耦合地表方向反射特性的城市地区气溶胶光学厚度遥感反演

田信鹏; 高志强; 刘强; 王德; 王跃启

doi:10.11834/jrs.20210217

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耦合地表方向反射特性的城市地区气溶胶光学厚度遥感反演
Retrieval of aerosol optical depth over urban area by coupling the characteristics of surface directional reflection
2022年26卷第11期页码：2219-2233
纸质出版日期： 2022-11-07 ，
DOI： 10.11834/jrs.20210217

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引用
田信鹏，高志强，刘强，王德，王跃启.2022.耦合地表方向反射特性的城市地区气溶胶光学厚度遥感反演.遥感学报，26（11）： 2219-2233

Tian X P，Gao Z Q，Liu Q，Wang D and Wang Y Q. 2022. Retrieval of aerosol optical depth over urban area by coupling the characteristics of surface directional reflection. National Remote Sensing Bulletin， 26（11）：2219-2233
田信鹏，高志强，刘强，王德，王跃启.2022.耦合地表方向反射特性的城市地区气溶胶光学厚度遥感反演.遥感学报，26（11）： 2219-2233 DOI： 10.11834/jrs.20210217.

Tian X P，Gao Z Q，Liu Q，Wang D and Wang Y Q. 2022. Retrieval of aerosol optical depth over urban area by coupling the characteristics of surface directional reflection. National Remote Sensing Bulletin， 26（11）：2219-2233 DOI： 10.11834/jrs.20210217.

耦合地表方向反射特性的城市地区气溶胶光学厚度遥感反演 Retrieval of aerosol optical depth over urban area by coupling the characteristics of surface directional reflection 1 2 first-author 田信鹏，研究方向为大气环境遥感。E-mail： xptian@yic.ac.cn 田信鹏，研究方向为大气环境遥感。E-mail： xptian@yic.ac.cn xptian@yic.ac.cn 1 2 corresp 高志强，研究方向为定量遥感、海岸带遥感应用等。E-mail： zqgao@yic.ac.cn 高志强，研究方向为定量遥感、海岸带遥感应用等。E-mail： zqgao@yic.ac.cn zqgao@yic.ac.cn 3 1 2 1 2 中国科学院烟台海岸带研究所海岸带环境过程与生态修复重点实验室, 烟台 264003 中国科学院烟台海岸带研究所海岸带环境过程与生态修复重点实验室, 烟台 264003 CAS Key Laboratory of Coastal Environmental Processes and Ecological Remediation, Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, Yantai 264003, China CAS Key Laboratory of Coastal Environmental Processes and Ecological Remediation, Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, Yantai 264003, China 中国科学院烟台海岸带研究所山东省海岸带环境过程重点实验室, 烟台 264003 中国科学院烟台海岸带研究所山东省海岸带环境过程重点实验室, 烟台 264003 Shandong Key Laboratory of Coastal Environmental Processes, Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, Yantai 264003, China Shandong Key Laboratory of Coastal Environmental Processes, Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, Yantai 264003, China 鹏成国家实验室, 深圳 518055 鹏成国家实验室, 深圳 518055 Peng Cheng Laboratory, Shenzhen 518055, China Peng Cheng Laboratory, Shenzhen 518055, China 地气分离是气溶胶光学厚度AOD（Aerosol Optical Depth）卫星遥感反演中的难点之一，当前大多反演算法一般将地表假定为朗伯体，这使得反演结果在城市等高异质地区具有较大的不确定性。本文利用长时间序列MODIS BRDF/Abledo产品，通过离散余弦变换的惩罚最小二乘估计时空滤波算法构建了地表BRDF形状因子先验数据集。通过耦合考虑地表各向异性反射特性的辐射传输前向模型及半经验核驱动模型，以先验数据集为驱动进行地表参数估算，实现考虑地表BRDF效应的气溶胶遥感反演。基于该算法，以北京为研究区开展了Landsat 8 OLI传感器反演实验，并使用AERONET地基观测数据及与朗伯假设和地表反射率数据库支持反演进行交叉对比，结果表明，新算法在城市/植被地区的反演点对在期望误差线内比重为84.6%/86.0%，可以有效改善朗伯假设对AOD的高估。通过与MODIS气溶胶产品（MOD04/MCD19A2）对比，新算法获取的AOD与AERONET观测值具有更高的一致性，城市站点反演结果在误差线内占比较DT、DB、DTDB及MAIAC产品分别提高了46.8%、13.9%、14.7%及4.4%，且有效对比点数高于MODIS产品。新算法可以获取500 m空间分辨AOD，能提供空间更为连续的气溶胶细节信息，显示了在支持区域污染精细管控及污染物溯源等领域的应用潜力。 Aerosols play an important role in determining the Earth's radiation budget and its impact on climate change. Aerosol optical depth (AOD) is a crucial fundamental parameter for meteorological observation and a basic optical property of aerosol derived from satellites. Over land, the aerosol contribution in satellite signals is small compared with the surface, making it difficult to separate the aerosol path radiance from satellite measurements, particularly over the urban area. In the past several decades, numerous different AOD retrieval algorithms have been proposed by using different satellite sensors, but most of them do not consider surface anisotropy. The main purpose of this work is to improve the accuracy of aerosol retrievals and reduce the uncertainty of the operational MODIS AOD products over mixed surfaces. On this basis, a new generic high-performance aerosol retrieval algorithm is presented and explained. The new method is developed by coupling the non-Lambertian atmospheric radiative transfer model and semiempirical linear kernel-driven BRDF model. First, an a priori surface BRDF shape parameter database is constructed using the daily MODIS BRDF/Albedo product by using penalized least square regression based on a 3D discrete cosine transform (DCT-PLS) method. Then, the estimation of surface reflectance, including bidirectional reflectance, directional to hemispheric reflectance, hemispheric to directional reflectance, and bi-hemispheric reflectance (also called white-sky albedo, WSA), is based on this database and kernel-driven BRDF model. The presented method is tested on the Landsat 8 OLI images around the Beijing area, which features highly heterogeneous surfaces and severe air pollution problems. AOD retrievals with 500 m resolution can be successfully obtained over dark and bright surfaces. An accuracy assessment of the new algorithm, WSA-derived and HARLS AOD retrievals against AERONET AOD, from the four selected stations indicated the superiority of new algorithm, which is reflected in the high PWE and low RMSE. The comparison results show that the new algorithm is in good agreement with ground-based AOD (R=0.911) compared with the WSA-derived and HARLS AOD retrievals. Furthermore, the new algorithm and MODIS aerosol algorithms have similar spatial patterns of AOD. The new algorithm significantly improves the accuracy of aerosol retrievals, which is verified by AERONET AOD data, especially over brighter surfaces, because surface anisotropy is considered in this algorithm. The new algorithm can provide a detailed AOD spatial distribution over mixed surfaces and shows high ability in capturing fine-scale features. The