热红外遥感地表温度与发射率地面验证进展

热红外遥感地表温度与发射率地面验证进展 Ground validation of land surface temperature and surface emissivity from thermal infrared remote sensing data 1 2 first-author 朱金顺，1996年生，男，博士研究生， 研究方向为热红外遥感地表温度与发射率验证的理论和应用。E-mail： j.zhu@pku.edu.cn 朱金顺，1996年生，男，博士研究生， 研究方向为热红外遥感地表温度与发射率验证的理论和应用。E-mail： j.zhu@pku.edu.cn j.zhu@pku.edu.cn 1 2 corresp 任华忠，1985年生，男，研究员，研究方向为热红外遥感的理论和应用。E-mail：renhuazhong@pku.edu.cn 任华忠，1985年生，男，研究员，研究方向为热红外遥感的理论和应用。E-mail：renhuazhong@pku.edu.cn renhuazhong@pku.edu.cn 1 2 1 2 1 2 1 2 1 2 北京大学 遥感与地理信息系统研究所, 北京 100871 北京大学 遥感与地理信息系统研究所, 北京 100871 Institute of Remote Sensing and Geographical Information System, School Earth and Space Sciences, Beijing 100871, China Institute of Remote Sensing and Geographical Information System, School Earth and Space Sciences, Beijing 100871, China 空间信息集成与3S工程应用北京市重点实验室, 北京 100871 空间信息集成与3S工程应用北京市重点实验室, 北京 100871 Beijing Key Laboratory of Spatial Information Integration and Its Application, Beijing 100871, China Beijing Key Laboratory of Spatial Information Integration and Its Application, Beijing 100871, China 地表温度与发射率是地表—大气系统长波辐射和潜热通量交换的直接驱动力，是描述区域和全球尺度上地表能量平衡与水平衡的重要参数，其时空变化信息在气象预测、气候变化、水循环、地质勘探、农林监测和城市热环境等诸多领域具有广泛的应用。热红外遥感作为当前获取区域或全球尺度上地表温度和发射率的最有效手段之一，相较于传统的地面点位测量方法，具有空间覆盖范围大和重复观测等优势。对热红外遥感定量反演的地表温度与发射率产品进行地表真实性验证，有利于发现遥感数据自身或其反演算法的缺陷，确定产品的精度与不确定度，便于遥感产品的应用与推广。本文首先回顾了地表温度和发射率的定义，阐述了热红外遥感可反演、地面可测量的地表温度和发射率的科学内涵，并对利用热红外遥感数据反演地表温度和发射率的理论和方法作了概述；对地表温度和发射率地面验证的框架体系、验证指标进行总结，建立了基于精度、精确度、不确定度、完整性和稳定性的验证评价指标体系；总结了地表温度和地表发射率的地面验证方法、地面测量方法、辅助数据的获取方法、地表温度地面测量的采样方法，以及在验证异质非同温地表时从点到像元尺度的地表温度尺度转换方法等，分析了地面验证过程的主要误差来源；归纳了目前地表温度和地表发射率主要验证站点、观测网络及其空间分布特征；最后，本文讨论了地表温度与发射率地面验证存在的若干问题，并对地表温度与发射率验证工作的发展前景和趋势进行了相关展望。 Land Surface Temperature (LST) and Land Surface Emissivity (LSE) are the direct driving force of long wave radiation and latent heat flux exchange at the surface-atmosphere interface, which are also two important parameters on surface energy budget balance and water balance at regional or global scales, its temporal and spatial variations on surface-atmosphere interface have a wide range of applications on weather forecasting, climate change, water cycle, geological exploration, agriculture, forestry monitoring and the urban thermal environment research, and many other scientific fields. Remote sensing provides an effective approach to obtain LST and LSE at global scale rather than point measurements for its rather wider spatial coverage and temporal revisit convenience. The validation of quantitative retrieval on LST and LSE products is conducive to find the defects of remote sensing data processing or drawbacks on retrieval algorithms, as well as clarify the accuracy and uncertainty of the operational products, which is of great convenience for the application and popularity of these products. In this paper, firstly different definitions of LST and LSE are reviewed, and then the scientific connotation of LST and LSE which can be retrieved from thermal infrared remote sensing data and measured from in-situ experiments is explained. The theoretical background, such as radiative transfer theory and methods of LST and LSE retrieval from remote sensing data are then summarized and outlined. After that, the framework of LST and LSE validation are summarized systematically, the validation metrics of LST and LSE derived from remotes sensing data including accuracy, precision, uncertainty, completeness and stability is constructed. Based on the validation framework, the methods of ground validation for LST and LSE are introduced (including directly validation and indirectly comparison), and followed by the methods of ground measurements of LST or related auxiliary data. The method of scale conversion method from point level to pixel level for heterogeneous and non-isothermal surfaces are emphasized and analyzed, and the main error sources of LST validation and LSE validation are discussed, respectively. A summarization of the main sites or networks for the validation of LST and LSE is conducted and the spatial distribution and the main characteristics (such as heterogeneity, land cover) of the typical LST and LSE validation sites or networks are briefly analyzed. The current LST and LSE products derived from satellite remote sensing data, which utilize the abovementioned validation sites or networks are summarized to report their validation accuracy or uncertainty, and related development on validation of LST and LSE are reviewed. Finally, some problems of validation of LST and LSE are also presented, and then the future outlook and trends of validation are outlined and justified. 热红外遥感 地表温度 发射率 地面验证 真实性检验 thermal infrared remote sensing land surface temperature emissivity ground validation verification 1　引言 1 地表温度LST（Land Surface Temperature）是地表—大气耦合系统辐射平衡和地表物理过程的重要参数（ Li，2013a Li，2013a ）。全球气候观测系统GEOS（Global Climate Observing System）组织与欧洲航天局ESA（European Space Agency）气候变化倡议项目CCI（Climate Change Initiative）将地表温度列为监测地球气候系统的基本气候变量ECVs（Essential Climate Variables）之一（ Bayat 等，2021 Bayat 等，2021 ； Bojinski 等，2014 Bojinski 等，2014 ）；国际地圈生物圈计划IGBP（International Geo-sphere and Biosphere Program）也将地表温度视为高优先级地表参数（ Townshend 等，1994 Townshend 等，1994 ），其时空变化信息在气象预测、气候变化、水循环、地质勘探、农林监测和城市热环境等领域具有重要的科学意义和应用价值（ Anderson 等，2012 Anderson 等，2012 ； Ghent 等，2010 Ghent 等，2010 ； Li 等，2013a Li 等，2013a ； Mokhtari 等，2019 Mokhtari 等，2019 ； Trigo 等，2015 Trigo 等，2015 ； Weng，2009 Weng，2009 ）。 地表发射率LSE（Land Surface Emissivity）是表征地表将热能转化为辐射能能力的度量，其与地表类型、地表粗糙度和观测角度等因素有关（ Becker和Li，1995 Becker和Li，1995 ； Sekertekin和Bonafoni，2020b Sekertekin和Bonafoni，2020b ； Sobrino 等，2001 Sobrino 等，2001 ）。作为描述地球表层系统辐射特性的特征物理量，地表发射率在气候模式、矿物识别、生态监测和能量平衡等方面应用广泛（ Gillespie 等，1998 Gillespie 等，1998 ； Jin和Liang，2006 Jin和Liang，2006 ； Li 等，2013b Li 等，2013b ）。 遥感尤其是热红外遥感是获取区域和全球尺度地表温度与发射率的主要手段（ Hulley和Ghent，2019 Hulley和Ghent，2019 ； Li 等，2013b Li 等，2013b ， 2013a 2013a ）。当前已有众多热红外遥感平台（如Terra和Aqua/MODIS、Terra/ASTER、Sentinel-3/SLSTR、Landsat 8/TIRS、风云卫星等）的对地观测数据被用来生产业务化的全球、区域尺度地表温度或发射率产品，其产品被应用到农林、气象、生态、资源等诸多领域。了解遥感反演地表温度和发射率产品的精度是保证地表温度与发射率在各个领域开展应用的重要前提。由于应用体系和目标的差异，不同应用领域对地表温度和发射率的精度需求也不尽相同。例如，世界气象组织WMO（World Meteorological Organization）设定了地表温度和地表发射率在不同应用领域的时间分辨率、空间分辨率以及精度需求（ Eyre，2010 Eyre，2010 ），详见 表1 表1 和 表2 表2 。 注： * 表示最终的精度目标； ** 表示现阶段的突破进展； *** 表示最低的阈值要求。 应用 空间分辨率/km 时间分辨率 精度/k 农业气象 0.1* 0.5** 10*** 60 min* 3 h** 3 d*** 0.3* 0.6** 2*** 数值预报 5* 15** 250*** 30 min* 3 h** 6 h*** 0.5* 1** 4*** 注： *表示最终的精度目标；**表示现阶段的突破进展；***表示最低的阈值要求。 应用 空间分辨率/km 时间分辨率 精度/% 数值预报 5* 15** 50*** 24 h* 5 d** 30 d*** 0.5* 1** 3*** 水文 0.01* 0.292** 250*** 24 h* 2 d** 12 d*** 5* 8** 20*** 总的来说，地面验证是评估遥感反演地表温度与地表发射率产品精度的关键（ 张仁华 等，2010 张仁华 等，2010 ）。定量遥感产品的验证工作不仅是其被合理、有效应用的前提，同时也可以提供对遥感数据质量、产品处理流程和反演算法等方面的反馈信息，便于遥感数据、反演算法和地表温度与发射率反演产品的进一步迭代优化。鉴于此，本文将系统性介绍对基于热红外遥感数据反演得到的地表温度与发射率产品进行地面验证的基本原理、方法、数据和评价指标等，指出当前地表温度和发射率地面验证存在的问题，并对其未来发展前景进行展望。 2　理论基础 1 2.1　地表温度与地表发射率的定义 2 明晰地表温度与发射率的科学定义是其真实性检验的基础。地表温度的定义很大程度上依赖其测量方式和应用目的（ Prata 等，1995 Prata 等，1995 ）。学者们针对地表温度提出了不同的定义，如基于热力学第二定律定义的热力学温度（thermodynamic temperature），表征了分子在物质内部做无规则热运动的程度；基于地物热辐射通量定义的辐射温度（radiative temperature），指对于所有波长范围内物体总出射辐射与绝对黑体的总出射辐射相等时对应的黑体温度；基于辐射亮度定义的辐射亮度温度（radiative brightness temperature），指在特定波长下，物体的出射辐射亮度与黑体的出射辐射亮度相等时对应的黑体温度，其依赖于探测波长；以及基于辐射计测量值而定义的辐射计温度（radiometric temperature），指从辐射计观测辐亮度中消除大气和发射率效应得到的辐射温度（ Becker和Li，1995 Becker和Li，1995 ； Norman和Becker，1995 Norman和Becker，1995 ）。对于达到热力学平衡的均匀等温面，上述定义的辐射温度与热力学温度在数值上相等；但是对于异质非等温表面，由于地表状况和温差分布的差异，上述定义的地表温度之间存在数值上的差异（ Li 等，2013a Li 等，2013a ； Norman和Becker，1995 Norman和Becker，1995 ）。从遥感可观测的角度出发，基于辐射通量观测数据反演的像元尺度地表温度（ 李小文和王锦地，1999 李小文和王锦地，1999 ； Li 等，2013b Li 等，2013b ）更近似于方向性辐射计温度（directional radiometric temperature）（ Becker和Li，1995 Becker和Li，1995 ； Norman和Becker，1995 Norman和Becker，1995 ； Wan，1999 Wan，1999 ），即指在传感器观测的亮度温度的基础上消除大气和发射率影响后，获得的地表非同温混合像元的等效温度，其表征了表面厚度等于穿透深度（0.1—10倍波长，在热红外观测谱段探测地表若干微米深度的热辐射）的地表表皮综合温度（也叫表皮温度，skin temperature）（ Becker和Li，1995 Becker和Li，1995 ； Wan，1999 Wan，1999 ），一般包括陆地表面温度、海洋表面温度、冰/雪表面温度以及水体表面温度等，单位为开尔文（K）。 方向性辐射计温度是至今为止唯一的一种可以通过遥感观测方式获得的区域甚至于全球尺度的表面温度形式（ Li 等，2013a Li 等，2013a ）。但是需要注意的是，由于地表的空间异质性，中、低空间分辨率遥感像元往往包含着不同温度的多种组分，这种非同温异质特性使得像元尺度的方向性辐射计温度不满足热力学温度所具有的普朗克热辐射分布规律，亦即其测量值会随观测波长的改变而改变，这严重限制了遥感反演的地表温度的物理内涵和应用场景，但有研究指出对于温差不太大的遥感像元来说，温度测量的变异性可以忽略不计（ Becker和Li，1995 Becker和Li，1995 ）。 地表发射率的定义与地表温度相辅相成。一般地，同温像元发射率可定义为地物的实际热辐射与同温同波长下黑体热辐射的比值，其数值随着波长、地表状况、土壤水分和纹理特征等发生变化（ Norman和Becker，1995 Norman和Becker，1995 ）；但是，混合像元的发射率则较复杂，目前有多种定义，其中使用较广且被大众接受的主要有： r -发射率（ r -emissivity）（ Becker和Li，1995 Becker和Li，1995 ）， e -发射率（ e -emissivity）（ Norman和Becker，1995 Norman和Becker，1995 ）和视在发射率（apparent emissivity）（ Li和Wang，1999 Li和Wang，1999 ）等。 假设非同温混合像元包含 N 个组分，组分内可视为温度均一，且各个组分在一定波长范围内的发射率已知； a k 表示特定观测角度下第 k 组分在混合像元内的面积比例， a k 的加和为1； ε k 为第 k 组分的发射率。如果假设混合像元的组分间的温度是均一的，则该同温混合像元在观测方向（ θ v ， φ v ）上的 r -发射率可定义为 <math display="block" id="M1"><msub><mrow><mi>ε</mi></mrow><mrow><mi>r</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>k</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>N</mi></mrow></munderover></mstyle><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>k</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639493&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639490&type= 38.26933289 8.29733276 实验室测量表明，自然地表大都遵循基尔霍夫定律（Kirchhoff’s law）（ Salisbury 等，1994 Salisbury 等，1994 ）。