利用POLDER多角度偏振数据反演陆上气溶胶光学厚度的群组残差最优方法

利用POLDER多角度偏振数据反演陆上气溶胶光学厚度的群组残差最优方法 Application of the optimal grouped residual method in retrieving the optical depth of aerosol over land with POLDER multi-angular polarized data 1 2 first-author 高鑫，研究方向为基于偏振多角度观测的气溶胶/云特性反演。E-mail：564994353@qq.com 高鑫，研究方向为基于偏振多角度观测的气溶胶/云特性反演。E-mail：564994353@qq.com 564994353@qq.com 3 corresp 胡秀清，研究方向为卫星光学遥感器的辐射定标，气溶胶、沙尘暴和大气可降水等大气参数的卫星反演算法。E-mail：huxq@cma.gov.cn 胡秀清，研究方向为卫星光学遥感器的辐射定标，气溶胶、沙尘暴和大气可降水等大气参数的卫星反演算法。E-mail：huxq@cma.gov.cn huxq@cma.gov.cn 2 3 中国科学院长春光学精密机械与物理研究所, 长春 130033 中国科学院长春光学精密机械与物理研究所, 长春 130033 Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China 中国科学院大学, 北京 100049 中国科学院大学, 北京 100049 University of Chinese Academy of Sciences, Beijing 100049, China University of Chinese Academy of Sciences, Beijing 100049, China 中国气象局 国家卫星气象中心, 北京 100081 中国气象局 国家卫星气象中心, 北京 100081 National Satellite Meteorological Centre, China Meteorological Administration, Beijing 100081, China National Satellite Meteorological Centre, China Meteorological Administration, Beijing 100081, China 陆上气溶胶光学厚度（AOD）反演作为气候、环境领域的一大研究方向，偏振多角度遥感在这个方向上有其特有的优势。本文使用法国POLDER （Polarization and Directionality of Earth’s Reflectance） 1级偏振多角度资料，提出了一种针对气溶胶反演的群组残差最优方法，反演了气溶胶AOD。首先，模拟计算了大气、地表和气溶胶的偏振多角度反射率；然后，通过辐射传输公式，推算卫星观测的偏振表观反射率的若干组模拟值；最后，使用群组残差最优方法，计算获得气溶胶AOD。通过和MODIS（Moderate-resolution Imaging Spectroradiometer）气溶胶数据产品（MYD04）的精确地理匹配和定量分析，验证了此方法的反演精度，结果表明：本文得到的AOD与MYD04建立的回归分析，其 R 2 可达到0.68以上，斜率与1接近，即此方法获得的反演产品与MYD04具有较好的一致性；与AERONET（Aerosol Robotic Network）的AOD数据也进行了坎普尔站、北京站上的统计与分析，AOD的变化趋势上也存在较好的一致性。本文方法能够应用于除POLDER以外的偏振多角度卫星数据，获得较为可靠的陆上气溶胶AOD产品。 Aerosol is one of the important components of the earth’s atmospheric environment, which has a profound impact on atmospheric transport, climate simulation, environmental research, remote sensing application, pollution monitoring and many other fields. The retrieval of the Aerosol Optical Depth (AOD) over land has always been an important research topic in the study of environment and climate. As an emerging remote sensing method in recent years, multi-angular polarized remote sensing has obvious advantages over traditional optical remote sensing in the problem of land-atmosphere decoupling, which has been rapidly applied and developed in the field of cloud and aerosol. In this study, an Optimal Grouped Residual Method for the aerosol was proposed, which uses the multi-angular polarized data of POLDER Level 1 datasets (Polarization and Directionality of Earth’s Reflectance, France). According to Mie scattering theory, the polarization scattering phase function of atmospheric aerosol were calculated. Then, the polarization reflectance contribution of aerosols was calculated based on the polarization scattering phase function of aerosols, and the polarization reflectance contribution of atmospheric gas molecules and the surface were calculated using empirical formula. Finally, the multi-angular apparent polarization reflectance of the top of the atmosphere under the assumption of single scattering was simulated according to the atmospheric radiative transfer theory, and AOD was retrieved. The retrieval results and accuracy were verified by precisely geographic matching and quantitatively comparing with MODIS (Moderate-resolution Imaging Spectroradiometer) aerosol product (MYD04). The results show that the R-square values of the regression analysis between AOD in this study and MYD04 can reach more than 0.68, and the slopes are close to 1, which reveal a good consistency. The AOD results were also compared with AERONET (Aerosol Robotic Network) in two sites, Beijing and Kanpur, revealing that the variation trends of AOD have good consistency. Furthermore, in order to verify the reliability of the method in this study from a broader spatial-temporal dimension, the AOD results were synthesized on a long time series of multi-day. Similarly, the multi-day synthetic AOD results obtained in this study also showed good consistency with the MODIS results. This method can be applied to multi-angular polarized satellite data (not only POLDER) to generate reliable optical depth products for the aerosol over land. 遥感 POLDER 多角度偏振遥感 陆上气溶胶光学厚度 群组残差最优方法 remote sensing POLDER multi-angular polarized remote sensing the optical depth of aerosol over land optimal grouped residual method 1　引言 1 气溶胶作为大气的一大组成部分，其对气候、大气环境、大气辐射收支、全球污染等方面都存在深远的影响。气溶胶遥感方法目前有卫星遥感和地基遥感两大类。地基遥感优势是反演精度高，但受到观测站点的限制，很难实现全球性、大规模的测量计算，目前应用最为广泛的是全球气溶胶自动化观测网络——AERONET（ Holben等，1998 Holben等，1998 ）。卫星遥感虽然起步较晚，从20世纪70年代开始发展，但目前也已有大量高精度的激光雷达卫星、气象卫星在进行全球性、大规模的气溶胶观测。其中，应用最广泛的是MODIS，众多学者利用其观测数据，提出了很多气溶胶AOD的反演算法，以暗目标方法（ Kaufman等，1997 Kaufman等，1997 ； Levy等，2007 Levy等，2007 ）和深蓝算法（ Hsu等，2004 Hsu等，2004 ）最为著名，并且已经积攒了从2002-07-04至今的气溶胶业务产品（MOD04/MYD04），得到了业界的普遍认可。此两种方法主要是根据大气辐射传输模型（如6SV、RT3等）构建查找表，再通过插值法来反演气溶胶光学厚度。 偏振、多角度遥感作为新兴遥感手段，与上述传统光学遥感相比，更适于在云和气溶胶研究领域发挥其独特作用（ Dubovik等，2019 Dubovik等，2019 ）。卫星观测的表观反射率主要由分子大气、地表和气溶胶3部分组成。其中，气溶胶和地表的反射率贡献存在耦合关系，在传统光学遥感中难以解耦。而在偏振多角度遥感中，研究证明，偏振反射率对地表不敏感而对气溶胶更加敏感，因此便于地气解耦（ Deuzé等，2001 Deuzé等，2001 ），从而在气溶胶反演方面更具优势。 在偏振多角度卫星载荷方面，法国从1996年—2004年先后发射了3颗偏振多角度载荷POLDER（Polarization and Directionality of Earth’s Reflectance）（ Deuzé等，2001 Deuzé等，2001 ），积累了1996年—2013年长达17 a的大量观测数据。由中国科学院上海技术与物理研究所研制的偏振多角度成像仪器（MAPI）于2016-09随天宫二号空间实验室发射升空，一直执行对地观测任务（ 殷德奎，2019 殷德奎，2019 ）；另外，高分五号卫星于2018-05发射升空，同样也具备了偏振多角度观测能力（ Li等，2018 Li等，2018 ）。 在算法方面， Leroy等（1997） Leroy等（1997） 基于POLDER1级1级数据，描述了全流程的“地表及陆上大气”运算算法，进行了云检测、陆上气溶胶AOD及气溶胶类型、地表双向反射率等多物理量的反演计算，而这也是POLDER的部分2级和3级产品的计算依据。 Deuzé等（2001） Deuzé等（2001） 给出了使用POLDER偏振观测数据来反演陆上气溶胶特性的方法，并与地基AERONET的反演产品作了对比，存在良好的一致性。 Dubovik等（2011） Dubovik等（2011） 利用POLDER偏振多角度数据进行了多变量拟合统计，实现了多个气溶胶重要特征参数的综合反演。 王舒鹏（2012） 王舒鹏（2012） 详细描述了基于偏振多角度卫星信号的粗细混合型城市气溶胶反演方法； 陈澄等（2015） 陈澄等（2015） 基于动态气溶胶模型改进了POLDER气溶胶光学厚度反演算法；都针对不同问题提供了更深入的反演策略。 目前的偏振多角度气溶胶反演算法大多都沿用了传统的气溶胶反演策略，即使用辐射传输公式建立表观偏振反射率查找表、查表插值法计算气溶胶AOD。 