new algorithm and MAIAC AOD retrievals have a similar spread of uncertainty envelopes. However, the new algorithm AOD retrievals have a higher correlation and smaller RMSE than the MAIAC retrievals, and the number of collections with AERONET for the new algorithm is almost 1.5 times those for MAIAC. This new AOD retrieval algorithm can provide a possibility for high-precision urban aerosol remote sensing monitoring and solve other pressing issues, such as long-term trend analysis of urban aerosols and air quality conditions, especially in heavily polluted areas. Based on the collocated observations, the new algorithm achieved satisfactory retrieval accuracy. However, several issues remain to be solved in the future. First, the retrieval errors of the MODIS BRDF kernel parameters are also a major source of uncertainty. Second, more analyses of the aerosol models and model selection are required. Third, the application in other regions and sensors is required in further work to evaluate the applicability of new algorithm. 气溶胶光学厚度地表方向反射核驱动模型 MODIS Landsat 8 OLI aerosol optical depth surface anisotropy kernel-driven BRDF model MODIS Landsat 8 OLI 1　引言 1 气溶胶光学厚度AOD（Aerosol Optical Depth）作为描述气溶胶光学特性的重要参数之一，准确获取其时空分布信息是当前大气科学的研究热点。卫星遥感反演是获取区域/全球尺度气溶胶信息的有效技术手段，而地表反射率估算作为影响反演精度的主要因素之一（杨磊库等，2022 杨磊库等，2022 ），降低地表参数的不确定性正是算法优化的重要方面。经过几十年的发展，依据反演过程中采取的地表反射率估算策略差异产生了不同算法，如波段经验比值（ Kaufman 等，1997 Kaufman 等，1997 ； Levy 等，2013 Levy 等，2013 ）、多天反射率数据合成（ Hsu 等，2013 Hsu 等，2013 ；田信鹏等，2018）、多源传感器联合反演（ Tang 等，2005 Tang 等，2005 ； Vermote 等，2007 Vermote 等，2007 ）、机器学习算法（贾臣等，2020 贾臣等，2020 ； Su 等，2020 Su 等，2020 ）等，气溶胶遥感已形成了一个丰富的研究体系。利用浓密植被地表反射率在红、蓝波段与短波红外具有较稳定的比值关系，且短波红外受大气影响相对较小的特点， Kaufman等（1997） Kaufman等（1997）提出了适用于浓密植被地区的DT（Dark Target）算法。 Levy等（2013） Levy等（2013）基于DT算法，结合散射角及短波红外归一化植被指数等，实现了MODIS气溶胶产品（MOD04）业务化生产，目前已发展到C6.1版本。葛邦宇等（2018）葛邦宇等（2018）将DT算法应用于Himawari-8卫星，实现了京津冀地区AOD反演。DT算法能够以较高精度获取浓密植被地表上空AOD信息，为提高气溶胶卫星遥感的空间覆盖度，国内外学者提出了多种适用于非浓密植被地表的反演算法。Hsu等（2004，2013）提出了适用于高亮地区的DB（Deep Blue）算法；孙林等（2016）孙林等（2016）利用多年MODIS地表反射率产品构建地表反射率先验数据集，提出了HARLS（High-resolution Aerosol Retrieval algorithm based on a priori Land Surface reflectance database support）算法，并将其用于GF-1 PMS等传感器； Lyapustin等（2018） Lyapustin等（2018）提出的MAIAC（Multiangle implementation of atmospheric correction）算法是近年来发展起来的另一较成熟的反演算法，该算法采用动态时间序列数据实现地气分离，能同时获取浓密植被及高反射地表上空气溶胶信息，基于该算法实现了MODIS 1 km分辨率气溶胶产品（MCD19A2）的生产。以上DT、DB及HARLS算法假设地表为各向同性反射的朗伯体，在反演过程中使用的地表反射率仅与时间和位置有关。这种假设在草原等区域影响不大，但在方向反射特征明显、地表结构复杂的城市地区，会存在地表参数刻画不确定性大的问题（ Wei 等，2019 Wei 等，2019 ），致使AOD反演精度较低。由于不同地表类型，其反射率变化呈现不同的时空变异性，且地表方向反射特性使地表信息确定变得更加复杂和困难（ Gatebe和King，2016 Gatebe和King，2016 ）。近年来，国内外诸多学者在地表反射估算方面做了许多努力， Diner等（2005） Diner等（2005）利用MISR传感器多角度多通道观测的特点，用经验正交函数描述地表信息，实现了考虑地表方向反射的AOD反演； Shi等（2017） Shi等（2017）基于比值梯度优化算法，实现了AATSR（Advanced Along Track Scanning Radiometer）传感器AOD及地表反射率同步反演。地表方向反射可用双向反射分布函数BRDF（Bidirectional Reflectance Distribution Function）刻画， Xue等（2009） Xue等（2009）通过MODIS BRDF/Albedo产品（MCD43）增加约束条件，基于AATSR传感器星下点及前向两个角度观测数据，提出了协同反演算法； Yang等（2014） Yang等（2014）利用非朗伯辐射传输前向模型，同时反演获取了AOD和Ångstrom指数信息； Tian等（2018） Tian等（2018）结合半经验核驱动模型估算地表反射率，实现了城市地区AOD反演； She等（2019） She等（2019）利用MCD43提供的核权重信息，实现了Himawari-8 AHI传感器的AOD和地表反射率联合反演。由于城市下垫面空间异质性的影响，其地表反射特征刻画困难，导致AOD反演结果存在空间连续性差、分辨率低及精度具有较大不确定性等问题。 Tian等（2021a） Tian等（2021a）通过耦合非朗伯辐射传输前向模型及半经验核驱动模型，提出以MODIS BRDF形状因子先验数据集为驱动的地表参数确定方法，实现了MODIS数据气溶胶遥感反演。为验证该算法在非同源传感器的适用性，本文基于该反演算法基本思路，以Landsat 8 OLI为数据源，在北京地区开展AOD反演实验，并对反演过程的可能误差进行定量分析。通过AERONET（Aerosol Robotic Network）站点数据及与MODIS气溶胶产品交叉对比验证，本算法可有效提高研究区AOD反演精度，能够为城市尺度大气复合污染防治和治理提供数据支持。 2　数据源 1 2.1　地面数据 2 AERONET作为一个全球地基气溶胶观测网络，可实现高精度气溶胶参数观测（ Holben 等，1998 Holben 等，1998 ）。该网络可提供无云条件下光谱范围为0.34—1.06 μm的AOD信息，同时保证数据的不确定性较低（约0.01—0.02）及高时间分辨率（约15 min）（ Smirnov 等，2000 Smirnov 等，2000 ）。AERONET将AOD产品分为3级：原始Level 1.0数据、经过云检测Level 1.5数据及严格质量控制的Level 2.0数据。目前，最新Version 3（V3）版本在V2基础上，云检测及数据质量控制得到进一步优化（ Giles等，2019 Giles等，2019 ）。AERONET已被广泛用于AOD卫星反演验证中（ Chu 等，2002 Chu 等，2002 ； Sayer 等，2014 Sayer 等，2014 ）。本研究搜集了研究区2013年—2018年Beijing（BJS）、Beijing_CAMS（BJC）、Beijing_RADI（BJR）及Xianghe（XHS）4个站点V3 AOD数据。其中，BJS、BJC及XHS站点为Level 2.0数据，BJR站点为Level 1.5数据。 2.2　遥感数据 2 Landsat 8陆地卫星于2013年2月11日发射升空，搭载OLI（Operational Land Imager）及TIRS（Thermal Infrared Sensor）两个传感器。OLI传感器有从可见光到短波红外9个波段，幅宽为185 km，重访周期为16 d，空间分辨率为30 m，此外还包括一个15 m分辨率的全色波段。研究中利用2013年—2018年云覆盖较小的OLI数据进行AOD反演实验，共收集到64景。MODIS传感器搭载于Terra及Aqua卫星上，基于该传感器有40多种遥感参数产品。本文使用的MODIS产品包括：AOD产品（MOD04、MCD19A2）、地表反射率产品（MOD09A1）及地表BRDF核驱动模型系数产品（MCD43A1）。其中，MOD04根据采用的反演算法不同分为DT、DB及两者融合的DTDB AOD产品，其空间分辨率均为10 km；MCD19A2产品采用MAIAC算法，空间分辨率为1 km。MOD09A1及MCD43A1产品空间分辨率均为500 m，使用该两种产品构建了地表反射率数据集及地表BRDF形状指示因子数据集，分别实现HARLS算法及本文新算法的气溶胶反演。表1 表1 给出了研究中使用的地面及遥感数据详细信息。注： *表示同时使用了数据集对应的质量标识数据集，QA = Quality Assurance flag。名称使用的数据字段空间/时间分辨率数据名称 AERONET — 15 min Version 3， Level 1.5/2.0 AOD Landsat 8 OLI — 30 m/16-day Calibrated radiances 3 MOD04 Optical_Depth_ Land_And_Ocean 10 km/daily DT AOD （QA = 3） Deep_Blue_Aerosol_Optical_Depth_550_Land_Best_Estimate 10 km/daily DB AOD （QA = 2， 3） AOD_550_Dark_Target_Deep_Blue_Combined * 10 km/daily DTDB AOD （QA = 3） MCD19A2 Optical_Depth_055 * 1 km/daily MAIAC AOD （QA = 0） MOD09A1 sur_refl_b03 * 500 m/8-day 地表反射率产品（QA = 0） MCD43A1 BRDF_Albedo_Parameters_Band3 * 500 m/daily BRDF产品（QA = 0） 3　原理与方法 1 3.1　基本原理 2 卫星传感器观测到的大气层顶TOA（Top Of the Atmosphere）入瞳辐亮度来自于地气系统对太阳辐射的后向散射，可分为两部分，一部分来源于大气后向散射（程辐射项），另一部分则是太阳下行辐射经地气系统作用后重新散射到大气顶层。大气辐射传输模型在模拟电磁波与地气相互作用时，通常假设地表为朗伯体。然而，真实地表为各向异性反射的非朗伯体，地表朗伯假设会影响到TOA辐射的估算，进而影响AOD反演。为了估算地表非朗伯下TOA反射率， Qin等（2001） Qin等（2001）提出了考虑地表方向反射特性的辐射传输模型CASBIR（Correction for Anisotropic Surface BIdirectional Reflection）。