因此，对于不透明地表，非同温像元的 r -发射率可以基于基尔霍夫定律来定义： <math display="block" id="M2"><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>ε</mi></mrow><mrow><mi>r</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>h</mi><mi>d</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mn mathvariant="normal">1</mn><mo>-</mo></mtd></mtr><mtr><mtd><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><mn mathvariant="normal">2</mn><mi mathvariant="normal">π</mi></mrow></msubsup><mrow><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><mrow><mrow><mi mathvariant="normal">π</mi></mrow><mo>/</mo><mrow><mn mathvariant="normal">2</mn></mrow></mrow></mrow></msubsup><mrow><mi>ρ</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>,</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></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>s</mi></mrow></msub><mi mathvariant="normal">d</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub><mi mathvariant="normal">d</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>s</mi></mrow></msub></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639498&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639496&type= 72.05133057 12.36133385 式中， θ s 和 φ s 分别表示入射天顶角和方位角； θ v 和 φ v 分别表示观测天顶角和方位角； <math id="M3"><mi>ρ</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>,</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639504&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639500&type= 22.18266678 4.57200003 是双向反射函数； <math id="M4"><msub><mrow><mi>ρ</mi></mrow><mrow><mi>h</mi><mi>d</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639512&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639510&type= 14.81666565 4.57200003 是半球—方向发射率，通过对二向性反射率在入射方向进行半球积分得到。 r -发射率忽略了像元内表面温差及其分布的影响，仅由材料和组分等决定，而与温差分布等因素无关。而 e -发射率则从单一波长发射率的经典定义出发，将混合像元在某一观测角度下的发射率定义为像元总的热辐射与理论上同样温度分布的黑体辐射加和的比值： <math display="block" id="M5"><msub><mrow><mi>ε</mi></mrow><mrow><mi>e</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>k</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>N</mi></mrow></munderover></mstyle><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>k</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>k</mi></mrow></msub><mi>B</mi><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>k</mi></mrow></msub><mo stretchy="false">)</mo></mrow></mrow><mrow><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>k</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>N</mi></mrow></munderover></mstyle><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>k</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mi>B</mi><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>k</mi></mrow></msub><mo stretchy="false">)</mo></mrow></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639518&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639515&type= 47.58266449 18.20333290 式中， B （ T k ）为第 k 组分在温度为 T k 时的黑体辐射亮度， a k 与 ε k 与 式（1） 式（1） 中含义相同。 e -发射率使得非同温混合像元的发射率不仅取决于各个组分的发射率，还受它们温度分布的影响。 为了保证异质非同温地表定义的地表温度及其辐射仍满足普朗克热辐射分布规律， Li等（1999） Li等（1999） 在原有 r -发射率的基础上，加入了组分温差引起的发射率视在增量（apparent emissivity increment），提出了视在发射率的概念（ 李小文和王锦地，1999 李小文和王锦地，1999 ； Li和Wang，1999 Li和Wang，1999 ）： <math display="block" id="M6"><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>ε</mi></mrow><mrow><mi>a</mi><mi>p</mi><mi>p</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>r</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>ε</mi><mo>=</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>r</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>K</mi></mrow><mrow><mi>λ</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo stretchy="false">)</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>k</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>N</mi></mrow></munderover></mstyle><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>k</mi></mrow></msub><msub><mrow><mi>ε</mi></mrow><mrow><mi>k</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">Δ</mi><msub><mrow><mi>T</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639524&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639522&type= 61.38333893 13.63133430 式中， ε r 为像元的 r -发射率， T 0 为不受波长范围和观测角度影响的参考温度，Δ T k 为第 k 个组分的温度与参考温度之间的差值； K λ （ T 0 ）表示为 K λ （ T 0 ）= B’ （ T 0 ）/ B （ T 0 ），其中 B’ （ T 0 ）为普朗克函数在参考温度 T 0 处的一阶导数。视在发射率本身会随着波长范围和参考温度 T 0 而变化，精确测量需要组分温度和发射率等先验知识，因此难以从遥感数据或地面测量中精确获得。此外，不合理的参考温度 T 0 和较大的温差Δ T k 可能使该发射率数值大于1，与发射率的传统物理意义不符。 r -发射率是目前热红外遥感反演的、具有通常意义的发射率，可以进行实地测量，且具有尺度不变性（ Becker和Li，1995 Becker和Li，1995 ），因此便于不同遥感平台反演地表发射率结果的对比（ Li等，2013b Li等，2013b ）。但是，该发射率定义使得相应的地表温度既依赖于观测波段和观测角度，也依赖于像元内组分温度和发射率的分布（ Li 等，2013b Li 等，2013b ）。但是考虑到地表温度反演过程中大气水汽等参数带来的误差，在8—14 μm热红外光谱范围内，非同温像元地表温度随波长的变化造成的误差可以忽略不计（ Becker和Li，1995 Becker和Li，1995 ； Li 等，2013a Li 等，2013a ），以保证基于多波段热红外遥感数据的地表温度与发射率反演过程在理论上可行。 2.2　地表温度与发射率的热红外遥感反演 2 通常情况下，搭载于星载平台或机载平台的被动红外传感器对地观测时入瞳处的热辐射包括地表和大气等两部分的辐射贡献。在晴空条件下，传感器第 i 通道探测到的大气层顶TOA(Top of Atmosphere)的表观辐亮度可以用如下辐射传输方程表示为 <math display="block" id="M7"><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>φ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mo>⋅</mo><msub><mrow><mi>τ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>φ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>a</mi><mi>t</mi><mi>i</mi><mo>↓</mo></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639530&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639529&type= 57.15000153 4.57200003 式中， θ v 和 φ v 分别表示观测天顶角和方位角， R i （ θ v ，φ v ） • τ i （ θ v ，φ v ）表示离地热辐射 R i （ θ v ，φ v ）经过大气的衰减作用后达到传感器的辐射， τ i （ θ v ，φ v ）表示传感器观测方向的大气上行透过率。 R ati↑ 表示到达传感器的大气上行热辐射。其中，离地热辐射 R i （ θ v ，φ v ）可以进一步表示为 <math display="block" id="M8"><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>φ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>φ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo></mrow></mfenced><mo>⋅</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>a</mi><mi>t</mi><mi>i</mi><mo>↓</mo></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639537&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639535&type= 75.18399811 5.16466665 式中，第1项 ε i （ θ v ， φ v ） • B （ T s ）表示地物在温度为 T s 时发射的热辐射；第2项为地物反射的大气下行热辐射 <math id="M9"><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>φ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mo>↓</mo></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639544&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639540&type= 29.20999908 4.57200003 。 基于上述热红外辐射传输的物理过程，可以从热红外遥感观测数据中定量反演出地表温度与发射率。目前学者们发展了众多基于热红外遥感数据定量反演地表温度与发射率的算法。 Li 等（2013a） Li 等（2013a） 对遥感地表温度反演方法进行了总结，将其概括为两类算法。（1）基于已知发射率的反演方法：该类方法需要发射率作为先验知识，如单通道算法（ Avdan和Jovanovska，2016 Avdan和Jovanovska，2016 ；Chen 等，2021；Jiménez‐Muñoz和Sobrino，2003； Qin 等，2001 Qin 等，2001 ； Zhou 等，2010 Zhou 等，2010 ）、多通道算法（ Niclòs 等，2021 Niclòs 等，2021 ； Wan和Dozier，1996 Wan和Dozier，1996 ； Yang 等，2020 Yang 等，2020 ； Zarei 等，2021 Zarei 等，2021 ； Zhao 等，2020b Zhao 等，2020b ）、多角度算法（ Prata，1993 Prata，1993 ； Sobrino 等，2004 Sobrino 等，2004 ）等；（2）发射率未知的反演方法：该类方法不需要发射率作为先验知识，如逐步反演法（ Ermida 等，2020 Ermida 等，2020 ； Lan 等，2021 Lan 等，2021 ； Vanhellemont，2020 Vanhellemont，2020 ； Wang 等，2020b Wang 等，2020b ； Yin 等，2020a Yin 等，2020a ）（首先确定地表发射率，而后反演地表温度）、同步地表温度与发射率反演方法，如双温算法（ Caselles 等，1997 Caselles 等，1997 ）、基于物理日/夜算法（ Wan和Li，1997 Wan和Li，1997 ， 2008 2008 ）、灰体发射率法（ Barducci和Pippi，1996 Barducci和Pippi，1996 ）、温度与发射率分离算法（ Gillespie 等，1998 Gillespie 等，1998 ；Nie 等，2020）、迭代光谱平滑的温度/发射率分离方法（ Borel，1997 Borel，1997 ）、线性发射率约束的温度/发射率分离方法等（ Wang 等，2011 Wang 等，2011 ）；以及同步反演地表温度、发射率和大气参数的方法，如人工神经网络方法（ Mas和Flores，2008 Mas和Flores，2008 ）、逐步物理反演方法（ Ren 等，2021 Ren 等，2021 ）等。目前，多通道算法中的劈窗算法和同步反演地表温度与发射率方法中的温度与发射率分离算法是生产全球尺度地表温度产品的主流算法（ Hulley 等，2016 Hulley 等，2016 ， 2021 2021 ； Li 等，2013a Li 等，2013a ）。 地表发射率的遥感反演方法则可以分为3类（ Li 等，2013b Li 等，2013b ； Sekertekin和Bonafoni，2020b Sekertekin和Bonafoni，2020b ， 2020a 2020a ）：（1）多通道温度与发射率分离法TES（Multi-channel Temperature Emissivity Separation），如双温法（ Peres和DaCamara，2004 Peres和DaCamara，2004 ），参考通道法（ Kahle 等，1980 Kahle 等，1980 ），温度与发射率分离算法（ Gillespie 等，1998 Gillespie 等，1998 ， Sobrino 等，2008 Sobrino 等，2008 ）等；（2）物理模型法PBMs（Physically Based Methods），如日夜算法（ Wan和Li，1997 Wan和Li，1997 ），两步反演法（ Li 等，2007 Li 等，2007 ）等；（3）半经验法SEMs（Semi-Empirical Methods），如基于NDVI的方法（ Cheng和Liang，2014 Cheng和Liang，2014 ； Li和Jiang，2018 Li和Jiang，2018 ），基于分类的方法（ Snyder 等，1998 Snyder 等，1998 ）等。其中，基于NDVI方法由于获取地表发射率简单易行，成为地表温度遥感反演过程中获取地表发射率最常用的方法（ Guo 等，2020 Guo 等，2020 ； Ren等，2017 Ren等，2017 ； Zheng 等，2019 Zheng 等，2019 ），而温度与发射率分离算法则是从热红外遥感数据直接获取全球尺度地表发射率产品的主要算法（ Göttsche和Hulley，2012 Göttsche和Hulley，2012 ； Hulley 等，2016 Hulley 等，2016 ； Wang 等，2020a Wang 等，2020a ）。 2.3　地表温度与发射率的验证体系 2 独立的定量遥感产品地面验证过程是应用部门合理、有效地使用遥感产品的重要保障，同时也可为算法的迭代更新和改进提供参考和反馈（ 晋锐等，2017 晋锐等，2017 ； Yu 等，2019 Yu 等，2019 ）。一般地，地表温度与发射率遥感产品的地面验证体系可归纳为 图1 图1 所示。 在验证前期，需要对站点的布设和站点区域卫星足迹内的空间异质性、验证站点的空间分布及其覆盖的地表类型等因素进行评估；在验证过程中进行地面点实地测量，获取地表温度与发射率参考值，通过适当的采样策略，得到验证站点一组测量参考值；之后通过尺度转换方法获取像元尺度的地表温度与发射率参考值，与遥感反演的地表温度和发射率产品进行空间配准、时间归一化以及角度归一化等处理，地表发射率验证还需要进行不同传感器光谱响应范围内发射率测量值的光谱匹配等；最后结合地表温度与发射率验证方法和验证指标对地表温度与发射率产品进行综合验证，得到地面验证报告。 