Entrance Pupil Irradiance Estimating Model for a Moon-Based Earth Radiation Observatory Instrument

Home , Lunar standstill, Near side of the Moon

remote sensing

Article Entrance Pupil Irradiance Estimating Model for a Moon-Based Earth Radiation Observatory Instrument

Wentao Duan 1, Shaopeng Huang 2,3,* and Chenwei Nie 4

1 School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an 710054, China; [email protected] 2 Institute of Deep Earth Science and Green Energy, Shenzhen University, Shenzhen 518060, China 3 Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, MI 48109, USA 4 Key Laboratory of Digital Earth Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100094, China; [email protected] * Correspondence: [email protected]

Received: 26 January 2019; Accepted: 6 March 2019; Published: 10 March 2019

Abstract: A Moon-based Earth radiation observatory (MERO) could provide a longer-term continuous measurement of radiation exiting the Earth system compared to current satellite-based observatories. In order to parameterize the detector for such a newly-proposed MERO, the evaluation of the instrument’s entrance pupil irradiance (EPI) is of great importance. The motivation of this work is to build an EPI estimating model for a simplified single-pixel MERO instrument. The rationale of this model is to sum the contributions of every location in the MERO-viewed region on the Earth’s top of atmosphere (TOA) to the MERO sensor’s EPI, taking into account the anisotropy in the longwave radiance at the Earth TOA. Such anisotropy could be characterized by the TOA anisotropic factors, which can be derived from the Clouds and the Earth’s Radiant Energy System (CERES) angular distribution models (ADMs). As an application, we estimated the shortwave (SW) (0.3–5 µm) and longwave (LW) (5–200 µm) EPIs for a hypothetic MERO instrument located at the Apollo 15 landing site. Results show that the SW EPI varied from 0 to 0.065 W/m2, while the LW EPI ranged between 0.061 and 0.075 W/m2 from 1 to 29 October, 2017. We also utilized this model to predict the SW and LW EPIs for any given location within the MERO-deployable region (region of 80.5◦W–80.5◦E and 81.5◦S–81.5◦N on the nearside of the Moon) for the future 18.6 years from October 2017 to June 2036. Results suggest that the SW EPI will vary between 0 and 0.118 W/m2, while the LW EPI will range from 0.056 to 0.081 W/m2. Though the EPI estimating model in this study was built for a simplistic single-pixel instrument, it could eventually be extended and improved in order to estimate the EPI for a multi-pixel MERO sensor.

Keywords: Earth radiation; MERO; entrance pupil irradiance; CERES; ADMs; TOA anisotropy

1. Introduction The balance between the incoming solar radiation and the outgoing radiation is the driving force of the Earth’s climate system. The incoming radiation mainly comes from solar radiation, while the outgoing radiation takes two forms: reflected solar shortwave (SW) radiation and longwave infrared (LW) radiation. Spaceborne platforms can provide global radiation observations, which are crucially needed for the Earth Radiation Budget (ERB) study. Thus, ERB research deeply relies on the development of space technology [1,2]. Since the early 1970s, several missions dedicated to the observation of Earth’s outgoing radiations have been launched. The Earth Radiation Budget Experiment (ERBE) wide-field-of-view (WFOV) radiometer onboard the Earth Radiation Budget Satellite (ERBS) provided a 15-year (1984–1999) high-quality record of the Earth’s radiant energy. It mainly measured the flux of SW and LW radiation at the Earth’s top of atmosphere (TOA) [3–5].

Remote Sens. 2019, 11, 583; doi:10.3390/rs11050583 www.mdpi.com/journal/remotesensing Remote Sens. 2019, 11, 583 2 of 18

Its successor, the Clouds and the Earth’s Radiant Energy System (CERES), onboard the Terra, Aqua, Suomi National Polar-orbiting Partnership (S-NPP), and National Oceanic and Atmospheric Administration-20 (NOAA-20) satellites, not only measured the TOA radiation, but the radiative fluxes at the surface and the atmospheric radiation fluxes [6–8]. This allows for a better understanding of air–land and air–sea energy transfer and better physically based weather forecasting. CERES has provided such observations since 2000, and there will still be several CERES instruments operating in coming decades. Furthermore, the Geostationary Earth Radiation Budget (GERB) instrument onboard the Meteosat Second Generation (MSG) satellite provided the first dedicated observation of the ERB from a geostationary orbit; the generated data could help to mitigate the lack of temporal samples in the low-orbit satellite observation data of the 60◦S–60◦N region on Earth [9–11]. These satellite-based observations have enhanced our understanding of the ERB; however, they still have several limitations. A satellite-based observatory is restricted by the limited longevity of its carrying satellite. For example, the Terra satellite (one of the CERES’s carrying platforms), which has the longest operational lifetime among all the current flying satellites carrying the Earth radiation observation system, will operate for 22 years and will be decommissioned around 2022 when it is due to run out of fuel [12]. The operational lifetime of the onboard instrument of around two decades could possibly be extended if the carrying satellite had longer longevity. Additionally, global radiation data from current polar-orbiting-satellite observations are time-averaging. Due to the limited temporal sampling, it may neglect some variations of small time-scales, which could be important for studies that need high temporal resolution Earth radiation data, such as research into the relationship between TOA flux and cloud fraction [13,14]. Though these polar-orbit-satellite observations can be temporally interpolated by measurements from geostationary satellites to provide better regional radiation estimates, the polar regions are not involved [10,15]. All of these necessitate the search for a complementary platform for the Earth’s radiation observation. The near-side of the Moon is a unique platform for observing the Earth’s radiation budget [16,17]. Compared to a man-made-satellite platform, a Moon-based Earth radiation observatory (MERO) may have several advantages. As the only natural satellite of the Earth, the Moon has a much more stable orbit, which will allow for a substantially longer longevity for a Moon-based observatory than a man-made satellite. This provides the possibility for instruments deployed on the near-side of the Moon to produce longer-term and continuous data. Due to the long distance between the Moon and the Earth, a sensor on the near-side of the Moon may have an all-time near-half-globe scope. Since spatial resolution depends on the number of detectors on the focal plane of a sensor [18], if the sensor has sufficient detectors, a MERO could provide observations with abundant temporal samples and high-spatial resolution for the globe, which could help enhance the current satellite-based Earth radiation estimates. Furthermore, more accurate in situ instrument calibration can be performed due to the stable selenographic radiation environment without complications from an atmosphere. However, leaving a sensor on the Moon would face significant challenges, which mainly result from the harsh lunar environment, including the significantly large difference in the day and night temperatures (~250 K) [16] and space radiation hazards caused by outer space high-energy particles [19]. Since man-made satellites also suffer from high-energy particles and a large day–night temperature difference in space, technologies have been developed to cope with the impacts of these two factors [20,21], which could be improved and then implemented for the Moon-based instrument. For the purpose of the prospective MERO instrumentation design, the detector’s parameterization is necessary, which is closely related to the irradiance at the entrance pupil plane of the instrument. The entrance pupil irradiance (EPI) is the radiation entering the instrument, which will finally arrive at the focal plane through the optics system; in other words, the focal plane irradiance (FPI) could be derived from the EPI. The FPI is the input energy of the instrument’s charge-coupled device (CCD), which converts the input radiation to a digital signal. For a specific CCD, there will be a certain device noise generated by the processing chips and circuits; thus, for the same input FPI, different CCDs will possess various signal-to-noise ratios (SNRs), and a larger SNR will lead to higher quality Remote Sens. 2019, 11, 583 3 of 18 data [18,22]. The quantification of EPI will help with the selection of the optimal CCD with the highest SNR for a MERO instrument. Currently, however, little research has focused on EPI and the follow-on parameterization for a MERO sensor. The objective of this study is to build a model to estimate the EPIs of a MERO instrument. Section2 is dedicated to presenting the model features, the detailedRemote Sens. construction 2019, 11, x FOR process, PEER REVIEW and the utilized satellite-based data. In Section3, we3 present of 18 the model applications which estimated the EPIs for a hypothetic MERO located at the Apollo 15 landing site andand predicted the follow-on the EPIs parameterization for any given for locationa MERO sensor MERO. The within objective the of MERO this study deployable is to build regiona model over an 18.6-yearto period.estimate Ourthe EPIs conclusions of a MERO are instrument. presented Sectio inn Section 2 is dedicated4. to presenting the model features, the detailed construction process, and the utilized satellite-based data. In Section 3, we present the 2. Modelmodel applications which estimated the EPIs for a hypothetic MERO located at the Apollo 15 landing site and predicted the EPIs for any given location MERO within the MERO deployable region over 2.1. Generalan 18.6-year Features period. Our conclusions are presented in Section 4. Unlike2. Model a low-orbit satellite platform, since the Moon–Earth distance (385,000 km on average) is about 60 times greater than the Earth’s mean radius (6400 km), a MERO would have a near half-globe 2.1. General Features coverage. This means that the MERO-viewed area on the Earth will have a significant curvature. Such characteristicsUnlike a low-orbit would result satellite in platform, a great effect since onthe buildingMoon–Earth the distance MERO (385,000 sensor’s km EPI on estimatingaverage) is model. about 60 times greater than the Earth’s mean radius (6400 km), a MERO would have a near half-globe Due to thecoverage. Moon’s This orbit means motion that the and MERO-viewed the Earth’s area rotation, on the Earth the spatialwill have distribution a significant curvature. of the near-half Such area viewedcharacteristics by a MERO onwould the Earthresult in is a great temporal effect variable.on building Furthermore, the MERO sensor’s as the EPI Moon–Earth estimating model. system orbits the Sun,Due it would, to the Moon’s in general, orbit motion contain and a the spatially Earth’s varyingrotation, the Sun-lit spatial part distribution (both emitting of the near-half LW and area reflecting solar SWviewed radiation by a MERO to a MERO) on the andEarth a is non-sunlit a temporal portionvariable. (onlyFurthermore, emitting as LWthe Moon–Earth radiation) (seesystem Figure 1). These willorbits result the Sun, in temporal it would, in variations general, contain of the a MERO spatially sensor’s varying SWSun-lit and part LW (both EPIs emitting due to LW the and difference reflecting solar SW radiation to a MERO) and a non-sunlit portion (only emitting LW radiation) (see in the outward radiations of different Earth locations. Thus, to derive the EPIs, the temporal–spatial Figure 1). These will result in temporal variations of the MERO sensor’s SW and LW EPIs due to the distributiondifference of the in MERO-viewedthe outward radiations area at of the differen Eartht TOA Earth and locations. its sunlit Thus, portion to derive should the EPIs, first bethe derived. Since thetemporal–spatial scope of a MERO distribution covers of nearlythe MERO-viewed half of the area globe at instantaneously,the Earth TOA and the its curvaturesunlit portion of such a hemisphericshould surface first be willderived. result Since in thethe differencescope of a MERO in geometries covers nearly of different half of the top globe of atmosphere instantaneously, (TOA) sites towardsthe the curvature MERO suchof such as a thehemispheric distance surface and the will viewing result in zeniththe difference angle in (see geometries Figure1 of), anddifferent this top geometry differenceof atmosphere will lead to(TOA) a distinction sites towards in the the MERO contributions such as theof distance different and TOAthe viewing sites zenith in the angle MERO-viewed (see Figure 1), and this geometry difference will lead to a distinction in the contributions of different TOA region to the MERO sensor’s SW and LW EPIs. sites in the MERO-viewed region to the MERO sensor’s SW and LW EPIs.

