融合物理机理与随机森林算法的FY-4A AGRI数据晴空大气可降水量遥感反演

融合物理机理与随机森林算法的FY-4A AGRI数据晴空大气可降水量遥感反演 Remote sensing retrieval of total precipitable water under clear-sky atmosphere from FY-4A AGRI data by combining physical mechanism and random forest algorithm 1 3 first-author 张环宇，1999年生，男，博士研究生，研究方向为热红外遥感定量反演。E-mail：2017301610128@whu.edu.cn 张环宇，1999年生，男，博士研究生，研究方向为热红外遥感定量反演。E-mail：2017301610128@whu.edu.cn 2017301610128@whu.edu.cn 2 3 corresp 唐伯惠，1973年生，男，教授，研究方向为热红外遥感定量反演。E-mail：tangbh@kust.edu.cn 唐伯惠，1973年生，男，教授，研究方向为热红外遥感定量反演。E-mail：tangbh@kust.edu.cn tangbh@kust.edu.cn 武汉大学 测绘学院, 武汉 430072 武汉大学 测绘学院, 武汉 430072 School of Geodesy and Geomatics, Wuhan University, Wuhan 430072, China School of Geodesy and Geomatics, Wuhan University, Wuhan 430072, China 昆明理工大学 国土资源工程学院, 昆明 650093 昆明理工大学 国土资源工程学院, 昆明 650093 Faculty of Land Resource Engineering, Kunming University of Science and Technology, Kunming 650093, China Faculty of Land Resource Engineering, Kunming University of Science and Technology, Kunming 650093, China 中国科学院地理科学与资源研究所 资源与环境信息系统国家重点实验室, 北京 100101 中国科学院地理科学与资源研究所 资源与环境信息系统国家重点实验室, 北京 100101 State Key Laboratory of Resources and Environment Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China State Key Laboratory of Resources and Environment Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China 作为中国发射的风云四号系列首颗卫星，FY-4A搭载了先进的静止轨道辐射成像仪AGRI。本文利用AGRI传感器的中红外到热红外波段观测数据、ERA5水汽再分析产品以及全球无线电探空数据集IGRA等数据进行晴空大气可降水量反演研究。在海洋表面，分别利用回归分析法与随机森林算法反演大气可降水量，反演结果与ERA5水汽产品相比，均方根误差为0.493 cm和0.247 cm。在陆地表面，利用随机森林模型反演大气可降水量，反演结果与ERA5水汽产品相比，均方根误差为0.155 cm；与IGRA水汽产品相比，均方根误差为0.215 cm。结果表明本文使用的随机森林算法可以有效地提升热红外遥感数据反演大气可降水量的精度。 Atmospheric water vapour, an important component of global greenhouse gases, is one of the key factors influencing global climate change, hydrologic cycle, matter-energy exchange and so on. The total water vapour content in the atmosphere is usually quantified with the parameter of Total Precipitable Water (TPW). As the first launched satellite of Chinese Fengyun-4 series, FY-4A satellite has been equipped with the Advanced Geosynchronous Radiation Imager (AGRI). This paper aims to retrieve the TPW under the clear-sky atmosphere with the combination of the middle- and thermal-infrared remote sensing observations of AGRI, ERA5 total column water vapour reanalysis product and Integrated Global Radiosonde Archive (IGRA). On the ocean surface, the regression analysis method and random forest algorithm have been introduced to retrieve the TPW successively. In random forest modeling, the standard deviation of every regression tree’s output value is used as quality control criterion, and the retrieval results are considered as reliable only when the standard deviation is less than 0.4 cm. On the land surface, the Split-Window Covariance-Variance Ratio (SWCVR) method and random forest algorithm have been developed to retrieve the TPW, and the elevation and Normalized Difference Vegetation Index (NDVI) estimated at the top of atmosphere have been added to the random forest model in order to reflect the information of land surface. In terms of TPW retrieval over ocean, the determination coefficient is 0.817, the Root Mean Square Error (RMSE) is 0.493 cm, and the Mean Absolute Error (MAE) of the retrieval results is 0.393 cm compared with the ERA5 total column water vapour product when using the regression analysis method. For the random forest model, the quality control passing rate of retrieval results accounts for 84.0%, the determination coefficient is 0.956, RMSE is 0.247 cm, and MAE is 0.183 cm when compared with the ERA5 total column water vapour product. In terms of TPW retrieval over land, for the reason that the spatial resolution of AGRI is only 4 km, the SWCVR method is unable to retrieve the TPW accurately using the observations of AGRI. For the random forest model, the passing rate of retrieval results accounts for 93.2%, the determination coefficient is 0.972, RMSE is 0.155 cm, and MAE is 0.106 cm when compared with the ERA5 total column water vapour product. In the end, the radio-sounding water vapour is introduced to evaluate the accuracy of the random forest model, and the passing rate of retrieval results accounts for 75.6%, the determination coefficient is 0.946, RMSE is 0.215 cm, and MAE is 0.163 cm. First of all, TPW over ocean can be retrieved with the middle- and thermal-infrared remote sensing observations of AGRI by using the regression analysis method and random forest algorithm, and the retrieval accuracy of random forest model is obviously higher. Besides, the SWCVR method is unable to retrieve the TPW over land accurately due to the low spatial resolution of AGRI, meanwhile the random forest algorithm performs well. The results indicate that the random forest algorithm can effectively improve the TPW retrieval accuracy with thermal infrared remote sensing observations. FY-4A AGRI 热红外遥感 大气可降水量 回归分析 随机森林 FY-4A AGRI thermal infrared remote sensing Total Precipitable Water (TPW) regression analysis random forest 1　引言 1 大气水汽是地球温室气体的重要成分之一，是全球气候变化、水循环、物质能量交换等过程中的关键参数（ Li等，2003 Li等，2003 ）。大气可降水量TPW（Total Precipitable Water）表征从地表到大气层顶水汽含量的垂直积分，反映大气中水汽的总含量，其单位在本文中统一取为cm。TPW的精确反演对于地表温度反演、大气校正等研究具有重要影响。 目前TPW的测量方法主要包括无线电探空法、地基探测法与卫星遥感反演法等。无线电探空法一般只在每日UTC 0 h与12 h进行探测，探空站的分布较为稀疏并且在海洋上几乎无覆盖；地基探测法主要包括地基GPS、地基微波辐射计与地基太阳辐射计探测等，反演精度与时间分辨率较高，但同样存在观测站分布稀疏以及海上几乎无覆盖等缺点。相较而言，利用卫星遥感观测数据能够以较低的成本和较高的时空分辨率在大尺度空间范围内反演出TPW，所以开展有关于卫星遥感反演TPW方面的研究具有必要性和实际意义。 根据波段的不同，遥感反演法可分为近红外反演法、热红外反演法和微波遥感反演法。近红外方法根据940 nm及其附近波段水汽吸收能力的差异来反演TPW，精度较高但仅可在白天使用。微波波段能够穿透云雾，可以全天候使用。其基本原理是从微波辐射信息中提取出大气信息（ 吴琼 等，2020 吴琼 等，2020 ）。由于在微波波段海表的比辐射率低于陆表，所以更容易区分出大气信息和表面辐射信息，故微波波段一般只用于探测海洋上空的TPW。热红外反演法可全天时地探测陆地与海洋区域的TPW。但是热红外波段无法穿透云层，故只能反演晴空TPW。此外，热红外波段观测数据的空间分辨率较低（尤其是静止轨道卫星传感器），反演TPW的精度也普遍偏低。 作为中国新一代静止轨道气象卫星——风云四号系列星座的首颗发射卫星，FY-4A搭载了先进的静止轨道辐射成像仪AGRI（Advanced Geosynchronous Radiation Imager），拥有14个辐射成像波段，覆盖可见光、短波红外、中波红外和长波红外等波段（ Yang等，2017 Yang等，2017 ）。AGRI传感器能够在短时间内对同一区域进行连续观测，故利用AGRI传感器的观测数据反演TPW对于天气预报和气象灾害监测等具有积极意义。 国内外目前已经开展了许多有关利用热红外遥感数据反演TPW方面的研究，反演方法大致可以归纳为回归分析法、劈窗算法、物理迭代回归法以及机器学习算法等。 回归分析法的基本思想是建立TPW与中红外和热红外多个波段观测亮温之间的数学关系，常用于反演海洋上空的TPW（ Dalu，1986 Dalu，1986 ；ECK等，1994； 朱元竞 等，1998 朱元竞 等，1998 ； 李万彪 等，1998 李万彪 等，1998 ； Shi等，2020 Shi等，2020 ）。由于陆表构成较为复杂，不同类型地物的比辐射率差异较大，导致回归分析得到的系数各异，所以针对陆表难以建立一个统一的数学表达式（ECK等，1994）。此外，先前学者的研究普遍存在样本数目偏少、研究区域较小等不足。 劈窗算法的基本思想是基于大气水汽对热红外分裂窗两波段吸收作用的差异，通过两波段的观测亮温估算出两波段大气透过率比值，再建立TPW与两波段大气透过率比值之间的数学关系（ Kleespies等，1990 Kleespies等，1990 ； Jedlovec，1990 Jedlovec，1990 ； Sobrino等，1994 Sobrino等，1994 ； Li等，2003 Li等，2003 ； Ren等，2015 Ren等，2015 ）。由于海面观测亮温变化幅度较小，所以劈窗方差、劈窗协方差—方差等算法一般只适用于陆地上空TPW的反演。此外，劈窗算法一般需要根据多个临近像元的观测数据估算出大气透过率比值，会进一步降低空间分辨率。 物理迭代回归是热红外遥感水汽反演业务产品常用的算法，通过物理迭代算法计算出大气廓线，进而积分获取TPW。该算法较为依赖初始的温湿廓线，并且当地表温度接近边界温度时反演结果的误差较大（ 林奕桐 等，2018 林奕桐 等，2018 ）。有关学者的验证表明，美国航空航天局NASA（National Aeronautics and Space Administration）发布的利用热红外波段数据反演的MOD05L2水汽产品的均方根误差RMSE（Root Mean Square Error）在0.4 cm—0.6 cm（ 林奕桐 等，2018 林奕桐 等，2018 ）。 机器学习算法包括神经网络、随机森林、极端梯度提升等算法，一般能够拟合复杂的非线性系统，反演精度较高，但目前在热红外遥感水汽反演方面的研究与应用还比较少。 Zhang等（2012） Zhang等（2012） 根据Aqua卫星AIRS传感器热红外41个波段的观测数据训练径向基神经网络，反演结果的RMSE为0.11 cm。 Lee等（2019） Lee等（2019） 采用随机森林模型、极端梯度提升模型和深度神经网络3种机器学习算法，根据Himawari-8卫星AHI传感器中红外与热红外波段观测亮温等数据训练水汽反演模型。3种模型反演的结果与探空数据相比，RMSE分别为0.607 cm、0.543 cm和0.503 cm。 本文根据AGRI传感器的观测数据、ERA5水汽再分析产品以及IGRA探空水汽值等数据构建数据集，利用回归分析与随机森林两种方法反演晴空海洋上空TPW；利用SWCVR算法和随机森林算法反演晴空陆地上空TPW。 