter the surface when thetemperature elevation ofdistributions the Sun is very when low, the and elevation a more recognizableof the Sun topographicis very low, featureand a ismore shown recognizable compared withtopographic the elevation feature map. is shown compared with the elevation map. Similar featuresfeatures alsoalso occuroccur atat sunset.sunset. Figure5 5ee isisthe the simulatedsimulatedtemperature temperature distribution distribution at at 17:30. 17:30. TheThe areasareas facingfacing thethe westwest presentpresent aa higherhigher temperature,temperature, suchsuch asas thethe westwest sideside of the Montes Jura and eastern inner wall of the Laplace A crater. Although the wrinkle ridges are not as obvious as at 06:00, thethe western mountain mountain ridge ridge of of the the Montes Montes Jura Jura is is more more clear, clear, which which again again indicates indicates the the advantage advantage of ofterrain terrain recognition. recognition. Small Small craters craters within within Sinus Sinus Ir Iridumidum are are clear, clear, the the temperature temperature difference difference (Td) between the sunny cratercrater wallwall andand shadyshady cratercrater wallwall isis greater.greater. TheThe highesthighest simulatedsimulated temperaturetemperature occurs at the east inner wall of Laplace A crater, whichwhich isis up to 287.8 K. Note that some regions have entered thethe night,night, suchsuch asas thethe easteast sideside ofof thethe MontesMontes Jura,Jura, wherewhere areare inin coolingcooling time.time. As shown in Figure5 5b,d,b,d, whenwhen thethe elevationelevation ofofthe theSun Sunis ismoderate, moderate,the thesimulated simulatedtemperature temperature increasesincreases significantly.significantly. ThereThere areare similarsimilar simulatedsimulated temperaturetemperature distributiondistribution featuresfeatures inin thethe morningmorning and afternoon.afternoon. Moreover, Moreover, the the simulated simulated temperature temperat distributionure distribution is less influenced is less influenced by the topography, by the andtopography, the plains and within the plains Sinus within Iridum Sinus and Iridum Mare and Imbrium Mare Imbrium show the show latitude the latitude effects. effects. The lowThe low temperatures only scatter in several small craters and hillsides, and the mare regions present a higher temperature distribution. Figure 5c is the simulated temperature distribution at noon, which is least influenced by the topography masking. Additionally, the temperatures of hillside, crater wall towards the equator and mountaintop are obviously higher than those of the arctic direction. The highest temperature is in the Laplace A crater, which is 382.1 K at the north crater wall, and the lowest temperature is 252.2 K

Sensors 2019, 19, 5545 11 of 23

temperatures only scatter in several small craters and hillsides, and the mare regions present a higher temperature distribution. Figure5c is the simulated temperature distribution at noon, which is least inﬂuenced by the

Sensorstopography 2019, 19, x masking. FOR PEER Additionally,REVIEW the temperatures of hillside, crater wall towards the equator11 of and22 mountaintop are obviously higher than those of the arctic direction. The highest temperature is in the atLaplace the south A crater,Bianchini which crater is 382.1 wall. K All at thethe north study crater areas wall, are illuminated and the lowest by the temperature Sun, which is 252.2shows K atthat the noonsouth is Bianchiniless affected crater by wall.the topography All the study occlusion. areas are The illuminated low simulated by the temperature Sun, which shows areas ap thatpear noon on is theless shady affected slope bys of the some topography small deep occlusion. craters. The Furthermore, low simulated the temperature temperature distribution areas appear within on the Sinus shady Iridumslopes is of obviously some small affected deep craters.by latitude, Furthermore, which is about the temperature 15 K from 47 distribution° N to 40° N within. Sinus Iridum is obviouslyFigure a6ffaected–e are by the latitude, temperature which distributionsis about 15 K fromcaused 47 ◦ byN the to 40 diffu◦ N.se reflection energy at five moments.Figure In 6general,a–e are the the effect temperature of diffuse distributions reflection is causedobvious, by and the the di ffsurroundinguse reflection thermal energy energy at five willmoments. increase In the general, temperature the eff ectespecially of diffuse at reflectionthe mountain is obvious, valleys and of the the highlands surrounding and thermal small crater energy rims.will Diffuse increase reflection the temperature has little especiallyeffect on most at the of mountainthe plain areas. valleys The of diffuse the highlands reflection and temperatures small crater atrims. the mare Diffuse regions reflection are numerous has little eandffect scattered. on most of Alt thehough plain the areas. direct The solar diffuse irradiance reflection is temperaturessmall when theat elevation the mare regionsof the Sun are is numerous low, the highest and scattered. temperature Although caused the by direct scattering solar irradiance of solar radiation is small whenand surroundingthe elevation infrared of the Sun emission is low, the is highest higher. temperature Moreover, alt causedhough by the scattering highest of diffusesolar radiation reflection and temperaturesurrounding is infrared the lowest emission at noon, is higher. it is still Moreover, about although 10 K. The the diffuse highest reflection diffuse reflection mainly temperatureaffects the temperaturesis the lowest of at small noon, craters it is still at the about mar 10e regions, K. The disuchffuse as reflectionthe Laplace mainly A crater affects and theBianchini temperatures G crater. of Forsmall the craters complex at the topography mare regions, at the such highlands, as the Laplace their A influences crater and vary Bianchini greatly, G crater. especially For the when complex the elevationtopography of the at theSun highlands, is low. Hence, their the influences temperatures vary greatly, caused especially by diffuse when reflection the elevation energy should of the Sun not is below. neglected. Hence, the temperatures caused by diffuse reflection energy should not be neglected.

Figure 6. Temperature distribution caused by the diﬀuse reﬂection energy at 6:00 (a), 9:00 (b), 12:00 (c), Figure 6. Temperature distribution caused by the diffuse reflection energy at 6:00 (a), 9:00 (b), 15:00 (d) and 17:30 (e), only the temperatures greater than 0.1 K are shown, and histogram equalization 12:00 (c), 15:00 (d) and 17:30 (e), only the temperatures greater than 0.1 K are shown, and histogram stretching is used. equalization stretching is used.

Sensors 2019, 19, 5545 12 of 23

3.3. Uncertainty Analysis Above simulation maps present the characteristics of temperature variation in Sinus Iridum. In order to verify the uncertainty of the results, we compare with the Diviner data. The thermal emission energy acquired by Diviner can be inverted to describe the thermal emission features of the Moon. The telescope focal planes of Diviner are nine 21-element thermopile detector arrays [15]. SensorsAmong 2019 its, 19 9, x channels, FOR PEER channelREVIEW 7 (25–41 µm) is a broadband thermal infrared channel and of12 highof 22 signal-to-noise ratio. The spectral emissivity (ε7) of 0.98 is a representative value for everywhere [1]. signal-to-noise ratio. The spectral emissivity (ε7) of 0.98 is a representative value for everywhere [1]. Thus, the surface temperature can be converted from the infrared TB as follows [52]: Thus, the surface temperature can be converted from the infrared TB as follows [52]: 0.25 T = TB/ε70.25 (20) T  TB /  7 (20)