该模型将辐射过程分为上行和下行分量，并且每个分量中包含直射和漫射两部分，TOA反射率（ <math id="M1"><msub><mrow><mi>ρ</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">O</mi><mi 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mathvariant="normal">v</mi></mrow></msub><mo>,</mo><mi>φ</mi></mrow></mfenced><mo>+</mo><mfrac><mrow><mi mathvariant="bold-italic">T</mi><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></mfenced><mo>⋅</mo><mi mathvariant="bold-italic">R</mi><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>,</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>,</mo><mi>φ</mi></mrow></mfenced><mo>⋅</mo><mi mathvariant="bold-italic">T</mi><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfenced><mo>-</mo><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">d</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></mfenced><mo>⋅</mo><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">d</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfenced><mo>⋅</mo><mfenced open="|" close="|" separators="|"><mrow><mi mathvariant="bold-italic">R</mi><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>,</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>,</mo><mi>φ</mi></mrow></mfenced></mrow></mfenced><mo>⋅</mo><mover accent="true"><mi>ρ</mi><mo>¯</mo></mover></mrow><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">h</mi></mrow></msub><mo>⋅</mo><mover accent="true"><mi>ρ</mi><mo>¯</mo></mover></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632867&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632865&type= 138.00666809 9.73666668 式中， <math id="M3"><mi mathvariant="bold-italic">T</mi><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632875&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632871&type= 8.80533314 4.40266657 、 <math id="M4"><mi mathvariant="bold-italic">T</mi><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632882&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632879&type= 8.89000034 4.40266657 为大气下行、上行透过率矩阵， <math id="M5"><mi mathvariant="bold-italic">R</mi><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>,</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>,</mo><mi>φ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632887&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632885&type= 20.40466690 4.40266657 为地表反射率矩阵： <math display="block" id="M6"><mtable columnalign="left"><mtr><mtd><mi mathvariant="bold-italic">T</mi><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></mfenced><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">d</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></mfenced><mtext> </mtext><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">h</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></mfenced></mrow></mfenced><mo>,</mo></mtd></mtr><mtr><mtd><mi mathvariant="bold-italic">T</mi><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfenced><mo>=</mo><msup><mrow><mfenced open="[" close="]" separators="|"><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">d</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfenced><mtext> </mtext><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">d</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfenced></mrow></mfenced></mrow><mrow><mi mathvariant="normal">T</mi></mrow></msup></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632891&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632889&type= 39.62400055 12.69999981 <math display="block" id="M7"><mi mathvariant="bold-italic">R</mi><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>,</mo><mtext> </mtext><mi>φ</mi></mrow></mfenced><mo>=</mo><mfenced open="[" close="]" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">d</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>,</mo><mtext> </mtext><mi>φ</mi></mrow></mfenced></mtd><mtd><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">h</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>φ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></mfenced></mtd></mtr><mtr><mtd><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">d</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>φ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfenced></mtd><mtd><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">h</mi></mrow></msub></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632895&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632893&type= 60.79066849 11.68400002 式中， <math id="M8"><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632899&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632897&type= 2.70933342 3.80999994 、 <math id="M9"><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632904&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632901&type= 2.79399991 3.80999994 、 <math id="M10"><msub><mrow><mi>φ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632909&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632906&type= 3.21733332 4.40266657 、 <math id="M11"><msub><mrow><mi>φ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632915&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632912&type= 3.30200005 4.40266657 及 <math id="M12"><mi>φ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632921&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632918&type= 2.28600001 3.30200005 分别为太阳天顶角、传感器天顶角、太阳方位角、传感器方位角及相对方位角； t 和 r 分别表示透过率和反射率，下标 h 和 d 分别表示半球（漫射）和方向（直射）。