FY-3D MERSI-II地表温度遥感反演与验证

FY-3D MERSI-II 地表温度遥感反演与验证 Retrieval and validation of the land surface temperature from FY-3D MERSI-II 1 2 first-author 程元良，1999年生，男，博士研究生， 研究方向为地表温度遥感反演与验证。E-mail： chengyuanliang@nuist.edu.cn 程元良，1999年生，男，博士研究生， 研究方向为地表温度遥感反演与验证。E-mail： chengyuanliang@nuist.edu.cn chengyuanliang@nuist.edu.cn 1 corresp 吴骅，1980生，男，研究员，研究方向为热红外遥感、尺度转换与真实性检验。E-mail：wuh@lreis.ac.cn 吴骅，1980生，男，研究员，研究方向为热红外遥感、尺度转换与真实性检验。E-mail：wuh@lreis.ac.cn wuh@lreis.ac.cn 3 4 中国科学院地理科学与资源研究所 资源与环境信息系统国家重点实验室, 北京 100101 中国科学院地理科学与资源研究所 资源与环境信息系统国家重点实验室, 北京 100101 State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China 南京信息工程大学 遥感与测绘工程学院, 南京 210044 南京信息工程大学 遥感与测绘工程学院, 南京 210044 School of Remote Sensing & Geomatics Engineering, NUIST, Nanjing 210044, China School of Remote Sensing & Geomatics Engineering, NUIST, Nanjing 210044, China 中国农业科学院农业资源与农业区划研究所 农业农村部农业遥感重点实验室, 北京 100081 中国农业科学院农业资源与农业区划研究所 农业农村部农业遥感重点实验室, 北京 100081 Chinese Academy of Agricultural Sciences, Institute of Agricultural Resources and Regional Planning, Beijing 100081, China Chinese Academy of Agricultural Sciences, Institute of Agricultural Resources and Regional Planning, Beijing 100081, China 中国科学院空天信息创新研究院 定量遥感信息技术重点实验室, 北京 100094 中国科学院空天信息创新研究院 定量遥感信息技术重点实验室, 北京 100094 Key Laboratory of Quantitative Remote Sensing Information Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China Key Laboratory of Quantitative Remote Sensing Information Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China 地表温度是是决定地表辐射能量收支的重要变量，在岩石圈、水圈、生物圈和大气圈的能量平衡和水量平衡研究中起着重要作用。利用热红外遥感技术可实现区域和全球尺度地表温度的快速获取，其受到了研究者的广泛关注。目前，FY-3D是国内光谱分辨率最高的对地观测卫星，极大的提高了对地观测能力，其搭载的中分辨率光谱成像仪（MERSI-II）经过大幅升级改进，性能有了显著提升，热红外数据的空间分辨率达到了250 m。本文使用大气辐射传输模型MODTRAN 5模拟了MERSI-II传感器热红外通道星上观测数据。在此基础上，构建了通用劈窗地表温度反演模型，结合ASTER GED全球地表发射率产品以及MERSI-II自身大气水汽反演算法，发展了地表温度遥感反演方法。最后，利用2019-08内蒙古乌海沙漠地区及美国SURFRAD多个站点的实测地表温度数据对本文提出的方法进行了验证。研究结果表明，相较地表实测数据，构建的劈窗算法反演的地表温度RMSE在1.6—2.6 K，反演精度达到了预期目标，还具有较高的空间分辨率，可以用于业务化的地表温度的反演，同时也说明其辐射定标精度有了一定保证，有效满足了区域和全球尺度地表温度遥感监测应用需求。 Surface temperature is an important variable that determines surface radiation energy budget, and plays an important role in the study of energy balance and water balance in the lithosphere, hydrosphere, biosphere and atmosphere. Thermal infrared remote sensing technology can be used to achieve rapid acquisition of regional and global land surface temperature, which has been widely concerned by researchers. At present, FY-3D is the earth observation satellite with the highest spectral resolution in China, which has greatly improved the earth observation capability. The Moderate Resolution Spectral Imager (MERSI-II) carried by FY-3D has been greatly upgraded and improved, and its performance has been significantly improved. The spatial resolution of thermal infrared data has reached 250 m. In this paper, the atmospheric radiation transfer model MODTRAN 5 is used to simulate the MERSI-II thermal infrared channel satellite observations. On this basis, construct the land surface temperature inversion model of the generalized split-window. Combined with ASTER GED global surface emissivity product and MERSI-II atmospheric water vapor content inversion algorithm, the technical process system of remote sensing inversion of land surface temperature is developed. Finally, the proposed method was verified by using the measured surface temperature data from several stations in the Wuhai of Inner Mongolia and SURFRAD stations in the United States in August 2019. The results show that compared with the measured surface temperature data, the RMSE of the land surface temperature inversion based on the generalized split-window algorithm is between 1.6 K and 2.6 K for all sites. The accuracy of inversion has reached the expected target, and it has a high spatial resolution, which can be used in the inversion of operational surface temperature. At the same time, it also shows that the accuracy of radiometric calibration is guaranteed to a certain extent, which effectively meets the application requirements of regional and global surface temperature remote sensing monitoring. 地表温度 劈窗算法 风云三号D星 MERSI-II MODTRAN land surface temperature split-window algorithm FY-3D MERSI-II MODTRAN 1　引言 1 地表温度（LST）是表征地表过程变化的重要特征物理量，是反映地球表面能量流和物质流时空变化最敏感的综合指标，是地球科学研究不可或缺的重要参数，涉及众多基础学科研究（ 李召良 等，2017 李召良 等，2017 ）。地表温度信息为农业灾害防治（ 马建文 等，2004 马建文 等，2004 ）、全球火点监测（ 郑伟 等，2020 郑伟 等，2020 ）、城市热岛效应（ 张勇 等，2006 张勇 等，2006 ； 王建凯等，2007 王建凯等，2007 ）、热环境研究（ 吴文渊 等，2019 吴文渊 等，2019 ）等领域研究提供了重要参数。由于影响地表温度的表面状态参数，例如反照率、土壤的物理和热特性以及植被等具有较强的空间非均匀性，地表温度在时空领域里变化相当快，要获取区域和全球尺度上地表温度的时空分布，常规的地面定点观测难以实现（ 李召良 等，2016 李召良 等，2016 ）。 利用卫星数据进行地表温度反演具有数据获取方便、高效、空间探测范围广、反演精度较髙、信息获取量大、可对比、成本低等优势，因此选择遥感数据进行地表温度反演对于进行地表过程的动态监测具有很大的应用价值，被认为是地表温度信息获取的重要手段。 现有的基于热红外数据的地表温度反演算法大致有以下4种：单通道法（ 覃志豪 等，2001 覃志豪 等，2001 ；Jiménez‐Muñoz和Sobrino，2003，2010； Jiménez-Muñoz，2009 Jiménez-Muñoz，2009 ）、劈窗算法（McMillin和Larry，1975； Wan和Dozier，1996 Wan和Dozier，1996 ； Atitar和Sobrino，2009 Atitar和Sobrino，2009 ）、多通道算法（Sun和 Pinker，2003，2005，2007）和多角度法（ Sobrino等，1996 Sobrino等，1996 ， 2004a 2004a ），劈窗算法是目前应用最广泛的地表温度遥感反演方法。劈窗算法的原理是利用10—12.5 <math id="M1"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642041&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642039&type= 5.16466665 3.38666677 之间相邻通道的对水汽吸收特性不同的特点，根据温度或波长对辐射传输方程进行线性化处理。 McMillin（1975） McMillin（1975） 最早提出了劈窗算法（SW），将地表温度表达为两个热红外通道亮度温度的线性组合，用于海面温度的反演。 Price（1984） Price（1984） 最先用劈窗算法进行陆面温度的反演。 Becker和Li（1990） Becker和Li（1990） 提出了局地劈窗算法并证明了用劈窗算法反演地表温度是可行的。 Wan和Dozier（1996） Wan和Dozier（1996） 针对MODIS的热红外通道（31和32通道）提出了通用劈窗算法GSW（Generalized Split Window）来反演地表温度，该算法在系数计算时考虑了观测角度、地表发射率和大气水汽以及近地表气温的影响。为了修正近地表逆温产生的反演误差， 战川等（2018） 战川等（2018） 为GSW算法加入了一个二次函数改正项。由于不依赖大气廓线数据且对传感器的限制条件较少，因此劈窗算法可以适用于MODIS（ Wan和Dozier，1996 Wan和Dozier，1996 ； Mao等，2005 Mao等，2005 ）、Landsat 8 TIRS（ Yu等，2014 Yu等，2014 ；Cristobal等，2014； 宋挺 等，2015 宋挺 等，2015 ）、Himawari 8 AHI（ 刘超 等，2017 刘超 等，2017 ）、GF-5 VIMS（ 杨以坤 等，2019 杨以坤 等，2019 ）等多种传感器。 对于国产风云系列卫星，劈窗算法也表现出良好的适用性。 Tang等（2008） Tang等（2008） 使用GSW算法针对FY-2C数据进行应用，发现GSW算法对其他劈窗算法表现出较高精度。随后，GSW算法被陆续应用于国产风云系列的静止和极轨卫星，如 Liu等（2014） Liu等（2014） 从FY-2C/D/E静止卫星搭载的SVISSR传感器中反演地表温度， Jiang等（2011 Jiang等（2011 ， 2015） 2015） 分别从FY-3A和FY-3B极轨卫星搭载的VIRR传感器中反演地表温度，都取得了较为满意的精度。Wang等（2019）开始尝试将劈窗算法应用于FY-3D极轨卫星的MERSI-II传感器，但其考虑到MERSI-II传感器的定标精度问题，首先利用与MODIS交叉定标的方式对MERSI-II传感器进行了辐射定标，随后利用依赖于大气透过率的劈窗算法来进行地表温度的反演，最后用11个地面观测数据来验证其地表温度的反演精度。虽然Wang等（2019）已经开展了FY-3D极轨卫星的MERSI-II的地表温度反演，但很显然利用依赖于大气透过率的劈窗算法不单依赖于地表发射率参数，而且还需要估算对应的通道大气透过率，其较GSW算法而言使用条件相对更苛刻，对于业务化处理来说相对较复杂，此外，有限的地面观测数据也无法全面反映出地表温度产品反演的精度。 地表发射率是地表温度反演中的一个重要输入参数，发射率对地表温度反演的影响非常显著，对于温度为300 K左右的常温地表，0.01的发射率误差就会导致地表温度反演误差在1 K以上（ Becker，1987 Becker，1987 ）。地表发射率反演方法大致可分为3种类型：半经验算法、多通道温度发射率分离算法以及基于物理的反演算法（ Li等，2013 Li等，2013 ），其中半经验算法包括NDVI阈值法（ Sobrino和Raissouni，2000 Sobrino和Raissouni，2000 ； Jiménez-Muñoz等，2009 Jiménez-Muñoz等，2009 ）、分类赋值法（ Snyder等，1998 Snyder等，1998 ）和基于植被覆盖度的方法VCM（Vegetation Cover Method）（ Valor和Caselles，1996 Valor和Caselles，1996 ； Coll等， 2012 Coll等， 2012 ）等；多通道温度发射率分离算法包括灰体法（ Barducci和Pippi，1996 Barducci和Pippi，1996 ）、参考通道法（RCM）（ Kahle，1980 Kahle，1980 ）、ASTER的温度发射率分离算法（TES）（ Gillespie 等，1998 Gillespie 等，1998 ）、ISSTES（Iterative Spectrally Smooth Temperature Emissivity Separation）（ Borel，1997 Borel，1997 ， 2008 2008 ）、WTTES（Wavelet Transform Method for Separating Temperature and Emissivity）（ Zhang等，2017 Zhang等，2017 ）和LECTES（Linear Emissivity Constraint Temperature and Emissivity Separation）（ Wang等，2011 Wang等，2011 ）等；基于物理的反演算法包括温度无关光谱指数（TISI）（ Becker和Li，1990a Becker和Li，1990a ； Li等，2000 Li等，2000 ）、日夜算法（ Wan和Li，1997 Wan和Li，1997 ）和TSRM（the Two-Step physical Retrieval Method）（ Li等，2007 Li等，2007 ）等。相对而言，多通道温度发射率分离算法和基于物理的反演算法对于热红外传感器的通道数目等限制较多，半经验算法适用范围更广。然而，已有研究表明半经验算法在裸露地表误差较大，存在明显高估或者不能动态变化等问题（ 孟翔晨 等，2018 孟翔晨 等，2018 ）。 孟翔晨等（2016） 孟翔晨等（2016） 利用ASTER全球地表发射率产品（ASTER GED）和基于植被覆盖度的方法，提出了一个改进的地表发射率估算方法，取得了较好的结果，能够应用在分裂窗算法中（ 刘超 等，2017 刘超 等，2017 ； 孟翔晨 等，2018 孟翔晨 等，2018 ）。 基于以上考虑，本文旨在基于FY-3D/MERSI-II数据，构建GSW地表温度反演模型，利用FY-3D自身数据估算GSW模型所需的实时地表发射率和大气水汽含量参数，并以不同下垫面温度作为实测数据，验证地表温度的反演精度，结合详尽的敏感性分析，评估GSW模型用于业务化获取地表温度产品的潜力。 2　数据和研究区概况 1 2.1　FY-3D和MERSI-II介绍 2 风云三号（FY-3）气象卫星是中国第二代极轨气象卫星，目标是实现对全球大气和地球物理要素的全天候、多光谱、三维观测，主要向中期数值天气预报提供卫星观测数据，监测生态环境和大范围自然灾害；同时为全球环境变化、全球气候变化研究以及海洋、农业、林业、航空和军事等部门提供卫星气象信息（ 徐娜 等，2019 徐娜 等，2019 ）。FY-3 D星于2017-11-15在太原卫星发射中心发射成功，其搭载的中分辨率光谱成像仪II型（MERSI-II）是FY-3 D星的主要载荷之一，是世界上首台能够获取全球250 m分辨率红外劈窗区资料的成像仪器，观测天顶角在0°—69°之间，共配备25个通道，波段范围为0.412—12 <math id="M2"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642041&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642039&type= 5.16466665 3.38666677 ，包括16个可见光—近红外通道、3个短波红外通道和6个中长波红外通道；25个通道中，250 m地面分辨率通道6个，1000 m地面分辨率通道19个（ Tang等，2020 Tang等，2020 ）。如 表1 表1 所示，1—7通道主要用于陆地、云边界和特征遥感；8—15通道主要用于海洋水色、浮游生物和生物地球化学遥感；16、17、18、22和23通道用于大气水汽遥感；19通道是卷云波段；20、21、24和25通道用于陆地、水和云的温度遥感（ 朱爱军 等，2018 朱爱军 等，2018 ）。 主要用途 通道编号 中心波长/ <math id="M3"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642047&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642045&type= 3.97933316 2.62466669 空间分辨率/m 7 陆地、云边界和特征遥感 1 0.470 250 2 0.550 250 3 0.650 250 4 0.865 250 5 1.38 1000 6 1.64 1000 7 2.13 1000 8 海洋水色、浮游生物、生物地球化学遥感 8 0.412 1000 9 0.443 1000 10 0.490 1000 11 0.555 1000 12 0.670 1000 13 0.709 1000 14 0.746 1000 15 0.865 1000 3 大气水汽 16 0.905 1000 17 0.936 1000 18 0.940 1000 卷云 19 1.03 1000 2 陆、水、云温度 20 3.8 1000 21 4.050 1000 2 大气水汽 22 7.2 1000 23 8.550 1000 2 陆、水、云温度 24 10.8 250 25 12.0 250 基于传感器特点和通用劈窗算法特性，本次研究选择8个通道用于发展通用劈窗地表温度反演方法，其中24通道（10.8 <math id="M4"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642055&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642053&type= 5.16466665 3.38666677 ）和25通道（12 <math id="M5"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642061&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642058&type= 5.16466665 3.38666677 ）用于GSW地表温度反演，3通道（0.650 <math id="M6"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642068&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642066&type= 5.16466665 3.38666677 ）和4通道（0.865 <math id="M7"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642210&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642208&type= 5.16466665 3.38666677 ）提取归一化植被指数（NDVI）为发射率反演提供辅助数据，4（0.865 <math id="M8"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642210&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642208&type= 5.16466665 3.38666677 ）、16（0.905 <math id="M9"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642210&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642208&type= 5.16466665 3.38666677 ）、17（0.936 <math id="M10"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642210&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642208&type= 5.16466665 3.38666677 ）、18（0.940 <math id="M11"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642210&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642208&type= 5.16466665 3.38666677 ）通道估算大气水汽含量（WVC）。 图1 图1 展示了MERSI-II热红外波段（24/25）与MODIS热红外31通道（10.78—11.28 <math id="M12"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642210&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642208&type= 5.16466665 3.38666677 ）和32通道（11.77—12.27 <math id="M13"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642210&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642208&type= 5.16466665 3.38666677 ）的通道响应函数，可以看出MERSI-II和MODIS热红外通道波段范围相似并且中心波长相近。 