DivinerDiviner level level 4 4 global global cumulative cumulative products products at channel at channel 7 provide 7 provide the thermal the thermal information information at various at variouslocal times. local The times. Diviner The data Diviner are the data average are calibratedthe average TB calibrated binned at 0.5 TB◦ latitude binned and at 0.5° longitude latitude during and longitudeabout 6-year during observations. about 6 According-year observations to its measuring. According time, the to averageits measurin temperatureg time is, calculatedthe average for temperaturecomparison withis calculated a time step for of comparison 3 h from 5 Julywith 2009 a time to 1 step April of 2015. 3 h from In this 5 July paper, 2009 we to select 1 April the 2015. location In thisP1 (32.25 paper,◦ W, we 44.25 select◦ N) the in location the mare P1 regions (32.25° and W, the44.25 location° N) in P2 the (30.75 mare◦ W,regions 49.25 ◦andN) the at the location highland P2 (30.75°for validation. W, 49.25° N) at the highland for validation. FigureFigure 77 presentspresents temperaturetemperature didifferencesﬀerences (Tds) between the Diviner channel channel 7 7 data and the simulatedsimulated temperature temperature versus versus lunar lunar local local time. time. The The results results indicate indicate a a good good agreement between the the Diviner data data and simulation results. Moreover, Moreover, the the Td Td variation variation near near the the noon noon is is the the most stable altalthoughhough thethe highesthighest Td Td at at P2 P2 is aboutis about6 K−6 at K 12:06. at 12:06. However, However, the Td the in theTd afternoonin the afternoon is more obvious,is more − obvious,more than more 20 K. than Considering 20 K. Considering the temperature the temperature model we used,model with we used, the decreasing with the ofdecreasing the elevation of the of elevationthe Sun, the of solar the Suirradiancen, the solar may not irradiance the dominate may not factor the a ﬀ dominateecting the surfacefactor affecting temperature, the andsurface the temperature,heat from lunar and subsurface the heat layer from should lunar subsurface not be neglected. layer shouldTherefore, not our be model neglected. can not Therefore, handle with our modelthis condition can not veryhandle well, with the this results condition near thevery sunset well, arethe forresults reference near the only. sunset are for reference only.

Td (K) -20

P1 P2 -40 6 8 10 12 14 16 18 Local time

FigureFigure 7. 7. TheThe Tds Tds between between the the Diviner Diviner channel channel 7 7 data data and and the the simulated simulated temperature temperature at at P1 P1 (32.25° (32.25◦ W,W, 44.25°44.25◦ N)N) and and P2 P2 (30.75° (30.75◦ W,W, 49.25° 49.25◦ N).N). The The Tds Tds at at P1 P1 and and P2 P2 are are in red and blue, respectively.

TheThe Reduced Data Data Record Record (RDR) (RDR) data data contain contain the the record record from the Diviner Lunar Radiometer Experiment collected during the orbital operations phase [53]. [53]. The The RDR RDR data data include include the the observation observation time,time, channel channel number, number, detector number, the measured TB data, the locallocal time, etc. In In order order to to further further verify the uncertainty temperature temperature at at noon, noon, we we select select the the RDR RDR data data measured measured on on 00:40, 00:40, 16 16 Jan Januaryuary 2017, and the local timetime isis 12.58.12.58. TheThe RDRRDR datadata thatthat we we adopted adopted records records the the TB TB from from the the 21 21 detectors detectors of ofchannel channel 7 at 7 1899 at 1899 locations, locations, and the and longitude the longitude is from 29.6 is from◦ W to 29.6° 28.4 ◦ WW. to We 28.4° simulate W. We the simulatetemperatures the temperaturesat corresponding at corresponding observation time. observation As shown time. in Figure As shown8, the in surface Figure temperatures 8, the surface are temperatures well simulated are wellin the simulated mare regions, in the mare and the regions, latitude and e ﬀtheect latitude of surface effect temperature of surface temperature is clearly displayed. is clearly displayed. Although Alttherehough are severalthere are inconsistencies several inconsistencies at the highlands, at the highlands, most of temperatures most of temperatures are within are the within data rangethe data of rangethe 21 of detectors, the 21 detectors, and the variation and the trend variation is similar. trend Consequently, is similar. Consequently, the result proves the result the rationality proves the of rationalityour temperature of ourmodel, temperature and the model, simulated and temperaturethe simulated at temperature noon is good at and noon suitable is good for and studying suitable its forgeological studying applications. its geological applications.

Sensors 2019, 19, x FOR PEER REVIEW 12 of 22 signal-to-noise ratio. The spectral emissivity (ε7) of 0.98 is a representative value for everywhere [1]. Thus, the surface temperature can be converted from the infrared TB as follows [52]:

0.25 T  TB /  7 (20)

Diviner level 4 global cumulative products at channel 7 provide the thermal information at various local times. The Diviner data are the average calibrated TB binned at 0.5° latitude and longitude during about 6-year observations. According to its measuring time, the average temperature is calculated for comparison with a time step of 3 h from 5 July 2009 to 1 April 2015. In this paper, we select the location P1 (32.25° W, 44.25° N) in the mare regions and the location P2 (30.75° W, 49.25° N) at the highland for validation. Figure 7 presents temperature differences (Tds) between the Diviner channel 7 data and the simulated temperature versus lunar local time. The results indicate a good agreement between the Diviner data and simulation results. Moreover, the Td variation near the noon is the most stable although the highest Td at P2 is about −6 K at 12:06. However, the Td in the afternoon is more obvious, more than 20 K. Considering the temperature model we used, with the decreasing of the elevation of the Sun, the solar irradiance may not the dominate factor affecting the surface temperature, and the heat from lunar subsurface layer should not be neglected. Therefore, our model can not handle with this condition very well, the results near the sunset are for reference only.

Td (K) -20

P1 P2 -40 6 8 10 12 14 16 18 Local time Figure 7. The Tds between the Diviner channel 7 data and the simulated temperature at P1 (32.25° W, 44.25° N) and P2 (30.75° W, 49.25° N). The Tds at P1 and P2 are in red and blue, respectively.

The Reduced Data Record (RDR) data contain the record from the Diviner Lunar Radiometer Experiment collected during the orbital operations phase [53]. The RDR data include the observation time, channel number, detector number, the measured TB data, the local time, etc. In order to further verify the uncertainty temperature at noon, we select the RDR data measured on 00:40, 16 January 2017, and the local time is 12.58. The RDR data that we adopted records the TB from the 21 detectors of channel 7 at 1899 locations, and the longitude is from 29.6° W to 28.4° W. We simulate the temperatures at corresponding observation time. As shown in Figure 8, the surface temperatures are well simulated in the mare regions, and the latitude effect of surface temperature is clearly displayed. Although there are several inconsistencies at the highlands, most of temperatures are within the data range of the 21 detectors, and the variation trend is similar. Consequently, the result proves the rationality of our temperature model, and the simulated temperature at noon is good and suitable forSensors studying2019, 19 ,its 5545 geological applications. 13 of 23

Figure 8. The simulated temperature versus the Diviner Reduced Data Record (RDR) channel 7 data

at 00:40, 16 January 2017. The longitude is from 29.6◦ W to 28.4◦ W. The RDR data and simulated temperature are in red and blue, respectively.

4. Discussions Thermophysical features are strongly influenced by the temperature. However, the results revealed by orbital remotely-sensed observations are greatly limited by the deficiency of original data and the observation time. Therefore, the simulated temperature hopefully allows better understanding of the findings from these data related to the temperatures.

4.1. Geological Application with Remote-Sensing Data Although the significance of surface temperature has been widely accepted, the observations in thermal infrared and microwave ranges are seldom to be fully considered using the temperature at the time of interest. Considering the parameters of lunar regolith are determined only by constants, inevitably these are influenced by different thermophysical features. However, these inconsistencies make it possible to distinguish different physical properties. Hence, the influence of latitude and topography should be eliminated. The spectral emissivity (e) represents its effectiveness in emitting energy as thermal radiation, which is directly related to the material features [54]. The parameter is introduced and expressed as follows: e = TB/Ts (21) where TB is the brightness temperature of the material, and Ts is the physical temperature. Here, we assume that the simulated temperature is approximately equal to the surface temperature. Therefore, the estimated emissivity derived by TB at different frequencies divided by simulated temperature can be use to understand the thermophysical difference of the lunar regolith [2,55]. Because the influence of latitude and topography will be greatly eliminated, and the composition and structure will play a more prominent role. Particularly, the simulated temperature at noon is used because of the best accuracy and less topographic influence. The CELMS data and Diviner TIR data are two feasible data strongly related to temperatures, their geological applications are evaluated by the estimated spectral emissivity maps.

