月球表面物理温度分布模型及数值计算
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摘要
探测月壤厚度是探索月球的重要目标之一,反演月壤厚度需要建立准确的微波辐射亮度温度模型。月球表面物理温度分布是模型的关键参数。月球表面物理温度是随月球表面经纬度、深度和时间变化的函数。
本文从热传导理论出发,结合之前学者提出的多种计算月表温度的物理模型,提出改进的求解月表温度的热传导模型。随后精确地推导和计算模型中的太阳辐照度、地球辐射和月球内部热流等各参数,详细地阐述了求解热传导方程数值计算的方法和过程,分析了热导率、热容、月壤密度等各参数对模型计算温度所产生的误差。通过与Apollo着陆地区实测结果及文献中结果的比较,表明此模型的计算结果能够较好地反映全月表温度分布情况。
针对月表地形起伏会产生互相遮挡而影响太阳辐射,使月球表面温度发生剧烈变化的情况,本文提出两种利用月表地形起伏修正物理温度的模型。最后结合实测的激光高度计数据进行了初步的温度计算。结果表明:月表地形起伏会对月表物理温度造成不可忽略的影响。
Detecting the lunar regolith depth is one of the most significant aims of lunar exploration. Exact lunar surface microwave transfer model is fundamental in retrieving the lunar regolith depth. The critical factor in this model is the distribution of lunar surface physical temperature. The lunar surface temperature is a function of lunar latitude, longitude, depth and time.
Firstly, the basic theory of thermal conduction is introduced. Considering the former researchers’kinds of physical model of lunar surface temperature, this paper proposed an improved transient model to simulate the temperature. The parameters such as solar irradiance, earthshine and heat flow in this model are accurately deduced and calculated, meanwhile, the approaches and processes in numerical calculation of lunar surface temperature are elaborated. The errors caused by thermal conductivity, density and heat capacity in calculating temperature are also discussed. Compared with Apollo landing sites’measurement and previous studies, it proves that this model could accurately calculate the lunar surface temperature.
Moreover, shading caused by the lunar surface topography would induce a obvious change of temperature, so this paper suggests two kinds of approaches to revise the temperature. Finally, considering the measured laser altimeter data, raw calculation is accomplished. The results show that topography would cause a significant change in calculating the lunar surface temperature.
本文从热传导理论出发,结合之前学者提出的多种计算月表温度的物理模型,提出改进的求解月表温度的热传导模型。随后精确地推导和计算模型中的太阳辐照度、地球辐射和月球内部热流等各参数,详细地阐述了求解热传导方程数值计算的方法和过程,分析了热导率、热容、月壤密度等各参数对模型计算温度所产生的误差。通过与Apollo着陆地区实测结果及文献中结果的比较,表明此模型的计算结果能够较好地反映全月表温度分布情况。
针对月表地形起伏会产生互相遮挡而影响太阳辐射,使月球表面温度发生剧烈变化的情况,本文提出两种利用月表地形起伏修正物理温度的模型。最后结合实测的激光高度计数据进行了初步的温度计算。结果表明:月表地形起伏会对月表物理温度造成不可忽略的影响。
Detecting the lunar regolith depth is one of the most significant aims of lunar exploration. Exact lunar surface microwave transfer model is fundamental in retrieving the lunar regolith depth. The critical factor in this model is the distribution of lunar surface physical temperature. The lunar surface temperature is a function of lunar latitude, longitude, depth and time.
Firstly, the basic theory of thermal conduction is introduced. Considering the former researchers’kinds of physical model of lunar surface temperature, this paper proposed an improved transient model to simulate the temperature. The parameters such as solar irradiance, earthshine and heat flow in this model are accurately deduced and calculated, meanwhile, the approaches and processes in numerical calculation of lunar surface temperature are elaborated. The errors caused by thermal conductivity, density and heat capacity in calculating temperature are also discussed. Compared with Apollo landing sites’measurement and previous studies, it proves that this model could accurately calculate the lunar surface temperature.