可以看出，式（1）式（1）由大气和地表参数两部分组成：（1）大气参数，包括表征大气程辐射的大气路径散射反射率 <math id="M13"><mfenced separators="|"><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632928&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632926&type= 6.26533365 4.48733330 、大气球形反照率 <math id="M14"><mfenced separators="|"><mrow><mover accent="true"><mi>ρ</mi><mo>¯</mo></mover></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632931&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632929&type= 4.99533367 4.48733330 、大气下行直射透过率 <math id="M15"><mfenced separators="|"><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">d</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632935&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632933&type= 12.02266598 5.07999992 、大气下行漫射透过率 <math id="M16"><mfenced separators="|"><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">h</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632940&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632938&type= 12.02266598 5.07999992 、大气上行直射透过率 <math id="M17"><mfenced separators="|"><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">d</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632943&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632941&type= 12.10733318 5.07999992 及大气上行漫射透过率 <math id="M18"><mfenced separators="|"><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">d</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632947&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632946&type= 12.27666664 5.07999992 ；2）地表参数，包括地表方向—方向反射率（ <math id="M19"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">d</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633621&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633616&type= 3.38666677 3.72533321 ）、方向—半球反射率（ <math id="M20"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">h</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632955&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632953&type= 3.38666677 3.72533321 ）、半球—方向反射率（ <math id="M21"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">d</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632960&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632957&type= 3.38666677 3.72533321 ，数值上等于 <math id="M22"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">h</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632963&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632961&type= 3.38666677 3.72533321 ）及半球—半球反射率（ <math id="M23"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">h</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632967&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632965&type= 3.38666677 3.72533321 ，即白空反照率WSA（White-Sky Albedo））。由于观测几何及地表非朗伯特性的不同， <math id="M24"><mfenced open="|" close="|" separators="|"><mrow><mi mathvariant="bold-italic">R</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632982&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632980&type= 4.65666676 3.72533321 可能为正值也可能为负值。当 <math id="M25"><mi mathvariant="bold-italic">R</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632975&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632973&type= 2.45533323 2.62466669 的4个变量用单一反射率 <math id="M26"><msub><mrow><mi>ρ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632978&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632977&type= 3.04800010 4.48733330 刻画时， <math id="M27"><mfenced open="|" close="|" separators="|"><mrow><mi mathvariant="bold-italic">R</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632982&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632980&type= 4.65666676 3.72533321 = 0，式（1）式（1）可简化为朗伯假设下 <math id="M28"><msub><mrow><mi>ρ</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632986&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632984&type= 5.92666674 4.48733330 计算公式，即： <math display="block" id="M29"><msub><mrow><mi>ρ</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>,</mo><mtext> </mtext><mi>φ</mi></mrow></mfenced><mo>=</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>,</mo><mtext> </mtext><mi>φ</mi></mrow></mfenced><mo>+</mo><mfrac><mrow><mi>τ</mi><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></mfenced><mo>⋅</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>⋅</mo><mi>τ</mi><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfenced></mrow><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>⋅</mo><mover accent="true"><mi>ρ</mi><mo>¯</mo></mover></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632990&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632988&type= 73.49066925 8.97466660 式中， <math id="M30"><mi>τ</mi><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632995&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632992&type= 8.04333401 4.40266657 、 <math id="M31"><mi>τ</mi><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632998&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37632996&type= 8.12800026 4.40266657 为大气下行、上行总透过率。由式（1）式（1）可知，在计算 <math id="M32"><msub><mrow><mi>ρ</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633002&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633000&type= 5.92666674 4.48733330 时需要确定与大气有关的透过率、程辐射等大气参数及与地表有关的反射率参数。大气参数根据成像几何条件，从利用辐射传输代码预先构建的反演查找表LUT（Look-Up Table）中查算获取，LUT构建过程将在3.3.1节介绍。地表参数则通过半经验核驱动模型及构建的地表BRDF形状因子先验数据集估算获得。 3.2　地表反射率估算 2 3.2.1　估算模型 3 地表对电磁波的反射具有明显的方向性，BRDF可以定量地描述地表反射的各向异性特征（张虎等，2015 张虎等，2015 ）。根据模型构建原理不同，BRDF可分为物理模型、经验模型、半经验模型及计算机模拟模型。