Figure 1. A sketch illustrating the sunlit and non-sunlit portions of the near-half-globe Moon-based Figure 1. A sketch illustrating the sunlit and non-sunlit portions of the near-half-globe Moon-based Earth radiation observatory (MERO) viewed area at the Earth’s top of atmosphere (TOA), the location- Earth radiationvarying viewing observatory zenith angle (MERO) 𝛽 and distance viewed to the area MERO. at the Earth’s top of atmosphere (TOA), the location-varying viewing zenith angle β and distance to the MERO.

Remote Sens. 2019, 11, 583 4 of 18

As a preliminary step, only a single-pixel detector with an all-time near-half-globe scope, which has a SW broadband channel (0.3–5 µm) for measuring reflected solar radiation and a LW broadband (5–200 µm) channel for measuring Earth-emitted thermal radiation, is considered to be deployed in the MERO instrument. To obtain a MERO sensor’s EPI, we subdivided the MERO-viewed area at the Earth TOA into finite geographic elements, and summed up the individual contributions of these elements to the MERO sensor’s EPI. In this paper, such individual contributions were derived through the radiance from the subdivided TOA area to the MERO sensor with some geometric parameters by utilizing the radiation transfer function, which uses the radiance, cosine weighting and solid angle to calculate the radiation transferred from an emitter to a receiver. Therefore, the calculation of the TOA radiance toward MERO is the core part of this model, which can be derived from the TOA radiation flux and TOA anisotropic factors. Ideally, if the Earth TOA surface is Lambertian, the TOA radiance can be derived by TOA radiation flux/π and is isotropic, irrespective of direction. However, the actual radiance depends on the direction, which is anisotropic. Such anisotropy can be described by utilizing the TOA anisotropic factor, which is defined as actual radiance/Lambertian radiance, i.e., (actual radiance) × π/(TOA radiation flux). Thus, the actual TOA radiance can be derived by (TOA anisotropic factor) × (TOA radiation flux)/π, where the TOA radiation flux can be obtained from the satellite-based Earth TOA flux dataset, and the TOA anisotropic factors can be derived by referring to the CERES anisotropic factors. The CERES anisotropic factor is (actual TOA radiance) × π/(TOA radiation flux) and is used to convert the measured TOA radiances to the TOA radiation flux data; such usage is inverse to the utilization in our work. The CERES anisotropic factors can be generated by angular distribution models (ADMs). The CERES SW ADMs determine the SW anisotropic factors as the function of the solar zenith angle, observer zenith angle, and relative azimuth angle (defining the azimuth angle position of the observer relative to the solar plane), while the CERES LW ADMs determine the LW anisotropic factors, which depend on the observer zenith angle, since the LW anisotropy is nearly irrelative to the solar zenith angle and relative azimuth angle. Notably, the CERES ADMs have been built for a variety of scene types, and each scene type’s ADMs are different. Such scene types are defined by the combination of surface type, e.g., ocean, land, with several other parameters, e.g., cloud optical depth and cloud fraction. The surface of a TOA region is defined as its directly projected area on the Earth’s surface [23–25]. The steps of our construction of the MERO’s EPI model are shown in Figure2. The first procedure is to mesh the MERO-viewed area at the Earth TOA and to derive the temporal–spatial distribution of the sunlit and non-sunlit portions of such area by utilizing the NASA JPL Horizons Ephemeris System. The JPL Horizons System takes into accounts more than 100 different astronomical aspects, such as the elliptical shape of the lunar orbit, lunar librations, apsidal precession, lunar standstill cycle, and the Earth’s axial precession and nutation [26]. Then, by retrieving the satellite-based Earth TOA flux dataset as a function of latitude and longitude, the TOA radiation flux of every grid node in the MERO-viewed area can be estimated. Additionally, the JPL Horizons can provide geometric parameters between the MERO and the MERO-viewed area at the Earth TOA such as distance and viewing zenith angle, which are crucial for the calculation of a MERO sensor’s EPI. Finally, combined with the TOA anisotropic factors, the MERO sensor’s EPIs are derived through the radiation transfer function. Remote Sens. 2019, 11, 583 5 of 18

Remote Sens. 2019, 11, x FOR PEER REVIEW 5 of 18

FigureFigure 2.2.Flowchart Flowchart of theof modelthe model construction construction for deriving for deriving a MERO a sensor’s MERO entrance sensor’s pupil entrance irradiances. pupil SW:irradiances. shortwave; SW: LW: shortwave; longwave. LW: longwave.

