热红外核驱动模型在垄行植被热辐射方向性特征拟合中的精度分析

热红外核驱动模型在垄行植被热辐射方向性特征拟合中的精度分析 Assessment of thermal infrared kernel-driven models over row-planted canopies 1 first-author 曹彪，1988年生，男，副研究员，研究方向为多角度热红外遥感。E-mail：caobiao@aircas.ac.cn 曹彪，1988年生，男，副研究员，研究方向为多角度热红外遥感。E-mail：caobiao@aircas.ac.cn caobiao@aircas.ac.cn 1 corresp 杜永明，1978年生，男，副研究员，研究方向为热红外定量遥感。E-mail：duym@aircas.ac.an 杜永明，1978年生，男，副研究员，研究方向为热红外定量遥感。E-mail：duym@aircas.ac.an duym@aircas.ac.an 1 1 2 3 4 1 1 1 1 中国科学院空天信息创新研究院 遥感科学国家重点实验室, 北京 100101 中国科学院空天信息创新研究院 遥感科学国家重点实验室, 北京 100101 State Key Laboratory of Remote Sensing Science, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100101, China State Key Laboratory of Remote Sensing Science, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100101, China 北京航空航天大学 仪器科学与光电工程学院, 北京 100191 北京航空航天大学 仪器科学与光电工程学院, 北京 100191 Key Laboratory of Precision Opto-Mechatronics Technology, Ministry of Education, School of Instrument Science and Opto-Electronics Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China Key Laboratory of Precision Opto-Mechatronics Technology, Ministry of Education, School of Instrument Science and Opto-Electronics Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China 卢森堡科学技术研究所 环境与创新研究中心, 卢森堡 4422 卢森堡科学技术研究所 环境与创新研究中心, 卢森堡 4422 Remote Sensing and Natural Resources Modeling, ERIN Department, Luxembourg Institute of Science and Technology (LIST), Belvaux, Luxembourg, 4422 Remote Sensing and Natural Resources Modeling, ERIN Department, Luxembourg Institute of Science and Technology (LIST), Belvaux, Luxembourg, 4422 电子科技大学 资源与环境学院, 成都 611731 电子科技大学 资源与环境学院, 成都 611731 School of Resources and Environment, University of Electronic Science and Technology of China, Chengdu 611731, China School of Resources and Environment, University of Electronic Science and Technology of China, Chengdu 611731, China 垄行种植是果园及农作物的常见种植结构，其冠层比连续和离散植被冠层具有更强的热辐射各向异性，开展垄行植被冠层的热辐射方向性校正对干旱监测等应用具有重要意义。热红外核驱动模型是热辐射方向性校正的基础，但现有核驱动模型在垄行植被冠层中的拟合精度未被讨论过。本文以在法国波尔多获取的两组不同朝向葡萄园冠层航空实测方向性特征为基础，对比分析了现有8个模型的拟合精度（含隶属可见光近红外核驱动建模扩展框架的Ross-Li、LSF-Li模型及隶属热红外核驱动建模通用框架的Vinnikov、RL、Vinnikov-RL、Vinnikov-Chen、LSF-RL、LSF-Chen模型），结果表明现有模型均无法拟合出垄行植被的行效应特征，精度整体较低（RMSE高达2 K， R 2 低于0.7）且各个模型之间的拟合能力差异小，现有热红外核驱动模型均不适用于垄行植被冠层，有待在核驱动建模通用框架下发展可刻画垄行特征的新核。 The ignoring of the land surface thermal radiation directionality hampered the accuracy improvement of current land surface temperature products. It is urgent to develop a practical method to correct the angle effect for the products. More and more attention has been paid to the thermal infrared kernel-drive model because of its simplicity and accuracy. For natural surface, there are widely used eight kernel-driven models. Their fitting abilities over continuous and discrete canopies is well-known, however, no report discussed their performances over the important row-planted stage. The objective of this study is to assess the fitting abilities of all existing eight thermal infrared kernel-driven models over row-planted canopies based on airborne measured datasets. Two multi-angle directional anisotropy datasets over row-planted vineyards were obtained through the airborne observation in several flights. The experiment sites were located at Château Talbot, Médoc region, 30 km north of Bordeaux, France. All the measurements were combined and corrected from nadir temperature to derive the directional anisotropy at 1° steps for view zenith angle (0°—60°) and view azimuth angle (0°—360°). The multi-angle directional anisotropy values were used as input to estimate the kernel coefficients of two 3-parameter models within the traditional visible and near infrared framework (Ross-Li and LSF-Li), two 3-parameter models within the new thermal infrared framework (Vinnikov and RL), and four 4-parameter models within the new thermal infrared framework (Vinnikov-RL, Vinnikov-Chen, LSF-RL, LSF-Chen). Then, the forward simulated directional anisotropy values of all models were compared taking the airborne measured values as reference. Results show that all eight kernel-driven models cannot simulate the row-structure signatures (i.e., axisymmetric feature). They have an overall large RMSE about 2 K and a low R 2 less than 0.7. In addition, the RMSE differences between the models are small. For the east-west canopy, RMSE is between 1.930 K and 2.153 K, R 2 is between 0.616 and 0.691. For the south-north canopy, RMSE is between 2.005 K and 2.353 K, R 2 is between 0.600 and 0.670. Therefore, developing a new specific kernel for row-structure to improve the fitting ability is demanded in the thermal infrared band currently. 遥感 地表温度 热辐射方向性 核驱动模型 垄行植被 remote sensing land surface temperature thermal radiation directionality kernel-driven model row-planted canopy 1　引言 1 地表温度是地球冷暖的直接指标，与地表能量平衡、水循环、碳循环过程紧密相关（ 段四波 等，2021 段四波 等，2021 ； 刘萌 等，2021 刘萌 等，2021 ； 杨以坤 等，2019 杨以坤 等，2019 ），被全球气候观测系统列为基本气候变量之一。遥感是直接观测区域及全球尺度地表温度的唯一手段（ Li等，2013 Li等，2013 ）。热辐射方向性是当前地表温度反演所面临的主要难题之一。热辐射方向性这一科学现象是在植被冠层的近地面实验中观测发现的（ Monteith和Szeicz，1962 Monteith和Szeicz，1962 ），它指的是利用相同的传感器从不同的角度准同步地观测相同场景得到不同亮温的现象。随后研究人员从不同的角度对地表热辐射方向性特征开展建模，相关模型包括以4SAIL（ Verhoef等，2007 Verhoef等，2007 ）、CE-P（ Cao等，2018 Cao等，2018 ）为代表的辐射传输模型、以MGP（ Pinheiro等，2006 Pinheiro等，2006 ）为代表的几何光学模型、以垄行模型（ Yu等，2004 Yu等，2004 ）为代表的混合模型、以DART、TGRM为代表的三维模型（ Gastellu-Etchegorry等，2017 Gastellu-Etchegorry等，2017 ； Liu等，2007 Liu等，2007 ； 卞尊健 等，2021 卞尊健 等，2021 ）和以Kernel-Hotspot（ Ermida等，2018 Ermida等，2018 ）为代表的核驱动模型5种（ Cao等，2019b Cao等，2019b ）。前4类模型的驱动均要求已知植被结构、组分发射率、组分温度、太阳角度、观测角度等10多个参数，部分参数（比如组分温度）在实际应用中难以获取，这导致利用它们来实现方向性校正的目标需要一定程度的简化。基于此，发展了第5类模型，核驱动模型将未知数显著降低到3—4个，因而具备更大的应用潜力。目前已发展很多针对城市下垫面的三维模型（ 陈云浩 等，2018 陈云浩 等，2018 ； 马伟 等，2013 马伟 等，2013 ）和核驱动模型（ Wang等，2020 Wang等，2020 ， 2018 2018 ； Wang和Chen，2019 Wang和Chen，2019 ），因本研究以植被冠层为研究对象，所以下文不展开论述城市热辐射方向性模型进展。 核驱动模型最早由 Roujean等（1992） Roujean等（1992） 提出，用于可见光近红外波段的地表二向反射方向性特征建模，沿着这个框架发展而来的RossThick-LiSparseR模型（ Lucht等，2000 Lucht等，2000 ）（下文简称Ross-Li模型）在2002年正式应用于MODIS BRDF/Albedo产品的官方算法中（ Schaaf等，2002 Schaaf等，2002 ）。同年， Su等（2002） Su等（2002） 提出了首个针对热红外波段热辐射方向性模拟的核驱动模型LiStrahlerFriedl-LiDenseR（下文简称LSF-Li模型）。之后， Peng等（2011） Peng等（2011） 将Ross-Li模型直接扩展到了热红外波段，被其他学者初步用于地表温度产品的方向性校正（ Ren等，2014 Ren等，2014 ）及地表上行长波辐射产品的方向性校正（ Hu等，2017 Hu等，2017 ）。三参数的Ross-Li和LSF-Li模型均沿用了 Roujean等（1992） Roujean等（1992） 提出的基本框架：各向同性核、辐射传输核、几何光学核的线性加权。 Liu等（2020a） Liu等（2020a） 基于Li-Strahler几何光学模型重新推导了4个用于离散植被的几何光学核，发现四组分和三组分的几何光学核在拟合森林热辐射方向性时均优于LiSparseR核。 Cao等（2021） Cao等（2021） 深入分析了热红外辐射特性和可见光近红外反射特性的差异，从植被冠层物理模型出发，经过系列推导首次提出了适用于热红外波段的核驱动模型的四参数通用框架：各向同性核、几何光学底核、几何光学顶核的线性加权。依据该框架组合已有的核，共提出4个新的热红外核驱动模型：Vinnikov-RL模型、LSF-RL模型、Vinnikov-Chen模型、LSF-Chen模型，其中Vinnikov-RL模型和 Ermida等（2018） Ermida等（2018） 提出的Kernel-Hotspot模型具有相似的数学表达形式。