我国陆表稳定目标TOA反射率模型构建方法及验证 ——以格尔木沙地场景为例

我国陆表稳定目标TOA反射率模型构建方法及验证 ——以格尔木沙地场景为例 Construction and validation of TOA reflectance reference model for stable land surface target- using Golmud desert site as an example 1 2 first-author 宋培兰，研究方向为卫星传感器可见近红外波段辐射定标。Email：songpeilan19@mails.ucas.ac.cn 宋培兰，研究方向为卫星传感器可见近红外波段辐射定标。Email：songpeilan19@mails.ucas.ac.cn songpeilan19@mails.ucas.ac.cn 1 corresp 马灵玲，主要从事遥感定标与真实性检验方法及高光谱遥感数据处理方法研究。E-mail： mall@aircas.ac.cn 马灵玲，主要从事遥感定标与真实性检验方法及高光谱遥感数据处理方法研究。E-mail： mall@aircas.ac.cn mall@aircas.ac.cn 1 1 1 3 1 1 1 1 1 中国科学院空天信息创新研究院 中国科学院定量遥感信息技术重点实验室,北京 100094 中国科学院空天信息创新研究院 中国科学院定量遥感信息技术重点实验室,北京 100094 Key Laboratory of Quantitative Remote Sensing Information Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China Key Laboratory of Quantitative Remote Sensing Information Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China 中国科学院大学 光电学院,北京 100049 中国科学院大学 光电学院,北京 100049 School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, China School of Optoelectronics, University of Chinese Academy of Sciences, Beijing 100049, China 中国资源卫星应用中心,北京 100094 中国资源卫星应用中心,北京 100094 China Centre for Resources Satellite Data and Application, Beijing 100094, China China Centre for Resources Satellite Data and Application, Beijing 100094, China 基于伪不变定标场（PICS）的大气层顶反射率（TOA）模型直接计算卫星过境入瞳辐亮度而无需地面测量，为高频次在轨辐射定标及长期性能监测提供了有效技术手段。然而由于严格的空间均匀性、时间稳定性和大气条件要求，现有的PICS定标场均分布在境外而难以满足多在境内成像的国产陆地卫星等定标需求。借鉴PICS的定标思路，本文开展了放宽场地、大气稳定性约束条件的我国陆表稳定目标TOA反射率模型构建方法研究。以我国西北区域的格尔木沙地稳定目标为例，将约束条件放宽至场地面积>3km×3km、云覆盖率<60%、空间均匀性<3%、时间稳定性<10%（11年），利用11年的Aqua/MODIS与ECMWF再分析资料分析观测几何及大气参数对TOA反射率的规律性影响，引入地表/大气辐射传输模型中定义的散射角，进一步表征TOA反射率模型中地表-大气间多次散射贡献，构建了一种适用于我国陆表稳定目标的TOA反射率模型。该模型系统偏差小于-0.10%，均方根误差小于0.0084；将Sentinel-2A/B MSI和Landsat-8/OLI的TOA反射率与本文模型计算TOA反射率进行比较，模型计算TOA反射率与Sentinel2A/B MSI观测TOA反射率的平均相对误差小于1.44%，标准差小于1.59%；与Landsat-8/OLI观测TOA反射率的平均相对误差小于1.77%，标准差小于2.11%。验证结果表明本文提出模型的计算值与卫星观测值具有较高的一致性和稳定性，能够应用于其他太阳反射谱段卫星载荷的在轨辐射定标和长期辐射特性监测。 The TOA reflectance model based on pseudo-invariant calibration sites (PICS) can directly calculate the apparent radiance of a satellite sensor without ground measurement, which provides an effective technical approach for high frequency in-orbit radiometric calibration and long-term satellite performance monitoring. However, due to the strict requirements of spatial uniformity, time stability and atmospheric conditions, the existing PICS calibration sites are all distributed abroad and it is difficult to meet the calibration requirements of China land satellites, which are mostly imaging in China. Using the experience of the radiometric calibration idea of PICS, this paper studied the construction model of TOA reflectance for inland surface stable target with relaxed sites and atmospheric stability constraints. Taking the stable target of Golmud destet in the northwest region as an example, the constraints were relaxed to site area greater than 3km×3km, cloud coverage less than 60%, spatial uniformity less than 3%, and temporal stability less than 10% (11 years). Then, Aqua/MODIS and ECMWF reanalysis data of 11 years were used to analyze the regularity of the observation geometry and atmospheric parameters on the TOA reflectance, and the scattering angle defined in the surface/atmospheric radiation transmission model was introduced to further characterize the multiple scattering contribution between the surface and atmosphere in the TOA reflectance model. Finally, a TOA reflectance model suitable for inland stable targets was proposed. The averaged bias and RMSE of the model is less than 0.10% and 0.0084, respectively. In addition, the TOA reflectance directly observed by Sentinel-2A/B MSI and Landsat-8/OLI were compared with the TOA reflectance calculated by the proposed model. The average relative error between the TOA reflectance calculated by the model and the observations of Sentinel2A/B MSI is less than 1.44%, and standard deviation of the relative error does not exceed 1.59%. The average relative error with Landsat-8/OLI observations is less than 1.77%, and the standard deviation of the relative error does not exceed 2.11%. The validation results show that the calculated TOA reluctances of the proposed model have high consistency and stability with satellite observations, and the model can be applied to the on-orbit radiometric calibration and long-term radiation characteristics monitoring of other satellite payloads in solar reflection spectrum. 陆表稳定目标 辐射定标 伪不变定标场 TOA反射率 观测几何 ECMWF inland surface stable target radiometric calibration pseudo-invariant calibration sites TOA reflectance observation geometry ECMWF 1　引 言 1 伪不变定标场（Pseudo-Invariant Calibration Sites，PICS）定标通过严格的条件筛选地表/大气特性极其稳定的地球目标区域，并构建高精度PICS大气层顶（Top of Atmosphere， TOA）反射率模型作为其辐射参考，实现载荷辐射性能长时序监测和跟踪。自1984年定标与真实性检验工作组（Working Group on Calibration & Validation，WGCV）成立以来，国际卫星对地观测委员会（Committee of Earth Observation Satellite，CEOS）就一直致力于全球范围内辐射定标场的优选，并于2008 年确定了Algeria 3、Algeria 5、Libya 1、Libya 4、Mauritania 1及Mauritania 2共6个PICS（ Lachérade等，2013 Lachérade等，2013 ），已被广泛用于Terra/MODIS、Landsat7/ETM+、FY-3A/MERSI、EO-1/ Hyperion、OCO-2等系列传感器长期稳定性评估（ Chander等，2010 Chander等，2010 ； Kim等，2014 Kim等，2014 ； Neigh等，2016 Neigh等，2016 ； Yu等，2020 Yu等，2020 ）。然而，PICS有着严格的约束条件，例如场地面积 > 20km×20km、云覆盖率 < 20%（1年）、空间均匀性 < 3%、时间稳定性 < 4%等。截至目前， Bacour 等人（2019） Bacour 等人（2019） 最新甄选的PICS均分布于国外北非撒哈拉沙漠地区，处于北回线附近，属于典型的热带沙漠气候，地表裸露、终年干旱炎热、四季变化不明显。在针对国外PICS场地的TOA反射率模型构建研究中， Helder等人（2013） Helder等人（2013） 使用Terra /MODIS和EO-1/ Hyperion建立了一种Libya4沙漠目标简化的绝对辐射定标模型，该模型只考虑太阳天顶角变化对TOA反射率的影响，可计算近似星下点观测条件（ <math id="M1"><mo>±</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274443&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274442&type= 1.77800000 2.62466669 7.5°）时目标上空的TOA反射率。 Mishra等人（2014） Mishra等人（2014） 进一步引入观测天顶角的影响，可实现非星下点观测、不同大气条件下目标上空TOA反射率的模拟计算，与Aqua/MODIS、Landsat 8/OLI、UK-2/DMC、ENVISAT/MERSI等卫星观测数据的相对误差标准差小于3%。 Raut等人（2019） Raut等人（2019） 将该模型推广到Egypt 1、Libya 1、Niger 1、Niger 2等场地，建立的通用TOA反射率模型在Libya 1的不确定度为1.07%~4.02%。由于PICS稳定的地表/大气特性，使得仅使用太阳天顶角和观测天顶角的组合就能够表征PICS场地TOA反射率的规律性变化，并在应用中达到较好效果。 由于我国陆地卫星成像资源多在国内，因此国内学者更多关注中国境内的陆表稳定目标甄选，何灵莉（2020）以时间稳定性 < 5%（16年），空间均匀性 < 5%为选场约束，选场结果主要集中在内蒙古以及西北区域。受温带大陆性气候及高原山地气候影响，这些场地的地表、大气特性不如PICS场地稳定。