半经验模型由于参数简单，且具有一定的物理意义，已得到广泛应用（ Lucht 等，2000 Lucht 等，2000 ），尤其是半经验核驱动模型，其可表示为几个核函数加权和的形式： <math display="block" id="M33"><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">d</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>,</mo><mtext> </mtext><mi>φ</mi><mo>,</mo><mtext> </mtext><mi>λ</mi></mrow></mfenced><mo>=</mo><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">o</mi></mrow></msub><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">v</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">v</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>,</mo><mtext> </mtext><mi>φ</mi></mrow></mfenced><mo>+</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">o</mi></mrow></msub><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">o</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>,</mo><mtext> </mtext><mi>φ</mi></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633007&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633005&type= 71.20466614 10.58333302 式中， <math id="M34"><mi>λ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633011&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633008&type= 2.28600001 2.62466669 为波长； <math id="M35"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">v</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633015&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633013&type= 4.82600021 3.72533321 、 <math id="M36"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">o</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633019&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633017&type= 5.16466665 3.72533321 分别为体散射核函数和几何光学核函数； <math id="M37"><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">o</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633022&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633021&type= 4.14866638 4.57200003 、 <math id="M38"><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">v</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633025&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633023&type= 4.23333359 4.57200003 及 <math id="M39"><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">o</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633030&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633028&type= 4.57200003 4.57200003 为核系数，分别表示各向同性散射、体散射及几何光学散射。研究表明，罗斯表层核（Ross-Thick）和李氏稀疏互易核（LiSparse-R）核函数组合模式的拟合能力最好（ Pokrovsky和Roujean，2003 Pokrovsky和Roujean，2003 ），MODIS BRDF/Albedo产品也正是采用了该组合模式。在已知核系数的基础上，式（3）式（3）中的 <math id="M40"><msub><mrow><mi>r</mi></mrow><mrow><mi>d</mi><mi>h</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633034&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633032&type= 3.38666677 3.72533321 、 <math id="M41"><msub><mrow><mi>r</mi></mrow><mrow><mi>h</mi><mi>d</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633038&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633036&type= 3.38666677 3.72533321 及 <math id="M42"><msub><mrow><mi>r</mi></mrow><mrow><mi>h</mi><mi>h</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633042&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633040&type= 3.38666677 3.72533321 可以通过积分获得， Strahler等（1999） Strahler等（1999）通过大量实验给出了多项式积分拟合式（6）式（6），表2 表2 给出了多项式的拟合系数。 <math display="block" id="M43"><mtable columnalign="left"><mtr><mtd><mi>r</mi><mfenced separators="|"><mrow><mi>θ</mi><mo>,</mo><mtext> </mtext><mi>φ</mi></mrow></mfenced><mo>=</mo><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">o</mi></mrow></msub><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced><mfenced separators="|"><mrow><msub><mrow><mi>g</mi></mrow><mrow><mn mathvariant="normal">0</mn><mo>,</mo><mtext> </mtext><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">o</mi></mrow></msub><mo>+</mo><msub><mrow><mi>g</mi></mrow><mrow><mn mathvariant="normal">1</mn><mo>,</mo><mtext> </mtext><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">o</mi></mrow></msub><msup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msub><mrow><mi>g</mi></mrow><mrow><mn mathvariant="normal">2</mn><mo>,</mo><mtext> </mtext><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">o</mi></mrow></msub><msup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msup></mrow></mfenced><mo>+</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">v</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced><mfenced separators="|"><mrow><msub><mrow><mi>g</mi></mrow><mrow><mn mathvariant="normal">0</mn><mo>,</mo><mtext> </mtext><mi mathvariant="normal">v</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub><mo>+</mo><msub><mrow><mi>g</mi></mrow><mrow><mn mathvariant="normal">1</mn><mo>,</mo><mtext> </mtext><mi mathvariant="normal">v</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub><msup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msub><mrow><mi>g</mi></mrow><mrow><mn mathvariant="normal">2</mn><mo>,</mo><mtext> </mtext><mi mathvariant="normal">v</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub><msup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msup></mrow></mfenced><mo>+</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">o</mi></mrow></msub><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced><mfenced separators="|"><mrow><msub><mrow><mi>g</mi></mrow><mrow><mn mathvariant="normal">0</mn><mo>,</mo><mtext> </mtext><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">o</mi></mrow></msub><mo>+</mo><msub><mrow><mi>g</mi></mrow><mrow><mn mathvariant="normal">1</mn><mo>,</mo><mtext> </mtext><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">o</mi></mrow></msub><msup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msub><mrow><mi>g</mi></mrow><mrow><mn mathvariant="normal">2</mn><mo>,</mo><mtext> </mtext><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">o</mi></mrow></msub><msup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msup></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633046&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633044&type= 