已有的三参数RL模型（ Lagouarde和Irvine，2008 Lagouarde和Irvine，2008 ）和Vinnikov模型（ Vinnikov等，2012 Vinnikov等，2012 ）也可以被视作新框架下的模型，差异之处在于：（1）RL模型没有考虑几何光学底核的贡献；（2）Vinnikov模型没有考虑几何光学顶核中热点宽度的自由度。 综上所述，历时20年（2002年—2021年），在热红外波段已经提出了8个实用化的核驱动模型。已有对比分析研究表明，三参数的核驱动模型在离散植被冠层拟合精度较高但是均会显著低估连续植被冠层的热点效应（ Duffour等，2016 Duffour等，2016 ； Liu等，2018 Liu等，2018 ； Cao等，2019a Cao等，2019a ）。 Cao等（2021） Cao等（2021） 对比了上述8个核驱动模型，研究结果表明新框架下的四参数模型解决了三参数模型的连续植被热点低估问题。 Ran等（2021） Ran等（2021） 进一步基于4SAIL模型模拟数据集对比了三参数模型和四参数模型在少量观测角度条件下（仅具备5—11个观测角度）的拟合能力，结果表明四参数模型仍然显著占优。 连续植被和离散植被冠层热辐射方向性的高精度拟合问题已经得到比较好的解决，然而，针对物理建模中广泛讨论的垄行植被冠层（Chen等，2002； Du等，2020 Du等，2020 ；Kimes，1983；Li等，2021； Ren等，2013 Ren等，2013 ；Sobrino和Caselles，1990；Yan等，2003； Yu等，2004 Yu等，2004 ），现有热红外核驱动模型的拟合精度到底如何尚没有被专门讨论过。垄行时期作为作物生长的关键过渡期，其热辐射方向性强度更加明显，其温度状态的高精度监测对田间水分管理、作物产量预测非常重要。本文基于2组在垄行种植的葡萄园冠层实测的航空多角度数据（ Lagouarde等，2014 Lagouarde等，2014 ）进行了深入的对比分析，对比分析了经典框架下的Ross-Li、LSF-Li模型和新框架下的Vinnikov-RL、LSF-RL、Vinnikov-Chen、LSF-Chen、Vinnikov、RL模型的拟合精度。 2　方法 1 2.1　可见光核驱动模型框架扩展 2 为了校正AVHRR观测的地表反射率 ρ 的方向性， Roujean等（1992） Roujean等（1992） 首次提出“三核线性加权”形式的可见光核驱动模型框架（见 式（1） 式（1） ）。 <math display="block" id="M1"><mtable columnalign="left"><mtr><mtd><mi>ρ</mi><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><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><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi 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http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642154&type= 72.05133057 9.99066734 “三核”包括各向同性核 K iso 、连续植被体散射核 K continuous 和离散植被几何光学核 K discrete 。 K iso 恒等于1， K continuous 和 K discrete 核的数值可以根据太阳天顶角 θ s 、观测天顶角 θ v 和相对方位角 ∆φ 计算。3个待求未知数（各向同性核系数 f iso ，连续植被体散射核系数 f continuous 、离散植被几何光学核系数 f discrete ）可通过多角度观测（≥3）构建的方程组最优化求解。 如 图1 图1 所示，可见光核驱动模型框架的基本构建思路是将地表反射方向性特征线性分解为3类典型地表的方向性特征。第1类是粗糙表面呈现的各向同性反射特征；第2类是辐射传输核表达的连续植被反射特征；第3类是几何光学核表达的离散植被反射特征。针对连续植被， Roujean等（1992） Roujean等（1992） 基于Ross植被辐射传输基本理论，在浓密连续植被的假设下推导了RossThick核。 Wanner等（1995） Wanner等（1995） 基于类似的思路提出了刻画稀疏连续植被的RossThin核。针对离散植被， Roujean等（1992） Roujean等（1992） 基于随机分布的不透光长方体推导了Roujean几何光学核。 Wanner等（1995） Wanner等（1995） 基于Li-Strahler系列模型提出了LiSparse及LiDense两个几何光学核。 Lucht等（2000） Lucht等（2000） 进一步提出了满足互易定理的LiSparseR核及LiDenseR核。经过优选，2002年MODIS BRDF/Albedo产品的基础模型采用的“三核”是各向同性核 K iso 、RossThick辐射传输核 K RossThick 及LiSparseR几何光学核 K LiSparseR ，该模型即被广泛应用的Ross-Li模型。 为了拟合热红外波段的地表热辐射方向性特征， Su等（2002） Su等（2002） 对可见光核驱动模型的经典框架（ 式（1） 式（1） ）进行了扩展，提出了由各向同性核、连续植被核、离散植被核线性加权构成的LSF-Li核驱动模型（ 式（2） 式（2） ）。 Peng等（2011） Peng等（2011） 将Ross-Li模型中的方向反射率替换为方向亮度温度 T ，提出了热红外版本的Ross-Li核驱动模型，该模型也隶属于扩展框架（ 式（2） 式（2） ）。 <math display="block" id="M2"><mtable columnalign="left"><mtr><mtd><mi>T</mi><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><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><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">s</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><mo>+</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">e</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">e</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642172&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642169&type= 72.81333160 9.99066734 2.1.1　Ross-Li模型 3 Peng等（2011） Peng等（2011） 将原本用于反射率方向性拟合的Ross-Li模型拓展到热红外波段，用来拟合方向亮温。 Ren等（2014） Ren等（2014） 进一步将其用于拟合热红外方向辐射亮度及方向有效发射率。 Hu等（2017） Hu等（2017） 用该模型来拟合热红外方向宽波段辐射亮度。热红外波段的Ross-Li模型计算公式如下： <math display="block" id="M3"><mtable columnalign="left"><mtr><mtd><mi>T</mi><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><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><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">T</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">k</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">T</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">k</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><mo>+</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">R</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">R</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642178&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642176&type= 72.30532837 9.99066734 <math display="block" id="M4"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">T</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">k</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mfenced separators="|"><mrow><mfrac bevelled="true"><mrow><mi mathvariant="normal">π</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mo>-</mo><mi>ξ</mi></mrow></mfenced><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi>ξ</mi><mo>+</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi>ξ</mi></mrow><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>+</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfrac><mo>-</mo><mfrac><mrow><mi mathvariant="normal">π</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642185&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642182&type= 70.27333069 11.34533310 <math display="block" id="M5"><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi>ξ</mi><mo>=</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>+</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">Δ</mi><mi>φ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642191&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642187&type= 56.38800049 4.48733330 <math display="block" id="M6"><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">R</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><mo>=</mo><mi>O</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>+</mo></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.5</mn><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msup><mrow><mi>ξ</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup></mrow></mfenced><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642197&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642195&type= 71.79733276 9.99066734 <math display="block" id="M7"><mi>O</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="normal">π</mi></mrow></mfrac><mfenced separators="|"><mrow><mi>t</mi><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi>t</mi><mo>⋅</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi>t</mi></mrow></mfenced><mfenced separators="|"><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>+</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642203&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642200&type= 69.08799744 7.70466709 <math display="block" id="M8"><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi>t</mi><mo>=</mo><mfrac><mrow><mi>h</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mfrac><mrow><mroot><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">Δ</mi><mi>φ</mi></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>+</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642211&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642205&type= 