2.2　ASTER GED数据 2 ASTER GED （Global Emissivity Dataset）是由美国国家航空航天局（NASA）发布的全球地表发射率数据集，包括ASTER GEDv3和ASTER GEDv4 两个版本（ Hulley等，2015 Hulley等，2015 ）。产品包括了ASTER传感器5个热红外波段发射率的平均值和标准差，地表温度的平均值和标准差，全球DEM，水体掩膜以及归一化植被指数（NDVI）的平均值和标准差，经纬度和观测次数。ASTER GED采用ASTER TES算法反演得到。ASTER GEDv3数据集利用2000年—2008年全球所有ASTER晴空数据拼接生产，采用1°×1°分幅，包括100 m和1 km两种空间分辨率的产品，发射率与NDVI均为多年平均值。ASTER GEDv4 提供2000年—2015年月度平均产品，分辨率为5 km。在本次研究中选用100 m空间分辨率的ASTER GEDv3数据集，其将用于混合像元内裸土的发射率估算。 2.3　研究区和地表温度实测数据介绍 2 为了验证通用劈窗算法反演地表温度的可用性，本次研究采用乌海实验站及SURFRAD的地表实测数据进行验证。 2.3.1　乌海实验站 3 乌海位于内蒙古西南部（106°39′ E， 39°52′ N），海拔大约1.12 km，属温带大陆性气候，多年平均气温9.6 ℃，年平均降水量159.8 mm。乌海实验站位于106.647°E，39.887°N。地表温度的观测架布设于沙地之上，其中观测架的高度约为4 m左右。同一个地表温度观测点，使用了两台SI-111红外辐射计进行目标和大气下行辐射亮温的观测，采样间隔为30 s。其中，大气下行辐射的观测采用53°天顶角倾斜向上的方式进行数据的采集（ Kondratyev，1969 Kondratyev，1969 ）。同时，在野外仪器布设之前，每台仪器均使用英国国家物理实验室NPL（National Physical Laboratory）黑体进行定标，绝对精度为±0.1 K，在实验室中有效发射率为0.9998。根据 Zhang等（2019） Zhang等（2019） 的研究，乌海站测量的地表温度不确定度小于0.8 K。乌海实验站已经被用于Landsat（ Yang等，2020 Yang等，2020 ）和Sentinel-3A（ Zhang等，2019 Zhang等，2019 ）等多种传感器地表温度反演结果的验证。 站点中总共配置5套仪器。由于数据传输问题，其中2套未获取有效数据，因此本次研究仅利用其中3套作为验证数据，分别命名为Station 1、Station 2和Station 3。 3.3.2　SURFRAD 3 SURFRAD（Surface Radiation Budget Network）建立于1993年，其目的是对美国地面辐射收支进行准确、连续和长期的测量（ Augustine等，2000 Augustine等，2000 ）。SURFRAD共计7个站点，每个站点每3 min（2009年之前）或每1 min（2009年之后）使用Eppley红外辐射计（Eppley Precision Infrared Radiometer），测量宽波段半球上行和下行辐射，不确定度为±5 <math id="M14"><mi mathvariant="normal">W</mi><mo>/</mo><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642099&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642097&type= 8.12800026 2.96333337 ，小于1 K（ Guillevic等，2014 Guillevic等，2014 ）。SURFRAD已经被用于ASTER（ Wang和Liang，2009 Wang和Liang，2009 ）和LANDSAT（ Duan等，2021 Duan等，2021 ）等地表温度产品的验证。考虑到由于三维结构、视场内地面异质性等原因，站点DRA、FPK以及TBL难以有效验证百米级空间分辨率地表温度产品（ Guillevic等， 2014 Guillevic等， 2014 ），而站点PSU在选定的日期内经常都存在有云的情况，因此本次研究使用站点BND（40.052°N，88.373°W）、GWN（34.255°N，89.873°W）和SXF（43.734°N，96.623°W）共3个站点对反演的地表温度进行精度验证。SURFRAD研究区观测仪器及其周边环境示意图如 图2 图2 所示。 （图片来源：Google Earth和NOAA Earth System Research Laboratory） 1;2;3; 2.3.3　空间异质性分析 3 为了评估地表异质性对地表温度验证产生的影响，本文参考其它学者的研究（ Coll等，2010 Coll等，2010 ； 孟翔晨 等，2018 孟翔晨 等，2018 ），以站点为中心，统计ASTER GED中的地表温度产品在3像元×3像元（300 m）尺度的标准差。以标准差作为异质性分析指标。得到结果如 表2 表2 所示。 注： 窗口大小3×3。 站点 标准差/K 乌海-Station 1 0.75 乌海-Station 2 0.32 乌海-Station 3 0.37 BND 0.27 GWN 0.39 SXF 1.84 乌海、BND和GWN标准差均小于1 K，说明这些站点下垫面较为均一；相比之下，SXF空间异质性较大，可作为参考数据，对MERSI-II反演地表温度进行验证。 3　地表温度劈窗建模 1 3.1　通用劈窗算法 2 在电磁波通过大气传输到卫星传感器的过程中，地表辐射会受到许多干扰，比如地表类型、土壤湿度、近地表气温和大气水汽含量。因此，准确量化地表温度和主要干扰因素之间的相互作用模式是反演地表温度的前提。根据辐射传输理论，在晴空大气条件下，大气层顶TOA（Top Of the Atmosphere）辐射亮温与地表温度的关系，在热红外波段可以定量表示为（ 赵英时，2013 赵英时，2013 ）： <math display="block" id="M15"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced><mo>=</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfenced><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">m</mi></mrow><mrow><mo>↑</mo></mrow></msubsup><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced><msub><mrow><mi>τ</mi></mrow><mrow><mi>i</mi></mrow></msub><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">m</mi></mrow><mrow><mo>↓</mo></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642130&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642127&type= 59.68999863 5.16466665 式中， <math id="M16"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642891&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642890&type= 9.14400005 5.16466665 表示遥感器通道 i 接收的热红外辐射亮度，其中 <math id="M17"><mi>B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642138&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642136&type= 2.28600001 2.62466669 表示普朗克黑体辐射定律， <math id="M18"><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642895&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642894&type= 2.79399991 3.72533321 表示大气层顶辐射亮温； <math id="M19"><msub><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642149&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642145&type= 9.39799976 5.16466665 表示地表物理温度为 <math id="M20"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642919&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642918&type= 2.96333337 3.72533321 （单位为K）时的普朗克黑体辐射亮度； <math id="M21"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642897&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642896&type= 2.70933342 3.72533321 是通道 i 的地表发射率； <math id="M22"><msub><mrow><mi>τ</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642165&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642162&type= 2.53999996 3.72533321 是从地面到遥感器的大气透过率； <math id="M23"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">m</mi></mrow><mrow><mo>↑</mo></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642171&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642168&type= 5.33400011 4.06400013 和 <math id="M24"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">m</mi></mrow><mrow><mo>↓</mo></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642177&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642174&type= 5.33400011 4.06400013 分别是通道 i 的大气上行辐射和下行辐射。 根据通用劈窗算法，考虑到10—13 <math id="M25"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642210&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642208&type= 5.16466665 3.38666677 大气窗口内，两个相邻通道对大气吸收作用的不同，可通过两个通道各种线性组合来剔除大气影响，即地表温度 <math id="M26"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642919&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642918&type= 2.96333337 3.72533321 可以表示为（ Wan和Dozier，1996 Wan和Dozier，1996 ）： <math display="block" id="M27"><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>+</mo><mfenced separators="|"><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mfrac><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi></mrow><mrow><mi>ε</mi></mrow></mfrac><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mfrac><mrow><mi mathvariant="normal">Δ</mi><mi>ε</mi></mrow><mrow><msup><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac></mrow></mfenced><mfrac><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mo>+</mo></mtd></mtr><mtr><mtd><mtext>          </mtext><mfenced separators="|"><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mfrac><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi></mrow><mrow><mi>ε</mi></mrow></mfrac><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub><mfrac><mrow><mi mathvariant="normal">Δ</mi><mi>ε</mi></mrow><mrow><msup><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac></mrow></mfenced><mfrac><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mrow><mrow><mi>ε</mi><mo>=</mo><mfenced separators="|"><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></mfenced></mrow><mo>/</mo><mrow><mn mathvariant="normal">2</mn></mrow></mrow></mtd></mtr><mtr><mtd><mi mathvariant="normal">Δ</mi><mi>ε</mi><mo>=</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>j</mi></mrow></msub></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642190&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642189&type= 67.73333740 33.61266708 式中， <math id="M28"><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642895&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642894&type= 2.79399991 3.72533321 与 <math id="M29"><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642772&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642771&type= 2.70933342 3.72533321 是传感器通道的大气层顶亮温，对于MERSI-II传感器， i 表示24波段（中心波长10.8 <math id="M30"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642207&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642204&type= 5.16466665 3.38666677 ）而 j 表示25波段（中心波长12.0 <math id="M31"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642210&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642208&type= 5.16466665 3.38666677 ）； <math id="M32"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642897&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642896&type= 2.70933342 3.72533321 和 <math id="M33"><msub><mrow><mi>ε</mi></mrow><mrow><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642219&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642217&type= 2.62466669 3.72533321 分别是 i 通道与 j 通道的地表发射率； <math id="M34"><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642592&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642591&type= 1.94733346 2.62466669 是两个通道发射率的地表发射率均值； <math id="M35"><mi mathvariant="normal">Δ</mi><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642603&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642601&type= 4.40266657 2.79399991 是地表发射率的差值； <math id="M36"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>-</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642847&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642846&type= 10.75266743 3.72533321 表示算法系数。 对于FY-3D/MERSI-II传感器，为了获取 式（2） 式（2） 中 <math id="M37"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>-</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642847&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642846&type= 10.75266743 3.72533321 的系数，切实可行的方法是使用大气辐射传输模型MODTRAN 5.2与MERIS-II热红外通道的通道响应函数进行数据模拟，借助模拟的大气层顶辐亮度数据来率定劈窗的系数。 考虑到算法应该适应全球大气变化，在本次研究中使用了TIGR大气廓线数据。由于热红外反演地表温度只适用于晴空大气条件，因此TIGR数据中相对湿度大于90%的大气廓线将被剔除，共从2311条廓线中选择了1413条大气廓线。 图3 图3 展示了大气廓线中大气水汽含量WVC随廓线第一边界层气温 <math id="M38"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642250&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642248&type= 3.21733332 3.72533321 的变化，其中 <math id="M39"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642250&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642248&type= 3.21733332 3.72533321 的变化范围是231—315 K，WVC变化范围是0.06—6.44 <math id="M40"><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642845&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642844&type= 8.12800026 3.72533321 。 通用劈窗算法系数获取需要考虑3方面因素：（1）大气层顶辐亮度随观测天顶角（VZA）变化而变化，因此将观测角分为10个不同观测角（0°、33.56°、44.42°、51.32°、56.25°、60°、62.96°、65.38°、67.38°、69.08°），针对不同观测角进行模拟；（2）为了使得模拟情况能更接近真实情况，更具代表性，我们对地表温度进行了扰动，将地表温度 <math id="M42"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642278&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642274&type= 2.96333337 3.72533321 设置如下：当廓线第一边界层气温 <math id="M43"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642300&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642298&type= 3.21733332 3.72533321 小于290 K，地表温度变化范围是 <math id="M44"><mo stretchy="false">[</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>-</mo><mn mathvariant="normal">5</mn><mi mathvariant="normal">K</mi><mo>,</mo><mtext> </mtext><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>+</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642291&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642287&type= 21.75933456 4.48733330 <math id="M45"><mn mathvariant="normal">5</mn><mi mathvariant="normal">K</mi><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642296&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642293&type= 5.92666674 3.38666677 ， 步长为5 K，当廓线第一边界层气温 <math id="M46"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642300&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642298&type= 3.21733332 3.72533321 大于290 K，地表温度变化范围是 <math id="M47"><mo stretchy="false">[</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>-</mo><mn mathvariant="normal">5</mn><mi mathvariant="normal">K</mi><mo>,</mo><mtext> </mtext><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>+</mo><mn mathvariant="normal">15</mn><mi mathvariant="normal">K</mi><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642303&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642302&type= 30.90333366 4.48733330 ，步长为5 K；（3）考虑到绝大部分地表覆盖面，平均发射率 <math id="M48"><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642307&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642305&type= 1.94733346 2.62466669 变化范围设置在0.9—1.0，步长为0.02，发射率差 <math id="M49"><mi mathvariant="normal">Δ</mi><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642311&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642309&type= 4.40266657 2.79399991 设置在0.025—0.015，步长为0.005。 