内陆水体藻蓝蛋白遥感反演研究进展

内陆水体藻蓝蛋白遥感反演研究进展 Advances in remote sensing of phycocyanin for inland waters 1 2 first-author 吕丽丽，1985年生，女，博士研究生， 研究方向为内陆水体藻蓝蛋白浓度遥感反演。E-mail： lvlili@iga.ac.cn 吕丽丽，1985年生，女，博士研究生， 研究方向为内陆水体藻蓝蛋白浓度遥感反演。E-mail： lvlili@iga.ac.cn lvlili@iga.ac.cn 1 3 corresp 宋开山，1974年生，男，研究员，研究方向为内陆水体水质参数遥感反演。E-mail： songkaishan@iga.ac.cn 宋开山，1974年生，男，研究员，研究方向为内陆水体水质参数遥感反演。E-mail： songkaishan@iga.ac.cn songkaishan@iga.ac.cn 1 1 1 1 中国科学院东北地理与农业生态研究所遥感中心,长春 130102 中国科学院东北地理与农业生态研究所遥感中心,长春 130102 Northeast Institute of Geography and Agroecology, Chinese Academy of Sciences, Changchun 130102, China Northeast Institute of Geography and Agroecology, Chinese Academy of Sciences, Changchun 130102, China 中国科学院大学, 北京 100049 中国科学院大学, 北京 100049 University of Chinese Academy of Sciences, Beijing 100049, China University of Chinese Academy of Sciences, Beijing 100049, China 聊城大学 环境与规划学院, 聊城 252000 聊城大学 环境与规划学院, 聊城 252000 School of Environment and Planning, Liaocheng University, Liaocheng 252000, China School of Environment and Planning, Liaocheng University, Liaocheng 252000, China 藻蓝蛋白（PC），作为蓝藻的标志性色素，通常被用作进行蓝藻水华遥感监测的标志物。近年来，内陆水体水质恶化，富营养化加剧，藻华频发，PC遥感反演研究越来越受到关注。本文从PC光学特性、反演算法开发、卫星传感器应用等方面难点及干扰因素，综合梳理了过去30 a PC遥感反演研究的发展历程和趋势，以期理解国内外相关研究的新思路和新方法，掌握未来PC遥感反演发展研究的新动态，为水质和水资源的监管提供数据和理论基础。过去的30 a里，PC遥感反演研究发文量持续走高，并在算法上取得突破性进展，先后出现了很多经典算法，如波段比法、基线法、嵌套波段比法、生物光学模型、衍生算法和机器学习算法等，成功地分离出PC特征吸收波段（620 nm）的光谱信息，弱化了其他光学活性物质的影响，获得了较可靠的精度。另外，除高光谱航空/卫星影像数据（Hyperion、HICO）外，多光谱卫星遥感平台的PC遥感反演研究也日趋成熟，可选择的数据源种类较多，如Landsat系列、MODIS、MERIS、Sentinel-2 MSI、Sentinel-3 OLCI，其中MERIS和Sentinel-3 OLCI由于其辐射分辨率、空间分辨率和波段设置更适合用于PC遥感反演，在PC遥感反演中被广泛使用。由于PC光谱信号较弱，且易受叶绿素a、悬浮颗粒物等的干扰，想获得高精度的PC遥感估算，仍然是个挑战，未来PC遥感反演研究将向着PC测试方法的标椎化、算法精细化、时空格局大尺度化及PC遥感反演应用深入化等方面发展。 Phycocyanin (PC), as the signature pigment of cyanobacteria, is usually used for remote sensing monitoring of cyanobacteria bloom. In recent years, the water quality of inland water has deteriorated, the eutrophication has intensified, and the algal blooms frequently occur. The research of remote sensing inversion of PC has attracted more and more attention. Therefore, it is urgent to sort out and write a comprehensive overview paper. In this paper, 178 relevant literatures were reviewed, and the development history and trend of PC remote sensing inversion research of PC in the past 30 years (1990—2020) were comprehensively summarized from the perspectives of PC optical characteristics, development of inversion algorithms, application of satellite sensors, difficulties and interference factors of quantitative remote sensing inversion of PC. This paper helps us to understand the new ideas and new methods emerging at home and abroad, master the new development trends of PC remote sensing inversion in the future, and provide data basis for the monitoring and management of water environment, water quality and water resources. Over the past 30 years, PC remote sensing inversion study number rising, and a breakthrough in the algorithm, has a lot of classic algorithms, such as band ratio method, the baseline method, nested band ratio method, biological optical model, derivative algorithm and machine learning algorithms, algorithm successfully isolated PC spectral characteristic of absorption coefficients at wavelength of 620 nm. Decreased the influence of other optically active substances (Chla、TSM) and obtained the high precision of inversion and validation . In addition, the development of PC inversion algorithms mostly based on in situ hyperspectral data or aerial images (CASI-2, AISA Eagle). In order to meet the needs of PC concentration distribution in a certain space and frequency, satellite image data sources are mostly used. PC. There are many types of multi-spectral satellite data sources to choose, such as Landsat series, MODIS, MERIS, Sentinel-2 MSI, Sentinel-3 OLCI, etc. However, due to the more appropriate band setting, MERIS and Sentinel-3 OLCI are still the most used data sources for PC remote sensing inversion research. Because PC spectrum signal is weak, and vulnerable to the interference of chlorophyll a, TSM, there is still a major difficult to get an accurate estimation result. Based on the above analysis, the future development direction of PC remote sensing inversion can be summarized as the following aspects: first, an international standard measurement method is urgently needed in PC extraction testing; secondly, the development of algorithm, adhere to the mechanism research related to the inherent optical properties, and the integrating machine learning algorithm to bring higher inversion accuracy; third, the scale of study area water body in space and time will toward a larger geographical space scale, longer time series history tracing and future prediction; fourth, at the aspect of the expansion of application, PC remote sensing inversion is not limited to the quantitative estimation of cyanobacteria biomass, but will predict distribution of algal toxins and related diseases based on the relationships between these parameters and PC concentration, furtherly establish a water risk factor rating system based on remote sensing in the future. 湖泊遥感 内陆水体 藻蓝蛋白 光学特性 反演算法 卫星传感器 lake remote sensing inland waters phycocyanin optical properties inversion algorithm satellite sensor 1　引言 1 相比海洋生态系统，内陆水体（湖泊、水库、河流）生态系统与人类生产生活的关系更加密切。内陆水体中各浮游动植物、颗粒和溶解性有机物、无机物、微生物、碳源和氮源等物质相互作用，共同维持着水体生物化学生态系统的平衡（ Duan等，2012 Duan等，2012 ； Song等，2019 Song等，2019 ； Wen等，2019 Wen等，2019 ）。在内陆水体中浮游藻类，因其含有的色素可以捕获太阳光并将其转化成能量，充当着一切能量的提供者 （ Hmimina等，2019 Hmimina等，2019 ）。有研究表明，色素组成及其比例的不同是引起藻类间吸收光谱变化的主要原因（ Zhao等，2018 Zhao等，2018 ）。藻蓝蛋白PC（ Phycocyanin ），是蓝藻的标志性色素，仅存在于蓝藻中，可以指示蓝藻生物量，具有吸收和传递光能的性质，分子量约为232 KDa，具有荧光性，呈亮蓝色，属于胞内蛋白，易溶于水、乙醇等极性溶剂 （ Zhao等，2018 Zhao等，2018 ）。PC是天然光学活性物质，在620 nm附近处有明显的特征吸收峰，这正给遥感监测其浓度提供了理论依据。近年来，内陆水体富营养化现象加剧，蓝藻水华现象频发，导致水生生态系统严重失衡，有些蓝藻产生藻毒素，严重威胁着人类和动物健康安全（ Matthews等，2010 Matthews等，2010 ； Shi等，2015a Shi等，2015a ； Song等，2021 Song等，2021 ）。利用遥感技术监测PC浓度，进而来监测水体中的蓝藻生物量，是一种有效地、大尺度、快速精确地监测蓝藻水华的策略（ Duan等，2017 Duan等，2017 ； Miao等，2020 Miao等，2020 ）。 PC第一次出现在遥感学科领域，应归功于美国的Gordon学者， Gordon等（1980） Gordon等（1980） 首次阐述了PC的光谱特征，标志着PC遥感应用的开端。20世纪90年代航空遥感传感器CAMS、CASI（Dekker等，1991； Millie等，1992 Millie等，1992 ； Dekker，1993 Dekker，1993 ）被应用于监测PC浓度；2000年以后随着各大卫星遥感平台数据的相继开放，MERIS以及欧空局的Sentinal-3 OLCI等数据增设了620 nm波段，加之3大分辨率的提升，算法的不断优化，大大提升了PC遥感监测技术在各个尺度和准实时监测的能力（ Ogashawara，2020 Ogashawara，2020 ； Yan等，2018 Yan等，2018 ）；在随后的十几年内PC遥感研究处于爆发期，无论是基础原理，算法开发，还是遥感平台的应用都得到了突飞猛进的发展，遥感技术已成为蓝藻监测及水质管理领域中不可或缺的有效工具。然而，与3大经典光学活性物质相比，PC的遥感研究相对较少，因为其620 nm的吸收峰光学信号较弱、且易受到水体类型和叶绿素a、悬浮物等的影响。另外，PC实际浓度的测定尚没有一个标准方法可循，目前主流的提取方法有手动研磨法、超声破壁法、冻融法、超声冻融联用法（ Hunter等，2010 Hunter等，2010 ； Sarada等，1999 Sarada等，1999 ）。测定方法有吸光度法（ Bennett和Bogorad，1973 Bennett和Bogorad，1973 ）、荧光分光光度计标准曲线法（ Lyu等，2013 Lyu等，2013 ）、酶联反应测定法（ Zimba，2012 Zimba，2012 ）、荧光探针测定法（ Mishra等，2009 Mishra等，2009 ； Song等，2013 Song等，2013 ）。以上萃取和测定方法间PC的测定值存在差异，尤其是在低浓度水体中，想要做到高精度反演仍是一个挑战（ Liu等，2018 Liu等，2018 ）。 PC定量遥感反演研究的意义在于，可利用PC与蓝藻生物量，与藻毒素之间强烈的正相关关系，定量监测水体中蓝藻生物量或藻毒素含量，这对理解蓝藻暴发机制及其早期预警具有重要意义。基于这点，关于PC光学性质（反射、吸收、荧光）、反演模型及应用拓展的研究，都成为近年来水环境遥感研究领域的热点。国际上已有几篇综述性论文发表（ Ogashawara，2020 Ogashawara，2020 ； Ogashawara等，2013 Ogashawara等，2013 ； Yan等，2018 Yan等，2018 ），他们的侧重点或是反演算法对比或是文献统计分析，缺少PC光学性质的全面概述，缺少PC反演的影响因素分析等。因此，本研究领域迫切需要一个从多角度、多维度、系统地综述论文来概括总结国内外PC遥感研究的发展趋势及取得的新成果。基于这点，本综述更注重对PC光学性质、反演算法开发和验证、影响因素以及多种卫星数据源应用的梳理，并深入挖掘其未来的发展方向。 2　文献计量分析及概述 1 在过去的30 a里，PC遥感研究不断发展进步，涉及到的研究区300余个，遍布全球各地，主要集中分布在欧美地区及中国境内，还有少数分布在非洲、印度、韩国等地区。经文献查阅，这些水体无论是湖泊、水库还是河流均属于富营养化或超富营养化水体类型。中国境内涉及的相关研究区多分布在南方富营养化较为严重的一些湖泊，例如，太湖、巢湖、滇池、洱海等。从PC遥感反演发文数量上看，自1990年至今一直呈持续增加的趋势（ 图1 图1 ），增加趋势可分为3个阶段，即2005年之前属于起步阶段，零星有些研究，2005年—2015年属于快速增加阶段，以算法开发，各数据源应用为主，2015年之后属于稳定发展阶段。这3个阶段也充分体现了30 a来PC遥感反演研究的发展和日趋成熟。 PC遥感反演研究在国家尺度上的分布情况表明（ 图2 图2 ），美国在该领域研究中发文数量遥遥领先，占研究发文总数量的40%；中国位居第二，占总数量的25%，欧洲国家占总数量的21%，韩国占总数量的8%，而南非、印度、加拿大、巴西等国家在这方面的研究则很少。总体来看，全球还有很多国家从来没有涉及PC遥感研究领域，并且，已有这些国家在此领域的发展极度不平衡，按照排名顺序发文数量呈断崖式下降。可喜的是，中国在此领域的研究数量超过了欧洲，但在文章质量和影响力上，中国离欧美还有一定差距。 3　藻蓝蛋白的光学性质 1 3.1　藻蓝蛋白的吸收特性 2 PC的吸收系数一般表示为 <math id="M1"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654287&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654286&type= 13.37733269 4.57200003 ，以 <math id="M2"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654287&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654286&type= 13.37733269 4.57200003 除以PC浓度来表示PC单位吸收系数，即 <math id="M3"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654306&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654304&type= 13.37733269 4.82600021 。