Comparison and Analysis of Scattering Phase-Function Truncation Approximations in Radiative Transfer Calculation

2017 ◽  
Vol 37 (2) ◽  
pp. 0229002
Author(s):  
罗 双 Luo Shuang ◽  
尹 球 Yin Qiu
Keyword(s):  
Radiative Transfer ◽  
Phase Function ◽  
Radiative Transfer Calculation ◽  
Scattering Phase ◽  
Comparison And Analysis ◽  
Scattering Phase Function

Radiative Transfer

2017 ◽  
Author(s):  
Kelly Chance ◽  
Randall V. Martin
Keyword(s):  
Energy Transfer ◽  
Radiative Transfer ◽  
Cross Sections ◽  
Optical Thickness ◽  
Phase Function ◽  
Thermal Emission ◽  
Atmospheric Radiation ◽  
Scattering Phase ◽  
Cloud Optical Thickness ◽  
Scattering Phase Function

Radiative transfer is the process of energy transfer during the propagation of electromagnetic radiation through a medium. The processes of extinction, due to absorption and scattering, and thermal emission are described. It is shown how they can be represented by wavelength-dependent optical thickness, due to absorption or emission cross sections and the number of absorbers, emitters, or scatterers. Cloud optical thickness and conservative scattering are described. The scattering phase function is introduced. Next, the general form of radiative transfer is given, and its applicability to the details of planetary atmospheric radiation shown.

scholarly journals Spectrally Invariant Approximation within Atmospheric Radiative Transfer

2011 ◽  
Vol 68 (12) ◽  
pp. 3094-3111 ◽  
Author(s):  
A. Marshak ◽  
Y. Knyazikhin ◽  
J. C. Chiu ◽  
W. J. Wiscombe
Keyword(s):  
Radiative Transfer ◽  
Phase Function ◽  
Single Scattering ◽  
Atmospheric Conditions ◽  
Water Vapor Absorption ◽  
Mathematical Basis ◽  
Invariant Approximation ◽  
Scattering Phase ◽  
Atmospheric Radiative Transfer ◽  
Scattering Phase Function

Abstract Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These “spectrally invariant relationships” are the consequence of wavelength independence of the extinction coefficient and scattering phase function in vegetation. In general, this wavelength independence does not hold in the atmosphere, but in cloud-dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accurately describe the extinction and scattering properties of cloudy atmospheres. The validity of the assumptions and the accuracy of the approximation are tested with 1D radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.

scholarly journals Semi-Analytic Monte Carlo Model for Oceanographic Lidar Systems: Lookup Table Method Used for Randomly Choosing Scattering Angles

2018 ◽  
Vol 9 (1) ◽  
pp. 48 ◽  
Author(s):  
Peng Chen ◽  
Delu Pan ◽  
Zhihua Mao ◽  
Hang Liu
Keyword(s):  
Monte Carlo ◽  
Radiative Transfer ◽  
Phase Function ◽  
Geometric Model ◽  
Airborne Lidar ◽  
Cumulative Distribution ◽  
Lookup Table ◽  
Transfer Model ◽  
Scattering Phase ◽  
Scattering Phase Function

Monte Carlo (MC) is a significant technique for finding the radiative transfer equation (RTE) solution. Nowadays, the Henyey-Greenstein (HG) scattering phase function (spf) has been widely used in most studies during the core procedure of randomly choosing scattering angles in oceanographic lidar MC simulations. However, the HG phase function does not work well at small or large scattering angles. Other spfs work well, e.g., Fournier-Forand phase function (FF); however, solving the cumulative distribution function (cdf) of the scattering phase function (even if possible) would result in a complicated formula. To avoid the above-mentioned problems, we present a semi-analytic MC radiative transfer model in this paper, which uses the cdf equation to build up a lookup table (LUT) of ψ vs. P Ψ ( ψ ) to determine scattering angles for various spfs (e.g., FF, Petzold measured particle phase function, and so on). Moreover, a lidar geometric model for analytically estimating the probability of photon scatter back to a remote receiver was developed; in particular, inhomogeneous layers are divided into voxels with different optical properties; therefore, it is useful for inhomogeneous water. First, the simulations between the inverse function method for HG cdf and the LUT method for FF cdf were compared. Then, multiple scattering and wind-driven sea surface condition effects were studied. Finally, we compared our simulation results with measurements of airborne lidar. The mean relative errors between simulation and measurements in inhomogeneous water are within 14% for the LUT method and within 22% for the inverse cdf (ICDF) method. The results suggest feasibility and effectiveness of our simulation model.

