气候变化领域集成服务门户(CCPortal): Mathematical Assessment of the Effects of Substituting the Band Radiative Transfer Equation (RTE) for the Spectral RTE in the Applications of Earth's Surface Temperature Retrievals from Spaceborne Infrared Imageries

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DOI	10.3390/rs11030226
	Mathematical Assessment of the Effects of Substituting the Band Radiative Transfer Equation (RTE) for the Spectral RTE in the Applications of Earth's Surface Temperature Retrievals from Spaceborne Infrared Imageries
	Liu, Chunguang; Shi, Jiancheng; Wang, Tianxing; Ram, Kirpa; Zhao, Tianjie
通讯作者	Wang, TX (通讯作者)
发表日期	2019
EISSN	2072-4292
卷号	11 期号:3
英文摘要	The Planck's thermal emission function, the reflectivity-emissivity decoupled Kirchhoff's law and the associated atmospheric radiative transfer equation (RTE) is a theoretical base for Earth surface temperature (ST) retrievals from spaceborne infrared imageries. The infrared (IR) instruments generally collect band averaged radiance which are usually different from the RT codes simulated spectral one. Although IR band RTE is widely used, the effects of substituting the band-averaged RTE for the corresponding spectral one for those broadband observations (e.g., the Moderate Resolution Imaging Spectroradiometer (MODIS) thermal IR bands) have not been evaluated. In this paper, mathematical analysis and numerical experiments have been conducted to clarify the uncertainties arising from this substitution treatment. Firstly, we present the IR spectral RTE in a concise manner, and then, based on the law of conservation of energy and the integral assumption, a detailed mathematical derivation of the commonly-used IR band RTE has been derived. The significant improvement of the derivation is the validation of the integral assumption, which states that over a small spectral region, the integral of a product is approximately equal to the product of integrals. In the IR spectral region, taking the most significant term of the IR band RTE as an example (i.e., the surface emission term), we confirmed that, for the satellite collected IR signals emitted from the Earth's surface, over any bandwidth at any band-location and under any instrument spectral response function (SRF), the integral approximation (IA) is a well-founded approximation and thus the IR band RTEs are good approximations for the corresponding spectral ones. Furthermore, in the ST, especially the land ST, product validation investigations, the ST errors introduced by the substituting treatment are negligible and do not need to be taken into consideration.
关键词	SPLIT-WINDOW ALGORITHM LANDSAT-TM DATA TRANSFER MODEL EMISSIVITY VALIDATION ATMOSPHERE EMISSIONS POPULATIONS CALIBRATION PROFILE
英文关键词	Lambertian reflection assumption; IR spectral RTE; spectral response function; bandwidth; IR band RTE; surface-leaving radiance; attenuated surface-leaving radiance; surface temperature
语种	英语
WOS研究方向	Environmental Sciences & Ecology ; Geology ; Remote Sensing ; Imaging Science & Photographic Technology
WOS类目	Environmental Sciences ; Geosciences, Multidisciplinary ; Remote Sensing ; Imaging Science & Photographic Technology
WOS记录号	WOS:000459944400014
来源期刊	REMOTE SENSING
来源机构	中国科学院青藏高原研究所
文献类型	期刊论文
条目标识符	http://gcip.llas.ac.cn/handle/2XKMVOVA/259491
推荐引用方式 GB/T 7714	Liu, Chunguang,Shi, Jiancheng,Wang, Tianxing,et al. Mathematical Assessment of the Effects of Substituting the Band Radiative Transfer Equation (RTE) for the Spectral RTE in the Applications of Earth's Surface Temperature Retrievals from Spaceborne Infrared Imageries[J]. 中国科学院青藏高原研究所,2019,11(3).
APA	Liu, Chunguang,Shi, Jiancheng,Wang, Tianxing,Ram, Kirpa,&Zhao, Tianjie.(2019).Mathematical Assessment of the Effects of Substituting the Band Radiative Transfer Equation (RTE) for the Spectral RTE in the Applications of Earth's Surface Temperature Retrievals from Spaceborne Infrared Imageries.REMOTE SENSING,11(3).
MLA	Liu, Chunguang,et al."Mathematical Assessment of the Effects of Substituting the Band Radiative Transfer Equation (RTE) for the Spectral RTE in the Applications of Earth's Surface Temperature Retrievals from Spaceborne Infrared Imageries".REMOTE SENSING 11.3(2019).