4.1.1. Estimated Spectral Emissivity Features with Chang’E-2 Microwave Radiometer (CELMS) Data The CELMS was the ﬁrst instrument that measured the microwave thermal emission of the lunar surface at 3.0, 7.8, 19.35 and 37.0 GHz [16]. After the system calibration and geometric correction, all the data were processed at 2C-level, including the observation time, TB of four-channels, incidence angle and azimuth at sub-solar point, selenographic longitude and latitude, orbit altitude, and data quality state [8]. The CELMS data have the highest temperature sensitivity and spatial resolution, and can reveal diﬀerent physical features of lunar regolith to a depth about 10 to 20 times of the used wavelength [56,57], whereas the application of the data is strongly limited. Therefore, we analyze the Sensors 2019, 19, 5545 14 of 23 lunar regolith thermophysical properties by generating the emissivity maps to improve the application of the CELMS data collected from the CE-2 satellite. According to the range of the study area, 8424 CELMS data points at noon from the study area were selected after hour angle calculation [12]. Figure9 is the scatter map of CELMS noon data at 37.0 GHz overlaying on the WAC (Wide Angle Camera) image, and each color point represents TB received by the CE-2 satellite at the observation point. It clearly indicates that the measurement is very high spatial resolution along the satellite orbit and about 1◦ spatial resolution between two neighbouring orbits. However, Figure9 can not provide detail information about the lunar regolith thermophysical parameters.Sensors 2019, This19, x FOR is also PEER one REVIEW of the most crucial problems for the CELMS data applications. 14 of 22

FigureFigure 9. Scatter 9. Scatter map map of 37.0 of GHz37.0 Chang’E-2 GHz Chang microwave’E-2 microwave radiometer radiometer (CELMS) data(CELMS) at noon data overlaying at noon onoverlay the Wideing Angle on the Camera Wide (WAC) Angle image, Camera The (WAC) white imageline is,the The geological white line boundary is the geological interpreted boundary in [50]. interpreted in [50]. The TB received by CELMS antenna is decided by the field of view. The spatial resolution of CE-2 CELMSThe data TB is received 25 km at by 3.0 CELMS GHz, and antenna 15 km atis otherdecided frequencies by the field [3]. of Hence, view. each The cell spatial can beresolution modeled of asCE a flat-2 CELMS surface compareddata is 25 withkm at the 3.0 CELMS GHz, and spatial 15 km resolution at other [58 frequencies]. With these [3] hypotheses,. Hence, each the cell CELMS can be datamodeled are processed as a flat assurface follows. compared Firstly, with according the CELMS the CELMS spatial observation resolution [58 time,]. With the averagethese hypotheses, surface temperaturethe CELMS in data the field are ofprocess viewed is calculated as follows. using Firstly, the surface according temperature the CELMS model observation for every CELMS time, the dataaverage points, surface which temperature is simplified asin thethe temperature field of view within is calculated a spatial using resolution. the surface Secondly, temperature the TBs of model four channelsfor every are CELMS divided data by the points, simulated which temperature is simplified to acquire as the theirtemperature estimated within emissivities, a spatial respectively. resolution. Thirdly,Secondly, the four-channel the TBs of four emissivities channels are are interpolated divided by by the natural simul neighborated temperature interpolating to acquire method their to improveestimated the emissivities, spatial resolution, respectively and the. estimatedThirdly, the spectral four-channel emissivity emissivities maps are generated are interpolated with the by spatialnatural resolution neighbor of interpolating 0.25 0.25 .method to improve the spatial resolution, and the estimated spectral ◦ × ◦ emissivityThe estimated maps are emissivity generated maps with arethe shownspatial resolution in Figure 10of 0.25°using × the0.25°. same range. Interestingly, the estimatedThe estimated emissivity emissivity maps indicate maps are the shown thermophysical in Figure 10 property using the di ffsameerences range in. emitting Interestingly, energy the atestimated four channels emissivity compared maps with indicate the visible the thermophysical images. The geological property di differencesfferences are in clearlyemitting presented energy at amongfour channels Sinus Iridum, compared Mare Imbrium,with the visible and the images. highlands. The geological differences are clearly presented among Sinus Iridum, Mare Imbrium, and the highlands.

(a) (b)

Sensors 2019, 19, x FOR PEER REVIEW 14 of 22

Figure 9. Scatter map of 37.0 GHz Chang’E-2 microwave radiometer (CELMS) data at noon overlaying on the Wide Angle Camera (WAC) image, The white line is the geological boundary interpreted in [50].

The TB received by CELMS antenna is decided by the field of view. The spatial resolution of CE-2 CELMS data is 25 km at 3.0 GHz, and 15 km at other frequencies [3]. Hence, each cell can be modeled as a flat surface compared with the CELMS spatial resolution [58]. With these hypotheses, the CELMS data are processed as follows. Firstly, according the CELMS observation time, the average surface temperature in the field of view is calculated using the surface temperature model for every CELMS data points, which is simplified as the temperature within a spatial resolution. Secondly, the TBs of four channels are divided by the simulated temperature to acquire their estimated emissivities, respectively. Thirdly, the four-channel emissivities are interpolated by natural neighbor interpolating method to improve the spatial resolution, and the estimated spectral emissivity maps are generated with the spatial resolution of 0.25° × 0.25°. The estimated emissivity maps are shown in Figure 10 using the same range. Interestingly, the estimated emissivity maps indicate the thermophysical property differences in emitting energy at four channels compared with the visible images. The geological differences are clearly presented Sensorsamong2019 Sinus, 19, 5545Iridum, Mare Imbrium, and the highlands. 15 of 23

Sensors 2019, 19, x FOR PEER REVIEW 15 of 22 (a) (b)

FigureFigure 10. EstimatedEstimated spectral spectral emissivity emissivity maps maps in microwave in microwave range. range. (a) 3.0 (GHz;a) 3.0 (b GHz;) 7.8 GHz; (b) 7.8 (c) GHz;19.35 (GHz;c) 19.35 (d) GHz; 37.0 (GHz.d) 37.0 The GHz. black The line black is the line geological is the geological boundary boundary in [50], in and [50 ],the and five the homogeneous ﬁve homogeneous units unitsare represented are represented by A by–E. A–E. Im1 Im1and and Im2 Im2 are are Imbrian Imbrian mare mare stratigraphic stratigraphic units, units, and and Em1 Em1 and and Em2 are EratosthenianEratosthenian maremare stratigraphicstratigraphic units,units, liwliw isis thethe wallwall materials.materials.