2　数据集构建 1 2.1　数据准备 2 从风云卫星遥感数据服务网下载2020年62景海面上云覆盖较少与61景陆地上云覆盖较少的AGRI成像仪全圆盘4KM L1数据以及对应的云检测产品（每月选取的图像数目大致相等，成像时间均为UTC 0 h或12 h）。数据下载网址为 http：//satellite.nsmc.org.cn/PortalSite/Data/Satellite.aspx http://satellite.nsmc.org.cn/PortalSite/Data/Satellite.aspx ［2021-04-15］。 本文选取云覆盖天数较少的中国南海（12°—21°N，113°—118°E）、孟加拉湾（8°—17.5°N，84°—91°E）、菲律宾海（5°—25°N，130°—150°E）、东印度洋（15°—30°S，90°—105°E）以及中国内陆（24°—40°N，100°—117°E）与澳大利亚内陆（17°—30°N，125°—145°E）作为研究区域。 首先利用定标表对全圆盘4KM L1数据进行辐射定标。然后根据风云卫星遥感数据服务网上发布的“FY-4A数据行列号和经纬度的互相转换方法”文件中所述方法完成几何校正。 由于AGRI传感器没有覆盖940 nm附近的近红外水汽吸收波段，故本文利用中红外与热红外波段数据反演TPW。 表1 表1 列出了AGRI传感器从中红外到热红外波段的参数信息。 注： 空间分辨率均为4 km。 波段号 中心波长/ <math id="M1"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639299&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639298&type= 3.97933316 2.62466669 波段宽度/ <math id="M2"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639299&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639298&type= 3.97933316 2.62466669 9 6.25 0.9 10 7.1 0.4 11 8.5 1.0 12 10.7 0.8 13 12.0 1.0 14 13.5 0.6 由于探空站分布较为稀疏并且可用的探空数据量较少，所以本文尝试利用水汽产品作为水汽标准值进行晴空TPW反演模型的训练与测试。 ERA5是由欧洲中期天气预报中心ECMWF（European Centre for Medium-Range Weather Forecasts）发布的第5代全球气候再分析数据，包含大量的大气、海浪、地表参数等（ Hoffmann等，2019 Hoffmann等，2019 ）。 本文选取2020年的ERA5 Total columnwater vapour产品（全球覆盖0.25°×0.25°网格，UTC 0 h和12 h）进行分析。有关数据的下载网址为 https：//cds.climate.copernicus.eu/cdsapp# https://cds.climate.copernicus.eu/cdsapp# ！/dataset/reanalysis-era5-single-levels［2021-04-15］。 同时下载由美国国家环境信息中心NCEI（National Centers for Environmental Information）发布的全球无线电探空数据集IGRA（Integrated Global Radiosonde Archive V2），用以验证ERA5水汽再分析产品的精度。该套探空数据集包含全球范围内超过2700个探空站的观测数据，一般在每日的UTC 0：00与12：00各探测一次，是目前数据质量最高、使用最广泛的探空数据集之一（ 吴琼 等，2020 吴琼 等，2020 ）。 本文下载位于亚洲、大洋洲内陆、海岸以及海岛上的45个探空站在2020年每月第1日和第15日UTC 0：00与12：00的探空观测数据，相关数据的下载网址为 https：//www. https://www. ‍ncdc.‍noaa.‍gov/data-access/weather-balloon/integrated-global-radiosonde-archive［2021-04-15］。 2.2　ERA5水汽再分析产品精度验证 2 首先针对探空数据进行质量检验。由于大气水汽一般集中于从地面到300 hPa高度范围内，如果探空数据的有效观测高度未达到300 hPa或有效观测层数小于10层，则剔除该次观测数据。在剔除质量不合格的探空数据后，利用分层气象元素计算出TPW。 TPW的积分定义式如下： <math display="block" id="M3"><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi><mi mathvariant="normal">W</mi><mo>=</mo><mfrac><mrow><mn 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http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639625&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639621&type= 1.69333339 3.47133350 为比湿； <math id="M7"><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639611&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639610&type= 2.28600001 2.62466669 为气压， <math id="M8"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639351&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639347&type= 3.47133350 3.72533321 为地面处气压。 由于实际的探空数据均是离散分层观测，所以需要通过数值积分计算出对应的TPW为 <math display="block" id="M9"><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi><mi mathvariant="normal">W</mi><mo>=</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">2</mn><mi>ρ</mi><mi>g</mi></mrow></mfrac><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>k</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>n</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></munderover></mstyle><mrow><mfenced separators="|"><mrow><msub><mrow><mi>q</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>+</mo><msub><mrow><mi>q</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfenced><mfenced separators="|"><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>-</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfenced></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639357&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639353&type= 57.40399933 8.55133343 式中， <math id="M10"><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi><mi mathvariant="normal">W</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639365&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639360&type= 7.45066643 2.70933342 的单位为 <math id="M11"><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639372&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639368&type= 4.31799984 2.70933342 ；水密度 <math id="M12"><mi>ρ</mi><mo>=</mo><mn mathvariant="normal">1</mn><mtext> </mtext><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">c</mi><msup><mrow><mi mathvariant="normal">m</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639382&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639376&type= 16.42533302 3.72533321 ；重力加速度 <math id="M13"><mi>g</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639386&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639384&type= 1.86266661 3.47133350 取980 cm/s 2 ； <math id="M14"><mi>n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639397&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639394&type= 1.86266661 2.62466669 代表从地面到大气层顶分层观测的层数； <math id="M15"><mi>k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640163&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640162&type= 1.69333339 2.62466669 为层序； <math id="M16"><msub><mrow><mi>q</mi></mrow><mrow><mi>k</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639651&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639648&type= 2.70933342 4.57200003 为第 <math id="M17"><mi>k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640163&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640162&type= 1.69333339 2.62466669 层的比湿，单位为 <math id="M18"><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">k</mi><mi mathvariant="normal">g</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639632&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639629&type= 6.18066692 3.47133350 ； <math id="M19"><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639434&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639431&type= 3.38666677 3.72533321 为第 <math id="M20"><mi>k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640163&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640162&type= 1.69333339 2.62466669 层的气压，单位为 <math id="M21"><mi mathvariant="normal">h</mi><mi mathvariant="normal">P</mi><mi mathvariant="normal">a</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639449&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639444&type= 5.58799982 2.70933342 。 IGRA探测数据包含气压 <math id="M22"><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639611&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639610&type= 2.28600001 2.62466669 （单位：hPa）、气温 <math id="M23"><mi>T</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639462&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639460&type= 2.11666679 2.62466669 （单位：℃）、温度露点差 <math id="M24"><mi>D</mi><mi>P</mi><mi>D</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639472&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639467&type= 9.48266602 2.62466669 （单位：℃）等分层气象要素。