经过以上设置，每个观测天顶角共模拟261090种情况。 3.2　发射率反演 2 根据植被覆盖度方法（VCM）（ Valor和Caselles，1996 Valor和Caselles，1996 ），地表发射率可以表示为： <math display="block" id="M50"><mi>ε</mi><mo>=</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>v</mi></mrow></msub><msub><mrow><mi>P</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>+</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><mi mathvariant="normal">d</mi><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642316&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642314&type= 40.47066879 4.57200003 式中， <math id="M51"><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642592&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642591&type= 1.94733346 2.62466669 是地表发射率； <math id="M52"><msub><mrow><mi>ε</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642351&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642349&type= 2.96333337 3.72533321 是植被发射率， <math id="M53"><msub><mrow><mi>ε</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642354&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642352&type= 2.79399991 3.72533321 是裸土发射率； <math id="M54"><msub><mrow><mi>P</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642338&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642334&type= 3.21733332 3.72533321 是植被覆盖度，可以根据NDVI计算得到（ Gutman和Ignatov，1998 Gutman和Ignatov，1998 ）； <math id="M55"><mi mathvariant="normal">d</mi><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642343&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642341&type= 3.80999994 2.70933342 表示腔体效应影响。 若不考虑植被与裸土之间的散射作用，可以将传感器像元发射率表示为植被和裸土两部分的加权和（ Cao等，2018 Cao等，2018 和2019； Jiménez-Muñoz 等，2009 Jiménez-Muñoz 等，2009 ； Duan等，2021 Duan等，2021 ）： <math display="block" id="M56"><mi>ε</mi><mo>=</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>v</mi></mrow></msub><msub><mrow><mi>P</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>+</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642348&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642346&type= 32.34266663 4.57200003 由于 <math id="M57"><msub><mrow><mi>ε</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642351&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642349&type= 2.96333337 3.72533321 比较稳定，可以直接由波谱库中的植被发射率计算得到，所以反演地表发射率的关键在于裸土发射率 <math id="M58"><msub><mrow><mi>ε</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642354&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642352&type= 2.79399991 3.72533321 。MERSI-II传感器24和25通道的土壤发射率，通过4步计算得到。 第1步，利用ASTER GED数据计算得到ASTER热红外通道的裸土发射率（ Hulley等，2015 Hulley等，2015 ； 孟翔晨 等，2016 孟翔晨 等，2016 ； 刘超 等，2017 刘超 等，2017 ）： <math display="block" id="M59"><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>s</mi><mi>i</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi></mrow></msubsup><mo>=</mo><mfrac><mrow><mfenced separators="|"><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>v</mi><mi>i</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi></mrow></msubsup><msubsup><mrow><mi>P</mi></mrow><mrow><mi>v</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msubsup><mrow><mi>P</mi></mrow><mrow><mi>v</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi></mrow></msubsup><mo stretchy="false">)</mo></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642357&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642356&type= 40.13199997 10.49866676 式中， <math id="M60"><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>s</mi><mi>i</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</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=19642361&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642359&type= 8.04333401 4.06400013 是 i 通道ASTER GED裸土发射率； <math id="M61"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642897&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642896&type= 2.70933342 3.72533321 是 i 通道发射率； <math id="M62"><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>v</mi><mi>i</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</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=19642367&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642365&type= 8.04333401 4.06400013 是 i 通道ASTER GED植被发射率；由ASTER波谱库中的各植被发射率波谱结合ASTER通道响应函数积分并取平均值得到； <math id="M63"><msubsup><mrow><mi>P</mi></mrow><mrow><mi>v</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</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=19642370&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642368&type= 8.29733276 4.06400013 是植被覆盖度，由ASTER GED中的多年平均NDVI计算得到。 第2步，通过波谱库计算MERSI-II和ASTER热红外通道的裸土发射率。用ASTER波谱库中的裸土发射率波谱分别结合MERSI-II 24和25波段通道响应函数与ASTER的13和14波段通道响应函数通过下式先计算通道发射率。 <math display="block" id="M64"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mfrac><mrow><msubsup><mo>∫</mo><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mrow><mi>f</mi></mrow><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced><mi>ε</mi><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced><msub><mrow><mi>B</mi></mrow><mrow><mi>λ</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfenced><mi>d</mi><mi>λ</mi></mrow><mrow><msubsup><mo>∫</mo><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></msubsup><mrow><mi>f</mi></mrow><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced><msub><mrow><mi>B</mi></mrow><mrow><mi>λ</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfenced><mi>d</mi><mi>λ</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642374&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642372&type= 42.41799927 15.23999977 式中， <math id="M65"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642897&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642896&type= 2.70933342 3.72533321 表示通道发射率； <math id="M66"><mi>f</mi><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642381&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642379&type= 7.19666624 3.80999994 是通道响应函数， <math id="M67"><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642385&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642383&type= 3.38666677 3.72533321 和 <math id="M68"><msub><mrow><mi>λ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642389&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642387&type= 3.38666677 3.72533321 分别表示通道响应的最小和最大波长； <math id="M69"><mi>ε</mi><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642392&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642390&type= 7.36600018 3.72533321 表示发射率波谱； <math id="M70"><msub><mrow><mi>B</mi></mrow><mrow><mi>λ</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642396&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642394&type= 9.90600014 5.16466665 表示温度为 <math id="M71"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642919&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642918&type= 2.96333337 3.72533321 时各波长的黑体辐亮度， <math id="M72"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642919&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642918&type= 2.96333337 3.72533321 可设置为300 K。 第3步，在第2步的基础上分别对MERSI-II 24波段与ASTER的13和14波段通道发射率和MERSI-II 25波段与ASTER的13和14波段通道发射率进行回归，得到传感器通道间裸土发射率的转换关系。 <math display="block" id="M73"><mfenced open="{" close="" separators="|"><mrow><mtable><mtr><mtd><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>s</mi><mn mathvariant="normal">24</mn></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">I</mi><mo>-</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">I</mi></mrow></msubsup><mo>=</mo><mo>-</mo><mn mathvariant="normal">0.0711</mn><mo>+</mo><mn mathvariant="normal">1.102</mn><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>s</mi><mn mathvariant="normal">13</mn></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi></mrow></msubsup><mo>-</mo><mn mathvariant="normal">0.029</mn><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>s</mi><mn mathvariant="normal">14</mn></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi></mrow></msubsup></mtd></mtr><mtr><mtd><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>s</mi><mn mathvariant="normal">25</mn></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">I</mi><mo>-</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">I</mi></mrow></msubsup><mo>=</mo><mn mathvariant="normal">0.339</mn><mo>-</mo><mn mathvariant="normal">0.408</mn><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>s</mi><mn mathvariant="normal">13</mn></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi></mrow></msubsup><mo>+</mo><mn mathvariant="normal">1.062</mn><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>s</mi><mn mathvariant="normal">14</mn></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi></mrow></msubsup></mtd></mtr></mtable><mtext>  </mtext></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642405&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642403&type= 72.72866058 8.29733276 式中， <math id="M74"><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>s</mi><mn mathvariant="normal">24</mn></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">I</mi><mo>-</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">I</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642409&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642407&type= 11.43000031 4.06400013 和 <math id="M75"><msubsup><mrow><mi>ε</mi></mrow><mrow><msub><mrow/><mrow><mi>s</mi><mn mathvariant="normal">25</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">I</mi><mo>-</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">I</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642413&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642411&type= 11.43000031 4.48733330 分别是MERSI-II传感器24波段和25波段裸土发射率， <math id="M76"><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>s</mi><mn mathvariant="normal">13</mn></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</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=19642417&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642415&type= 8.04333401 4.06400013 和 <math id="M77"><msubsup><mrow><mi>ε</mi></mrow><mrow><msub><mrow/><mrow><mi>s</mi><mn mathvariant="normal">14</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</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=19642422&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642420&type= 8.04333401 4.48733330 分别是ASTER 13和14波段裸土发射率。 