DLR-Logo -> http://www.dlr.de
DLR Portal Home | Imprint | Privacy Policy | Contact | Deutsch
Fontsize: [-] Text [+]

The contribution and weighting functions of radiative transfer - theory and application to the retrieval of upper-tropospheric humidity

Gierens, Klaus Martin and Eleftheratos, Kostas (2020) The contribution and weighting functions of radiative transfer - theory and application to the retrieval of upper-tropospheric humidity. Meteorologische Zeitschrift, pp. 1-10. Borntraeger Science Publishers. doi: 10.1127/metz/2020/0985. ISSN 0941-2948.

[img] PDF - Postprint version (accepted manuscript)

Official URL: https://www.schweizerbart.de/papers/metz/detail/prepub/92839/The_contribution_and_weighting_functions_of_radiative_transfer_theory_and_application_to_the_retrieval_of_upper_tropospheric_humidity


Several interesting problems in remote sensing can be traced back to the question of the origin along the line of sight of the registered photons. In this paper we revive old concepts that directly follow from the equation of radiative transfer, namely the contribution and weighting functions. We give them, however, a new mathematical form by transforming them into a pair of probability density functions which have the advantage that they can be used in a more flexible manner. We derive these functions, demonstrate a simple relation between them and show how they can be used in principle. Then we proceed with simple applications to a case of upper-tropospheric humidity (UTH) retrieval. In particular, we show how the mean emission pressure level and mean emission temperature change with increasing UTH. We show that the mean emission pressure increases with increasing humidity and remains almost unchanged for UTH values greater than 50 %. The mean emission temperature is decreasing exponentially as UTH increases. The sensitivities of the mean emission pressure to various quantities, e.g. the temperature lapse rate, or retrieval situations, e.g. whether UTH or UTH with respect to ice is considered or which of two different versions of a receiver is used, is generally small compared to the 2σp-width of the layer. The relation of the contribution and weighting functions to Jacobians is discussed as well. We note that the dependence of the mean emission pressure level and other statistical quantities can be formulated using the radiances or brightness temperatures directly. The new method thus offers additional possibilities for interpretation of data from passive remote sensing, and examples are given. In addition of deriving the desired product (for instance, UTH) one can derive and map the mean emission location, its width, and other physical properties like mean temperature of the emission layer. The necessary probability density functions are contained in the solution of the radiative transfer equation and can thus be obtained from runs of the corresponding models. We recommend that radiative transfer models be equipped with facilities to compute and output the contribution and weighting functions.

Item URL in elib:https://elib.dlr.de/134904/
Document Type:Article
Title:The contribution and weighting functions of radiative transfer - theory and application to the retrieval of upper-tropospheric humidity
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Gierens, Klaus MartinDLR, IPAhttps://orcid.org/0000-0001-6983-5370UNSPECIFIED
Eleftheratos, KostasNational and Kapodistrian University of Athens, Athen, GriechenlandUNSPECIFIEDUNSPECIFIED
Journal or Publication Title:Meteorologische Zeitschrift
Refereed publication:Yes
Open Access:Yes
Gold Open Access:Yes
In ISI Web of Science:Yes
Page Range:pp. 1-10
Publisher:Borntraeger Science Publishers
Keywords:statistical methods, upper-tropospheric humidity, satellite data, contribution function
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:air traffic management and operations
DLR - Research area:Aeronautics
DLR - Program:L AO - Air Traffic Management and Operation
DLR - Research theme (Project):L - Climate, Weather and Environment (old)
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Atmospheric Physics
Institute of Atmospheric Physics > Earth System Modelling
Deposited By: Gierens, Dr.rer.nat. Klaus Martin
Deposited On:13 May 2020 12:28
Last Modified:24 Oct 2023 14:15

Repository Staff Only: item control page

Help & Contact
electronic library is running on EPrints 3.3.12
Website and database design: Copyright © German Aerospace Center (DLR). All rights reserved.