TheThe geological geological units units of Sinus of Sinus Iridum Iridum are analyzed are analyzed in detail in in detail [50], andin [50] in order, and to in better order understand to better theunderstand thermophysical the thermophysical features of the features geological of the units, geological the interpretation units, the interpretation results within results Sinus Iridum within andSinus the Iridum northwest and of the Mare northwest Imbrium of are Mare vectorized Imbrium and are overlaid vectorized on the and emissivity overlaid mapson the in emissivity black line. Asmaps shown in black in Figure line. 10As, thereshown are in five Figure homogeneous 10, there are units five (A–E) homogeneous in Sinus Iridum units and (A– northwesternE) in Sinus Iridum Mare Imbriumand northwestern region. The Mare Im1 Imbrium and Im2 region. are Imbrian The Im1 mare and stratigraphic Im2 are Imbrian units, mare and stratigraphic Im1 is older units, than Im2.and TheIm1 Em1is older and than Em2 areIm2. Eratosthenian The Em1 and mare Em2 stratigraphic are Eratosthenian units, andmare Em1 stratigraphic is older than units, Em2. and The Em1 liw isis theolder wall than materials, Em2. The which liw is are the hummocky wall materials, to smooth which material are hummocky on moderate to smooth to steep material slopes inside on moderate Iridum craterto steep rim slopes [47,49 inside,50]. The Iridum outside crat ofer therim wall[47,49,50]. materials The atoutside the highland of the wall distributed materials the at rim the materials, highland whichdistributed was reported the rim materials, to be the debris which ejected was reported from the to impact-formed be the debris Iridumejected craterfrom the and impact blanketed-formed the olderIridum materials crater and [47 ,blanketed49]. the older materials [47,49]. FromFrom Figure Figure 10 10, the, t spectralhe spectral emissivity emissivity distribution distribution at highlands at highlands indicates indicates the complex the geological complex evolutionarygeological evolutionary history of Sinus history Iridum. of Sinus The highland Iridum. The can be highland divided can into be three divided parts accordinginto three to parts the emissivityaccording features.to the emissivity First, the features. wall materials First, twerehe wall interpreted materials as were the complex interpreted mixture as the of slumpedcomplex Iridummixture ejecta of slumped and reworked Iridum by ejecta the Imbrium and reworked basin ejecta by the [47 ]. Imbrium They always basin present ejecta a [47 higher]. They emissivity always atpresent four channels, a higher emissivity indicating theirat four higher channels effectiveness, indicating in their emitting higher energy. effectiveness Second, comparedin emitting with energy the. emissivitySecond, compared of wall materials, with the those emissivity of the north of wall and northwest materials, rimthose material of the are north lower and at four northwest frequencies, rim andmaterial closer are to thoselower within at four Sinus frequencies, Iridum. Third, and closer the rim to materials those within at the Sinus west Iridum. and northeast Third, of the Sinus rim Iridummaterial indicates at the higherwest and emissivity northeast and of more Sinus complex Iridum distributions, indicate higher which emissivity is more and consistent more withcomplex the geologicaldistributions, interpretation which is more results consistent given in w [ith49]. the geological interpretation results given in [49]. AtAt thethe maremare regions,regions, thethe emissivityemissivity withinwithin SinusSinus IridumIridum isis lowerlower thanthan thosethose inin thethe northwestnorthwest ofof MareMare Imbrium,Imbrium, indicating indicating the the di ffdifferenterent regolith regolith thermophysical thermophysical features. features. At the At flat the mare flat regionsmare regions within Sinuswithin Iridum, Sinus Iridum the emissivities, the emissivit are similaries are at similar low frequencies. at low frequencies. The emissivities The emissivities in unit A andin unit unit A B and are almostunit B consistent are almost with consistent each other with at 3.0 each GHz, other but at they 3.0 are GHz, distinguishable but they are at distinguishable higher frequencies, at higherwhich hintsfrequencies, the change which of the hints regolith the change thermophysical of the regolith features thermophysic with depthal in featuresSinus Iridum. with depth The emissivity in Sinus Iridum. The emissivity in unit A is not so homogeneous. At the northwest within Sinus Iridum, the emissivity is low as well as the lowest elevation. There exists a higher emissivity at 37.0 GHz near the Bianchini G crater, indicating the inhomogeneous material composition might form in Copernian age. In addition, the emissivity near the foot of the Montes Jura in unit A is also higher than that in the northwest part, which shows the different material distributions when shaping Sinus Iridum. Unit B and unit C are both considered as the Eratosthenian unit, but the younger unit B presents a higher emissivity than that in unit C. Moreover, although the Laplace A crater locates in unit C, its emissivity is much higher than that in most parts of unit C and approximate to emissivity of the nearby wrinkle ridge in unit D. Questionably, there exists an obvious data anomaly within Sinus Iridum at 19.35 GHz, the emissivity distribution is quite different from those in other frequencies. According to the similar situation in previous works [8,11], the result at 19.35 GHz is only used for reference in this study.

Sensors 2019, 19, 5545 16 of 23 in unit A is not so homogeneous. At the northwest within Sinus Iridum, the emissivity is low as well as the lowest elevation. There exists a higher emissivity at 37.0 GHz near the Bianchini G crater, indicating the inhomogeneous material composition might form in Copernian age. In addition, the emissivity near the foot of the Montes Jura in unit A is also higher than that in the northwest part, which shows the different material distributions when shaping Sinus Iridum. Unit B and unit C are both considered as the Eratosthenian unit, but the younger unit B presents a higher emissivity than that in unit C. Moreover, although the Laplace A crater locates in unit C, its emissivity is much higher than that in most parts of unit C and approximate to emissivity of the nearby wrinkle ridge in unit D. Questionably, there exists an obvious data anomaly within Sinus Iridum at 19.35 GHz, the emissivity distribution is quite different from those in other frequencies. According to the similar situation in Sensors 2019, 19, x FOR PEER REVIEW 16 of 22 previous works [8,11], the result at 19.35 GHz is only used for reference in this study. Moreover,Moreover, the the emissivity emissivity performance performance of of younger younger Eratosthenian-aged Eratosthenian-aged basalts basalts (unit (unit D D and and unit unit E) E) isis apparentlyapparently higherhigher thanthan thethe older older Imbrian-aged Imbrian-aged basaltsbasalts withinwithin SinusSinus Iridum.Iridum. WithWith thethe increaseincrease ofof frequency,frequency, the the strata strata superposition superposition at at unit unit D andD and unit unit E is E more is mo obvious,re obvious, and and the youngerthe younger stratum stratum still presentsstill presents a higher a emissivity higher emissivity performance, performance, which hints which at the hints change atof the the regolithchange thermophysical of the regolith featuresthermophysical with depth. features with depth. TheThe relationship relationship between between the the TiO TiO22 abundanceabundance and and the the CE-2 CE-2 CELMS CELMS data data has has been been studied studied quantitativelyquantitatively inin[ 5[5],], which which clearly clearly indicates indicates the the great great influence influence of of TiO TiO22abundance abundance onon TB.TB. AsAs shownshown inin FigureFigure 11 11,, TiOTiO22 abundanceabundance mapmap isis inversedinversed withwith ClementineClementine UVVISUVVIS data,data, thethe oldestoldest unitunit AA hashas relativelyrelatively lowlow TiOTiO22 contents,contents, thethe youngeryounger unitunit BB andand unitunit CC areare slightlyslightly higher,higher, andand thethe youngestyoungest Eratosthenian-agedEratosthenian-aged unit unit D D andand unitunit EE havehave thethe highesthighest TiOTiO22contents, contents, whichwhich showshow thatthat thethe emissivityemissivity featuresfeatures atat highhigh frequenciesfrequencies areare mainlymainly broughtbrought byby the the TiO TiO2 2abundance. abundance. TheThe resultsresults alsoalso hinthint atat thethe changechange ofof thethe regolithregolith thermophysical thermophysical features features with with depth depth in in Sinus Sinus Iridum. Iridum.

FigureFigure 11.11. TiOTiO22 abundanceabundance mapmap ofof SinusSinus Iridum.Iridum. The blackblack lineline isis thethe geologicalgeological boundaryboundary inin [[50].50]. HistogramHistogram equalizationequalization stretching stretching is is used. used.

FigureFigure 12 12 is is the the scatter scatter plot plot between between TiO 2 TiOabundance2 abundance and emissivity and emissivity of every of CELMS every CELMS data points data atpoints four frequencies.at four frequencies. In general, In general, the correlation the correlation between between low titanium low titanium and emissivities and emissivities is not obvious. is not Exceptobvious. at 3.0Except GHz, at the 3.0 highGHz, emissivity the high mostlyemissivity corresponds mostly corresponds to high TiO 2toabundance. high TiO2 abundance The correlation. The coefficient (R) is 0.349 at 3.0 GHz, but the Rs are 0.793, 0.689 and 0.774 at 7.8, 19.35 and 37.0 GHz, correlation coefficient− (R) is −0.349 at 3.0 GHz, but the Rs are 0.793, 0.689 and 0.774 at 7.8, 19.35 and respectively.37.0 GHz, respectively. The results The clearly results show clearly that there show is that a great there influence is a great of influence TiO2 abundance of TiO2 onabundance microwave on thermalmicrowave emission thermal at theemission shallower at the lunar shallower regolith. lunar regolith.