这两个参数对定量遥感反演PC浓度都是至关重要的。从中国几个典型水体的藻类吸收光谱曲线（ 图3 图3 ），可以看到3个明显的吸收峰，绿色线指示Chla的吸收峰（443 nm、675 nm），蓝色线指示了PC的吸收峰（620 nm）。相比于Chla的吸收峰，PC吸收信号较弱，大概只有Chla吸收峰强度的20%（ Schalles和Yacobi，2000 Schalles和Yacobi，2000 ）。所以要想在遥感上得到与Chla等效的光谱信号，需要较高的PC浓度（ Shi等，2015a Shi等，2015a ； Yan等，2018 Yan等，2018 ）。 1,2,3;4,5,6;7,8; 不同类型内陆水体的 <math id="M4"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654331&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654330&type= 13.37733269 4.57200003 值差异较大， <math id="M5"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654333&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654332&type= 13.37733269 4.57200003 在中国东部湖泊数值范围为0.05—1.56 m -1 （ Duan等，2012 Duan等，2012 ），在荷兰北部湖泊为0.002-1.2 m -1 （ Simis等，2005 Simis等，2005 ），在美国印第安纳州水库为0.008-1.25 m -1 （ Li等，2015 Li等，2015 ），这表明内陆水体 <math id="M6"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654335&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654334&type= 13.37733269 4.57200003 有强烈的变异性。有研究表明， <math id="M7"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo stretchy="false">(</mo><mn 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stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654624&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654623&type= 13.37733269 4.57200003 不仅具有时空变异性，同时也受水质类型的影响。 根据定义，PC单位吸收 <math id="M10"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654356&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654398&type= 13.37733269 4.82600021 可以反映 <math id="M11"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654624&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654623&type= 13.37733269 4.57200003 与PC浓度的关系，一般的 <math id="M12"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654300&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654345&type= 13.37733269 4.82600021 与PC浓度呈负相关关系（ Duan等，2012 Duan等，2012 ； Shi等，2015a Shi等，2015a ）。不同地区不同类型水体， <math id="M13"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654369&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654367&type= 13.37733269 4.82600021 差别较大，中国东部湖泊 <math id="M14"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654349&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654348&type= 13.37733269 4.82600021 的范围为0.001—1.2 m 2 ·mg -1 （ Duan等，2012 Duan等，2012 ），荷兰北部湖泊为0.0088—0.1868 m 2 ·mg -1 （ Simis等，2005 Simis等，2005 ）。 <math id="M15"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654347&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654350&type= 13.37733269 4.82600021 受多种因素影响，包括细胞形态、光利用率、其他色素物质的干扰（ Simis等，2005 Simis等，2005 ）。同时，PC浓度测定的不确定性也是 <math id="M16"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654356&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654398&type= 13.37733269 4.82600021 强变异性的重要因素。利用生物光学模型精确反演PC的关键是选择一个合适的 <math id="M17"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654369&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654367&type= 13.37733269 4.82600021 值，因此 <math id="M18"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654356&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654398&type= 13.37733269 4.82600021 的变异是不可忽略的（ Duan等，2012 Duan等，2012 ； Lyu等，2013 Lyu等，2013 ； Ruiz-Verdú等，2008 Ruiz-Verdú等，2008 ； Simis等，2005 Simis等，2005 ）。Simis算法中将 <math id="M19"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654376&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654374&type= 13.37733269 4.82600021 值固定为0.0095 m 2 ·mg -1 （ Simis等，2005 Simis等，2005 ），但后来他们又调整到0.007 m 2 ·mg -1 （ Simis等，2007 Simis等，2007 ），因为新的PC提取方法使PC的萃取效率提高了28%。但是， Le等（2011） Le等（2011） 和 Mishra等（2013） Mishra等（2013） 等人认为0.007 m 2 ·mg -1 仍然偏高，在研究中则使用了较低的 <math id="M20"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654381&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654379&type= 13.37733269 4.82600021 ，如0.0043 m 2 ·mg -1 （ Jupp等，1994 Jupp等，1994 ）和0.0048 m 2 ·mg -1 （ Mishra等，2013 Mishra等，2013 ），甚至在有的研究中，没有测定 <math id="M21"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654356&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654398&type= 13.37733269 4.82600021 的值，而是直接使用已报道的平均值0.0046 m 2 ·mg -1 （ Li等，2015 Li等，2015 ）。基于 <math id="M22"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654387&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654385&type= 13.37733269 4.82600021 易变的性质， Mishra 等（2013） Mishra 等（2013） 利用同一组数据集，考察了3种 <math id="M23"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654353&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654389&type= 13.37733269 4.82600021 （报道过的0.0048 m 2 ·mg -1 、平均值、模拟值）对PC浓度反演精度的影响，3种情况下得到的PC估算平均相对误差在10%—22%变异。结果还表明， <math id="M24"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654356&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654398&type= 13.37733269 4.82600021 随着 <math id="M25"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo><mo>/</mo><mtext> </mtext><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">665</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654397&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654395&type= 27.85533524 4.57200003 的比值呈线性增加。总而言之， <math id="M26"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654356&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654398&type= 13.37733269 4.82600021 值不是一个固定值，受季节、细胞形态、蓝藻种类、色素浓度等多种因素影响。 3.2　藻蓝蛋白的反射光谱特性 2 在富含蓝藻的水体中，反射光谱曲线具有3个明显的反射峰（ 图3 图3 ），第1个反射峰位于500—600 nm，是由藻类散射吸收引起的最大最宽的绿峰，第2个峰位于640—660 nm，是由位于两边的620 nm、670 nm波段处的 PC吸收，Chla吸收，共同作用形成的（ Hunter等，2008 Hunter等，2008 ），第3个峰位于700—710 nm，是由Chla强吸收和散射引起的。然而，这些峰并不是孤立的，固定不变的。有研究表明，PC光谱特征的位置是随着PC浓度在Chla浓度比例中改变而变化的（ Hunter等，2010 Hunter等，2010 ），可能小于620 nm也可能大于620 nm。在贫营养水体中，PC浓度很低，光谱曲线620 nm处没有明显的吸收谷，导致低浓度时，PC反演精度较低（ Li等，2012 Li等，2012 ； Simis等，2007 Simis等，2007 ），而在中营养、富营养水体中620 nm处有明显的吸收谷，且PC浓度越高，620 nm的吸收谷越深。而在浮渣出现以后，即水面被蓝藻覆盖，光谱呈现典型植被特征（光谱上753 nm反射峰高于709 nm）时，PC反演算法已经没有意义，此时应该考虑更换算法去检测浮渣蓝藻生物量（ Shi等，2019 Shi等，2019 ）。 与其他两个散射峰相比，反映PC吸收的反射峰信号是最弱的，这给遥感反演PC浓度带来了一定难度，多数研究使用实测高光谱数据或高光谱航空遥感影像（AISA、CASI、CHRIS），以获得满意的离水辐亮度信号。对于多光谱卫星传感器，含有620 nm波段设置的，也多被用于PC遥感反演研究。总之，结合PC光谱特征和其他峰、谷的分析，包括其量级的大小、位置、峰高、峰面积、求导等方法、开发各种PC反演算法。 4　藻蓝蛋白与叶绿素a、蓝藻生物量的关系 1 叶绿素a存在于所有藻类中，研究多以Chla为代理指示总藻的含量，PC只存在于蓝藻中，可以指示蓝藻生物量。藻毒素大多存在与藻蓝细胞中，随藻蓝生物量增加而增多。他们之间的关系不仅可以用于妥善处理PC反演精度的问题，还可以用于间接估算蓝藻生物量，藻毒素浓度等，拓展PC遥感反演的意义及实际应用价值。 一般的，内陆水体中，PC与Chla的关系有两种情况：第一，只有在蓝藻主导的水体中，他们之间才存在显著正相关性，例如南非的Hart bees poort水库、韩国Baekje水库，PC与Chla均具有很好的正相关关系；而对于非蓝藻主导的水体，南非的Thee water skloof水库，两者相关性较弱。第二，只有在适宜的PC：Chla比值范围内，两者关系才成立，当PC：Chla < 0.5时，两者关系较弱，当PC：Chla≥0.5时，两者关系增强（ Hunter等，2008 Hunter等，2008 ； Li等，2012 Li等，2012 ； Simis等，2005 Simis等，2005 ， 2007 2007 ）。太湖PC浓度为7—50 μg·L -1 范围内时，PC与Chla高度相关（ 郭一洋 等，2016 郭一洋 等，2016 ）。 Ahn等（2007） Ahn等（2007） 利用两者的紧密关系，以PC代替Chla，提出了基于PC浓度的蓝藻预警系统，得出PC浓度为0.1 μg·L -1 、30 μg·L -1 和700 μg·L -1 时分别指示安全水平、警惕水平、警告水平。 相比于Chla，PC与蓝藻生物量间的关系更加稳定，据报道两者相关关系高达0.7—0.8（ 表1 表1 ）。但也有研究表明，不同种类蓝藻含有PC浓度是不同。例如PC在 Planktothrix agardhi 藻中比在 Lemmemanniella sp 藻中的含量低4倍多，（ Mishra等，2013 Mishra等，2013 ）。另外，PC也可以作为桥梁连接Chla和蓝藻生物量，从而实现大量的Chla反演算法被应用于蓝藻生物量监测的目的（ Pyo等，2020 Pyo等，2020 ）。值得一提的是，PC：Chla比值赋有特别的意义，即可以指示总藻中蓝藻的比列，这对早期蓝藻水华预警以及理解内陆水体中浮游生物群落结构具有重要意义。 注： <math id="M47"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654498&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654485&type= 3.89466691 2.87866688 代表藻蓝蛋白浓度，单位μg·L -1 ； <math id="M48"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">a</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654501&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654500&type= 5.07999992 2.87866688 代表叶绿素a浓度，单位μg·L -1 ； <math id="M49"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">Y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654504&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654503&type= 4.14866638 2.87866688 代表蓝藻生物量，单位cells/mL； <math id="M50"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">C</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654490&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654488&type= 4.31799984 2.87866688 代表藻毒素，单位μg·L -1 。 