Zhang等（2018） Zhang等（2018） 提出了分组残差排序方法，着重反演和研究了中国东部地区的细模态气溶胶AOD，算法中将气溶胶模式、观测几何角度和波段相关参数输入6SV辐射传输模型来建立单角度查找表，再查表获得光学厚度结果； Wang等（2018） Wang等（2018） 提出了基于自适应方法实现地气解耦合的气溶胶反演算法，能够精确拟合地表偏振反射率，算法中同样是使用RT3辐射传输模型建立的单角度查找表、查表得到最优AOD取值的方法。然而对于不同的观测角度，先建表、再查表插值的过程是相互独立的，可能导致单角度下获得的气溶胶光学厚度值并不相同，因此还需要制定相应的取值策略来获得反演结果，这在一定程度上就弱化了多角度数据之间的物理关联性。 针对多角度反射率数据的物理关联性被弱化问题，本文基于粒子散射相函数理论和矢量辐射传输理论，提出一种将多角度表观偏振反射率设为群组，对整个群组进行模拟计算，求取多个群组残差，取其中最优结果的新方法——群组残差最优方法。此方法更加强调多角度数据的关联性，为有效、可靠地反演陆上气溶胶AOD提供了一个新的思路，并希望可以应用于中国天宫二号偏振多角度成像仪、高分五号偏振多角度相机等载荷的观测数据，实现国产偏振多角度卫星观测气溶胶AOD产品的生成和应用服务。 2　数据与方法 1 2.1　数据 2 （1）POLDER 1级数据。法国国家空间研究中心（CNES）研制了3颗POLDER载荷，分别于1996-11—1997-06、2003-04—2003-10、2004-12—2013-12执行对地观测任务。POLDER载荷是多角度、多光谱和偏振成像光谱仪，共覆盖9个光谱测量波段（ 表1 表1 ），其中490 nm，670 nm，865 nm是偏振通道，各设置3个偏振子通道来推算该通道的Stokes参量。同时也记录了云标识、水陆标识、观测几何角（太阳天顶角 <math id="M1"><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472737&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472732&type= 2.70933342 3.80999994 、卫星天顶角 <math id="M2"><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472747&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472741&type= 2.79399991 3.80999994 、相对方位角 <math id="M3"><mi>φ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472757&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472752&type= 2.20133328 3.30200005 ）等多样的观测信息。 波段/nm 中心波长/nm 波段宽度/nm 是否偏振 443 443.9 13.5 否 490 491.5 16.5 是 565 563.9 15.5 否 670 669.9 15.0 是 763 762.8 11.0 否 765 762.5 38.0 否 865 863.4 33.5 是 910 906.9 21.0 否 1020 1019.4 17.0 否 （2）MODIS气溶胶产品。基于Aqua/Terra载荷的MODIS数据得到的气溶胶产品，其产品标识分别是MYD04和MOD04，目前有3 km和10 km两种分辨率，分别标记为_3K和_L2。数据主要存储了全球海洋以及部分大陆的大气气溶胶光学特性（AOD和尺度分布等）、质量浓度、反射和透射通量以及一些辅助参数。本文章中使用的是_3K产品。数据可以在 https：//modis.gsfc.nasa.gov https://modis.gsfc.nasa.gov ［2019-08-08］获得。 2.2　群组残差最优算法原理及描述 2 POLDER 1级1级数据中的Stokes参量，即 <math id="M4"><mi>I</mi><mo>,</mo><mi>Q</mi><mo>,</mo><mi>U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472778&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472774&type= 9.90600014 3.47133350 参量均为归一化辐亮度单位，其与辐亮度、归一化反射率遵从以下关系： <math display="block" id="M5"><mi>I</mi><mo>=</mo><mfrac><mrow><mi mathvariant="normal">π</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>I</mi></mrow></msub></mrow><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>λ</mi></mrow></msub></mrow></mfrac><mo>,</mo><mtext>  </mtext><mi>Q</mi><mo>=</mo><mfrac><mrow><mi mathvariant="normal">π</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>Q</mi></mrow></msub></mrow><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>λ</mi></mrow></msub></mrow></mfrac><mo>,</mo><mtext>  </mtext><mi>U</mi><mo>=</mo><mfrac><mrow><mi mathvariant="normal">π</mi><msub><mrow><mi>L</mi></mrow><mrow><mi>U</mi></mrow></msub></mrow><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>λ</mi></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472789&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472787&type= 44.70399857 8.72066593 <math display="block" id="M6"><mi>R</mi><mo>=</mo><mfrac><mrow><mi>I</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></mfrac><mo>,</mo><mtext>  </mtext><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow></msub><mo>=</mo><mfrac><mrow><mroot><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>U</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472800&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472797&type= 41.74066544 10.32933331 式中， <math id="M7"><msub><mrow><mi>L</mi></mrow><mrow><mi>I</mi></mrow></msub><mo>,</mo><mtext>  </mtext><msub><mrow><mi>L</mi></mrow><mrow><mi>Q</mi></mrow></msub><mo>,</mo><mtext>  </mtext><msub><mrow><mi>L</mi></mrow><mrow><mi>U</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472809&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472804&type= 16.42533302 4.23333359 均为辐亮度单位（W/（m 2 ·sr））下的Stokes参量， <math id="M8"><msub><mrow><mi>E</mi></mrow><mrow><mi>λ</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472822&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472814&type= 3.64066648 3.72533321 为大气层顶太阳通量，单位为W/m 2 。 R 为归一化反射率。 <math id="M9"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472834&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472828&type= 3.47133350 3.72533321 为归一化偏振反射率，下文中均简称为偏振反射率。 并定义 <math id="M10"><mi>Θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472843&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472838&type= 2.87866688 2.79399991 为散射角，表达为 <math display="block" id="M11"><mi>Θ</mi><mo>=</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mtext> </mtext><mfenced separators="|"><mrow><mo>-</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi>φ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472855&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472850&type= 63.41533279 5.24933338 对于地面无云遮挡目标，卫星探测器接收到的大气层顶偏振反射率（即表观偏振反射率 <math id="M12"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi>*</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473219&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473217&type= 3.47133350 4.06400013 ）由3部分构成：大气偏振反射率 <math id="M13"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472976&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472973&type= 5.33400011 4.06400013 、气溶胶偏振反射率 <math id="M14"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473206&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473204&type= 4.91066647 4.06400013 和地表偏振反射率 <math id="M15"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472894&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472891&type= 5.41866684 4.06400013 。 