64.09266663 18.71133423 参数 k = iso k = Ross-Thick k = LiSparse-R <math id="M45"><msub><mrow><mi>g</mi></mrow><mrow><mn>0</mn><mo>,</mo><mi>k</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633053&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633052&type= 4.14866638 3.47133350 1.0 -0.007574 -1.284909 <math id="M46"><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>k</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633058&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633055&type= 4.14866638 3.47133350 0.0 -0.070987 -0.166314 <math id="M47"><msub><mrow><mi>g</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>k</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633062&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633059&type= 4.14866638 3.47133350 0.0 0.307588 0.041840 <math id="M48"><msub><mrow><mi>r</mi></mrow><mrow><mi>h</mi><mi>h</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633065&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633063&type= 2.87866688 2.87866688 1.0 0.189184 -1.377622 <math id="M49"><msub><mrow><mi>g</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>=</mo><msub><mrow><mi>g</mi></mrow><mrow><mn mathvariant="normal">0</mn><mo>,</mo><mi>k</mi></mrow></msub><mo>+</mo><msub><mrow><mi>g</mi></mrow><mrow><mn mathvariant="normal">1</mn><mo>,</mo><mi>k</mi></mrow></msub><msup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msub><mrow><mi>g</mi></mrow><mrow><mn mathvariant="normal">2</mn><mo>,</mo><mi>k</mi></mrow></msub><msup><mrow><mi>θ</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633074&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633072&type= 33.78200150 4.06400013 3.2.2　地表先验数据集构建方法 3 由以上可知，式（4）式（4）中地表反射率估算的关键是核系数的确定。MCD43A1产品虽然提供3个核系数，但在反演过程中算法受到多种因素影响，包括大气参数不确定性导致的反射率误差、拟合数据的角度范围不足及模型拟合方法无法有效抵抗噪声等（ Liang 等，2002 Liang 等，2002 ），且受云、云阴影等影响，产品存在数据缺失、质量低等问题，特别是在城市地区（ Tian 等，2021b Tian 等，2021b ）。因此，本文利用长时间序列MCD43A1产品，通过离散余弦变换的惩罚最小二乘估计DCT-PLS（Discrete Cosine Transform-Penalized Least Square regression）时空滤波算法进行数据合成（ Garcia 等，2010 Garcia 等，2010 ），并采用与地物类型更为相关的BRDF形状指示因子（体散射核形状因子： <math id="M50"><msub><mrow><mi>A</mi></mrow><mrow><mi mathvariant="normal">v</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub><mo>=</mo><mrow><mrow><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">v</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow></msub></mrow><mo>/</mo><mrow><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">o</mi></mrow></msub></mrow></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633078&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633076&type= 17.94933319 3.89466691 、几何光学核形状因子： <math id="M51"><msub><mrow><mi>A</mi></mrow><mrow><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">o</mi></mrow></msub><mo>=</mo><mrow><mrow><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">o</mi></mrow></msub></mrow><mo>/</mo><mrow><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">o</mi></mrow></msub></mrow></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633082&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633080&type= 18.79599953 4.23333359 ）进行先验数据集的构建（ Tian 等，2021a Tian 等，2021a ）。 DCT-PLS算法的基本思想是通过计算残差平方和及反映平滑数据粗糙度的惩罚项来平衡数据保真度，其对异常点较为敏感（ Garcia 等，2010 Garcia 等，2010 ）。为降低缺失值及离群值对拟合的偏差，可使用迭代分配权重来避免，即缺失值或离群值权重低，质量高的数据则权重高。这里参考 Xiao等（2015） Xiao等（2015）在重构地表反射率数据时采用的Bisquare加权函数进行权重分配。 3.2.3　地表先验数据集构建结果 3 基于上述数据滤波方法，本文使用2013年—2017年研究区MCD43A1产品构建了8 d间隔、500 m分辨率地表BRDF形状指示因子先验数据集。图1 图1 给出了第17天及第97天结果，可以看出，数据集在植被及城市地区均有较好的覆盖度。由于城市结构复杂、反射率较高，其 f iso 变化特征明显高于植被和耕地地区。植被地区 A vol 大于城市地区，而 A geo 在空间分布上整体较为均匀。利用该数据集，结合遥感影像成像几何条件，通过式（5）式（5）和（6）即可计算获取式（1）式（1）中各地表反射率参数，图2 图2 给出了一个计算结果实例。从图中可以看出，北京及周边地区4种反射率整体分布趋势一致，值在0.04—0.10之间，各反射率之间存在明显差异，其中 <math id="M52"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">h</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633086&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633083&type= 3.38666677 3.72533321 大于其他反射率。 1;2;3; 1,2;3,4;5; 3.2.4　先验数据集拟合能力评估 3 为评估本文构建的先验数据集拟合地表反射率的能力，我们对研究区3种典型地物类型（耕地、人工地表及自然植被）进行了反射率拟合实验，结果如图3 图3 。其中，估算地表反射率采用构建的先验数据集，结合半经验核驱动模型计算获得，观测地表反射率数据则为MODIS逐日地表反射率产品（MOD09GA）。从图3 图3 中可以看出，估算的地表反射率与观测值具有较好的一致性，尤其在耕地及自然植被地表，相关系数 R 大于0.985，RMSE值小于0.005；在人工地表，反射率估算结果平均绝对误差MAE为0.005。 3.3　气溶胶光学厚度反演 2 3.3.1　查找表构建 3 气溶胶及大气分子共同决定了式（1）式（1）中与大气有关的参数，大气气溶胶的组成随时间和地点变化而不同，气溶胶遥感另一个关键是气溶胶类型的确定（李正强等，2019 李正强等，2019 ）。MODIS气溶胶反演算法根据季节和位置从预先建立的全球气溶胶类型数据库中选择合适的气溶胶类型（ Omar 等，2005 Omar 等，2005 ）。研究发现，北京及周边地区气溶胶状况可以用大陆型气溶胶描述（ Sun 等，2016 Sun 等，2016 ；田信鹏等，2018）。本文利用MODTRAN 5辐射传输代码构建通用大气参数数据集，该数据集包含不同观测几何及AOD条件下0.3—2.5 μm光谱范围、15 cm -1 光谱分辨率的6个大气输出参数，如表3 表3 所示。基于此数据集，结合传感器光谱响应函数即可快速构建某特定传感器AOD反演查找表。类型参数参数设置及描述个数来源文件 4 输入参数太阳天顶角 0∶5∶85 18 — 传感器天顶角 0∶5∶70 15 — 相对方位角 0∶10∶180 19 — AOD 0.05， 0.1， 0.15， 0.2∶0.1∶1.0， 1.0， 1.2， 1.5， 2.0， 3.0 16 — 6 输出参数 <math id="M53"><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">d</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633157&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633154&type= 7.45066643 3.72533321 上行直射透过率 — acd <math id="M54"><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">d</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633163&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633160&type= 7.36600018 3.72533321 下行直射透过率 — acd <math id="M55"><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">d</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633168&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633165&type= 7.45066643 3.72533321 上行漫射透过率 — acd <math id="M56"><msub><mrow><mi>t</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">h</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633174&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633171&type= 7.36600018 3.72533321 下行漫射透过率 — acd <math id="M57"><mover><mrow><mi>ρ</mi></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633179&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633177&type= 1.26999998 2.96333337 大气球形反照率 — acd <math id="M58"><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633184&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633182&type= 2.62466669 3.38666677 大气路径散射反射率 — tp7 3.3.2　像元筛选 3 气溶胶遥感反演的成功不仅与地表反射率的精确确定有关，在很大程度上也依赖于不合适像元的有效剔除，例如云、云阴影、冰\雪及内陆水体等（ Levy 等，2013 Levy 等，2013 ）。 