关系式 参考文献 <math id="M27"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo>=</mo><mn>8.7</mn><mo>×</mo><msup><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">a</mi></mrow></msub></mrow><mrow><mn>0.74</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654360&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654359&type= 22.86000061 3.13266683 ， <math id="M28"><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0.87</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654402&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654361&type= 11.09133339 2.28600001 Matthews等，2020 Matthews等，2020 <math id="M29"><mi mathvariant="normal">L</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mfenced separators="|"><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">a</mi></mrow></msub></mrow></mfenced><mo>=</mo><mn>0.375</mn><mo>×</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mtext> </mtext><mo stretchy="false">(</mo><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><mn>0.914</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654409&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654404&type= 44.53466415 4.40266657 ， <math id="M30"><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0.83</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654478&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654477&type= 11.09133339 2.28600001 Pyo等，2017 Pyo等，2017 <math id="M31"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo>=</mo><mn>4.7</mn><mo>×</mo><msup><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">a</mi></mrow></msub></mrow><mrow><mn>0.4199</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654412&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654425&type= 24.55333328 3.13266683 ， <math id="M32"><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0.32</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654430&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654428&type= 11.09133339 2.28600001 Matthews等，2020 Matthews等，2020 <math id="M33"><mi mathvariant="normal">L</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mfenced separators="|"><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">Y</mi></mrow></msub></mrow></mfenced><mo>=</mo><mn>1.705</mn><mo>×</mo><mi mathvariant="normal">L</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mfenced separators="|"><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub></mrow></mfenced><mo>+</mo><mn>1.606</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654434&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654432&type= 44.45000076 4.40266657 ， <math id="M34"><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0.73</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654439&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654437&type= 11.09133339 2.28600001 Kudela等，2015 Kudela等，2015 <math id="M35"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">Y</mi></mrow></msub><mo>=</mo><mn>109,98.2</mn><mo>×</mo><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo>-</mo><mn>150.2</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654417&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654415&type= 35.22133255 3.30200005 ， <math id="M36"><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0.6</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654420&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654418&type= 9.65200043 2.28600001 Torbick和Corbiere，2015 <math id="M37"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">Y</mi></mrow></msub><mo>=</mo><mn>3.558</mn><mo>×</mo><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo>+</mo><mn>110.11</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654454&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654422&type= 32.42733002 2.87866688 ， <math id="M38"><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0.79</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654460&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654457&type= 11.09133339 2.28600001 Li等，2010 Li等，2010 <math id="M39"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo>=</mo><mn>0.001</mn><mo>×</mo><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">Y</mi></mrow></msub><mo>+</mo><mn>2.4263</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654465&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654463&type= 32.42733002 2.87866688 ， <math id="M40"><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0.99</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654444&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654443&type= 11.09133339 2.28600001 Mishra等，2013 Mishra等，2013 <math id="M41"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo>=</mo><mn>0.004</mn><mo>×</mo><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">Y</mi></mrow></msub><mo>+</mo><mn>1.7287</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654471&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654469&type= 32.42733002 2.87866688 ， <math id="M42"><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0.99</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654444&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654443&type= 11.09133339 2.28600001 Mishra等，2013 Mishra等，2013 <math id="M43"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">C</mi></mrow></msub><mo>=</mo><mn>0.0796</mn><mo>×</mo><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">a</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654476&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654474&type= 23.96066666 2.87866688 ， <math id="M44"><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0.83</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654478&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654477&type= 11.09133339 2.28600001 Shi等，2015b Shi等，2015b <math id="M45"><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">M</mi><mi mathvariant="normal">C</mi></mrow></msub><mi mathvariant="normal">∞</mi><msub><mrow><mi>C</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654480&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654445&type= 10.32933331 2.87866688 ， <math id="M46"><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>0.90</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654482&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654447&type= 11.09133339 2.28600001 Hunter等，2008 Hunter等，2008 PC与藻毒素关系研究不多。 Shi等（2015b） Shi等（2015b） 通过两步估算法，利用藻毒素与Chla、Chla与MODIS指数这两个紧密的关系，反演得到2003到2013年的藻毒素浓度年际变化规律。其他研究也发现藻毒素浓度与PC浓度强烈正相关（ Hunter等，2008 Hunter等，2008 ； Sridhar和Vincent，2007 Sridhar和Vincent，2007 ）。由于藻毒素不是光学活性物质，理论上不能直接与遥感反射率（ <math id="M51"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654509&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654508&type= 3.89466691 3.72533321 ）数据建立关系，所以，这些关系为二步法反演藻毒素提供了理论基础。 5　藻蓝蛋白的遥感反演算法 1 5.1　经验算法 2 经验算法是直接使用统计回归方法，建立实测PC浓度与实测光谱反射率或各种光学传感器观测的反射率数据之间的关系，此方法很少考虑辐射原理，操作简单，是PC定量遥感反演研究中使用较多的算法（ 表2 表2 ），但此算法具有空间局限性，只适用于选定研究区的当次数据集（ Yan等，2018 Yan等，2018 ）。在经验算法中，波段比算法能消除一些干扰因素，如大气的影响，例如 <math id="M52"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">710</mn><mo stretchy="false">)</mo><mo>/</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654491&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654510&type= 27.26266861 4.57200003 （Seppälä等，2007）， <math id="M53"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">709</mn><mo stretchy="false">)</mo><mo>/</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654512&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654493&type= 27.17799950 4.57200003 （ Chi等，2016 Chi等，2016 ； Kwon等，2020 Kwon等，2020 ）， <math id="M54"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">747</mn><mo stretchy="false">)</mo><mo>/</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">665</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654514&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654513&type= 27.00866890 4.57200003 （ Sòria-Perpinyà等，2020 Sòria-Perpinyà等，2020 ）， <math id="M55"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">700</mn><mo stretchy="false">)</mo><mo>/</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">600</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654516&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654515&type= 27.26266861 4.57200003 （ Mishra等，2009 Mishra等，2009 ）， <math id="M56"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">764</mn><mo stretchy="false">)</mo><mo>/</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">628</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654494&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654517&type= 27.09333420 4.57200003 （ Schalles和Yacobi，2000 Schalles和Yacobi，2000 ）。