在对定量遥感产品进行地面验证时，由精度、精确度、不确定度、稳定性、完整性等5个参数组成验证指标体系对定量遥感产品进行精度评价（ Guillevic等，2018 Guillevic等，2018 ； GUM，2008 GUM，2008 ； Mittaz等，2019 Mittaz等，2019 ），由上述指标组成的评价指标体系见 表3 表3 。 参数 评价指标 描述 精度 （Accuracy） 偏差（Bias） 绝对偏差（Absolute Bias） 测量值与真实值之间的一致程度 精确度 （Precision） 标准偏差 （Standard Deviation） 相同测量条件下连续测量结果之间的一致性 不确定度 （Uncertainty） 均方根误差 （Root Mean Square Error） 合理地归因于被测量因素的测量值离散度 完整性 （Completeness） — 反演结果中被验证分析的占比 稳定性 （Stability） — 测量结果长时间尺度上的一致性 从产品应用角度来说，精度、精确度和不确定度等指标一般被较多关注，其评价指标分别为偏差、绝对偏差、标准偏差和均方根误差等。以地表温度为例，以上各个指标对应的算术表达式分别为 <math display="block" id="M10"><mtable 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http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639622&type= 9.82133293 3.47133350 是温度差值的平均值。 3　地表温度的地面验证 1 3.1　地表温度的地面验证方法 2 现有4种主要的地表温度验证方法（ Guillevic 等，2018 Guillevic 等，2018 ； Li 等，2013a Li 等，2013a ； Sekertekin和Bonafoni，2020a Sekertekin和Bonafoni，2020a ），包括基于温度的验证T-based（Temperature-based method）、基于辐亮度的验证R-based（Radiance-based method）、交叉验证（Cross-validation method）和基于时间序列的验证（Time series method）等（ 马晋 等，2017 马晋 等，2017 ； Guillevic 等，2018 Guillevic 等，2018 ； Li 等，2013a Li 等，2013a ）。 （1）基于温度的验证方法。基于温度的验证方法直接比较遥感反演的像元尺度地表温度和由地面同步测量尺度上推到像元尺度的地表温度，以评价星载传感器的辐射校正精度和反演地表温度的精度（ Coll 等，2005 Coll 等，2005 ； Malakar 等，2018 Malakar 等，2018 ； Martin 等，2019 Martin 等，2019 ； Meng 等，2019 Meng 等，2019 ； Pinker 等，2009 Pinker 等，2009 ； Wan 等，2002 Wan 等，2002 ； Wan，2014 Wan，2014 ； Wang 等，2019 Wang 等，2019 ， 2020b 2020b ； Yang 等，2020 Yang 等，2020 ； Zhang 等，2016 Zhang 等，2016 ）。该方法依赖于地面温度测量精度，以及尺度转换后像元尺度地表温度对地表异质性的表征能力（ Coll 等，2009 Coll 等，2009 ； Li 等，2013a Li 等，2013a ； Sekertekin和Bonafoni，2020a Sekertekin和Bonafoni，2020a ）。考虑到现有尺度转换模型对异质地表的表征能力不足，同时为了减小地面站点测量的地表温度与像元尺度的地表温度之间的匹配误差，基于温度的验证方法一般适用于均一平坦地表类型如内陆水体、沙地、冰雪、草地、农田等或者在地物同温性更好的夜间地表进行验证（ Coll 等，2005 Coll 等，2005 ， 2012b 2012b ； Meng 等，2017 Meng 等，2017 ； Wan 等，2004 Wan 等，2004 ， 2002 2002 ）。尽管有学者将基于温度的方法用于白天数据验证，但研究表明夜间数据地表温度的验证结果一般优于白天数据的验证结果（ Guillevic 等，2014 Guillevic 等，2014 ； Hale 等，2011 Hale 等，2011 ； Li 等，2014a Li 等，2014a ； Liu 等，2015 Liu 等，2015 ； Simó 等，2016 Simó 等，2016 ； Wang和Liang，2009 Wang和Liang，2009 ）。这可能与异质地表像元在白天的同温性差、由太阳照射和遥感观测的角度关系造成像元内光照、阴影区域温度差异大等有关（ Coll 等，2019a Coll 等，2019a ； Jiménez 等，2012 Jiménez 等，2012 ； Li 等，2014a Li 等，2014a ； Malakar 等，2018 Malakar 等，2018 ； Pinheiro 等，2006 Pinheiro 等，2006 ； Trigo 等，2021 Trigo 等，2021 ）。 （2）基于辐亮度的验证方法。基于辐亮度的验证方法通过将反演的地表温度与通过辐射传输建模调整优化的地表温度进行对比，给出地表温度产品的反演精度。该种方法需要给定地面测量对应的大气廓线、地表发射率等数据，将基于大气辐射传输模型，如MODTRAN（ Berk 等，1999 Berk 等，1999 ， 2006 2006 ）或RTTOV（ Saunders 等，1999 Saunders 等，1999 ， 2018 2018 ）等正向模拟得到的辐射亮度与传感器过境时的同步辐射亮度的差值作为优化目标，通过不断调整输入到辐射传输模型中的地表温度，迭代得到地表温度的最优值作为真值，以此对遥感反演的地表温度进行验证评价（ Coll 等，2009， Coll 等，2009， ， 2012b 2012b ， 2012a 2012a uan 等，2018 uan 等，2018 ； Li 等，2021 Li 等，2021 ； Wan，2014 Wan，2014 ； Wan 等，2002 Wan 等，2002 ； Wan和Li，2008 Wan和Li，2008 ； Yu 等，2019 Yu 等，2019 ），其详细流程见 图2 图2 。该方法具有全天候验证地表温度产品的优点，同时避免了对地面地表温度的直接测量，为难以进行实地测量的地表或难以表征等效地表温度的异质地表提供了验证地表温度产品的可能（ Li 等，2013a Li 等，2013a ； Yu 等，2017 Yu 等，2017 ， 2019 2019 ），此外，由于基于辐亮度的验证一般选择地表发射率相对稳定的区域，其避免了对地面发射率的重复测量，适合在全球范围内进行大规模的验证（ Coll 等，2012b Coll 等，2012b ）。但该方法需要额外提供精确的地表发射率和大气探空数据，因此为验证带来了额外的误差来源（ Coll 等，2009 Coll 等，2009 ； Wan和Li，2008 Wan和Li，2008 ）。 （3）交叉验证方法。交叉验证将地表温度反演结果与其他已经验证过且精度较高的地表温度产品进行对比（Chen 等，2021； Jiménez 等，2012 Jiménez 等，2012 ； Qian 等，2013 Qian 等，2013 ； Silvestri 等，2020 Silvestri 等，2020 ； Trigo 等，2008 Trigo 等，2008 ， 2021 2021 ； Zhao 等，2020a Zhao 等，2020a ），从而对反演地表温度产品的相对精度进行评估。当无法获得地表实测温度或同步大气廓线时，常使用该方法对地表温度产品的精度进行评估（ Trigo 等，2008 Trigo 等，2008 ； Yu 等，2019 Yu 等，2019 ）。该方法虽然不需要进行繁琐的地面测量，但只能得到相对于参考地表温度产品的相对精度（ Tang 等，2015 Tang 等，2015 ）。 （4）基于时间序列的验证方法。基于时间序列的验证首先对长时间序列中相对稳定的地表类型（如内陆水体）进行长时间序列观测（ Hook 等，2007 Hook 等，2007 ），得到背景参考值；然后分析地表温度产品的时序稳定性，根据其偏离背景参考值的程度，反映地表温度产品的精度和稳定性。该方法同样无法得到反演地表温度的绝对精度，但具有检测在轨运行的星载传感器由于云覆盖（ Merchant 等，2013 Merchant 等，2013 ）或者校准漂移（ Hook 等，2007 Hook 等，2007 ）等因素造成的观测异常值的能力，配合地面验证站点或海上浮标等地面观测网络还可以对在轨热红外传感器进行辐射再校正，如先进星载热发射和反射辐射仪（ASTER）（ Hook 等，2007 Hook 等，2007 ）、中分辨率成像光谱仪（MODIS）（ Hulley和Hook，2011 Hulley和Hook，2011 ）、多光谱热成像仪（MTI）（ Hook 等，2005 Hook 等，2005 ）、Landsat 5搭载的专题制图仪（TM）（ Barsi 等，2007 Barsi 等，2007 ； Hook 等，2004 Hook 等，2004 ），Landsat 8搭载的热红外传感器（TIRS）（ Barsi 等，2014 Barsi 等，2014 ）和可见光红外成像辐射仪（VIIRS）（ Guillevic 等，2014 Guillevic 等，2014 ）等传感器均采用该方法进行辅助辐射校正。 3.2　地表温度的地面测量 2 地面表层是大气与土壤、植被等地物进行热量交换和辐射传输的复杂媒介，通过接触式温度计测得的温度受测量环境条件的影响，与传感器获取的辐射温度并不相同（ Krishnan 等，2020 Krishnan 等，2020 ）。由于大气热辐射的存在以及地表温度与发射率的耦合作用，难以在地面使用辐射计直接测得地表温度。常规的地表温度测量方法是测量一组离地和大气下行的辐射亮度或亮度温度，然后通过辐射传输方程进行温度与发射率分离，间接求解地表温度。离地和大气下行辐射亮度或亮度温度的测量通常使用两类测量仪器，包括（1）宽/多波段红外辐射计或热成像仪和（2）宽视场的半球长波辐射计（ Krishnan 等，2020 Krishnan 等，2020 ）。二者的主要区别在于测量光谱范围和测量视场不同。一般地，红外辐射计或热成像仪视场较窄，主要测量波长范围8—14 μm的辐射亮度温度（ Sekertekin和Bonafoni， 2020b Sekertekin和Bonafoni， 2020b ； Valor 等，2018 Valor 等，2018 ）；而长波辐射计则测量半球方向上光谱范围更宽（3—50 μm）的总辐射通量密度（ Valor 等，2018 Valor 等，2018 ）。常见的红外辐射计、热成像仪和长波辐射计的参数指标见 表4 表4 。 注： *DT表示日累计（daily totals）。 仪器类型 测量仪器型号 光谱范围/μm 测量精度/℃ 测温范围/℃ FOV/（°） 5 宽波段红外辐射计 Apogee （SI-111） 8—14 ±0.2 -10—65 44 Apogee （IRTS-P） 6.5—14 ±0.3 -10—55 56 Everest（112.2L） 8—13 ±0.3 -30—100 3 Heitronics （KT19.85） 9.6—15 ±0.2 -20—70 3 JPLR （500 Series） 8—14 ±0.1 4—40 36 多波段红外辐射计 CIMEL CE312（1宽波段、3或5个窄波段） 8—14 ±0.1 -80—60 10 红外相机 FLIR（Tau2） 7.5—13 ±5.0 -40—165 45×35 长波辐射计 Kipp and Zonen （CNR1/CNR4） 4.5—42 DT * ±10%（Wm -2 ） -10—40 上：180 下：150 地表温度由离地和大气下行辐射亮度或亮度温度间接求解。近地测量可忽略大气对红外辐射的削减效应和大气上行辐射，地面红外传感器测量离地红外辐射 <math id="M20"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi><mtext> </mtext></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639775&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639772&type= 5.50333309 3.72533321 包括地表目标辐射和反射的大气下行辐射两部分： <math display="block" id="M21"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi><mtext> </mtext></mrow></msub><mo>=</mo><mi>ε</mi><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi><mtext> </mtext></mrow></msub><mo>+</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi><mo stretchy="false">)</mo><msub><mrow><mi>L</mi></mrow><mrow><mo>↓</mo></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639657&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639653&type= 38.01533508 4.57200003 式中， <math id="M22"><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639850&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639847&type= 1.94733346 2.62466669 为地表发射率， <math id="M23"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi><mtext> </mtext></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639670&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639666&type= 6.77333355 3.72533321 为地表目标辐射， <math id="M24"><msub><mrow><mi>L</mi></mrow><mrow><mo>↓</mo></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639783&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639779&type= 4.06400013 3.72533321 为大气半球方向下行辐射亮度。需要注意的是，该式对于宽/窄波段红外辐射计和长波辐射计（即使测定的辐射包括中红外辐射的太阳贡献）等均可适用。但是，不同类型仪器需要不同的温度求解策略： （1）针对多波段红外辐射计（如CE312）数据，通常需使用多波段地表温度与发射率分离TES（Temperature Emissivity Separation）算法（ Gillespie 等，1998 Gillespie 等，1998 ）同时估算地表温度 <math id="M25"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639683&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639680&type= 2.96333337 3.72533321 和发射率 <math id="M26"><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639688&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639686&type= 1.94733346 2.62466669 ，算法描述见4.2节地表发射率的地面测量，更多细节可以参阅地表温度与发射率分离算法文档（ Gillespie 等，1999 Gillespie 等，1999 ）。 （2）对于宽波段红外辐射计测量的亮度温度可以合理假设8—14 μm辐射近似满足斯蒂芬—玻尔兹曼定律（ Zheng 等，2019 Zheng 等，2019 ）： <math display="block" id="M27"><mi>M</mi><mo>=</mo><mi>σ</mi><mi mathvariant="normal">'</mi><msup><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639694&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639692&type= 14.64733315 2.96333337 式中， <math id="M28"><mi>M</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639701&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639698&type= 2.87866688 2.62466669 为通量密度， <math id="M29"><mi>σ</mi><mi mathvariant="normal">'</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639706&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639703&type= 3.72533321 2.70933342 为不等于史蒂芬—玻尔兹曼常数的常量， <math id="M30"><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639711&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639709&type= 2.11666679 2.62466669 为物体的温度。