Waquet等（2009a） Waquet等（2009a） 给出其相互关系为 <math display="block" id="M16"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo>=</mo><mfenced separators="|"><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msubsup></mrow></mfenced><mo>+</mo><msup><mrow><mi>T</mi></mrow><mrow><mo>↑</mo></mrow></msup><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi></mrow></msubsup><msup><mrow><mi>T</mi></mrow><mrow><mo>↓</mo></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472903&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472901&type= 42.50266647 5.24933338 式中， <math id="M17"><msup><mrow><mi>T</mi></mrow><mrow><mo>↑</mo></mrow></msup><mi>、</mi><msup><mrow><mi>T</mi></mrow><mrow><mo>↓</mo></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472911&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472908&type= 8.46666718 3.30200005 是与大气辐射传输关系相关的系数，与气溶胶光学厚度 <math id="M18"><mi>τ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473304&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473301&type= 1.77800000 2.62466669 、分子大气光学厚度 <math id="M19"><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472926&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472922&type= 4.82600021 3.72533321 等参数有关，定义与 Waquet等（2009b） Waquet等（2009b） 的表述一致。 以下对 <math id="M20"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msubsup><mo>,</mo><mtext>  </mtext><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472933&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472930&type= 20.99733353 4.57200003 的计算过程进行深入解释： （1）分子大气的散射特性遵从Rayleigh散射理论，可以使用经验公式计算散射偏振相函数： <math display="block" id="M21"><msub><mrow><mi>Q</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced><mo>=</mo><mfrac><mrow><mn mathvariant="normal">3</mn></mrow><mrow><mn mathvariant="normal">4</mn></mrow></mfrac><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>Θ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472940&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472935&type= 36.99933624 7.28133297 分子大气光学厚度 <math id="M22"><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472945&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472941&type= 4.82600021 3.72533321 可以由 式（6） 式（6） （ 蒋秀兰 等，2007 蒋秀兰 等，2007 ）得到： <math display="block" id="M23"><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">0.008569</mn><msup><mrow><mi>λ</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msup><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mn mathvariant="normal">0.0113</mn><msup><mrow><mi>λ</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mn mathvariant="normal">0.00013</mn><msup><mrow><mi>λ</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msup></mrow></mfenced><mfrac><mrow><mi>P</mi></mrow><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472953&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472950&type= 72.64399719 8.38199997 式中， <math id="M24"><mi>λ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473225&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473222&type= 2.28600001 2.62466669 为波长， P 为目标点处大气压， <math id="M25"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472970&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472966&type= 3.47133350 3.72533321 为标准大气压，可以根据POLDER记录的海拔高度数据来求算。 于是大气分子偏振反射率 <math id="M26"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472976&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472973&type= 5.33400011 4.06400013 表达为 <math display="block" id="M27"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msubsup><mo>=</mo><mfrac><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub><msub><mrow><mi>Q</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">4</mn><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472982&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472979&type= 27.43199921 8.72066593 （2） <math id="M28"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473083&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473080&type= 5.41866684 4.06400013 是由 Nadal和Bréon（1999） Nadal和Bréon（1999） 的BPDF半经验模型给出的，表达为 <math display="block" id="M29"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>Ω</mi><mo stretchy="false">)</mo><mo>=</mo><mi>ρ</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mtext> </mtext><mfenced separators="|"><mrow><mo>-</mo><mi>β</mi><mfrac><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub><mo stretchy="false">(</mo><mi>Ω</mi><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>+</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfrac></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472995&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472992&type= 61.38333893 10.66800022 Ω 为太阳相对于地面点的入射角（即 Ω =（π- <math id="M30"><mi>Θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473000&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25472997&type= 2.87866688 2.79399991 ）/2） F p （ Ω ）为菲涅尔反射系数，是入射角 <math id="M31"><mi>Ω</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473007&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473003&type= 2.62466669 2.79399991 和折射角 <math id="M32"><msup><mrow><mi>Ω</mi></mrow><mrow><mi>'</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473014&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473011&type= 3.64066648 3.04800010 的函数（即 <math id="M33"><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mtext> </mtext><mi>Ω</mi><mo>=</mo><mi>N</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mtext> </mtext><msup><mrow><mi>Ω</mi></mrow><mrow><mi>'</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473033&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473029&type= 23.96066666 3.13266683 ， <math id="M34"><mtext> </mtext><mi>N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473041&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473037&type= 3.30200005 2.70933342 是介质折射系数，本研究中取典型值1.5）： <math display="block" id="M35"><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub><mfenced separators="|"><mrow><mi>Ω</mi></mrow></mfenced><mo>=</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mfenced close="" separators="|"><mrow><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mi>N</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msup><mrow><mi>Ω</mi></mrow><mrow><mi>'</mi></mrow></msup><mo>-</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mtext> </mtext><mi>Ω</mi></mrow><mrow><mi>N</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msup><mrow><mi>Ω</mi></mrow><mrow><mi>'</mi></mrow></msup><mo>+</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mtext> </mtext><mi>Ω</mi></mrow></mfrac></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>-</mo></mrow></mfenced></mtd></mtr><mtr><mtd><mfenced