56.13399887 11.26066685 <math display="block" id="M9"><mi>D</mi><mo>=</mo><mroot><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><msup><mrow><mi mathvariant="normal">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>+</mo><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><msup><mrow><mi mathvariant="normal">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>-</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">Δ</mi><mi>φ</mi></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642218&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642215&type= 64.60066223 4.91066647 <math display="block" id="M10"><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msup><mrow><mi>ξ</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup><mo>=</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>+</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">Δ</mi><mi>φ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642225&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642220&type= 57.40399933 4.82600021 <math display="block" id="M11"><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><msup><mrow><mi mathvariant="normal">n</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mfenced separators="|"><mrow><mfrac><mrow><mi>b</mi></mrow><mrow><mi>r</mi></mrow></mfrac><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><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=19642229&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642227&type= 27.77066803 8.80533314 <math display="block" id="M12"><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><msup><mrow><mi mathvariant="normal">n</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><mfenced separators="|"><mrow><mfrac><mrow><mi>b</mi></mrow><mrow><mi>r</mi></mrow></mfrac><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><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=19642235&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642232&type= 27.94000053 8.80533314 式中， K RossThick 和 K LiSparseR 分别为 RossThick 体散射核和 LiSparseR 几何光学核， f iso 、 f RossThick 、 f LiSparseR 分别代表各向同性核系数、体散射核系数和几何光学核系数。当观测角度不低于3个，即可采用最小二乘法求解这3个核系数。 式（8） 式（8） 中的 h/b 和式（ 11 11 ）、（ 12 12 ）中的 b/r 通常取值为2和1。 2.1.2　LSF-Li模型 3 考虑到热红外波段连续植被的辐射特性不再由散射相函数主导， Su等（2002） Su等（2002） 基于李小文等提出的非同温像元有效发射率的概念模型（ Li等，1999 Li等，1999 ； 李小文 等，1999 李小文 等，1999 ），提出了考虑叶片层和土壤层温差的适用于连续植被热辐射方向性模拟的LSF核，并将LiSparseR核替换为LiDenseR核，构建了三核线性加权的LSF-Li模型（ 式（13） 式（13） ）。该模型中的LSF核仅仅与观测天顶角有关（ 式（14） 式（14） ），与太阳位置无关，但LiDenseR核的取值同时由观测方向和太阳方向决定（ 式（15） 式（15） ）。 Bian等（2021） Bian等（2021） 以cos θ v 为自变量对LSF核的公式进行了简化（ 式（16） 式（16） ）。 Cao等（2021） Cao等（2021） 进一步对LSF核进行了归一化，即减去该核在天顶方向的取值（1.0304）（ 式（17） 式（17） ）。 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stretchy="false">)</mo><mo>+</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">R</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">R</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math> 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mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfrac><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">4</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></mfrac><mo>+</mo></mtd></mtr><mtr><mtd><mn mathvariant="normal">0.15</mn><mo>⋅</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>-</mo><mn mathvariant="normal">0.75</mn><mo>/</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></mrow></msup></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642247&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642244&type= 80.68733978 17.18733406 <math display="block" id="M15"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">R</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msup><mrow><mi>ξ</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup></mrow></mfenced><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>+</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>-</mo><mi>O</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msubsup><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mfrac><mo>-</mo><mn mathvariant="normal">2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642254&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642251&type= 72.81333160 9.39799976 <math display="block" id="M16"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">F</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><mo>=</mo><mn mathvariant="normal">0.069</mn><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">0.215</mn><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>+</mo><mn mathvariant="normal">1.176</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642260&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642256&type= 76.70800018 4.91066647 <math display="block" id="M17"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">F</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><mo>=</mo><mn mathvariant="normal">0.069</mn><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">0.215</mn><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>+</mo><mn mathvariant="normal">0.1456</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642265&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642263&type= 78.57066345 4.91066647 2.2　热红外核驱动模型通用框架 2 连续植被和离散植被的反射率方向性特征差异大，因此分别构建核的思路在可见光近红外波段是可行的。然而，在热红外波段，针对连续植被而言，太阳光的照射不会直接反射进入传感器，因此并非散射相函数在主导方向性特征。其真正的物理过程是首先通过辐射强迫对光照组分进行“加热”，且热惯量会导致一定的延时现象（Liu等，2019b），在产生了光照叶片与阴影叶片温差、光照土壤与阴影土壤温差之后，可视四组分面积比例的方向性决定了冠层热辐射的方向性，即可视的光照组分越多，则该方向的亮温就越大。因此，在热红外波段，连续植被和离散植被的方向性特征均由面积比例主导，他们的特征可以合并表达。基于此， Cao等（2021） Cao等（2021） 从植被冠层热辐射方向性几何光学物理模型出发，经过系列推导和简化，首次提出了热红外核驱动模型通用框架（ 式（18） 式（18） ）。 <math display="block" id="M18"><mtable columnalign="left"><mtr><mtd><mi>T</mi><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><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><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">B</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">e</mi></mrow></msub><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">B</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">e</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">t</mi></mrow></msub><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">t</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo>,</mo><mi>w</mi><mi>i</mi><mi>d</mi><mi>t</mi><mi>h</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642271&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642268&type= 61.80666733 9.99066734 该框架的整体构建思路如 图2 图2 所示，其将植被冠层热辐射方向性特征分解为上层叶片和下层土壤温差导致的方向性特征（通常土壤比叶片温度高，该特征为方位向无关的倒碗型）以及光照组分和阴影组分温差导致的方向性特征（离热点越远，该温差贡献越弱，所以该特征为以热点为中心的山脊型）。