2.2.2.2. Temporal–SpatialTemporal–Spatial DistributionDistribution ofof MERO-ViewedMERO-ViewedArea Areaat atthe the Earth Earth TOA TOA FigureFigure3 3 showsshows the process process of of deriving deriving the the time-dependent time-dependent spatial spatial distribution distribution of the ofMERO- the ◦ MERO-viewedviewed area and area its andsunlit its portion sunlit portion at the atEarth the EarthTOA. TOA.The globe The globeis discretized is discretized in 1° inlatitude 1 latitude ⨉ 1° ◦ ×longitude1 longitude grids grids since since the theutilized utilized satellite-based satellite-based TOA TOA flux ﬂux data data in in this this study study came came from CERESCERES ◦ ◦ datasets,datasets, ofof whichwhich thethe spatialspatial resolutionresolution is is 11°latitude latitude× ⨉ 11° longitude. The MERO viewing zenith angleangle ◦ ββ isis utilizedutilized to to pick pick out out grid grid nodes nodes in in the the MERO-viewed MERO-viewed area area on on Earth Earth by βby≤ β90 ≤ 90°.. β can β can be obtainedbe obtained by by Li·Ni βi = arccos (1) |L𝑳i||∙𝑵Ni| 𝛽 =arccos (1) |𝑳||𝑵| where Li is the MERO viewing vector of node i and Ni is the normal vector (see Figure4). where 𝑳 is the MERO viewing vector of node i and 𝑵 is the normal vector (see Figure 4). WGS-84 WGS-84 Cartesian coordinates of Li can be derived from Cartesian coordinates of 𝑳 can be derived from   D γ ϕ − G θ ϕ 𝐷LE cos 𝛾cos cos v𝜑 −𝐺i cos 𝜃i coscos 𝜑i =  D − G  Li  𝐷LE coscos γ𝛾sin sinϕ v𝜑 −𝐺i cos θ𝜃i sinsin ϕ𝜑i  (2) 𝑳 = 2 (2) D sin γ − G 𝑏b sin θ 𝐷LE sin 𝛾 − 𝐺 i a2 sin 𝜃i 𝑎 a𝑎 Gi = q (3) 𝐺 = − e2 2 (3) 11−𝑒 sin sin θ𝜃i 𝑎2 𝑒 sin 𝜃 cos𝜃 ! ae sin θV cos θV γ 𝛾=𝜃= θV −−arcsinarcsin (4)(4) 𝐷 p 1−𝑒2 sin2𝜃 DLE 1 − e sin θV wherewherea 𝑎and andb are𝑏 are the the semi-major semi-major axis axis and and the semi-minorthe semi-minor axis ofaxis the of Earth the Earth TOA ellipsoid,TOA ellipsoid,√ which which is the WGS-84is the WGS-84 Earth ellipsoid Earth ellipsoid plus the pl atmosphere,us the atmosphere, respectively; respectively;e is the ﬁrst 𝑒 eccentricityis the first (eccentricitye = a2 − b 2(/𝑒=a); D√LE𝑎 −𝑏is the/𝑎 distance); 𝐷 is fromthe distance the Earth’s from center the Earth’s OE to center the MERO OE to location the MERO L, which location can L, be which derived can bybe multiplyingderived by multiplying the light speed the light by the speed parameter by the para 399_ins_LT_LEmeter 399_ins_LT_LE (see Table (see1) generated Table 1) generated from the from JPL the JPL Horizons System; 𝜃 and 𝜑 are the WGS-84 latitude and longitude of the sub-MERO point V, respectively, which can be derived from the JPL Horizons System generated parameters sub-

Remote Sens. 2019, 11, 583 6 of 18

Horizons System; θV and ϕV are the WGS-84 latitude and longitude of the sub-MERO point V, respectively, which can be derived from the JPL Horizons System generated parameters sub-MERO latitude and sub-MERO longitude (see Table1). Given MERO location L, the sub-MERO point V is deﬁned as the intersection point of the Earth reference TOA ellipsoid and the Earth–MERO connection line perpendicular to this ellipsoid (see Figure4). θi and ϕi are the WGS-84 latitude and longitude of Remote Sens. 2019, 11, x FOR PEER REVIEW 6 of 18 node i, respectively, which are given by the initial meshing. Ni in Equation (1) can be derived from MERO latitude and sub-MERO longitude (see Table 1). Given MERO location L, the sub-MERO point V is defined as the intersection point of the Earthcos θ ireferencecos ϕi TOA ellipsoid and the Earth–MERO N =  cos θ sin ϕ  (5) connection line perpendicular to this ellipsoidi  (see Figurei 4).i 𝜃 and 𝜑 are the WGS-84 latitude and longitude of node i, respectively, which are given sinby theθi initial meshing. 𝑵 in Equation (1) can be derived from Thereafter, the sunlit and shadowed portions of a MERO-viewed area on Earth can be cos 𝜃 cos 𝜑 discriminated by Sun elevations (Se), which can be derived from 𝑵 = cos 𝜃 sin 𝜑 (5) sin 𝜃 S·Ni Thereafter, the sunlit and shadowedSe = 90 −portionsarccos of a MERO-viewed area on Earth can be (6) i |S||N | discriminated by Sun elevations (𝑆𝑒), which can be derived fromi where S is the Sun direction vector at the input time. It can𝑺∙𝑵 be derived from 𝑆𝑒 = 90 − arccos( ) (6) |𝑺||𝑵 |   cos θ cos ϕ where 𝑺 is the Sun direction vector at the input time.S It canS be derived from   S =  cos θS sin ϕS  (7) cos 𝜃 cos 𝜑 sin θS 𝑺=cos 𝜃 sin 𝜑 (7) sin 𝜃 where θS and ϕS are the WGS-84 latitude and longitude of the sub-solar point S at the input time. 𝜃 𝜑 Thesewhere can be achievedand are from the theWGS-84 JPL Horizons latitude and System-generated longitude of the sub-solar parameters point of S sub-solar at the input latitude time. and These can be achieved from the JPL Horizons System-generated parameters of sub-solar latitude and sub-solar longitude (see Table1). sub-solar longitude (see Table 1).

FigureFigure 3. Flowchart3. Flowchart to to derivederive the the temporal-spatial temporal-spatial distribution distribution of the ofMERO-viewed the MERO-viewed area at the area Earth at the TOA. Earth TOA.

Remote Sens. 2019, 11, 583 7 of 18 Remote Sens. 2019, 11, x FOR PEER REVIEW 7 of 18

Figure 4. 4. AA sketch sketch to toillustrate illustrate the thegeometry geometry of a ofMERO’s a MERO’s sight sightline towards line towards a grid node a grid innode the MERO- in the viewedMERO-viewed area at the area Earth at the TOA. Earth TOA.

TableTable 1. TheThe JPL Horizons System generated parameters used in this study.

ParameterParameter Depiction Depiction Unit Unit Time UTC time Time DLE UTC time 399_ins_LT_LE ( light speed ) Instantaneous light-time of MERO location with respect to the Earth center at the set-time Minutes Sub-MERO399_ins_LT_LE latitude (θ V)Instantaneous light-time WGS-84 latitude of MERO of the sub-MERO location point with V respect to the Degree Sub-MERO longitude (ϕ ) WGS-84 longitude of the sub-MERO point VMinutes Degree ( ) V Sub-solar latitude (θS)Earth WGS-84 center latitude ofat the the sub-solar set-time point S Degree Sub-MEROSub-solar longitude latitude(ϕS) WGS-84 longitude of the sub-solar point S Degree WGS-84 latitude of the sub-MERO point V Degree (𝜃) 2.3.Sub-MERO Radiation longitude Transfer Function WGS-84 longitude of the sub-MERO point V Degree The rationale(𝜑) of this function is to sum the individual contributions of every grid node in the MERO-viewedSub-solar latitude area (𝜃 at) the Earth TOA WGS-84 to the MEROlatitude instrument’s of the sub-solar EPI point (see FigureS 5). An individual Degree contributionSub-solar longitude can be derived from the node’s TOA radiation ﬂux utilizing the radiation transfer function. WGS-84 longitude of the sub-solar point S Degree Therefore,( the𝜑) MERO sensor’s SW EPI (ψSW) and LW EPI (ψLW) can be derived through

−1 −2 2.3. Radiation Transfer FunctionψSW = ∑ Fswiπ Rswi cos βi Ai cos ηiDLi (8) i∈SLN The rationale of this function is to sum the individual contributions of every grid node in the MERO-viewed area at the Earth TOA to the MERO−1 instrument’s EPI− (see2 Figure 5). An individual ψLW = ∑ Flwiπ Rlwi cos βi Ai cos ηiDLi (9) contribution can be derived from ithe∈M Nnode’s TOA radiation flux utilizing the radiation transfer function. Therefore, the MERO sensor’s SW EPI (𝜓 ) and LW EPI (𝜓 ) can be derived through where Fswi and Flwi are the TOA SW and TOA LW flux of node i, respectively, which could be derived by seeking the satellite-based TOA radiation flux data by the coordinates of node i. The coordinates of 𝜓 =𝐹𝑠𝑤 𝜋 𝑅𝑠𝑤 cos 𝛽 𝐴 cos 𝜂 𝐷 i (8) node have been given in the spatial distribution∈ generation process as described in Section 2.2. In our study, the CERES SYN1deg Ed4A dataset serves as the source of the satellite-based TOA flux data [27]. CERES can provide a relatively accurate measurement of multiple Earth radiation parameters and 𝜓 =𝐹𝑙𝑤 𝜋 𝑅𝑙𝑤 cos 𝛽 𝐴 cos 𝜂 𝐷 (9) cloud properties including the SW and∈ LW TOA outward radiation flux. The CERES has continuously collected about 18 years of data, and in the future, there will still be a series of such instruments where 𝐹𝑠𝑤 and 𝐹𝑙𝑤 are the TOA SW and TOA LW flux of node i, respectively, which could be derivedoperating by onboard. seeking the This satellite-based indicates that TOA the CERESradiation has flux the data potential by the to coordinates provide the of longest-termnode i. The coordinates of node i have been given in the spatial distribution generation process as described in Section 2.2. In our study, the CERES SYN1deg Ed4A dataset serves as the source of the satellite-based