open="" separators="|"><mrow><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mi>N</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mtext> </mtext><mi>Ω</mi><mo>-</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msup><mrow><mi>Ω</mi></mrow><mrow><mi>'</mi></mrow></msup></mrow><mrow><mi>N</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mtext> </mtext><mi>Ω</mi><mo>+</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msup><mrow><mi>Ω</mi></mrow><mrow><mi>'</mi></mrow></msup></mrow></mfrac></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473046&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473044&type= 50.63066483 23.02933502 <math id="M36"><mi>ρ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473053&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473048&type= 1.69333339 3.38666677 和 <math id="M37"><mi>β</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473059&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473055&type= 1.86266661 3.38666677 是随地表覆盖类型和归一化植被指数NDVI调整的系数。对于POLDER载荷， Nadal和Bréon（1999） Nadal和Bréon（1999） 给出的NDVI计算式为 <math display="block" id="M38"><mi mathvariant="normal">N</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">I</mi><mo>=</mo><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">865</mn></mrow></msub><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">670</mn></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">865</mn></mrow></msub><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">670</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>I</mi></mrow><mrow><mn mathvariant="normal">865</mn></mrow></msub><mo>-</mo><msub><mrow><mi>I</mi></mrow><mrow><mn mathvariant="normal">670</mn></mrow></msub></mrow><mrow><msub><mrow><mi>I</mi></mrow><mrow><mn mathvariant="normal">865</mn></mrow></msub><mo>+</mo><msub><mrow><mi>I</mi></mrow><mrow><mn mathvariant="normal">670</mn></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473066&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473064&type= 47.66733551 8.72066593 式中， <math id="M39"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">865,670</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473072&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473070&type= 9.31333351 3.72533321 和 <math id="M40"><msub><mrow><mi>I</mi></mrow><mrow><mn mathvariant="normal">865,670</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473079&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473075&type= 8.29733276 3.72533321 分别为865 nm和670 nm通道的归一化反射率和Stokes I 参量。根据目标处的地表覆盖类型、NDVI值所处区间，就可以推算得该处的地表偏振反射率 <math id="M41"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473083&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473080&type= 5.41866684 4.06400013 。 （3）气溶胶的散射特性最为复杂，为简化运算，提升算法可行性，本文采用了球形粒子、单次散射的假设，基于Mie散射理论，模拟了气溶胶的偏振反射率。 由Mie散射理论，对于单个球形粒子，入射光和散射光之间可以通过散射相矩阵 P 建立联系（ Li等，2004 Li等，2004 ），形如： <math display="block" id="M42"><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mtable columnalign="left"><mtr><mtd><mi>I</mi></mtd></mtr><mtr><mtd><mi>Q</mi></mtd></mtr></mtable></mtd></mtr><mtr><mtd><mtable columnalign="left"><mtr><mtd><mi>U</mi></mtd></mtr><mtr><mtd><mi>V</mi></mtd></mtr></mtable></mtd></mtr></mtable></mrow></mfenced><mo>=</mo><mi mathvariant="bold-italic">P</mi><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>I</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mrow><mi>Q</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mtd></mtr></mtable></mtd></mtr><mtr><mtd><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>U</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mtd></mtr></mtable></mtd></mtr></mtable></mrow></mfenced><mo>=</mo><mfrac><mrow><msub><mrow><mi>Ω</mi></mrow><mrow><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi><mi mathvariant="normal">f</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">4</mn><mi mathvariant="normal">π</mi></mrow></mfrac><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mtable><mtr><mtd><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">11</mn></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced></mtd><mtd><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced></mtd></mtr><mtr><mtd><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced></mtd><mtd><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">22</mn></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced></mtd></mtr></mtable></mtd><mtd><mtable><mtr><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mtext>      </mtext><mn mathvariant="normal">0</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mtext>      </mtext><mn mathvariant="normal">0</mn></mtd></mtr></mtable></mtd></mtr><mtr><mtd><mtable><mtr><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mtext>     </mtext><mn mathvariant="normal">0</mn></mtd></mtr><mtr><mtd><mn mathvariant="normal">0</mn></mtd><mtd><mtext>     </mtext><mn mathvariant="normal">0</mn></mtd></mtr></mtable></mtd><mtd><mtable><mtr><mtd><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">33</mn></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced></mtd><mtd><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">34</mn></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mo>-</mo><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">34</mn></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced></mtd><mtd><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">44</mn></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced></mtd></mtr></mtable></mtd></mtr></mtable></mrow></mfenced><mfenced