可以看出，这些算法的反演精度均较高。 Mishra等（2009） Mishra等（2009） 认为使用600 nm代替620 nm，可以有效消除Chla的影响，反演精度得到提高。 Millie等（1992） Millie等（1992） 基于CAMS影像的Orange/red与PC浓度建立经验回归关系，但由于实测PC浓度值准确度的问题，反演精度不高）。 Vincent等（2004） Vincent等（2004） 在美国Lake Erie，基于Landsat TM数据，利用多个波段比为自变量，PC浓度为因变量，进行多元线性回归，取得较好的反演精度。 Medina-Cobo等（2014） Medina-Cobo等（2014） 在西班牙的几个湖泊中，基于MERIS数据的B9和B6波段的差与和之比，成功反演PC浓度。 Varunan和Shanmugam（2017） Varunan和Shanmugam（2017） 在印度富营养化湖泊中，利用实测光谱数据开发了波段比 <math id="M57"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo><mo>/</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">652</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654496&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654495&type= 27.17799950 4.57200003 算法，反演出 <math id="M58"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654518&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654497&type= 13.37733269 4.57200003 的值，然后利用固定 <math id="M59"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654640&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654639&type= 4.31799984 4.06400013 （620）=0.0072，成功反演PC浓度值，然后将算法应用到HICO影像，同样获得了较高反演精度。 Torbick等（2018） Torbick等（2018） 在英格兰北部湖泊，基于Landsat 7 ETM+，Landsat OLI数据，利用NIR/green+NIR/blue算法，反演了PC浓度，并利用GIS空间分析方法将PC浓度与肌肉萎缩病联系起来，建立了肌肉萎缩病风险因子评价体系。Sòria-Perpinyàd等（2020）基于Sentinel-2 MSI影像数据，利用 B 5和 B 4比值算法，成功反演PC浓度。 算法 研究区 数据源 PC/（μg·L -1 ） 模型/算法 验证精度 参考文献 2 经验算法 基线法 Vecht Lakes 实测CASI CAESAR <math id="M60"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mo>-</mo><mn>24.6</mn><mo>+</mo><mn>13686</mn><mfenced separators="|"><mrow><mn>0.5</mn><mfenced separators="|"><mrow><mi>R</mi><mo stretchy="false">(</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>-</mo></mrow></msup><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>600</mn></mrow></msub><mo>+</mo><mi>R</mi><mo stretchy="false">(</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>-</mo></mrow></msup><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>648</mn></mrow></msub></mrow></mfenced><mo>-</mo><mi>R</mi><mo stretchy="false">(</mo><msup><mrow><mn>0</mn></mrow><mrow><mo>-</mo></mrow></msup><msub><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>624</mn></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654533&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654531&type= 67.39466858 4.99533367 R 2 =0.99， RMSE=2.34 μg·L -1 ， N=17 Dekker，1993 Dekker，1993 Lakes in Spain， Netherlands 实测 50—200 R 2 =0.46， RMSE=119.66 μg·L -1 ， N =64 Ruiz-Verdú等，2008 Ruiz-Verdú等，2008 互补 橙线高法 Lake Loosdrecht Landsat 8 OLI 0.01—329.41 <math id="M61"><mtable columnalign="left"><mtr><mtd><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi></mrow></msubsup><mo>=</mo><mn>2.2861</mn><mfenced separators="|"><mrow><mo>±</mo><mn>0.1303</mn></mrow></mfenced><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msubsup><mo>-</mo></mtd></mtr><mtr><mtd><mn>0.9467</mn><mfenced separators="|"><mrow><mo>±</mo><mn>0.0611</mn></mrow></mfenced><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">g</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi></mrow></msubsup><mo>-</mo><mn>0.1989</mn><mfenced separators="|"><mrow><mo>±</mo><mn>0.0712</mn></mrow></mfenced><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">d</mi></mrow></msubsup></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654523&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654521&type= 63.58466721 8.12800026 <math id="M62"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>∝</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654525&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654536&type= 13.54666710 3.13266683 RMSE%=5.39%， N =132 Castagna等，2020 Castagna等，2020 9 波段比 Mississippi impoundments CAMS 22.5—1343.8 <math id="M63"><mi mathvariant="normal">L</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mfenced separators="|"><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mn>3.3</mn><mo>-</mo><mn>0.02</mn><mo>×</mo><mfrac><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">h</mi><mn>3</mn></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">h</mi><mn>4</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">d</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654527&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654526&type= 48.85266495 5.58799982 R 2 =0.35， SE =0.6， N =24 Millie，1992 Millie，1992 Lake Carter 实测 10—530 <math id="M64"><mi mathvariant="normal">L</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mfenced separators="|"><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></mfenced><mo>=</mo><mo>-</mo><mn>117.8</mn><mo>-</mo><mn>99.61</mn><mo>×</mo><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>647</mn></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>628</mn></mrow></msub></mrow></mfrac></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>218.5</mn><mo>×</mo><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>647</mn></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>628</mn></mrow></msub></mrow></mfrac></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654544&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654543&type= 64.93933105 8.63599968 R 2 =0.62， SE =30.92， N =80 Schalles等，2000 Schalles等，2000 Lake Erie Landsat 5 TM Landsat 7 ETM+ 0.9—5 <math id="M65"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mn>47.7</mn><mo>-</mo><mn>9.21</mn><mfrac><mrow><mi>B</mi><mn>3</mn></mrow><mrow><mi>B</mi><mn>1</mn></mrow></mfrac><mo>+</mo><mn>29.7</mn><mfrac><mrow><mi>B</mi><mn>4</mn></mrow><mrow><mi>B</mi><mn>1</mn></mrow></mfrac><mo>-</mo><mn>118</mn><mfrac><mrow><mi>B</mi><mn>4</mn></mrow><mrow><mi>B</mi><mn>3</mn></mrow></mfrac><mo>-</mo><mn>6.81</mn><mfrac><mrow><mi>B</mi><mn>5</mn></mrow><mrow><mi>B</mi><mn>3</mn></mrow></mfrac><mo>+</mo><mn>41.9</mn><mfrac><mrow><mi>B</mi><mn>7</mn></mrow><mrow><mi>B</mi><mn>3</mn></mrow></mfrac><mo>-</mo><mn>14.7</mn><mfrac><mrow><mi>B</mi><mn>7</mn></mrow><mrow><mi>B</mi><mn>4</mn></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654538&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654545&type= 85.59799957 5.58799982 R 2 =0.77， N =30 Vincent等， 2004 Vincent等， 2004 Barton Broad CASI-2 36.62—138.76 <math id="M66"><mi mathvariant="normal">L</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mfenced separators="|"><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></mfenced><mo>=</mo><mn>1.29</mn><mo>+</mo><mn>4.12</mn><mo>×</mo><mi mathvariant="normal">L</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>710</mn></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>620</mn></mrow></msub></mrow></mfrac></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654558&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654540&type= 42.67200089 7.95866632 R 2 =0.95， RMSE=11.9 μg·L -1 Hunter等，2008 Hunter等，2008 Laboratory cultured 实测 <math id="M67"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>a</mi><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>700</mn></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>600</mn></mrow></msub></mrow></mfrac></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654548&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654547&type= 21.25133324 7.95866632 R 2 =0.97， N =79 Mishra等， 2009 Mishra等， 2009 Oneida Lake 实测 0.5—5 <math id="M68"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mo>-</mo><mn>1.6</mn><mo>+</mo><mn>6.8</mn><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn>710</mn><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn>620</mn><mo stretchy="false">)</mo></mrow></mfrac></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654551&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654550&type= 32.76599884 8.29733276 R 2 =0.71， N =22 Effler等，2012 Effler等，2012 Funil Reservoir， Catfish Ponds 实测 R 2 =0.7， RMSE%=18.49%， N =5 Ogashawara等，2013 Ogashawara等，2013 Spanish MERIS 17.1—456.51 <math id="M69"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mn>46.478</mn><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mn>5.186</mn><mfenced separators="|"><mrow><mfenced separators="|"><mrow><mi>B</mi><mn>9</mn><mo>-</mo><mi>B</mi><mn>6</mn></mrow></mfenced><mo>/</mo><mfenced separators="|"><mrow><mi>B</mi><mn>9</mn><mo>+</mo><mi>B</mi><mn>6</mn></mrow></mfenced></mrow></mfenced></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654553&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654552&type= 