Moreover, shading caused by the lunar surface topography would induce a obvious change of temperature, so this paper suggests two kinds of approaches to revise the temperature. Finally, considering the measured laser altimeter data, raw calculation is accomplished. The results show that topography would cause a significant change in calculating the lunar surface temperature.
引文
[1]欧阳自远.月球科学概论.北京:中国宇航出版社, 2005.
[2]李雄耀,王世杰,陈丰等.月壤厚度的研究方法与进展.矿物学报, 2007.3, 27(1): 64-68.
[3]李雄耀,王世杰,程安云.月球表面温度物理模型研究现状.地球科学进展, 2007, 22(5): 480-485.
[4]王振占,李芸,姜景山等.用“嫦娥一号”卫星微波探测仪亮温反演月壤厚度和3He资源量评估的方法及初步结果分析.中国科学D辑:地球科学, 2009, 39(8): 1069-1084.
[5]孟治国.月壤参数的辐射传输模拟与查找表反演技术研究[博士学位论文].吉林大学, 2008.
[6] Fa Wenzhe, Jin Yaqiu. Inversion of lunar regolith layer thickness using microwae radiance simulation of three layer model and clementine UV-VIS data. Chin. J. Space Sci., 2007, 27(1): 55-65.
[7]蓝爱兰.月球表层媒质的被动遥感机理及厚度反演研究[硕士学位论文].中国科学院研究生院, 2004.
[8] Wenzhe Fa, and Ya-Qiu Jin. Simulation of brightness temperature from lunar surface and inversion of regolith-layer thickness. Journal of Geography Research, 2007, 112: E05003.
[9] Zhenzhan Wang, Yun Li, Jingshan Jiang, et al. Microwave transfer models and brightness temperature simulations of MWS for remote sensing lunar surface on CE-1 satellite. ICMMT Proceedings. Nanjing, 2008.
[10] Ulaby F T, Moore R K, Fung A K. Microwave Remote Sensing, Active and Passive, Vol.I. Addison-Wesley Publishing Company, 1981.
[11] Pettit E, Nicholson S.B. Lunar radiation and temperatures. Astrophysical Journal, 1930, 71(1022): 135.
[12] Sinton W M, Physics and Astronomy of the Moon. New York Academic Press. 1962.
[13] Murray B C, Wildey M J. Surface temperature variations during the lunar nighttime. The Astrophysical Journal, 1964, 139(7342): 750.
[14] Saari J M. The surface temperture of the antisolar point of the Moon. ICARUS,1964, 3(1612): 163.
[15] Low F J. Lunar Nighttime Temperature Measured at 20 Microns. Astrophysical Journal, 1965, 142(8062): 808.
[16] Ingrao H C, Young A T, Linsky J L. The Nature of the Lunar Surface. Baltimore the Johns Hopkins Press. 1966.
[17] Stimp son L D, Lucas J W. Revised Lunar Surface Thermal Characteristics Obtained from the Surveyor V Spacecraft. IAA Paper: San Francisco, California. 1969.
[18] Pugh M J, Bastin J A. Infrared observations of the Moon and their interpretation. Earth, Moon and Planets, 1972, 5(162): 30.
[19] Lawson S L, Jakosky B M. Brightness Temperatures of the lunar Surface. in The Clementin Longwave Infrared Global Data Set,30th Annual Lunar and Planetary Science Conference. 1999.
[20] Lawson S L. Brightness temperatures of the lunar surface, in Calibration and analysis of Clementine longwave infrared camera images. Boulder University of Colorado. 2000.
[21] Lawson S L, Jakosky B M. Lunar surface thermophysical properties derived from Clementine LW IR and UVV IS images. Jounal of Geophysical Research, 2001, 106(27): 932.
[22] Lawson S L, Jakosky B M, Park H S. Brightness temperature of the lunar surface:Calibration and global analysis of the Clementine longwave infrared camera data. Jounal of Geophysical Research, 2000, 105(427): 290.