Remote Sens. 2019, 11, 583 8 of 18 continuous Earth radiation data over recent decades. The CERES data are now widely used to help us to better understand the ERB [28]. Among all of the CERES datasets, the SYN1deg-1hourly Ed4A product could provide the highest temporal resolution for the TOA flux dataset with a 1◦ latitude × 1◦ longitude spatial resolution by incorporating hourly geostationary satellite (GEO) imager data and by taking advantage of additional GEO imager channels to improve the quality of the generated TOA radiation fluxes. These hourly Earth TOA flux data could help to maximize the temporal resolution of the model-derived MERO sensor’s EPI [15,27,29]. In Equations (8) and (9), Rswi and Rlwi are the SW and LW anisotropic factors of TOA node i, respectively, which will be described in details in Section 2.4. SLN is the set of all sunlit nodes in the MERO-viewed area at the Earth TOA and MN is the set of all grid nodes in this area. The second term cos βi Ai is the size of the projected area of node i toward ◦ ◦ the MERO, where Ai is the size of the area that node i represents (1 latitude × 1 longitude area −2 on Earth). The third term cos ηiDLi is the solid angle from node i to per square meter of the MERO sensor’s entrance pupil surface. DLi is the distance between the MERO and node i, which is the length of Li and can be derived from Equations (2)–(4). ηi is the angle between Li and the MERO instrument orientation vector LV (see Figure5), where LV can be used to represent the instrument’s orientation since a MERO sensor always faces straight toward the sub-MERO point V. ηi can be derived from

Li·Lv ηi = arccos (10) |Li||Lv| where Li can be derived from Equations (2)–(4), and LV can be derived from   DLE cos γ cos ϕV − Gv cos θv cos ϕv  −  Lv =  DLE cos γ sin ϕV Gv cos θv sin ϕv  (11) − b2 DLE sin γ Gv a2 sin θv a Gv = (12) p 2 2 1 − e sin θv where γ can be derived from Equation (4). DLE, θv, and ϕv are given by the parameters 399_ins_LT_LE, sub-MERO latitude, and sub-MERO longitude, respectively, from the JPL Horizons System (see Table1). Remote Sens. 2019, 11, 583 9 of 18 Remote Sens. 2019, 11, x FOR PEER REVIEW 9 of 18

Figure 5. A sketch to illustrate the function for calculating the MERO sensor’s entrance pupil Figure 5. A sketch to illustrate the function for calculating the MERO sensor’s entrance pupil irradiances. βi irradiances. 𝛽 is the MERO viewing zenith angle; 𝑆𝑒 is the Sun elevation; 𝜇 is the relative is the MERO viewing zenith angle; Sei is the Sun elevation; µi is the relative azimuth angle; ηi is the MERO azimuth angle; 𝜂 is the MERO zenith angle of grid node i in the MERO-viewed area at the Earth zenith angle of grid node i in the MERO-viewed area at the Earth TOA; and V is the sub-MERO point. TOA; and V is the sub-MERO point. 2.4. Earth TOA Anisotropic Factors 2.4. Earth TOA Anisotropic Factors In our study, the TOA SW anisotropic factor (Rsw) and TOA LW anisotropic factor (Rlw) are In our study, the TOA SW anisotropic factor ( 𝑅𝑠𝑤) and TOA LW anisotropic factor (𝑅𝑙𝑤) are derived with several simplifications based on the CERES ADMs: derived with several simplifications based on the CERES ADMs: 1. 1. SinceSince it it is is not not feasible feasible for for usus toto establishestablish a reasonablereasonable function function to to characterize characterize the the SW SW radiance radiance anisotropyanisotropy based based on on the the CERES CERES ADM ADM references references [23, 25[23,25],], at this at stagethis stage of research, of research, the SW the radiance SW exitingradiance the exiting Earth TOAthe Earth is assumed TOA is assumed to be isotropic, to be isotropic, thus Rsw thusis 1 𝑅𝑠𝑤 constantly; is 1 constantly; 𝑅𝑙𝑤 2. 2. AccordingAccording to to the the CERES CERES LW LW ADMs ADMs [[25],25], thethe TOATOA LW anisotropic factor factor Rlw isis determined determined by by a a set of viewing-zenith-angle-dependent functions under several scene types. We simplified set of viewing-zenith-angle-dependent functions under several scene types. We simplified these these scene types as a combination of surface types (ocean, land, desert, and snow) with two scene types as a combination of surface types (ocean, land, desert, and snow) with two cloud cloud conditions (clear sky and cloudy sky), and the surface of a TOA node is defined as the 1° conditions (clear sky and cloudy sky), and the surface of a TOA node is defined as the 1◦ latitude latitude × 1° longitude area at the Earth’s surface directly beneath this node. The clear condition × 1◦ longitude area at the Earth’s surface directly beneath this node. The clear condition is is defined by cloud coverage f ≤ 0.1%. f could be derived from the CERES SYN1deg Ed4A dataset. defined by cloud coverage f ≤ 0.1%. f could be derived from the CERES SYN1deg Ed4A dataset. For the TOA grid nodes of the ocean, land, and desert surface types, the 𝑅𝑙𝑤, as the function of theFor MERO the TOAviewing grid zenith nodes angle of the (β), ocean, is shown land, in Figure and desert 6a. The surface 𝑅𝑙𝑤 ranges types, from the Rlw ~0.78, as to the ~1.04 function under of thethe MERO clear viewingcondition, zenith and from angle ~0 ( βto), ~1.18is shown under in the Figure cloudy6a. condition. The Rlw ranges A value from of 1.04 ~0.78 implies to ~1.04 that underthe theactual clear radiance condition, is bigger and from than ~0the toideally ~1.18 Lambertian under the radiance cloudy condition.at the nadir Adirection, value of as 1.04 does implies the value that theof actual 1.18, while radiance for isthe bigger TOA thannodes the with ideally the snow Lambertian surface radiance type, the at 𝑅𝑙𝑤 the nadiragainst direction, β under asthe does clear the valuecondition of 1.18, is whilevery similar for the to TOA that nodesunder withthe cloudy the snow condition surface (see type, Figure the 6b).Rlw against β under the clear conditionThe is surface very similar type of to every that underTOA grid the cloudynode in condition the MERO-viewed (see Figure area6b). is determined using the CERES surface type data [30], which utilize 18 categories with IDs from 1 to 18 to represent the Earth’s

Remote Sens. 2019, 11, x FOR PEER REVIEW 10 of 18

surface with a spatial resolution of 1° latitude × 1° longitude. In our study, except for the TOA grid Remotenodes Sens. 2019with, 11 an, 583 ID of 15, which represented the snow surface type, others are defined as the TOA10 of 18 nodes with land, ocean, and desert surface types.

FigureFigure 6. Earth 6. Earth TOA TOA LW LW anisotropic anisotropic factors factors for for (a ()a the) the land, land, ocean, ocean, andand desert surface surface types; types; and and (b ()b ) the snowthe surface snow surface type, as type, a function as a function of the of MERO the MERO viewing viewing zenith zenith angle angleβ .β.