37.33800125 2.96333337 Medina-Cobo，等，2014 Lake Taihu 实测 158—580 <math id="M70"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mn>585.7</mn><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn>709</mn><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn>620</mn><mo stretchy="false">)</mo></mrow></mfrac><mo>-</mo><mn>667.6</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654555&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654554&type= 33.86666870 7.45066643 R 2 =0.75， N =54 Chi等，2016 Chi等，2016 Daechung Reservoir 实测无人机 0.39—803.01 <math id="M71"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mi>a</mi><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn>709</mn><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn>620</mn><mo stretchy="false">)</mo></mrow></mfrac><mo>+</mo><mi>b</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654557&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654556&type= 23.87599945 7.45066643 R 2 =0.87-0.94， RMSE=14.45 μg·L -1 ， N =96 Kwon，等，2020 Northern New England Landsat 7 ETM+ Landsat 8 OLI 10—100，>100 <math id="M72"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>∝</mo><mfrac><mrow><mi>N</mi><mi>I</mi><mi>R</mi></mrow><mrow><mi>G</mi><mi>r</mi><mi>e</mi><mi>e</mi><mi>n</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654574&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654573&type= 13.97000027 5.58799982 + <math id="M73"><mfrac><mrow><mi>N</mi><mi>I</mi><mi>R</mi></mrow><mrow><mi>B</mi><mi>l</mi><mi>u</mi><mi>e</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654576&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654575&type= 5.58799982 5.58799982 R 2 =0.86， RMSE=11.92 μg·L -1 ， N =305 Torbick等，2018 Torbick等，2018 Sentinel-2 MSI 10—1287.96 <math id="M74"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mi>a</mi><mfrac><mrow><mi>B</mi><mn>5</mn></mrow><mrow><mi>B</mi><mn>4</mn></mrow></mfrac><mo>+</mo><mi>b</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654578&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654577&type= 17.01799965 5.58799982 R 2 =0.84， RMSE%=40%， N =21 Sòria-Perpinyà等，2020 Sòria-Perpinyà等，2020 Lakes in Netherlands 实测 50—200 <math id="M75"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>r</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>709</mn><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>r</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>620</mn><mo stretchy="false">)</mo></mrow></mfrac><mo>-</mo><mn>0.97</mn></mrow></mfenced><mo>×</mo><mn>1096.5</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654580&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654579&type= 39.53932953 8.29733276 R 2 =0.21， RMSE=135.47 μg L -1 ， N =64 Ruiz-Verdú等，2008 Ruiz-Verdú等，2008 4 波段组合回归 Lake Champlain Landsat 8 OLI 0—21 <math id="M76"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mo>-</mo><mn>2.85</mn><mo>+</mo><mi>B</mi><mn>1</mn><mfenced separators="|"><mrow><mn>0.013</mn></mrow></mfenced><mo>+</mo><mi>B</mi><mn>3</mn><mfenced separators="|"><mrow><mo>-</mo><mn>0.43</mn></mrow></mfenced><mo>+</mo><mi>B</mi><mn>4</mn><mo stretchy="false">(</mo><mn>0.76</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654582&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654581&type= 57.99666977 2.87866688 R 2 =0.83， RMSE=1.33 μg L -1 ， N=42 Torbick和Corbiere，2015 Lake Champlain CHRIS 0—21 <math id="M77"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mn>6.2</mn><mo>+</mo><mi>B</mi><mn>2</mn><mfenced separators="|"><mrow><mn>334.8</mn></mrow></mfenced><mo>+</mo><mi>B</mi><mn>6</mn><mfenced separators="|"><mrow><mo>-</mo><mn>1644.3</mn></mrow></mfenced><mo>+</mo><mi>B</mi><mn>8</mn><mfenced separators="|"><mrow><mn>203.16</mn></mrow></mfenced><mo>+</mo><mi>B</mi><mn>11</mn><mfenced separators="|"><mrow><mo>-</mo><mn>709.4</mn></mrow></mfenced><mo>+</mo><mi>B</mi><mn>14</mn><mo stretchy="false">(</mo><mo>-</mo><mn>1324.3</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654584&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654583&type= 96.60466003 2.87866688 R 2 =0.88， RMSE=1.02 μg L -1 Lake Champlain Rapid Eye 0—21 <math id="M78"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mo>-</mo><mn>56.13</mn><mo>+</mo><mi>B</mi><mn>3</mn><mfenced separators="|"><mrow><mn>0.12</mn></mrow></mfenced><mo>+</mo><mi>B</mi><mn>1</mn><mo>/</mo><mi>B</mi><mn>3</mn><mfenced separators="|"><mrow><mn>9.94</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654586&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654585&type= 46.65133286 2.87866688 R 2 =0.77， RMSE=1.52 μg L -1 Laboratory cultured CCD 0—600 <math id="M79"><mi mathvariant="normal">m</mi><mi mathvariant="normal">N</mi><mi mathvariant="normal">D</mi><mi mathvariant="normal">i</mi><mo>=</mo><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">b</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mn>1</mn></mrow></msub><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">b</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mn>2</mn></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">b</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">b</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mn>2</mn></mrow></msub><mo>-</mo><mn>2</mn><mo>×</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">b</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mn>3</mn></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654588&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654587&type= 40.72467041 7.11199999 R 2 =0.96， RMSE=23.16 μg L -1 Hmimina等，2019 Hmimina等，2019 4 多元线性回归 Guarapiranga Reservoir Landsat 5 TM Landsat 7 ETM+ 0.5—40 <math id="M80"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mfenced close="" separators="|"><mrow><mi>A</mi><mo>-</mo><mfenced separators="|"><mrow><mi>B</mi><mfenced separators="|"><mrow><mfrac><mrow><mi>B</mi><mn>3</mn></mrow><mrow><mi>B</mi><mn>1</mn></mrow></mfrac></mrow></mfenced></mrow></mfenced><mo>+</mo><mfenced separators="|"><mrow><mi>C</mi><mfenced separators="|"><mrow><mfrac><mrow><mi>B</mi><mn>4</mn></mrow><mrow><mi>B</mi><mn>1</mn></mrow></mfrac></mrow></mfenced></mrow></mfenced><mo>-</mo></mrow></mfenced></mtd></mtr><mtr><mtd><mfenced separators="|"><mrow><mi>D</mi><mfenced separators="|"><mrow><mfrac><mrow><mi>B</mi><mn>4</mn></mrow><mrow><mi>B</mi><mn>3</mn></mrow></mfrac></mrow></mfenced></mrow></mfenced><mo>-</mo><mfenced separators="|"><mrow><mi>E</mi><mfenced separators="|"><mrow><mfrac><mrow><mi>B</mi><mn>5</mn></mrow><mrow><mi>B</mi><mn>3</mn></mrow></mfrac></mrow></mfenced></mrow></mfenced><mo>-</mo><mfenced separators="|"><mrow><mi>F</mi><mfenced separators="|"><mrow><mfrac><mrow><mi mathvariant="normal">B</mi><mn>7</mn></mrow><mrow><mi mathvariant="normal">B</mi><mn>3</mn></mrow></mfrac></mrow></mfenced></mrow></mfenced><mo>-</mo></mtd></mtr><mtr><mtd><mfenced open="" separators="|"><mrow><mfenced separators="|"><mrow><mi>G</mi><mfenced separators="|"><mrow><mfrac><mrow><mi>B</mi><mn>7</mn></mrow><mrow><mi>B</mi><mn>4</mn></mrow></mfrac></mrow></mfenced></mrow></mfenced></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654590&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654589&type= 47.92133331 25.31533241 R 2 =0.96， N =6 Ogashawara等，2013 Ogashawara等，2013 Lake Dianchi Landsat 5 TM Landsat 7 ETM+ Landsat 8 OLI 77.6—754.9 <math id="M81"><mi mathvariant="normal">L</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mfenced