open="[" close="]" separators="|"><mrow><mtable><mtr><mtd><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>I</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mrow><mi>Q</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mtd></mtr></mtable></mtd></mtr><mtr><mtd><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>U</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mrow><mi>V</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mtd></mtr></mtable></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473089&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473086&type= 93.21800232 24.29933357 式中， <math id="M43"><msub><mrow><mi>Ω</mi></mrow><mrow><mi mathvariant="normal">e</mi><mi mathvariant="normal">f</mi><mi mathvariant="normal">f</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473094&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473092&type= 4.74133301 3.89466691 是散射过程的立体角， <math id="M44"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">11</mn></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473103&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473098&type= 10.41399956 4.23333359 项和 <math id="M45"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473111&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473106&type= 10.41399956 4.23333359 项就是散射相函数 <math id="M46"><msub><mrow><mi>p</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473119&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473115&type= 10.24466610 4.23333359 和偏振相函数 <math id="M47"><msub><mrow><mi>q</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473123&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473122&type= 10.24466610 4.23333359 ，与波长 <math id="M48"><mi>λ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473131&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473126&type= 2.28600001 2.62466669 、粒子半径 <math id="M49"><mi>r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473230&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473227&type= 1.26999998 2.62466669 、复折射率系数 <math id="M50"><mi>m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473234&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473232&type= 2.70933342 2.62466669 相关，由Mie散射理论计算得出。 对于粒子组成的粒子群而言，粒子群整体偏振相函数 <math id="M51"><msub><mrow><mi>Q</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473151&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473148&type= 11.09133339 4.23333359 计算式（ 黄朝军 等，2012 黄朝军 等，2012 ）为 <math display="block" id="M52"><msub><mrow><mi>Q</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced><mo>=</mo><mfrac><mrow><msubsup><mo>∫</mo><mrow><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub></mrow></msubsup><mrow><msub><mrow><mi>q</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msub><mfenced separators="|"><mrow><mi>Θ</mi></mrow></mfenced><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>m</mi><mo stretchy="false">)</mo><mi>n</mi><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo><mi mathvariant="normal">d</mi><mi>r</mi></mrow></mrow><mrow><msubsup><mo>∫</mo><mrow><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></mrow><mrow><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub></mrow></msubsup><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>m</mi><mo stretchy="false">)</mo><mi>n</mi><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo><mi mathvariant="normal">d</mi><mi>r</mi></mrow></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473157&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473153&type= 59.01266098 15.74800014 式中， <math id="M53"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473165&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473161&type= 4.99533367 3.72533321 是单个粒子的散射截面，与波长 <math id="M54"><mi>λ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473172&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473169&type= 2.28600001 2.62466669 、粒子半径 <math id="M55"><mi>r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473179&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473176&type= 1.26999998 2.62466669 、复折射率系数 <math id="M56"><mi>m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473186&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473182&type= 2.70933342 2.62466669 相关，同样由Mie散射理论计算得出； <math id="M57"><mi>n</mi><mfenced separators="|"><mrow><mi>r</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473192&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473189&type= 6.77333355 3.72533321 是粒径分布函数，定义为粒子平均半径 r g 、标准差 <math id="M58"><mi>σ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473197&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473195&type= 2.45533323 2.62466669 的函数（ Wang等，2018 Wang等，2018 ）： <math display="block" id="M59"><mi>n</mi><mfenced separators="|"><mrow><mi>r</mi></mrow></mfenced><mo>=</mo><mfrac><mrow><mi mathvariant="normal">d</mi><mtext> </mtext><mi>N</mi></mrow><mrow><mi mathvariant="normal">d</mi><mtext> </mtext><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mi>r</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow><mrow><mi>σ</mi><mroot><mrow><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi></mrow><mrow/></mroot></mrow></mfrac><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mfenced separators="|"><mrow><mo>-</mo><mfrac><mrow><msup><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mtext> </mtext><mi>r</mi><mo>-</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mtext> </mtext><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">g</mi></mrow></msub></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow><mn mathvariant="normal">2</mn><msup><mrow><mi>σ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473202&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473200&type= 66.80200195 13.20800018 于是气溶胶偏振反射率 <math id="M60"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473206&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473204&type= 4.91066647 4.06400013 表达为 <math display="block" id="M61"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msubsup><mo>=</mo><mfrac><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msub><msub><mrow><mi>Q</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">4</mn><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473214&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473210&type= 27.00866890 8.72066593 至此，完成了陆上无云目标的多角度表观偏振反射率 <math id="M62"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi>*</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473219&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473217&type= 3.47133350 4.06400013 的模拟。