因此，建立于地表/大气特性稳定性极高基础之上的PICS场地TOA反射率模型难以准确表征国内陆表稳定目标由角度、大气以及季节等因素引起的TOA反射率规律性变化。为满足我国多系列陆地卫星的定标需求，有必要针对国内目标特性相对稳定的场地开展场地特性研究，发展适用于国内稳定目标场地的TOA反射率模型，开展高频次的卫星在轨辐射定标和性能监测，将是对国产卫星业务化场地定标的有益补充，对提高其辐射定标频次和稳定性具有重要意义。近几年，一些学者在国内稳定目标TOA反射率建模研究中，借鉴地表BRDF模型（ 赵春艳等，2019 赵春艳等，2019 ）建立的经验，基于中国敦煌辐射定标场和格尔木场地一年中晴天MODIS TOA反射率和角度信息建立TOA反射率半经验核驱动模型（ Liu等，2019 Liu等，2019 ），但使用两个场地分别得出的定标系数一致性较差，在绿波段（B4）的相对差异高达7.70%。 Wang等人（2017） Wang等人（2017） 考虑下垫面地物类型选择雪面BRDF模型对Kunlun1 的TOA反射率进行建模，未考虑大气季节性变化对TOA反射率的影响，导致模型在夏季出现较大偏差。此外， 王诗圣等人（2020） 王诗圣等人（2020） 基于6S模型分别建立了TOA反射率随观测天顶角和相对方位角变化的经验公式，但未考虑太阳角度影响。总的来说，国内稳定目标TOA反射率模型构建多是从描述地表二向反射特性的半经验模型出发，均忽略了国内场地大气季节性变化对TOA反射率的影响，难以表征国内稳定目标由角度、大气以及季节等多因素综合影响引起的TOA反射率规律性变化。 本文提出一种考虑“太阳-目标-传感器”观测几何及地表/大气季节性变化的TOA反射率模型构建方法，在放宽场地目标空间均匀性、地表/大气稳定性以及BRDF特性等约束条件下，选取了中国青海省柴达木盆地周边5 km×5 km的格尔木沙地稳定目标，以MODIS和ECMWF数据产品作为稳定目标的TOA反射率、大气状况先验知识库，分析观测几何以及大气参数对TOA反射率的影响规律，构建陆表稳定目标TOA反射率模型，并利用高精度的Landsat-8/OLI、Sentinel-2A/B MSI观测数据进行了定标结果分析，以验证所发展模型的有效性。 2　研究区域及数据 1 2.1　研究区域概况 2 借鉴国外PICS目标甄选标准，并参考国内稳定目标选取的经验和规则，本文首先制定了国内陆表稳定目标的约束条件。其中，场地面积从PICS的20 km × 20 km放宽至3 km × 3 km；年度云覆盖率小于60%以便获取足够的晴空影像，晴空条件下地表反射率应在VIS>0.15，NIR>0.3；当太阳及传感器天顶角小于65°时，角度效应小于60%；空间均匀性应优于3%，时间稳定性<10%（10年以上）。 本文基于2020年3~10月Sentinel-2A\2B地表反射率图像，以3 km × 3 km 的滑动窗口评价了过境中国青海省格尔木市附近区域的19景晴空影像的空间均匀性，以3%为阈值筛选出5 km×5 km的格尔木稳定目标。其下垫面类型为沙地，如 图1 图1 所示。 图2 图2 为在研究区实地拍摄的沙地图像，其颗粒较粗。2019年8月9日及14日分别实测了格尔木沙地稳定目标的光谱反射率，如 图3 图3 所示，约20%~40%。经2010~2020年地表反射率产品MCD43A4分析，研究区域在可见-近红外波段（B3、B4、B1、B2）的时间稳定性分别为8.37%、6.70%、5.26%、5.07%。距格尔木市约50km，地理坐标为：36.41°~36.46°N，94.20° ~94.25°E，总面积约5 km × 5 km ，中心海拔高度约2.84km。海拔高、大气干洁稳定，年平均晴空MODIS影像数量约为150天。 2.2　数据介绍 2 稳定目标TOA反射率模型构建依赖于包含卫星TOA反射率、大气参数等在内的场地特性数据，因此，针对本文研究区域，基于卫星数据、产品以及再分析资料搜集了建模所需的陆表稳定目标特性数据集，主要包括： （1）Aqua/MODIS、Sentinel-2A/B MSI以及Landsat-8/OLI卫星数据。Aqua/MODIS具有多角度观测能力，利用其宽视场角带来的轨道重叠获取多时相数据，可累积形成多角度数据集（阎广建 等，2020）。本研究选择2010~2020年Aqua卫星过境格尔木沙地目标的Collection 6.0版本MYD021KM辐射定标产品、MYD03地理定位产品作为研究数据，筛选出无云无雪晴空影像1232景，提取其太阳反射波段TOA反射率及观测几何参数构建模型构建所需的稳定目标数据集。选择2018~2021年30景Sentinel-2A/B MSI影像及2013~2020年27景Landsat-8/OLI影像作为验证数据。 图4 图4 展示了这三个卫星载荷对应波段的光谱响应曲线，其中黄色线表示的是Sentinel-2B卫星上搭载的MSI的光谱响应曲线，Sentinel-2A/MSI光谱响应曲线与其相似。 1,2,3;4,5; （2）再分析资料。本文使用欧洲中期天气预报中心（European Center for Medium-Range Weather Forecasts，ECMWF）再分析资料产品，从空间分辨率为0.25°× 0.25°的ERA5数据库以及空间分辨率为0.75°× 0.75°的EAC4数据库中提取2010-2020年Aqua/MODIS卫星过境格尔木沙地目标时的陆表降水量、降水类型、水汽含量、气溶胶光学厚度、风速、臭氧等大气参数。 3　方法及原理 1 3.1　基本思路 2 本文提出一种适用于国内陆表稳定目标的TOA反射率模型建模方法，该模型引入观测几何参数及大气参数，能够较好的表征观测几何、大气条件引起的场地目标TOA反射率变化，基本思路如 图5 图5 所示： （1）考虑“太阳-目标-传感器”观测几何、地表/大气特性参数等因素，分析其对场地目标TOA反射率的影响。包括：分析TOA反射率随观测角度或太阳角度的变化规律，对TOA反射率随太阳及传感器观测角度变化进行建模；同时分析降水量、水汽含量、臭氧含量、气溶胶光学厚度等因素的影响，对大气季节性影响进行建模。 （2）制定包含观测几何、大气参数的模型适用性约束条件，并构建陆表稳定目标TOA反射率模型。主要考虑太阳、观测角度对大气路径影响，并考虑风沙、降雨、降雪等天气不满足辐射定标条件。当满足观测几何、大气参数约束条件时，以陆表稳定目标大气及场地特性为辐射参考，耦合观测几何及大气参数，建立的TOA反射率模型为： <math display="block" id="M2"><msub><mrow><mi>ρ</mi></mrow><mrow><mi>T</mi><mi>O</mi><mi>A</mi></mrow></msub><mo>=</mo><mi>f</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>,</mo><mi>W</mi><mi>V</mi><mi>C</mi><mo>,</mo><msub><mrow><mi>O</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><mi>A</mi><mi>O</mi><mi>D</mi><mo>,</mo><mo>⋯</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274072&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274071&type= 54.77933884 4.74133301 式（1） 式（1） 中， <math id="M3"><msub><mrow><mi>ρ</mi></mrow><mrow><mi>T</mi><mi>O</mi><mi>A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274074&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274073&type= 5.33400011 4.48733330 是TOA反射率， <math id="M4"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 、 <math id="M5"><msub><mrow><mi>φ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274276&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274275&type= 3.04800010 4.40266657 、 <math id="M6"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 、 <math id="M7"><msub><mrow><mi>φ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274280&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274279&type= 3.21733332 4.40266657 、 <math id="M8"><mi>W</mi><mi>V</mi><mi>C</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274086&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274085&type= 7.19666624 2.62466669 、 <math id="M9"><msub><mrow><mi>O</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274088&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274087&type= 3.64066648 3.72533321 、及 <math id="M10"><mi>A</mi><mi>O</mi><mi>D</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274090&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274089&type= 7.02733374 2.62466669 是太阳观测几何、传感器观测几何、水汽含量、臭氧含量、气溶胶光学厚度等影响因素。 3.2　观测几何影响建模 2 3.2.1　观测天顶角对TOA反射率的影响 3 为分析观测天顶角引起的TOA反射率规律性变化，本文利用了2010~2020年间Aqua/MODIS的TOA反射率时间序列数据。其中，Aqua/MODIS过境格尔木沙地目标时观测天顶角覆盖范围为： <math id="M11"><msup><mrow><mn mathvariant="normal">0</mn></mrow><mrow><mo>°</mo></mrow></msup><mo>~</mo><msup><mrow><mn mathvariant="normal">65</mn></mrow><mrow><mo>°</mo></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274092&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274091&type= 9.39799976 2.96333337 ，受卫星轨道周期性变化影响，卫星观测角度也呈现规律性趋势，主要集中在不连续的17组数据中。 图6 图6 展示了格尔木沙地稳定目标TOA反射率随观测天顶角的变 1,2; 化规律，其中卫星和太阳同向时观测天顶角记为正，对向观测时记为负。从图中展示的数据可以看出，随着卫星逐渐偏离垂直观测，反射率有逐渐增大的趋势。在不考虑太阳观测几何的情况下，为建立TOA反射率与观测天顶角 <math id="M12"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 的关系模型，使用余弦函数对不同波段的TOA反射率数据进行拟合，拟合结果如 图6 图6 所示。其第一项常数项不为0，表征卫星和太阳同向观测与对向观测时TOA反射率的不对称现象；第二项常数项反映了对应波段TOA反射率均值大学；一次项表示观测天顶角 <math id="M13"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 对各波段TOA反射率的影响高低。对于Band 3波段， <math id="M14"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 的变化对TOA反射率的影响最为显著，对应一次项绝对值最大。对于Band 7波段，相应的一次项绝对值数相对较小，但是 <math id="M15"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 对TOA反射率仍有影响。 随着 <math id="M16"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 的变化，辐射能量穿透大气的光学路径长度也随之变化。以AQUA卫星为例，分析了不同 <math id="M17"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 下卫星星下点与目标场地的距离，结果如 图7 图7 所示。当 <math id="M18"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>=</mo><msup><mrow><mn mathvariant="normal">35</mn></mrow><mrow><mo>°</mo></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274115&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274114&type= 11.59933376 4.06400013 度时，星下点与观测目标之间的距离约493.65km，因此，本文通过约束 <math id="M19"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 以限制大气路径长度。 