首先根据温度露点差计算出露点温度 <math id="M25"><msub><mrow><mi>T</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>=</mo><mi>T</mi><mo>-</mo><mi>D</mi><mi>P</mi><mi>D</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639484&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639478&type= 24.21466637 3.72533321 ，再利用 式（3） 式（3） 计算出各观测层对应的水汽压 e w （单位：hPa）为 <math display="block" id="M26"><msub><mrow><mi>e</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">6.1078</mn><mo>·</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mfrac><mrow><mi>a</mi><mo>·</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow><mrow><mi>b</mi><mo>+</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></mfrac></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639492&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639488&type= 26.67000008 7.70466709 式中，等式右侧的 <math id="M27"><mi mathvariant="normal">e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639506&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639501&type= 1.69333339 2.70933342 为自然指数；系数 <math id="M28"><mi>a</mi><mi>、</mi><mi>b</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639608&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639606&type= 5.33400011 2.87866688 由气温决定：若 <math id="M29"><mi>T</mi><mo>></mo><mn mathvariant="normal">0</mn><mo>℃</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639533&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639528&type= 11.93799973 2.79399991 ， <math id="M30"><mi>a</mi><mo>=</mo><mn mathvariant="normal">17.26</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639548&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639543&type= 14.64733315 2.70933342 ， <math id="M31"><mi>b</mi><mo>=</mo><mn mathvariant="normal">237.29</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639558&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639554&type= 16.17133331 2.70933342 ；若 <math id="M32"><mi>T</mi><mo><</mo><mo>-</mo><mn mathvariant="normal">40</mn><mo>℃</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639579&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639573&type= 15.83266735 2.79399991 ， <math id="M33"><mi>a</mi><mo>=</mo><mn mathvariant="normal">21.87</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639590&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639584&type= 14.64733315 2.70933342 ， <math id="M34"><mi>b</mi><mo>=</mo><mn mathvariant="normal">265.49</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639602&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639599&type= 16.17133331 2.70933342 ；否则 <math id="M35"><mi>a</mi><mi>、</mi><mi>b</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639608&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639606&type= 5.33400011 2.87866688 通过线性内插得到。 接着利用气压 <math id="M36"><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639611&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639610&type= 2.28600001 2.62466669 和水汽压 <math id="M37"><msub><mrow><mi>e</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639619&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639616&type= 2.87866688 3.72533321 计算出分层比湿 <math id="M38"><mi>q</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639625&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639621&type= 1.69333339 3.47133350 （单位： <math id="M39"><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">k</mi><mi mathvariant="normal">g</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639632&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639629&type= 6.18066692 3.47133350 ）为 <math display="block" id="M40"><mi>q</mi><mo>=</mo><mfrac><mrow><mn mathvariant="normal">622</mn><msub><mrow><mi>e</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub></mrow><mrow><mi>P</mi><mo>-</mo><mn mathvariant="normal">0.378</mn><msub><mrow><mi>e</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639644&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639636&type= 24.72266769 9.14400005 最终将分层比湿 <math id="M41"><msub><mrow><mi>q</mi></mrow><mrow><mi>k</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639651&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639648&type= 2.70933342 4.57200003 代入 式（2） 式（2） 中便可以计算出探空大气可降水量 <math id="M42"><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi><msub><mrow><mi mathvariant="normal">W</mi></mrow><mrow><mi mathvariant="normal">I</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639681&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639678&type= 12.19200039 3.80999994 。 由于绝大多数IGRA测站的坐标与ERA5格网点坐标并不重合，所以利用双线性插值计算出测站位置处对应的ERA5再分析大气可降水量 <math id="M43"><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi><msub><mrow><mi mathvariant="normal">W</mi></mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">A</mi><mn mathvariant="normal">5</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639674&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639669&type= 12.36133385 3.80999994 ，将其与 <math id="M44"><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi><msub><mrow><mi mathvariant="normal">W</mi></mrow><mrow><mi mathvariant="normal">I</mi><mi mathvariant="normal">G</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639681&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639678&type= 12.19200039 3.80999994 对比的结果如 图1 图1 所示。 二者之间的决定系数 <math id="M45"><msup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640415&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640414&type= 3.38666677 2.96333337 =0.989，均方根误差RMSE=0.193 cm，平均绝对误差MAE（Mean Absolute Error）为0.136 cm。所以ERA5水汽再分析产品在陆地与海洋区域均具有较高的精度，可以将其作为TPW的标准值进行使用。 2.3　数据集生成 2 首先计算出研究区域内的ERA5格网点对应的卫星观测天顶角，然后对AGRI观测影像与ERA5水汽产品进行时空匹配，提取出ERA5格网点在每一景AGRI影像中对应的像元观测数据以及成像时刻的水汽值。接下来利用云检测产品进行晴空条件判别，当以格网点对应像元为中心的5×5窗口内的像元全部晴空无云时，方才判断该格网点处于晴空状态。 最终生成140879个晴空海洋区域有效观测数据对和239510个陆地区域有效观测数据对（包括像元对应水汽值、像元观测亮温以及卫星观测天顶角）。以水汽间隔0.2 cm为步长对数据集进行分组，在每组内随机选取80%作为训练集，剩余的20%为测试集，以保证训练集和测试集具有相同的概率密度分布。数据集分布直方图如 图2 图2 和 图3 图3 所示。 3　海洋上空大气可降水量反演 1 3.1　回归分析法 2 Dalu（1986） Dalu（1986） 推导出海洋上空TPW与热红外分裂窗两波段观测亮温差值之间近似呈现线性关系。针对AVHRR传感器，常按照 式（5） 式（5） 的形式进行回归分析，以建立TPW与观测亮温之间的关系（ECK等，1994）： <math display="block" id="M46"><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi><mi mathvariant="normal">W</mi><mo>=</mo><mi>A</mi><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>-</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub></mrow></mfenced><mo>+</mo><mi>B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639741&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639737&type= 34.79800034 5.24933338 式中， <math id="M47"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639752&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639746&type= 3.21733332 3.72533321 和 <math id="M48"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639762&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639754&type= 3.21733332 3.72533321 分别代表AVHRR传感器第4波段（11 <math id="M49"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640251&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640249&type= 5.16466665 3.38666677 ）与第5波段（12 <math id="M50"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640251&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640249&type= 5.16466665 3.38666677 ）的观测亮温。 