(a) (b)

Sensors 2019, 19, x FOR PEER REVIEW 16 of 22

Moreover, the emissivity performance of younger Eratosthenian-aged basalts (unit D and unit E) is apparently higher than the older Imbrian-aged basalts within Sinus Iridum. With the increase of frequency, the strata superposition at unit D and unit E is more obvious, and the younger stratum still presents a higher emissivity performance, which hints at the change of the regolith thermophysical features with depth. The relationship between the TiO2 abundance and the CE-2 CELMS data has been studied quantitatively in [5], which clearly indicates the great influence of TiO2 abundance on TB. As shown in Figure 11, TiO2 abundance map is inversed with Clementine UVVIS data, the oldest unit A has relatively low TiO2 contents, the younger unit B and unit C are slightly higher, and the youngest Eratosthenian-aged unit D and unit E have the highest TiO2 contents, which show that the emissivity features at high frequencies are mainly brought by the TiO2 abundance. The results also hint at the change of the regolith thermophysical features with depth in Sinus Iridum.

Figure 11. TiO2 abundance map of Sinus Iridum. The black line is the geological boundary in [50]. Histogram equalization stretching is used.

Figure 12 is the scatter plot between TiO2 abundance and emissivity of every CELMS data points at four frequencies. In general, the correlation between low titanium and emissivities is not obvious. Except at 3.0 GHz, the high emissivity mostly corresponds to high TiO2 abundance. The correlation coeﬃcient (R) is −0.349 at 3.0 GHz, but the Rs are 0.793, 0.689 and 0.774 at 7.8, 19.35 and 37.0 GHz, respectively. The results clearly show that there is a great influence of TiO2 abundance on Sensors 2019, 19, 5545 17 of 23 microwave thermal emission at the shallower lunar regolith.

Sensors 2019, 19, x FOR PEER REVIEW 17 of 22 (a) (b)

FigureFigure 12. Estimated spectral emissivityemissivity versusversus TiO TiO22abundance abundance of of every every CELMS CELMS data data points, points and, and R R is isthe the correlation correlation coe coefficient.ﬃcient. (a ()a 3.0) 3.0 GHz; GHz; (b ()b 7.8) 7.8 GHz; GHz; (c )(c 19.35) 19.35 GHz; GHz; (d ()d 37.0) 37.0 GHz. GHz.

CComparedompared with with previous previous geological geological interpretation interpretation methods, methods, the emissivity the emissivity performance performance expresses expressesthe diﬀerent the geologicaldifferent geological units in Sinusunits in Iridum Sinus well,Iridum and well, is ofand great is of signiﬁcance great significance for studying for study someing somepotential potential geological geological issues. issues.

4.1.2.4.1.2. Estimated Estimated Spectral Spectral Emissiv Emissivityity Features Features with with Diviner Diviner Thermal Infrared ( (TIR)TIR) Data DivinerDiviner has systematic systematicallyally measure measuredd the the solar solar reflections reflections and and infrared infrared emissions emissions of of the whole Moon.Moon. For For the the deficiency deficiency of of the the original original data, data, Diviner Diviner channel channel 6 6 (13 (13–23–23 μm)µm) w wasas used used to to reveal reveal the the TB distri distributionsbutions of of Sinus Sinus Iridum Iridum based based on on over over 7 7-year-year measurements measurements,, t thehe result result at at 12:00 12:00 is is shown shown in in FigureFigure 1133a,a, the the spatial spatial resolution resolution is isalso also 1/64° 1/64 [14]◦ [14. Although]. Although the the differences differences of the of thehighlands highlands and andthe marethe mare regions regions are shown are shown properly, properly, the recognition the recognition of flat of mar flate mare regions regions is not is as not good. as good. There There are also are somealsosome inconsistencies inconsistencies between between the two the results,two results, such such as the as lowest the lowest simulated simulated temperature temperature and and the temperaturethe temperature variations variations in complex in complex terrain terrain areas. areas. This This is is not not only only due due to to the the huge huge topographic fluctuation,fluctuation, but butalso also brought brought by the by great the great change change of the temperature of the temperature with the latitudewith the and latitude observation and observationtime. Furthermore, time. Furthermore, the stripe phenomenon the stripe phenomenon caused by caused data anomaly by data inanomaly the push in broomthe push detection broom detectionprocess of process Diviner of is Divinernoticeable. is noticeable Nevertheless,. Nevertheless, this result providesthis result us provides the infrared us the TB infrareddistribution TB distributionreference with reference high spatial with high resolution, spatial which resolution, is also which a valuable is also reference a valuable for reference our study. for our study. FigureFigure 13 13bb is is the the estimated estimated emissivity emissivity map using map Diviner using Diviner TIR data TIR and the data simulated and the temperature. simulated temperatureHere, we set. theHere, range we ofset colorbar the range from of 0.9colorbar to 1.1 tofrom increase 0.9 to contrast, 1.1 to increase which includescontrast, 99.8%which of includes all data. 99.8%Compared of all with data. Figure Compared 13a, Figure with 13 b Figure postulates 13a, that Figure the change 13b postulates of the temperature that the changewith latitude of the is temperatureeliminated well, with confirming latitude the is rationality eliminated of thewell, simulated confirming temperature. the rationality From Figure of the13b, simulatedin general, temperaturethe estimated. From emissivities Figure 1 at3b, the in mare gener regionsal, the estimated are slightly emissivities lower than at those the mare at the regions highlands. are slight Exceptly lowtheer emissivities than those in at the the stripe highlands. regions, Except those the at the emissivities south mare in regionthe stripe is nearly regions the, samethose asat thatthe south at the marenorth region mare region.is nearly In the addition, same as becausethat at the the north acquirement mare region. of the In addition, Diviner data because is not the in acquirement one time of ofa daythe Diviner but from data the i similars not in localone time time of on a didayfferent but from days, the the similar emissivity local di timefference on different resulted days, from the the emissivity difference resulted from the regolith thermophysical features is severely weakened due to different observation conditions in the stripe region. The results also imply that, the temporal and spatial resolution of Diviner data can be improved in the long-term observation, whereas the push-broom method inevitably leads to the lack of temporal and spatial coverage of the data over the whole Moon. Moreover, the emissivity behaviors in large craters as Bianchini and Maupertuis are similar as the nearby mountains, but not corresponding to the topographic features, implying the rationality of our model. However, there are some higher emissivities at the shady slopes than those in other regions, which indicates that the thermal environments is more complex than what we simulated.

Sensors 2019, 19, 5545 18 of 23 regolith thermophysical features is severely weakened due to diﬀerent observation conditions in the stripe region. The results also imply that, the temporal and spatial resolution of Diviner data can be improved in the long-term observation, whereas the push-broom method inevitably leads to the lack of temporal and spatial coverage of the data over the whole Moon. Moreover, the emissivity behaviors in large craters as Bianchini and Maupertuis are similar as the nearby mountains, but not corresponding to the topographic features, implying the rationality of our model. However, there are some higher emissivities at the shady slopes than those in other regions, which indicates that the thermalSensors 2019 environments, 19, x FOR PEER is REVIEW more complex than what we simulated. 18 of 22

(a) (b)

Figure 13. 13. Infrared brightness temperature ( (TB)TB) distribution of Sinus Iridum at 12:00 [[14]14]( (a) and and estimated emissivity map usingusing Diviner TBTB andand thethe simulatedsimulated temperaturetemperature ((bb).).

In summary, compared compared with with the the Diviner Diviner data, data, the CELMS data can be used to evaluate evaluate the didifferencefference in thermophysicalthermophysical features of the deeper lunar regolith. The superficialsuperficial layer of the lunar regolith may bebe greatlygreatly aaffectedffected byby otherother factors,factors, suchsuch asas strongstrong spacespace weathering.weathering. The estimated emissivity mapsmaps provide provide a referencea reference of theof the effectiveness effectiveness in emitting in emitting thermal thermal energy energy of the lunarof the regolith lunar atregolith different at different depths. depths.