3.2.2　太阳天顶角对TOA反射率的影响 3 考虑太阳天顶角变化对稳定目标TOA反射率的影响，本文采用控制变量法，分析并建立TOA反射率与太阳天顶角 <math id="M20"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 的参数化关系，也就是说，在限制 <math id="M21"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 及传感器观测方位角 <math id="M22"><msub><mrow><mi>φ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274280&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274279&type= 3.21733332 4.40266657 变化范围的基础上，分析TOA反射率随 <math id="M23"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 的变化规律。 本文使用的MODIS数据过境时间为：UTC6：00~7：40， <math id="M24"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 覆盖范围为：0°~65°。依据 <math id="M25"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 的数值变化，将这些数据划分为17组。同一组数据中 <math id="M26"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 的增量不超过2°。不同组数据间 <math id="M27"><msub><mrow><mi>φ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274280&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274279&type= 3.21733332 4.40266657 变化的增量为0.23°~2.60°，仅当-3° <math id="M28"><mo>≤</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>≤</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274156&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274155&type= 8.97466660 3.80999994 -1°时， <math id="M29"><msub><mrow><mi>φ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274280&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274279&type= 3.21733332 4.40266657 的变化范围为77.10°~97.60°，增量为20.50°。因此，每组数据对应的传感器观测姿态变化较小，可以假定TOA反射率主要受太阳天顶角影响。 图8 图8 展示了其中6组特定观测天顶角下TOA反射率（MODIS B7波段）随 <math id="M30"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 的变化规律。综合分析，当-64° <math id="M31"><mo>≤</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>≤</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274156&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274155&type= 8.97466660 3.80999994 -41°、47° <math id="M32"><mo>≤</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>≤</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274156&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274155&type= 8.97466660 3.80999994 64°时，TOA反射率随 <math id="M33"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 的增大而明显增大；当-35° <math id="M34"><mo>≤</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>≤</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274156&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274155&type= 8.97466660 3.80999994 -24°、40° <math id="M35"><mo>≤</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>≤</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274156&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274155&type= 8.97466660 3.80999994 42°时，TOA反射率随 <math id="M36"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 而增加的趋势减缓；当-15° <math id="M37"><mo>≤</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>≤</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274156&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274155&type= 8.97466660 3.80999994 33°时，TOA反射率随 <math id="M38"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 的增大而明显减小。结合3.2.1节的分析可知， <math id="M39"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 =35°近似同向观测场景下数据趋势变化的临界值。 1,2,3;4,5,6; 为建立TOA反射率与 <math id="M50"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 的关系模型，使用 <math id="M51"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 余弦的一次函数对不同波段的TOA反射率数据进行拟合。 图7 图7 给出了B7波段的拟合结果，在限定 <math id="M52"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>≤</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274206&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274205&type= 5.84200001 3.80999994 <math id="M53"><mo>±</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274443&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274442&type= 1.77800000 2.62466669 35°时，均方根误差小于0.01。此外，在拟合曲线中，一次项 <math id="M54"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274367&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274366&type= 3.04800010 3.72533321 和常数项 <math id="M55"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274222&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274221&type= 3.04800010 3.72533321 与各组数据的 <math id="M56"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 均值具有显著的相关性，如 图9 图9 所示。随着传感器逐渐偏离垂直观测，一次项 <math id="M57"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274367&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274366&type= 3.04800010 3.72533321 逐渐减小，与3.2.1节TOA反射率与 <math id="M58"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 的关系相反，且 <math id="M59"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>b</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>×</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>+</mo><msub><mrow><mi>b</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>b</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274220&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274219&type= 40.21666718 4.57200003 ；但常数项 <math id="M60"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274222&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274221&type= 3.04800010 3.72533321 随着传感器逐渐偏离垂直观测，其数值逐渐增大，与3.2.1节TOA反射率与 <math id="M61"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 的关系相同，同时有： <math id="M62"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>=</mo><msub><mrow><mi>c</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>×</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>+</mo><msub><mrow><mi>c</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>c</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274226&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274225&type= 39.62400055 4.57200003 。