这两个特征对应着热红外波段的两个新核：叶片土壤温差特征由几何光学底核（ K BaseShape ，也可叫做基础形状核）刻画，光照阴影温差特征由几何光学顶核（ K Hotspot ，也可叫做热点核）刻画。连续植被的孔隙通常比离散植被小，因此其热点宽度通常比离散植被窄，为了同时适用这两种典型植被冠层，在新提出的几何光学顶核中，热点宽度是可调整的自由变量。因此， Cao等（2021） Cao等（2021） 提出的热红外核驱动模型通用框架包含4个未知数：各向同性核系数 f iso 、基础形状核系数 f BaseShape 、热点高度 f Hotspot 和热点宽度 width （ 式（18） 式（18） ）。 2.2.1　Vinnikov模型 3 为了对美国静止卫星组网（GOES-EAST和GOES-WEST）得到的地表温度产品进行方向性校正， Vinnikov等（2012） Vinnikov等（2012） 提出了一个三核线性核驱动模型（式（ 19 19 ）—（ 21 21 ）），包含各向同性核、发射率核以及太阳核。该模型中核的表达式并非基于严格的物理模型推导得来，属于数学统计模型的范畴。作者称之为纯经验核，并尝试对发射率核和太阳核的功能进行了初步的解释。这个模型可以视作热红外核驱动模型通用框架的一个实例，即用发射率核刻画基础形状，用太阳核刻画热点贡献，最大的差异在于热点宽度不是自由变量。 <math display="block" id="M19"><mtable columnalign="left"><mtr><mtd><mi>T</mi><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>+</mo><mfenced separators="|"><mrow><mi>A</mi><mo>⋅</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></mfenced><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi><mi 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http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642284&type= 64.51599884 12.19200039 <math display="block" id="M20"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">y</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642294&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642289&type= 34.12067032 4.57200003 <math display="block" id="M21"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><mo>=</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>-</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">Δ</mi><mi>φ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642299&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642297&type= 77.72399902 4.65666676 式中，共有3个未知数，其中 T N （ 式（18） 式（18） 中的 f iso ）表示天顶方向的亮度温度， A 和 D 为待求解的系数。 2.2.2　RL模型 3 Roujean（2000） Roujean（2000） 提出一个双参数（热点高度和热点宽度）的热点模型来描述地表反射率曲线在主平面内的趋势。当观测方向偏离太阳时，传感器可以看到更多的阴影元素，这会同时导致反射率和方向亮温的降低，因此反射过程和辐射过程的物理特性有类似之处。基于此， Lagouarde和Irvine（2008） Lagouarde和Irvine（2008） 用地表亮温替换反射率将原始模型扩展到热红外波段（热红外版本称为Roujean-Lagouarde模型，简称RL模型， 式（22） 式（22） ）。与Ross-Li模型一样，RL模型也是直接拓展自可见光近红外领域的模型，但是RL模型不属于经典框架（ 式（1） 式（1） ）而是属于新框架（ 式（18） 式（18） ），其特点是基本形状核为空、仅包括各项同性核（ T N ）和热点宽度可调的非线性热点核 K RL 。 K RL 在天顶方向取值为0，即该核是经过归一化之后的结果。 <math display="block" id="M22"><mtable columnalign="left"><mtr><mtd><mi>T</mi><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>N</mi></mrow></msub><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">B</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">e</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">B</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">e</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo></mtd></mtr><mtr><mtd><mi mathvariant="normal">Δ</mi><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">S</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">L</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo>,</mo><mi>k</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642306&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642304&type= 63.24599838 9.99066734 <math display="block" id="M23"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">B</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">e</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mn mathvariant="normal">0</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642310&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642308&type= 22.86000061 4.57200003 <math display="block" id="M24"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">L</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo>-</mo><mi>k</mi><mi>f</mi></mrow></msup><mo>-</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo>-</mo><mi>k</mi><mo>⋅</mo><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></msup></mrow><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo>-</mo><mi>k</mi><mo>⋅</mo><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub></mrow></msup></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642313&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642312&type= 44.02666473 9.22866726 <math display="block" id="M25"><mi>f</mi><mo>=</mo><mroot><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><msup><mrow><mi mathvariant="normal">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>+</mo><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><msup><mrow><mi mathvariant="normal">n</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">Δ</mi><mi>φ</mi></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642317&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642315&type= 63.83866882 5.33400011 式中，包括3个待求解系数：天顶方向的地表亮温 T N ，热点高度（Δ T HS ）和热点宽度（ k ）。 2.2.3　Vinnikov-RL模型 3 Ermida等 （2018） Ermida等 （2018） 发现白天RL模型相比Vinnikov模型具有更好的刻画热点的能力，但RL模型不能应用于夜晚观测及稀疏植被冠层的观测，因为这两种情况下的热辐射方向性是由于发射率本身的方向性决定的，而不是太阳照射导致的光照阴影组分温差决定的。于是他们提出将Vinnikov模型中的发射率核 K Emissivity 与RL模型中的热点核 K RL 组合在一起构建新模型的思路，并称之为Kernel-Hotspot模型（ 式（26） 式（26） ），为了保持命名规则的一致性，本文称之为Vinnikov-RL模型。 <math display="block" id="M26"><mtable columnalign="left"><mtr><mtd><mi>T</mi><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">N</mi></mrow></msub><mo>+</mo><mfenced separators="|"><mrow><mi>A</mi><mo>⋅</mo><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">N</mi></mrow></msub></mrow></mfenced><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">y</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo></mtd></mtr><mtr><mtd><mi mathvariant="normal">Δ</mi><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">S</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">L</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo>,</mo><mi>k</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642325&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642321&type= 64.51599884 11.68400002 Cao等（2021） Cao等（2021） 基于热红外核驱动模型通用框架实例化得到了Vinnikov-RL模型在内的4个模型，但是在新框架内， K Emissivity 的功能不仅在于刻画夜间发射率方向性的影响，其在白天刻画几何光学底核的作用同样十分重要，这正是在白天Vinnikov-RL模型拟合能力显著优于RL模型的原因。Vinnikov-RL模型含有4个未知数：天底亮温 T N ，系数 A ，热点高度（ ΔT HS ）和热点宽度（ k） 。 2.2.4　Vinnikov-Chen模型 3 为了准确模拟热点主导的反射率变化趋势， Chen和Cihlar（1997） Chen和Cihlar（1997） 基于四尺度冠层反射率几何光学模型，提出了一个指数形式热点核函数 K chen （ 式（28） 式（28） ）。在可见光近红外领域中，该核通常作为一个修正项与其他的核（如RossThick）联合使用（比如乘积形式）。考虑到 K Chen 与 K RL 具有十分相似的模拟能力（差异在于 K Chen 没有归一化，在天顶方向取值不等于0）， Cao等（2021） Cao等（2021） 将 K Chen 作为一个单独的热点核代替Vinnikov-RL模型中的 K RL ，构建了新的模型Vinnikov-Chen（ 式（27） 式（27） ）。该模型包含4个待求参数，分别是 f iso ， f Emissivity ， f Chen 和 B 。 <math display="block" id="M27"><mtable columnalign="left"><mtr><mtd><mi>T</mi><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><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><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">y</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">y</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo>,</mo><mtext> </mtext><mi>B</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642329&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642327&type= 62.39933777 9.99066734 <math display="block" id="M28"><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>,</mo><mi mathvariant="normal">Δ</mi><mi>ϕ</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mo>-</mo><mfrac><mrow><mi>ξ</mi></mrow><mrow><mi mathvariant="normal">π</mi><mo>⋅</mo><mi>B</mi></mrow></mfrac></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642333&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642331&type= 34.12067032 7.02733374 <math display="block" id="M29"><mi>ξ</mi><mo>=</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>⋅</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>+</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">s</mi></mrow></msub><mo>⋅</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo>⋅</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">Δ</mi><mi>ϕ</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642339&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642336&type= 69.51132965 4.65666676 2.2.5　LSF-RL模型 3 LSF核与发射率核的公式形式类似，均是仅与观测天顶角相关的函数，他们之间的差异在于LSF核与冠层方向孔隙率之间物理相关，而发射率核是与观测天顶角的余弦值之间数学相关。LSF核的详细推导过程可参见（ Cao等，2019a Cao等，2019a ）的附录 A — B 。 Cao等（2021） Cao等（2021） 用 K LSF 代替Vinnikov-RL模型中的 K Emissivity ，构建了新的四参数热红外核驱动模型LSF-RL（ 式（30） 式（30） ）。该模型的4个未知数是：天顶方向的地表亮温 T N ，LSF核系数 f LSF ，热点高度（Δ T HS ）和热点宽度（ k ）。 <math display="block" id="M30"><mtable columnalign="left"><mtr><mtd><mi>T</mi><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">N</mi></mrow></msub><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">F</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">F</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo></mtd></mtr><mtr><mtd><mi mathvariant="normal">Δ</mi><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">H</mi><mi mathvariant="normal">S</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">L</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo>,</mo><mi>k</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642345&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642342&type= 55.79533768 9.99066734 2.2.6　LSF-Chen模型 3 在热红外核驱动模型通用框架内，将LSF-RL模型中的 K RL 代替为 K Chen 。可以得到新模型LSF-Chen的表达式，如下所示： <math display="block" id="M31"><mtable columnalign="left"><mtr><mtd><mi>T</mi><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo stretchy="false">)</mo><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><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">F</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>L</mi><mi>S</mi><mi>F</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi mathvariant="normal">v</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>f</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>⋅</mo><msub><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">(</mo><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 mathvariant="normal">Δ</mi><mi>φ</mi><mo>,</mo><mi>B</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642350&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19642347&type= 55.45666885 9.99066734 该模型同样有4个未知数：各向同性核系数 f iso 、基础形状核系数 f LSF 、热点核系数 f Chen 和热点宽度 B 。 2.3　核驱动模型适用性的分析方法 2 热红外核驱动模型在垄行植被中的适用性分析方法包括3个主要步骤：（1）计算核系数，利用实测的多角度方向亮温的角度信息计算核的取值，将核的取值和亮温值输入核驱动模型构建超定方程组求解核系数，如 图3 图3 中红色箭头所示；（2）拟合多角度亮温，利用实测的多角度方向亮温的角度信息计算核的取值，将核的取值和核系数代入核驱动模型可直接计算方向亮温，如 图3 图3 中紫色箭头所示；（3）将实测的多角度方向亮温和拟合的多角度方向亮温进行比较，计算RMSE和 R 2 指标，如 图3 图3 中蓝色箭头所示，RMSE最大的模型即为拟合能力最弱的模型，若RMSE超过给定阈值则为不适用。 3　数据 1 本文采用的多角度方向亮温数据包括两组，采集数据的实验区坐落在法国波尔多北部30 km处的Médoc地区（45°09′N，0°46'W）。实验区域内90%是垄行种植的葡萄园。葡萄园具备相似的垄行结构：垄宽0.35 m，垄间距1.30 m，垄高1.25 m，离地层高度0.40 m，垄向以东西朝向和南北朝向为主。1996-08-03，法国农业科学研究院在该实验区组织了航空热红外观测实验。实验采用的热红外设备为宽波段8—12 μm的Inframetrics M760，该设备加载了一个宽视场镜头（航向视场为80°，旁向视场为60°），为了获取最大60°的方向亮温观测，整个相机按照后向20°倾角安装在飞机上。飞机在4个平面内往返飞行：太阳主平面、垂直太阳主平面以及两个交叉平面。飞机飞行高度为430 m，飞行速度为50 m/s，相机采样频率为50 Hz。 数据处理包括辐射定标、镜头畸变校正、几何定位、大气校正、时空平滑5个主要步骤。其中时空平滑指的是将覆盖感兴趣区（比如南北垄向的葡萄园）的所有图像按照某个间隔（天顶角及方位角均为1°）离散为很多子图像，然后将所有具备相同观测角度的子图像合并计算平均值，该均值即代表感兴趣区在该方向的亮温。东西垄向葡萄园观测时间为12：15—13：06（UTC时间），观测期间太阳的位置从（26.7°，183.1°）移动到（29.2°，208.7°）。南北垄向葡萄园观测时间为12：29—13：06（UTC时间），观测期间太阳位置从（27.0°，190.5°）移动到（29.2°，208.7°）。最终，提取的时空平滑后的垄行植被冠层热辐射方向性强度分布如 图4 图4 所示。关于实验观测及信息提取的细节，可参考 Lagouarde等（2014） Lagouarde等（2014） 的文献。 1,2;3; 图4 图4 并非直接绘制的方向亮温绝对值，而是热辐射方向性强度，即方向亮温与天顶方向的亮温之间的差值。可以看出该垄行场景的热辐射方向性强度高达16 K（-12—4 K），方向亮温分布和热辐射方向性强度具有完全相同的特征刻画能力， 图4 图4 所给出的垄行植被热辐射方向性强度分布与垄行物理模型（ Du等，2020 Du等，2020 ； Liu等，2007 Liu等，2007 ； Ren等，2013 Ren等，2013 ； Yu等，2004 Yu等，2004 ）模拟的趋势十分接近，其具备3个基本特征：（1）整体呈现关于垄向轴对称的同心椭圆现象，而不是连续植被冠层常见的关于太阳主平面对称的同心圆现象。在近似平行垄行方向出现的高值条带区特征通常称为行效应，其产生的原因在于近似平行垄行方向可视的土壤面积比大且土壤温度比叶片高；（2）热点同侧的方向亮温比热点异侧高；（3）最大方向亮温出现在热点附近（即热点效应特征）。 4　结果 1 图5 图5 — 图6 图6 给出了东西垄向葡萄园冠层拟合结果及拟合精度对比图。从 图5 图5 可以看出，Vinnikov模型的拟合结果没有明显的热点特征，其他模型模拟的结果非常接近，均表现为以太阳主平面为对称轴、以热点为中心的同心圆或者同心椭圆。RL，Vinnikov-RL和LSF-RL共3个包括RL顶核的模型的同心椭圆的长轴在垂直垄向、短轴在顺垄方向。Ross-Li，LSF-Li，Vinnikov-Chen和LSF-Chen模型模拟结果特征更接近同心圆。从 图6 图6 可以看出，8个核驱动模型的拟合精度均较低，整体上RMSE处于2.0 K（Vinnikov-RL模型）至2.4 K（Vinnikov-Chen模型）之间， R 2 处于0.60（LSF-Chen模型）至0.67（Vinnikov-RL模型）之间。在经典框架内，针对该场景，Ross-Li的模拟精度优于LSF-Li。在新框架内的三参数模型中，Vinnikov模型优于RL模型。在新框架内的四参数模型中，Vinnikov-RL模型与LSF-RL精度相当，Vinnikov-Chen和LSF-Chen精度相当，且RL系列显著优于Chen系列。 1,2,3,4;5,6,7,8;9; 1,2,3,4;5,6,7,8; 与此类似， 图7 图7 — 图8 图8 对比了南北垄向葡萄园冠层拟合结果及拟合精度。RL模型拟合结果为长轴在垂直垄向的同心椭圆（圆心为热点）。Ross-Li、LSF-Li、Vinnikov-RL、Vinnikov-Chen、LSF-RL、LSF-Chen的模拟结果均为以热点为中心的同心圆。Vinnikov模型拟合结果也是同心圆，但其圆心不与热点方向重合，而是偏向天顶方向。整体拟合精度与东西垄向葡萄园冠层接近，RMSE处于1.9 K（Ross-Li模型）至2.2 K（RL模型）， R 2 处于0.62（RL模型）至0.69（Ross-Li模型）。在经典框架内，Ross-Li的模拟精度优于LSF-Li。在新框架内的三参数模型中，Vinnikov模型略优于RL模型，且这两个模型的精度最低。在新框架内的四参数模型中，Vinnikov-RL、Vinnikov-Chen、LSF-RL和LSF-Chen拟合结果非常接近，且均比Ross-Li模型模拟精度略低。 1,2,3,4;5,6,7,8;9; 1,2,3,4;5,6,7,8; 对比 图5 图5 和 图7 图7 可以发现，虽然驱动数据存在（ 图4（a） 图4（a） 和 图4（b） 图4（b） ）显著差异，但是用现有的8个核驱动模型模拟的结果却十分相似，这是因为现有的核驱动模型的核均与垄向无关，并不具备垄行特征（即行效应）的刻画能力，所以它们的拟合结果均对垄向不敏感。 5　结论 1 本文首先回顾了热红外核驱动模型经典框架下的两个模型（Ross-Li、LSF-Li）和热红外核驱动模型新框架下的6个模型（Vinnikov、RL、Vinnikov RL，Vinnikov-Chen、LSF-RL、LSF-Chen），然后利用它们对2组航空实测的垄行葡萄园冠层方向亮温数据进行拟合。结果表明（1）两类框架下的模型在垄行植被冠层方向亮温上的拟合能力非常接近，新框架未表现出优势；（2）两类框架下的模型的方向亮温拟合RMSE约2 K，拟合精度均有待提高；（3）现有核驱动模型的建立未参照垄行植被物理模型发展，未来将垄向作为未知变量，有待发展新的可刻画垄行特征的核。 本文的创新点在于首次利用实测数据量化了热红外核驱动模型在垄行植被冠层上的拟合精度，发现了现有热红外核驱动模型在垄行植被冠层上的拟合能力不足，指出了精度较低的原因在于无法模拟行效应特征。本文的不足之处在于使用的实测数据仅两组，未来需要开展更多的野外多角度观测实验、获取更多的数据来验证本文的结论。此外，下一步研究计划将重点关注适用于垄行植被冠层的新核的推导。 参考文献（References） Bian Z J , Qi J B , Wu S B , Wang Y S , Liu S Y , Xu B D , Du Y M , Cao B , Li H , Huang H G , Xiao Q and Liu Q H . 