3.The Application surface type Results of everyand Discussion TOA grid node in the MERO-viewed area is determined using the CERES surface type data [30], which utilize 18 categories with IDs from 1 to 18 to represent the Earth’s surface3.1. withEPIs over a spatial the Moon’s resolution Orbital ofPeriod 1◦ latitude × 1◦ longitude. In our study, except for the TOA grid nodes withAs ana model ID of 15,application, which represented the SW and theLW snowEPIs of surface a hypothetic type, othersMERO areinstrument defined located as the TOAat the nodes withApollo land, ocean,15 landing and site desert (selenographic surface types. coordinates: 3.628°E, 26.133°N) over the Moon’s orbital period are evaluated. Results show that the SW EPI ranged from about 0 to 0.065 W/m2, while for the LW 3. ApplicationEPI, the maximum Results value and was Discussion about 0.075 W/m2 and the minimum was about 0.061 W/m2 (see Figure 7a,b). The latitude of the sub-MERO point on Earth of this hypothetical MERO over the Moon’s orbital 3.1. EPIsperiod over from the October Moon’s 1 Orbital to October Period 29, 2017 is shown in Figure 7c. The positive latitude means that the sub-MERO point V is on the Earth’s Northern Hemisphere, whereas the negative latitude means the As a model application, the SW and LW EPIs of a hypothetic MERO instrument located at the sub-MERO point V is on the Earth’s Southern Hemisphere. Since the sub-MERO point is the center Apollo 15 landing site (selenographic coordinates: 3.628◦E, 26.133◦N) over the Moon’s orbital period of the MERO-viewed area, the Northern-Hemisphere-located-V would imply that the MERO-viewed 2 are evaluated.area at the ResultsEarth TOA show is primarily that the SWsituated EPI in ranged the Northern from about Hemisphere, 0 to 0.065 while W/m the ,Southern- while for the 2 2 LW EPI,Hemisphere-located-V the maximum value indicates was aboutthat the 0.075 MERO-viewed W/m and area the at minimumthe Earth TOA was is about primarily 0.061 situated W/m (see Figurein7 thea,b). Southern The latitude Hemisphere. of the sub-MERO A comparison point of onFigu Earthres 7a–c of this indicates hypothetical that the MEROSW EPI over during the the Moon’s orbitalperiod period when from the sub-MERO October 1 point to October V is located 29, 2017 in the is Northern shown in Hemisphere Figure7c. is The greater positive than that latitude during means thatthe Southern-Hemisphere-located-V sub-MERO point V is on the period. Earth’s This Northern is probably Hemisphere, because the whereas SW reflectivity the negative of the land latitude meansis greater the sub-MERO than that of point the ocean, V is on and the the Earth’s Northern Southern Hemisphere Hemisphere. has a larger Since land thefraction sub-MERO than the point is theSouthern center ofHemisphere. the MERO-viewed This finding area, is thealso Northern-Hemisphere-located-Vapplicable to the LW EPI because the would TOA imply LW flux that the distributions in the Northern Hemisphere and Southern Hemisphere were not symmetrical over MERO-viewed area at the Earth TOA is primarily situated in the Northern Hemisphere, while the October 2017 (see Figure 8); i.e., although the TOA LW flux in the 0–60°N region was symmetrical to Southern-Hemisphere-located-V indicates that the MERO-viewed area at the Earth TOA is primarily that in the area of 0–60°S, the Arctic region had a bigger value than the Antarctic region. If the sub- situatedMERO in thepoint Southern (V) was Hemisphere.in the Northern A comparisonHemisphere (more of Figure of the7a–c Arctic indicates zone was that included the SW EPIin the during the periodMERO-viewed when the area sub-MERO than the Antarctic point Vzone), is located more LW in theradiation Northern will be Hemisphere emitted to the is MERO greater sensor than that duringthan the the Southern-Hemisphere-located-V scene where V was located in the Southe period.rn ThisHemisphere is probably (more because of the Antarctic the SW zone reflectivity was of the landincluded is greater in the MERO-viewed than that of the area ocean, than the and Arctic the zone), Northern since the Hemisphere MERO-viewed has area a larger covers land almost fraction thanhalf the of Southern the globe. Hemisphere. This finding is also applicable to the LW EPI because the TOA LW flux distributions in the Northern Hemisphere and Southern Hemisphere were not symmetrical over October 2017 (see Figure8); i.e., although the TOA LW flux in the 0–60 ◦N region was symmetrical to that in the area of 0–60◦S, the Arctic region had a bigger value than the Antarctic region. If the sub-MERO point (V) was in the Northern Hemisphere (more of the Arctic zone was included in the MERO-viewed area than the Antarctic zone), more LW radiation will be emitted to the MERO sensor than the scene where V was located in the Southern Hemisphere (more of the Antarctic zone was included in the MERO-viewed area than the Arctic zone), since the MERO-viewed area covers almost half of the globe. Remote Sens. 2019, 11, 583 11 of 18 RemoteRemote Sens. Sens. 2019 2019, ,11 11, ,x x FOR FOR PEER PEER REVIEW REVIEW 11 11 of of 18 18

FigureFigureFigure 7. 7.SW7. SWSW (a (),(aa), LW), LWLW (b (),(bb), entrance), entranceentrance pupil pupilpupil irradiance irradianceirradiance (EPI)(EPI) and andand the the latitudelatitude ofof of thethe the sub-MEROsub-MERO sub-MERO pointpoint point onon on EarthEarthEarth (c ),( (cc of),), of theof the the hypothetic hypothetic hypothetic MERO MERO MERO located located located atat at thethe the ApolloApollo 15 1515 landing landing site site site over over over about about about the the the Moon’s Moon’s Moon’s orbital orbital orbital periodperiodperiod from fromfrom October OctoberOctober 1 1to1 toto October OctoberOctober 29, 29,29, 2017. 2017.2017.

FigureFigureFigure 8. 8.Monthly8. MonthlyMonthly average averageaverage Earth EarthEarth TOA TOATOA LW LWLW ﬂux fluxflux onon OctoberOctober 2017 2017 derivedderived fromfrom from thethe the CERESCERES CERES SYN1degSYN1deg SYN1deg Ed4AEd4AEd4A dataset. dataset.dataset.

Remote Sens. 2019, 11, 583 12 of 18

3.2. EPIs over the Future 18.6 Years In order to predict SW and LW EPIs for any MERO sensor at any given location over the future 18.6 years (a major lunar standstill cycle), the previously derived EPI of the hypothetic MERO instrument located at the Apollo 15 landing site during the month of October 2017 is set as the benchmark; then, anomalies relative to this benchmark, resulting from the Earth TOA ﬂux variation, the shift of the Moon–Earth orbit, and various MERO selenographic locations over the next 18.6 years is estimated. These three factors are evaluated for prediction since they are likely to be the predominant factors involved in the variation of a MERO sensor’s EPIs. The month of October 2017 is chosen as the benchmark month since data from this period are the most recent among the CERES SYN1deg-1hourly Ed4A archive, which is the TOA ﬂux data source for the model. Hereafter, the MERO located at the Apollo 15 landing site is abbreviated as A15 MERO.

3.2.1. Earth TOA Flux Variation of the MERO sensor’s EPI is sensitive to the Earth’s TOA flux change. Ascertaining such sensitivity would facilitate predicting anomalies in the MERO sensor’s EPI relative to the benchmark, resulting from the Earth’s TOA flux perturbation in the future. We quantify this sensitivity by the MERO sensor’s EPI response as a function of the uniform increase of global Earth TOA fluxes. The MERO sensor’s EPI response (%) is defined as the monthly mean of the A15 MERO sensor’s EPI perturbation divided by this sensor’s EPI over October 2017. Therefore, for the uniform increase of different global TOA fluxes, e.g., 2 W/m2 and 4 W/m2, denominators of both of their EPI responses are the same, whereas the numerator of the EPI response of 4 W/m2 TOA flux increase is twice as large as that of 2 W/m2, making the EPI response in relative terms (%) to the uniform increase of global Earth TOA fluxes in absolute terms (W/m2) linear for both the SW and LW. This sensitivity for SW was found to be a 1 W/m2 global TOA flux uniform increase, resulting in about a 0.85% augmentation in the MERO sensor’s EPI, whereas a 1 W/m2 global TOA LW flux uniform increase would lead to approximately a 0.38% augmentation in the LW EPI. SW sensitivity is about twice as large as LW sensitivity, most likely because the denominator of the EPI response is the sensor’s EPI, which is derived from the TOA flux (Equations (8) and (9)), as indicated by the CERES Energy Balanced and Filled (EBAF) dataset, and the global mean TOA SW flux was ~100 W/m2, whereas the LW was ~200 W/m2 (see Figure9), which would make the SW EPI response about twice as large as the LW EPI response for the same amount of uniform increase of global TOA fluxes. As suggested by the CERES global mean TOA flux data from the CERES EBAF dataset [31], over the past 17 years from March 2000 to October 2017, both the TOA SW and LW flux variations were periodic oscillations with a nearly stable peak-to-peak amplitude and were within –9 to 10 W/m2 and –5 to 5 W/m2, respectively, relative to the value of the benchmark month of October 2017 (see Figure9). This stable-peak-to-peak-amplitude periodic oscillation indicates that although there are many factors such as atmospheric aerosol changing and snow cover variation which have consequences for the TOA flux, the sum of these effects may be small. This suggests a possibility of the same periodical variation of TOA flux over the next 18.6-year lunar standstill cycle as the past 17 years. Therefore, when considering the sensitivity depicted above, it can be concluded that the corresponding MERO sensor’s SW and LW EPI anomalies would be within −7.65 to 8.50% and −1.90 to 1.90 % relative to the benchmark, respectively, over the period from October 2017 to June 2036. Remote Sens. 2019, 11, 583 13 of 18 Remote Sens. 2019, 11, x FOR PEER REVIEW 13 of 18

FigureFigure 9. 9.Global Global mean mean Earth Earth TOA TOA SW SW and and LW LW ﬂuxes fluxes from from March March 2000 2000 to to October October 2017 2017 derived derived from from thethe CERES CERES EBAF EBAF dataset. dataset.