此时有 <math id="M31"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi><mtext> </mtext></mrow></msub><mo>=</mo><mi>σ</mi><mi mathvariant="normal">'</mi><msup><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639716&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639714&type= 20.57399940 4.06400013 ， <math id="M32"><msub><mrow><mi>L</mi></mrow><mrow><mo>↓</mo></mrow></msub><mo>=</mo><mi>σ</mi><mi mathvariant="normal">'</mi><msubsup><mrow><mi>T</mi></mrow><mrow><mo>↓</mo></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639721&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639719&type= 16.59466553 4.06400013 ， <math id="M33"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi><mtext> </mtext></mrow></msub><mo>=</mo><mi>σ</mi><mi mathvariant="normal">'</mi><msubsup><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639727&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639725&type= 18.79599953 4.06400013 ，地表温度 <math id="M34"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639732&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639730&type= 2.96333337 3.72533321 为 <math display="block" id="M35"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mi>σ</mi><mi mathvariant="normal">'</mi><msup><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msup><mo>-</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi><mo stretchy="false">)</mo><mi>σ</mi><mi mathvariant="normal">'</mi><msubsup><mrow><mi>T</mi></mrow><mrow><mo>↓</mo></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msubsup></mrow><mrow><mi>ε</mi><mi>σ</mi><mi mathvariant="normal">'</mi></mrow></mfrac></mrow></mfenced></mrow><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">4</mn></mrow></mfrac></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639740&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639736&type= 46.14333344 12.19200039 式中， <math id="M36"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639749&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639745&type= 5.24933338 3.72533321 和 <math id="M37"><msubsup><mrow><mi>T</mi></mrow><mrow><mo>↓</mo></mrow><mrow/></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639753&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639751&type= 4.23333359 4.06400013 分别是离地辐射、大气下行辐射对应的亮度温度， <math id="M38"><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639850&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639847&type= 1.94733346 2.62466669 是宽波段发射率。 （3）对于长波辐射计，假设仪器测量谱段辐射满足斯蒂芬—玻尔兹曼定律，反解方程可以得到地表温度： <math display="block" id="M39"><msub><mrow><mi>T</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi><mtext> </mtext></mrow></msub><mo>-</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi><mo stretchy="false">)</mo><msub><mrow><mi>L</mi></mrow><mrow><mo>↓</mo></mrow></msub></mrow><mrow><mi>ε</mi><mi>σ</mi></mrow></mfrac></mrow></mfenced></mrow><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">4</mn></mrow></mfrac></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639763&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639761&type= 37.50733566 12.02266598 式中， <math id="M40"><mi>σ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639769&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639767&type= 2.45533323 2.62466669 是史蒂芬—玻尔兹曼常数（5.67×10 -8 W/m -2 K -4 ）， <math id="M41"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi><mtext> </mtext></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639775&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639772&type= 5.50333309 3.72533321 和 <math id="M42"><msub><mrow><mi>L</mi></mrow><mrow><mo>↓</mo></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639783&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639779&type= 4.06400013 3.72533321 分别是离地辐射、大气下行辐射， <math id="M43"><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639850&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639847&type= 1.94733346 2.62466669 是宽波段发射率。 除上述通过测量一组离地辐射、大气下行辐射获取地表温度真值的方法之外，还有其他间接的方式获取地表温度的方法。例如，通过构建接触式热电偶的温度测量值或气象观测站的近地表气温与地表温度的回归模型，估算地表温度（ Agbor和Makinde，2018 Agbor和Makinde，2018 ； Gallo 等，2011 Gallo 等，2011 ； Hachem 等，2012 Hachem 等，2012 ； Mildrexler 等，2011 Mildrexler 等，2011 ； Urban 等，2013 Urban 等，2013 ）；或利用低空航空飞行器（如无人机等）搭载的红外相机对地面进行大范围的温度测量，可以使地面地表温度的测量空间范围与遥感反演的像元地表温度尺度更加匹配。但目前航空遥感红外传感器受定标环境所限，其辐射校正精度低，相关研究仍处于发展阶段（ Krishnan 等，2015 Krishnan 等，2015 ， 2020 2020 ）。 3.3　地表温度测量辅助数据获取 2 由于地表温度和发射率的耦合作用以及环境辐射的影响，通过实测数据计算地表温度往往需要宽波段发射率 <math id="M44"><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639850&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639847&type= 1.94733346 2.62466669 作为先验知识。此外，对于只能探测特定方向红外辐射（ Sekertekin和Bonafoni， 2020a Sekertekin和Bonafoni， 2020a ）的宽波段红外辐射计，其大气半球下行辐射 <math id="M45"><msub><mrow><mi>L</mi></mrow><mrow><mo>↓</mo><mtext> </mtext></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639800&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639796&type= 4.14866638 3.72533321 的测量需要特别界定。 （1）宽波段发射率 <math id="M46"><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639805&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639802&type= 1.94733346 2.62466669 。宽波段辐射计求解地表温度需要与地面测温传感器光谱匹配的宽波段发射率作为先验知识。然而，目前的地表温度验证站点很少同步测量宽波段发射率（ Sekertekin和Bonafoni，2020b Sekertekin和Bonafoni，2020b ）。 Wang和Liang（2009） Wang和Liang（2009） 说明宽波段发射率±0.01的不确定性会带来站点实测温度0.1—0.4 K的误差，但由此带来的误差相对于仪器校正等因素可以忽略（ Heidinger 等，2013 Heidinger 等，2013 ）。因此有研究将地表宽波段发射率设为定值0.97（ Heidinger 等，2013 Heidinger 等，2013 ； Ndossi和Avdan，2016 Ndossi和Avdan，2016 ； Wang和Liang，2009 Wang和Liang，2009 ； Wang 等，2005 Wang 等，2005 ）。此外，可利用红外光谱仪或多波段热辐射计直接测量验证点发射率；或结合地表分类和NDVI数据，通过加权赋值的方式获得验证点发射率（ Ermida 等，2020 Ermida 等，2020 ； Guo 等，2020 Guo 等，2020 ； Ren 等，2017 Ren 等，2017 ； Trigo 等，2021 Trigo 等，2021 ； Zheng 等，2019 Zheng 等，2019 ）；还可以直接利用现有窄/宽波段地表发射率产品拟合宽波段发射率（ Cheng 等，2013 Cheng 等，2013 ；Eva和Benjamin，2010； Guillevic 等，2014 Guillevic 等，2014 ； Li等，2014b Li等，2014b ； Malakar 等，2018 Malakar 等，2018 ； Ogawa 等，2008 Ogawa 等，2008 ；Ren 等，2012，2012； Zhang 等，2016 Zhang 等，2016 ）。 （2）大气下行辐射 <math id="M47"><msub><mrow><mi>L</mi></mrow><mrow><mo>↓</mo></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639810&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639807&type= 4.06400013 3.72533321 。红外波段地表发射率一般都很大，所以大气下行辐射的测量对地表温度的影响很小（ Krishnan 等，2015 Krishnan 等，2015 ）。目前一般有以下3种测量或估计大气下行辐射的方法：1）朝某一方向测量天空。有研究表明在晴空条件下天顶角53°朝上观测的大气方向性下行辐射与大气半球下行辐射在数值上相当（ Kondratyev，1969 Kondratyev，1969 ）；或者建立垂直朝上观测的辐射亮度与半球下行辐射的经验关系 <math id="M48"><msub><mrow><mi>L</mi></mrow><mrow><mo>↓</mo></mrow></msub><mo>=</mo><mn mathvariant="normal">1.3</mn><mo>×</mo><mi mathvariant="normal">B</mi><mfenced separators="|"><mrow><mi>T</mi><mfenced separators="|"><mrow><msup><mrow><mn mathvariant="normal">0</mn></mrow><mrow><mo>°</mo></mrow></msup></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639816&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639814&type= 31.32666588 5.07999992 （ García-Santos 等，2012 García-Santos 等，2012 ； Rubio 等，1997 Rubio 等，1997 ）。此类方法需要求地势空旷，且只能在晴空天气下进行观测，其应用受环境条件限制；2）测量已知发射率的低发射率金属板（如金板、铝板 等）反射的环境辐射，求解下行辐射。该类方法无需对天气和周围环境的特殊要求，精度最高，其使用的场景也最广；3）利用探空廓线数据或气象再分析数据（如NCEP）提取大气廓线，而后利用大气辐射传输软件模拟得到大气下行辐射。该类方法受制于再分析数据或探空仪的精度，其精度最差。但在气象再分析数据可获得的情况下，该方法易用性最好。 3.4　地表温度测量地面站点选择和采样方式 2 地表温度地面测量站点及采样策略的选择对于验证中、低分辨率遥感数据反演的地表温度产品至关重要（ Li 等，2020 Li 等，2020 ； Zeng 等，2015 Zeng 等，2015 ）。为了获得精确的地表温度，地表温度采样通常针对均匀地表，如湖泊、沙漠和浓密植被等（ Göttsche 等，2013 Göttsche 等，2013 ； Guillevic 等，2012 Guillevic 等，2012 ）。在均匀地表，将采样点随机或均匀分布在一个卫星像素内，并在卫星过境附近的3 min内测量采样，可以减少卫星和地面传感器采样结果在空间和时间上的不匹配（ Coll 等，2005 Coll 等，2005 ； Trigo 等，2021 Trigo 等，2021 ）。 Wan 等（2002） Wan 等（2002） 指出地表温度验证站点应是均匀且足够大，最好覆盖几十个卫星像元。 Snyder等（1997） Snyder等（1997） 也指出验证站点应该具有良好的空间均一性且地面平坦，避免混合像元带来的误差。虽然现有的典型验证站点和全球/区域通量观测网（如全球长期通量观测网络FLUXNET、地表辐射观测网SURFRAD和黑河生态水文遥感试验网HiWATER等）（Li 等，2013； Wang和Liang，2009 Wang和Liang，2009 ）可以连续观测地面地表温度，但地表温度产品包括异质像元在内的整体精度评估仍具有挑战性（ Quan 等，2014 Quan 等，2014 ， 2016 2016 ），因为在自然条件下，大多数地表在公里级像元尺度上是不均匀的（ Becker和Li，1995 Becker和Li，1995 ）。地表参数在地理空间的异质性往往是由不同地表覆盖类型间的差异性导致的（ 栾海军 等，2018 栾海军 等，2018 ）。如果采样样本不覆盖总体的所有地表覆盖类型，则样本数据偏离总体数据的分布，从而失去了采样数据的异质代表性（ Wang 等，2012 Wang 等，2012 ）。 因此对于非均一地表，单个辐射计的点测量值无法表征研究区域的空间变异性，需要配合地面采样进行地表温度的地面测量。现有地表温度验证最常用的采样方法包括随机采样（Random Sampling）、系统采样（Systematic Sampling）和分层采样（Stratified Sampling）等（ Coll 等，2005 Coll 等，2005 ； Wan 等，2002 Wan 等，2002 ； Wang 等，2016a Wang 等，2016a ）。随机采样表示随机选择每个样本；系统采样则将研究区域划分为几个有规则的部分，并根据一定的规则（如每个部分的中心或角落）从每个部分中选择相同数量的样本。系统采样和随机采样适用于均一地表，而异质地表往往需要进行分层采样。分层采样首先根据先验信息（如土地覆盖类型）对研究区域进行分层；然后在每个地类中随机抽取样本。分层采样可以有效地捕捉地表温度的空间变化，但可能会导致样本的冗余测量。为了提高样本的代表性，减少样本的冗余， Minasny和McBratney（2006） Minasny和McBratney（2006） 提出了一种改进的分层采样策略，称为条件拉丁超立方CLH（Conditioned Latin Hypercube）方法。条件拉丁超立方采样方法优化了分层过程，同时采用模拟退火算法来加速优化迭代。与传统分层采样方法相比，条件拉丁超立方采样方法可以减小采样样本量，提高小样本采样的精度，被广泛用于土壤制图、叶面积指数的验证和土地覆盖变化等研究（ Lin 等，2009 Lin 等，2009 ； Mulder 等，2013 Mulder 等，2013 ； Yin 等，2016 Yin 等，2016 ； Zeng 等，2015 Zeng 等，2015 ）。针对条件拉丁超立方方法在时间样本上的代表性不足问题，有学者进一步提出了基于日温周期DTC（Diurnal Temperature Cycle）的空间和日温周期约束采样方法SDCS（spatial and diurnal temperature cycle-constrained sampling），研究表明该模型优于条件拉丁超立方和传统的分层采样方法（ Li 等，2020 Li 等，2020 ）。尽管地面地表采样方法各异，但在实际采样过程中，需要保证采样区域内每个端元采样至少一次，对于同一端元的光照、阴影区域也应该分别进行采样，以提高采样的代表性；此外，采样过程需要保证准同步进行，避免相邻采样时间间隔过大而造成的验证精度损失（ Schneider 等，2012 Schneider 等，2012 ）。 3.5　地表温度测量的尺度转换 2 地表的空间异质性，是地表尺度效应的根本原因（ 栾海军 等，2018 栾海军 等，2018 ）。卫星观测像元尺度（亚百米到公里级）和地面仪器观测尺度（覆盖范围小于10 m 2 ）存在尺度不匹配（ Yin 等，2020b Yin 等，2020b ； Yu 等，2019 Yu 等，2019 ； Zhou 等，2016 Zhou 等，2016 ）。地面仪器观测尺度多为单一类型均匀地表，而像元尺度覆盖范围通常不少于一种地表类型，为地面验证过程带来巨大的不确定性（ Wang 等，2016b Wang 等，2016b ）。由于像元内地表异质性及异质像元各不同组分的升温效应、太阳照射—遥感观测的角度关系导致的像元内光照和阴影组分温差效应等（ 彭志兴 等，2016 彭志兴 等，2016 ； Malakar 等，2018 Malakar 等，2018 ），日间地表温度的空间异质性较夜间往往更加明显（Arabi 等，2021； Peng等，2017 Peng等，2017 ）。有研究指出在特定的地表类型下，不到几厘米的空间范围内不同地类的温度差异可能达到10 K（ Coll 等，2009 Coll 等，2009 ），而在一分钟的时间尺度上同一区域的地表温度变化可以超过1 K（ Tang，2018 Tang，2018 ）。像元覆盖范围内地表温度的时空异质性使得地表温度不再具备“尺不变”的特性（ 李小文 等，1999 李小文 等，1999 ）。如果忽略地表异质性，使用单点测量代表像元尺度的地表温度进行验证，将可能造成超过1 K的误差（ Yu和Ma，2015 Yu和Ma，2015 ）。鉴于此，需要对地面点测量温度数据进行尺度转换，以得到像元尺度的地表温度测量值（ Coll 等，2009 Coll 等，2009 ）。如果不进行必要的尺度转换过程，对热红外反演地表温度产品基于温度的验证方法只能适用于湖泊、沙漠和茂密植被等相对均一地表或者地表同温性更好的夜间数据，这大大减少了可供验证的地面站点和地表类型等（ Dodd 等，2019 Dodd 等，2019 ； Guillevic 等，2012 Guillevic 等，2012 ； Liu 等，2015 Liu 等，2015 ）。 