此模拟结果与输入的波长 <math id="M63"><mi>λ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473225&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473222&type= 2.28600001 2.62466669 、粒子半径 <math id="M64"><mi>r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473230&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473227&type= 1.26999998 2.62466669 、复折射率系数 <math id="M65"><mi>m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473234&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473232&type= 2.70933342 2.62466669 、散射角 <math id="M66"><mi>Θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473242&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473237&type= 2.87866688 2.79399991 、NDVI、地物类型、气溶胶AOD <math id="M67"><mi>τ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473304&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473301&type= 1.77800000 2.62466669 直接相关。当其他量都取定值时，就可以根据 <math id="M68"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi>*</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473255&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473252&type= 3.47133350 4.06400013 的模拟计算值和观测值之间的差异系数，来实现气溶胶光学厚度 <math id="M69"><mi>τ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473304&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473301&type= 1.77800000 2.62466669 这一个物理量的反演。 2.3　算法流程 2 群组残差最优反演算法的整体流程图如 图1 图1 所示。需注意的是，POLDER 1级数据中，存储了16个观测几何角度层的数据，但一些角度层下存在无效值（填充值）。为了保证程序的通用性，剔除了1—11个角度层以外的数据。 以下对算法流程作详细说明： （1）对于每个有效的目标像元，可以读取11个670 nm通道下的偏振反射率测量值—— R p 1—11_meas 。 （2）由 式（5） 式（5） — 式（7） 式（7） 可以预先设置大气偏振反射率贡献模拟计算值；由 式（8） 式（8） — 式（10） 式（10） 及NDVI，预先计算670 nm波段下地表贡献。 （3）气溶胶的复折射率在本研究中取典型值，标准差 <math id="M70"><mi>σ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473275&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473273&type= 2.45533323 2.62466669 取为0.5，粒子平均半径 r g 取 N 个不同的值，由 式（11） 式（11） — 式（13） 式（13） 可以推算气溶胶的偏振散射相函数 <math id="M71"><msub><mrow><mi>Q</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473282&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473279&type= 5.07999992 4.48733330 ，共 N 组； （4）初始光学厚度值取 <math id="M72"><mi>τ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473287&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473284&type= 1.77800000 2.62466669 的小值0、中值2.5、大值5。由式（ 4 4 ， 7 7 ， 8 8 ， 14 14 ）计算11个不同角度下的偏振反射率 R p 1—11_cal 的小值、中值、大值，由二分法，测量值 R p 1—11_meas 和值将落于 R p 1—11_cal 和值的两个二分区间的其中之一。 （5）以上述二分结果为依据，继续不断二分更新 <math id="M73"><mi>τ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473304&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473301&type= 1.77800000 2.62466669 的小值、中值、大值，重复步骤（4），使 <math id="M74"><mi>τ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473304&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473301&type= 1.77800000 2.62466669 值与 R p 1—11_cal 的和值同步不断迭代。迭代结束后，可以得到 N 个光学厚度 <math id="M75"><mi>τ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473304&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473301&type= 1.77800000 2.62466669 及对应的偏振反射率模拟计算值 R p 1—11_cal 。 （6）设置一个差异系数，文章中取观测值与模拟计算值的均方根误差RMSE i ： <math display="block" id="M76"><mi mathvariant="normal">R</mi><mi mathvariant="normal">M</mi><mi mathvariant="normal">S</mi><msub><mrow><mi mathvariant="normal">E</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mroot><mrow><mfrac><mrow><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>l</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">11</mn></mrow></munderover></mstyle><mrow><mo stretchy="false">(</mo><mi>R</mi><msub><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mo>,</mo><mi>l</mi><mo>,</mo><mi>i</mi></mrow></msub><mo>-</mo><mi>R</mi><msub><mrow><mi mathvariant="normal">p</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">s</mi><mo>,</mo><mi>l</mi><mo>,</mo><mi>i</mi></mrow></msub><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mrow><mrow><mn mathvariant="normal">11</mn></mrow></mfrac></mrow><mrow/></mroot><mo>,</mo><mtext> </mtext><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mtext> </mtext><mi>N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473310&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473307&type= 69.08799744 13.80066681 （7）取RMSE最小的一组，即对应了光学厚度值 <math id="M77"><msub><mrow><mi>τ</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473316&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25473313&type= 4.31799984 3.72533321 的最终反演值。 为保证数据质量，还设置了两个边界条件： 1）若 R p 1—11_meas 的和值超出了初始区间，则说明模拟计算值设置不合理，应直接跳出迭代，并返回空值。 2）若某一目标像元最优结果下RMSE仍大于10 -3 ，则认为模拟计算值与测量值偏差过大，反演无法准确，需要将此像元的反演结果作剔除处理，并返回空值。 2.4　群组残差最优方法的可行性分析 2 从上述模拟计算过程可以推得，多角度下偏振反射率随散射角变化的曲线应当是平滑的，即，因此，多角度的偏振反射率的群组观测值应处于某一条平滑的多角度曲线上。为了直观说明，从POLDER 1级数据中选取了一个典型的无云目标（云标志取无云值），展示了算法的迭代过程，如 图2 图2 所示。将其次计算过程中的模拟计算值列为 表2 表2 ，发现在迭代次数达10次以后，测量值与模拟计算值已经十分接近，并且，群组的模拟值能较好地同时与测量值拟合，于是印证了此群组方法的可行性。 1,2,3;4; 2 R p 6 观测几何编号 11 9 7 5 3 11个反射率的和 R p_meas 0.028501 0.018491 0.009339 0.001838 0.002220 0.107976 R p_cal （迭代1次） 0.076640 0.052923 0.029312 0.009412 0.000730 0.298892 R p_cal （迭代5次） 0.027473 0.019455 0.010982 0.001404 0.000263 0.109890 R p_cal （迭代10次） 0.026882 0.019053 0.010762 0.003554 0.000257 0.107618 R p_cal （迭代15次） 0.026974 0.019116 0.010797 0.003565 0.000258 0.107973 另外，还选取了4个不同地表覆盖类型的典型无云目标，分别展示了本文方法的模拟计算情况（ 图3 图3 ），从 图3 图3 中看到，不同地表覆盖类型下，多角度的偏振反射率模拟计算值与测量值都能很好地拟合。 1,2;3,4;5; 3　气溶胶反演计算结果及对比论证 1 3.1　气溶胶反演计算结果与分析 2 本文主要使用部分亚太区域的POLDER 1级数据进行了气溶胶AOD的反演实验，此地理区域气溶胶空间分布多样且差异足够明显（内陆—海滨，人口密集—人口稀少等），十分适合对比研究。以下提供了两个实例及其结果的对比分析。 实例1、实例2分别取自中国东南部、印度两个区块，POLDER与MODIS的轨道时间差基本在1 h时以内。如图 4 4 、 5 5 所示，分别为两实例下的真彩图、经地理精确匹配后的AOD反演结果和MYD04产品。 