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A Real-Time Model of the Seasonal Temperature of Lunar Polar Region and Data Validation

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A Real-Time Model of the Seasonal Temperature of Lunar Polar Region and Data Validation 1892 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 58, NO. 3, MARCH 2020 A Real-Time Model of the Seasonal Temperature of Lunar Polar Region and Data Validation Niutao Liu , Student Member, IEEE,andYa-QiuJin , Life Fellow, IEEE Abstract— A small tilt in the spin axis of the moon over the properties of the regolith media have been well studied for data ecliptic plane causes seasonal incidence variation of solar illumi- validation [8], [9]. Temperature maps of lunar polar in summer nation and, especially, causes significant temperature difference and winter are generated with the Diviner data collected before at the polar region. In this article, following the position of the subsolar point, the real-time model of solar illumination the end of 2017 [10]. incidence over the moon polar region is developed. Based on Then, in 2007 and 2010, respectively, Chinese this model with solving the 1-D heat conduction equation, Chang’e-1 and Chang’e-2 (CE-1,-2) with four-channel the seasonal temperature of the lunar surface is obtained and is in microwave (MW) radiometers made the first measurement of agreement with the Diviner infrared (IR) data. Meanwhile, using MW brightness temperature (TB) of the lunar regolith. Due to the fluctuation-dissipation theorem and the Wentzel–Kramers– Brillouin (WKB) approach for lunar regolith media, the seasonal the MW penetration depth, this TB contains contribution from microwave (MW) brightness temperature (TB) is also obtained the regolith media at the depth as deep as 3–5 m [11], [12]. and validated by Chang’e-2 (CE-2) 37-GHz TB data. These data CE-2 TB at 37 GHz has been employed in the fusion study also show that the lunar surface temperature and the MW TB of the IR surface temperature [13]–[15]. even in the permanent shaded region (PSR) undergo seasonal Due to cosine variation, the temperature and TB around variation as well. It might be due to the seasonal thermal radiation on the topographic PSR coming from the sunlit crater the lunar polar are especially sensitive to the incidence angle walls caused by seasonal temperature variation. The Diviner IR of solar illumination. In other words, a small change in the data show that the highest temperature in the Hermite-A crater incident angle causes large temperature variation. The position at the north polar PSR can reach 109 K in summer. of the subsolar point can be determined by the planetary theory Index Terms— Chang’E (CE), infrared (IR) and microwave VSOP82 and the Chapront ELP-2000/82 lunar theory, which (MW) brightness temperature (TB), moon, permanent shaded includes the 18.6-year nodal precession [16]. Then, the real- region (PSR), seasonal temperature variation. time model of the incident angle of solar illumination can I. INTRODUCTION be developed. Solving the 1-D heat conduction equation with the thermal–physical profiles, the seasonal temperature of the HE lunar polar regions are always of low temperatures lunar polar region for a year period can be calculated. due to less illumination at high latitude. Especially, T In this article, the Diviner T channel (50–100 μm) is the permanent shaded region (PSR) totally without solar 8 employed. Calculation is then well validated by the Diviner illumination is in extremely low physical temperature [1]. ◦ IR data. Meanwhile, using the fluctuation-dissipation theorem A small tilted angle, 1 32 , of the spin axis of the moon over and the WKB approach for the lunar regolith media with a the ecliptic plane yields different incidence angles of the solar temperature profile [14], [15], the MW TB at 37 GHz for a illumination during a year’s seasons [2], [3]. To take account of year period can be calculated and validated by CE-2 data as the illumination condition, the topography of the lunar polar well. Especially, by checking these data in the PSR, it is found surface had been also studied [4]–[6]. Moreover, the small that there is also seasonal variation of IR temperature and MW tilted angle would also cause seasonal temperature variation TB in the PSR even without solar illumination. The seasonal of the lunar surface. variation in the MW TB was studied with CE-2 data [17]. As one of the most important lunar remote sensing This article is organized as follows. In Section II, the motion programs, the Diviner onboard the LRO measured the of the moon is briefly illustrated. Section III presents the real- mid-infrared (IR) irradiance of the lunar surface [7]. Based time model of the lunar surface temperature and