[23] Hagermann A, Tanaka S, Yoshida S. Regolith thermal property inversion in the Lunar heatflow experiment. Bulletin of the American Astronomical Society, 2001, 33(1): 147.
[24] Little R C, Feldman W C, Maurice S. Latitude Variation of the Subsurface Lunar Temperature:Lunar Prospector Thermal Neutrons. in American Geophysical Union Spring Meeting. 2001.
[25] G. H. Heiken, D. T. Vaniman, B. M. French. Lunar sourcebook: a user's guide to the moon. Cambridge University Press. 1991.
[26]詹宗勉.工程热力学和传热学.大连:大连海事大学出版社. 1995.
[27] John H. Lienhard IV, John H. Lienhard V, A Heat Transfer Textbook. Massachusetts: Philogiston Press. 2005.
[28] A. F. Wesselink. Heat conductivity and nature of the lunar surface material.Bulletin of the Astronomical Institutes of the Netherlands, 1948, X(390): 351-363.
[29] J. C. Jarger. The surface temperature of the moon. Australian Journal of Physics, 1953, 6: 10-21.
[30] Ted A. Calvert, George C. Themal And Dielectric Properties Of a Homogeneous Moon Based on Microwave and Infrared Temperature Observations. National Aeronautics and Space Asministration: Washington D.C. 1969.
[31] William P. Jones, James R. Watkins, and Teda Calvert. Temperatures and thermophysical properties of the lunar outermost layer. The moon, 1975, 13: 475-494.
[32] David L. Mitchell, and Imke de Pater. Microwave Imaging of Mercury's Thermal Emission at Wavelengths from 0.3 to 20.5 cm. ICARUS, 1994, 110: 2-32.
[33] Guuseppe D. Racca. Moon surface thermal characteristics for moon orbiting spacecraft thermal analysis. Planet. Space Sci., 1995, 43(6): 835-842.
[34] Vasavada A.R., Paige D.A., and Wood S.E. Near-Surface Temperatures on Mercury and the Moon and the Stability of Polar Ice Deposits. ICARUS, 1999, 141: 179-193.
[35] A.Snyder Hale, and B. Hapke. A Time-Dependent Model of Radiative and Conductive Thermal Energy Transport in Planetary Regoliths with Applications to the Moon and Mercury. ICARUS, 2002, 156: 318-334.
[36]李雄耀,王世杰,程安云.月表有效太阳辐照度实时模型.地球物理学报, 2008, 51(1): 25-30.
[37]郑永春.模拟月壤研制与月壤的微波辐射特性研究[博士学位论文].中国科学院地球化学研究所, 2005.
[38] Carrer W D, Olhoeft G R, Mendell W. Physical properties of the lunar surface. Lunar Source Book. New York: Cambridge University Press. 1991.
[39] Horai K, Fujii N. Thermophysical Properties of Lunar Material Returned by Apollo Missions, Conference on Lunar Geophysics. Tech-nical Report. 1969.
[40] Michael J.Ledlow, Jack O. Burns, Galen R.Gisler, Jun-Hui Zhao. Subsurface Emissions from Mercury: vla Radio Observations at 2 and 6 Centimeters, The Astrophysical Journal, 1992(384): 640-655.
[41] Xiaowen Li, Jindi Wang, Baoxin Hu, and Alan H. Strahler. On utilization of apriori knowledge in inversion of remote sensing models. Science in China Series D: Earth Sciences, 1998, 41(6): 580-585.
[42]王世杰,李雄耀,唐红,李阳.月面环境与月壤特性研究的主要问题探讨.地球化学, 2010, 39(1): 73-81.
[43] Marcus G. Langseth, Stenphen J. Keihm, and Kenneth Peters. Revised lunar heat-flow values. Proc. Lunar Sci. Conf. 7th. 1976.
[44]徐建良,汤炳书.一维热传导方程的数值解.淮阴师范学院学报, 2004, 3: 210-214.