2021 . A review on the development and application of three dimensional computer simulation mode of optical remote sensing . Journal of Remote Sensing , 25 ( 2 ): 559 - 576 A review on the development and application of three dimensional computer simulation mode of optical remote sensing 卞尊健 , 漆建波 , 吴胜标 , 王雨生 , 刘守阳 , 徐保东 , 杜永明 , 曹彪 , 历华 , 黄华国 , 肖青 , 柳钦火 . 2021 . 光学遥感三维计算机模拟模型的研究进展与应用 . 遥感学报 , 25 ( 2 ): 559- 576 [ DOI: 10.11834/jrs.20219274 http://dx.doi.org/10.11834/jrs.20219274 ] 光学遥感三维计算机模拟模型的研究进展与应用 Bian Z J , Roujean J L , Cao B , Du Y M , Li H , Gamet P , Fang J Y , Xiao Q and Liu Q H . 2021 . Modeling the directional anisotropy of fine-scale TIR emissions over tree and crop canopies based on UAV measurements . Remote Sensing of Environment , 252 : 112150 [ DOI: 10.1016/j.rse.2020.112150 http://dx.doi.org/10.1016/j.rse.2020.112150 ] Modeling the directional anisotropy of fine-scale TIR emissions over tree and crop canopies based on UAV measurements Cao B , Gastellu-Etchegorry J P , Du Y M , Li H , Bian Z J , Hu T , Fan W J , Xiao Q and Liu Q H . 2019a . Evaluation of four kernel-driven models in the thermal infrared band . IEEE Transactions on Geoscience and Remote Sensing , 57 ( 8 ): 5456 - 5475 [ DOI: 10.1109/TGRS.2019.2899600 http://dx.doi.org/10.1109/TGRS.2019.2899600 ] Evaluation of four kernel-driven models in the thermal infrared band Cao B , Guo M Z , Fan W J , Xu X R , Peng J J , Ren H Z , Du Y M , Li H , Bian Z J , Hu T , Xiao Q and Liu Q H . 2018 . A new directional canopy emissivity model based on spectral invariants . IEEE Transactions on Geoscience and Remote Sensing , 56 ( 12 ): 6911 - 6926 [ DOI: 10.1109/TGRS.2018.2845678 http://dx.doi.org/10.1109/TGRS.2018.2845678 ] A new directional canopy emissivity model based on spectral invariants Cao B , Liu Q H , Du Y M , Roujean J L , Gastellu-Etchegorry J P , Trigo I F , Zhan W F , Yu Y Y , Cheng J , Jacob F , Lagouarde J P , Bian Z J , Li H , Hu T and Xiao Q . 2019b . A review of earth surface thermal radiation directionality observing and modeling: historical development, current status and perspectives . Remote Sensing of Environment , 232 : 111304 [ DOI: 10.1016/j.rse.2019.111304 http://dx.doi.org/10.1016/j.rse.2019.111304 ] A review of earth surface thermal radiation directionality observing and modeling: historical development, current status and perspectives Cao B , Roujean J L , Gastellu-Etchegorry J P , Liu Q H , Du Y M , Lagouarde J P , Huang H , Li H , Bian Z J , Hu T , Qin B X , Ran X T and Xiao Q . 2021 . A general framework of kernel-driven modeling in the thermal infrared domain . Remote Sensing of Environment , 252 : 112157 [ DOI: 10.1016/j.rse.2020.112157 http://dx.doi.org/10.1016/j.rse.2020.112157 ] A general framework of kernel-driven modeling in the thermal infrared domain Chen J M and Cihlar J . 1997 . A hotspot function in a simple bidirectional reflectance model for satellite applications . Journal of Geophysical Research : Atmospheres , 102 ( D22 ): 25907 - 25913 [ DOI: 10.1029/97JD02010 http://dx.doi.org/10.1029/97JD02010 ] A hotspot function in a simple bidirectional reflectance model for satellite applications Chen Y H , Wu J T and Wang D D . 2018 . Review of the study on generalized computer simulation of land surface thermal anisotropy . Advances in Earth Science , 33 ( 6 ): 555 - 567 Review of the study on generalized computer simulation of land surface thermal anisotropy 陈云浩 , 吴佳桐 , 王丹丹 . 2018 . 广义地表热辐射方向性计算机模拟研究进展 . 地球科学进展 , 33 ( 6 ): 555- 567 [ DOI: 10.11867/j.issn.1001-8166.2018.06.0555 http://dx.doi.org/10.11867/j.issn.1001-8166.2018.06.0555 ] 广义地表热辐射方向性计算机模拟研究进展 Duan S B , Ru C , Li Z L , Wang M M , Xu H Q , Li H , Wu P H , Zhan W F , Zhou J , Zhao W , Ren H Z , Wu H , Tang B H , Zhang X , Shang Guo F and Qin Z H . 2021 . Reviews of methods for land surface temperature retrieval from Landsat thermal infrared data . National Remote Sensing Bulletin , 25 ( 8 ): 1591 - 1617 Reviews of methods for land surface temperature retrieval from Landsat thermal infrared data 段四波 , 茹晨 , 李召良 , 王猛猛 , 徐涵秋 , 历华 , 吴鹏海 , 占文凤 , 周纪 , 赵伟 , 任华忠 , 吴骅 , 唐伯惠 , 张霞 , 尚 国琲 , 覃志豪 . 2021 . Landsat卫星热红外数据地表温度遥感反演研究进展 . 遥感学报 , 25 ( 8 ): 1591- 1617 [ DOI: 10.11834/jrs.20211296 http://dx.doi.org/10.11834/jrs.20211296 ] Landsat卫星热红外数据地表温度遥感反演研究进展 Du Y M , Cao B , Li H , Bian Z J , Qin B X , Xiao Q , Liu Q H , Zeng Y J and Su Z B . 2020 . Modeling directional brightness temperature (DBT) over crop canopy with effects of intra-row heterogeneity . Remote Sensing , 12 ( 17 ): 2667 [ DOI: 10.3390/rs12172667 http://dx.doi.org/10.3390/rs12172667 ] Modeling directional brightness temperature (DBT) over crop canopy with effects of intra-row heterogeneity Duffour C , Lagouarde J P and Roujean J L . 2016 . A two parameter model to simulate thermal infrared directional effects for remote sensing applications . Remote Sensing of Environment , 186 : 250 - 261 [ DOI: 10.1016/j.rse.2016.08.012 http://dx.doi.org/10.1016/j.rse.2016.08.012 ] A two parameter model to simulate thermal infrared directional effects for remote sensing applications Ermida S L , Trigo I F , DaCamara C C and Roujean J L . 2018 . Assessing the potential of parametric models to correct directional effects on local to global remotely sensed LST . Remote Sensing of Environment , 209 : 410 - 422 [ DOI: 10.1016/j.rse.2018.02.066 http://dx.doi.org/10.1016/j.rse.2018.02.066 ] Assessing the potential of parametric models to correct directional effects on local to global remotely sensed LST Gastellu-Etchegorry J P , Lauret N , Yin T G , Landier L , Kallel A , Malenovský Z , Al Bitar A , Aval J , Benhmida S , Qi J B , Medjdoub G , Guilleux J , Chavanon E , Cook B , Morton D , Chrysoulakis N and Mitraka Z . 2017 . DART: recent advances in remote sensing data modeling with atmosphere, polarization, and chlorophyll fluorescence . IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing , 10 ( 6 ): 2640 - 2649 [ DOI: 10.1109/jstars.2017.2685528 http://dx.doi.org/10.1109/jstars.2017.2685528 ] DART: recent advances in remote sensing data modeling with atmosphere, polarization, and chlorophyll fluorescence Hu T , Cao B , Du Y M , Li H , Wang C , Bian Z J , Sun D L and Liu Q H . 2017 . Estimation of surface upward longwave radiation using a direct physical algorithm . IEEE Transactions on Geoscience and Remote Sensing , 55 ( 8 ): 4412 - 4426 [ DOI: 10.1109/TGRS.2017.2692261 http://dx.doi.org/10.1109/TGRS.2017.2692261 ] Estimation of surface upward longwave radiation using a direct physical algorithm Lagouarde J P , Dayau S , Moreau P and Guyon D . 