the simulation on the Diviner IR data, the parameters of the thermal–physical of the seasonal variation of the temperature during a year and Manuscript received April 18, 2019; revised July 2, 2019 and the validation by the Diviner IR data. The seasonal and diurnal October 16, 2019; accepted October 24, 2019. Date of publication temperature variations, especially, in the PSR are discussed as November 19, 2019; date of current version February 26, 2020. This work was supported in part by the National Key Research and Development Program of well. In Section IV, the seasonal variation of the MW TB is China under Grant 2017YFB0502703. (Corresponding author: Ya-Qiu Jin.) simulated and validated by the CE-2 37-GHz TB data. The N. Liu is with the Key Laboratory of EMW Information, Fudan University, seasonal MW TB in the PSR is also found. Finally, Section V Shanghai 200433, China. Y.-Q. Jin is with the Key Laboratory of Wave Scattering and Remote gives the conclusion. Sensing Information, Fudan University, Shanghai 200433, China (e-mail: [email protected]). II. MOTION OF THE MOON Color versions of one or more of the figures in this article are available online at http://ieeexplore.ieee.org. In 1683, Cassini stated three empirical laws: 1) the moon Digital Object Identifier 10.1109/TGRS.2019.2950300 rotates eastward about a fixed axis with a constant angular 0196-2892 © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See https://www.ieee.org/publications/rights/index.html for more information. Authorized licensed use limited to: University of Science & Technology of China. Downloaded on April 29,2021 at 11:44:50 UTC from IEEE Xplore. Restrictions apply. LIU AND JIN: REAL-TIME MODEL OF THE SEASONAL TEMPERATURE OF LUNAR POLAR REGION AND DATA VALIDATION 1893 Fig. 2. Global and local coordinate systems. when the subsolar point is at the south hemisphere, it is defined as the summer in the southern hemisphere and the winter in the northern hemisphere, and vice versa [Fig. 1(b)]. III. REAL-TIME MODEL OF LUNAR SURFACE TEMPERATURE A. Real-Time Information Based on the position of the subsolar point, a real-time Fig. 1. Position of the subsolar point. (a) Subsolar longitude. (b) Subsolar model is presented. The real-time total solar irradiance (TSI) latitude. A positive latitude is at the northern hemisphere and a negative and illumination incidence angle are used as the inputs of latitude is at the southern hemisphere. The season depends on the subsolar latitude. the heat conduction model to obtain the real-time temperature profile of the lunar regolith. / 2 velocity and in a period equal to that for one complete TSI is given as 1371W m when the distance between the revolution about the earth; 2) the planes of the moon’s equator sun and the moon is 1 Astronomical Unit (AU) [19]. The ± . and the earth’s orbit (ecliptic) meet at a fixed angle, namely, distance between the earth and the sun is about 1 0 02AU, 1◦32; and 3) the normal to the ecliptic, the normal to the plane and the distance between the moon and the earth is about of the moon’s orbit, and the axis of rotation of the moon all 0.0025 AU. Here, the distance between the moon and the lie on the same plane [18]. Due to the tilt in the spin axis, earth is not considered. The real-time TSI is determined by the incidence angle of solar illumination varies at different the distance between the earth and the sun as θ seasons. The solar incidence angle i is very large toward TSI = 1371/d2 (1) the polar region. The solar irradiance on the unit area can se be expressed as TSI × cos θi , where TSI is the total solar where dse is the distance between the earth and the sun in the irradiance on the moon [19]. Due to the functional dependence unit of AU. At the aphelion and perihelion, TSI is 1326W/m2 of cosine, for example, given the incidence angle on a flat and 1418W/m2, respectively. ◦ ◦ region changing from 88.5 into 87 , the solar irradiance on θi is the incident angle of solar illumination on the lunar this unit lunar surface doubles. This small angular change in surface, which is determined by the position of the subsolar the polar region can cause huge temperature variation. It takes point, the region location, and its surface topography, i.e., the ascending node of the moon about 18.6 years to move surface slope denoted by the angles (ω, γ ). Suppose that the through 360◦ relative to the vernal equinox, and the direction subsolar longitude is λ and the subsolar latitude is ϕ.The of motion is westward [20]. The period of the axis precession longitude of the local region is λ0 and the latitude is ϕ0.The is 18.6 years as well, resulting in the periodic change of moon is seen as an ideal sphere with the radius of 1737.4 km.
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