separators="|"><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></mfenced><mo>=</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><mi>B</mi><mn>1</mn></mrow></mfenced><mo>+</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><mi>B</mi><mn>2</mn></mrow></mfenced><mo>+</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><mi>B</mi><mn>3</mn></mrow></mfenced><mo>+</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>4</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><mi>B</mi><mn>4</mn></mrow></mfenced><mo>+</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>5</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><mfrac><mrow><mi>B</mi><mn>4</mn></mrow><mrow><mi>B</mi><mn>3</mn></mrow></mfrac></mrow></mfenced><mo>+</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>6</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><mfrac><mrow><mi>B</mi><mn>4</mn></mrow><mrow><mi>B</mi><mn>2</mn></mrow></mfrac></mrow></mfenced><mo>+</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>7</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><mfrac><mrow><mi>B</mi><mn>4</mn></mrow><mrow><mi>B</mi><mn>1</mn></mrow></mfrac></mrow></mfenced><mo>+</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>8</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><mfrac><mrow><mi>B</mi><mn>3</mn></mrow><mrow><mi>B</mi><mn>2</mn></mrow></mfrac></mrow></mfenced><mo>+</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>9</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><mfrac><mrow><mi>B</mi><mn>3</mn></mrow><mrow><mi>B</mi><mn>1</mn></mrow></mfrac></mrow></mfenced><mo>+</mo><msub><mrow><mi>k</mi></mrow><mrow><mn>10</mn></mrow></msub><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mfrac><mrow><mi>B</mi><mn>2</mn></mrow><mrow><mi>B</mi><mn>1</mn></mrow></mfrac><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654592&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654591&type= 168.57133484 6.43466663 R 2 > 0.97， RMSE < 10%， N =14 Sun等，2015 Sun等，2015 Chao Hu MODIS 6.57—4807.72 <math id="M82"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn>4</mn></mrow></msub><msub><mrow><mi>T</mi></mrow><mrow><mn>4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654594&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654593&type= 43.26466751 3.38666677 R 2 =0.6， RMSE=57%， N =15 Tao等，2017 Tao等，2017 Taihu Lake， ChaoHu Lake 实测MERIS 3.26—804.11 <math id="M83"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mfenced separators="|"><mrow><mn>89.1711</mn><mo>×</mo><mi>B</mi><mn>5</mn><mo>-</mo><mn>262.292</mn><mo>×</mo><mi>B</mi><mn>6</mn><mo>+</mo><mn>221.193</mn><mo>×</mo><mi>B</mi><mn>7</mn><mo>-</mo><mn>1.7065</mn><mo>×</mo><mi>B</mi><mn>8</mn><mo>-</mo><mn>26.1116</mn><mo>×</mo><mi>B</mi><mn>9</mn><mo>+</mo><mn>0.363418</mn></mrow></mfenced><mo>×</mo><mn>100</mn><mi mathvariant="normal">%</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654561&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654595&type= 123.78267670 2.87866688 R 2 =0.72， RMSE=7.56， N =50 Jin等，2017 Jin等，2017 2 高斯函数 Culture ponds， Taihu Lake 实测 77—3032.47 <math id="M84"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>∝</mo><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">g</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654563&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654562&type= 15.74800014 3.38666677 <math id="M85"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">h</mi></mrow></msub><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced><mo>=</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></munderover></mstyle><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>g</mi><mi>u</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mfenced separators="|"><mrow><mo>-</mo><mn>0.5</mn><mo stretchy="false">(</mo><mfrac><mrow><mi>λ</mi><mo>-</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfrac><mo stretchy="false">)</mo></mrow></mfenced></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654565&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654564&type= 46.48199844 7.95866632 <math id="M86"><msub><mrow><mi>σ</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654567&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654566&type= 2.53999996 2.87866688 和 <math id="M87"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">g</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654569&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654568&type= 8.97466660 3.47133350 是第 i 个高斯波段中心波段的 宽度和量级 R 2 =0.94， RMSE=26%， N =40 Wang等，2016 Wang等，2016 Lakes in USA HICO MODIS 0—200 R 2 =0.93， UPAD=34%， N =56 Wang等，2017 Wang等，2017 2 半分析算法嵌套波段比法 Lake Loosdrecht， Lake Ijsselmeer 实测 21.7—79.8 0.8—64.8 <math id="M88"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mfenced separators="|"><mrow><mn>620</mn></mrow></mfenced><mo>=</mo><mfenced separators="|"><mrow><mfenced separators="|"><mrow><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn>709</mn><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn>620</mn><mo stretchy="false">)</mo></mrow></mfrac></mrow></mfenced><mo>×</mo><mfenced separators="|"><mrow><msub><mrow><mi>a</mi></mrow><mrow><mi>w</mi></mrow></msub><mfenced separators="|"><mrow><mn>709</mn></mrow></mfenced><mo>+</mo><msub><mrow><mi>b</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></mfenced></mrow></mfenced><mo>-</mo><msub><mrow><mi>b</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>-</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>w</mi></mrow></msub><mfenced separators="|"><mrow><mn>620</mn></mrow></mfenced></mrow></mfenced><mo>×</mo><msup><mrow><mi>δ</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>-</mo><mfenced separators="|"><mrow><mi>ε</mi><mo>×</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>C</mi><mi>h</mi><mi>l</mi><mi>a</mi></mrow></msub><mfenced separators="|"><mrow><mn>665</mn></mrow></mfenced></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654598&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654597&type= 97.36666107 9.48266602 <math id="M89"><mfenced open="[" close="]" separators="|"><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></mfenced><mo>=</mo><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mfenced separators="|"><mrow><mn>620</mn></mrow></mfenced><mo>/</mo><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup><mo stretchy="false">(</mo><mn>620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654600&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654599&type= 30.81866837 3.55599999 R 2 =0.94， RMSE=6.5 μg·L -1 ， N =34 Simis等，2005 Simis等，2005 Netherlands MERIS Simis等，2007 Simis等，2007 Spain， Netherlands 实测 50—200 同上 R 2 =0.92， RMSE=47.48 μg·L -1 ， N =56 Ruiz-Verdú等，2008 Ruiz-Verdú等，2008 Geist Reservoir， Morse Reservoir 实测 2.1—185.1 同上 R 2 =0.85， RMSE=19.54 μg·L -1 ， N =64 Randolph等，2008 Randolph等，2008 Albufera MERIS 同上 R 2 =0.99， RMSE=28.84 μg·L -1 ， N =38 Guanter等，2010 Guanter等，2010 Valmayor reservoir， Lake Ontario OCMMERIS 3.2—200 同上 R 2 =0.75， RMSE= 36.92μg·L -1 ， N =62 Dash等，2011 Dash等，2011 Geist Reservoir， Morse Reservoir Eagle， Creek Reservoir 实测 1.4—146.1 同上 同上 R 2 =0.86， RMSE%=31.4%， N =37 Li等，2012 Li等，2012 Ge Hu， Dongjiu Hu， Tai Hu 实测 0.09—7.71 同上 R 2 =0.88， RMSE=0.56 μg·L -1 Duan等，2012 Duan等，2012 Lake Champlain Quick Bird MERIS 4.1—105 R 2 =0.68， N =68 Wheeler等，2012 Wheeler等，2012 Lake Taihu 实测 同上 R 2 =0.55， RMSE=58.89 μg·L -1 ， N =52 Lyu等，2013 Lyu等，2013 Lake Chivero， Lake Manyame MERIS 32—114.6 Chawira等，2013 Chawira等，2013 Baekje reservoir AISA 同上 RMSE=14.57 μg·L -1 ， N =45 Pyo等，2018 Pyo等，2018 Lake Balaton MERIS 同上 R 2 =0.75， RMSE=11.8 μg·L -1 ， N =36 Riddick等，2019 Riddick等，2019 Muttukadu coastal 实测HICO 32.7—273.7 同上 R 2 =0.89， RMSE=0.3 μg·L -1 ， N =42 Varunan和Shanmugam，2017 Lake Erie 实测 0.1—5.5 同上 R 2 =0.88， N =28 Ortiz等， 2013 Ortiz等， 2013 5 基于吸收的反演模型 Chennai coastal 155.62—222.64 <math id="M90"><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo stretchy="false">(</mo><mn>620</mn><mo stretchy="false">)</mo><mo>=</mo><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">h</mi></mrow></msub><mo stretchy="false">(</mo><mn>620</mn><mo stretchy="false">)</mo><mo>-</mo><mfenced close="" separators="|"><mrow><mi>ω</mi><mo>×</mo><mi>C</mi><mi>h</mi><mi>l</mi><msup><mrow><mi>a</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>×</mo><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn>620</mn><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mo stretchy="false">(</mo><mn>652</mn><mo stretchy="false">)</mo></mrow></mfrac></mrow></mfenced></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>×</mo></mrow></mfenced></mtd></mtr><mtr><mtd><mfenced separators="|"><mrow><mo stretchy="false">(</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mn>713</mn><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><msup><mrow><mn>652</mn><mo stretchy="false">)</mo></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654602&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654601&type= 62.73799896 16.42533302 R 2 =0.85， RMSE=0.1 μg·L -1 ， N =25 Varunan和Shanmugam，2017 Lake Taihu 实测 5—68 R 2 =0.76， SD =12.58， N =20 Yang等，2005 Yang等，2005 Geist Reservoir， Morse Reservoir， Eagle Creek Reservoir 实测 0.73—370.95 同上 R 2 =0.81， rRMSE%=33.60% Li等，2015 