李万彪等（1998） 李万彪等（1998） 针对GMS-5传感器的分裂窗波段与水汽波段观测亮温，同时考虑卫星观测天顶角，提出如下的经验关系： <math display="block" id="M51"><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi><mi mathvariant="normal">W</mi><mo>=</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi mathvariant="normal">T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><msub><mrow><mi mathvariant="normal">T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfenced><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi mathvariant="normal">T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><msub><mrow><mi mathvariant="normal">T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfenced><mfenced separators="|"><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639792&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639788&type= 101.93866730 5.24933338 式中， <math id="M52"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639801&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639799&type= 3.21733332 3.72533321 — <math id="M53"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639812&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639808&type= 3.21733332 3.72533321 分别代表11 <math id="M54"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639833&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639831&type= 5.16466665 3.38666677 、12 <math id="M55"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639833&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639831&type= 5.16466665 3.38666677 以及6.85 <math id="M56"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639833&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639831&type= 5.16466665 3.38666677 波段亮温； <math id="M57"><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640059&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640058&type= 7.02733374 2.70933342 为卫星观测天顶角。 Shi等（2020） Shi等（2020） 针对FY-4A AGRI传感器观测数据，增加考虑第11波段（8.5 <math id="M58"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640251&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640249&type= 5.16466665 3.38666677 ）的观测亮温，对 式（6） 式（6） 加以改进： <math display="block" id="M59"><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi><mi mathvariant="normal">W</mi><mo>=</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi mathvariant="normal">T</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub><mo>-</mo><msub><mrow><mi mathvariant="normal">T</mi></mrow><mrow><mn mathvariant="normal">13</mn></mrow></msub></mrow></mfenced><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi mathvariant="normal">T</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub><mo>-</mo><msub><mrow><mi mathvariant="normal">T</mi></mrow><mrow><mn mathvariant="normal">13</mn></mrow></msub></mrow></mfenced><mfenced separators="|"><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">9</mn></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">11</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639856&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639854&type= 118.78733826 5.24933338 式中，观测亮温的下标数字代表AGRI传感器的波段号。 本文结合先前学者的研究工作，增加考虑AGRI传感器第10波段（7.1 <math id="M60"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640251&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640249&type= 5.16466665 3.38666677 ）和第14波段（13.5 <math id="M61"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640251&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640249&type= 5.16466665 3.38666677 ）的观测亮温对TPW反演的影响： <math display="block" id="M62"><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi><mi mathvariant="normal">W</mi><mo>=</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi mathvariant="normal">T</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub><mo>-</mo><msub><mrow><mi mathvariant="normal">T</mi></mrow><mrow><mn mathvariant="normal">13</mn></mrow></msub></mrow></mfenced><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi mathvariant="normal">T</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub><mo>-</mo><msub><mrow><mi mathvariant="normal">T</mi></mrow><mrow><mn mathvariant="normal">13</mn></mrow></msub></mrow></mfenced><mfenced separators="|"><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">9</mn></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">5</mn></mrow></msub><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">10</mn></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">6</mn></mrow></msub><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">11</mn></mrow></msub><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow></msub><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">14</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639873&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639869&type= 142.91732788 5.24933338 式中，等式右侧第2、3项表示水汽反演的主要贡献部分；第4项表示对水汽量的角度修正；第5项反映对流层高层的水汽分布；第6项反映对流层中层的水汽分布；第7项蕴含大气中灰尘、 <math id="M63"><mi mathvariant="normal">S</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639878&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639876&type= 5.50333309 3.80999994 等信息；第8项则主要反映大气温度以及 <math id="M64"><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639884&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639880&type= 5.92666674 3.80999994 含量等。 利用训练集分别对 式（5） 式（5） — 式（8） 式（8） 进行回归分析得到各项回归系数，再利用测试集测试，反演精度的对比如 表2 表2 所示。 表达式 <math id="M65"><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640272&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640270&type= 2.62466669 2.28600001 <math id="M66"><mi mathvariant="normal">R</mi><mi mathvariant="normal">M</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">E</mi><mo>/</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640277&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640274&type= 11.26066685 2.03200006 <math id="M67"><mi mathvariant="normal">M</mi><mi mathvariant="normal">A</mi><mi mathvariant="normal">E</mi><mo>/</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640280&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640278&type= 9.90600014 2.03200006 式（5） 0.782 0.538 0.425 式（6） 0.794 0.523 0.414 式（7） 0.799 0.516 0.410 式（8） 0.817 0.493 0.393 其中， 式（8） 式（8） 中系数 <math id="M68"><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>—</mo><msub><mrow><mi>a</mi></mrow><mrow><mn mathvariant="normal">7</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639924&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639920&type= 10.15999985 3.72533321 依次为-27.351、-0.095、1.340、0.264、0.022、-0.038、0.088、0.132。 在测试集上利用 式（8） 式（8） 反演的TPW与ERA5再分析水汽总量之间的对比如 图4 图4 所示。 TPW反演的残差分布如 图5 图5 所示。残差概率密度大致呈现出以0为均值的正态分布，残差平均值为-0.08 cm，大多数残差的绝对值小于0.5 cm。 3.2　随机森林法 2 随机森林算法是一种常用的集成学习算法，被广泛应用于分类与回归问题。针对回归问题，随机森林模型对输入的数据进行有放回的样本采样与特征采样进而生成多棵回归树，将所有回归树预测结果的加权平均值作为模型最终的输出，能够较好地拟合复杂非线性系统。大量的实验证明随机森林算法具有较好的抗噪声能力，不易陷入过拟合状态（ Liaw等，2002 Liaw等，2002 ； Wu等，2019 Wu等，2019 ）。由于随机森林模型具有多次建模的独立性与变量选择的随机性，所以可以对比特定自变量参与建模和未参与建模时的精度变化程度，进而反映出各个自变量在回归时的重要性分数。 对于晴空海洋上空TPW反演，本文选取AGRI传感器的中红外与热红外6个波段的观测亮温、观测天顶角正割值以及热红外分裂窗两波段观测亮温差值作为输入特征，各个参数的具体物理意义如 表3 表3 所示。 