4.2. Useful Suppleme Supplementaryntary Information With the start start of thethe CE-4CE-4 mission,mission, the selection of the landing landing site has become increasingly popular inin currentcurrent lunarlunar study.study. ToTo select select the the landing landing site site scientifically, scientifically, the the temperature temperature distribution distribution is alwaysis always thought thought as the as first the important first important factor. Moreover,factor. Moreover, the Diviner the TIR Diviner data proves TIR data the uncertainty proves the dueuncertainty to the long due term to observation, the long term however, observation, this effect however, has not been this studied effect hasquantitatively. not been Against studied thisquantitatively. background, Against the study this on background, temperature the changed study on with temperature time is a useful changed supplement with time in suchis a useful work. Therefore,supplement the in temperature such work. variationsTherefore, arethe quantitativelytemperature variations analyzed basedare quantitatively on the temperature analyzed model. based on theIt cantemperature be deduced model. from the foregoing that the motion of the Sun and the Moon will directly affect the parametersIt can be deduced of IS in thefrom temperature the foregoing model. that Hence, the motion the lunar of the orbital Sun and motion the shouldMoon will be seriously directly reconsidered. Although the previous studies showed the orbital period effect on temperature should affect the parameters of IS in the temperature model. Hence, the lunar orbital motion should be notseriously be ignored reconsidered. by reanalyzing Although the Apollo the previous 15 and 17 studies measurements, showed the the changes orbital of period the temperature effect on basedtemperature on lunar should days not have be ignored not been by thoroughly reanalyzing studied the Apollo [26,59 15]. and The 17 precession measurements, of 18.6 the years changes and rotationof the temperature of 29.5 Earth based days on are lunar two typicaldays have periodic not been motions thoroughly of the Moon, studied and [26,59]. we discuss The precession the variation of of18.6 the years highest and temperature rotation of 29.5 in a lunarEarth daydays from are 2005two typical to 2045, periodic which reveals motions the of greatest the Moon, influence and we of lunardiscuss motions the variation on temperature. of the highest temperature in a lunar day from 2005 to 2045, which reveals the greatestFigure influence 14 is the of variationlunar motions of the on highest temperature. temperature of a lunar day at (32◦ W, 44◦ N) for 40 years, whichFigure includes 14 is 494 the lunar variation days. of Figure the highest 14 postulates temperature that of the a highestlunar day temperature at (32° W, 44° varies N) periodicallyfor 40 years, withwhich time, includes which 494 can lunar be concluded days. Figure as having 14 postulates three characteristics. that the highest temperature varies periodically with time, which can be concluded as having three characteristics.

356

354

352

350

348

346 Highest Temperature (K)

344

342 2005 2010 2015 2020 2025 2030 2035 2040 Year

Sensors 2019, 19, x FOR PEER REVIEW 18 of 22

(a) (b)

Figure 13. Infrared brightness temperature (TB) distribution of Sinus Iridum at 12:00 [14] (a) and estimated emissivity map using Diviner TB and the simulated temperature (b).

In summary, compared with the Diviner data, the CELMS data can be used to evaluate the difference in thermophysical features of the deeper lunar regolith. The superficial layer of the lunar regolith may be greatly affected by other factors, such as strong space weathering. The estimated emissivity maps provide a reference of the effectiveness in emitting thermal energy of the lunar regolith at different depths.

4.2. Useful Supplementary Information With the start of the CE-4 mission, the selection of the landing site has become increasingly popular in current lunar study. To select the landing site scientifically, the temperature distribution is always thought as the first important factor. Moreover, the Diviner TIR data proves the uncertainty due to the long term observation, however, this effect has not been studied quantitatively. Against this background, the study on temperature changed with time is a useful supplement in such work. Therefore, the temperature variations are quantitatively analyzed based on the temperature model. It can be deduced from the foregoing that the motion of the Sun and the Moon will directly affect the parameters of IS in the temperature model. Hence, the lunar orbital motion should be seriously reconsidered. Although the previous studies showed the orbital period effect on temperature should not be ignored by reanalyzing the Apollo 15 and 17 measurements, the changes of the temperature based on lunar days have not been thoroughly studied [26,59]. The precession of 18.6 years and rotation of 29.5 Earth days are two typical periodic motions of the Moon, and we discuss the variation of the highest temperature in a lunar day from 2005 to 2045, which reveals the greatest influence of lunar motions on temperature. Figure 14 is the variation of the highest temperature of a lunar day at (32° W, 44° N) for 40 years, whichSensors 2019includes, 19, 5545 494 lunar days. Figure 14 postulates that the highest temperature varies periodically19 of 23 with time, which can be concluded as having three characteristics.

356

354

352

350

348

346 Highest Temperature Highest (K) Temperature

344

342 2005 2010 2015 2020 2025 2030 2035 2040 Year

Figure 14. The variations of the highest temperature (black dots) in a lunar day at (32◦ W, 44◦ N) from 2005 to 2045.

Firstly, the change of the highest temperature ranges from 0 to 3.1 K in two neighboring lunar days. For example, in the 5th and 6th lunar day of 2024, the highest temperatures are both 349.4 K; however, the change of the highest temperature between the 3rd and 4th lunar day in 2034 is up to 3.1 K. These results indicate that the change of temperature can not be ignored even if two observations are at the nearest same local time, which is essentially significant for the application of the Diviner data. Secondly, although there are also four seasons on the Moon in a year, the change of the temperature with season is apparent in different years. Specifically speaking, the greatest change of the highest temperature is up to 11.9 K in 2015, while this value is only about 1.2 K in 2042. This indicates that the influence of seasonal variations on temperature needs to be carefully analyzed in different years. Thirdly, there occur two similar trends within the 40 years. Each period is about 19 years: the one is from 2005 to 2024, and the other is from 2024 to 2043. Particularly, the highest temperature in 2024 is 349.4 K, but that in 2015 is 355.3 K, the range of temperature is up to 5.9 K at half of the lunar precession. Also, the lowest temperature in 2024 is 348.9 K, but that is 343.4 K in 2015 and 2034, the Td is 4.5 K. These clearly show the influence of lunar precession on the temperature. The results again prove that the temperature data collected by the probes in orbit are heavily affected by the observation time, even if in the same position and local time. This phenomenon has been proved by the Diviner TIR data used in Figure 13. Although there are small changes of the temperature in some years, the Td resulted from observation time should be analyzed carefully, especially using the long-term orbit temperature data. This also shows the advantage of the numerical simulation model.

5. Conclusions In this paper, a daytime surface temperature model is established focusing on the lunar superficial layer with high spatial-temporal resolution. The lunar superficial layer temperature distributions of Sinus Iridum are simulated at five local times with a spatial resolution of 1/64◦. Thereafter, combined with CELMS data and Diviner TIR data, the spectral emissivity distributions are estimated as a geological application of surface temperature. Finally, the importance of using the parameters at the time of interest is proved. The main results are as follows. Firstly, the temperature model established in this study is based on the parameters at the time of interest, including the effective solar irradiance, large-scale topographic shading and slope, lunar libration and diffuse reflection energy from the thermal environment. The results simulated in Sinus Iridum show the effects of diffuse reflection, latitude and topography. Secondly, the same local time temperature distribution plays an essential role in evaluating the regolith thermophysical parameters. The thermophysical properties difference in emitting energy may be expressed better using the estimated spectral emissivity maps combined with the CELMS data and Diviner TIR data. Sensors 2019, 19, 5545 20 of 23

Thirdly, the influence of observation time should be analyzed carefully when using the orbital remotely-sensed data related to temperatures. Lunar orbiting revolution and precession are both important factors affecting the surface temperature, and their effects vary with time. The temperature model can be used to study the lunar regolith properties with other source data, and also provide an important reference for simulating the surface temperature of airless heavenly bodies. The temperature distribution with high spatiotemporal resolution should be further studied to reveal more geological issues.