因此，可以得出TOA反射率与 <math id="M63"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 及 <math id="M64"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 的关系式： <math display="block" id="M65"><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>ρ</mi></mrow><mrow><mi>T</mi><mi>O</mi><mi>A</mi></mrow></msub><mo>=</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>×</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mtd></mtr><mtr><mtd><msup><mrow/><mrow/></msup><msup><mrow/><mrow/></msup><mo>=</mo><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274232&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274231&type= 43.01066971 10.15999985 其中， <math id="M66"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 为观测天顶角，函数 <math id="M67"><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274236&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274235&type= 8.46666718 4.74133301 及 <math id="M68"><msub><mrow><mi>f</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274238&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274237&type= 8.46666718 4.74133301 描述了TOA反射率随 <math id="M69"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 的变化规律， <math id="M70"><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274242&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274241&type= 10.83733368 4.57200003 是采用控制变量法推导出的TOA反射率随 <math id="M71"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 的变化规律。 1,2; 3.2.3　散射角对TOA反射率的影响 3 为刻画“太阳-目标-传感器”观测几何中方位角差异带来的TOA反射率变化，本文引入了Ross-Li模型体散射核（ Zhou等，2020 Zhou等，2020 ）中定义的散射角并分析其对TOA反射率的影响规律。基于 <math id="M76"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 、 <math id="M77"><msub><mrow><mi>φ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274276&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274275&type= 3.04800010 4.40266657 、 <math id="M78"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 及 <math id="M79"><msub><mrow><mi>φ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274280&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274279&type= 3.21733332 4.40266657 计算散射角 <math id="M80"><mi mathvariant="normal">Θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274365&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274364&type= 2.87866688 2.70933342 的表达式为： <math display="block" id="M81"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">Θ</mi><mo>=</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>×</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>+</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>×</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></mtd></mtr><mtr><mtd><mo>×</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>φ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>-</mo><msub><mrow><mi>φ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274272&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274271&type= 57.23466873 9.22866726 式中： <math id="M82"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 为太阳天顶角； <math id="M83"><msub><mrow><mi>φ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274276&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274275&type= 3.04800010 4.40266657 为太阳方位角； <math id="M84"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 为传感器观测天顶角； <math id="M85"><msub><mrow><mi>φ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274280&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274279&type= 3.21733332 4.40266657 为传感器观测方位角； <math id="M86"><mi mathvariant="normal">Θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274365&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274364&type= 2.87866688 2.70933342 是散射角，即太阳入射方向与传感器观测方向在4π空间中的夹角（ Liou等，2002 Liou等，2002 ）。 针对格尔木沙地稳定目标，当-35° <math id="M87"><mo><</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>-</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo><</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274284&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274283&type= 15.91733265 3.80999994 35°时， <math id="M88"><mi mathvariant="normal">Θ</mi><mo><</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274286&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274285&type= 6.01133299 2.70933342 52°。此时，AQUA/MODIS传感器太阳反射率波段的TOA反射率随 <math id="M89"><mi mathvariant="normal">Θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274365&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274364&type= 2.87866688 2.70933342 的变化如 图10 图10 所示。其中，后向散射（相对方位角 <math id="M90"><mi>R</mi><mi>A</mi><mi>A</mi><mo><</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274290&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274289&type= 9.48266602 2.70933342 180°）时 <math id="M91"><mi mathvariant="normal">Θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274365&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274364&type= 2.87866688 2.70933342 记为正，前向散射（相对方位角 <math id="M92"><mi>R</mi><mi>A</mi><mi>A</mi><mo>></mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274294&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274293&type= 9.48266602 2.70933342 180°）时 <math id="M93"><mi mathvariant="normal">Θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274365&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274364&type= 2.87866688 2.70933342 记为负。从图中可以看出， <math id="M94"><mi mathvariant="normal">Θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274365&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274364&type= 2.87866688 2.70933342 绝对值越大，太阳入射方向与传感器观测方向间的夹角越大，TOA反 1,2; 射率越大。受瑞利散射影响， http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274458&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274460&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274459&type= 4.49800014 5.02700043 的变化对蓝波段（B3）TOA反射率的影响最显著。本文为建TOA反射率与 <math id="M95"><mi mathvariant="normal">Θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274365&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274364&type= 2.87866688 2.70933342 的关系模型，使用 式（4） 式（4） 所示的傅里叶级数对不同波段的TOA反射率数据进行拟合，本文选择n=1。 <math display="block" id="M96"><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow><mrow><mn mathvariant="normal">2</mn></mrow></mfrac><mo>+</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>n</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>∞</mi></mrow></munderover></mstyle><mrow><mo stretchy="false">(</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><mi>c</mi><mi>o</mi><mi>s</mi><mo stretchy="false">(</mo><mi>n</mi><mi>x</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>b</mi></mrow><mrow><mi>n</mi></mrow></msub><mi>s</mi><mi>i</mi><mi>n</mi><mo stretchy="false">(</mo><mi>n</mi><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274310&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274309&type= 61.80666733 8.38199997 3.3　大气季节性影响建模 2 本文从ECMWF再分析资料中提取了AQUA/MODIS传感器过境格尔木沙地稳定目标时对应的大气参数，其中水汽及臭氧含量变化如 图11 图11 所示，有明显的季节性特征。