3.2.2.3.2.2. The The Moon–Earth Moon–Earth Orbit Orbit ◦ DueDue to to the the variation variation of of the the angle angle between between the the orbit orbit of of the the Moon Moon and and the the Earth’s Earth’s Equator Equator (18.30 (18.30° ◦ toto 28.60 28.60°,, 18.6-year 18.6-year cycle), cycle), a a MERO-viewed MERO-viewed areaarea on on Earth Earth appears appears to to shake shake up up and and down down during during an an 18.6-year18.6-year lunar lunar standstill standstill cycle, cycle, which which willwill result result in in differences differences between between the the MERO MERO sensor’s sensor’sEPI EPI at at differentdifferent Moon Moon orbital orbital periods. periods. Furthermore,Furthermore, thethe apsidalapsidal precessionprecession (8.7-year(8.7-year cycle)cycle) ofofthe the Moon’s Moon’s orbitorbit would would also also lead lead to to such such differences. differences. InIn orderorder toto characterize characterize thethe anomaly anomaly inin the the MERO’s MERO’s EPI EPI relativerelative to to the the benchmark benchmark resulting resulting from from the the shift shift of the of Moon–Earththe Moon–Earth orbit, orbit, the distribution the distribution of the Earthof the TOAEarth flux TOA is assumedflux is assumed as temporally as temp constant,orally constant, since thesince Earth the TOAEarth fluxTOA temporal flux temporal variation variation can also can causealso cause a change a change to the to MERO the MERO sensor’ sensor’ EPI. Specifically, EPI. Specifically, during during the next the lunar next standstill lunar standstill cycle (18.6 cycle years), (18.6 thisyears), temporally this temporally constant constant Earth TOA Earth flux TOA is set flux as theis set monthly as the monthly mean of themean benchmark of the benchmark month October month 2017October from 2017 the CERESfrom the SYN1 CERES degree SYN1 dataset. degree This dataset. monthly This meanmonthly flux mean is chosen flux asis chosen it can make as it can the TOAmake SWthe fluxTOA available SW flux all available over the all globe over during the globe the future during 18.6 the years. future The 18.6 all-time years. globally The all-time available globally SW TOAavailable flux isSW crucially TOA flux required is crucially due to required the fact thatdue theto th spatiale fact that distribution the spatial of thedistribution sunlit portion of the of sunlit the MERO-viewedportion of the MERO-viewed area at the Earth area TOA at the is temporallyEarth TOA is varying temporally and thisvarying sunlit and portion this sunlit may portion sometimes may notsometimes have location-matched not have location-matched TOA SW fluxes TOA without SW flux thees all-time without globally the all-time available globally TOA available SW flux data.TOA FigureSW flux 10 data.illustrates Figure the 10 model-derivedillustrates the model- monthlyderived maximum monthly and maximum minimum an EPIsd minimum of the A15 EPIs MERO of the sensorA15 MERO over a lunarsensor standstill over a periodlunar standstill from October period 2017 from to June October 2036. During2017 to the June benchmark 2036. During month the of 2 Octoberbenchmark 2017, month the monthly of October maximum 2017, the MERO monthly sensor’s maximum SW EPI MERO is about sensor’s 0.055 W/m SW EPI; however, is about due 0.055 to 2 theW/m Moon’s2; however, orbital due variation, to the Moon’s it would orbital increase variatio up ton, about it would 0.075 increase W/m over up to the about following 0.075 W/m 18.6 years2 over 2 (Figurethe following 10a), whereas 18.6 years the minimum (Figure 10a), of this whereas SW irradiance the minimum remains atof approximatelythis SW irradiance 0 W/m remains. For the at 2 MEROapproximately sensor’s 0 LW W/m EPI,2. For the the maximum MERO valuesensor’s over LW October EPI, the 2017 maximum is 0.077 value W/m over, and October will increase 2017 is 2 up0.077 to aboutW/m2,0.082 and will W/m increaseover up the to next about 18.6 0.082 years; W/m the2 over minimum the next value 18.6 ofyears; the the benchmark minimum month value isof the benchmark month is approximately 0.062 W/m2 and that of the future 18.6 years will decrease to 0.058 W/m2 (Figure 10b). These indicate that, over the period from October 2017 to June 2036, the

Remote Sens. 2019, 11, 583 14 of 18

Remote Sens. 2019, 11, x FOR PEER REVIEW 14 of 18 approximately 0.062 W/m2 and that of the future 18.6 years will decrease to 0.058 W/m2 (Figure 10b). Moon’sThese indicateorbital variation that, over would the period result from in up October to about 2017 a to36.36% June 2036,increase the Moon’sin the maximum orbital variation A15 MERO would sensor’sresult in SW up EPI, to about and up a 36.36% to about increase a 6.49% in increase the maximum and 6.45% A15 decrease MERO sensor’s in the maximum SW EPI, andand upminimum to about A15a 6.49% MERO increase sensor’s and LW 6.45% EPIs, decrease respectively, in the maximumrelative to and the minimumbenchmark, A15 which MERO is sensor’sthe A15 LWMERO EPIs, sensor’srespectively, EPI over relative October to the 2017. benchmark, which is the A15 MERO sensor’s EPI over October 2017.

FigureFigure 10. 10. (a()a )Monthly Monthly maximum maximum and and minimum minimum SW SW entrance entrance pupil pupil irradiances irradiances (EPIs); (EPIs); (b ()b )monthly monthly maximummaximum and and minimum minimum LW LW EPIs of aa hypotheticalhypothetical MEROMERO sensor sensor located located at at the the Apollo Apollo 15 15 landing landing site siteover over a major a major lunar lunar standstill standstill cycle cycle from Octoberfrom Oc 2017tober to 2017 June to 2036 June with 2036 an assumptionwith an assumption of temporally of temporallyconstant Earth constant TOA Earth SW and TOA LW SW ﬂuxes. and LW fluxes.

3.2.3. Selenographic Location 3.2.3. Selenographic Location Different MERO locations on the near-side of the Moon would result in a difference in the Different MERO locations on the near-side of the Moon would result in a difference in the instantaneous MERO-viewed area at the Earth TOA, leading to a difference in the MERO sensor’s EPI. instantaneous MERO-viewed area at the Earth TOA, leading to a difference in the MERO sensor’s Since the MERO’s deployable region is within the area of 80.5◦W–80.5◦E and 81.5◦S–81.5◦N on the EPI. Since the MERO’s deployable region is within the area of 80.5°W–80.5°E and 81.5°S–81.5°N on near-side of the Moon [32], to illustrate the extreme scene, two location pairs—the EW pair (ME, 80◦E, the near-side of the Moon [32], to illustrate the extreme scene, two location pairs—the EW pair (ME, 0◦ and MW, 80◦W, 0◦) and NS pair (MN, 0◦, 81◦N and MS, 0◦, 81◦S)—are utilized. The EW pair is 80°E, 0° and MW, 80°W, 0°) and NS pair (MN, 0°, 81°N and MS, 0°, 81°S)—are utilized. The EW pair used to evaluate the difference in the MERO sensor’s EPI resulting from the maximum longitudinal is used to evaluate the difference in the MERO sensor’s EPI resulting from the maximum longitudinal selenographic distance between two MEROs, and the NS pair is for the evaluation of the maximum selenographic distance between two MEROs, and the NS pair is for the evaluation of the maximum latitudinal distance. Due to the temporal variation of the MERO-viewed area at the Earth TOA, such latitudinal distance. Due to the temporal variation of the MERO-viewed area at the Earth TOA, such differences will change with time. The MERO sensor’s EPI differences resulting from the EW pair and differences will change with time. The MERO sensor’s EPI differences resulting from the EW pair NS pair over the Moon’s orbital period (October 1, 2017 to October 29, 2017) are illustrated in Figure 11, and NS pair over the Moon’s orbital period (October 1, 2017 to October 29, 2017) are illustrated in which shows that the NS pair will cause up to a 36.10% difference in the MERO sensor’s SW EPI, that Figure 11, which shows that the NS pair will cause up to a 36.10% difference in the MERO sensor’s was higher than the maximum value (20.82%) resulting from the EW pair. However, for the MERO SW EPI, that was higher than the maximum value (20.82%) resulting from the EW pair. However, for sensor’s LW EPI, this difference is much smaller, with the maximum value resulting from the EW pair the MERO sensor’s LW EPI, this difference is much smaller, with the maximum value resulting from (0.23%) being slightly higher than that from the NS pair (0.20%). the EW pair (0.23%) being slightly higher than that from the NS pair (0.20%).

