Availability of an equation to evaluate error by optical path discretization in radiative transfer computation based on the successive order of scattering method

2011 ◽  
Vol 68 (1) ◽  
pp. 215-218 ◽  
Author(s):  
Akihiko Tanaka ◽  
Masahiko Fujii ◽  
Tomohiko Oishi
Keyword(s):  
Radiative Transfer ◽  
Optical Path ◽  
Scattering Method

scholarly journals An Improved Small-Angle Approximation for Forward Scattering and Its Use in a Fast Two-Component Radiative Transfer Method

2017 ◽  
Vol 74 (6) ◽  
pp. 1959-1987 ◽  
Author(s):  
Bingqiang Sun ◽  
George W. Kattawar ◽  
Ping Yang ◽  
Eli Mlawer
Keyword(s):  
Radiative Transfer ◽  
Small Angle ◽  
Delta Function ◽  
Computational Effort ◽  
Forward Scattering ◽  
Scattering Method ◽  
Diffuse Component ◽  
Dirac Delta ◽  
Small Angle Approximation ◽  
Two Component

Abstract The vector radiative transfer equation is decomposed into two components: a forward component and a diffuse component. The forward component is analytically solved with a small-angle approximation. The solution of the forward component becomes the source for the diffuse component. In the present study, the diffuse component is solved using the successive order of scattering method. The strong anisotropy of the scattering of radiation by a medium is confined to the forward component for which a semianalytical solution is given; consequently, the diffuse component slowly varies as a function of scattering angle once the forward-scattering peak is removed. Moreover, the effect on the diffuse component induced by the forward component can be interpreted by including the low orders of the generalized spherical function expansion of the forward component or even replaced by the Dirac delta function. As a result, the computational effort can be significantly reduced. The present two-component method is validated using the benchmarks related to predefined aerosol and cloud layers with a totally absorbing underlying surface. As a canonical application, the optical properties of water clouds and ice clouds used for the Moderate Resolution Imaging Spectroradiometer (MODIS) Collection 6 cloud-property retrieval products are used for radiative transfer simulations under cloudy conditions.

Multi-coupled single scattering method of solving vector radiative transfer equations

2012 ◽  
Vol 21 (12) ◽  
pp. 129501 ◽  
Author(s):  
Bin Sun ◽  
Han Wang ◽  
Xiao-Bing Sun ◽  
Jin Hong ◽  
Yun-Jie Zhang
Keyword(s):  
Radiative Transfer ◽  
Single Scattering ◽  
Scattering Method ◽  
Transfer Equations ◽  
Radiative Transfer Equations

scholarly journals Impact of 3D radiative transfer on airborne NO<sub>2</sub> imaging remote sensing over cities with buildings

2021 ◽  
Vol 14 (10) ◽  
pp. 6469-6482
Author(s):  
Marc Schwaerzel ◽  
Dominik Brunner ◽  
Fabian Jakub ◽  
Claudia Emde ◽  
Brigitte Buchmann ◽  
...  
Keyword(s):  
Remote Sensing ◽  
High Resolution ◽  
Radiative Transfer ◽  
Urban Canopy ◽  
Optical Path ◽  
Monte Carlo Code ◽  
Transfer Effects ◽  
Noise Component ◽  
Resolution Model ◽  
Airborne Imaging