参数 物理意义 <math id="M69"><msub><mrow><mi>T</mi></mrow><mrow><mn>9</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639952&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639949&type= 2.45533323 2.87866688 对流层高层水汽含量 <math id="M70"><msub><mrow><mi>T</mi></mrow><mrow><mn>10</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639960&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639955&type= 3.21733332 2.87866688 对流层中层水汽含量 <math id="M71"><msub><mrow><mi>T</mi></mrow><mrow><mn>11</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639969&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639965&type= 3.21733332 2.87866688 大气中灰尘、 <math id="M72"><mi mathvariant="normal">S</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639978&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639974&type= 4.23333359 2.87866688 含量等 <math id="M73"><msub><mrow><mi>T</mi></mrow><mrow><mn>12</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639984&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639981&type= 3.21733332 2.87866688 大气水汽总量、表面温度等 <math id="M74"><msub><mrow><mi>T</mi></mrow><mrow><mn>13</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639991&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639987&type= 3.21733332 2.87866688 大气水汽总量、表面温度等 <math id="M75"><msub><mrow><mi>T</mi></mrow><mrow><mn>14</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639997&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19639994&type= 3.21733332 2.87866688 大气温度、 <math id="M76"><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640006&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640002&type= 4.48733330 2.87866688 含量等 <math id="M77"><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640012&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640009&type= 8.97466660 2.03200006 倾斜路径改正 <math id="M78"><msub><mrow><mi>T</mi></mrow><mrow><mn>12</mn></mrow></msub><mo>—</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>13</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640020&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640018&type= 9.48266602 2.87866688 大气水汽总量 通过试验，当回归树的数目分别设置为100、500与1000时，模型的精度变化不明显，并且当回归树的数目过大时运算耗时较大，所以最终选定100棵回归树。此外经过有关学者的验证，随机森林算法输出的结果对于参数设置不太敏感（ Wu等，2019 Wu等，2019 ），所以随机森林中其余参数均使用默认值。 利用训练集对模型进行训练后，输出模型中每个参数的重要性得分，如 图6 图6 所示。由 图6 图6 可知，参数 <math id="M79"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub><mo>—</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">13</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640317&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640315&type= 12.44600010 3.72533321 的重要性得分最高，很好地印证了分裂窗两波段亮温差值与TPW之间关系密切。此外， <math id="M80"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">9</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640321&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640319&type= 3.21733332 3.72533321 、 <math id="M81"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">11</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640044&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640041&type= 4.23333359 3.72533321 、 <math id="M82"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640051&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640046&type= 4.23333359 3.72533321 、 <math id="M83"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">14</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640056&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640053&type= 4.23333359 3.72533321 、sec <math id="M84"><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640059&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640058&type= 7.02733374 2.70933342 等参数对于模型的精度同样也有重要影响。 将模型应用到测试集上，反演的TPW与ERA5水汽量之间对比的结果如 图7 图7 所示。 随机森林模型在测试集上的 <math id="M85"><msup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640415&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640414&type= 3.38666677 2.96333337 达到0.925，RMSE为0.315 cm，MAE为0.225 cm，精度相较于回归分析法有明显提升。 图7 图7 中存在少量与ERA5水汽值偏差较大的反演结果，可能是由于在该时刻AGRI传感器某些波段的观测噪声较大导致的。在随机森林算法中，每棵回归树会对输入特征进行随机下采样操作，所以只有部分回归树的输入特征中包含这些噪声较大的波段亮温。该部分回归树与其余回归树的输出结果之间的差异会比较大，故可以利用各棵回归树输出结果之间的标准差 <math id="M86"><mi>s</mi><mi>t</mi><mi>d</mi><mi>e</mi><mi>v</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640091&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640089&type= 7.02733374 2.62466669 作为质量控制准则。 通过试验，本文选取质量控制阈值 <math id="M87"><mi>s</mi><mi>t</mi><mi>d</mi><mi>e</mi><msub><mrow><mi>v</mi></mrow><mrow><mi mathvariant="normal">t</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">d</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">0.4</mn><mtext> </mtext><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640096&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640094&type= 28.70199966 3.80999994 ，小于这一阈值的反演结果被认为可靠性较高。经过质量控制后，在测试集28174个反演结果中共有23676个结果被认为可靠性较高，可靠结果占比 <math id="M88"><mn mathvariant="normal">84.0</mn><mi>%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640100&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640098&type= 9.56733322 2.70933342 。经过质量控制后的反演结果如 图8 图8 所示。 经过质量控制后， <math id="M89"><msup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640415&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640414&type= 3.38666677 2.96333337 进一步提升至0.956，RMSE减少至0.247 cm，MAE减少至0.183 cm。残差的平均值为0.001 cm，绝大多数残差的绝对值都小于0.2 cm。残差分布如 图9 图9 所示。 模型在UTC 0 h与UTC 12 h的反演效果对比如 表4 表4 所示： 时刻 样本数 质量控制通过率/% RMSE/cm UTC 0 h 2555 88.9 0.245 UTC 12 h 25619 83.6 0.247 0 h+12 h 28174 84.0 0.247 在UTC 0 h模型反演结果的质量检验通过率略高于UTC 12 h的反演结果，而在两个时刻的反演精度差异不大。由于FY-4A卫星是静止轨道卫星，所以针对本文的研究区域，UTC 0 h代表白天，UTC 12 h代表傍晚与黑夜。 由于目前可用的船载探空数据较少，位于海岸或岛屿上的探空站数目较少并且对应的遥感观测数据容易受到陆面“污染”，所以本文仅利用了ERA5水汽数据对海洋上空TPW反演模型进行精度验证。 4　陆地上空大气可降水量反演 1 4.1　SWCVR算法 2 劈窗协方差—方差算法SWCVR（Split-Window Covariance-Variance Ratio）由 Sobrino等（1994） Sobrino等（1994） 提出并经由Li等（2004）改善，是目前反演晴空陆地上空TPW的常用方法之一。该算法的基本思想是基于晴空条件下的热红外辐射传输理论，取临近的 <math id="M90"><mi>N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640173&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640172&type= 2.53999996 2.62466669 个像元为研究区域，假定在该区域内大气条件和地表比辐射率不变，最终推导出分裂窗两波段大气透过率比值与传感器入瞳处亮温以及地表比辐射率之间的数学关系： <math display="block" id="M91"><mfrac><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><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><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>-</mo><msub><mrow><mover accent="true"><mi>T</mi><mo>¯</mo></mover></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>-</mo><msub><mrow><mover accent="true"><mi>T</mi><mo>¯</mo></mover></mrow><mrow><mi>j</mi></mrow></msub><mo stretchy="false">)</mo></mrow></mrow><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>j</mi></mrow></msub><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><msup><mrow><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>-</mo><msub><mrow><mover accent="true"><mi>T</mi><mo>¯</mo></mover></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640136&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640135&type= 44.36533356 18.20333290 式中， <math id="M92"><msub><mrow><mi>τ</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640138&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640137&type= 2.53999996 3.72533321 和 <math id="M93"><msub><mrow><mi>τ</mi></mrow><mrow><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640140&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640139&type= 2.45533323 3.72533321 分别代表波段 <math id="M94"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640169&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640168&type= 1.10066664 2.62466669 和 <math id="M95"><mi>j</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640171&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640170&type= 0.84666669 3.47133350 的大气透过率； <math id="M96"><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>k</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640149&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640148&type= 4.65666676 3.72533321 为波段 <math id="M97"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640169&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640168&type= 1.10066664 2.62466669 第 <math