Li等，2015 Taihu Lake OLCI <math id="M91"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mfenced separators="|"><mrow><mn>620</mn></mrow></mfenced><mo>=</mo><mfrac><mrow><msub><mrow><mi>φ</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">h</mi></mrow></msub><mo stretchy="false">(</mo><mn>620</mn><mo stretchy="false">)</mo><mo>-</mo><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">h</mi></mrow></msub><mo stretchy="false">(</mo><mn>665</mn><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>φ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>-</mo><msub><mrow><mi>φ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654604&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654603&type= 40.72467041 7.28133297 R 2 =0.69， N =148 Miao等，2020 Miao等，2020 Loskop Dam， Hartbeespoort Dam， Theewaterskloof Dam 实测 0.5—4.8 <math id="M92"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mfenced separators="|"><mrow><mn>620</mn></mrow></mfenced><mo>=</mo><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">h</mi></mrow></msub><mo stretchy="false">(</mo><mn>620</mn><mo stretchy="false">)</mo><mo>-</mo><mn>0.24</mn><mo>×</mo><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">h</mi></mrow></msub><mo stretchy="false">(</mo><mn>665</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654606&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654605&type= 45.63533020 3.38666677 R 2 =0.95， RMSE=0.41 μg·L -1 Matthews等，2020 Matthews等，2020 3 三波段 Loch Leven， Esthwaite Water CASI-2 AISA 58.1—93.7 5.74—24.9 <math id="M93"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mi>a</mi><mfenced separators="|"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfenced></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfenced></mrow></mfrac></mrow></mfenced><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced><mo>+</mo><mi>b</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654608&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654607&type= 46.56666946 8.55133343 R 2 =0.98， RMSE=3.98 μg·L -1 ， N =56 Hunter等，2010 Hunter等，2010 Lake Taihu 实测 Zhang等，2015 Zhang等，2015 Eagle Creek Reservoir 实测 0.7—234.3 同上 R 2 =0.73， RMSE=7.31 μg·L -1 ， N =222 Song等， 2013 Song等， 2013 aquacultureponds 实测 68.13—3032.47 同上 R 2 =0.99， RMSE=30.70%， N =38 Mishra等， 2013 Mishra等， 2013 2 四波段 Lake Taihu 实测 0.13—90.96 <math id="M94"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mfenced separators="|"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>r</mi><mi>s</mi></mrow></msub><mfenced separators="|"><mrow><mn>625</mn></mrow></mfenced></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>r</mi><mi>s</mi></mrow></msub><mfenced separators="|"><mrow><mn>650</mn></mrow></mfenced></mrow></mfrac></mrow></mfenced><mfenced separators="|"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>r</mi><mi>s</mi></mrow></msub><mfenced separators="|"><mrow><mn>730</mn></mrow></mfenced></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>r</mi><mi>s</mi></mrow></msub><mfenced separators="|"><mrow><mn>695</mn></mrow></mfenced></mrow></mfrac></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654610&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654609&type= 60.62133789 8.55133343 R 2 =0.86， RMSE=6.8 μg·L -1 ， N =62 Le等，2011 Le等，2011 Lake Dianchi 实测 0—350 <math id="M95"><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi><mo>=</mo><mfenced separators="|"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>r</mi><mi>s</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfenced></mrow></mfrac><mo>-</mo><mfrac><mrow><mi>η</mi></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>r</mi><mi>s</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfenced></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>1</mn><mo>-</mo><mi>η</mi></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi>r</mi><mi>s</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow></mfrac></mrow></mfenced><msub><mrow><mi>R</mi></mrow><mrow><mi>r</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>4</mn></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654612&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654611&type= 52.15466690 10.66800022 R 2 =0.69， RMSE=27.69 μg·L -1 ， N =68 Liu，2018 Liu，2018 2 准分析模型 Lake Erie MODIS QAA Becker等， 2009 Becker等， 2009 Culture ponds 实测 68.13—3032.47 QAA RMSE%=10.06%， N =44 Mishra等， 2013 Mishra等， 2013 10 机器学习算法 Morse Reservoir 实测AISA 1.4—371.0 遗传算法（GA） R 2 =0.88， RMSE=18.6 μg·L -1 ， N =61 Song等， 2012a Song等， 2012a Lake Taihu， Lake Chaohu， Lake Dianchi 实测 支持向量机（SVR Machine） R 2 =0.9， RMSE=53.1 μg·L -1 ， N =824 Sun等，2013 Sun等，2013 Lake Alexandrina， Eagle Creek Reservoir 实测 0.3—220.7 偏最小二乘—神经网络（PLS-ANN） R 2 =0.92， RMSE=15.24 μg·L -1 ， N =376 Song等， 2014 Song等， 2014 Geum River Aisa FENIX 人工神经网络（ANN） Park等，2017 Park等，2017 Baekje Reservoir 实测AISA 0.02—280.87 叠堆自编码神经网络（SAE-DNN） R 2 =0.87， RMSE=14.45 μg·L -1 Yim等，2020 Yim等，2020 Baekje Reservoir 实测AISA 0.19—150.9 卷积神经网络（CNN） R 2 =0.86， RMSE < 10， N =45 Pyo等，2019 Pyo等，2019 Meramec River， Carlye Lake， Lake Decatur 实测 0.1—6 多元线性回归（MLR） 偏最小二乘（PLSR） 高斯函数 R 2 =0.78， RMSE=1.586 μg·L -1 ， N =60 R 2 =0.96， RMSE=0.92μg·L -1 R 2 =0.97， RMSE=0.886μg·L -1 Peterson等，2019 Peterson等，2019 支持向量机（SVR） R 2 =0.96， RMSE=0.79 μg·L -1 极端机器学习（ELR） R 2 =0.97， RMSE=0.86 μg·L -1 Baekje Reservoir 实测AISA 0.19—146.9 叠堆自编码支持向量机（SAE-SVR） R 2 =0.80， RMSE=17.94 μg·L -1 ， N =45 Pyo等，2020 Pyo等，2020 3 衍生算法 光谱形状 Michigan lake， Huron Lake， Bear Lake 实测 <math id="M96"><mi>S</mi><mi>S</mi><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced><mo>=</mo><mi>r</mi><mi>e</mi><mi>f</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mfenced separators="|"><mrow><mi>λ</mi></mrow></mfenced><mo>-</mo><mi>r</mi><mi>e</mi><mi>f</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mfenced separators="|"><mrow><msup><mrow><mi>λ</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></mfenced><mo>-</mo><mfenced separators="|"><mrow><mi>r</mi><mi>e</mi><mi>f</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mfenced separators="|"><mrow><msup><mrow><mi>λ</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></mfenced><mo>-</mo><mi>r</mi><mi>e</mi><mi>f</mi><mi>l</mi><mi>e</mi><mi>c</mi><mi>t</mi><mfenced separators="|"><mrow><msup><mrow><mi>λ</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></mfenced></mrow></mfenced><mo>×</mo><mfrac><mrow><mo stretchy="false">(</mo><mi>λ</mi><mo>-</mo><msup><mrow><mi>λ</mi></mrow><mrow><mo>-</mo></mrow></msup><mo stretchy="false">)</mo></mrow><mrow><msup><mrow><mi>λ</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>-</mo><msup><mrow><mi>λ</mi></mrow><mrow><mo>-</mo></mrow></msup></mrow></mfrac></math> 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http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654615&type= 30.64933395 3.38666677 <math id="M98"><msubsup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow><mrow><mi>'</mi></mrow></msubsup><mfenced separators="|"><mrow><mn>620</mn></mrow></mfenced><mo>=</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><mn>560</mn></mrow></mfenced><mo>+</mo><mfrac><mrow><mn>620</mn><mo>-</mo><mn>560</mn></mrow><mrow><mn>665</mn><mo>-</mo><mn>560</mn></mrow></mfrac><mo>×</mo><mo stretchy="false">(</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><mn>665</mn></mrow></mfenced><mo>-</mo><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">r</mi><mi mathvariant="normal">s</mi></mrow></msub><mfenced separators="|"><mrow><mn>560</mn></mrow></mfenced><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654618&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654617&type= 67.64866638 5.58799982 R 2 =0.79， RMSE%=58%， N =37 Qi等，2014 Qi等，2014 Pinto Lake，Kelly Lake，UCSB Lagoon 实测HICO MASTER 12.8—156.7， 0—261.5 R 2 =0.24， N =20 Kudela等，2015 Kudela等，2015 除了波段比使用较多外，由 Dekker（1993） Dekker（1993） 提出的基线法，也经常用于PC遥感反演，Ruiz-Verdú等人在西班牙荷兰水体中，对比了基线法和Simis嵌套法对PC反演的效果，两个算法都取得较高精度，Simis嵌套法精度更高一些（ Ruiz-Verdú等，2008 Ruiz-Verdú等，2008 ）。另外， Castagna等（2020） Castagna等（2020） 基于Landsat 8 OLI互补色橙线高算法，成功反演PC浓度。 Tao等（2017） Tao等（2017） 基于MODIS影像，利用多元线性回归，成功地反演了中国巢湖PC浓度。 Sun等（2015） Sun等（2015） 在中国巢湖，基于Landsat系列卫星，利用可见光、近红外及两者之比，进行多元线性回归，成功反演PC浓度。除这些算法外，还有高斯函数（ Wang等，2016 Wang等，2016 ， 2017 2017 ），正交函数（ Soja-Woźniak等，2017 Soja-Woźniak等，2017 ），波段差（ Beck等，2017 Beck等，2017 ）等经验算法用于PC浓度的遥感估算。 5.2　半分析算法 2 为了克服上述经验算法的缺点，近年来基于水体固有光学特性（IOPs）结合一些经验关系及水体辐射传输理论，提出的半分析方法受到更多关注。