式（7） 式（7） 的估算的发射率的RMSE为0.004。 第4步，根据 式（7） 式（7） 将第一步得到的ASTER通道裸土发射率转化为MERSI-II通道裸土发射率。在得到MERSI-II传感器24和25通道裸土发射率后，根据VCM方法计算24与25通道对应的地表发射率。 <math display="block" id="M78"><mtable columnalign="left"><mtr><mtd><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">I</mi><mo>-</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">I</mi></mrow></msubsup><mo>=</mo><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>v</mi><mi>i</mi></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">I</mi><mo>-</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">I</mi></mrow></msubsup><msubsup><mrow><mi>P</mi></mrow><mrow><mi>v</mi></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">I</mi><mo>-</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">I</mi></mrow></msubsup><mo>+</mo></mtd></mtr><mtr><mtd><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>s</mi><mi>i</mi></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">I</mi><mo>-</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">I</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msubsup><mrow><mi>P</mi></mrow><mrow><mi>v</mi></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">I</mi><mo>-</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">I</mi></mrow></msubsup><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642426&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642424&type= 48.00600052 9.31333351 式中， <math id="M79"><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">I</mi><mo>-</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">I</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642431&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642429&type= 11.43000031 4.06400013 是MERSI-II传感器 i 通道像元的发射率； <math id="M80"><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>v</mi><mi>i</mi></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">I</mi><mo>-</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">I</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642435&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642432&type= 11.43000031 4.06400013 是 i 通道植被发射率，可以根据ASTER波谱库中的植被发射率波谱与通道响应函数结合进行积分得到，其中 <math id="M81"><msubsup><mrow><mi>ε</mi></mrow><mrow><msub><mrow/><mrow><mi>v</mi><mn mathvariant="normal">24</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">I</mi><mo>-</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">I</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642443&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642441&type= 11.43000031 4.48733330 =0.982， <math id="M82"><msubsup><mrow><mi>ε</mi></mrow><mrow><msub><mrow/><mrow><mi>v</mi><mn mathvariant="normal">24</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">I</mi><mo>-</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">I</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642443&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642441&type= 11.43000031 4.48733330 =0.984； <math id="M83"><msubsup><mrow><mi>ε</mi></mrow><mrow><mi>s</mi><mi>i</mi></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">I</mi><mo>-</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">I</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642447&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642445&type= 11.43000031 4.06400013 是 i 通道裸土发射率； <math id="M84"><msubsup><mrow><mi>P</mi></mrow><mrow><msub><mrow/><mrow><mi>v</mi></mrow></msub></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">I</mi><mo>-</mo><mi mathvariant="normal">I</mi><mi mathvariant="normal">I</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642452&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642450&type= 11.76866722 4.48733330 是植被覆盖度，可以由NDVI计算得到，其中NDVI从MERSI-II传感器的红光波段（3通道）和近红外波段（4通道）中提取。 3.3　大气水汽含量估算 2 在比值法的基础上进行发展， Abbasi等（2020） Abbasi等（2020） 提出了一种适用于MERSI-II传感器的大气水汽含量反演方法（ Abbasi等，2020 Abbasi等，2020 ）。该方法的基础原理是通过MERSI-II传感器水汽吸收波段（16波段，0.905 μm；17波段，0.935 μm；18波段，0.940 μm）辐亮度与大气窗口波段（4波段，0.865 μm）辐亮度之比经过回归和加权平均得到大气水汽含量，即 <math display="block" id="M85"><mfenced open="{" close="" separators="|"><mrow><mtable><mtr><mtd><msub><mrow><mi>ω</mi></mrow><mrow><mn mathvariant="normal">16</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">27.298</mn><mo>-</mo><mn mathvariant="normal">61.336</mn><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">16</mn></mrow></msub><mo>+</mo><mn mathvariant="normal">34.754</mn><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">16</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></mtd></mtr><mtr><mtd><msub><mrow><mi>ω</mi></mrow><mrow><mn mathvariant="normal">17</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">7.723</mn><mo>-</mo><mn mathvariant="normal">27.945</mn><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">17</mn></mrow></msub><mo>+</mo><mn mathvariant="normal">26.136</mn><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">17</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mtext>  </mtext></mtd></mtr><mtr><mtd><msub><mrow><mi>ω</mi></mrow><mrow><mn mathvariant="normal">18</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">11.541</mn><mo>-</mo><mn mathvariant="normal">34.942</mn><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">18</mn></mrow></msub><mo>+</mo><mn mathvariant="normal">27.143</mn><msubsup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">18</mn></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642455&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642453&type= 58.92800140 13.20800018 式中， <math id="M86"><msub><mrow><mi>ω</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642459&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642457&type= 3.13266683 3.72533321 表示通过 i 通道的 <math id="M87"><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642465&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642463&type= 3.04800010 3.72533321 回归计算的大气水汽含量； <math id="M88"><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642465&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642463&type= 3.04800010 3.72533321 表示 i 通道与4通道辐亮度之比： <math display="block" id="M89"><mfenced open="{" close="" separators="|"><mrow><mtable><mtr><mtd><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">16</mn></mrow></msub><mo>=</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">16</mn></mrow></msub><mo>/</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">17</mn></mrow></msub><mo>=</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">17</mn></mrow></msub><mo>/</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">18</mn></mrow></msub><mo>=</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">18</mn></mrow></msub><mo>/</mo><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642468&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642467&type= 18.88066673 13.12333298 式中， <math id="M90"><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642471&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642469&type= 2.62466669 3.72533321 是 i 通道辐亮度。 由于大气水汽含量可以更精确的表示为3个水汽吸收通道的线性组和，因此，经过加权，大气水汽含量计算式可以写为： <math display="block" id="M91"><mi>ω</mi><mo>=</mo><mn mathvariant="normal">0.208</mn><msub><mrow><mi>ω</mi></mrow><mrow><mn mathvariant="normal">16</mn></mrow></msub><mo>+</mo><mn mathvariant="normal">0.433</mn><msub><mrow><mi>ω</mi></mrow><mrow><mn mathvariant="normal">17</mn></mrow></msub><mo>+</mo><mn mathvariant="normal">0.359</mn><msub><mrow><mi>ω</mi></mrow><mrow><mn mathvariant="normal">18</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642475&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642474&type= 54.86399841 3.80999994 4　研究结果与分析 1 4.1　劈窗系数的率定 2 想要获取适用于MERSI-II的算法系数，共分3步。第1步：针对不同观测天顶角和不同大气廓线，利用MODTRAN 5.2结合MERSI-II传感器热红外波段通道响应函数，得到大气参数上行辐亮度（ <math id="M92"><msubsup><mrow><mi>R</mi></mrow><mrow><mi>a</mi><mi>t</mi><mi>m</mi><mo>_</mo><mi>i</mi></mrow><mrow><mo>↑</mo></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642480&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642477&type= 6.94266701 4.06400013 和 <math id="M93"><msubsup><mrow><mi>R</mi></mrow><mrow><mi>a</mi><mi>t</mi><mi>m</mi><mo>_</mo><mi>j</mi></mrow><mrow><mo>↑</mo></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642483&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642481&type= 6.85799980 4.06400013 ）、大气下行辐亮度（ <math id="M94"><msubsup><mrow><mi>R</mi></mrow><mrow><mi>a</mi><mi>t</mi><mi>m</mi><mo>_</mo><mi>i</mi></mrow><mrow><mo>↓</mo></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642487&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642485&type= 6.94266701 4.06400013 和 <math id="M95"><msubsup><mrow><mi>R</mi></mrow><mrow><mi>a</mi><mi>t</mi><mi>m</mi><mo>_</mo><mi>j</mi></mrow><mrow><mo>↓</mo></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642492&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642489&type= 6.85799980 4.06400013 ）和大气透过率（ <math id="M96"><msub><mrow><mi>τ</mi></mrow><mrow><mi>λ</mi><mo>_</mo><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642495&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642493&type= 4.65666676 3.72533321 和 <math id="M97"><msub><mrow><mi>τ</mi></mrow><mrow><mi>λ</mi><mo>_</mo><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642499&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642498&type= 4.57200003 3.72533321 ）；第2步，结合地表温度 <math id="M98"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642919&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642918&type= 2.96333337 3.72533321 和地表发射率 <math id="M99"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642897&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642896&type= 2.70933342 3.72533321 根据 式（1） 式（1） ，获取不同情况下大气上层辐亮度 <math id="M100"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced><mtext> </mtext></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642508&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642506&type= 9.90600014 5.16466665 和 <math id="M101"><msub><mrow><mi>B</mi></mrow><mrow><mi>j</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642514&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642511&type= 8.89000034 5.16466665 ，并根据普朗克函数反函数，得到大气层顶亮温 <math id="M102"><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642895&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642894&type= 2.79399991 3.72533321 与 <math id="M103"><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642772&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642771&type= 2.70933342 3.72533321 ；第3步，根据 式（2） 式（2） ，将第2步得到的大气层顶亮温 <math id="M104"><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642895&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642894&type= 2.79399991 3.72533321 和 <math id="M105"><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642772&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642771&type= 2.70933342 3.72533321 与平均发射率 <math id="M106"><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642592&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642591&type= 1.94733346 2.62466669 、发射率差 <math id="M107"><mi mathvariant="normal">Δ</mi><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642603&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642601&type= 4.40266657 2.79399991 、地表温度 <math id="M108"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642919&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642918&type= 2.96333337 3.72533321 结合，进行回归得到系数 <math id="M109"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>-</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642847&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642846&type= 10.75266743 3.72533321 。 