id="M98"><mi>k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640163&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640162&type= 1.69333339 2.62466669 个像元入瞳处亮温； <math id="M99"><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640159&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640157&type= 4.57200003 3.72533321 为波段 <math id="M100"><mi>j</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640171&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640170&type= 0.84666669 3.47133350 第 <math id="M101"><mi>k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640163&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640162&type= 1.69333339 2.62466669 个像元入瞳处亮温； <math id="M102"><msub><mrow><mover accent="true"><mi>T</mi><mo>¯</mo></mover></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640165&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640164&type= 2.79399991 4.23333359 和 <math id="M103"><msub><mrow><mover accent="true"><mi>T</mi><mo>¯</mo></mover></mrow><mrow><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640167&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640166&type= 2.70933342 4.23333359 表示波段 <math id="M104"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640169&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640168&type= 1.10066664 2.62466669 和 <math id="M105"><mi>j</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640171&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640170&type= 0.84666669 3.47133350 的 <math id="M106"><mi>N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640173&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640172&type= 2.53999996 2.62466669 个临近像元入瞳处亮温平均值（或中位数）； <math id="M107"><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640175&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640174&type= 2.70933342 3.72533321 和 <math id="M108"><msub><mrow><mi>ε</mi></mrow><mrow><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640177&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640176&type= 2.62466669 3.72533321 表示两个波段的地表比辐射率。 由于在热红外分裂窗波段大多数地物的地表比辐射率变化幅度较小，所以可以将 式（9） 式（9） 等号右侧的地表比辐射率项省略，即： <math display="block" id="M109"><mfrac><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfrac><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><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>-</mo><msub><mrow><mover accent="true"><mi>T</mi><mo>¯</mo></mover></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>-</mo><msub><mrow><mover accent="true"><mi>T</mi><mo>¯</mo></mover></mrow><mrow><mi>j</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><msup><mrow><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>-</mo><msub><mrow><mover accent="true"><mi>T</mi><mo>¯</mo></mover></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mrow></mfrac><mo>=</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>j</mi><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640179&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640178&type= 48.76800156 18.20333290 Li等（2003） Li等（2003） 引入了线性相关系数 <math id="M110"><msup><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640240&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640239&type= 2.45533323 2.96333337 对反演结果进行质量检验： <math display="block" id="M111"><msup><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>=</mo><mfrac><mrow><mfenced separators="|"><mrow><msup><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><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>-</mo><msub><mrow><mover accent="true"><mi>T</mi><mo>¯</mo></mover></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>-</mo><msub><mrow><mover accent="true"><mi>T</mi><mo>¯</mo></mover></mrow><mrow><mi>j</mi></mrow></msub><mo stretchy="false">)</mo></mrow></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfenced></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><msup><mrow><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>-</mo><msub><mrow><mover accent="true"><mi>T</mi><mo>¯</mo></mover></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></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><msup><mrow><mfenced separators="|"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>-</mo><msub><mrow><mover accent="true"><mi>T</mi><mo>¯</mo></mover></mrow><mrow><mi>j</mi></mrow></msub></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640183&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640182&type= 49.02199936 19.89666748 同时注意到 <math id="M112"><msup><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640240&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640239&type= 2.45533323 2.96333337 的理论值等于1： <math display="block" id="M113"><msup><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>=</mo><mfrac><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>j</mi></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfrac><mo>×</mo><mfrac><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><msub><mrow><mi>ε</mi></mrow><mrow><mi>j</mi></mrow></msub><msub><mrow><mi>τ</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></mfrac><mo>=</mo><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640187&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640186&type= 30.05666542 9.05933285 所以在实际工作中利用 <math id="M114"><msup><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640240&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640239&type= 2.45533323 2.96333337 与1的接近程度来评价反演结果的质量。本文设置阈值为0.97，剔除 <math id="M115"><msup><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640240&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640239&type= 2.45533323 2.96333337 小于该值的反演结果。 下载TIGR（Thermodynamic Initial Guess Retrieval）大气廓线数据集。该数据集包含从极地到热带地区探测的共2311条大气廓线数据，给出特定气压层上对应的气温、水汽混合比、臭氧混合比等，可以较好地代表全球范围内的大气垂直结构。有关数据的下载网址为 https：//ara.lmd.polytechnique.fr/index.php https://ara.lmd.polytechnique.fr/index.php ？‍page=tigr［2021-04-15］。 在晴空条件下，大气廓线的层相对湿度一般不高于90%，所以通过筛选最终提取出总共1446条晴空大气廓线，将之输入到大气辐射传输模拟软件MODTRAN（MODerate resolution atmospheric TRANsmission）中，并设置6个卫星观测天顶角，分别为 <math id="M116"><mn mathvariant="normal">0</mn><mo>°</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640193&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640192&type= 3.38666677 2.70933342 、 <math id="M117"><mn mathvariant="normal">11.77</mn><mo>°</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640195&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640194&type= 9.82133293 2.62466669 、 <math id="M118"><mn mathvariant="normal">23.45</mn><mo>°</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640197&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640196&type= 9.82133293 2.70933342 、 <math id="M119"><mn mathvariant="normal">32.68</mn><mo>°</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640199&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640198&type= 9.82133293 2.70933342 、 <math id="M120"><mn mathvariant="normal">41.78</mn><mo>°</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640201&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640200&type= 9.82133293 2.70933342 和 <math id="M121"><mn mathvariant="normal">50.72</mn><mo>°</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640203&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640202&type= 9.82133293 2.70933342 。 