2014 . Directional anisotropy of brightness surface temperature over vineyards: case study over the Medoc region (SW France) . IEEE Geoscience and Remote Sensing Letters , 11 ( 2 ): 574 - 578 [ DOI: 10.1109/LGRS.2013.2282492 http://dx.doi.org/10.1109/LGRS.2013.2282492 ] Directional anisotropy of brightness surface temperature over vineyards: case study over the Medoc region (SW France) Lagouarde J P and Irvine M . 2008 . Directional anisotropy in thermal infrared measurements over Toulouse city centre during the CAPITOUL measurement campaigns: first results . Meteorology and Atmospheric Physics , 102 : 173 - 185 [ DOI: 10.1007/s00703-008-0325-4 http://dx.doi.org/10.1007/s00703-008-0325-4 ] Directional anisotropy in thermal infrared measurements over Toulouse city centre during the CAPITOUL measurement campaigns: first results Li X W , Strahler A H and Friedl M A . 1999 . A conceptual model for effective directional emissivity from nonisothermal surfaces . IEEE Transactions on Geoscience and Remote Sensing , 37 ( 5 ): 2508 - 2517 [ DOI: 10.1109/36.789646 http://dx.doi.org/10.1109/36.789646 ] A conceptual model for effective directional emissivity from nonisothermal surfaces Li X W , Wang J D and Strahler A H . 1999 . Scale effect of Planck’s law over nonisothermal blackbody surface . Science in China Series E : Technological Sciences , 42 ( 6 ): 652 - 656 Scale effect of Planck’s law over nonisothermal blackbody surface 李小文 , 王锦地 , Strahler A H . 1999 . 非同温黑体表面上Planck定律的尺度效应 . 中国科学E辑 , 29 ( 5 ): 422- 426 [ DOI: 10.1007/BF02917003 http://dx.doi.org/10.1007/BF02917003 ] 非同温黑体表面上Planck定律的尺度效应 Li Z L , Tang B H , Wu H , Ren H Z , Yan G J , Wan Z M , Trigo I F and Sobrino J A . 2013 . Satellite-derived land surface temperature: current status and perspectives . Remote Sensing of Environment , 131 : 14 - 37 [ DOI: 10.1016/j.rse.2012.12.008 http://dx.doi.org/10.1016/j.rse.2012.12.008 ] Satellite-derived land surface temperature: current status and perspectives Liu M , Tang R L , Li Z L , Gao M F and Yao Y J . 2021 . Progress of data-driven remotely sensed retrieval methods and products on land surface evapotranspiration . National Remote Sensing Bulletin , 25 ( 8 ): 1517 - 1537 Progress of data-driven remotely sensed retrieval methods and products on land surface evapotranspiration 刘萌 , 唐荣林 , 李召良 , 高懋芳 , 姚云军 . 2021 . 数据驱动的蒸散发遥感反演方法及产品研究进展 . 遥感学报 , 25 ( 8 ): 1517- 1537 [ DOI: 10.11834/jrs.20211310 http://dx.doi.org/10.11834/jrs.20211310 ] 数据驱动的蒸散发遥感反演方法及产品研究进展 Liu Q H , Huang H G , Qin W H , Fu K H and Li X W . 2007 . An extended 3-D radiosity-graphics combined model for studying thermal-emission directionality of crop canopy . IEEE Transactions on Geoscience and Remote Sensing , 45 ( 9 ): 2900 - 2918 [ DOI: 10.1109/TGRS.2007.902272 http://dx.doi.org/10.1109/TGRS.2007.902272 ] An extended 3-D radiosity-graphics combined model for studying thermal-emission directionality of crop canopy Liu X Y , Tang B H and Li Z L . 2018 . Evaluation of three parametric models for estimating directional thermal radiation from simulation, airborne, and satellite data . Remote Sensing , 10 ( 3 ): 420 [ DOI: 10.3390/rs10030420 http://dx.doi.org/10.3390/rs10030420 ] Evaluation of three parametric models for estimating directional thermal radiation from simulation, airborne, and satellite data Liu X Y , Tang B H , Li Z L and Rasmussen M O . 2020b . Influence of temperature inertia on thermal radiation directionality modeling based on geometric optical model . IEEE Transactions on Geoscience and Remote Sensing , 58 ( 5 ): 3445 - 3457 [ DOI: 10.1109/TGRS.2019.2956258 http://dx.doi.org/10.1109/TGRS.2019.2956258 ] Influence of temperature inertia on thermal radiation directionality modeling based on geometric optical model Liu X Y , Tang B H , Li Z L , Zhang X and Shang G F . 2020a . On the derivation of geometric optical kernels for directional thermal radiation . Earth and Space Science , 7 ( 1 ): e2019 EA 000895 [ DOI: 10.1029/2019EA000895 http://dx.doi.org/10.1029/2019EA000895 ] On the derivation of geometric optical kernels for directional thermal radiation Lucht W , Schaaf C B and Strahler A H . 2000 . An algorithm for the retrieval of albedo from space using semiempirical BRDF models . IEEE Transactions on Geoscience and Remote Sensing , 38 ( 2 ): 977 - 998 [ DOI: 10.1109/36.841980 http://dx.doi.org/10.1109/36.841980 ] An algorithm for the retrieval of albedo from space using semiempirical BRDF models Ma W , Chen Y H , Zhan W F and Zhou J . 2013 . Thermal anisotropy model for simulated three dimensional urban targets . Journal of Remote Sensing , 17 ( 1 ): 62 - 76 Thermal anisotropy model for simulated three dimensional urban targets 马伟 , 陈云浩 , 占文凤 , 周纪 . 2013 . 城市模拟目标的3维热辐射方向性模型 . 遥感学报 , 17 ( 1 ): 62- 76 [ DOI: 10.11834/jrs.20131361 http://dx.doi.org/10.11834/jrs.20131361 ] 城市模拟目标的3维热辐射方向性模型 Monteith J L and Szeicz G . 1962 . Radiative temperature in the heat balance of natural surfaces . Quarterly Journal of the Royal Meteorological Society , 88 ( 378 ): 496 - 507 [ DOI: 10.1002/qj.49708837811 http://dx.doi.org/10.1002/qj.49708837811 ] Radiative temperature in the heat balance of natural surfaces Peng J J , Liu Q , Liu Q H , Li J H , Ma H Z and Fang L . 2011 . Kernel-driven model fitting of multi-angle thermal infrared brightness temperature and its application . Journal of Infrared and Millimeter Waves , 30 ( 4 ): 361 - 365, 371 Kernel-driven model fitting of multi-angle thermal infrared brightness temperature and its application 彭菁菁 , 刘强 , 柳钦火 , 李加洪 , 马红章 , 方莉 . 2011 . 多角度热红外亮温值的模型拟合与应用 . 红外与毫米波学报 , 30 ( 4 ): 361 - 365 , 371 [ DOI: 10.3724/SP.J.1010.2011.00361 http://dx.doi.org/10.3724/SP.J.1010.2011.00361 ] 多角度热红外亮温值的模型拟合与应用 Pinheiro A C T , Privette J L and Guillevic P . 2006 . Modeling the observed angular anisotropy of land surface temperature in a Savanna . IEEE Transactions on Geoscience and Remote Sensing , 44 ( 4 ): 1036 - 1047 [ DOI: 10.1109/TGRS.2005.863827 http://dx.doi.org/10.1109/TGRS.2005.863827 ] Modeling the observed angular anisotropy of land surface temperature in a Savanna Ran X T , Cao B , Qin B X , Bian Z J , Du Y M , Li H , Xiao Q and Liu Q H . 2021 . Assessment of five thermal infrared kernel-driven models using limited multiangle observations . IEEE Geoscience and Remote Sensing Letters , 1 - 5 [ DOI: 10.1109/LGRS.2021.3078647 http://dx.doi.org/10.1109/LGRS.2021.3078647 ] Assessment of five thermal infrared kernel-driven models using limited multiangle observations Ren H Z , Liu R Y , Yan G J , Mu X H , Li Z L , Nerry F and Liu Q . 