同时，为了更好地逼近线性表达，减小误差，通用劈窗算法采用分组的方式确定出多组系数。为了达到提高精度的目的，将地表温度、大气水汽含量、平均发射率分为几个含有重叠范围的连续子区（Wan和Dozier，996； Tang等，2008 Tang等，2008 ； 战川 等，2018 战川 等，2018 ）。地表温度 <math id="M110"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642919&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642918&type= 2.96333337 3.72533321 分为5组： <math id="M111"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>≤</mo><mn mathvariant="normal">280</mn><mtext> </mtext><mi mathvariant="normal">K</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642660&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642659&type= 16.34066582 3.80999994 ， <math id="M112"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">275</mn><mtext> </mtext><mi mathvariant="normal">K</mi><mo>,</mo><mn mathvariant="normal">295</mn><mtext> </mtext><mi mathvariant="normal">K</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642549&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642547&type= 21.92866707 3.89466691 ， <math id="M113"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">290</mn><mtext> </mtext><mi mathvariant="normal">K</mi><mo>,</mo><mn mathvariant="normal">310</mn><mtext> </mtext><mi mathvariant="normal">K</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642553&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642551&type= 22.26733208 3.89466691 ， <math id="M114"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">305</mn><mtext> </mtext><mi mathvariant="normal">K</mi><mo>,</mo><mn mathvariant="normal">325</mn><mtext> </mtext><mi mathvariant="normal">K</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642557&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642555&type= 21.92866707 3.89466691 ， <math id="M115"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>≥</mo><mn mathvariant="normal">320</mn><mtext> </mtext><mi mathvariant="normal">K</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642560&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642559&type= 16.34066582 3.80999994 ，重叠范围为5 K。将大气水汽含量WVC分为6组： <math id="M116"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0,1.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642565&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642562&type= 11.34533310 3.89466691 ， <math id="M117"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">1.0,2.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642569&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642567&type= 14.05466747 3.89466691 ， <math id="M118"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">2.0,3.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642572&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642571&type= 14.05466747 3.89466691 ， <math id="M119"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">3.0,4.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642576&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642574&type= 14.05466747 3.89466691 ， <math id="M120"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">4.0,5.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642580&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642578&type= 14.05466747 3.89466691 ， <math id="M121"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">5.0,6.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642584&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642583&type= 14.05466747 3.89466691 ，重叠范围为0.5 <math id="M122"><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642670&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642669&type= 8.89000034 3.72533321 。平均发射率 <math id="M123"><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642592&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642591&type= 1.94733346 2.62466669 分为两组： <math id="M124"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0.90,0.96</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642612&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642610&type= 17.78000069 3.89466691 和 <math id="M125"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0.94,1.0</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642615&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642613&type= 15.91733265 3.89466691 ，步长为0.002。发射率差 <math id="M126"><mi mathvariant="normal">Δ</mi><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642603&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642601&type= 4.40266657 2.79399991 在0.025—0.015，步长为0.005。 图4 图4 展示了地表温度 <math id="M127"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642919&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642918&type= 2.96333337 3.72533321 在290—310 K之间，大气水汽含量在0—1.5 <math id="M128"><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642845&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642844&type= 8.12800026 3.72533321 之间，平均地表发射率分别在 <math id="M129"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0.90,0.96</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642612&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642610&type= 17.78000069 3.89466691 和 <math id="M130"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0.94,1.0</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642615&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642613&type= 15.91733265 3.89466691 区间内，通用劈窗算法 <math id="M131"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>-</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642847&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642846&type= 10.75266743 3.72533321 随观测天顶角正割值的变化。从图中可以看出 <math id="M132"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>-</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642847&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642846&type= 10.75266743 3.72533321 都与1/cos（VZA）具有良好的线性关系，在其他子区内也有相似的结果，所以可以使用内插方法获取任一观测天顶角的算法系数 <math id="M133"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>-</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642847&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642846&type= 10.75266743 3.72533321 。 1,2; 在得到算法系数后，对经过数据预处理的实际卫星数据地表温度反演分4步进行。第1步，在已知发射率和大气水汽含量WVC的情况下，不对地表温度进行分组，仅确定发射率和大气水汽含量WVC的分组；第2步，从查找表中提取出该分组所有观测天顶角VZA情况下的系数 <math id="M140"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>-</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642847&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642846&type= 10.75266743 3.72533321 ，并根据像元实际的观测天顶角VZA的正割进行内插得到算法系数；第3步，利用 式（2） 式（2） 估算出地表温度LST的近似值，并根据LST近似值结合发射率和WVC重新选择分组，在此基础上，重复第2步得到算法系数；最后，利用 式（2） 式（2） 再次估算出更精确的LST。 图5 图5 给出了对于发射率不同的两组子区，实际地表温度 <math id="M141"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642919&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642918&type= 2.96333337 3.72533321 与估计的地表温度之间的均方根误差随观测天顶角VZA的正割值的变化。 由于地表温度越低，大气水汽含量WVC越小，所以当 <math id="M152"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>≤</mo><mn mathvariant="normal">280</mn><mtext> </mtext><mi mathvariant="normal">K</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642660&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642659&type= 16.34066582 3.80999994 时，WVC最大为2.5 <math id="M153"><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642670&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642669&type= 8.89000034 3.72533321 ，当 <math id="M154"><mn mathvariant="normal">275</mn><mtext> </mtext><mi mathvariant="normal">K</mi><mo>≤</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>≤</mo><mn mathvariant="normal">295</mn><mtext> </mtext><mi mathvariant="normal">K</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642667&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642664&type= 29.29466629 3.80999994 时，WVC最大为5.5 <math id="M155"><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642670&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642669&type= 8.89000034 3.72533321 。 从 图6 图6 可以看出，RMSE随着1/cos（VZA）的增大而增大，但较为干燥的天气里即WVC小于2.5 <math id="M156"><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642672&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642671&type= 8.89000034 3.72533321 时RMSE增加较少。除 图5（f） 图5（f） 外，当 ε <math id="M157"><mo>∈</mo><mtext> </mtext></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642674&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642673&type= 3.30200005 2.62466669 <math id="M158"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0.94,1.0</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642676&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642675&type= 17.78000069 3.89466691 ， <math id="M159"><mi mathvariant="normal">W</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">C</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">5.0</mn><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>,</mo><mn mathvariant="normal">6.0</mn><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642678&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642677&type= 45.12733078 4.57200003 ， <math id="M160"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">305</mn><mtext> </mtext><mi mathvariant="normal">K</mi><mo>,</mo><mn mathvariant="normal">325</mn><mtext> </mtext><mi mathvariant="normal">K</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642680&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642679&type= 31.41133499 4.14866638 （VZA =69°）时，有最大均方根误差，最大均方根误差为3.55 K。 与 图5（f） 图5（f） 相比， 图5（a） 图5（a） — 图5（d） 图5（d） 的均方根误差都有明显下降，这表明划分地表温度区间进行反演有利于降低RMSE误差并提高反演精度。对比同样使用GSW算法与TIGR大气廓线结合反演地表温度的FY-2C/S-VISSR（ Tang等，2008 Tang等，2008 ）的RMSE分布，本文具有相似性，但是由于传感器通道响应函数及观测角等原因略有区别。对于FY-2C/S-VISSR当VZA < 30°或VZA < 60°并且WVC < 3.5 <math id="M167"><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642700&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642699&type= 8.89000034 3.72533321 时，RMSE小于1 K（ Tang等，2008 Tang等，2008 ）；对于本文中的FY-3D/MERSI-II当观测天顶角小于30°并且WVC小于4.5 <math id="M168"><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642700&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642699&type= 8.89000034 3.72533321 时，均方根误差均小于1 K。 4.2　敏感性分析 2 参数的敏感性分析在算法的实现与实际应用中是十分重要的。通用劈窗算法反演地表温度的误差来源主要有3个：仪器噪声、地表发射率和大气效应（ Wan和Dozier，1996 Wan和Dozier，1996 ）。 