A Comparison of Aphelion Cloud Belt Phase Functions Before and After the Mars Year 34 Global Dust Storm

2021 ◽  
Author(s):  
Alex Innanen ◽  
Brittney Cooper ◽  
Charissa Campbell ◽  
Scott Guzewich ◽  
Jacob Kloos ◽  
...  
Keyword(s):  
Dust Storm ◽  
Phase Function ◽  
Dust Storms ◽  
Ice Crystal ◽  
Ice Clouds ◽  
Water Ice ◽  
Ice Cloud ◽  
Sky Survey ◽  
Scattering Phase ◽  
Scattering Phase Function

<p>1. INTRODUCTION</p><p>The Mars Science Laboratory (MSL) is located in Gale Crater (4.5°S, 137.4°E), and has been performing cloud observations for the entirety of its mission, since its landing in 2012 [eg. 1,2,3]. One such observation is the Phase Function Sky Survey (PFSS), developed by Cooper et al [3] and instituted in Mars Year (MY) 34 to determine the scattering phase function of Martian water-ice clouds. The clouds of interest form during the Aphelion Cloud Belt (ACB) season (L<sub>s</sub>=50°-150°), a period of time during which there is an increase in the formation of water-ice clouds around the Martian equator [4]. The PFSS observation was also performed during the MY 35 ACB season and the current MY 36 ACB season.</p><p>Following the MY 34 ACB season, Mars experienced a global dust storm which lasted from L<sub>s</sub>~188° to L<sub>s</sub>~250° of that Mars year [5]. Global dust storms are planet-encircling storms which occur every few Mars years and can significantly impact the atmosphere leading to increased dust aerosol sizes [6], an increase in middle atmosphere water vapour [7], and the formation of unseasonal water-ice clouds [8]. While the decrease in visibility during the global dust storm itself made cloud observation difficult, comparing the scattering phase function prior to and following the global dust storm can help to understand the long-term impacts of global dust storms on water-ice clouds.</p><p>2. METHODS</p><p>The PFSS consists of 9 cloud movies of three frames each, taken using MSL’s navigation cameras, at a variety of pointings in order to observe a large range of scattering angles. The goal of the PFSS is to characterise the scattering properties of water-ice clouds and to determine ice crystal geometry.  In each movie, clouds are identified using mean frame subtraction, and the phase function is computed using the formula derived by Cooper et al [3]. An average phase function can then be computed for the entirety of the ACB season.</p><p><img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.eda718c85da062913791261/sdaolpUECMynit/1202CSPE&app=m&a=0&c=67584351a5c2fde95856e0760f04bbf3&ct=x&pn=gnp.elif&d=1" alt="Figure 1 – Temporal Distribution of Phase Function Sky Survey Observations for Mars Years 34 and 35" width="800" height="681"></p><p>Figure 1 shows the temporal distributions of PFSS observations taken during MYs 34 and 35. We aim to capture both morning and afternoon observations in order to study any diurnal variability in water-ice clouds.</p><p>3. RESULTS AND DISCUSSION</p><p>There were a total of 26 PFSS observations taken in MY 35 between L<sub>s</sub>~50°-160°, evenly distributed between AM and PM observations. Typically, times further from local noon (i.e. earlier in the morning or later in the afternoon) show stronger cloud features, and run less risk of being obscured by the presence of the sun. In all movies in which clouds are detected, a phase function can be calculated, and an average phase function determined for the whole ACB season.  </p><p>Future work will look at the water-ice cloud scattering properties for the MY 36 ACB season, allowing us to get more information about the interannual variability of the ACB and to further constrain the ice crystal habit. The PFSS observations will not only assist in our understanding of the long-term atmospheric impacts of global dust storms but also add to a more complete image of time-varying water-ice cloud properties.</p>

Sign in / Sign up

Export Citation Format

Share Document