Remote Sens. 2019, 11, 583 15 of 18 Remote Sens. 2019, 11, x FOR PEER REVIEW 15 of 18

FigureFigure 11. 11. TimeTime series series of of (a ()a differences) differences in in the the MERO MERO sensor’s sensor’s SW SW entrance entrance pupil pupil irradiance irradiance (EPI) (EPI) and and (b()b differences) differences in in the the LW LW EPI, EPI, resulting resulting from thethe hypotheticalhypothetical EWEW MERO MERO location location pair pair and and from from the the NS NSMERO MERO location location pair pair over over a Moon’sa Moon’s orbital orbital period period from from October October 1, 20171, 2017 to to October October 29, 29, 2017. 2017.

AsAs indicated indicated above, above, over over the the following following 18.6 18.6 years years from from October October 2017 2017 to June to June2036, 2036, relative relative to the to benchmarkthe benchmark (which (which is the is A15 the A15MERO MERO sensor’s sensor’s EPI EPIover over October October 2017), 2017), the the anomaly anomaly in inthe the MERO MERO sensor’ssensor’s SW SW EPI EPI resulting resulting from from the the Earth Earth TOA TOA flux ﬂux variations variations is is within within −−7.657.65 to to 8.50% 8.50% and and that that in in the the MEROMERO sensor’s sensor’s LW LW EPI EPI is is within within −1.9−1.9 to to1.9%. 1.9%. The The Moon’s Moon’s orbital orbital variation variation would would lead lead to to up up to to about about a a36.36% 36.36% increase increase in in the the maximum maximum MERO MERO sensor’s sensor’s SW SW EPI, EPI, and and up up to to an an approximate approximate 6.49% 6.49% increase increase andand 6.45% 6.45% decrease decrease in in the the maximum maximum and and minimum minimum ME MERORO sensor’s LW EPIs,EPIs, respectively,respectively, relative relative to tothe the benchmark. benchmark. Furthermore, Furthermore, the the anomaly anomaly in the in MEROthe MERO sensor’s sensor’s SW EPI SW resulting EPI resulting from the from MERO’s the MERO’sdeployment deployment location location is up to 36.10%is up to relative 36.10% to relative the benchmark, to the benchmark, and that in and the that MERO in sensor’sthe MERO LW sensor’sEPI is up LW to EPI 0.23%. is up All to of 0.23%. these All suggest of these that suggest the maximum that the sensor’s maximum SW sensor’s EPI of a SW MERO, EPI of which a MERO, can be whichlocated can anywhere be located within anywhere the MERO within deployable the MERO region, deployable over theregion, future over 18.6 the years future will 18.6 be greateryears will than bethe greater maximum than ofthe the maximum benchmark of bythe less benchmark than 80.96%. by less Note than that 80.96%. the maximum Note that and the minimum maximum SW and EPIs minimumof the benchmark SW EPIs areof the 0.065 be andnchmark 0 W/m are2, respectively0.065 and 0 (FigureW/m2, respectively7). On the other (Figure hand, 7). for On the the sensor’s other hand,LW EPI,for the such sensor’s an increase LW EPI, in thesuch maximum an increase value in the and maximum decrease value in the and minimum decrease value in the compared minimum to valuethe benchmark compared to would the benchmark be less than would 8.62% be and less 8.58%, than 8.62% respectively. and 8.58%, In particular, respectively. the maximumIn particular, and theminimum maximum LW and EPIs minimum of the benchmark LW EPIs of are the about benchmark 0.075 and are 0.061 about W/m 0.0752, and respectively. 0.061 W/m In2, summary, respectively. over Inthe summary, next lunar over standstill the next period lunar standstill from October period 2017 from to JuneOctober 2036, 2017 the to sensor’s June 2036, SW the EPI sensor’s of any givenSW EPIlocation of any MERO, given location located withinMERO, the located MERO within deployable the MERO region, deployable would vary region, between would 0 and vary 0.118 between W/m 2, 0 whileand 0.118 the rangeW/m2 of, while the MERO the range sensor’s of the LW MERO EPI issensor’s from 0.056 LW toEPI 0.081 is from W/m 0.0562. to 0.081 W/m2. InIn this this paper, paper, we established we established a framework a framework for the MERO for the sensor’s MERO EPI sensor’s estimation. EPI However, estimation. a limitationHowever, still a limitation exists in the still model. exists inThe the SW model. radiance The exiting SW radiance the Earth exiting TOA the is Earthcurrently TOA set is as currently isotropic set whenas isotropic in fact whenit should in fact be it shouldanisotropic. be anisotropic. In order to In orderestimate to estimate the EPI themore EPI precisely, more precisely, a function a function to reasonablyto reasonably characterize characterize such such anisotropy anisotropy is crucially is crucially needed. needed.

4.4. Conclusions Conclusions AA Moon-based Moon-based Earth Earth radiation radiation observatory observatory (M (MERO)ERO) could could provide provide longer-term longer-term continuous continuous measurementsmeasurements of of radiation radiation exitin exitingg the the Earth Earth system system when when compared compared to to the the current current satellite-based satellite-based platforms.platforms. For For the the parameterization parameterization of of a aMERO MERO sensor, sensor, quantifying quantifying the the entrance entrance pupil pupil irradiances irradiances (EPI)(EPI) is is of of great great importance. importance. However, However, little little research research has has focused focused on on such such EPI. EPI. In In this this study, study, we we built built a ashortwave shortwave (SW) (SW) (0.3–5 (0.3–5 µm)µm) and and longwave longwave (LW) (LW) (5–200 (5–200 µm)µm) EPI EPI estimating estimating model model for for a asimplified simpliﬁed single-pixelsingle-pixel MERO MERO sensor. ForFor thethe model model application, application, the the sensor’s sensor’s EPIs EPIs for afor hypothetic a hypothetic MERO MERO located locatedat the Apolloat the Apollo 15 landing 15 landing site were site evaluated.were evaluate Thed. results The results showed showed that thethat SW the EPISW wouldEPI would vary vary from from 0 to 0.065 W/m2, and the LW EPI ranged between 0.061 and 0.075 W/m2 from October 1 to October 29, 2017. Additionally, we also utilized this model to predict the SW and LW EPIs for a

Remote Sens. 2019, 11, 583 16 of 18

0 to 0.065 W/m2, and the LW EPI ranged between 0.061 and 0.075 W/m2 from October 1 to October 29, 2017. Additionally, we also utilized this model to predict the SW and LW EPIs for a MERO at any given location within the MERO deployable region (region of 80.5◦W–80.5◦E and 81.5◦S–81.5◦N on the near-side of the Moon) over the future 18.6 years. The results suggest that the SW EPI will vary between 0 and 0.118 W/m2, while the range of the LW EPI is from 0.056 to 0.081 W/m2. Note that the magnitudes of a MERO sensor’s SW and LW EPIs are not significantly different from the CERES instrument flying onboard the Terra, Aqua and Suomi-NPP satellites, of which both the magnitudes of the SW and LW EPIs are of the magnitude of the order of about 10−2 W/m2 [33]. This suggests that current technology could meet the requirement of the MERO sensor’s design specification in EPI. In the actual design, a MERO sensor should have multiple pixels either for the SW and LW channel, since the spatial resolution depends on the number of the pixels. There is spatial–temporal variability in the Earth radiation. The multi-pixel non-scanner MERO instrument has the potential to provide long-term continuous data with adequate spatial resolution to characterize such spatial dependence. Though this study only established an EPI estimating model for a simplified single-pixel sensor, this model could still be implemented to ascertain the pixel-scale EPI for the prospective multiple-pixel non-scanner instrument with some improvements. The most important next step is to ascertain the temporal spatial distribution of the relatively smaller pixel-viewed area on Earth, which can be derived from the combination of the MERO-viewed area positioning approach that we proposed in this study and the pixel array structure.