[45]王振占,李芸,张晓辉等.“嫦娥一号”卫星微波探测仪数据处理模型和月表微波亮温反演方法.中国科学D辑:地球科学, 2009, 39(8): 1029-1044.
[2]李雄耀,王世杰,陈丰等.月壤厚度的研究方法与进展.矿物学报, 2007.3, 27(1): 64-68.
[3]李雄耀,王世杰,程安云.月球表面温度物理模型研究现状.地球科学进展, 2007, 22(5): 480-485.
[4]王振占,李芸,姜景山等.用“嫦娥一号”卫星微波探测仪亮温反演月壤厚度和3He资源量评估的方法及初步结果分析.中国科学D辑:地球科学, 2009, 39(8): 1069-1084.
[5]孟治国.月壤参数的辐射传输模拟与查找表反演技术研究[博士学位论文].吉林大学, 2008.
[6] Fa Wenzhe, Jin Yaqiu. Inversion of lunar regolith layer thickness using microwae radiance simulation of three layer model and clementine UV-VIS data. Chin. J. Space Sci., 2007, 27(1): 55-65.
[7]蓝爱兰.月球表层媒质的被动遥感机理及厚度反演研究[硕士学位论文].中国科学院研究生院, 2004.
[8] Wenzhe Fa, and Ya-Qiu Jin. Simulation of brightness temperature from lunar surface and inversion of regolith-layer thickness. Journal of Geography Research, 2007, 112: E05003.
[9] Zhenzhan Wang, Yun Li, Jingshan Jiang, et al. Microwave transfer models and brightness temperature simulations of MWS for remote sensing lunar surface on CE-1 satellite. ICMMT Proceedings. Nanjing, 2008.
[10] Ulaby F T, Moore R K, Fung A K. Microwave Remote Sensing, Active and Passive, Vol.I. Addison-Wesley Publishing Company, 1981.
[11] Pettit E, Nicholson S.B. Lunar radiation and temperatures. Astrophysical Journal, 1930, 71(1022): 135.
[12] Sinton W M, Physics and Astronomy of the Moon. New York Academic Press. 1962.
[13] Murray B C, Wildey M J. Surface temperature variations during the lunar nighttime. The Astrophysical Journal, 1964, 139(7342): 750.
[14] Saari J M. The surface temperture of the antisolar point of the Moon. ICARUS,1964, 3(1612): 163.
[15] Low F J. Lunar Nighttime Temperature Measured at 20 Microns. Astrophysical Journal, 1965, 142(8062): 808.
[16] Ingrao H C, Young A T, Linsky J L. The Nature of the Lunar Surface. Baltimore the Johns Hopkins Press. 1966.
[17] Stimp son L D, Lucas J W. Revised Lunar Surface Thermal Characteristics Obtained from the Surveyor V Spacecraft. IAA Paper: San Francisco, California. 1969.
[18] Pugh M J, Bastin J A. Infrared observations of the Moon and their interpretation. Earth, Moon and Planets, 1972, 5(162): 30.
[19] Lawson S L, Jakosky B M. Brightness Temperatures of the lunar Surface. in The Clementin Longwave Infrared Global Data Set,30th Annual Lunar and Planetary Science Conference. 1999.
[20] Lawson S L. Brightness temperatures of the lunar surface, in Calibration and analysis of Clementine longwave infrared camera images. Boulder University of Colorado. 2000.
[21] Lawson S L, Jakosky B M. Lunar surface thermophysical properties derived from Clementine LW IR and UVV IS images. Jounal of Geophysical Research, 2001, 106(27): 932.
[22] Lawson S L, Jakosky B M, Park H S. Brightness temperature of the lunar surface:Calibration and global analysis of the Clementine longwave infrared camera data. Jounal of Geophysical Research, 2000, 105(427): 290.
[23] Hagermann A, Tanaka S, Yoshida S. Regolith thermal property inversion in the Lunar heatflow experiment. Bulletin of the American Astronomical Society, 2001, 33(1): 147.