2010~2020年11年间晴空条件下格尔木沙地实验区水汽柱含量呈“M型”分布，春季和秋季水汽柱含量最大，最高为2.05g/cm 2 ；夏季和冬季水汽柱含量明显降低，最低为0.04g/cm 2 。臭氧柱含量刚好相反，呈“W型”分布，春季和秋季臭氧柱含量最小，最低为5.11×10 -4 g/cm 2 ；夏季和冬季臭氧柱含量明显升高，最高为8.41×10 -4 g/cm 2 。2010~2020年格尔木沙地研究区晴空条件下总AOD@550nm无季节变化特征，但是黑炭、有机质、海盐、盐酸盐4种AOD的变化呈“W型”的季节循环特征，如 图12 图12 所示。11年间，这4种AOD从春季到夏季迅速增加，秋季降低，冬季又开始上升。 1,2; 1,2;3,4;5,6; 大气中臭氧、水汽、气溶胶光学厚度等参数季节性变化的同时将对TOA反射率数据产生季节性影响。如 图13 图13 所示，消除 <math id="M97"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 、 <math id="M98"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 及 <math id="M99"><mi mathvariant="normal">Θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274365&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274364&type= 2.87866688 2.70933342 等观测几何对TOA反射率的影响后，模型残差表现出季节性变化。其中，模型残差用观测值与模拟值的比值表示。本文通过使用正弦函数对不同波段的模型残差值进行拟合，建立TOA反射率受臭氧含量、水汽含量、气溶胶光学厚度等参数影响的大气模型。拟合结果发现，尽管B1、B2、B3、B4、B5、B7波段的振幅不同，但 <math id="M100"><mi>w</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274347&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274346&type= 2.28600001 2.62466669 均为0.0173，即周期约363.19天，近似1年。 1,2; 3.4　TOA反射率模型 2 <math display="block" id="M101"><mtable columnalign="left"><mtr><mtd><msubsup><mrow><mi>ρ</mi></mrow><mrow><mi>T</mi><mi>O</mi><mi>A</mi><mo>,</mo><mi>M</mi><mi>O</mi><mi>D</mi><mi>I</mi><mi>S</mi></mrow><mrow><mi>s</mi><mi>i</mi><mi>m</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>i</mi><mo>,</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>,</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>,</mo><mi mathvariant="normal">Θ</mi><mo>,</mo><mi>D</mi><mi>O</mi><mi>Y</mi><mo stretchy="false">)</mo><mo>=</mo><mfenced separators="|"><mrow><mfrac><mrow><mo stretchy="false">(</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">1</mn><mo>,</mo><mi>i</mi></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">2</mn><mo>,</mo><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">3</mn><mo>,</mo><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">4</mn><mo>,</mo><mi>i</mi></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mo stretchy="false">(</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">5</mn><mo>,</mo><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">6</mn><mo>,</mo><mi>i</mi></mrow></msub><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">Θ</mi><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">7</mn><mo>,</mo><mi>i</mi></mrow></msub><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">Θ</mi><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">8</mn><mo>,</mo><mi>i</mi></mrow></msub></mrow></mfrac><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">9</mn><mo>,</mo><mi>i</mi></mrow></msub></mrow></mfenced></mtd></mtr><mtr><mtd><mo>×</mo><mfenced separators="|"><mrow><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">10</mn><mo>,</mo><mi>i</mi></mrow></msub><mo>×</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><mfrac><mrow><mn mathvariant="normal">2</mn><mi>π</mi></mrow><mrow><mn mathvariant="normal">365</mn></mrow></mfrac><mo>×</mo><mi>D</mi><mi>O</mi><mi>Y</mi><mo stretchy="false">)</mo><mo>+</mo><mn mathvariant="normal">1</mn></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274357&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274356&type= 125.05266571 20.31999969 基于3.2及3.3节的分析，建立的TOA反射率模型如 式（5） 式（5） 所示。其中， <math id="M102"><msubsup><mrow><mi>ρ</mi></mrow><mrow><mi>T</mi><mi>O</mi><mi>A</mi><mo>,</mo><mi>M</mi><mi>O</mi><mi>D</mi><mi>I</mi><mi>S</mi></mrow><mrow><mi>s</mi><mi>i</mi><mi>m</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274413&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274412&type= 16.59466553 4.99533367 是基于TOA反射率模型推导出的MODIS传感器各波段TOA反射率模拟值； <math id="M103"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 、 <math id="M104"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 、 <math id="M105"><mi mathvariant="normal">Θ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274365&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274364&type= 2.87866688 2.70933342 分别是卫星传感器图像采集时的太阳天顶角、观测天顶角以及散射角， DOY表示卫星传感器图像采集时的年积日，即图像采集当天在该年中的连续计数累计值，最大为366天； <math id="M106"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274367&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274366&type= 3.04800010 3.72533321 、 <math id="M107"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274369&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274368&type= 3.04800010 3.72533321 、 <math id="M108"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274371&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274370&type= 3.04800010 3.72533321 、 <math id="M109"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274373&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274372&type= 3.04800010 3.72533321 、 <math id="M110"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274375&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274374&type= 3.04800010 3.72533321 是表征TOA反射率随 <math id="M111"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274377&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274376&type= 2.53999996 3.80999994 及 <math id="M112"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274378&type= 2.70933342 3.80999994 变化的模型系数，如3.2.1及3.2.2节所述； <math id="M113"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274381&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274380&type= 3.04800010 3.72533321 、 <math id="M114"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274383&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274382&type= 3.04800010 3.72533321 、 <math id="M115"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">8</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274385&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274384&type= 3.04800010 3.72533321 是BRDF模型中体散射核的近似表达，如3.2.3节所述； <math id="M116"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">9</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274387&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274386&type= 3.04800010 3.72533321 是常数项；大气的季节性变化对TOA反射率的影响用周期性正弦函数表达，振幅为 <math id="M117"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">10</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274389&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274388&type= 4.06400013 3.72533321 ，周期的经验值为365天。 