4.2.1　仪器噪声敏感性分析 3 由于仪器噪声（ <math id="M169"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642949&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642948&type= 9.31333351 2.79399991 ）会被环境温度和仪器布局等因素影响，并且会随着仪器老化而增加，因此为了评估仪器噪声在地表温度反演过程中的影响参考 Tang等（2008） Tang等（2008） 的研究，分别将 <math id="M170"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642949&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642948&type= 9.31333351 2.79399991 =0.1 K、 <math id="M171"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642949&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642948&type= 9.31333351 2.79399991 =0.2 K和 <math id="M172"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642949&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642948&type= 9.31333351 2.79399991 =0.5 K作为高斯随机分布的标准差加入到 式（2） 式（2） 的大气层顶亮度温度 <math id="M173"><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642895&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642894&type= 2.79399991 3.72533321 、 <math id="M174"><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642772&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642771&type= 2.70933342 3.72533321 中，然后使用有仪器噪声的大气层顶亮温数据利用GSW算法反演地表温度。以子区 <math id="M175"><mi>ε</mi><mo>∈</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642714&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642713&type= 5.07999992 2.62466669 <math id="M176"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0.94,1.0</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642716&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642715&type= 15.91733265 3.89466691 ， <math id="M177"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">290</mn><mtext> </mtext><mi mathvariant="normal">K</mi><mo>,</mo><mn mathvariant="normal">310</mn><mtext> </mtext><mi mathvariant="normal">K</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642718&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642717&type= 29.80266571 4.14866638 为例，比较加入 <math id="M178"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642949&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642948&type= 9.31333351 2.79399991 前后反演地表温度的变化。当 <math id="M179"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642949&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642948&type= 9.31333351 2.79399991 =0.1 K，RMSE=0.36 K；当 <math id="M180"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642949&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642948&type= 9.31333351 2.79399991 =0.2 K，RMSE=0.40 K；当 <math id="M181"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642949&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642948&type= 9.31333351 2.79399991 =0.5 K，RMSE=0.62 K。对比 <math id="M182"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi><mo>=</mo><mn mathvariant="normal">0</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642728&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642727&type= 15.83266735 2.79399991 ，RMSE=0.34 K的情况下，当 <math id="M183"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642730&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642729&type= 9.31333351 2.79399991 分别等于0.1 K、0.2 K和0.5 K时，RMSE分别增加了0.02 K、0.06 K、0.28 K。 图6 图6 展示了实际LST和估计LST之差的直方图，在各个 <math id="M184"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642732&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642731&type= 9.31333351 2.79399991 下差值与频数均呈现较好的正态分布， <math id="M185"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi><mo>=</mo><mn mathvariant="normal">0</mn><mtext> </mtext><mi mathvariant="normal">K</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642734&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642733&type= 18.79599953 2.79399991 、 <math id="M186"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi><mo>=</mo><mn mathvariant="normal">0.1</mn><mtext> </mtext><mi mathvariant="normal">K</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642736&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642735&type= 21.25133324 2.79399991 、 <math id="M187"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi><mo>=</mo><mn mathvariant="normal">0.2</mn><mtext> </mtext><mi mathvariant="normal">K</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642738&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642737&type= 21.59000015 2.79399991 误差主要集中在0 K附近； <math id="M188"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi><mo>=</mo><mn mathvariant="normal">0.5</mn><mtext> </mtext><mi mathvariant="normal">K</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642740&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642739&type= 21.67466736 2.79399991 误差比较分散，但主要也分布在误差0 K左右。伴随着 <math id="M189"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642742&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642741&type= 9.31333351 2.79399991 的增大，集中在0 K附近的样本也逐渐减少。 4.2.2　地表发射率敏感性分析 3 基于热红外通道的反演算法对地表发射率（LSEs）十分敏感，地表发射率的微小改变也会对反演结果造成不同。在GSW算法中LSEs的不确定性主要取决于项 <math id="M190"><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi></mrow></mfenced><mo>/</mo><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642744&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642743&type= 14.13933277 3.80999994 和 <math id="M191"><mi mathvariant="normal">Δ</mi><mi>ε</mi><mo>/</mo><mfenced separators="|"><mrow><msup><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642746&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642745&type= 11.76866722 4.31799984 。根据 式（2） 式（2） ， <math id="M192"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642919&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642918&type= 2.96333337 3.72533321 可以表示成 <math id="M193"><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi></mrow></mfenced><mo>/</mo><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642819&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642818&type= 14.22399998 3.80999994 和 <math id="M194"><mi mathvariant="normal">Δ</mi><mi>ε</mi><mo>/</mo><mfenced separators="|"><mrow><msup><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642833&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642832&type= 11.76866722 4.31799984 的函数： <math display="block" id="M195"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mi>α</mi><mfrac><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi></mrow><mrow><mi>ε</mi></mrow></mfrac><mo>+</mo><mi>β</mi><mfrac><mrow><mi mathvariant="normal">Δ</mi><mi>ε</mi></mrow><mrow><msup><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac><mo>+</mo><mi>C</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642754&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642753&type= 37.76133347 8.04333401 <math display="block" id="M196"><mfenced open="{" close="" separators="|"><mrow><mtable><mtr><mtd><mi>α</mi><mo>=</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mfrac><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><mfrac><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mi>β</mi><mo>=</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mfrac><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub><mfrac><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642756&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642755&type= 41.90999985 18.88066673 式中， <math id="M197"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642794&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642793&type= 2.20133328 2.62466669 与 <math id="M198"><mi>β</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642796&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642795&type= 1.86266661 3.38666677 分别与 <math id="M199"><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi></mrow></mfenced><mo>/</mo><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642819&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642818&type= 14.22399998 3.80999994 和 <math id="M200"><mi mathvariant="normal">Δ</mi><mi>ε</mi><mo>/</mo><mfenced separators="|"><mrow><msup><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642833&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642832&type= 11.76866722 4.31799984 相关； C 是与发射率无关的量。 考虑两种极端情况：极端干燥大气条件（ <math id="M201"><mi mathvariant="normal">W</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">C</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0</mn><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>,</mo><mn mathvariant="normal">1.5</mn><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642766&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642765&type= 40.97866440 4.57200003 ）与极端湿润大气条件（ <math id="M202"><mi mathvariant="normal">W</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">C</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">5.0</mn><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>,</mo><mn mathvariant="normal">6.0</mn><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642768&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642767&type= 43.85733414 4.57200003 ）。利用 式（13） 式（13） 结合算法回归系数与模拟得到的大气层顶亮温 <math id="M203"><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642895&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642894&type= 2.79399991 3.72533321 和 <math id="M204"><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642772&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642771&type= 2.70933342 3.72533321 ，可以得到 <math id="M205"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642794&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642793&type= 2.20133328 2.62466669 和 <math id="M206"><mi>β</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642796&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642795&type= 1.86266661 3.38666677 的变化。在 <math id="M207"><mi>ε</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0.94,1.0</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642859&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642858&type= 22.18266678 3.89466691 ， <math id="M208"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">290</mn><mtext> </mtext><mi mathvariant="normal">K</mi><mo>,</mo><mn mathvariant="normal">310</mn><mtext> </mtext><mi mathvariant="normal">K</mi></mrow></mfenced><mfenced separators="|"><mrow><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi><mo>=</mo><mn mathvariant="normal">0</mn><mo>°</mo></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642780&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642779&type= 47.83666611 4.14866638 的条件下， <math id="M209"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642794&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642793&type= 2.20133328 2.62466669 和 <math id="M210"><mi>β</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642796&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642795&type= 1.86266661 3.38666677 的变化如 表2 表2 所示。 从 表3 表3 可以看出在极端干燥大气条件（ <math id="M211"><mi mathvariant="normal">W</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">C</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0,1.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642853&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642852&type= 23.53733444 3.89466691 ）下， <math id="M212"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642794&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642793&type= 2.20133328 2.62466669 的均值与 <math id="M213"><mi>β</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642796&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642795&type= 1.86266661 3.38666677 均值分别是极端湿润大气条件（ <math id="M214"><mi mathvariant="normal">W</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">C</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">5.0,6.