一般的，半分析算法包括：三波段算法、四波段算法、嵌套波段比算法、准分析算法（QAA）、衍生算法（光谱形状算法SS）等。这些算法主要致力于解决以下3个问题：大气校正、620 nm处藻类吸收的分解和足够的光谱分辨率（ Yan等，2018 Yan等，2018 ）。未来的半分析算法将致力于最小化其他色素对PC反演的影响。 嵌套波段比算法最早由 Simis等（2005） Simis等（2005） 开发出来，此算法基于3个假设：第一， <math id="M99"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">h</mi></mrow></msub><mfenced separators="|"><mrow><mi mathvariant="normal">λ</mi></mrow></mfenced><mo>=</mo><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">a</mi></mrow></msub><mfenced separators="|"><mrow><mi mathvariant="normal">λ</mi></mrow></mfenced><mo>+</mo><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mfenced separators="|"><mrow><mi mathvariant="normal">λ</mi></mrow></mfenced></math> 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http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654634&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654633&type= 14.39333248 4.14866638 的贡献；第三，固定单位吸收 <math id="M102"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654640&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654639&type= 4.31799984 4.06400013 （620）的值，此算法在其特定研究区内，反演精度很高。然而，在其他研究区，第二和第三假设引起的误差较大，因为这两个值都不是固定的，是随地域和时间变异的。后来，以此算法为基础的各种变体算法被广泛用于各个地区的PC反演研究。其中， Randolph等（2008） Randolph等（2008） 将算法的 <math id="M103"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654640&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654639&type= 4.31799984 4.06400013 （620）更改为0.007，应用于美国印第安那州的3个富营养化的水库，取得很好的反演精度。 Duan等（2012） Duan等（2012） 和 Yin等（2011） Yin等（2011） 将此算法应用于中国太湖，取得较高反演精度。 Wheeler等（2012） Wheeler等（2012） 则是将此算法应用到法国Champlain湖，利用Quick Bird和MERIS数据，获得良好的反演精度。 Lyu等（2013） Lyu等（2013） 是以高度富营养化的太湖为研究对象，改进了算法中两个系数，并用非线性幂函数来代替固定的 <math id="M104"><msubsup><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow><mrow><mi>*</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654640&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654639&type= 4.31799984 4.06400013 （620），并阐述了总悬浮颗粒物（TSM）对反演结果的影响。 Chawira 等（2013） Chawira 等（2013） 和 Zhang等（2015） Zhang等（2015） 利用此算法，基于MERIS数据分别对非洲津巴布韦和美国大部分湖泊进行了PC反演。除嵌套波段比算法，一些从遥感反射率估算 <math id="M105"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mfenced separators="|"><mrow><mn mathvariant="normal">620</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654642&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654641&type= 13.03866673 4.14866638 的半分析算法不断涌现（ Li等，2015 Li等，2015 ； Matthews等，2020 Matthews等，2020 ； Miao等，2020 Miao等，2020 ）。这些算法主要是从总吸收中分离出PC在620 nm的吸收，消除了Chla、CDOM和非PC物质的干扰。另一种是基于准分析模型（QAA）来分离各组分的吸收系数，将QAA算法的波段修改后，应用于 <math id="M106"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654624&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654623&type= 13.37733269 4.57200003 的估算，修改的算法成功的从总藻类吸收中分离出 <math id="M107"><msub><mrow><mi>a</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">C</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">620</mn><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654624&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28654623&type= 13.37733269 4.57200003 。该算法的优点在于没有忽略CDOM和非藻类颗粒物吸收的贡献（ Mishra等，2013 Mishra等，2013 ； Lee等，2002 Lee等，2002 ）。 三波段和四波段算法最早被发明用与Chla的遥感反演研究。 Hunter等（2010） Hunter等（2010） 将算法中的Chla特征吸收波段更改为PC特征吸收波段，第一次将此算法引入到PC遥感反演研究中，并获得较高的反演精度。后来 Song等（2012a） Song等（2012a） 对比了三波段和波段比模型对PC反演的效果，发现三波段算法优于波段比算法。 Le等（2011） Le等（2011） 是将算法中的Chla特征吸收波段更改为PC特征吸收波段，第一次将四波段算法引入到PC遥感反演研究中，随后 Liu等（2018） Liu等（2018） 将修改后的四波段算法应用滇池。 QAA算法最早由 Lee等（2002） Lee等（2002） 提出，其优点是基于表观光学量AOPs和经验关系，将水体中3大光学活性物质CDOM、藻类、非藻类颗粒物在总吸收的贡献中分解成每个独立的变量，最后，依据各物质吸收系数实现其浓度的定量反演。QAA算法可以最大程度的减少各物质间的干扰，但需要大量实测数据。QAA算法多用于3大光学活性物质定量遥感反演，很少应用于PC遥感反演。 Becker等（2009） Becker等（2009） 和 Mishra等（2013） Mishra等（2013） 将QAA算法中相关波段修改成PC特征波段，分别基于MODIS和实测高光谱数据，实现了PC遥感估算。 5.3　衍生算法 2 衍生算法最早由 Wynne等（2008） Wynne等（2008） 提出，又叫做光谱形状算法 SS （ λ ），此算法是基于光谱曲线中PC特征吸收谷和其他峰或谷的位置形成特定的光谱形状，可用波段有620 nm、560 nm、654 nm、681 nm、714 nm等。 Wynne等（2008） Wynne等（2008） 和 Wynne等（2010） Wynne等（2010） 基于实测光谱数据和MERIS影像，利用SS（681）算法对美国密歇根湖和伊利湖PC浓度进行遥感估算。 Qi等（2014） Qi等（2014） 将其修改的光谱形状算法称之为PCI指数基于实测光谱，在太湖PC遥感反演中取得较好精度，随后PCI指数多次被用于PC遥感估算（ Kudela等，2015 Kudela等，2015 ； Sayers等，2019 Sayers等，2019 ）。 5.4　基于机器学习的算法 2 近年来，随着计算机技术的迅速发展，遥感反演研究算法开发越来越依赖计算机，以期获得高精度反演结果。机器学习是一门多领域交叉学科，涉及概率论、统计学、逼近论、凸分析、算法复杂度理论等多门学科。他是人工智能的核心，在全球人工智能浪潮的背景下，遥感算法开发也融入了机器学习算法，先后出现了遗传算法（ Song等，2012b Song等，2012b ）、支持向量机算法（ Sun等，2013 Sun等，2013 ）、人工神经网络算法（ Park等，2017 Park等，2017 ； Song等，2014 Song等，2014 ）、堆叠自编码算法（ Yim等，2020 Yim等，2020 ）、机器学习（ Peterson等，2019 Peterson等，2019 ； Pyo等，2020 Pyo等，2020 ）。尤其是近两年，机器学习算法大量地出现在PC遥感反演研究中，与上述几种算法相比，这类算法遥感估算精度很高， R 2 > 0.88，RMSE较低，且其适用多种数据源。但是，这类算法过多地依赖数理分析，缺少与水体固有光学特性和表观光学特性关联的机理研究。所以，未来PC算法的发展还是会以机理研究为主，机器学习为辅。 5.5　间接估算方法 2 上述反演算法多数是利用遥感反射率数据或影像直接与实测PC浓度建立关系，然而一些利用中间桥梁，如浊度、漫衰减系数 K d ，经二步法间接实现PC遥感估算的方法也鲜有报道。Gitelson发现PC浓度与 K d 值相关性很好（ Gitelson等，1995 Gitelson等，1995 ），虽然文中并没有利用这个关系反演PC浓度，但这一发现为未来间接反演PC奠定了基础。另外，Richard Beck研究发现，PC浓度与浊度的关系为良好的正相关关系，并借助浊度与遥感反射率的关系，成功反演了PC浓度（ Beck等，2019 Beck等，2019 ）。 6　卫星传感器 1 PC遥感反演算法开发的最终目的是可以将这些算法成功地应用到卫星影像上，以期进行水体中PC浓度在时间空间的遥感估算，为相关部门水质监管提供技术支撑。目前，PC反演算法的开发、验证多使用实测高光谱数据或航空影像（CASI-2、AISA Eagle），然而，为满足一定空间和频次上的PC浓度分布需要，多使用卫星影像数据源。首先，对于多光谱卫星数据，只有MERIS、Sentinel-3 OLCI影像数据具有PC敏感波段，是应用于PC遥感反演研究最多的数据源。对于一些不具备PC敏感波段的传感器，如Landsat系列、MODIS等，则可以通过构建多参数模型算法来弥补其波段设置的缺点。除多光谱传感器外，高光谱卫星影像数据（如Hyperion、HICO）也被用于PC空间反演研究中。 6.1　Landsat系列数据 2 Landsat数据具有较高的空间分辨率（30 m）和较长时间跨度（1980年代），但其波段设置没有覆盖PC特征吸收波段（620 nm）。尽管如此，一些研究者仍然开发了一些巧妙的算法利用Landsat数据，成功进行PC反演制图。 Vincent等（2004） Vincent等（2004） 等利用Landsat 5 TM，Landsat 7 ETM+，结合多个波段比线性回归算法B3/B1、B4/B1、B4/B3、B5/B3、B7/B3、B7/B4对美国伊利湖PC浓度进行反演并制图，适用于PC浓度范围为0.9—5μg·L -1 。 Torbick等（2018） Torbick等（2018） 利用Landsat 7 ETM+数据和Landsat 8 OLI数据，结合NIR/green和NIR/blue波段比回归模型对英格兰北部湖泊PC含量进行反演并制图（ Torbick等，2018 Torbick等，2018 ）。 Sun等（2015 Sun等（2015 利用相同的方法在滇池进行了PC浓度制图。最有趣的是， Castagna等（2020） Castagna等（2020） 利用Landsat 8 OLI波段互补色与PC浓度建立关系，提出橙线高Orange Line Height（OLH）算法，成功的反演PC浓度。 6.2　MERIS/Sentinel 3 OLCI数据 2 MERIS影像数据具有300 m空间分辨率，2—3 d的重访周期，15个波段设置，较高的信噪比。对比于其他卫星，MERIS数据在615—905 nm具有更多的波段，这个区域覆盖了多个反射率特征用于PC遥感估算。大多数研究使用MERIS数据进行PC反演，已经证明其良好的辐射、空间、时间、光谱分辨率。 Simis等（2005） Simis等（2005） 基于MERIS影像数据结合嵌套波段比算法，获得较高PC反演精度。 Guanter等（2010） Guanter等（2010） 基于MERIS影像数据结合嵌套波段比算法，对欧洲75个湖泊的PC浓度进行遥感估算。 Wynne等（2010） Wynne等（2010） 基于MERIS数据，利用光谱形状算法，对伊利湖进行了PC浓度遥感估算。不幸的是，MERIS数据在2012年停止提供，但欧空局的Sentinel-3 OLCI数据继承了MERIS数据的配置和优点，继续被用于PC遥感反演研究。 Miao（2020） Miao（2020） 基于OLCI影像结合半分析算法，反演太湖、巢湖PC浓度。 Song等（2013） Song等（2013） 利用实测光谱数据模拟OLCI波段，采用三波段算法，很好的估算了PC浓度。 Beck等（2019） Beck等（2019） 利用同一套数据对比了多个传感器，WorldView-2/3、Sentinel-2 MSI、Landsat 8 OLI、MODIS、MERIS、OLCI对PC估算的能力，结果表明，相比于其他传感器，OLCI具有与MERIS一样的高精度。OLCI数据也被用于其他卫星传感器反演结果的验证（ Castagna等，2020 Castagna等，2020 ）。 6.3　MODIS数据 2 MODIS数据具有2景/d影像的高重访时间，前两个波段具有相对高的空间分辨率250 m，然而MODIS波段设置没有覆盖PC特征吸收波段。基于这个特点，大多数利用MODIS数据进行PC反演的研究，通常使用经验算法，如多项式拟合，多元线性回归（ Tao等，2017 Tao等，2017 ），高斯函数（ Wang等，2017 Wang等，2017 ）等。 7　结语 1 本综述通过文献计量方法，从多角度系统地对当前藻蓝蛋白光学特性（吸收特性和反射特性）、反演算法、与其他水质参数的关系、多源遥感影像应用的研究、发展趋势及取得的新成果进行了梳理。结果表明，PC的光学特性随营养等级、季节、空间变异。目前已开发了多种PC反演算法，包括经验模型，半分析模型、生物光学模型等，应用多种遥感数据源对水体进行了PC空间反演，对富营养化水体蓝藻生物量估算、水环境检测与保护具有重要意义。本综述注重对PC光学性质、反演算法开发和验证、影响因素分析的梳理，并指出当前研究的难点和未来的发展方向。在研究难点方面，首先，PC的萃取测试方法无统一标准，导致多个报道中实测PC浓度无法进行对比和引用，使得基于文献收集的更大尺度，例如全国尺度、或全球尺度的PC遥感反演建模难以建立，另外，PC光谱信号弱，易受大气和其他光学活性物质的干扰。PC：Chla比值作为蓝藻在总藻中的相对比例，是对PC估算干扰最大的因素（ Hunter等，2008 Hunter等，2008 ； Li等，2015 Li等，2015 ； Simis等，2005 Simis等，2005 ）。另外，由于非藻类颗粒物后向散射可以掩盖PC光谱信号，所以PC：TSM比值是对PC估算干扰的第二大因素。有些报道称，根据Chla、TSM取值范围，对水体进行分类后，再反演PC，可以有效消除二者的干扰（ 郭一洋等，2016 郭一洋等，2016 ）。因此，合理处理这些干扰因素，正是准确反演PC的关键。 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Harmful Algae , 17 : 35 - 39 [ DOI: 10.1016/j.hal.2012.02.009 http://dx.doi.org/10.1016/j.hal.2012.02.009 ] An improved phycobilin extraction method 致谢:此论文感谢温志丹副研究员、刘阁副研究员、尚盈辛特别研究助理等老师们在文章写作构思上的指导和帮助，同时还感谢陶慧、王翔、蒲静、王强、侯俊斌、徐世琦、陈方方等同学们在数据查找收集过程中的帮助。 10.11834/jrs.20221276 1007-4619（2022）01-0032-17 吕丽丽，宋开山，刘阁，温志丹，尚盈辛，李思佳.2022.内陆水体藻蓝蛋白遥感反演研究进展.遥感学报，26（1）： 32-48 吕丽丽，宋开山，刘阁，温志丹，尚盈辛，李思佳.2022.内陆水体藻蓝蛋白遥感反演研究进展.遥感学报，26（1）： 32-48 Lyu L L，Song K S，Liu G，Wen Z D，Shang Y X and Li S J. 2022. Advances in remote sensing of phycocyanin for inland waters. National Remote Sensing Bulletin， 26（1）：32-48 Lyu L L，Song K S，Liu G，Wen Z D，Shang Y X and Li S J. 2022. Advances in remote sensing of phycocyanin for inland waters. National Remote Sensing Bulletin， 26（1）：32-48 国家自然科学基金（编号：41730104） Supported by National Natural Science Foundation of China (No. 41730104) 2021-04-30 2022-01-07 2022-05-31 2021-11-18 遥感学报 1 26