式（5） 式（5） 表征了 Aqua/MODIS过境陆表稳定目标时随观测几何和大气季节性影响的TOA反射率变化规律，即任意时间MODIS的TOA反射率可以通过该公式计算。 4　结果及验证 1 4.1　基于AQUA/MODIS数据的建模结果 2 由于本文所采用的ERA5数据库和EAC4数据库空间分辨率分别为0.25°× 0.25°、0.75°× 0.75°，因此尽管在数据下载及检查阶段已经剔除掉15km×15km范围内云覆盖率较高、过境时刻降水或降雪的影像，但在0.25°× 0.25°的大区域范围内仍有云覆盖、降水及降雪。受昆仑山常年积雪影响，格尔木沙地实验区0.25°× 0.25°分辨率的夏季雪密度大于0.1g/cm 3 。故，本文在建立 式（5） 式（5） 所示的TOA反射率模型时除了制定与观测几何相关的模型适用性约束条件外，还基于ECMWF再分析资料制定了大气参数等适用性约束条件以筛选MODIS TOA反射率，如 表1 表1 所示。 约束要素 约束条件 备注 观测天顶角 -35° < <math id="M118"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274393&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274392&type= 2.11666679 2.87866688 < 35° 该参数确保MODIS成像时星下点距观测目标500km以内。 散射角 -35° < <math id="M119"><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274393&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274392&type= 2.11666679 2.87866688 - <math id="M120"><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274395&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274394&type= 2.03200006 2.87866688 < 35° （仅同向观测时） 该参数约束了辐射能量二次穿透大气至MODIS传感器的路径长度，并可筛除MODIS传感器大部分冬季影像。 降水类型 Precipitation Type = 0 该参数确保成像时天气晴朗，0.25°×0.25°范围内无降雨、降雪。 雪深 Snow Density < 0.16 g/cm 3 参数确保成像时0.25°×0.25°空间范围内积雪较少，并在冬季去除研究区陆表被雪覆盖的影像。 云覆盖率 Total Cloud Cover < 0.80 该参数确保成像时0.25°×0.25°空间范围内20%的区域无云。 气溶胶 Total AOD < 0.40（500nm） 该参数筛除成像时0.75°×0.75°空间范围内含沙尘天气的数据。 水汽含量 Total CWV < 2.00 g/cm 2 该参数确保模型仅用于大气中水汽含量适中的影像。 本文按照 表1 表1 制定的观测几何及约束条件，筛选2010~2019年AQUA\MODIS的多角度TOA反射率数据共288景。对建立的TOA反射率模型，采用最小二乘法，以模拟值与观测值的误差最小为约束条件，求解TOA反射率模型系数。 图14 图14 展示了B7波段的模型系数并对比了该模型模拟TOA反射率与AQUA/MODIS的B7波段的观测TOA反射率。从图中可以看出：TOA反射率模型不仅能有效计算不同观测几何、地表\大气条件的TOA反射率，同时保留了陆表稳定目标TOA反射率的季节性变化特征。二者的相对误差频数分布直方图如 图15 图15 所示，总体优于4%，基本符合正态分布。统计所有波段对应相对误差的均值、标准差及均方根误差，结果见 表2 表2 。各波段的平均相对误差在-0.10%以内，模型计算值与卫星观测值之间不存在明显的系统偏差。相对误差的标准差在3.07%以内，均方根误差小于0.0084。 Channel N0. Average relative error STD of relative error RMSE R 2 B1 -0.07% 2.56% 0.0068 0.69 B2 -0.06% 2.44% 0.0075 0.66 B3 -0.10% 3.07% 0.0057 0.86 B4 -0.08% 2.88% 0.0061 0.76 B5 -0.04% 2.06% 0.0071 0.66 B7 -0.06% 2.08% 0.0084 0.59 4.2　基于Sentinel-2及Landsat-8观测数据的模型验证 2 4.2.1　光谱匹配因子 3 利用Sentinel-2B/MSI及Landsat-8/OLI观测数据对本文建立的TOA反射率模型进行验证，为解决传感器间的光谱差异，本文使用 式（6） 式（6） 及 式（7） 式（7） 将预测的MODIS传感器相应波段TOA反射率转换成目标传感器对应通道的TOA反射率。 <math display="block" id="M121"><msubsup><mrow><mi>ρ</mi></mrow><mrow><mi>T</mi><mi>O</mi><mi>A</mi><mo>,</mo><mi>s</mi><mi>e</mi><mi>n</mi><mi>s</mi><mi>o</mi><mi>r</mi></mrow><mrow><mi>s</mi><mi>i</mi><mi>m</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo><mo>=</mo><msubsup><mrow><mi>ρ</mi></mrow><mrow><mi>T</mi><mi>O</mi><mi>A</mi><mo>,</mo><mi>M</mi><mi>O</mi><mi>D</mi><mi>I</mi><mi>S</mi></mrow><mrow><mi>s</mi><mi>i</mi><mi>m</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo><mo>×</mo><mi>S</mi><mi>B</mi><mi>A</mi><mi>F</mi><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274407&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274406&type= 52.49333191 4.99533367 <math display="block" id="M122"><mi>S</mi><mi>B</mi><mi>A</mi><mi>F</mi><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mrow><mrow><mo>∫</mo><mrow><mi>ρ</mi><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><msub><mrow><mi mathvariant="normal">Γ</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>n</mi><mi>s</mi><mi>o</mi><mi>r</mi><mo>,</mo><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mi>d</mi><mi>λ</mi></mrow></mrow><mo>/</mo><mrow><mo>∫</mo><mrow><msub><mrow><mi mathvariant="normal">Γ</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>n</mi><mi>s</mi><mi>o</mi><mi>r</mi><mo>,</mo><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mi>d</mi><mi>λ</mi></mrow></mrow></mrow></mrow><mrow><mrow><mrow><mo>∫</mo><mrow><mi>ρ</mi><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><msub><mrow><mi mathvariant="normal">Γ</mi></mrow><mrow><mi>M</mi><mi>O</mi><mi>D</mi><mi>I</mi><mi>S</mi><mo>,</mo><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mi>d</mi><mi>λ</mi></mrow></mrow><mo>/</mo><mrow><mo>∫</mo><mrow><msub><mrow><mi mathvariant="normal">Γ</mi></mrow><mrow><mi>M</mi><mi>O</mi><mi>D</mi><mi>I</mi><mi>S</mi><mo>,</mo><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo><mi>d</mi><mi>λ</mi></mrow></mrow></mrow></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274409&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274408&type= 71.12000275 15.07066536 式（6） 式（6） 中， <math id="M123"><msubsup><mrow><mi>ρ</mi></mrow><mrow><mi>T</mi><mi>O</mi><mi>A</mi><mo>,</mo><mi>s</mi><mi>e</mi><mi>n</mi><mi>s</mi><mi>o</mi><mi>r</mi></mrow><mrow><mi>s</mi><mi>i</mi><mi>m</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274411&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274410&type= 15.40933418 4.99533367 为目标卫星传感器的TOA反射率， <math id="M124"><msubsup><mrow><mi>ρ</mi></mrow><mrow><mi>T</mi><mi>O</mi><mi>A</mi><mo>,</mo><mi>M</mi><mi>O</mi><mi>D</mi><mi>I</mi><mi>S</mi></mrow><mrow><mi>s</mi><mi>i</mi><mi>m</mi></mrow></msubsup><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274413&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274412&type= 16.59466553 4.99533367 为MODIS传感器第 <math id="M125"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274415&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274414&type= 1.10066664 2.62466669 波段的TOA反射率模拟值； <math id="M126"><mi>S</mi><mi>B</mi><mi>A</mi><mi>F</mi><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274425&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274424&type= 12.78466606 3.47133350 为目标卫星传感器与MODIS传感器间相似波段的光谱匹配因子（Spectral Band Adjustment Factor，SBAF），其表达式如 式（7） 式（7） 所示。 