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642792&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642791&type= 26.33133125 3.89466691 ）下 <math id="M215"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642794&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642793&type= 2.20133328 2.62466669 的均值的2倍， <math id="M216"><mi>β</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642796&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642795&type= 1.86266661 3.38666677 均值的3倍，这说明极端干燥大气条件相比于极端湿润大气条件来源于 <math id="M217"><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi></mrow></mfenced><mo>/</mo><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642819&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642818&type= 14.22399998 3.80999994 的误差增加了2倍，来源于 <math id="M218"><mi mathvariant="normal">Δ</mi><mi>ε</mi><mo>/</mo><mfenced separators="|"><mrow><msup><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642833&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642832&type= 11.76866722 4.31799984 的误差增加了3倍。 注： <math id="M225"><mi mathvariant="normal">L</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">290</mn><mtext> </mtext><mi mathvariant="normal">K</mi><mo>,</mo><mn mathvariant="normal">310</mn><mtext> </mtext><mi mathvariant="normal">K</mi></mrow></mfenced><mo>,</mo><mi>ε</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0.94,1.0</mn></mrow></mfenced><mo>,</mo><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi><mo>=</mo><mn mathvariant="normal">0</mn><mo>°</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642817&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642816&type= 56.38800049 2.96333337 。 2 变量 2 干燥条件 <math id="M219"><mi mathvariant="normal">W</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">C</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn>0,1.5</mn><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642803&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642802&type= 24.55333328 3.72533321 2 湿润条件 <math id="M220"><mi mathvariant="normal">W</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">C</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn>5.0</mn><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mn>6.5</mn><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642805&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642804&type= 33.52799988 3.72533321 <math id="M221"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642811&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642810&type= 1.69333339 2.03200006 <math id="M222"><mi>β</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642813&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642812&type= 1.43933344 2.53999996 <math id="M223"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642811&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642810&type= 1.69333339 2.03200006 <math id="M224"><mi>β</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642813&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642812&type= 1.43933344 2.53999996 范围/K 46.05—55.97 -100.95—-90.97 12.05—31.43 -45.46—-6.47 均值/K 50.65 -95.44 22.49 -27.73 标准差/K 1.91 2.15 3.53 6.99 根据 式（2） 式（2） ，由于项 <math id="M226"><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi></mrow></mfenced><mo>/</mo><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642819&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642818&type= 14.22399998 3.80999994 和 <math id="M227"><mi mathvariant="normal">Δ</mi><mi>ε</mi><mo>/</mo><mfenced separators="|"><mrow><msup><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642833&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642832&type= 11.76866722 4.31799984 的不确定性引起的地表温度的反演误差 <math id="M228"><mi>δ</mi><mi mathvariant="normal">L</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642823&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642822&type= 7.53533268 2.70933342 可以表示为 <math display="block" id="M229"><mi>δ</mi><mi mathvariant="normal">L</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi><mo>=</mo><mroot><mrow><msup><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>δ</mi><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi></mrow></mfenced></mrow><mrow><mi>ε</mi></mrow></mfrac></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi>δ</mi><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mi mathvariant="normal">Δ</mi><mi>ε</mi></mrow><mrow><msup><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642825&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642824&type= 56.98066711 11.43000031 式中， <math id="M230"><mi>δ</mi><mfenced separators="|"><mrow><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi></mrow></mfenced><mo>/</mo><mi>ε</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642827&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642826&type= 19.13466644 4.57200003 和 <math id="M231"><mi>δ</mi><mfenced separators="|"><mrow><mi mathvariant="normal">Δ</mi><mi>ε</mi><mo>/</mo><msup><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642829&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642828&type= 13.37733269 4.31799984 分别是 <math id="M232"><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi></mrow></mfenced><mo>/</mo><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642831&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642830&type= 14.22399998 3.80999994 和 <math id="M233"><mi mathvariant="normal">Δ</mi><mi>ε</mi><mo>/</mo><mfenced separators="|"><mrow><msup><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642833&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642832&type= 11.76866722 4.31799984 的不确定度。 假设不确定度 <math id="M234"><mi>δ</mi><mfenced separators="|"><mrow><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi></mrow></mfenced><mo>/</mo><mi>ε</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642835&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642834&type= 19.30400085 4.57200003 与 <math id="M235"><mi>δ</mi><mfenced separators="|"><mrow><mi mathvariant="normal">Δ</mi><mi>ε</mi><mo>/</mo><msup><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642837&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642836&type= 13.37733269 4.31799984 均为1%，那么在极端干燥大气条件下，地表温度的反演误差 <math id="M236"><mi>δ</mi><mi mathvariant="normal">L</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">1.0</mn><mtext> </mtext><mi mathvariant="normal">K</mi><mo>,</mo><mn mathvariant="normal">1.2</mn><mtext> </mtext><mi mathvariant="normal">K</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642839&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642838&type= 32.42733002 3.89466691 ，均值为1.08 K；在极端湿润大气条件下，地表温度的误差 <math id="M237"><mi>δ</mi><mi mathvariant="normal">L</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi><mo>∈</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642841&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642840&type= 10.75266743 2.70933342 <math id="M238"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0.1</mn><mtext> </mtext><mi mathvariant="normal">K</mi><mo>,</mo><mn mathvariant="normal">0.6</mn><mtext> </mtext><mi mathvariant="normal">K</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642843&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642842&type= 20.06599998 3.89466691 ，均值为0.36 K。 4.2.3　大气水汽含量敏感性分析 3 利用卫星资料获取大气水汽含量依然是十分困难的。在本次研究中，使用对大气水汽含量进行错误分组的方式，来确定大气水汽含量的不确定性对通用劈窗算法反演地表温度的影响。在4.1节中，将大气水汽含量分为了6个部分重叠的区间，每个区间的重叠范围是0.5 <math id="M239"><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642845&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642844&type= 8.12800026 3.72533321 。这意味着重叠范围内的大气水汽含量可以被分到两个相邻区间内，即重叠范围内的大气水汽含量对应着两组不同的系数 <math id="M240"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>-</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642847&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642846&type= 10.75266743 3.72533321 。所以可以通过分析重叠范围内的大气水汽含量来定量评价大气水汽含量的不确定性的影响。 如 图7 图7 所示，以 <math id="M241"><mi mathvariant="normal">W</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">C</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">1.0,1.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642851&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642850&type= 26.33133125 3.89466691 为例， <math id="M242"><mi mathvariant="normal">W</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">C</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">1.0,1.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642851&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642850&type= 26.33133125 3.89466691 可以划分到 <math id="M243"><mi mathvariant="normal">W</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">C</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0,1.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642853&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642852&type= 23.53733444 3.89466691 ，也可以被划分到 <math id="M244"><mi mathvariant="normal">W</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">C</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">1.0,2.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642871&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642870&type= 26.33133125 3.89466691 。在 <math id="M245"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">290,310</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642857&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642856&type= 23.53733444 4.14866638 ， <math id="M246"><mi>ε</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0.94,1.0</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642859&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642858&type= 22.18266678 3.89466691 <math id="M247"><mfenced separators="|"><mrow><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi><mo>=</mo><mn mathvariant="normal">0</mn><mo>°</mo></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642861&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642860&type= 17.35666656 3.80999994 子区，当使用 <math id="M248"><mi mathvariant="normal">W</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">C</mi><mo>∈</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642863&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642862&type= 10.75266743 2.70933342 <math id="M249"><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0,1.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642865&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642864&type= 13.20800018 3.89466691 条件下的系数时，RMSE=0.56 K；当使用 <math id="M250"><mi mathvariant="normal">W</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">C</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">1.0,2.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642871&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642870&type= 26.33133125 3.89466691 条件下的系数时，RMSE=0.66 K。若WVC分组正确， <math id="M251"><mi mathvariant="normal">W</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">C</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0,1.