学者们提出众多尺度转换模型，将点尺度地表参数转换为像元尺度地表参数，包括基于几何模型的方法、基于地表模型的方法和基于先验统计的方法等（ De Gruijter 等，2006 De Gruijter 等，2006 ； Ge 等，2019 Ge 等，2019 ）。 （1）基于几何模型的方法。 Ermida 等（2014） Ermida 等（2014） 使用基于几何模型的尺度转换方法，该模型考虑具有三维结构的稀疏植被在不同太阳—观测几何条件下的光照地面、阴影地面和冠层等3个组分的比例变化，将通过面积加权各组分辐射得到的总辐射值与通过植被覆盖度比例加权得到的等效发射率联立求解辐射传输方程，得到尺度转换后的地表温度。该模型可以部分解决异质地表代表性问题（ Krishnan 等，2015 Krishnan 等，2015 ），但是其只能适用于具有某一形状规律的特定地表类型（ 彭志兴 等，2016 彭志兴 等，2016 ）。 （2）基于地表模型的方法。 Guillevic 等（2012 Guillevic 等（2012 ， 2014） 2014） 假设亚像元温度异质性主要是由地表类型和地表生化参数的变异性引起，通过测量大气、地表生化参数以及单点地表温度输入到地表模型SEtHyS（ Coudert 等，2006 Coudert 等，2006 ）中，进而得到像元覆盖范围内各地表类型组分温度的空间分布和面积比例，通过面积加权的方式，获取像元尺度的等效地表温度，如 式（12） 式（12） 所示： <math display="block" id="M49"><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">L</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi><mo>=</mo><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>ε</mi></mrow></mfrac><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>n</mi></mrow></munderover></mstyle><mrow><msub><mrow><mi>f</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><msubsup><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow><mrow><mn 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http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639819&type= 32.76599884 32.25799942 式中， <math id="M50"><msub><mrow><mi>f</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639828&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639826&type= 1.77800000 4.57200003 是组分温度为 <math id="M51"><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639835&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639832&type= 2.79399991 3.72533321 且组分的宽波段发射率为 <math id="M52"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640039&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640037&type= 2.70933342 3.72533321 时地表类型 <math id="M53"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639845&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639842&type= 1.10066664 2.62466669 对应的面积比例，此处的发射率 <math id="M54"><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639850&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639847&type= 1.94733346 2.62466669 是 Norman和Becker（1995） Norman和Becker（1995） 定义的宽波段像元尺度的 <math id="M55"><mi>r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639853&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639851&type= 1.26999998 2.62466669 发射率。该模型考虑了像元内部温度分布的差异，因此对异质地表的代表性更好，但模型复杂度为其应用带来困难（ 彭志兴 等，2016 彭志兴 等，2016 ）。 Dodd和Ghent（2019） Dodd和Ghent（2019） 使用空间分辨率高于卫星像元尺度的辅助数据（如叶面积指数、地表反射率等）代替地表模型获得像元覆盖范围的地表温度空间分布，然后通过面积加权的方式得到聚合后的像元尺度地表温度参考值，避免了辅助参数的测量，降低了模型的应用难度。基于地表模型的方法需要精确的地表发射率和各地表类型的面积比例等辅助参数，在地面验证过程中这些参数往往难以准确估算（ Quan 等，2016 Quan 等，2016 ）。 （3）基于先验统计的方法。基于先验统计模型的尺度转换方法通过先验统计模型（如地统计分析中的克里格法、贝叶斯估计法等）融合空间先验信息得到验证站点周围在像元覆盖范围内的地表温度空间分布特征，进而加权得到像元尺度地表温度参考值，在保证全局无偏最优估计的同时，可以捕捉多尺度的空间变异特征（ 李新 等，2016 李新 等，2016 ）。基于先验统计模型的方法已经被应用于土壤水分（ Gao 等，2014 Gao 等，2014 ； Kang 等，2015 Kang 等，2015 ， 2017 2017 ； Liu 等，2016 Liu 等，2016 ； Wang 等，2015 Wang 等，2015 ； Zhang 等，2017 Zhang 等，2017 ）、感热通量（ Ge 等，2015 Ge 等，2015 ； Hu 等，2015 Hu 等，2015 ）、蒸散（ Li 等，2018 Li 等，2018 ； Liu 等，2016 Liu 等，2016 ）、反照率（ Wu 等，2017 Wu 等，2017 ）等参数的尺度转换，但目前研究仍较少涉及地表温度的尺度转换，相关研究有待进一步开展。基于先验统计模型需要大量的地面定点观测数据用以估计空间先验知识，当定点观测分布稀疏时，先验统计模型往往难以得到满意的尺度转换结果（ 李新 等，2016 李新 等，2016 ）。 3.6　地表温度地面测量的误差分析 2 地表温度地面验证的难点在于地面实测点地表温度的获取、像元尺度地表温度的代表性问题以及地面测量数据和遥感数据时间、空间、角度匹配问题等。地表温度的地面测量误差也主要来自这3个方面： （1）实测点地表温度测量不确定性。根据 式（11） 式（11） 所示的地表温度的计算方程和误差传递原理，实测地表温度的误差可以表示为 式（13） 式（13） ，其中 <math id="M56"><msubsup><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi></mrow></msub></mrow><mrow/></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639859&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639855&type= 5.92666674 4.31799984 ， <math id="M57"><msub><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mo>↓</mo></mrow></msub></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639864&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639862&type= 5.16466665 4.57200003 ， <math id="M58"><msub><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><mi>ε</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639870&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639867&type= 3.72533321 3.80999994 ， <math id="M59"><msub><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><mi>L</mi><mi>S</mi><mi>T</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639874&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639871&type= 5.75733376 3.80999994 分别为离地辐射、大气下行辐射、宽波段发射率和所测地表温度的不确定度。 在热红外谱段，地物的发射率普遍较大，造成 式（13） 式（13） 中大气下行辐射的系数远小于离地辐射的系数，因此离地辐射对测量不确定度的影响往往更大（ Sekertekin和Bonafoni，2020b Sekertekin和Bonafoni，2020b ）。实验室测量结果则表明由于下行辐射的不确定性造成地表温度误差为0.1—0.2 K（ Coll 等，2019b Coll 等，2019b ）；参考 表3 表3 中测温仪器的测量精度，由地面辐射计测量造成的误差一般为0.2—0.3 K；此外，实测发现由于宽波段发射率影响造成的不确定度一般为0.4—0.6 K（ Coll 等，2005 Coll 等，2005 ， 2019b 2019b ）。总的来说，在282—316 K范围内，地表温度测量的综合误差在0.6—0.9 K（ Coll 等，2019b Coll 等，2019b ； Niclòs 等，2021 Niclòs 等，2021 ）。 （2）像元尺度地表温度的代表性。在点尺度的地表温度被转换为像元尺度的地表温度时由于无法合理描述卫星足迹内的地表温度的时空异质性而造成地表温度验证结果的误差，其往往与地表的异质程度、选择的采样策略和尺度转换模型等的不确定性有关（ 栾海军 等，2013 栾海军 等，2013 ； 姚远 等，2019 姚远 等，2019 ； Li 等，2020 Li 等，2020 ； Wu 等，2019 Wu 等，2019 ）。 Yu和Ma（2015） Yu和Ma（2015） 指出由于尺度不匹配和代表性不足等问题造成的地表温度误差最大超过3 K。 <math display="block" id="M60"><msub><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><mi mathvariant="normal">L</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">T</mi></mrow></msub><mo>=</mo><mroot><mrow><mtable columnalign="left"><mtr><mtd><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn mathvariant="normal">0.25</mn></mrow><mrow><mi>σ</mi><mi>ε</mi></mrow></mfrac><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi></mrow></msub><mo>-</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi><mo stretchy="false">)</mo><msub><mrow><mi>L</mi></mrow><mrow><mo>↓</mo></mrow></msub></mrow><mrow><mi>σ</mi><mi>ε</mi></mrow></mfrac></mrow></mfenced></mrow><mrow><mo>-</mo><mn mathvariant="normal">0.75</mn></mrow></msup></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mtd></mtr><mtr><mtd><mfenced separators="|"><mrow><msubsup><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>+</mo><msup><mrow><mfenced separators="|"><mrow><msub><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mo>↓</mo></mrow></msub></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi><mo stretchy="false">)</mo></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi mathvariant="normal">Δ</mi></mrow><mrow><mi>ε</mi></mrow></msub><mfenced separators="|"><mrow><mo>-</mo><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mo>↓</mo></mrow></msub></mrow></mfenced></mrow><mrow><mi>ε</mi></mrow></mfrac></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></mtd></mtr></mtable></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639877&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639875&type= 80.09466553 31.32666588 （3）时—空—角匹配的不确定性。遥感反演的地表温度与地面实测经过尺度转换后的地表温度在进行验证对比前需要先经过进行空间的配准、时间的配准和角度归一化等处理流程，该过程会造成地表温度验证结果的误差。空间配准的误差来自于遥感平台和站点定位的不确定度。尽管常见的遥感影像经过地理精校准往往达到亚像元定位精度，但相比于验证点的覆盖区域仍可能出现点与像元错误匹配的可能（ 马晋 等，2017 马晋 等，2017 ）。由于地面测量的偶然误差以及离散化采样难以同步进行等原因，地面验证过程同样会产生时间匹配误差，一般通过计算像元获取时间前后3 min内的地表温度测量均值来降低其不确定性（ Trigo 等，2021 Trigo 等，2021 ）。由于传感器非垂直观测或宽幅成像，像元观测地表温度还存在明显的角度效应。研究表明，由于角度效应的存在，在稀疏植被林地地类中观测角度不同的MODIS反演地表温度产品和SEVIRI反演地表温度产品的温度差异高达12 K（ Guillevic 等，2012 Guillevic 等，2012 ， 2014 2014 ； Trigo等，2008 Trigo等，2008 ）。因此，在进行产品验证时，对数据进行角度归一化处理，由此可能带来额外误差来源。 3.7　地表温度验证网络与产品验证精度 2 与气象领域的气温不同，地表温度还未在全球范围建立标准化的地表温度验证系统（ Bayat 等，2021 Bayat 等，2021 ）。星载遥感地表温度反演产品可以提供区域或全球地表温度空间分布，但一般极轨卫星载荷都是瞬时观测，时间分辨率不足（ Krishnan 等，2020 Krishnan 等，2020 ）。考虑到卫星过境时地面同步或准同步测量的需求，以及地表温度在不同的地表类型、不同季节、不同气候条件下具有较大的时空变异性（Le Page和Zribi，2019）等客观因素，需要在全球范围内建立长期观测的地表温度验证网络，以对不同遥感平台获得的地表温度产品进行全面、广泛的验证。如地球观测卫星委员会CEOS（Committee on Earth Observation Satellites）校准和验证工作组的地表温度验证子组LPV（Land Product Validation Subgroup）就确定了包括FLUXNET、JPL、SURFRAD、USCRN 、GCU和KIT stations等6个地面网络作为其地表温度验证的固定站点（ Guillevic 等，2018 Guillevic 等，2018 ）。 表5 表5 列举了现阶段世界范围内若干公开地表温度验证网络的名称、分布、地表类型以及数据访问途径。现有地表温度验证网络的验证站点主要分布在美国和欧洲，而亚洲、南美洲和非洲的验证站点仍较少；此外，大多数验证站点集中在北半球，南半球的验证站点较少；覆盖极地的站点仍很少，地表温度验证网络的空间分布仍很不均衡。 验证网络 站点分布 地表类型 访问方式 ARM 美国 多类型 https：//www.archive.arm.gov/discovery/ JPL 美国 水体和农田 https：//laketahoe.jpl.nasa.gov/ https：//saltonsea.jpl.nasa.gov/ https：//russellranch.jpl.nasa.gov/ FLUXNET 美国 多类型 https：//fluxnet.org/ SURFRAD 美国 灌丛和裸土 ftp：//aftp.cmdl.noaa.gov/data/radiation/surfacerad USCRN 美国 灌丛和裸土 http：//www.ncdc.noaa.gov/crn/ GCU 西班牙 多类型 https：//www.uv.es/ucg/ KIT 非洲、葡萄牙 多类型 https：//www.imk-asf.kit.edu/english/MSA-Validiation.php OzFLUX 澳洲 多类型 http：//www.ozflux.org.au/ TERN 澳洲 多类型 https：//www.tern.org.au/ AsiaFlux 亚洲 多类型 http：//asiaflux.net AmeriFlux 北美洲 多类型 http：//ameriflux.lbl.gov/ EuroFlux 欧洲 多类型 http：//europe-fluxdata.eu/ AWI 两极冻土区 冰\雪地 https：//www.awi.de/ LTER 美国 荒地 https：//lter.jornada.nmsu.edu/ NDBC 全球 水体 https：//www.ndbc.noaa.gov/ LAW 欧洲，澳洲 森林和农田 https：//law.acri-st.fr/data-access NEON 欧洲 多类型 https：//data.neonscience.org/ GBOV 全球 多类型 https：//gbov.acri.fr/dataaccessLP/ BSRN 全球 多类型 https：//bsrn.awi.de/ HiWATER 中国 农田和裸地 https：//data.tpdc.ac.cn PKULSTNet 中国 农田和裸地 renhuazhong@pku.edu.cn 站点的异质性是地表温度验证站点选取时需要考虑的问题，如SURFRAD 等7个站点中包括DRA（Desert Rock）、FPK（Fort Peck）和TBL（Table Mountain）等3个站点都被报道由于三维结构、视场内地面异质性等原因存在正偏差的现象，因此难以对百米级或更高空间分辨率地表温度产品进行基于地面实测温度的验证（ Guillevic 等，2014 Guillevic 等，2014 ； Malakar 等，2018 Malakar 等，2018 ； Wang和Liang，2009 Wang和Liang，2009 ； Wang和Prigent，2020 Wang和Prigent，2020 ）；而JPL的水体验证点，如Lake Tahoe、Salton Sea等具有很好的温度均一性（ Hook 等，2007 Hook 等，2007 ， 2020 2020 ），可以以点代面验证公里级分辨率的地表温度产品（ Hook 等，2020 Hook 等，2020 ）。 