[24] Little R C, Feldman W C, Maurice S. Latitude Variation of the Subsurface Lunar Temperature:Lunar Prospector Thermal Neutrons. in American Geophysical Union Spring Meeting. 2001.
[25] G. H. Heiken, D. T. Vaniman, B. M. French. Lunar sourcebook: a user's guide to the moon. Cambridge University Press. 1991.
[26]詹宗勉.工程热力学和传热学.大连:大连海事大学出版社. 1995.
[27] John H. Lienhard IV, John H. Lienhard V, A Heat Transfer Textbook. Massachusetts: Philogiston Press. 2005.
[28] A. F. Wesselink. Heat conductivity and nature of the lunar surface material.Bulletin of the Astronomical Institutes of the Netherlands, 1948, X(390): 351-363.
[29] J. C. Jarger. The surface temperature of the moon. Australian Journal of Physics, 1953, 6: 10-21.
[30] Ted A. Calvert, George C. Themal And Dielectric Properties Of a Homogeneous Moon Based on Microwave and Infrared Temperature Observations. National Aeronautics and Space Asministration: Washington D.C. 1969.
[31] William P. Jones, James R. Watkins, and Teda Calvert. Temperatures and thermophysical properties of the lunar outermost layer. The moon, 1975, 13: 475-494.
[32] David L. Mitchell, and Imke de Pater. Microwave Imaging of Mercury's Thermal Emission at Wavelengths from 0.3 to 20.5 cm. ICARUS, 1994, 110: 2-32.
[33] Guuseppe D. Racca. Moon surface thermal characteristics for moon orbiting spacecraft thermal analysis. Planet. Space Sci., 1995, 43(6): 835-842.
[34] Vasavada A.R., Paige D.A., and Wood S.E. Near-Surface Temperatures on Mercury and the Moon and the Stability of Polar Ice Deposits. ICARUS, 1999, 141: 179-193.
[35] A.Snyder Hale, and B. Hapke. A Time-Dependent Model of Radiative and Conductive Thermal Energy Transport in Planetary Regoliths with Applications to the Moon and Mercury. ICARUS, 2002, 156: 318-334.
[36]李雄耀,王世杰,程安云.月表有效太阳辐照度实时模型.地球物理学报, 2008, 51(1): 25-30.
[37]郑永春.模拟月壤研制与月壤的微波辐射特性研究[博士学位论文].中国科学院地球化学研究所, 2005.
[38] Carrer W D, Olhoeft G R, Mendell W. Physical properties of the lunar surface. Lunar Source Book. New York: Cambridge University Press. 1991.
[39] Horai K, Fujii N. Thermophysical Properties of Lunar Material Returned by Apollo Missions, Conference on Lunar Geophysics. Tech-nical Report. 1969.
[40] Michael J.Ledlow, Jack O. Burns, Galen R.Gisler, Jun-Hui Zhao. Subsurface Emissions from Mercury: vla Radio Observations at 2 and 6 Centimeters, The Astrophysical Journal, 1992(384): 640-655.
[41] Xiaowen Li, Jindi Wang, Baoxin Hu, and Alan H. Strahler. On utilization of apriori knowledge in inversion of remote sensing models. Science in China Series D: Earth Sciences, 1998, 41(6): 580-585.
[42]王世杰,李雄耀,唐红,李阳.月面环境与月壤特性研究的主要问题探讨.地球化学, 2010, 39(1): 73-81.
[43] Marcus G. Langseth, Stenphen J. Keihm, and Kenneth Peters. Revised lunar heat-flow values. Proc. Lunar Sci. Conf. 7th. 1976.
[44]徐建良,汤炳书.一维热传导方程的数值解.淮阴师范学院学报, 2004, 3: 210-214.
[45]王振占,李芸,张晓辉等.“嫦娥一号”卫星微波探测仪数据处理模型和月表微波亮温反演方法.中国科学D辑:地球科学, 2009, 39(8): 1029-1044.