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642869&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642868&type= 23.11400032 3.89466691 时，RMSE=0.21 K， <math id="M252"><mi mathvariant="normal">W</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">C</mi><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">1.0,2.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642871&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642870&type= 26.33133125 3.89466691 时，RMSE=0.32 K，即当对WVC进行错误分组后，RMSE分别增加了0.35 K和0.24 K，被错分到低WVC组时RMSE增加更多。 1,2; 4.3　地表温度的真实性检验 2 4.3.1　地表实测数据的处理 3 对于乌海实验站，SI-111测量的离地地表辐亮度可以表示为下式： <math display="block" id="M257"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced><mo>=</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfenced><mo>+</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced><mi>R</mi><mo>↓</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642889&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642888&type= 49.19132996 5.16466665 式中， <math id="M258"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642891&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642890&type= 9.14400005 5.16466665 表示观测辐亮度，其中， <math id="M259"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642893&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642892&type= 3.04800010 3.72533321 是普朗克函数， <math id="M260"><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642895&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642894&type= 2.79399991 3.72533321 表示测量的辐射亮温； <math id="M261"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642897&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642896&type= 2.70933342 3.72533321 为SI-111通道地物发射率； <math id="M262"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642919&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642918&type= 2.96333337 3.72533321 表示地表温度； <math id="M263"><mi>R</mi><mo>↓</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642909&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642908&type= 7.19666624 3.72533321 表示大气下行辐亮度，由同时布设的天顶角为53°的SI-111辐射计获取。 对于SI-111宽波段辐亮度 <math id="M264"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642903&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642902&type= 8.38199997 4.06400013 可以用亮温 T 的二次函数表示，即： <math display="block" id="M265"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced><mo>=</mo><mn mathvariant="normal">28.773</mn><mo>-</mo><mn mathvariant="normal">0.278</mn><mi>T</mi><mo>+</mo><mn mathvariant="normal">7.125</mn><mo>×</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msup><msup><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642905&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642904&type= 62.06066895 4.06400013 利用站点观测的离地辐亮度 <math id="M266"><msub><mrow><mi>B</mi></mrow><mrow><mi>λ</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642907&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642906&type= 9.73666668 5.16466665 与大气下行辐亮度 <math id="M267"><mi>R</mi><mo>↓</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642909&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642908&type= 7.19666624 3.72533321 ，通过 式（15） 式（15） 估算目标对应的黑体辐亮度 <math id="M268"><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642911&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642910&type= 9.22866726 5.16466665 ，而后通过 式（16） 式（16） 的反函数估算地表温度 <math id="M269"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642919&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642918&type= 2.96333337 3.72533321 。 式（15） 式（15） 中的光谱发射率由实地测量沙地的光谱发射率得到，计算通道发射率也需要结合SI-111的通道响应函数： <math display="block" id="M270"><mi>ε</mi><mo>=</mo><mfrac><mrow><mo>∑</mo><mi>f</mi><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced><mi>ε</mi><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced><mi>B</mi><mfenced separators="|"><mrow><mi>λ</mi><mo>,</mo><mi>T</mi></mrow></mfenced><mi>d</mi><mi>λ</mi></mrow><mrow><mo>∑</mo><mi>f</mi><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced><mi>B</mi><mfenced separators="|"><mrow><mi>λ</mi><mo>,</mo><mi>T</mi></mrow></mfenced><mi>d</mi><mi>λ</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642915&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642914&type= 42.24866486 9.82133293 式中，计算时假定温度 T =300 K。 对于SURFRAD站点实测数据，地表温度可以用斯特藩—玻尔兹曼定律表示为： <math display="block" id="M271"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>F</mi></mrow><mrow><mi>u</mi></mrow></msub><mo>-</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>b</mi></mrow></msub><mo stretchy="false">)</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow><mrow><mi>σ</mi><msub><mrow><mi>ε</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></mfrac></mrow></mfenced></mrow><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">4</mn></mrow></mfrac></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642917&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642916&type= 35.64466476 12.19200039 式中， <math id="M272"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642919&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642918&type= 2.96333337 3.72533321 表示地表温度； <math id="M273"><msub><mrow><mi>F</mi></mrow><mrow><mi>u</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642921&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642920&type= 3.47133350 3.72533321 和 <math id="M274"><msub><mrow><mi>F</mi></mrow><mrow><mi>d</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642923&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642922&type= 3.47133350 3.72533321 表示上行辐射和下行辐射； <math id="M275"><mi>σ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642925&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642924&type= 2.45533323 2.62466669 表示斯特藩-玻尔兹曼常数（ <math id="M276"><mn mathvariant="normal">5.67</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">8</mn></mrow></msup><mtext> </mtext><mi mathvariant="normal">W</mi><mo>/</mo><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>/</mo><msup><mrow><mi mathvariant="normal">K</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642927&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642926&type= 30.98800087 2.96333337 ）； <math id="M277"><msub><mrow><mi>ε</mi></mrow><mrow><mi>b</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642929&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642928&type= 3.04800010 3.72533321 是地表宽波段发射率，可以利用ASTER GED产品计算得到（Cheng等，2013）： <math display="block" id="M278"><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>ε</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">0.197</mn><msub><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">10</mn></mrow></msub><mo>+</mo><mn mathvariant="normal">0.025</mn><msub><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">10</mn></mrow></msub><mo>+</mo><mn mathvariant="normal">0.057</mn><msub><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">11</mn></mrow></msub><mo>+</mo></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.237</mn><msub><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub><mo>+</mo><mn mathvariant="normal">0.333</mn><msub><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">13</mn></mrow></msub><mo>+</mo><mn mathvariant="normal">0.146</mn><msub><mrow><mi>ε</mi></mrow><mrow><mn mathvariant="normal">14</mn></mrow></msub></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642931&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642930&type= 57.91199875 8.29733276 4.3.2　地表温度反演结果的比对分析 3 为了较全面的进行地表温度的真实性检验，本次研究选择2019-08的MERSI-II数据进行分析，进行日间地表温度反演，以验证地表温度反演结果的准确性，结果如 表4 表4 所示，在白天MERSI-II反演地表温度RMSE在1.55—2.56 K，除BND站点外，其它站点RMSE均小于1.6 K，且与NDVI的变化无关，所有站点的Bias都比较小，达到了预期目标。 站点 个数 NDVI RMSE/K Bias/K BND 5 0.71 2.56 0.19 GWN 9 0.6 1.53 -0.59 SXF 7 0.67 1.58 0.03 乌海 42 0.11 1.55 0.10 图8 图8 是实测数据与MERSI-II反演数据的散点图。 4.4　地表温度的反演实例 2 图9 图9 给出了2019-08-29北京时间14：25 FY-3D卫星扫描中国内蒙古自治区乌海周边反演LST的实例。模型输入是通道亮温、地表发射率、大气水汽含量和观测天顶角。通道亮温与观测天顶角直接从FY-3D卫星数据中提取。使用VCM方法计算地表发射率，其中，NDVI来源于MERSI-II传感器3和4通道表观反射率数据，裸土发射率从ASTER GED产品中提取，并由MERSI-II 24和25波段与ASTER的13和14波段裸土发射率间的转换关系转换而来；大气水汽含量使用Abbasi和Qin提出的适用于MERSI-II传感器的大气水汽含量反演方法进行估算。与真彩色遥感影像对比，发现在裸土和城市地区温度高；农田与山地等植被覆盖地表以及水体区域温度低。 5　结论 1 利用 Wan和Dozier（1996） Wan和Dozier（1996） 提出的GSW算法，解决了从世界上首台能够获取全球250 m空间分辨率FY-3D/MERSI-II传感器的两个热红外通道：24通道（10.3—11.3 <math id="M279"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642941&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642940&type= 5.16466665 3.38666677 ）和25通道（11.5—12.5 <math id="M280"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642943&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642942&type= 5.16466665 3.38666677 ）数据中反演地表温度的问题。为了能够直接从MERIS-II传感器直接反演地表温度，本文使用VCM方法计算地表发射率，其中，NDVI来源于与热红外通道同步观测的MERSI-II传感器3和4通道表观反射率数据，裸土发射率从ASTER GED产品中提取，并由MERSI-II 24和25波段与ASTER的13和14波段裸土发射率间的转换关系转换而来。同时，采用 Abbasi等（2020） Abbasi等（2020） 提出的适用于MERSI-II传感器的大气水汽含量反演方法用于估算大气水汽含量。利用2019-08期间的反演结果与地表同步实测数据进行对比，结果显示，RMSE在1.6—2.6 K之间，表明基于通用劈窗算法反演的250 m的地表温度精度较高。同时也说明FY-3D/MERSI-II目前辐射定标精度可以满足地表温度反演的需要，并不需要与 Wang等（2019b） Wang等（2019b） 一样先进行交叉辐射定标。由于MODIS和MERSI-II的空间分辨率不一致，而地面实测站点获取的地表温度的空间代表性也不同，地表热不均匀性及卫星传感器与实测站点传感器间的几何差异也会导致两者反演的地表温度真实性检验的结果存在差异（ Duan等，2019 Duan等，2019 b），此外，受条件限制，验证的数据量有限，因此当前无法有效评价两者的差别以及优劣，后续还需进一步开展相关的深入研究。总的说来，基于较高空间分辨率的MERSI-II数据，实现了地表温度较高精度的反演，达到了预期目标。 在本文的研究中，在发射率已知的情况下，对比实际地表温度与估计的地表温度，结果显示当观测天顶角小于30°并且WVC小于4.5 <math id="M281"><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642945&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642944&type= 8.12800026 3.72533321 时，均方根误差均小于1 K；对划分地表温度区间进行反演有利于降低误差并提高反演精度。其次，对仪器噪声、地表发射率和大气效应进行敏感性分析，分析结果表明， <math id="M282"><mtext> </mtext><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642947&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642946&type= 10.07533360 2.79399991 对于地表温度反演具有显著影响，当 <math id="M283"><mi>N</mi><mi>E</mi><mi mathvariant="normal">Δ</mi><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642949&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642948&type= 9.31333351 2.79399991 分别等于0.1 K、0.2 K和0.5 K时，RMSE分别增大了0.02 K、0.06 K和0.28 K；相比于湿润地表，干燥地表对地表发射率更为敏感，不确定度为1%时，对于湿润地表RMSE=0.36 K，对于干燥地表RMSE=1.08 K；对WVC敏感性分析表明，当对WVC进行错误分组时，被分到低WVC组和高WVC组RMSE分别增加了0.35 K和0.24 K。最后，采用地面实测数据与反演温度进行对比验证。验证结果表明，利用GSW算法与MERSI-II自身数据估算实时地表发射率和大气水汽含量参数反演高精度地表温度产品，为业务化运行提供了技术支撑。 虽然取得了较好的反演结果，但是本次研究仍有不足。由于VCM方法获取地表发射率需要NDVI数据，但是在夜晚这个条件无法实现，因此造成此方法只能在日间反演地表温度，下一步应该寻找一种能在夜间提取高精度地表发射率的方法。其次，此次研究只使用了4个站点用于评估精度，对于全球地表温度反演研究这是远远不够的，有必要在进一步研究中使用全球多个站点数据更加广泛地验证。 参考文献（References） Abbasi B , Qin Z H , Du W H , Fan J L , Zhao C L , Hang Q Y , Zhao S H and Li S F . 2020 . 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National Remote Sensing Bulletin， 25（8）：1792-1807 Cheng Y L，Wu H，Li Z L and Qian Y G. 2021. Retrieval and validation of the land surface temperature from FY-3D MERSI-II. National Remote Sensing Bulletin， 25（8）：1792-1807 国家重点研发计划（编号：2016YFB0500400）； 国家自然科学基金（编号： 41871267， 42071331） Supported by National Key Research and Development Program of China (No. 2016YFB0500400)； National Natural Science Foundation of China (No.418711267, 42071331) 2021-05-10 2021-08-07 2021-09-09 2021-07-17 遥感学报 8 25