目前，随着星载红外载荷的陆续发射，已经存在众多业务化的全球地表温度产品，学者们对其进行了系统的验证，如MODIS（ Coll 等，2009 Coll 等，2009 ； Duan 等，2019 Duan 等，2019 ； Yu 等，2014a Yu 等，2014a ），TM/ETM+/TIRS（ Coll 等，2010 Coll 等，2010 ； Guo 等，2020 Guo 等，2020 ； Srivastava 等，2009 Srivastava 等，2009 ； Yu 等，2014b Yu 等，2014b ； Zhou 等，2012 Zhou 等，2012 ），AVHRR（ Prata，2003 Prata，2003 ），AATSR（ Coll 等，2005 Coll 等，2005 ）、SEVIRI（ Göttsche 等，2013 Göttsche 等，2013 ， 2016 2016 ），VIIRS（ Guillevic 等，2012 Guillevic 等，2012 ），ABI（ Yu 等，2012 Yu 等，2012 ）等。通过查询文献， 表6 表6 总结了不同学者对不同地表温度遥感产品的使用基于地面实测温度验证方法的验证结果。综合现有研究可以得出，通过基于温度的验证方法，目前主要遥感反演温度产品的验证偏差（Bias）从0.5—2.5 K不等，而验证均方根误差（RMSE）一般小于2 K（ Heidinger 等，2013 Heidinger 等，2013 ； Li 等，2014b Li 等，2014b ； Malakar 等，2018 Malakar 等，2018 ； Yu 等，2012 Yu 等，2012 ）。 遥感平台（传感器） 产品 Bias/K RMSE/K 验证站点 参考文献 Terra/Aqua（MODIS） MxD21 0.5 1.1 JPL和非公开站点 Li 等（2020a） Malakar和Hulley（2016） MSG（SEVIRI） LSALST 0.24 1.94 KIT Göttsche 等（2016） Trigo 等（2021） Envisat（AASTR） ESA_LST_2P 0.4—0.6 <2 JPL和非公开站点 Coll 等（2012b） Suomi-NPP（VIIRS） VNP21 <0.5 <1.5 SURFRAD Islam 等（2017） GOES-R（ABI） ABI-FD_LST12 2.5 2.3 SURFRAD Yu 等（2012） Seybold 等（2016） Sentinel-3（SLSTR） SL_2_LST 1 <2 KIT， SURFRAD， ARM， USCRN Ghent 等（2017） ISS（ECOSTRESS） ECO2LSTE — 1.07 JPL， KIT Hulley 等（2021） Metop（AVHRR） EDLST -0.0 1.86 KIT， SURFRAD， BSRN Trigo 等（2021） Terra（ASTER） AST08 -0.99 <1.5 JPL和非公开站点 Sabol 等（2009） 4　地表发射率的地面验证 1 4.1　地表发射率的地面验证方法 2 地物表面光谱发射率取决于材料类型、表面特征、粗糙度、土壤水分、发射方向、波长等参数（ Hulley和Hook，2011 Hulley和Hook，2011 ； Nerry 等，1988 Nerry 等，1988 ）。在室内测量中，估算地物发射率的方法是利用分光光谱仪将被测样品的辐射与黑体的辐射进行比较。由于实验成本和仪器系统较笨重等原因，野外直接测量地表光谱发射率在实际应用中存在困难（ Coll 等，2019b Coll 等，2019b ； Gillespie 等，1998 Gillespie 等，1998 ； Nerry 等，1988 Nerry 等，1988 ； Qin 等，2005 Qin 等，2005 ； Rubio 等，1997 Rubio 等，1997 ； Zhang 等，2014 Zhang 等，2014 ）。为避免频繁的地面发射率测量过程，往往需要利用地表发射率作为地表固有特征且在短时间内变化较小的这一性质，来选择长时间尺度上发射率变异性小的典型地表作为发射率验证场。如在冰盖、沙漠、水体（海洋、湖泊）等伪不变场（pseudo-invariant sites）上可以进行地表发射率的长时间序列观测与验证（ Hulley 等，2009 Hulley 等，2009 ）。目前ASTER、GLASS等发射率产品均使用了伪不变场进行地面验证（ Dong 等，2013 Dong 等，2013 ； Sabol 等，2009 Sabol 等，2009 ）。 地表发射率的地面验证也可以分为直接验证和交叉验证。直接验证将实测的地表发射率与遥感反演地表发射率直接对比（ Cheng 等，2014 Cheng 等，2014 a； Mushkin 等，2020 Mushkin 等，2020 ），得到反演地表发射率的精度指标，包括偏差（Bias）和不确定度（Uncertainty）等；交叉验证则将发射率反演结果与其他已经进行了良好验证的高精度发射率遥感产品进行交叉对比（ Cheng 等，2014 Cheng 等，2014 b； Masiello 等，2019 Masiello 等，2019 ），从而得到地表发射率产品的相对精度。 4.2　地表发射率的地面测量与误差 2 如上文所述，地表发射率与地表温度的相互耦合使得地表发射率难以直接测量。目前测量地表发射率的方法主要包括实验室光谱仪测量、野外光谱仪测量、多波段辐射计测量和箱法测量等方法。 （1）实验室光谱测量。实验室光谱测量是假设观测像元的发射率短时间变化很小，通过采集野外实验中样品到实验室中测量其实际发射率，以避免卫星观测与地面测量的准同步限制。实验室测量发射率一般使用分光光谱仪如Nicolet FTIR光谱仪等，首先使用Labsphere积分球测量样品某波长的方向—半球反射率 <math id="M61"><mi mathvariant="normal">D</mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">R</mi><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639891&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639888&type= 12.78466606 3.47133350 (Directional-Hemispheric Reflectance)，根据基尔霍夫定律得到特定波长 <math id="M62"><mi>λ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639923&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639921&type= 2.28600001 2.62466669 下发射率 <math id="M63"><mi>ε</mi><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639900&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639898&type= 7.11199999 3.47133350 ，将其代入到辐射传输方程 <math id="M64"><mi>L</mi><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mo>=</mo><mi>ε</mi><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mi>B</mi><mo stretchy="false">(</mo><mi>λ</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi></mrow></msub><mo stretchy="false">)</mo><mtext> </mtext><mo>+</mo><mtext> </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><msub><mrow><mi>L</mi></mrow><mrow><mo>↓</mo></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639906&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639903&type= 64.68533325 4.57200003 中可以得到样品温度 <math id="M65"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639910&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639908&type= 7.70466709 3.72533321 ，然后测量金板反射的下行辐射 <math id="M66"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">W</mi><mi mathvariant="normal">R</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639917&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639913&type= 6.43466663 3.72533321 ，最终样品在任意波长 <math id="M67"><mi>λ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639923&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639921&type= 2.28600001 2.62466669 下，观测角度为 <math id="M68"><mi>θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639928&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639926&type= 1.77800000 2.70933342 处的发射率为 <math display="block" id="M69"><msub><mrow><mi>ε</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo>,</mo><mi>θ</mi><mo stretchy="false">)</mo><mo>-</mo><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">W</mi><mi mathvariant="normal">R</mi></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo>,</mo><mi>θ</mi><mo stretchy="false">)</mo></mrow><mrow><mi>B</mi><mo stretchy="false">(</mo><mi>λ</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi></mrow></msub><mo stretchy="false">)</mo><mo>-</mo><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">W</mi><mi mathvariant="normal">R</mi></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo>,</mo><mi>θ</mi><mo stretchy="false">)</mo></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639933&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639930&type= 53.08599854 9.14400005 式中， <math id="M70"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo>,</mo><mi>θ</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639937&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639934&type= 16.67933464 4.57200003 为样品自身的发射辐射， <math id="M71"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">W</mi><mi mathvariant="normal">R</mi></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo>,</mo><mi>θ</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639946&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639942&type= 15.57866764 4.57200003 为半球下行辐射， <math id="M72"><mi>B</mi><mo stretchy="false">(</mo><mi>λ</mi><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639951&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639948&type= 17.01799965 4.57200003 为与样品相同温度下的黑体辐射。 一般而言，实验室的光谱测量方法减少了由于野外大气条件和环境辐射带来的误差，其测量精度更高（ Langsdale 等，2020a Langsdale 等，2020a ），常用的发射率光谱库如ECOSTRESS光谱库、ASTER光谱库等即由此法测得（ Baldridge 等，2009 Baldridge 等，2009 ； Meerdink 等，2019 Meerdink 等，2019 ），其测量发射率不确定性约为0.2%（ Korb 等，1999 Korb 等，1999 ）。然而，由于实验室测量对样品的延后测量或者破环性处理（如需要碾碎样品）等，会增加测量的不确定性（ Langsdale 等，2020b Langsdale 等，2020b ）。 （2）野外光谱仪测量。实验室光谱仪由于其自身便携性和测量过程过于繁琐等缺陷难以直接用于野外的同步测量。诸如102F、THIRSPEC、μFTIR、BOMEN MR304等便携式红外光谱仪可在野外实时测量红外辐射（ Hook和Kahle，1996 Hook和Kahle，1996 ），进而求解得到地表发射率。如μFTIR作为轻量级分光光谱仪可以测量2—15 μm的自然地表红外发射光谱，通过使用黑体温度从测得的表面辐射率中减去大气下行热辐射（使用金板测得）而直接得到光谱发射率，同时也可以使用如光谱平滑度迭代算法ISSTES（Iterative Spectrally Smooth Temperature/Emissivity Separation）（ Borel，1997 Borel，1997 ）、逐步优化温度与发射率分离法SRTES（Stepwise Refining Temperature/Emissivity Separation）（ Cheng 等，2010 Cheng 等，2010 ）、线性发射率温度与发射率分离法LECTES（Linear Emissivity Constraint Temperature Emissivity Separation Method）（ Wang 等，2011 Wang 等，2011 ）以及光谱平滑抗噪算法（ Qiu 等，2021 Qiu 等，2021 ）等算法进行地物光谱发射率的求解。 （3）多波段辐射计测量。除使用便捷式分光光谱仪测量野外光谱发射率外，手持多波段红外辐射计CAMEL CE-312也可用于野外发射率的测量（ Brogniez 等，2003 Brogniez 等，2003 ）。CE-312包含5个窄波段（8.25—8.60 μm，8.49—8.86 μm，8.95—9.34 μm，10.16—10.96 μm和10.86—11.71 μm）和一个宽波段（8.01—13.34 μm），其中5个窄波段的波段配置与搭载在Terra平台的ASTER传感器5个热红外波段配置类似（ Mira 等，2009 Mira 等，2009 ），其观测视场角为10°，响应时间为1 s，传感器的光谱响应见 图3 图3 。 多波段辐射计CE-312同样测量一组离地和大气下行热辐射求解地表发射率，传感器测量的地物辐射由 式（8） 式（8） 给出，包括地物发射辐射和地表反射的大气热辐射两部分贡献。CE312等5个窄波段配置使得可以利用多波段温度与发射率分离TES（Temperature and Emissivity Separation）算法（ Gillespie 等，1998 Gillespie 等，1998 ； Hulley和Hook，2009 Hulley和Hook，2009 ； Zhang等，2019 Zhang等，2019 ）可以从地物辐射求解地物发射率，TES算法主要包括以下3个模块（ Coll 等，2019b Coll 等，2019b ； Gillespie 等，1998 Gillespie 等，1998 ）： 1）NEM模块。