1,2,3; 1,2,3; 本文的精确地理匹配是指，POLDER的空间分辨率约达6 km×7 km，而MYD04产品的空间分辨率约达3 km×3 km，因此对于POLDER数据，在对应轨道、相近时刻内，总存在经纬度相近的MYD04数据（文章中取经纬差值小于0.2）可以形成精确匹配。 从 图4 图4 和 图5 图5 中看到，两个实例的反演结果与MYD04产品的特征是相近的。具体而言，实例1研究区域内，大部分地区的光学厚度值偏大，处于0.4—0.8区间；仅北部、南部地区光学厚度均较小（ < 0.2）。此区域对应的是中国人口或工业密集区，人为活动较为频繁，因此会导致光学厚度较大。实例2中，印度北部有条带区域光学厚度显著偏大，同样是典型的工业、人口密集区。反演结果能够得到合理解释。 进一步地，对两实例的反演数值结果和对应的MYD04两个AOD数据集建立了回归分析模型，分析计算其相关性，如散点图（ 图6 图6 ）所示。实例1中有效像元目标为27358个，实例2中为26905个，散点图中只展示了其中随机选取的1/50的数据点，且回归分析是针对全部数据点进行的，因此图示结果是具有代表性的。 1,2; 两个实例得到的回归模型，回归系数（ R 2 ）分别达到0.699和0.687，斜率分别达到1.039（ y =1.039 x -0.002）和0.927（ y =0.927 x +0.028）。 Wang等（2018） Wang等（2018） 的实验结果与本文结果是相近的。 最后，综合2005-10-01后15 d内亚太区域的反演结果，得到了15 d天陆上气溶胶AOD平均值合成图，如 图7（a） 图7（a） 所示。 对15 d光学厚度合成结果与MODIS的光学厚度合成结果（ 图7（b） 图7（b） ）进行对比分析，如 图7（c） 图7（c） 。合成结果的回归系数达0.402，相比于单轨数据略低；但回归线斜率仍可达1.185，说明在引入其他误差后，光学厚度合成结果还是保持了一定的相关性。 另外还可以看到，15 d平均光学厚度反演结果与MODIS光学厚度产品的空间分布存在一致性，在中国东南部和印度北部区域，气溶胶AOD普遍偏大（约达到0.4—0.7），成因可以合理推测是由两区域内较高频率的工业以及人类活动导致的。 1,2;3; 3.2　AOD反演结果与地基数据（AERONET）的对比分析 2 将本文光学厚度结果与AERONET的地基光学厚度反演产品进行了统计对比。主要关注两个典型地面站，分别是北京（39.97°N，116.28°E，Beijing，China）和坎普尔（26.51°N，80.23°E，Kanpur，India）。 研究样本为2005-09—2005-10两个月期间，即2005年第243—304天的光学厚度结果，POLDER和AERONET都有足够的样本数据作为研究支撑。光学厚度有效值对比结果如 图8 图8 所示。 1,2;3; 最后，将2005年整年的两地面站点上POLDER和AERONET的日光学厚度有效值统计对比如 图9 图9 。 1,2; 从 图8 图8 、 图9 图9 可以得出，北京、坎普尔站点上的反演结果与AERONET记录值的变化趋势上有较好的一致性；且光学厚度有效值在两个站点的大部分日期内呈现出较明显的正相关性，比较均匀地分布在斜率为1直线的两侧，对比结果良好。 4　结论 1 本文基于大气辐射传输理论和粒子散射理论，提出了一种群组残差最优方法，将其应用于适用于气溶胶AOD反演。针对POLDER在亚太区域实际观测资料进行了反演试验，并将结果与MODIS产品和地基AERONET观测作了比对分析验证。 利用本方法反演了两个典型地区（中国东南部、印度）的气溶胶AOD，并与MODIS参考气溶胶产品进行匹配和相关性分析，得到的 R 2 分别为0.699、0.687，回归斜率为1.039、0.927，证明本文得到的气溶胶AOD结果与MODIS参考产品之间的一致性。 进一步地，对15 d内的亚太地区做了多轨、多天平均光学厚度合成处理，发现气溶胶空间分布特征与实际情况相符合。另外，将本文AOD反演结果与AERONET两个典型站点上数据产品进行了统计分析，同样具备较高的相关性。 研究也发现本方法在大值光学厚度反演上还存在一定偏差，尚需进一步完善。 本文方法理论上并不仅局限于POLDER一个偏振多角度遥感卫星，可以在后续研究中，将此方法应用于中国偏振多角度成像卫星（如天宫二号、高分五号等）的观测数据，有望形成国产偏振多角度卫星气溶胶AOD系列产品。 参考文献（References） Chen C , Li Z Q , Hou W Z , Li D H and Zhang Y H . 2015 . Dynamic model in retrieving aerosol optical depth from polarimetric measurements of PARASOL . Journal of Remote Sensing , 19 ( 1 ): 25 - 33 Dynamic model in retrieving aerosol optical depth from polarimetric measurements of PARASOL 陈澄 , 李正强 , 侯伟真 , 李东辉 , 张玉环 . 2015 . 动态气溶胶模型的PARASOL多角度偏振卫星气溶胶光学厚度反演算法 . 遥感学报 , 19 ( 1 ): 25- 33 [ DOI: 10.11834/jrs.20154043 http://dx.doi.org/10.11834/jrs.20154043 ] 动态气溶胶模型的PARASOL多角度偏振卫星气溶胶光学厚度反演算法 Deuzé J L , Bréon F M , Devaux C , Goloub P , Herman M , Lafrance B , Maignan F , Marchand A , Nadal F , Perry G and Tanré D . 2001 . Remote sensing of aerosols over land surfaces from POLDER-ADEOS-1 polarized measurements . Journal of Geophysical Research : Atmospheres , 106 ( D5 ): 4913 - 4926 [ DOI: 10.1029/2000JD900364 http://dx.doi.org/10.1029/2000JD900364 ] Remote sensing of aerosols over land surfaces from POLDER-ADEOS-1 polarized measurements Dubovik O , Herman M , Holdak A , Lapyonok T , Tanré D , Deuzé J L , Ducos F , Sinyuk A and Lopatin A . 2011 . Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations . Atmospheric Measurement Techniques , 4 ( 5 ): 975 - 1018 [ DOI: 10.5194/amt-4-975-2011 http://dx.doi.org/10.5194/amt-4-975-2011 ] Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations Dubovik O , Li Z Q , Mishchenko M I , Tanré D , Karol Y , Bojkov B , Cairns B , Diner D J , Espinosa W R , Goloub P , Gu X F , Hasekamp O , Hong J , Hou W Z , Knobelspiesse K D , Landgraf J , Li L , Litvinov P , Liu Y , Lopatin A , Marbach T , Maring H , Martins V , Meijer Y , Milinevsky G , Mukai S , Parol F , Qiao Y L , Remer L , Rietjens J , Sano I , Stammes P , Stamnes S , Sun X B , Tabary P , Travis L D , Waquet F , Xu F , Yan C X and Yin D K . 2019 . Polarimetric remote sensing of atmospheric aerosols: instruments, methodologies, results, and perspectives . Journal of Quantitative Spectroscopy and Radiative Transfer , 224 : 474 - 511 [ DOI: 10.1016/j.jqsrt.2018.11.024 http://dx.doi.org/10.1016/j.jqsrt.2018.11.024 ] Polarimetric remote sensing of atmospheric aerosols: instruments, methodologies, results, and perspectives Holben B N , Eck T F , Slutsker I , Tanré D , Buis J P , Setzer A , Vermote E , Reagan J A , Kaufman Y J , Nakajima T , Lavenu F , Jankowiak I and Smirnov A . 1998 . AERONET—a federated instrument network and data archive for aerosol characterization . Remote Sensing of Environment , 66 ( 1 ): 1 - 16 [ DOI: 10.1016/S0034-4257(98)00031-5 http://dx.doi.org/10.1016/S0034-4257(98)00031-5 ] AERONET—a federated instrument network and data archive for aerosol characterization Hsu N C , Tsay S C , King M D and Herman J R . 2004 . Aerosol properties over bright-reflecting source regions . IEEE Transactions on Geoscience and Remote Sensing , 42 ( 3 ): 557 - 569 [ DOI: 10.1109/tgrs.2004.824067 http://dx.doi.org/10.1109/tgrs.2004.824067 ] Aerosol properties over bright-reflecting source regions Huang C J , Wu Z S , Liu Y F , Shi P , Xiong X J and Jing M Y . 2012 . Numerical calculation of phase function of atmospheric aerosol particles . Infrared and Laser Engineering , 41 ( 3 ): 580 - 585 Numerical calculation of phase function of atmospheric aerosol particles 黄朝军 , 吴振森 , 刘亚锋 , 史平 , 熊晓军 , 井敏英 . 2012 . 大气气溶胶粒子散射相函数的数值计算 . 红外与激光工程 , 41 ( 3 ): 580- 585 [ DOI: 10.3969/j.issn.1007-2276.2012.03.007 http://dx.doi.org/10.3969/j.issn.1007-2276.2012.03.007 ] 大气气溶胶粒子散射相函数的数值计算 Jiang X L , Liu Y G , Liu Y H and Zhou L M . 2007 . Five channel hand-held sunphotometer. Meteorological, Hydrological and Marine Instruments, (3): 54 - 58 Five channel hand-held sunphotometer. Meteorological, Hydrological and Marine Instruments, (3): 蒋秀兰 , 刘玉光 , 刘亚豪 , 周良明 . 2007 . 手持式五波段太阳光度计. 气象水文海洋仪器, (3): 54 - 58 [DOI: 10.3969/j.issn.1006-009X.2007.03.017] 手持式五波段太阳光度计. 气象水文海洋仪器, (3): Kaufman Y J , Wald A E , Remer L A , Gao B C , Li R R and Flynn L . 