式（7） 式（7） 中， <math id="M127"><mi>ρ</mi><mo stretchy="false">(</mo><mi>λ</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274419&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274418&type= 6.94266701 3.55599999 是基于MODTRAN模型模拟的光谱式TOA反射率，覆盖300至2500nm范围； <math id="M128"><msub><mrow><mi mathvariant="normal">Γ</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>n</mi><mi>s</mi><mi>o</mi><mi>r</mi><mo>,</mo><mi>i</mi></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=25274421&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274420&type= 14.13933277 4.57200003 和 <math id="M129"><msub><mrow><mi mathvariant="normal">Γ</mi></mrow><mrow><mi>M</mi><mi>O</mi><mi>D</mi><mi>I</mi><mi>S</mi><mo>,</mo><mi>i</mi></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=25274423&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274422&type= 15.32466698 4.57200003 分别是目标卫星传感器及MODIS传感器的光谱响应函数（Spectral Response Function，SRF）。受格尔木沙地稳定目标实验区的大气季节性变化影响，不同载荷间的 <math id="M130"><mi>S</mi><mi>B</mi><mi>A</mi><mi>F</mi><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274425&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274424&type= 12.78466606 3.47133350 在每次观测时都不同。 4.2.2　验证结果 3 2018年1月~2021年8月Sentinel-2A/B卫星过境格尔木的晴空影像共79景，过境时1.21° <math id="M131"><mo><</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo><</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274427&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274426&type= 8.89000034 3.80999994 1.28°、42° <math id="M132"><mo><</mo><msub><mrow><mi>φ</mi></mrow><mrow><mi>v</mi></mrow></msub><mo><</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274429&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274428&type= 9.39799976 4.40266657 49°、19° <math id="M133"><mo><</mo><msub><mrow><mi>θ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo><</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274431&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274430&type= 8.80533314 3.80999994 60°、123° <math id="M134"><mo><</mo><msub><mrow><mi>φ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo><</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274433&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274432&type= 9.31333351 4.40266657 166°，其中30景（Sentinel-2A 15景，Sentinel-2B 15景）符合3.4节定义的观测几何及大气参数约束条件。比较格尔木沙地稳定目标模型计算的TOA反射率（B8A波段）与Sentinel-2A/B MSI卫星观测TOA反射率，如 图16 图16 所示。该波段模型模拟TOA反射率与卫星观测TOA反射率间的相对差异如 图17 图17 所示，在 <math id="M135"><mo>±</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274443&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274442&type= 1.77800000 2.62466669 2%以内，其平均相对误差为-0.38%，RMSE约0.0039，在Sentinel-2A/B MSI传感器3%的定标不确定度范围内。同时由于地表/大气的季节性变化，相对误差存在1.22%的随机变化。 图 18 18 、 19 19 展示了本文TOA反射率模型应用于Landsat-8/OLI传感器B5波段的结果，通过分析可知，相对误差基本在 <math id="M136"><mo>±</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274443&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=25274442&type= 1.77800000 2.62466669 2%以内，模型计算值与卫星观测值间的RMSE为0.0047，平均相对误差为0.71%，相对误差的标准差为1.35%，表明模型计算值与Landsat-8/OLI传感器观测值具有较好的一致性。 本文提出的TOA反射率模型计算的TOA反射率与卫星观测TOA反射率间的相对差异见 表3 表3 。从表中可知，Sentinel-2B/MSI传感器在B3、B4、B8A波段的观测TOA反射率与模拟TOA反射率的平均相对误差分别为：-0.41%、-0.04%、-0.38%，RMSE在0.0039以内，相对误差的标准差不超过1.42%。Landsat-8/OLI传感器在B3、B4、B5波段的观测TOA反射率与模拟TOA反射率的平均相对误差分别为：1.77%、0.21%、0.71%，RMSE在0.0055以内，相对误差的标准差不超过1.72%。由于MSI、OLI与MODIS传感器在短波红外波段显著的光谱响应函数差异，导致TOA反射率模型在Sentinel2A/B MSI、Landsat-8/OLI传感器B12、B7波段的模拟TOA反射率与观测TOA反射率的RMSE最高，分别为0.0080、0.0086。对于蓝色波段，2个传感器的模拟TOA反射率与观测TOA反射率的平均相对差异分别为1.44%、1.50%。 2 波段 4 Sentinel-2B/MSI 4 Landsat-8/OLI 通道 相对误差的均值 相对误差的标准差 均方根误差 通道 相对误差的均值 相对误差的标准差 均方根误差 Blue B2 1.44% 1.59% 0.0040 B2 1.50% 2.11% 0.0049 Green B3 -0.41% 1.42% 0.0031 B3 1.77% 1.72% 0.0055 Red B4 -0.04% 1.24% 0.0034 B4 0.21% 1.69% 0.0046 NIR B8A -0.38% 1.22% 0.0039 B5 0.71% 1.35% 0.0047 SWIR B12 1.43% 1.44% 0.0080 B7 1.72% 1.44% 0.0086 5　结 论 1 针对国产卫星高精度、高频次在轨辐射定标需求，本文提出了一种综合考虑“太阳-目标-传感器”观测几何及场地地表/大气季节性变化的稳定目标TOA反射率模型构建方法。以格尔木沙地稳定目标为例，结合Aqua/MODIS数据和ECMWF的大气参数产品，建立了陆表稳定目标TOA反射率模型，并以具有高定标精度的Sentinel2A/B MSI和Landsat-8/OLI传感器为参考，对其太阳反射率波段进行了绝对辐射定标验证。研究结果表明：以格尔木沙地为例建立的陆表稳定目标TOA反射率模型较为稳定，充分考虑了我国本土陆表稳定目标的季节性特征，能够提供晴空条件下、满足观测几何及大气参数约束条件的光学卫星传感器不同通道的TOA反射率参考。其中，模拟的参考TOA反射率与Sentinel2A/B MSI观测值的平均相对误差优于1.44%，RMSE在0.0080以内，相对误差的标准差不超过1.59%；与Landsat-8/OLI观测值的平均相对误差优于1.77%，RMSE在0.0086以内，相对误差的标准差不超过2.11%。 本文提出的陆表稳定目标TOA反射率模型可用于卫星传感器场地绝对辐射定标的同时，还可用于基于高精度卫星载荷的交叉辐射定标，这两种定标方法无需任何同步测量，对国产陆地卫星载荷的高精度、高频次辐射定标具有重要意义。在下一步工作中，本研究将继续解决以下问题：（1）分析TOA反射率模型的不确定度以及基于TOA反射率模型的绝对辐射定标和交叉定标的不确定度。（2）将模型推广至我国其他陆表稳定目标。 参考文献（References） Bacour C , Briottet X , Bréon F M , Françoise V R and Bouvet M . 2019 . Revisiting Pseudo Invariant Calibration Sites (PICS) Over Sand Deserts for Vicarious Calibration of Optical Imagers at 20 km and 100 km Scales . Remote Sensing , 11 ( 10 ): 1166 - 1192 [ DOI: 10.3390/rs11101166 http://dx.doi.org/10.3390/rs11101166 ] Revisiting Pseudo Invariant Calibration Sites (PICS) Over Sand Deserts for Vicarious Calibration of Optical Imagers at 20 km and 100 km Scales Chander G , Xiong X X , Choi T and Angal A . 2010 . Monitoring on-orbit calibration stability of the Terra MODIS and Landsat 7 ETM+ sensors using pseudo-invariant test sites . Remote Sensing of Environment , 114 : 925 - 939 [ DOI: 10.1016/j.rse.2009.12.003 http://dx.doi.org/10.1016/j.rse.2009.12.003 ] Monitoring on-orbit calibration stability of the Terra MODIS and Landsat 7 ETM+ sensors using pseudo-invariant test sites Helder D , Thome K J , Mishra N , Chander G , Xiong X X , Angal A and Choi T . 2013 . Absolute Radiometric Calibration of Landsat Using a Pseudo Invariant Calibration Site . IEEE Transactions on Geoscience and Remote Sensing , 51 ( 3 ): 1360 - 1369 [ DOI: 10.1109/TGRS.2013.2243738 http://dx.doi.org/10.1109/TGRS.2013.2243738 ] Absolute Radiometric Calibration of Landsat Using a Pseudo Invariant Calibration Site He L L . 2020 . Selection, evaluation and radiometric calibration application of pseudo-invariant calibration sites(PICS) in northwest China . Beijing : Chinese Academy of Meteorological Sciences : 14 - 18 . (何灵莉 , 2020. 我国西北准不变定标场(PICS)的选取评价和辐射定标应用. 北京: 中国气象科学研究院: 14-18.) [ DOI: 10.27631/d.cnki.gzqky.2020.000014 http://dx.doi.org/10.27631/d.cnki.gzqky.2020.000014 ] Selection, evaluation and radiometric calibration application of pseudo-invariant calibration sites(PICS) in northwest China Kim W , Cao C Y and Liang S L . 2014 . Assessment of Radiometric Degradation of FY-3A MERSI Reflective Solar Bands Using TOA Reflectance of Pseudoinvariant Calibration Sites . IEEE Geoscience and Remote Sensing Letters , 11 ( 4 ): 793 - 797 [ DOI: 10.1109/LGRS.2013.2279134 http://dx.doi.org/10.1109/LGRS.2013.2279134 ] Assessment of Radiometric Degradation of FY-3A MERSI Reflective Solar Bands Using TOA Reflectance of Pseudoinvariant Calibration Sites Lachérade S , Fougnie B , Henry P , and Gamet P . 