Author Contributions: Conceptualization, J.Z., J.P., Z.Z. and M.W.; Methodology, J.Z. and Y.Y.; Software, J.Z.; Validation, J.Z.; Writing—original draft preparation, J.Z. and X.L.; Writing—review and editing, J.Z., J.P. and X.L.; Project administration, J.P. and J.Z.; Funding acquisition, J.P. and J.Z.; All authors read and approved the final manuscript. Funding: This work was supported in part by the National Natural Science Foundation of China under Grant 41604150, 41590851 and 41574097, in part by National Basic Research Program of China Grant 2015CB857101, and in part by Graduate Innovation Fund of Jilin University Grant 101832018C040. Acknowledgments: The LOLA data, Diviner RDR data and Diviner level 4 global cumulative products data were available at the following website: https://pds-geosciences.wustl.edu. The Clementine UVVIS mosaic data was available at: https://astrogeology.usgs.gov/search/map/Moon/Clementine/UVVIS/Lunar_Clementine_UVVIS_ WarpMosaic_5Bands_200m. The TiO2 abundance data and WAC image data were downloaded from JMARS SOFTWARE: https://jmars.mars.asu.edu. The Diviner channel 6 data was provided by Ma Ming. We are grateful for being allowed to use their data. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Vasavada, A.R.; Bandfield, J.L.; Greenhagen, B.T.; Hayne, P.O.; Siegler, M.A.; Williams, J.-P.; Paige, D.A. Lunar equatorial surface temperatures and regolith properties from the Diviner Lunar Radiometer Experiment. J. Geophys. Res. 2012, 117, E00H18. [CrossRef] 2. Meng, Z.G.; Xu, Y.; Cai, Z.C.; Chen, S.B.; Lian, Y.; Huang, H. Influence of lunar topography on simulated surface temperature. Adv. Space Res. 2014, 54, 2131–2139. 3. Fang, T.; Fa, W.Z. High frequency thermal emission from the lunar surface and near surface temperature of the Moon from Chang’E-2 microwave radiometer. Icarus 2014, 232, 34–53. [CrossRef] 4. Hayne, P.O.; Bandfield, J.L.; Siegler, M.A.; Vasavada, A.R.; Ghent, R.R.; Williams, J.-P.; Greenhagen, B.T.; Aharonson, O.; Elder, C.M.; Lucey, P.G.; et al. Global Regolith Thermophysical Properties of the Moon from the Diviner Lunar Radiometer Experiment. J. Geophys. Res. Planets 2017, 122, 2371–2400. [CrossRef] 5. Liu, N.T.; Fa, W.Z.; Jin, Y.Q. Brightness Temperature of Lunar Surface for Calibration of Multichannel Millimeter-Wave Radiometer of Geosynchronous FY-4M. IEEE Trans. Geosci. Remote Sens. 2019, 57, 3055–3063. [CrossRef] 6. Li, X.Y.; Wang, S.J.; Cheng, A.Y. A lunar surface effective solar irradiance real-time model. Chin. J. Geophys. 2008, 51, 25–30. [CrossRef] 7. Hu, G.P.; Zheng, Y.C.; Xu, A.A.; Tang, Z.S. Lunar Surface Temperature of Global Moon: Preparation of Database with Topographic and Albedo Effects. IEEE Trans. Geosci. Remote Sens. 2016, 13, 110–114. [CrossRef] 8. Meng, Z.G.; Zhang, J.D.; Cai, Z.C.; Ping, J.S.; Tang, Z.S. Microwave Thermal Emission Features of Mare Orientale Revealed by CELMS Data. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 2017, 10, 2991–2998. [CrossRef] 9. Yu, S.R.; Fa, W.Z. Thermal conductivity of surficial lunar regolith estimated from Lunar Reconnaissance Orbiter Diviner Radiometer data. Planet Space Sci. 2016, 124, 48–61. [CrossRef] 10. Williams, J.-P.; Paige, D.A.; Greenhagen, B.T.; Sefton-Nash, E. The global surface temperatures of the moon as measured by the diviner lunar radiometer experiment. Icarus 2017, 283, 300–325. [CrossRef] 11. Meng, Z.G.; Hu, S.; Wang, T.X.; Li, C.; Cai, Z.C.; Ping, J.S. Passive Microwave Probing Mare Basalts in Mare Imbrium Using CE-2 CELMS Data. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 2018, 11, 3097–3104. [CrossRef] Sensors 2019, 19, 5545 21 of 23

12. Meng, Z.G.; Li, X.Y.; Chen, S.B.; Zheng, Y.C.; Shi, J.C.; Wang, T.X.; Zhang, Y.Z.; Ping, J.S.; Lu, Y. Thermophysical Features of Shallow Lunar Crust Demonstrated by Typical Copernican Craters Using CE-2 CELMS Data. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 2019, 12, 2565–2574. [CrossRef] 13. Zheng, Y.C.; Tsang, K.T.; Chan, K.L.; Zou, Y.L.; Zhang, F.; Ouyang, Z.Y. First microwave map of the Moon with Chang’E-1 data: The role of local time in global imaging. Icarus 2012, 219, 194–210. [CrossRef] 14. Ma, M.; Chen, S.B.; Li, J.; Yu, Y.; Xiao, Y. The Sinus Iridum surface brightness temperature temporal-spatial distributions by LRO diviner data. J. Infrared Millim. Waves 2017, 36, 628–635, 640. 15. Paige, D.A.; Foote, M.C.; Greenhagen, B.T.; Schofield, J.T.; Calcutt, S.; Vasavada, A.R. The lunar reconnaissance orbiter diviner lunar radiometer experiment. Space Sci. Rev. 2010, 150, 125–160. [CrossRef] 16. Wang, Z.Z.; Li, Y.; Zhang, X.H.; Jiang, J.S.; Xu, C.D.; Zhang, D.H.; Zhang, W.G. Calibration and brightness temperature algorithm of CE-1 Lunar Microwave Sounder (CELMS). Sci. China Earth Sci. 2010, 53, 1392–1406. [CrossRef] 17. Pettit, E.; Nicholson, S.B. Temperature of the dark side of the Moon and of the Moon during eclipse. Publ. Astron. Soc. Pac. 1927, 39, 227–228. [CrossRef] 18. Pettit, E.; Nicholson, S.B. Lunar radiation and temperatures. Astrophys. J. 1930, 71, 102–135. [CrossRef] 19. Langseth, M.G.; Clark, S.P.; Chute, J.L.; Keihm, S.J.; Wechsler, A.E. The Apollo 15 lunar heat-flow measurement. Moon 1972, 4, 390–410. [CrossRef] 20. Heiken, G.H.; Vaniman, D.T.; French, B.M. A User’s Guide to the Moon; Cambridge Univ. Press: London, UK, 1991. 21. Wesselink, A.J. Heat conductivity and nature of the lunar surface material. Bull. Astron. Inst. Neth. 1948, 10, 351–363. 22. Jaeger, J.C. The surface temperature of the Moon. Aust. J. Phys. 1953, 6, 10–21. [CrossRef] 23. Jones, W.P.; Watkins, J.R.; Calvert, T.A. Temperatures and thermophysical properties of the lunar outermost layer. Moon 1975, 13, 475–494. [CrossRef] 24. Racca, G.D. Moon surface thermal characteristics for moon orbiting spacecraft thermal analysis. Planet. Space Sci. 1995, 43, 835–842. [CrossRef] 25. Vasavada, A.R.; Paige, D.A.; Wood, S.E. Near-surface temperatures on Mercury and the Moon and the stability of polar ice deposits. Icarus 1999, 141, 179–193. [CrossRef] 26. Li, Y.; Wang, Z.Z.; Jiang, J.S. Simulations on the influence of lunar surface temperature profiles on CE-1 lunar microwave sounder brightness temperature. Sci. China Earth Sci. 2010, 53, 1379–1391. [CrossRef] 27. Feng, X.; Guo, Q. The lunar surface temperature real-time model. J. Remote Sens. 2017, 21, 928–938. 28. Davidsson, B.J.R.; Rickman, H. Surface roughness and three-dimensional heat conduction in thermophysical models. Icarus 2014, 243, 58–77. [CrossRef] 29. Buhl, D.; Welch, W.J.; Rea, D.G. Reradiation and thermal emission from illuminated craters on the lunar surface. J. Geophys. Res. Planets 1968, 73, 5281–5295. [CrossRef] 30. Rubanenko, L.; Aharonson, O. Stability of ice on the Moon with rough topography. Icarus 2017, 141, 179–193. [CrossRef] 31. Yang, Y.Z.; Li, J.L.; Ping, J.S.; Hideo, H. Determination of the free lunar libration modes from ephemeris DE430. Res. Astron. Astrophys. 2017, 17, 91–96. [CrossRef] 32. Gan, H.; Li, X.Y.; Wei, G.F. Numerical simulation of effective solar irradiance and temperatures at simple crater of lunar dayside (in Chinese). Sci. Sin.-Phys. Mech. Astron. 2019, 49, 101–112. 33. Song, Y.T.; Wang, X.Q.; Bi, S.S.; Wu, J.T.; Huang, S.P. Effects of solar radiation, terrestrial radiation and lunar interior heat flow on surface temperature at the nearside of the Moon: Based on numerical calculation and data analysis. Adv. Space Res. 2017, 60, 938–947. [CrossRef] 34. Fountain, F.A.; West, E.A. Thermal conductivity of particulate basalt as a function of density in simulated lunar and Martian environments. J. Geophys. Res. Planets 1970, 75, 4063–4069. [CrossRef] 35. Ritter, P. A vector-based slope and aspect generation algorithm. Photogramm. Eng. Remote Sens. 1987, 53, 1109–1111. 36. Jones, K.H. A comparison of algorithms used to compute hill slope as a property of the DEM. Comput. Geosci.-UK 1998, 24, 315–323. [CrossRef] 37. Zhou, Q.; Liu, X. Error Analysis on Grid-Based Slope and Aspect Algorithms. Photogramm. Eng. Remote Sens. 2004, 70, 957–962. [CrossRef] Sensors 2019, 19, 5545 22 of 23