Abstract. Airborne imaging remote sensing is increasingly used to map the spatial distribution of nitrogen dioxide (NO2) in cities. Despite the small ground-pixel size of the sensors, the measured NO2 distributions are much smoother than one would expect from high-resolution model simulations of NO2 over cities. This could partly be caused by 3D radiative transfer effects due to observation geometry, adjacency effects and effects of buildings. Here, we present a case study of imaging a synthetic NO2 distribution for a district of Zurich using the 3D MYSTIC (Monte carlo code for the phYSically correct Tracing of photons In Cloudy atmospheres) solver of the libRadtran radiative transfer library. We computed NO2 slant column densities (SCDs) using the recently implemented 3D-box air mass factors (3D-box AMFs) and a new urban canopy module to account for the effects of buildings. We found that for a single ground pixel (50 m × 50 m) more than 50 % of the sensitivity is located outside of the pixel, primarily in the direction of the main optical path between sun, ground pixel, and instrument. Consequently, NO2 SCDs are spatially smoothed, which results in an increase over roads when they are parallel to the optical path and a decrease otherwise. When buildings are included, NO2 SCDs are reduced on average by 5 % due to the reduced sensitivity to NO2 in the shadows of the buildings. The effects of buildings also introduce a complex pattern of variability in SCDs that would show up in airborne observations as an additional noise component (about 12 µmol m−2) similar to the magnitude of typical measurement uncertainties. The smearing of the SCDs cannot be corrected using 1D-layer AMFs that assume horizontal homogeneity and thus remains in the final NO2 map. The 3D radiative transfer effects by including buildings need to be considered to compute more accurate AMFs and to reduce biases in NO2 vertical columns obtained from high-resolution city-scale NO2 remote sensing.

scholarly journals A benchmark for testing the accuracy and computational cost of shortwave top-of-atmosphere reflectance calculations in clear-sky aerosol-laden atmospheres

2019 ◽  
Vol 12 (2) ◽  
pp. 805-827 ◽  
Author(s):  
Jeronimo Escribano ◽  
Alessio Bozzo ◽  
Philippe Dubuisson ◽  
Johannes Flemming ◽  
Robin J. Hogan ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Reference Model ◽  
Computational Cost ◽  
Atmospheric Composition ◽  
Scattering Method ◽  
Atmospheric Sciences ◽  
Clear Sky ◽  
Transfer Equations ◽  
Potential Resource ◽  
Radiative Transfer Equations

Abstract. Accurate calculations of shortwave reflectances in clear-sky aerosol-laden atmospheres are necessary for various applications in atmospheric sciences. However, computational cost becomes increasingly important for some applications such as data assimilation of top-of-atmosphere reflectances in models of atmospheric composition. This study aims to provide a benchmark that can help in assessing these two requirements in combination. We describe a protocol and input data for 44 080 cases involving various solar and viewing geometries, four different surfaces (one oceanic bidirectional reflectance function and three albedo values for a Lambertian surface), eight aerosol optical depths, five wavelengths, and four aerosol types. We first consider two models relying on the discrete ordinate method: VLIDORT (in vector and scalar configurations) and DISORT (scalar configuration only). We use VLIDORT in its vector configuration as a reference model and quantify the loss of accuracy due to (i) neglecting the effect of polarization in DISORT and VLIDORT (scalar) models and (ii) decreasing the number of streams in DISORT. We further test two other models: the 6SV2 model, relying on the successive orders of scattering method, and Forward-Lobe Two-Stream Radiance Model (FLOTSAM), a new model under development by two of the authors. Typical mean fractional errors of 2.8 % and 2.4 % for 6SV2 and FLOTSAM are found, respectively. Computational cost depends on the input parameters but also on the code implementation and application as some models solve the radiative transfer equations for a range of geometries while others do not. All necessary input and output data are provided as a Supplement as a potential resource for interested developers and users of radiative transfer models.

scholarly journals A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method

2009 ◽  
Vol 17 (4) ◽  
pp. 2057 ◽  
Author(s):  
Peng-Wang Zhai ◽  
Yongxiang Hu ◽  
Charles R. Trepte ◽  
Patricia L. Lucker
Keyword(s):  
Radiative Transfer ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
Scattering Method

scholarly journals A benchmark for testing the accuracy and computational cost of shortwave top-of-atmosphere reflectance calculations in clear-sky aerosol-laden atmospheres