利用AGRI传感器波段响应函数计算出第12、13波段的大气透过率，进而求出两波段大气透过率比值 <math id="M122"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">13,12</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640222&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640221&type= 7.36600018 3.72533321 。利用 式（2） 式（2） 计算出每条大气廓线对应的TPW，最终回归分析出TPW与 <math id="M123"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">13,12</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640222&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640221&type= 7.36600018 3.72533321 之间的数学关系。 当卫星观测天顶角 <math id="M124"><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi><mo>=</mo><mn mathvariant="normal">0</mn><mo>°</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640209&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640208&type= 14.73200035 2.70933342 时，TPW与 <math id="M125"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">13,12</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640222&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640221&type= 7.36600018 3.72533321 之间的关系如 图10 图10 所示。 在其余的观测天顶角下，TPW与 <math id="M129"><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">13,12</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640222&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640221&type= 7.36600018 3.72533321 之间依然近似呈现出一次关系，即： <math display="block" id="M130"><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi><mi mathvariant="normal">W</mi><mo>=</mo><mi>k</mi><mo stretchy="false">(</mo><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi><mo stretchy="false">)</mo><msub><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">13,12</mn></mrow></msub><mo>+</mo><mi>l</mi><mo stretchy="false">(</mo><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640224&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640223&type= 46.56666946 4.57200003 此外，线性系数 <math id="M131"><mi>k</mi><mi>、</mi><mi>l</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640226&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640225&type= 4.57200003 2.87866688 与 <math id="M132"><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mtext> </mtext><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640228&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640227&type= 12.36133385 2.70933342 之间也近似呈现出一次关系： <math display="block" id="M133"><mi>k</mi><mo>=</mo><mo>-</mo><mfenced separators="|"><mrow><mn mathvariant="normal">9.406</mn><mo>·</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mtext> </mtext><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi><mo>+</mo><mn mathvariant="normal">4.611</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640230&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640229&type= 46.65133286 3.80999994 <math display="block" id="M134"><mi>l</mi><mo>=</mo><mn mathvariant="normal">9.441</mn><mo>·</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mtext> </mtext><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi><mo>+</mo><mn mathvariant="normal">4.655</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640232&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640231&type= 41.31733322 2.70933342 下载2019-01-01—2021-02-13期间共21景AGRI观测影像以及云检测产品，先后设置窗口尺寸为3×3、5×5、7×7以及9×9，反演的TPW与内陆地区探空站观测水汽值对比的结果如 表5 表5 所示。 窗口尺寸 RMSE/cm MAE/cm 3×3 2.137 1.656 5×5 1.143 0.946 7×7 1.030 0.830 9×9 1.045 0.861 限于篇幅仅展示窗口尺寸为7×7时的反演结果，如 图11 图11 所示。 当窗口尺寸过小时，有效观测数据量较少，无法较好地平滑仪器的观测噪声，进而导致 <math id="M135"><msup><mrow><mi>r</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640240&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640239&type= 2.45533323 2.96333337 偏低；而当窗口尺寸过大时，由于AGRI传感器热红外波段观测数据的空间分辨率较低，会导致实际的研究区域过大，从而不满足研究区域内大气条件和地表比辐射率不变这一前提假设，同样会降低反演精度。这一对矛盾可能是SWCVR算法无法很好地应用于AGRI观测数据的主要原因。 鉴于在3.2节中使用随机森林算法根据单一像元的观测数据即可较好地反演出晴空海洋上空的TPW，所以尝试将该算法引入到晴空陆地上空TPW反演工作之中。 4.2　随机森林法 2 相较于海洋表面，陆地表面构成更为复杂，主要体现在地物覆盖种类的多样性以及地势的起伏等方面。所以相较于3.2节中反演晴空海洋上空TPW时选取的8个参数，本文在陆地上空TPW反演时增加输入海拔高度 <math id="M136"><mi>H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640358&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640356&type= 2.53999996 2.62466669 与大气层顶归一化植被指数 <math id="M137"><mi mathvariant="normal">N</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">V</mi><msub><mrow><mi mathvariant="normal">I</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640244&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640243&type= 12.53066730 3.80999994 这两个参数，以考虑地表信息对于TPW反演的影响。 研究区域内的ERA5格网点和IGRA探空测站位置处对应的海拔高度 <math id="M138"><mi>H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640358&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640356&type= 2.53999996 2.62466669 通过调用Google Elevation API获取。Google Elevation API提供的高程数据以SRTM（Shuttle Radar Topography Mission）数字高程模型为基准，精度较高（ Hu等，2020 Hu等，2020 ）。Google Elevation API提供的高程数据基于WGS-84坐标系统（ Hu等，2020 Hu等，2020 ），与FY-4A数据行列号转换为经纬度的坐标系统相同。关于探空站坐标以及ERA5格网点坐标的参考系统未在官网上找到详细说明，所以本文没有进行坐标系统转换工作。 根据AGRI传感器第2波段（0.65 <math id="M139"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640251&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640249&type= 5.16466665 3.38666677 ）和第3波段（0.825 <math id="M140"><mi mathvariant="normal">μ</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640251&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640249&type= 5.16466665 3.38666677 ）的大气层顶波段反射率可以计算出 <math id="M141"><mi mathvariant="normal">N</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">V</mi><msub><mrow><mi mathvariant="normal">I</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640405&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640404&type= 12.53066730 3.80999994 ： <math display="block" id="M142"><mi mathvariant="normal">N</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">V</mi><msub><mrow><mi mathvariant="normal">I</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>-</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>+</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640261&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640259&type= 28.36333466 9.14400005 大气层顶归一化植被指数可以在一定程度上反映出地表特性和大气状况。 同样设置回归树数目为100，通过输入不同的参数组合训练模型，然后利用测试集测试模型效果，对比结果如 表6 表6 所示。通过对比可知，在输入特征中增加 <math id="M143"><mi>H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640358&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640356&type= 2.53999996 2.62466669 与 <math id="M144"><mi mathvariant="normal">N</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">V</mi><msub><mrow><mi mathvariant="normal">I</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640405&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640404&type= 12.53066730 3.80999994 可以有效地提升模型的反演精度。 