2013 . Cross Calibration Over Desert Sites: Description, Methodology, and Operational Implementation . IEEE Transactions on Geoscience and Remote Sensing , 51 : 1098 - 1113 [ DOI: 10.1109/TGRS.2012.2227061 http://dx.doi.org/10.1109/TGRS.2012.2227061 ] Cross Calibration Over Desert Sites: Description, Methodology, and Operational Implementation Liu Q Y , Yu T and Gao H L . 2019 . Radiometric Cross-Calibration of GF-1 PMS Sensor with a New BRDF Model . Remote Sensing , 11 ( 6 ): 707 - 728 [ DOI: 10.3390/rs11060707 http://dx.doi.org/10.3390/rs11060707 ] Radiometric Cross-Calibration of GF-1 PMS Sensor with a New BRDF Model Liou K N . 2002 . An Introduction to Atmospheric Radiation . California : An imprint of Elsevier Science : 106 - 108 . An Introduction to Atmospheric Radiation Mishra N , Helder D , Angal A , Choi J and Xiong X X . 2014 . Absolute Calibration of Optical Satellite Sensors Using Libya 4 Pseudo Invariant Calibration Site . Remote Sensing , 6 ( 2 ): 1327 - 1346 [ DOI: 10.3390/rs6021327 http://dx.doi.org/10.3390/rs6021327 ] Absolute Calibration of Optical Satellite Sensors Using Libya 4 Pseudo Invariant Calibration Site Neigh C , McCorkel J , Campbell P , Ong L , Ly V , Landis D and Middleton E . 2016 . Monitoring Orbital Precession of EO-1 Hyperion With Three Atmospheric Correction Models in the Libya-4 PICS . IEEE Geoscience and Remote Sensing Letters , 13 ( 12 ): 1797 - 1801 [ DOI: 10.1109/LGRS.2016.2612539 http://dx.doi.org/10.1109/LGRS.2016.2612539 ] Monitoring Orbital Precession of EO-1 Hyperion With Three Atmospheric Correction Models in the Libya-4 PICS Raut B , Kaemanee M , Angal A , Xiong X X and Helder D . 2019 . Empirical Absolute Calibration Model for Multiple Pseudo-Invariant Calibration Sites . Remote Sensing , 11 ( 9 ): 1105 - 1126 [ DOI: 10.3390/rs11091105 http://dx.doi.org/10.3390/rs11091105 ] Empirical Absolute Calibration Model for Multiple Pseudo-Invariant Calibration Sites Wang S S , Xiang J M , Zhu S Y and Chen B Y . 2020 . Cross Radiation Calibration for Blue Channel of FY4A AGRI Sensor by Using MODIS Data . Remote Sensing Information , 35 ( 6 ): 115 - 121 Cross Radiation Calibration for Blue Channel of FY4A AGRI Sensor by Using MODIS Data 王诗圣 , 向嘉敏 , 祝善友 , 陈博洋 . 2020 . 利用MODIS数据对FY4A AGRI传感器蓝光通道交叉辐射定标 . 遥感信息 , 35 ( 6 ): 115 - 121 [ DOI: 10.3969/j.issn.1000-3177.2020.06.017 http://dx.doi.org/10.3969/j.issn.1000-3177.2020.06.017 ] 利用MODIS数据对FY4A AGRI传感器蓝光通道交叉辐射定标 Wang L , Hu X Q and Chen L . 2017 . Assessment of BRDF effect of Kunlun Mountain glacier on Tibetan Plateau as a potential pseudo-invariant calibration site // Sensors, Systems, and Next-generation Satellites [ DOI: 10.1117/12.2278203 http://dx.doi.org/10.1117/12.2278203 ] Assessment of BRDF effect of Kunlun Mountain glacier on Tibetan Plateau as a potential pseudo-invariant calibration site Yu S S , Rosenberg R , Bruegge C , Chapsky L , Fu D , Lee R and Taylor T . 2020 . Stability Assessment of OCO-2 Radiometric Calibration Using Aqua MODIS as a Reference . Remote Sensing , 12 ( 8 ): 1269 - 1286 [ DOI: 10.3390/rs12081269 http://dx.doi.org/10.3390/rs12081269 ] Stability Assessment of OCO-2 Radiometric Calibration Using Aqua MODIS as a Reference Yan G J , Jiang H L , Yan K , Cheng S Y , Song W J , Tong Y Y , Liu Y N , Qi J B , Mu X H , Zhang W M , Xie D H and Zhou H M . 2021 . Review of optical multi-angle quantitative remote sensing . National Remote Sensing Bulletin , 25 ( 1 ): 83 - 108 Review of optical multi-angle quantitative remote sensing 阎广建 , 姜海兰 , 闫凯 , 程诗宇 , 宋婉娟 , 童依依 , 刘雅楠 , 漆建波 , 穆西晗 , 张吴明 , 谢东辉 , 周红敏 . 2021 . 多角度光学定量遥感 . 遥感学报 , 25 ( 1 ): 83 - 108 [ DOI: 10.11834/jrs.20218355 http://dx.doi.org/10.11834/jrs.20218355 ］ 多角度光学定量遥感 Zhao C Y , Zhang Y N , Wei W , Zhang M , Chen L , Zhang L , Li X and Zheng X B . 2019 . Absolute Radiometric Calibration Method Based on Surface Hyperspectral BRDF Model . Acta Photonica Sinica , 48 ( 5 ): 1 - 10 Absolute Radiometric Calibration Method Based on Surface Hyperspectral BRDF Model 赵春艳 , 张艳娜 , 韦玮 , 张孟 , 陈林 , 张璐 , 李新 , 郑小兵 . 2019 . 基于场地高光谱BRDF模型的绝对辐射定标方法 . 光子学报 , 48 ( 5 ): 1 - 10 [ DOI: 10.3788/gzxb20194805. 0528001 http://dx.doi.org/10.3788/gzxb20194805.0528001 ] 基于场地高光谱BRDF模型的绝对辐射定标方法 Zhou Q , Tian L Q , Li J and Li Wen Kai . 2020 . Assesment of bidirectional reflectance effects on desert and forest for radiometetric cross-calibration of satellite sensors . ISPRS Journal of Photogrammetry and Remote Sensing , 160 : 180 - 194 [ DOI: 10.1016/j.isprsjprs.2019.12.007 http://dx.doi.org/10.1016/j.isprsjprs.2019.12.007 ] Assesment of bidirectional reflectance effects on desert and forest for radiometetric cross-calibration of satellite sensors 致谢:文中使用的MODIS、Sentinel及Landsat-8数据分别来源于NASA的LAADS DAAC网站、ESA网站、USGS数据分发网站，文中使用的ECMWF再分析数据来源于Atmosphere Data Store网站及Climate Data Store网站，在此表示感谢！ 10.11834/jrs.20221655 TP79 A 宋培兰，马灵玲，赵永光，王宁，李婉，韩启金，刘耀开，姚微源，张贝贝，任璐，牛沂芳.XXXX.我国陆表稳定目标TOA反射率模型构建方法及验证 ——以格尔木沙地场景为例.遥感学报，XX（XX）： 1-16 宋培兰，马灵玲，赵永光，王宁，李婉，韩启金，刘耀开，姚微源，张贝贝，任璐，牛沂芳.XXXX.我国陆表稳定目标TOA反射率模型构建方法及验证 ——以格尔木沙地场景为例.遥感学报，XX（XX）： 1-16 Song Peilan，Ma Lingling，Zhao Yongguang，Wang Ning，Li Wan，Han Qijin，Liu Yaokai，Yao Weiyuan，Zhang Beibei，Ren Lu，Niu Yifang. XXXX. Construction and validation of TOA reflectance reference model for stable land surface target- using Golmud desert site as an example. National Remote Sensing Bulletin， XX（XX）：1-16 Song Peilan，Ma Lingling，Zhao Yongguang，Wang Ning，Li Wan，Han Qijin，Liu Yaokai，Yao Weiyuan，Zhang Beibei，Ren Lu，Niu Yifang. XXXX. Construction and validation of TOA reflectance reference model for stable land surface target- using Golmud desert site as an example. National Remote Sensing Bulletin， XX（XX）：1-16 国家重点研发计划（编号：2018YFB0504800， 2018YFB0504801）、中欧龙计划五期项目（编号：ID.59166）、中科院空天院重点部署项目（编号：E0Z206010F、E0Z206030F） Supported by Supported by National Key R&D Program of China (NO.2018YFB0504800, NO.2018YFB0504801), Dragon 5 ESA-MOST Cooperation Programme (NO.ID.59166), Innovation Program of Aerospace Information Research Institute (AIR), Chinese Academy of Science (CAS) (NO.E0Z206010F、NO.E0Z206030F). 2021-09-30 2022-03-22 遥感学报