Author Contributions: Conceptualization, W.D. and S.H.; methodology, W.D.; software, W.D.; validation, W.D., S.H., and C.N.; formal Analysis, W.D.; investigation, W.D. and C.N.; writing—original draft preparation, W.D.; writing—review and editing, W.D., S.H., and C.N.; project administration, S.H.; funding acquisition, W.D., S.H., and C.N. Funding: This research was funded by the National Natural Science Foundation of China (grant number 41590855) and by the China Scholarship Council (grant number 201706280348). Acknowledgments: We thank Xianglei Huang and Yisuan Chen from the Department of Climate and Space Science and Engineering of University of Michigan for their assistance. The Jet Propulsion Lab (JPL) Horizons data used in this study were downloaded from the online ephemeris system at https://ssd.jpl.nasa.gov/?horizons. The CERES SYN1deg Ed4A dataset was downloaded from the online CERES data ordering system at https: //ceres.larc.nasa.gov/order_data.php. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Wielicki, B.A.; Wong, T.; Allan, R.P.; Slingo, A.; Kiehl, J.T.; Soden, B.J.; Gordon, C.T.; Miller, A.J.; Yang, S.K.; Randall, D.A.; et al. Evidence for large decadal variability in the tropical mean radiative energy budget. Science 2002, 295, 841–844. [CrossRef][PubMed] 2. Pinker, R.T.; Zhang, B.; Dutton, E.G. Do satellites detect trends in surface solar radiation? Science 2005, 308, 850–854. [CrossRef][PubMed] 3. Luther, M.R.; Cooper, J.E.; Taylor, G.R. The Earth Radiation Budget Experiment Nonscanner Instrument. Rev. Geophys. 1986, 24, 391–399. [CrossRef] 4. Barkstrom, B.R.; Smith, G.L. The Earth Radiation Budget Experiment: Science and implementation. Rev. Geophys. 1986, 24, 379–390. [CrossRef] 5. Kopia, L.P. Earth Radiation Budget Experiment Scanner Instrument. Rev. Geophys. 1986, 24, 400–406. [CrossRef] 6. Wielicki, B.A.; Barkstrom, B.R.; Baum, B.A.; Charlock, T.P.; Green, R.N.; Kratz, D.P.; Lee, R.B.; Minnis, P.; Smith, G.L.; Wong, T. Clouds and the Earth’s Radiant Energy System (CERES): Algorithm overview. IEEE Trans. Geosci. Remote Sens. 1998, 36, 1127–1141. [CrossRef] 7. Wielicki, B.A.; Barkstrom, B.R.; Harrison, E.F.; Lee, R.B., III; Smith, G.L.; Cooper, J.E. Clouds and the Earth’s Radiant Energy System (CERES): An Earth Observing System Experiment. Bull. Am. Meteorol. Soc. 1996, 77, 853–868. [CrossRef] Remote Sens. 2019, 11, 583 17 of 18

8. Loeb, N.G.; Manalo-Smith, N.; Su, W.; Shankar, M.; Thomas, S. CERES top-of-atmosphere earth radiation budget climate data record: Accounting for in-orbit changes in instrument calibration. Remote Sens. 2016, 8, 182. [CrossRef] 9. Harries, J.; Crommelynck, D. The geostationary earth radiation budget experiment on MSG-1 and its potential applications. Adv. Space Res. 1999, 24, 915–919. [CrossRef] 10. Harries, J.E.; Russell, J.; Hanafin, J.; Brindley, H.; Futyan, J.; Rufus, J.; Kellock, S.; Matthews, G.; Wrigley, R.; Last, A. The geostationary earth radiation budget project. Bull. Am. Meteorol. Soc. 2005, 86, 945–960. [CrossRef] 11. De Paepe, B.; Ignatov, A.; Dewitte, S.; Ipe, A. Aerosol retrieval over ocean from SEVIRI for the use in GERB Earth’s radiation budget analyses. Remote Sens. Environ. 2008, 112, 2455–2468. [CrossRef] 12. Mantziaras, D. EOS Terra Mission Status. In Proceedings of the Earth Science Constellation MOWG Meeting, Goddard Space Flight Center, Greenbelt, MD, USA, 13–15 June 2017. 13. Smith, G.L.; Wong, T.; Bush, K.A. Time-Sampling Errors of Earth Radiation From Satellites: Theory for Outgoing Longwave Radiation. IEEE Trans. Geosci. Remote Sens. 2015, 53, 1656–1665. [CrossRef] 14. Smith, G.L.; Wong, T. Time-Sampling Errors of Earth Radiation from Satellites: Theory for Monthly Mean Albedo. IEEE Trans. Geosci. Remote Sens. 2016, 54, 3107–3115. [CrossRef] 15. Doelling, D.R.; Loeb, N.G.; Keyes, D.F.; Nordeen, M.L.; Morstad, D.; Nguyen, C.; Wielicki, B.A.; Young, D.F.; Sun, M. Geostationary enhanced temporal interpolation for CERES flux products. J. Atmos. Ocean. Technol. 2013, 30, 1072–1090. [CrossRef] 16. Huang, S. Surface temperatures at the nearside of the Moon as a record of the radiation budget of Earth’s climate system. Adv. Space Res. 2008, 41, 1853–1860. [CrossRef] 17. Pallé, E.; Goode, P.R. The Lunar Terrestrial Observatory: Observing the Earth using photometers on the Moon’s surface. Adv. Space Res. 2009, 43, 1083–1089. [CrossRef] 18. Rogalski, A. Next decade in infrared detectors. In Proceedings of the Electro-Optical and Infrared Systems: Technology and Applications XIV, Warsaw, Poland, 9 October 2017. 19. Lohmeyer, W.Q.; Cahoy, K. Space weather radiation effects on geostationary satellite solid-state power amplifiers. Space Weather 2013, 11, 476–488. [CrossRef] 20. Durante, M.; Cucinotta, F.A. Physical basis of radiation protection in space travel. Rev. Modern Phys. 2011, 83, 1245–1281. [CrossRef] 21. Cressler, J.D.; Mantooth, H.A. Extreme Environment Electronics, 1st ed.; CRC Press: Boca Raton, FL, USA, 2012. 22. Chen, T. Digital Camera System Simulator and Applications; Stanford University: Stanford, CA, USA, 2003. 23. Loeb, N.G.; Kato, S.; Loukachine, K.; Manalo-Smith, N. Angular Distribution Models for Top-of-Atmosphere Radiative Flux Estimation from the Clouds and the Earth‘s Radiant Energy System Instrument on the Terra Satellite. Part I: Methodology. J. Atmos. Ocean. Technol. 2005, 22, 338–351. [CrossRef] 24. Loeb, N.G.; Kato, S.; Loukachine, K.; Manalo-Smith, N.; Doelling, D.R. Angular distribution models for top-of-atmosphere radiative flux estimation from the Clouds and the Earth’s Radiant Energy System instrument on the Terra satellite. Part II: Validation. J. Atmos. Ocean. Technol. 2007, 24, 564–584. [CrossRef] 25. Su, W.; Corbett, J.; Eitzen, Z.; Liang, L. Next-generation angular distribution models for top-of-atmosphere radiative flux calculation from CERES instruments: Methodology. Atmos. Meas. Tech. 2015, 7, 8817–8880. [CrossRef] 26. Giorgini, J.D. Status of the JPL horizons ephemeris system. In Proceedings of the IAU General Assembly, Honolulu, HI, USA, 3–14 August 2015. 27. CERES_SYN1deg_Ed4A Data Quality Summary. Available online: https://ceres.larc.nasa.gov/documents/ DQ_summaries/CERES_SYN1deg_Ed4A_DQS.pdf (accessed on 10 January 2018). 28. Smith, G.; Priestley, K.; Loeb, N.; Wielicki, B.; Charlock, T.; Minnis, P.; Doelling, D.; Rutan, D. Clouds and Earth Radiant Energy System (CERES), a review: Past, present and future. Adv. Space Res. 2011, 48, 254–263. [CrossRef] 29. Doelling, D.R.; Sun, M.; Nguyen, L.T.; Nordeen, M.L.; Haney, C.O.; Keyes, D.F.; Mlynczak, P.E. Advances in geostationary-derived longwave fluxes for the CERES synoptic (SYN1deg) product. J. Atmos. Ocean. Technol. 2016, 33, 503–521. [CrossRef] 30. CERES Surface Type ID. Available online: https://ceres.larc.nasa.gov/science_information.php?page= CeresSurfID# (accessed on 20 September 2017). Remote Sens. 2019, 11, 583 18 of 18

31. CERES EBAF TOA Ed4.0 Data Ordering. Available online: https://ceres-tool.larc.nasa.gov/ord-tool/jsp/ EBAF4Selection.jsp (accessed on 15 February 2018). 32. Duan, W.; Huang, S.; Nie, C. Conceptual design of a Moon-based Earth radiation observatory. Int. J. Remote Sens. 2018, 39, 5834–5849. [CrossRef] 33. CERES Algorithm Theoretical Basis Document. Available online: https://ceres.larc.nasa.gov/documents/ ATBD/pdf/r2_2/ceres-atbd2.2-s4.4.pdf (accessed on 10 November 2017).

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).