输入参数 <math id="M145"><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640272&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640270&type= 2.62466669 2.28600001 <math id="M146"><mi mathvariant="normal">R</mi><mi mathvariant="normal">M</mi><mi mathvariant="normal">S</mi><mi mathvariant="normal">E</mi><mo>/</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640277&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640274&type= 11.26066685 2.03200006 <math id="M147"><mi mathvariant="normal">M</mi><mi mathvariant="normal">A</mi><mi mathvariant="normal">E</mi><mo>/</mo><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640280&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640278&type= 9.90600014 2.03200006 与3.3节相同 0.946 0.234 0.152 + <math id="M148"><mi>H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640296&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640294&type= 1.94733346 2.03200006 0.956 0.211 0.136 + <math id="M149"><mi mathvariant="normal">N</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">V</mi><msub><mrow><mi mathvariant="normal">I</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640300&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640298&type= 9.56733322 2.87866688 0.956 0.212 0.138 + <math id="M150"><mi>H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640296&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640294&type= 1.94733346 2.03200006 + <math id="M151"><mi mathvariant="normal">N</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">V</mi><msub><mrow><mi mathvariant="normal">I</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640300&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640298&type= 9.56733322 2.87866688 0.964 0.190 0.124 输出模型中每个参数的重要性得分，如 图12 图12 所示。由 图12 图12 可知， <math id="M152"><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640346&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640344&type= 11.68400002 2.70933342 、 <math id="M153"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">12</mn></mrow></msub><mo>—</mo><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">13</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640317&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640315&type= 12.44600010 3.72533321 、 <math id="M154"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">9</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640321&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640319&type= 3.21733332 3.72533321 、 <math id="M155"><msub><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">10</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640326&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640324&type= 4.23333359 3.72533321 以及新增的 <math id="M156"><mi>H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640358&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640356&type= 2.53999996 2.62466669 和 <math id="M157"><mi mathvariant="normal">N</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">V</mi><msub><mrow><mi mathvariant="normal">I</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640405&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640404&type= 12.53066730 3.80999994 等参数的重要性得分均较高，进一步证明 <math id="M158"><mi>H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640358&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640356&type= 2.53999996 2.62466669 和 <math id="M159"><mi mathvariant="normal">N</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">V</mi><msub><mrow><mi mathvariant="normal">I</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640342&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640338&type= 12.53066730 3.80999994 可以较好地反映出地表信息，提高模型的反演精度。其中卫星观测天顶角正割值 <math id="M160"><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">V</mi><mi mathvariant="normal">Z</mi><mi mathvariant="normal">A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640346&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640344&type= 11.68400002 2.70933342 得分最高的原因之一可能是在陆地上空TPW反演时选取的研究区域的纬度更高，使得卫星观测天顶角普遍更大，所以此时倾斜路径水汽与垂直水汽之间的差异也更大。 增加输入 <math id="M161"><mi>H</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640358&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640356&type= 2.53999996 2.62466669 与 <math id="M162"><mi mathvariant="normal">N</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">V</mi><msub><mrow><mi mathvariant="normal">I</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640405&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640404&type= 12.53066730 3.80999994 后训练的模型在测试集上的表现如 图13 图13 所示。经过质量控制后，在47898个测试数据中有44694个预测结果被认为可靠性较高，占比 <math id="M163"><mn mathvariant="normal">93.2</mn><mi>%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640369&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640365&type= 9.56733322 2.70933342 。质量控制后的结果如 图14 图14 所示。 经过质量控制后， 图13 图13 中与水汽标准值偏差较大的反演结果被有效剔除， <math id="M164"><msup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640392&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640390&type= 3.38666677 2.96333337 进一步提升至0.972，RMSE降低至0.155 cm，MAE则降为0.106 cm，残差平均值为-0.002 cm。残差分布如 图15 图15 所示。 模型昼夜反演效果对比如 表7 表7 所示。模型在日间的水汽反演精度与质量检验通过率略高于夜间。由于目前昼夜样本昼夜数目不均衡，关于模型昼夜反演精度的对比还有待于进一步的分析与验证。 时刻 样本数 质量检验通过率/% RMSE/cm UTC 0 h 39248 94.4 0.152 UTC 12 h 8650 88.1 0.168 0 h+12 h 47898 93.2 0.155 4.3　结果验证 2 下载与2.1节中61景AGRI观测影像成像时刻所对应的内陆地区IGRA探空数据，首先剔除非晴空状态的测站；然后对AGRI影像和探空数据进行时空匹配，并对探空数据进行质量检验。针对符合条件的探空数据，通过数值积分计算出TPW并提取出其对应的海拔高度；同时从AGRI影像中提取出中红外与热红外波段观测亮温，并计算出探空测站对应的卫星观测天顶角与 <math id="M165"><mi mathvariant="normal">N</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">V</mi><msub><mrow><mi mathvariant="normal">I</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">A</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640405&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640404&type= 12.53066730 3.80999994 。最终提取出总共484个符合条件的有效观测数据对并输入到模型中。模型反演的TPW与探空观测水汽值之间的对比如 图16 图16 所示。 经过质量控制后，有366个反演结果被认为可靠性较高，占比 <math id="M166"><mn mathvariant="normal">75.6</mn><mi>%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640410&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640409&type= 9.56733322 2.70933342 ，如 图17 图17 所示。 此时 <math id="M167"><msup><mrow><mi>R</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640415&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=19640414&type= 3.38666677 2.96333337 提升至0.946，RMSE降低至0.215 cm，MAE降为0.163 cm，残差的平均值为0.02 cm。残差分布如 图18 图18 所示。 5　结论 1 本文利用FY-4A卫星AGRI传感器的中红外与热红外波段观测数据、ERA5水汽再分析产品以及IGRA探空数据等进行晴空TPW遥感反演研究，主要得到如下结论： （1）利用AGRI传感器的中红外与热红外波段观测数据可以较精确地反演出晴空海洋上空的TPW。分别采用回归分析法和随机森林算法反演并与ERA5水汽再分析产品进行对比，RMSE为0.493 cm和0.247 cm。 （2）可以根据随机森林模型中每棵回归树输出结果之间的标准差对反演结果进行质量控制。经过质量控制后，可以有效地剔除与水汽标准值偏差较大的反演结果。 （3）由于AGRI传感器空间分辨率较低，所以使用传统的SWCVR算法可能无法精确地反演出晴空陆地上空的TPW，这也有待于后续的进一步研究与验证。 （4）采用随机森林算法可以较好地反演出晴空陆地上空的TPW，增加能够反映地表信息的参数可以提高模型的反演精度。经过质量控制后的反演结果与ERA5水汽再分析产品对比，RMSE为0.155 cm；与IGRA探空水汽值对比，RMSE为0.215 cm。 参考文献（References） Dalu G . 1986 . 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Quarterly Journal of Applied Meteorology , 1998, 9 ( 1 ): 8 - 14 Study of Precipitable Water by GMS-5 朱元竞 , 李万彪 , 陈勇 . 1998 . GMS-5估计可降水量的研究 . 应用气象学报 , 9 ( 1 ): 8 - 14 GMS-5估计可降水量的研究 感谢国家卫星气象中心提供的FY-4A AGRI传感器观测数据与产品、ECMWF机构提供的全球水汽总量再分析产品、Google公司提供的全球高程数据、NCEI机构提供的探空观测数据。 10.11834/jrs.20211217 1007-4619（2021）08-1836-12 张环宇，唐伯惠.2021.融合物理机理与随机森林算法的FY-4A AGRI数据晴空大气可降水量遥感反演.遥感学报，25（8）： 1836-1847 张环宇，唐伯惠.2021.融合物理机理与随机森林算法的FY-4A AGRI数据晴空大气可降水量遥感反演.遥感学报，25（8）： 1836-1847 Zhang H Y and Tang B H. 2021. Remote sensing retrieval of total precipitable water under clear-sky atmosphere from FY-4A AGRI data by combining physical mechanism and random forest algorithm. National Remote Sensing Bulletin， 25（8）：1836-1847 Zhang H Y and Tang B H. 2021. Remote sensing retrieval of total precipitable water under clear-sky atmosphere from FY-4A AGRI data by combining physical mechanism and random forest algorithm. National Remote Sensing Bulletin， 25（8）：1836-1847 国家自然科学基金（编号：41871244） Supported by National Natural Science Foundation of China (No. 41871244) 2021-04-15 2021-08-07 2021-09-09 2021-06-12 遥感学报 8 25