假定5个通道的发射率初值 <math id="M73"><msub><mrow><mi>ε</mi></mrow><mrow><mi mathvariant="normal">N</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">M</mi><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640017&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640015&type= 6.68866634 3.72533321 均为0.98，代入 式（8） 式（8） 得到5个通道的NEM温度 <math id="M74"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">N</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">M</mi><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640004&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640003&type= 6.85799980 3.72533321 ： <math display="block" 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mathvariant="normal">M</mi><mi>i</mi></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639971&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639968&type= 47.92133331 10.58333302 选择5个波段NEM温度 <math id="M76"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">N</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">M</mi><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640004&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640003&type= 6.85799980 3.72533321 中的最大值 <math id="M77"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640008&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640007&type= 5.41866684 3.72533321 （ <math id="M78"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">N</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">M</mi><mi>i</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639983&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639980&type= 26.16200066 5.24933338 ， <math id="M79"><mi>i</mi><mo>=</mo><mn mathvariant="normal">1,2</mn><mo>,</mo><mn mathvariant="normal">3,4</mn><mo>,</mo><mn mathvariant="normal">5</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639988&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639985&type= 22.09799957 3.13266683 ），得到初步的NEM发射率 <math id="M80"><msub><mrow><mi>ε</mi></mrow><mrow><mi mathvariant="normal">N</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">M</mi><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640017&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640015&type= 6.68866634 3.72533321 ： <math display="block" id="M81"><msub><mrow><mi>ε</mi></mrow><mrow><mi mathvariant="normal">N</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">M</mi><mi>i</mi></mrow></msub><mo>=</mo><mfrac><mrow><msubsup><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">f</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow><mrow><mo>↓</mo></mrow></msubsup></mrow><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub></mrow></mfenced><mo>-</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow><mrow><mo>↓</mo></mrow></msubsup></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639996&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639995&type= 32.25799942 10.83733368 将 式（16） 式（16） 得到的NEM发射率 <math id="M82"><msub><mrow><mi>ε</mi></mrow><mrow><mi mathvariant="normal">N</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">M</mi><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640017&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640015&type= 6.68866634 3.72533321 作为输入代入到 式（15） 式（15） 重新计算NEM温度 <math id="M83"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">N</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">M</mi><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640004&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640003&type= 6.85799980 3.72533321 ，选取最大值 <math id="M84"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640008&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640007&type= 5.41866684 3.72533321 代入 式（16） 式（16） ，重复该过程迭代消除大气下行辐射到指定阈值，初步获取地表发射率 <math id="M85"><msub><mrow><mi>ε</mi></mrow><mrow><mi mathvariant="normal">N</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">M</mi><mi mathvariant="normal">i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640014&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640011&type= 6.68866634 3.72533321 。 2）RATIO模块。利用NEM发射率 <math id="M86"><msub><mrow><mi>ε</mi></mrow><mrow><mi mathvariant="normal">N</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">M</mi><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640017&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640015&type= 6.68866634 3.72533321 及其均值 <math id="M87"><mover accent="true"><mi>ε</mi><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640021&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640019&type= 1.94733346 2.62466669 ，在保留 NEM发射率的波谱形状的同时，计算得到对温度变化不敏感的相对辐射率 <math id="M88"><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640029&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640028&type= 2.62466669 4.48733330 ： <math display="block" id="M89"><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi mathvariant="normal">N</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">M</mi><mi mathvariant="normal">i</mi></mrow></msub></mrow><mrow><mover accent="true"><mi>ε</mi><mo>¯</mo></mover></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640026&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640025&type= 14.73200035 7.95866632 3）MMD模块。利用相对辐射率 <math id="M90"><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640029&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640028&type= 2.62466669 4.48733330 最大值与最小值的差值MMD（Maximum Minimum Difference）与最小波段发射率 <math id="M91"><msub><mrow><mi>ε</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640052&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640049&type= 5.07999992 3.72533321 经验关系得到最小波段发射率 <math id="M92"><msub><mrow><mi>ε</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640052&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640049&type= 5.07999992 3.72533321 ，最终求解各波段发射率 <math id="M93"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640039&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640037&type= 2.70933342 3.72533321 ： <math display="block" id="M94"><msub><mrow><mi>ε</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">0.9951</mn><mo>-</mo><mn mathvariant="normal">0.7264</mn><mo>×</mo><mi mathvariant="normal">M</mi><mi mathvariant="normal">M</mi><msup><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mn mathvariant="normal">0.7873</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640042&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640040&type= 52.23933029 4.06400013 <math display="block" id="M95"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub><mfrac><mrow><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mfenced separators="|"><mrow><msub><mrow><mi>β</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640047&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640045&type= 25.31533241 10.49866676 式中，MMD与发射率最小值 <math id="M96"><msub><mrow><mi>ε</mi></mrow><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640052&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640049&type= 5.07999992 3.72533321 的经验关系由ASTER光谱响应函数和岩石、土壤、植被、雪、水体等典型地物发射率光谱（ Hulley和Hook，2009 Hulley和Hook，2009 ）拟合得到，该经验关系同样适用于CE312（ Mira 等，2009 Mira 等，2009 ）。基于CE312多波段辐射计的发射率测量方法操作便捷，其发射率测量不确定度约为0.9%（ Mira 等，2009 Mira 等，2009 ）。目前该方法已经被广泛用于地表发射率的验证研究（ 杨以坤 等，2019 杨以坤 等，2019 ； Brogniez 等，2003 Brogniez 等，2003 ；Chen 等，2020； Coll 等，2019b Coll 等，2019b ； Legrand 等，2000 Legrand 等，2000 ； Niclòs 等，2018 Niclòs 等，2018 ， 2021 2021 ；Nie 等，2020； Ren 等，2021 Ren 等，2021 ； Wang 等，2020a Wang 等，2020a ）。 （4）箱法（box method）测量。箱法被用于测量视场内均一或者由单一地物组合而成的混合地表（ Rubio 等，2003 Rubio 等，2003 ），如纯裸土、纯草地或土壤和低矮植组成的混合地表类型等（Griend 等，1991）的方向性发射率，其具有隔离环境辐射影响的优点（ Mira 等，2009 Mira 等，2009 ）。箱法一般包括两种方式，即单盖法（ Combs 等，1965 Combs 等，1965 ）和双盖法（ Buettner和Kern，1965 Buettner和Kern，1965 ）。两种方式均使用无盖的箱体、箱体顶部和底部附带可改变的盖子（即冷盖和热盖），盖子中心开孔便于辐射计测量来自箱体底部的辐射。理想箱体的内壁和冷盖都是理想的全反射体（发射率为0），而热盖则是理想的黑体（发射率为1）（ Rubio 等，2003 Rubio 等，2003 ）。 1）单盖法。 Combs（1965） Combs（1965） 提出单盖法测量发射率。该法依赖实验环境温度，但是对实验要求较低。其假设箱体与环境同温且发射率为1。 如 图4 图4 ，单盖法首先测量离地辐射 <math id="M97"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">B</mi><mi mathvariant="normal">B</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640055&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640054&type= 4.48733330 3.72533321 、大气下行辐射 <math id="M98"><msubsup><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">a</mi></mrow><mrow><mo>↓</mo></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640060&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640057&type= 4.06400013 4.06400013 ，而后测量地物辐射 <math id="M99"><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640093&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640092&type= 3.04800010 2.96333337 ，最后测量箱体发出的辐射 <math id="M100"><msub><mrow><mi>B</mi></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640104&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640102&type= 3.38666677 3.72533321 。根据辐射传输方程可求解得到地物发射率，其表达式为 <math display="block" id="M101"><mi>ε</mi><mo>=</mo><mfrac><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">B</mi><mi mathvariant="normal">B</mi></mrow></msub><mo>-</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">a</mi></mrow><mrow><mo>↓</mo></mrow></msubsup></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>-</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">a</mi></mrow><mrow><mo>↓</mo></mrow></msubsup></mrow></mfrac><mo>+</mo><mi>δ</mi><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640071&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640070&type= 28.10933495 9.90600014 <math display="block" id="M102"><mi>δ</mi><mi>ε</mi><mo>=</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></mfenced><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mfrac><mrow><mfenced separators="|"><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>-</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">a</mi></mrow><mrow><mo>↓</mo></mrow></msubsup></mrow></mfenced></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>-</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">a</mi></mrow><mrow><mo>↓</mo></mrow></msubsup><mo>-</mo><mi>R</mi><mfenced separators="|"><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>-</mo><msub><mrow><mi>B</mi></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msub></mrow></mfenced></mrow></mfrac></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640076&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640074&type= 62.39933777 13.20800018 由于发射率箱并非理想黑体，因此需要加入修正项 <math id="M103"><mi>δ</mi><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640112&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640110&type= 3.55599999 2.62466669 修正发射率箱自身辐射造成的误差。