1997 . The MODIS 2.1- μ m channel-correlation with visible reflectance for use in remote sensing of aerosol . IEEE Transactions on Geoscience and Remote Sensing , 35 ( 5 ): 1286 - 1298 [ DOI: 10.1109/36.628795 http://dx.doi.org/10.1109/36.628795 ] The MODIS 2.1-μm channel-correlation with visible reflectance for use in remote sensing of aerosol Leroy M , Deuzé J L , Bréon F M , Hautecoeur O , Herman M , Buriez J C , Tanré D , Bouffiès S , Chazette P and Roujean J L . 1997 . Retrieval of atmospheric properties and surface bidirectional reflectances over land from POLDER/ADEOS . Journal of Geophysical Research : Atmospheres , 102 ( D14 ): 17023 - 17037 [ DOI: 10.1029/96JD02662 http://dx.doi.org/10.1029/96JD02662 ] Retrieval of atmospheric properties and surface bidirectional reflectances over land from POLDER/ADEOS Levy R C , Remer L A , Mattoo S , Vermote E F and Kaufman Y J . 2007 . Second-generation operational algorithm: retrieval of aerosol properties over land from inversion of Moderate Resolution Imaging Spectroradiometer spectral reflectance . Journal of Geophysical Research : Atmospheres , 112 ( D13 ): D 13211 [ DOI: 10.1029/2006JD007811 http://dx.doi.org/10.1029/2006JD007811 ] Second-generation operational algorithm: retrieval of aerosol properties over land from inversion of Moderate Resolution Imaging Spectroradiometer spectral reflectance Li Z Q , Goloub P , Devaux C , Gu X F , Qiao Y L , Zhao F S and Chen H B . 2004 . Aerosol polarized phase function and single-scattering albedo retrieved from ground-based measurements . Atmospheric Research , 71 ( 4 ): 233 - 241 [ DOI: 10.1016/j.atmosres.2004.06.001 http://dx.doi.org/10.1016/j.atmosres.2004.06.001 ] Aerosol polarized phase function and single-scattering albedo retrieved from ground-based measurements Li Z Q , Hou W Z , Hong J , Zheng F X , Luo D G , Wang J , Gu X F and Qiao Y L . 2018 . Directional Polarimetric Camera (DPC): monitoring aerosol spectral optical properties over land from satellite observation . Journal of Quantitative Spectroscopy and Radiative Transfer , 218 : 21 - 37 [ DOI: 10.1016/j.jqsrt.2018.07.003 http://dx.doi.org/10.1016/j.jqsrt.2018.07.003 ] Directional Polarimetric Camera (DPC): monitoring aerosol spectral optical properties over land from satellite observation Nadal F and Bréon F M . 1999 . Parameterization of surface polarized reflectance derived from POLDER Spaceborne measurements . IEEE Transactions on Geoscience and Remote Sensing , 37 ( 3 ): 1709 - 1718 [ DOI: 10.1109/36.763292 http://dx.doi.org/10.1109/36.763292 ] Parameterization of surface polarized reflectance derived from POLDER Spaceborne measurements Wang H , Sun X B , Yang L K , Zhao M R , Lui P and Du W B . 2018 . Aerosol retrieval algorithm based on adaptive land-atmospheric decoupling for polarized remote sensing over land surfaces . Journal of Quantitative Spectroscopy and Radiative Transfer , 219 : 74 - 84 [ DOI: 10.1016/j.jqsrt.2018.08.011 http://dx.doi.org/10.1016/j.jqsrt.2018.08.011 ] Aerosol retrieval algorithm based on adaptive land-atmospheric decoupling for polarized remote sensing over land surfaces Wang S P . 2012 . Retrieval of Aerosol Properties of Fine-Coarse Mode Mixtures over Urban Areas from Multi-Directional Polarized Satellite Measurements . Beijing : University of Chinese Academy of Sciences Retrieval of Aerosol Properties of Fine-Coarse Mode Mixtures over Urban Areas from Multi-Directional Polarized Satellite Measurements 王舒鹏 . 2012 . 基于多角度偏振卫星信号的粗细混合型城市气溶胶反演 . 北京 : 中国科学院大学 基于多角度偏振卫星信号的粗细混合型城市气溶胶反演 Waquet F , Cairns B , Knobelspiesse K , Chowdhary J , Travis L D , Schmid B and Mishchenko M I . 2009a . Polarimetric remote sensing of aerosols over land . Journal of Geophysical Research : Atmospheres , 114 ( D1 ): D 01206 [ DOI: 10.1029/2008JD010619 http://dx.doi.org/10.1029/2008JD010619 ] Polarimetric remote sensing of aerosols over land Waquet F , Léon J F , Cairns B , Goloub P , Deuzé J L and Auriol F . 2009b . Analysis of the spectral and angular response of the vegetated surface polarization for the purpose of aerosol remote sensing over land . Applied Optics , 48 ( 6 ): 1228 - 1236 [ DOI: 10.1364/AO.48.001228 http://dx.doi.org/10.1364/AO.48.001228 ] Analysis of the spectral and angular response of the vegetated surface polarization for the purpose of aerosol remote sensing over land Yin D K . 2019 . Multi-angle polarization detection technology . Infrared , 40 ( 1 ): 1 - 6, 23 Multi-angle polarization detection technology 殷德奎 . 2019 . 多角度偏振探测技术 . 红外 , 40 ( 1 ): 1 - 6 , 23 [ DOI: 10.3969/j.issn.1672-8785.2019.01.001 http://dx.doi.org/10.3969/j.issn.1672-8785.2019.01.001 ] 多角度偏振探测技术 Zhang Y , Li Z Q , Liu Z H , Zhang J , Qie L , Xie Y S , Hou W Z , Wang Y Q and Ye Z X . 2018 . Retrieval of the fine-mode aerosol optical depth over East China Using a Grouped Residual Error Sorting (GRES) method from multi-angle and polarized satellite data . Remote Sensing , 10 ( 11 ): 1838 [ DOI: 10.3390/rs10111838 http://dx.doi.org/10.3390/rs10111838 ] Retrieval of the fine-mode aerosol optical depth over East China Using a Grouped Residual Error Sorting (GRES) method from multi-angle and polarized satellite data 10.11834/jrs.20219279 1007-4619（2022）03-0505-11 高鑫，胡秀清，方伟，张鹏.2022.利用POLDER多角度偏振数据反演陆上气溶胶光学厚度的群组残差最优方法.遥感学报，26（3）： 505-515 高鑫，胡秀清，方伟，张鹏.2022.利用POLDER多角度偏振数据反演陆上气溶胶光学厚度的群组残差最优方法.遥感学报，26（3）： 505-515 Gao X，Hu X Q，Fang W and Zhang P. 2022. Application of the optimal grouped residual method in retrieving the optical depth of aerosol over land with POLDER multi-angular polarized data. National Remote Sensing Bulletin， 26（3）：505-515 Gao X，Hu X Q，Fang W and Zhang P. 2022. Application of the optimal grouped residual method in retrieving the optical depth of aerosol over land with POLDER multi-angular polarized data. National Remote Sensing Bulletin， 26（3）：505-515 国家重点研发计划（编号： 2018YFB0504900，2018YFB0504901）；国家自然科学基金（编号： 41871249，41471302） Supported by National Key Research and Development Program of China (No. 2018YFB0504900, 2018YFB0504901)；National Natural Science Foundation of China (No. 41871249，41471302) 2019-08-08 2022-03-07 2022-03-28 2021-10-17 遥感学报 3 26