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本节介绍了从月基平台观测地球向外辐射的模拟方法。主要基于地球上地物与月基平台的相对运动,首先介绍了地月之间的几何关系。模拟了大气层顶地面100 km高度地球向外辐射,地球地形可以忽略。由于地月之间距离较大,月基平台的高度所引起的与距离有关的地球辐射能量的模拟误差同样也可以忽略。
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图1给出了地月之间的几何关系示意图。可看出,从月球可一次观测整个面向月球的地球半球,并且在一个轨道周期可观测到地球全部区域。另外,地球赤道与月球平面轨道夹角为18.3°~28.3°,能够观测整个极地区域。传感器适合观测整个地球的视场是1.79°~1.95°。
从月球上对地球观测可实现空间连续和时间一致性观测,这种时间一致和空间连续性的大尺度观测和反演无疑为理解地球系统科学提供了新的材料,有助于补充以后的对地观测数据。此外,与星载平台不同的是,因月球表面空间广阔,可选择不同位置布设传感器,随之带来的对地球的能见度、视线向量和观测时间也有所不同。因此,月基平台布设位置需要进行精确计算。
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基于地月几何关系,提出了涉及一系列坐标转换的仿真方法。它的核心是将在地球上在观测视野中的地物位置与图像坐标对应起来,这个过程可分为两步:①通过国际地球参考系(International Terrestrial Reference System,ITRS)到月表站心参考系(lunar topocentric system,LT)的转换,将地球上点的位置转换到LT坐标系中,LT坐标系原点位于月基平台,z轴指向天顶方向,n轴指向月球北极方向,此外传感器视线向量和在此坐标系下的地球上的点都可用高度角和方位角表示;②一一映射过程本质上是描述传感器视线向量与地面点的几何关系,定义一个图像坐标系,原点是视线向量穿过的点,x轴平行于当地地平面,y轴是高度角变化方向。
总之,本文提出的仿真方法是利用月基平台与地面点的几何关系来模拟月基传感器获得的图像,从而对月基对地向外辐射模拟进行更详细的几何分析。
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地面上的点经历了一系列坐标转换,首先位于ITRS坐标系下,为了将其与月基平台联系起来,需采用美国喷气推进实验室(Jet Propulsion Laboratory,JPL)发展的行星星历,将地面点转化到惯性坐标系下,及地心天球参考系(Geocentric Celestial Reference System, GCRS),之后利用月球天平动欧拉角将其转化到月心天球参考系(Selenocentric Celestial Reference System, SCRS)。此时,地面点已经可以表达为在月心参考系下月球表面某一位置坐标。转换公式如下
$$ \left[ {\begin{array}{*{20}{c}} {{x_{\text{L}}}} \\ {{y_{\text{L}}}} \\ {{z_{\text{L}}}} \end{array}} \right] = {\boldsymbol{MCL}}({\boldsymbol{PN}}{{\boldsymbol{R}}_{\text{z}}}{\boldsymbol{WB}}\left[ {\begin{array}{*{20}{c}} {{x_{\text{T}}}} \\ {{y_{\text{T}}}} \\ {{z_{\text{T}}}} \end{array}} \right]{\text{ + }}\left[ {\begin{array}{*{20}{c}} {{x_{\text{M}}}} \\ {{y_{\text{M}}}} \\ {{z_{\text{M}}}} \end{array}} \right]) $$ (1) 其中:(xT,yT,zT)T是地面点在ITRS坐标系下的表达;(xL,yL,zL)T是其在LT坐标系下的表达;(xM,yM,zM)T是月球在GCRS下的表达;M为月心坐标系到地平坐标系的旋转矩阵;C和L是月球姿态矩阵;P,N,Rz,W,B是地球方向的变换矩阵。因此,地面点在月心坐标系下可以表示为另一种形式
$$ \left\{ \begin{gathered} {\lambda _{\text{L}}} = \arctan (\frac{{{y_{\text{L}}}}}{{{x_{\text{L}}}}}) \hfill \\ {\varphi _{\text{L}}}{\text{ = }} = \frac{{{z_{\text{L}}}}}{{\sqrt {x_{_{\text{L}}}^2 + y_{_{\text{L}}}^2 + z_{_{\text{L}}}^2} }} \hfill \\ \end{gathered} \right. $$ (2) -
为实现地面点到图像点的一一映射,需建立图像坐标系。如图2所示,图像坐标系是场景映射到传感器镜头上的部分,假设地球上的点到传感器观测视场这个过程经历了日晷投影,投影中心就是视线向量的方向,将视线向量l用高度角和方位角表示成(λc,φc),从图2中可以看出,点的位置向量记为p,其坐标为(λL,φL)。
当映射到图像平面上时,图像坐标系上的位置取决于月基传感器镜头和投影中心之间的距离以及视线向量于地面上的点位置向量之间的夹角。因此,月心坐标系下的坐标到图像坐标系下的转换可以表示为