上式 <math id="M104"><mi>R</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640087&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640085&type= 2.28600001 2.62466669 是取决于箱壁发射率 <math id="M105"><msub><mrow><mi>ε</mi></mrow><mrow><mi>c</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640116&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640114&type= 2.96333337 3.72533321 的系数，取值范围为0—1（ Rubio 等，2003 Rubio 等，2003 ）。实际测量中该方法的平均实验误差为±0.5％（ Guillevic 等，2018 Guillevic 等，2018 ； Hulley等，2019 Hulley等，2019 ； Rubio 等，2003 Rubio 等，2003 ）。 2）双盖法。 Buettner和Kern（1965） Buettner和Kern（1965） 提出使用双盖法测量发射率。双盖法不依赖实验环境温度，但是对实验要求较高，需要控制盖表面温度分布均一且保证理想状态下冷盖发射率接近0和热盖发射率接近1。双盖法具体测量方式见 图5 图5 ，首先，将冷盖置于箱顶，地物置于箱底测量地物发出的辐射 <math id="M106"><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640093&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640092&type= 3.04800010 2.96333337 ；之后用热盖代替冷盖来测量 <math id="M107"><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640097&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640095&type= 3.04800010 2.96333337 ，此时传感器接收辐射包括地物发射辐射和热盖发射辐射后经地物反射后到达传感器的辐射等两部分贡献；然后再将冷盖置于箱底测量理想情况下热盖发射的黑体辐射 <math id="M108"><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640101&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640099&type= 3.04800010 2.96333337 ；最后，将冷盖同时置于箱顶和箱底来测量箱体自身发射的辐射 <math id="M109"><msub><mrow><mi>B</mi></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640104&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640102&type= 3.38666677 3.72533321 。该方法测得的样品发射率由 式（22） 式（22） 和 式（23） 式（23） 给出： <math display="block" id="M110"><mi>ε</mi><mo>=</mo><mfrac><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msup><mo>-</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msup></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msup><mo>-</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac><mo>+</mo><mi>δ</mi><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640105&type= 25.73866653 8.21266651 <math display="block" id="M111"><mi>δ</mi><mi>ε</mi><mo>=</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></mfenced><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mfrac><mrow><mfenced separators="|"><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msup><mo>-</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>ε</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></mfenced></mrow><mrow><mfenced separators="|"><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msup><mo>-</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced><mo>-</mo><mfenced separators="|"><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msup><mo>-</mo><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msup></mrow></mfenced><mi>P</mi><mo>+</mo><mfenced separators="|"><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>-</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></mfenced><mi>Q</mi></mrow></mfrac></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640109&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640108&type= 79.50199890 13.20800018 式中， <math id="M112"><mi>δ</mi><mi>ε</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640112&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640110&type= 3.55599999 2.62466669 是对非理想箱体（现实的热盖的发射率不为1，冷盖的发射率不为0）的发射率修正（ Rubio 等，2003 Rubio 等，2003 ）， <math id="M113"><msub><mrow><mi>ε</mi></mrow><mrow><mi>c</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640116&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640114&type= 2.96333337 3.72533321 是非理想箱体（一般为铝板）的发射率， <math id="M114"><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640120&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640118&type= 2.28600001 2.62466669 和 <math id="M115"><mi>Q</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640122&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640121&type= 2.53999996 3.38666677 是冷盖、热盖的发射率和其热传导因子的函数。双盖法在低风力和无云的条件下，其平均误差为±0.5%（ Mira 等，2009 Mira 等，2009 ； Nerry 等，1990 Nerry 等，1990 ）。 Rubio（1992）比较了上述两种箱法测量方法的优劣，指出单盖法更适于野外测量地表发射率。（ Mira 等，2009 Mira 等，2009 ）比较了使用箱法和多波段辐射计测量法获取地表发射率的优劣，指出多波段辐射计测量方法耗时更短且与实验室光谱结果的一致性更好。 Langsdale 等（2020a） Langsdale 等（2020a） 将野外光谱仪测得的光谱发射率处理得到宽波段发射率，然后与使用双盖箱法测量的宽波段发射率进行对比，结果表明尽管箱法测量更加经济便利，但其测量的发射率一致性往往较差，且测量精度一般低于基于野外光谱仪的测量方法。发射率箱法常用于地物发射率的长期观测，在MODIS发射率验证（ Göttsche 等，2015 Göttsche 等，2015 ）、获取MSG/SEVIRI地表温度产品验证过程中使用的地表发射率数据（ Göttsche 等，2013 Göttsche 等，2013 ）等研究中被使用。 4.3　地表发射率测量的尺度转换 2 地面实测的发射率大都是 r -发射率，其可以通过地面实测的反射率和基尔霍夫定律得到。然而通过地面实地测量 r -发射率获取与遥感反演地表发射率尺度匹配的非均一地表像元发射率较为困难。目前较为有效的办法是先结合高空间分辨率的遥感产品（如叶面积指数、植被覆盖度和地面反射率等），划分卫星足迹内的地表类型，并测量各个地表类型的组分发射率，然后通过面积加权的方式获取卫星足迹内的像元的 e -发射率，其计算方式见 式（3） 式（3） 。在组分温度差异不大的情况下该方法可以替代像元 r -发射率的测量，实现地表发射率的尺度转换。 4.4　地表发射率验证网络与产品验证精度 2 现有地表发射率验证站点往往选择那些伪不变场，如美国喷气推进实验室JPL（Jet Propulsion Laboratory）发起了联合发射率数据库计划JEDI（Joint Emissivity Database Initiative）（ https：//emissivity.jpl.nasa.gov/ https://emissivity.jpl.nasa.gov/ ［2021-05-12］），其主要验证站点大都为沙地等伪不变场（ Hulley和Hook，2009 Hulley和Hook，2009 ）。 表7 表7 列举了常用于发射率验证的站点，站点大都分布在美国本土，地表的主要组成矿物多为石英。此外，也有学者利用新疆维吾尔自治区塔克拉玛干沙漠、内蒙古自治区西部的浑善达克沙地和毛乌素沙漠以及甘肃敦煌戈壁辐射校正场等国内伪不变场进行地表发射率的验证（ Cheng 等，2014 Cheng 等，2014 a； Dong 等，2013 Dong 等，2013 ； Li 等，2021 Li 等，2021 ）。 站点名称 粒度 主要矿物 位置 Algodones 中—粗 石英 32.95° N， 115.07° W Coral Pink 中 石英 37.04° N， 112.72° W Great Sands 中—粗 石英 37.77° N， 105.54° W Kelso 中 石英 34.91° N， 115.73° W Killpecker 中 石英 41.98° N， 109.10° W Little Sahara 细 石英 39.7° N， 112.39° W Stovepipe Wells 中 石英 36.62° N， 117.11° W Moses Lake 细 石英 47.05° N， 119.31° W White Sands 细 石膏 32.89° N， 106.33° W 利用上述发射率验证站点，学者们对常见的地表发射率产品进行了验证，验证结果见 表8 表8 ，从表中可以得出目前主要的发射率产品精度在0.01—0.02。 遥感平台（传感器） 产品 RMSE 参考文献 Terra （ASTER） AST05 0.015 Mushkin等（2020）； Sabol等（2009） Terra （ASTER） NAALSED 0.016 Hulley等（2009） Suomi-NPP （VIIRS） VNP21 0.015 Islam等（2017） Terra/Aqua （MODIS） MxD21 0.01 Malakar和Hulley（2016） ISS （ECOSTRESS） ECO2LSTE 0.023 Hulley等（2021） Terra/Aqua （ASTER/MODIS） CAMEL 0.02 Feltz等（2018） Loveless等（2021） Terra/Aqua/NOAA （AVHRR/MODIS） GLASS LSE 0.02 Dong等（2013） 5　结语 1 地表温度和发射率的地面验证是地表温度和发射率定量遥感产品应用的前提和基础。但是目前地表温度和发射率还缺乏业务化、标准统一的验证协议和在线验证平台，其验证水平仍弱于叶面积指数、土壤湿度和地表覆盖等其他陆地遥感参数（ Bayat 等，2021 Bayat 等，2021 ）。地表温度和发射率地面验证的不足主要体现在以下几个方面： （1）现有地表温度验证网络空间上过于稀疏，未能包含典型的地表覆盖类型（ Ghent，2020 Ghent，2020 ），如城市、山区、雨林等。因此，现有算法或产品往往只能在小范围、短时间尺度上进行验证，而难以充分评估算法或产品在区域、全球尺度上的总体精度。此外，从应用角度来说，当前地表温度和发射率站点的时空分布可能与地表温度或发射率的实际应用如辐射平衡、生物群落等特征分布不相匹配，而在这些验证站点之上构建的验证体系能否说明产品的应用精度值得怀疑； （2）目前地表温度验证站点主要服务于气象、通量观测等应用，并未专为地表温度验证设计，由此带来额外的不确定性。如验证过程需要精确的地表发射率和大气廓线等，而验证站点往往缺乏这些高精度的辅助信息；此外，验证站点的地表温度测量仪器并未针对热红外传感器而设计。例如FLUXNET验证网络常用的长波辐射计光谱响应范围为3—50 μm，白天时刻中红外太阳辐射会成为干扰进而降低地面地表温度的测量精度（ Miller 等，2020 Miller 等，2020 ）。 （3）验证站点的代表性。针对星载地表温度产品的验证大都在均一地表进行（ Coll等，2009 Coll等，2009 ； Li 等，2013a Li 等，2013a ； Wan 等，2004 Wan 等，2004 ； Wan和Li，2008 Wan和Li，2008 ； Yu 等，2017 Yu 等，2017 ），较少研究涉及非均质地表的地表温度验证，地表发射率等的验证也集中在伪不变场（ Feltz 等，2018 Feltz 等，2018 ； Hulley，2012 Hulley，2012 ）。 Sekertekin和Bonafoni（2020a） Sekertekin和Bonafoni（2020a） 指出遥感产品的地表验证精度会随着卫星数据的数量和获取时间的多少出现较大差异，这与验证的完整性和广泛性不足有关。算法精度验证和产品精度验证应该使用充足的验证数据集，在长时间序列尺度上加以验证。由于地表温度与发射率遥感产品的空间分辨率较粗，像元空间异质性概率大，那么二者的地面验证还需要认真地解决地面测量数据到像元尺度转换过程的代表性误差（ Mohamadi 等，2019 Mohamadi 等，2019 ）。 （4）多角度地面热辐射观测的缺失。现有地面验证站点以垂直观测为主，难以描述或者消除地表热辐射的角度效应。理论上对于宽视场或多角度传感器获取的数据都具有较强的角度效应，其反演地表温度与方向性发射率产品，往往不能直接使用地面测量结果进行验证，而需要经过红外BRDF模型进行角度纠正后才可进行验证工作（ Bian 等，2021 Bian 等，2021 ； Cao 等，2019 Cao 等，2019 ； Ren 等，2014 Ren 等，2014 ）。但目前热辐射角度纠正模型还未达到成熟使用阶段，往往可能带来新的误差来源。 （5）现有验证站点质量参差不齐，缺乏统一的质量控制体系。缺乏对地面验证数据的质量控制处理流程容易造成地面验证站点数据被误用或滥用，由此地面数据对地表温度与发射率验证的结果难以让人信服。 针对现有地表温度和发射率遥感产品地面验证工作的进展与不足，本文作者认为可以在以下几个方面开展研究：（1）针对现有验证站点数目少、空间分布稀疏的问题，在亚洲、非洲或其他验证站点低密度区部署新的地面观测站点，构建区域密集的、标准统一的地表验证观测网络以及数据共享机制；（2）设计专用于地表温度与发射率验证的地面测量仪器与规范（ Miller 等，2020 Miller 等，2020 ），加强仪器的周期性定标过程，以保证长时间测量数据的精度和一致性；（3）增设针对非均质像元（如城市、山区等）的公开验证站点，建立针对异质复杂地表的温度和发射率尺度转换模型；（4）设置实验性的多角度观测站点及其配套多角度观测装置（ Niclòs 等，2015 Niclòs 等，2015 ）进行多角度产品的地面验证；（5）建立统一的地表温度和发射率验证框架与流程，构建地表温度和发射率验证基准平台（ Wang 等，2016b Wang 等，2016b ）；明确各个验证站点的地面测量精度，增加对测量数据的质量控制，完善产品的元数据描述；开发在线地表温度与发射率验证数据分发平台等。 参考文献（References） Agbor C F and Makinde E O . 2018 . 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National Remote Sensing Bulletin， 25（8）：1538-1566 Zhu J S，Ren H Z，Ye X，Zeng H，Nie J，Jiang C C and Guo J X. 2021. Ground validation of land surface temperature and surface emissivity from thermal infrared remote sensing data： A review. National Remote Sensing Bulletin， 25（8）：1538-1566 国家自然科学基金（编号： 41771369） Supported by National Natural Science Foundation of China (No. 41771369) 2021-05-12 2021-08-07 2021-09-09 2021-07-09 遥感学报 8 25