Zhu等（2015） Zhu等（2015）针对Landsat 8 OLI传感器提出的Fmask（Function of mask）算法可实现云、云阴影、雪及内陆水体检测。本文在反演AOD前，首先基于该算法进行可反演区域的像元筛选。 3.3.3　光谱转换 3 不同传感器间光谱响应条件存在差异，导致具有相同反射特性的地物在不同传感器表现为不同特征。在利用由先验数据集支持非同源其它传感器AOD反演时，需将先验数据集的反射率转化为待反演传感器对应的反射率，消除两传感器之间的光谱差异（ Tian 等，2018 Tian 等，2018 ）。为将MODIS反射率转化为OLI波段反射率，本文选用《定量遥感：理念与算法》（梁顺林等，2013 梁顺林等，2013 ）所附光盘中波谱数据及北京师范大学“中国典型地物标准波普数据库”植被和土壤波谱数据作为样本，拟合获取OLI与MODIS蓝关波段反射率转换关系，结果为： <math id="M59"><msubsup><mrow><mi>ρ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">O</mi><mi mathvariant="normal">L</mi><mi mathvariant="normal">I</mi></mrow></msubsup><mo>=</mo><mn mathvariant="normal">1.047</mn><mo>×</mo><msubsup><mrow><mi>ρ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">I</mi><mi mathvariant="normal">S</mi></mrow></msubsup><mo>+</mo><mn mathvariant="normal">0.001</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633195&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633192&type= 43.09533310 4.74133301 。图4 图4 给出了本文AOD反演算法的具体流程。 4　结果与讨论 1 4.1　空间分布对比 2 图5 图5 对比展示了不同算法获取的研究区AOD空间分布情况，包括本文算法（AOD_BRDF）、地表朗伯假设（WSA反射率支持）反演（AOD_WSA）、HARLS算法（AOD_HARLS）及MODIS DT、DB、DTDB、MAIAC产品。整体来看，各算法获取的AOD在空间分布上具有较好的一致性，均表现为城市地区高、植被地区低的特点。其中，AOD_BRDF整体小于AOD_WSA及AOD_HARLS，MODIS DT及DB产品较其他反演结果偏大。 1,2,3,4;5,6,7,8;9; 4.2　精度验证 2 地面测量可提供站点周围高质量、高频率气溶胶数据，而卫星遥感则提供过境时刻、一定空间范围气溶胶综合状况。利用地面观测资料验证遥感产品时，需对二者进行时空匹配（ Yang 等，2014 Yang 等，2014 ）。一般采取的空间匹配策略为选取站点周围一定大小窗口内遥感产品平均值作为最终反演值，时间匹配策略为将卫星过境前后一定时间段的地面测量平均值作为最终测量值（ Levy 等，2010 Levy 等，2010 ）。因此，在后续验证过程中，本文对反演结果进行5×5空间平均处理，对AERONET站点数据进行卫星过境前后30 min时间平均处理。为定量描述算法反演精度，采用的评价指标包括：匹配点个数（ N ），相关系数（ R ），均方根误差（RMSE）及定义为±（0.05+0.15×AOD AERONET ）的期望误差EE（Expected Error）。此外，为分析算法的高估和低估情况，将在EE误差线以内（Within）的点对百分比称为PWE，在EE误差线以上（Above）和以下（Below）的点对占比分别称为PAE和PBE。 4.2.1　AERONET验证 3 由于BJS、BJC及BJR站点地表类型均为城市，且3个站点距离较近。受云污染及数据量限制，BJS、BJC及BJR站点 N 分别为39、41、37，XHS站点 N = 43。鉴于此，本文将BJS、BJC及BJR站点作为城市站点对其进行整体评价，XHS站点作为植被站点进行评价分析。图6 图6 展示了城市站点不同反演算法反演值与地面实测值对比结果，其中红色实线为拟合线，黑色实线为1∶1线，黑色虚线为EE误差线；从中可以看出，AOD_HARLS（图6（c）图6（c））各精度指标（PWE = 73.5%， R = 0.978，RMSE = 0.164）比AOD_WSA（图6（b）图6（b））稍有提高（PWE = 65.8%， R = 0.977，RMSE = 0.173），两者PAE值分别为22.2%、27.4%，拟合线斜率分别为1.19、1.21，表明对AOD均存在高估。图6（a）图6（a）为新算法反演值与实测值对比结果，可以看出，两者具有较高的一致性（ R = 0.986，RMSE = 0.102），PWE值达到84.6%，较AOD_WSA、AOD_HARLS分别提高了18.8%、11.1%。AOD_BRDF结果改善主要体现在对高估的有效抑制，其PAE =14.5%，比AOD_WSA、AOD_HARLS分别低了12.9%、7.7%。 1,2,3;4; 图7 图7 为XHS植被站点不同算法获取的AOD反演值与地面实测值对比散点图，从中可以看出，AOD_BRDF精度最高（PWE = 86.0%， R = 0.991，RMSE = 0.086），PWE较AOD_WSA及AOD_HARLS分别提高了20.9%和9.3%；其次为AOD_HARLS（PWE = 76.7%， R = 0.985，RMSE = 0.119），AOD_WSA反演精度最低（PWE = 65.1%， R = 0.976，RMSE = 0.165）。与城市站点一样，AOD_BRDF精度的提高也体现在对AOD高估的抑制，其PAE值比AOD_WSA、AOD_HARLS分别低了18.6%、9.3%。 1,2,3; 以上分析表明，在城市及植被地区，本文提出的反演算法均可有效改善地表朗伯假设（即使用WSA反射率支持）及HARLS算法的高估，提高AOD遥感反演精度。 4.2.2　与MODIS产品对比 3 图 8（a） 8（a） — 8（d） 8（d）给出了AOD_BRDF与MODIS DT、DB、DTDB及MAIAC产品在城市站点的精度对比，其中红色点为新算法反演结果，蓝色点为相应的MODIS产品。从图8 图8 中可以看出，DT、DB、DTDB及MAIAC算法 N 分别为47、79、61及92，表明各算法中，MAIAC算法在城市地区适用性最好，其次为DB算法，DT算法适用性最差，但均要小于本文AOD_BRDF结果（ N = 117，见图6 图6 ）。与DT算法相比，AOD_BRDF与实测值具有更好的一致性： R 由0.975提高到0.996，RMSE值由0.154降为0.117。新算法有效降低了DT算法的高估，PAE由57.4%减小到10.6%，PWE提高了46.8%；DB与DTDB算法的PWE分别为70.9%、62.3%，与这两种产品相比，AOD_BRDF同样有不同幅度精度提升，PWE分别提高了13.9%及14.7%。新算法精度的提高同样表现在对高估现象的改善，PAE分别降低了5.1%及14.7%。MODIS各算法中，MAIAC算法在城市站点具有最高的精度（PWE = 79.3%），本文新算法与之相比PWE提高了4.4%，精度也有小幅度提升。 1,2;3,4;5; 图9 图9 展示了本文算法与MODIS AOD产品在XHS植被站点的交叉对比。通过与城市站点对比可以看出，DT算法在植被地区有了较大改善（PWE =68.4%）（图9（a）图9（a））。DT、DB及DTDB算法在XHS站点对AOD同样存在高估现象，PAE分别为31.6%、41.9%及48.3%。与DT、DB及DTDB相比，本文新算法在该站点精度有不同幅度提升：PAE分别降低了21.1%、22.5%及27.6%，PWE提高超过21.1%。新算法与MAIAC相比，PWE均为82.9%，但具有更高的 R 值（0.992）及更小的RMSE（0.085），表明新算法与实测值有更好的一致性。 1,2;3,4;5; 通过以上分析表明，本文反演算法比WSA反射率支持及HARLS算法反演结果具有更高的精度。由于AOD_BRDF、AOD_WSA及AOD_HARLS反演中使用的LUT相同，因此，新算法反演精度的提高是地表参数估算优化的结果。此外，新算法在城市及植被站点均表现出比MODIS产品更好的适用性，可以有效地改善当前气溶胶遥感反演在研究区的高估。 4.3　不确定性分析 2 4.3.1　地表反射率影响 3 本文新算法、WSA反射率支持及HARLS算法采用不同地表反射率估算策略进行AOD反演，图10 图10 给出了BJS及XHS站点沿主平面方向，观测天顶角 <math id="M60"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633504&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633499&type= 2.70933342 3.80999994 = 0°时的方向‒方向反射率（ <math id="M61"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">d</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633515&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633511&type= 3.38666677 3.72533321 ）、半球‒半球反射率（ <math id="M62"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">h</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633525&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633520&type= 3.38666677 3.72533321 ，WSA）及MOD09A1产品合成反射率（ <math id="M63"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">d</mi><mn mathvariant="normal">09</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633535&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633530&type= 6.68866634 3.72533321 ）随太阳天顶角（ <math id="M64"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633545&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633540&type= 2.53999996 3.80999994 ）的变化情况。 <math id="M65"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">h</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633553&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633549&type= 3.38666677 3.72533321 是通过构建的地表BRDF形状因子先验数据集利用式（6）式（6）计算获得， <math id="M66"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">d</mi><mn mathvariant="normal">09</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633562&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633559&type= 6.68866634 3.72533321 为HARLS算法使用的地表反射率。从图中可以看出，BJS、XHS站点的 <math id="M67"><msub><mrow><mi>r</mi></mrow><mrow><mi>d</mi><mi>d</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633572&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633567&type= 3.38666677 3.72533321 在主平面方向均随 <math id="M68"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633612&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633610&type= 2.53999996 3.80999994 远离“热点”角度（ <math id="M69"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633612&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633610&type= 2.53999996 3.80999994 = <math id="M70"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633595&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633591&type= 2.70933342 3.80999994 ）减小，在“热点”方向达到最大值0.064、0.048。随着 <math id="M71"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633612&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633610&type= 2.53999996 3.80999994 的变化，两站点 <math id="M72"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">d</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633607&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633603&type= 3.38666677 3.72533321 值变化幅度超过0.030。Landsat 8影像行/列号为163/47时，OLI传感器成像 <math id="M73"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633612&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633610&type= 2.53999996 3.80999994 的范围约为20°—65°（图10 图10 中虚线）。在该角度内，两站点 <math id="M74"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">d</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633621&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633616&type= 3.38666677 3.72533321 值变化范围为0.025。因此，在AOD反演中若不考虑地表非朗伯特性对地表反射率估算的影响势必会带来较大的误差。 WSA反射率支持的AOD反演及HARLS算法在反演过程中使用的 <math id="M77"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">h</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633670&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633668&type= 3.38666677 3.72533321 和 <math id="M78"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">d</mi><mn mathvariant="normal">09</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633666&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633661&type= 6.68866634 3.72533321 均为固定值，且BJS及XHS两站点的 <math id="M79"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">h</mi><mi mathvariant="normal">h</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633670&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633668&type= 3.38666677 3.72533321 值小于 <math id="M80"><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">d</mi><mn mathvariant="normal">09</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633676&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=37633673&type= 6.68866634 3.72533321 。因此，图6 图6 城市站点和图7 图7 植被站点中AOD_WSA比AOD_HARLS有更严重高估主要原因来自于地表反射率因素。以上分析表明，由于城市和植被下垫面方向反射特性，导致不同成像几何条件下地表反射率具有较大差异。在AOD反演过程中如果使用单一角度或合成反射率来刻画地表信息，将会给反演带来较大误差。 4.3.2　空间尺度转换影响 3 由于地表异质的普遍性，单个遥感像元往往包含多种地表覆盖类型（陈晋等，2016 陈晋等，2016 ）。本文利用Landsat 8 OLI 30 m空间分辨率数据反演气溶胶，算法中地气分离策略是基于500 m分辨率先验数据集。由于OLI数据与先验数据集存在空间尺度不一致问题，反演过程中将OLI高空间分辨率数据升尺度到与先验数据集相同的500 m分辨率，重采样会使遥感数据的表观反射率发生变化，进而影响AOD反演。为定量分析空间升尺度所带来的反演不确定性，我们分析了研究区3种典型地物（耕地、人工地表和自然植被）空间尺度转化对TOA反射率重采样的影响，如图11（a）图11（a）所示。从中可以看出，3种地物由30 m升尺度到500 m分辨率，其TOA反射率绝对差值分别为0.0029、0.0017和0.0013。图11（b）图11（b）为基于辐射传输模型模拟获取的不同AOD及地表反射率条件下的表观反射率。当AOD < 1.5时，耕地、人工地表和自然植被拟合斜率分别为0.040、0.034和0.052。因此，上述表观反射率绝对差值对应的AOD误差约为0.073、0.050和0.025。可见耕地和人工地表在升尺度过程导致的AOD误差最大，这可能是由于北京地区该地表类型空间异质性较自然植被更高，升尺度所带来的表观反射率差异更大造成的。 1;2;3; 5　结论 1 本文结合非朗伯大气辐射传输前向模型及半经验核驱动模型，提出以地表先验数据集为驱动的地表参数确定方法，实现了考虑地表BRDF效应的气溶胶遥感反演。利用Landsat 8 OLI数据在北京地区进行了反演实验，得到主要结论如下：（1）利用长时间序列MODIS BRDF/Albedo产品，基于离散余弦变换的惩罚最小二乘估计（DCT-PLS）时空滤波算法构建了8 d间隔、500 m分辨率地表BRDF形状指示因子先验数据集。（2）利用MODTRAN 5辐射传输代码构建了通用大气参数数据集，基于该数据集，结合传感器光谱响应函数即可快速构建查找表。（3）通过分析非朗伯辐射传输前向模型及半经验核驱动模型特点，实现了两模型的一体化耦合，提出了考虑地表BRDF效应的AOD反演算法，突破传统算法的地表朗伯假设。（4）基于本文算法实现了Landsat 8 OLI数据在北京地区AOD反演实验。通过与朗伯假设反演及HARLS算法反演结果的交叉对比，结果表明，新算法在城市/植被地区误差线内比重达到了84.6%/86.0%，分别较前两种算法提高了18.8%/20.9%和11.1%/9.3%。由于3种算法反演中采用相同的LUT，因此，新算法精度提高是地表参数优化的结果。（5）通过与MODIS DT、DB、DTDB及MAIAC气溶胶产品交叉对比，新算法在城市及植被站点均表现出与实测值更好的一致性及反演精度。（6）误差分析表明，由于地表方向反射会导致不同成像几何条件下地表反射率差异较大，在AOD反演中若忽略地表非朗伯特性，使用单一角度或合成反射率来刻画地表信息，会带来较大不确定性。参考文献（References） Chen J , Ma L , Chen X H and Rao Y H . 2016 . 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Retrieval of aerosol optical depth over urban area by coupling the characteristics of surface directional reflection. National Remote Sensing Bulletin， 26（11）：2219-2233 Tian X P，Gao Z Q，Liu Q，Wang D and Wang Y Q. 2022. Retrieval of aerosol optical depth over urban area by coupling the characteristics of surface directional reflection. National Remote Sensing Bulletin， 26（11）：2219-2233 国家自然科学基金（编号：42206240，31870468）；山东省自然科学基金（编号：ZR2020QD055）；山东省自然科学基金重点项目（编号：ZR2020KF031） Supported by National Natural Science Foundation of China (No. 42206240, 31870468); Shandong Provincial Natural Science Foundation, China (No. ZR2020QD055); Key Program of Shandong Natural Science Foundation (No. ZR2020KF031) 2020-06-27 2022-11-07 2022-12-09 2021-03-27 遥感学报 11 26

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