$$ \left\{ \begin{gathered} x = \frac{{\cos ({\varphi _{\text{L}}})\sin ({\lambda _{\text{L}}}-{\lambda _{\text{C}}})}}{{\sin ({\varphi _{\text{C}}})\sin ({\varphi _{\text{L}}}) + \cos ({\varphi _{\text{L}}})\cos ({\varphi _{\text{C}}})\cos ({\lambda _{\text{L}}}-{\lambda _{\text{C}}})}} \hfill \\ y = \frac{{\sin ({\varphi _{\text{C}}})\sin ({\varphi _{\text{L}}}) - \cos ({\varphi _{\text{L}}})\cos ({\varphi _{\text{C}}})\cos ({\lambda _{\text{L}}}-{\lambda _{\text{C}}})}}{{\sin ({\varphi _{\text{C}}})\sin ({\varphi _{\text{L}}}) + \cos ({\varphi _{\text{L}}})\cos ({\varphi _{\text{C}}})\cos ({\lambda _{\text{L}}}-{\lambda _{\text{C}}})}} \hfill \\ \end{gathered} \right. $$ (3) 其中,(x, y)代表图像坐标系中的坐标。
Geometric Simulation of Earth’s Outgoing Radiation Viewed from a Moon-Based Platform
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摘要:月基平台以其整体性、多角度、长周期等特点,可望实现对地球整体辐射收支进行精确估算。为了评估月基平台对地球辐射能量的观测能力,建立了基于地月几何关系的一一映射算法,使用戈达德地球观测系统模型第五版(Goddard Earth Observation System model version 5,GEOS-5)数据作为模型输入,用以模拟月基视场地球向外辐射能量,从而形成对月基观测的地球辐射能量规律性认识。结果表明:月基传感器可以观测包括极区在内约178°跨度的经纬度区域;月球变轨道倾角将为地球高纬度地区提供更好的观测条件,极区观测高度角可达到60°。该模拟方法可以为观测地球向外辐射提供有效支持,为后续研究打下坚实的基础。Abstract:Due to the characteristics of integrity, multi-angle and long period, a Moon-based platform is expected to accurately estimate Earth outgoing radiation. To evaluate this platform’s capabilities, this paper established a one-to-one mapping algorithm based on the geometric relationship and used the Goddard Earth Observing System model version 5 (GEOS-5) data as model input to simulate Earth’s outgoing radiation viewed from a Moon-based platform, so as to learn about the regularity of Earth outgoing radiation viewed from the Moon-based platform. Results show that a Moon-based platform can cover about 178° both in latitudinal and longitudinal direction in one image, including the polar regions. The changing inclination of the orbit of the Moon gives a better observation condition for high latitude regions, and the viewing zenith angle in polar regions can reach to 60°. These results indicate the simulation method can effectively support the observation of Earth’s outgoing radiation observation and lay the foundation for future research.Highlights
● A simulation method for Earth outgoing radiation viewed from a Moon-based platform is proposed based on one-to-one mapping method considering observation geometry of the Earth and the Moon. ● Experiments of Earth outgoing longwave and shortwave radiation viewed from a Moon-based sensor in one year are carried out and the regularity is found out according to the characteristics of the lunar orbit. ● The characteristics of spatial coverage and angular distribution are analyzed. ● The simulation method can effectively support the observation of Earth’s outgoing radiation and lay the foundation for future research. -
图 6传感器位于月球南极观测地球[24]
Fig. 6Observation duration of North Pole and South Pole of the Earth when the Moon-based sensor is located at the South Pole of the Moon[24]
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