2018 ◽  
Author(s):  
Jeronimo Escribano ◽  
Alessio Bozzo ◽  
Philippe Dubuisson ◽  
Johannes Flemming ◽  
Robin J. Hogan ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Reference Model ◽  
Computational Cost ◽  
Atmospheric Composition ◽  
Scattering Method ◽  
Atmospheric Sciences ◽  
Clear Sky ◽  
Transfer Equations ◽  
Potential Resource ◽  
Radiative Transfer Equations

Abstract. Accurate calculations of shortwave reflectances in clear-sky aerosol-laden atmospheres are necessary for various applications in atmospheric sciences. However computational cost becomes increasingly important for some applications such as data assimilation of top-of-atmosphere reflectances in models of atmospheric composition. This study aims to provide a benchmark that can help in assessing these two requirements in combination. We describe a protocol and input data for 44,080 cases involving various solar and viewing geometries, four different surfaces (one oceanic bidirectional reflectance function and three albedo values for a Lambertian surface), eight aerosol optical depths, five wavelengths, and four aerosol types. We first consider two models relying on the discrete ordinate method: VLIDORT (in vector and scalar configurations) and DISORT (scalar configuration only). We use VLIDORT in its vector configuration as a reference model and quantify the loss of accuracy due to (i) neglecting the effect of polarisation in the DISORT and VLIDORT (scalar) models and (ii) decreasing the number of streams in DISORT. We further test two other models: the 6SV2 model relying on the successive orders of scattering method and FLOTSAM, a new model under development by two of the authors. Typical mean fractional errors of 2.8 and 2.4 % for 6SV2 and FLOTSAM are found, respectively. Computational cost depends on the input parameters but also on the code implementation and application as some models solve the radiative transfer equations for a range of geometries while others do not. All necessary input and output data are provided as Supplementary Material as a potential resource for interested developers and users of radiative transfer models.

A Fast Two-Stream-Like Multiple-Scattering Method for Atmospheric Characterization and Radiative Transfer

2017 ◽  
Vol 56 (11) ◽  
pp. 3049-3063 ◽  
Author(s):  
Jarred L. Burley ◽  
Steven T. Fiorino ◽  
Brannon J. Elmore ◽  
Jaclyn E. Schmidt
Keyword(s):  
Radiative Transfer ◽  
Multiple Scattering ◽  
Function Parameter ◽  
Scattering Method ◽  
Particle Count ◽  
Energy Applications ◽  
Spectral Bands ◽  
Institute Of Technology ◽  
Directed Energy ◽  
Multiple Scattering Method

AbstractMultiple-scattering effects can significantly impact radiative transfer calculations for remote sensing and directed-energy applications. This study describes the development and implementation of a fast-calculating two-stream-like multiple-scattering algorithm that captures azimuthal and elevation variations into the Air Force Institute of Technology Center for Directed Energy’s Laser Environmental Effects Definition and Reference (LEEDR) atmospheric characterization and radiative transfer code. LEEDR is a fast-calculating, first-principles, worldwide surface-to-100-km, atmospheric characterization package for the creation of vertical profiles of temperature, pressure, water vapor content, optical turbulence, atmospheric particulates, and hydrometeors as they relate to line-by-line layer transmission and radiance from the ultraviolet to radio frequencies. The newly implemented multiple-scattering algorithm fully solves for molecular, aerosol, cloud, and precipitation single-scatter layer effects with a Mie algorithm at every atmospheric layer. A unique set of asymmetry and backscattering phase-function parameter calculations accounts for radiance loss due to the molecular and aerosol constituent reflectivity within a layer and accurately characterize diffuse layers that contribute to multiple-scattered radiances in inhomogeneous atmospheres. LEEDR is valid for spectral bands between 200-nm and radio wavelengths. Accuracy is demonstrated by comparing LEEDR results with published sky radiance observations and experimental data. Determining accurate aerosol loading via an iterative visibility/particle-count calculation method is ultimately essential to achieve agreement between observations and model results for realistic atmospheres.

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