2014 . Angular normalization of land surface temperature and emissivity using multiangular middle and thermal infrared data . IEEE Transactions on Geoscience and Remote Sensing , 52 ( 8 ): 4913 - 4931 [ DOI: 10.1109/TGRS.2013.2285924 http://dx.doi.org/10.1109/TGRS.2013.2285924 ] Angular normalization of land surface temperature and emissivity using multiangular middle and thermal infrared data Ren H Z , Yan G J , Liu R Y , Nerry F , Li Z L and Hu R H . 2013 . Impact of sensor footprint on measurement of directional brightness temperature of row crop canopies . Remote Sensing of Environment , 134 : 135 - 151 [ DOI: 10.1016/j.rse.2013.02.025 http://dx.doi.org/10.1016/j.rse.2013.02.025 ] Impact of sensor footprint on measurement of directional brightness temperature of row crop canopies Roujean J L . 2000 . A parametric hot spot model for optical remote sensing applications . Remote Sensing of Environment , 71 ( 2 ): 197 - 206 [ DOI: 10.1016/S0034-4257(99)00080-2 http://dx.doi.org/10.1016/S0034-4257(99)00080-2 ] A parametric hot spot model for optical remote sensing applications Roujean J L , Leroy M and Deschamps P Y . 1992 . A bidirectional reflectance model of the Earth’s surface for the correction of remote sensing data . Journal of Geophysical Research : Atmospheres , 97 ( D18 ): 20455 - 20468 [ DOI: 10.1029/92JD01411 http://dx.doi.org/10.1029/92JD01411 ] A bidirectional reflectance model of the Earth’s surface for the correction of remote sensing data Schaaf C B , Gao F , Strahler A H , Lucht W , Li X W , Tsang T , Strugnell N C , Zhang X Y , Jin Y F , Muller J P , Lewis P , Barnsley M , Hobson P , Disney M , Roberts G , Dunderdale M , Doll C , d’Entremont R P , Hu B X , Liang S L , Privette J L and Roy D . 2002 . First operational BRDF, albedo nadir reflectance products from MODIS . Remote Sensing of Environment , 83 ( 1/2 ): 135 - 148 [ DOI: 10.1016/S0034-4257(02)00091-3 http://dx.doi.org/10.1016/S0034-4257(02)00091-3 ] First operational BRDF, albedo nadir reflectance products from MODIS Su L H , Li X W , Friedl M , Strahler A and Gu X F . 2002 . A kernel-driven model of effective directional emissivity for non-isothermal surfaces . Progress in Natural Science , 12 ( 8 ): 603 - 607 A kernel-driven model of effective directional emissivity for non-isothermal surfaces Verhoef W , Jia L , Xiao Q and Su Z . 2007 . Unified optical-thermal four-stream radiative transfer theory for homogeneous vegetation canopies . IEEE Transactions on Geoscience and Remote Sensing , 45 ( 6 ): 1808 - 1822 [ DOI: 10.1109/TGRS.2007.895844 http://dx.doi.org/10.1109/TGRS.2007.895844 ] Unified optical-thermal four-stream radiative transfer theory for homogeneous vegetation canopies Vinnikov K Y , Yu Y Y , Goldberg M D , Tarpley D , Romanov P , Laszlo I and Chen M . 2012 . Angular anisotropy of satellite observations of land surface temperature . Geophysical Research Letters , 39 : L 23802 [ DOI: 10.1029/2012GL054059 http://dx.doi.org/10.1029/2012GL054059 ] Angular anisotropy of satellite observations of land surface temperature Wang D D and Chen Y H . 2019 . A geometric model to simulate urban thermal anisotropy in simplified dense neighborhoods (GUTA-Dense) . IEEE Transactions on Geoscience and Remote Sensing , 57 ( 8 ): 6226 - 6239 [ DOI: 10.1109/TGRS.2019.2904871 http://dx.doi.org/10.1109/TGRS.2019.2904871 ] A geometric model to simulate urban thermal anisotropy in simplified dense neighborhoods (GUTA-Dense) Wang D D , Chen Y H , Voogt J A , Krayenhoff E S , Wang J F and Wang L B . 2020 . An advanced geometric model to simulate thermal anisotropy time-series for simplified urban neighborhoods (GUTA-T) . Remote Sensing of Environment , 237 : 111547 [ DOI: 10.1016/j.rse.2019.111547 http://dx.doi.org/10.1016/j.rse.2019.111547 ] An advanced geometric model to simulate thermal anisotropy time-series for simplified urban neighborhoods (GUTA-T) Wang D D , Chen Y H and Zhan W F . 2018 . A geometric model to simulate thermal anisotropy over a sparse urban surface (GUTA-sparse) . Remote Sensing of Environment , 209 : 263 - 274 [ DOI: 10.1016/j.rse.2018.02.051 http://dx.doi.org/10.1016/j.rse.2018.02.051 ] A geometric model to simulate thermal anisotropy over a sparse urban surface (GUTA-sparse) Wanner W , Li X and Strahler A H . 1995 . On the derivation of kernels for kernel-driven models of bidirectional reflectance . Journal of Geophysical Research : Atmospheres , 100 ( D10 ): 21077 - 21089 [ DOI: 10.1029/95JD02371 http://dx.doi.org/10.1029/95JD02371 ] On the derivation of kernels for kernel-driven models of bidirectional reflectance Yang Y K , Li H , Sun L , Du Y M , Cao B , Liu Q H and Zhu J S . 2019 . Land surface temperature and emissivity separation from GF-5 visual and infrared multispectral imager data . Journal of Remote Sensing , 23 ( 6 ): 1132 - 1146 Land surface temperature and emissivity separation from GF-5 visual and infrared multispectral imager data 杨以坤 , 历华 , 孙林 , 杜永明 , 曹彪 , 柳钦火 , 朱金山 . 2019 . 高分五号全谱段光谱成像仪地表温度与发射率反演 . 遥感学报 , 23 ( 6 ): 1132- 1146 [ DOI: 10.11834/jrs.20198053 http://dx.doi.org/10.11834/jrs.20198053 ] 高分五号全谱段光谱成像仪地表温度与发射率反演 Yu T , Gu X F , Tian G L , LeGrand M , Baret F , Hanocq J F , Bosseno R and Zhang Y . 2004 . Modeling directional brightness temperature over a maize canopy in row structure . IEEE Transactions on Geoscience and Remote Sensing , 42 ( 10 ): 2290 - 2304 [ DOI: 10.1109/tgrs.2004.834196 http://dx.doi.org/10.1109/tgrs.2004.834196 ] Modeling directional brightness temperature over a maize canopy in row structure 致谢:感谢法国农业科学院的Lagouarde，J.-P.研究员为本研究提供的葡萄园冠层航空实测多角度方向亮温数据。 10.11834/jrs.20211300 1007-4619（2021）08-1710-12 曹彪，杜永明，卞尊健，董亚冬，赵峰，胡添，冉雪婷，秦伯雄，历华，肖青，柳钦火.2021.热红外核驱动模型在垄行植被热辐射方向性特征拟合中的精度分析.遥感学报，25（8）： 1710-1721 曹彪，杜永明，卞尊健，董亚冬，赵峰，胡添，冉雪婷，秦伯雄，历华，肖青，柳钦火.2021.热红外核驱动模型在垄行植被热辐射方向性特征拟合中的精度分析.遥感学报，25（8）： 1710-1721 Cao B，Du Y M，Bian Z J，Dong Y D，Zhao F，Hu T，Ran X T，Qin B X，Li H，Xiao Q and Liu Q H. 2021. Assessment of thermal infrared kernel-driven models over row-planted canopies. National Remote Sensing Bulletin， 25（8）：1710-1721 Cao B，Du Y M，Bian Z J，Dong Y D，Zhao F，Hu T，Ran X T，Qin B X，Li H，Xiao Q and Liu Q H. 2021. Assessment of thermal infrared kernel-driven models over row-planted canopies. National Remote Sensing Bulletin， 25（8）：1710-1721 国家自然科学基金（编号：41871258，41930111，42071317，41901287）；中国科学院青年创新促进会（编号：2020127）；中国科学院空天信息创新研究院“未来之星”（编号：Y920570ZIF） Supported by National Natural Science of Foundation of China （No. 41871258, 41930111, 42071317, 41901287）; The Youth Innovation Promotion Association CAS （No. 2020127); The “Future Star” Talent Plan of the Aerospace Information Research Institute of Chinese Academy of Sciences (No. Y920570Z1F) 2021-05-10 2021-08-07 2021-09-09 2021-07-19 遥感学报 8 25