38. Zhang, J.D.; Meng, Z.G.; Ping, J.S.; Li, W.X.; Wang, M.Y.; Zhao, R. Preliminary study of illumination characteristics of Aristarchus plateau using LOLA data. J. Deep Space Explor. 2017, 4, 171–177. 39. Zhang, J.D. Research on the Illumination Model of the Moon Using LOLA Data and Its Significance. Master’s Thesis, College of Geoexploration Science and Technology, Jilin University, Changchun, China, 2017. 40. Keihm, S.J. Interpretation of the Lunar Microwave Brightness Temperature Spectrum: Feasibility of Orbital Heat Flow Mapping. Icarus 1984, 60, 568–589. [CrossRef] 41. Eliason, E.; Isbell, C.; Lee, E.; Becker, T.; Gaddis, L.; McEwen, A.; Robinson, M. Mission to the Moon: The Clementine UVVIS Global Lunar Mosaic, PDS Volumes USA_NASA_PDS_CL_4001 through 4078, produced by the U.S. Geological Survey and distributed on CD media by the Planetary Data System. 1999. Available online: http://www.mapaplanet.org (accessed on 10 October 2019). 42. Lawson, S.L.; Jakosky, B.M. Lunar surface thermophysical properties derived from Clementine LWIR and UVVIS images. J. Geophys. Res. 2001, 106, 27911–27932. [CrossRef] 43. Logan, L.M.; Hunt, G.R.; Balsamo, S.R.; Salisbury, J.W. Midinfrared emission spectra of Apollo 14 and 15 soils and remote compositional mapping of the moon. In Proceedings of the 3rd Lunar Science Conference, Houston, TX, USA, 10–13 January 1972; pp. 3069–3076. 44. Perry, C.H.; Agrawal, D.K.; Anastassakis, E.; Lowndes, R.P.; Tornberg, N.E. Far infrared and Raman spectroscopic investigations of lunar materials from Apollo 11, 12, 14 and 15. In Proceedings of the 3rd Lunar Science Conference, Houston, TX, USA, 10–13 January 1972; pp. 3077–3095. 45. Bandfield, J.L.; Hayne, P.O.; Williams, J.P.; Greenhagen, B.T.; Paige, D.A. Lunar surface roughness derived from LRO Diviner radiometer observations. Icarus 2015, 248, 357–372. [CrossRef] 46. Smith, D.E.; Zuber, M.T.; Neumann, G.A.; Mazarico, E.; Lemoine, F.G.; Head, J.W., III; Lucey, P.G.; Aharonson, O.; Robinson, M.S.; Sun, X.L.; et al. Summary of the results from the lunar orbiter laser altimeter after seven years in lunar orbit. Icarus 2017, 283, 70–91. [CrossRef] 47. Schaber, G.G. Geologic Map of the Sinus Iridum Quadrangle of the Moon; 1-602(LAC-24); US Geological Survey: Washington, DC, USA, 1969. 48. Hiesinger, H.; Jaumann, R.; Neukum, G.; Head, J.W., III. Ages of Mare basalts on the lunar nearside. J. Geophys. Res. Planets 2000, 105, 29239–29275. [CrossRef] 49. Chen, S.B.; Meng, Z.G.; Cui, T.F.; Lian, Y.; Wang, J.Y.; Zhang, X.Q. Geologic investigation and mapping of the Sinus Iridum quadrangle from Clementine, SELENE, and Chang’e-1 data. Sci. China Phys. Mech. 2010, 53, 2179–2187. [CrossRef] 50. Qiao, L.; Xiao, L.; Zhao, J.N.; Huang, Q.; Haruyama, J. Geological features and evolution history of Sinus Iridum, the Moon. Planet. Space Sci. 2014, 101, 37–52. [CrossRef] 51. Wu, Y.Z.; Li, L.; Luo, X.X.; Lu, Y.; Chen, Y.; Pieters, C.M.; Basilesky, A.T.; Head, J.W., III. Geology, tectonism and composition of the northwest Imbrium region. Icarus 2018, 303, 67–90. [CrossRef] 52. Ran, Z.; Wang, Z.Z. Simulations of lunar equatorial regolith temperature profile based on measurements of Diviner on lunar reconnaissance orbiter. Sci. China Earth Sci. 2014, 57, 2232–2241. [CrossRef] 53. Sullivan, M.T.; Paige, D.A.; Arvidson, R.E.; Grayzeck, E. Lunar Reconnaissance Orbiter Diviner Lunar Radiometer Experiment: Reduced Data Record and Derived Products Software Interface Specification. In Technical Report; Version 1.14; PDS Geosciences Node: Los Angeles, CA, USA, 2017. 54. Ulaby, F.T.; Moore, R.K.; Fung, A.K. Microwave Remote Sensing Fundamentals and Radiometry. In Microwave Remote Sensing: Active and Passive; Artech House: Norwood, MA, USA, 1981; Volume 1, pp. 186–205. 55. Meng, Z.G.; Wang, H.H.; Zheng, Y.C.; Wang, Y.Z.; Miyamoto, H.; Cai, Z.C.; Ping, J.S.; Zhu, Y.Z. Several Geological Issues of Schrödinger Basin Exposed by CE-2 CELMS Data. Adv. Astron. 2019, 2019, 1–13. [CrossRef] 56. Hagfors, T. Remote probing of the moon by infrared and microwave emissions and by radar. Radio Sci. 1970, 5, 189–227. [CrossRef] 57. Campbell, B.A.; Campbell, D.B.; Margot, J.L.; Ghent, R.; Nolan, M.; Chandler, J.; Carter, L.M.; Stacy, N.J.S. Focused 70-cm wavelength radar mapping of the Moon. IEEE Trans. Geosci. Remote Sens. 2007, 45, 4032–4042. [CrossRef] Sensors 2019, 19, 5545 23 of 23

58. Hu, G.P.; Chen, K.; Huang, Q.L.; Guo, W.; Li, Q.X.; Gui, L.Q.; Cheng, Y.B. Brightness Temperature Calculation of Lunar Crater: Interpretation of Topographic Eﬀect on Microwave Data from Chang’E. IEEE Trans. Geosci. Remote Sens. 2014, 52, 4499–4510. 59. Wieczorek, M.A.; Huang, S. A reanalysis of Apollo 15 and 17 Surface and Subsurface Temperature Series. In Proceedings of the 37th Lunar and Planetary Science, Houston, TX, USA, 13–17 March 2006; p. 1682.

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