Monte Carlo algorithms for reconstructing the scattering phase function with allowance for polarization

2008 ◽  
Vol 78 (3) ◽  
pp. 839-842
Author(s):  
G. A. Mikhailov ◽  
S. A. Ukhinov ◽  
A. S. Chimaeva
Author(s):  
Leonid Dombrovsky ◽  
Wojciech Lipin´ski

A combined two-step computational method incorporating (1) transport approximation of the scattering phase function, (2) P1 approximation and the finite element method for computing the radiation source function at the first step, and (3) the Monte Carlo method for computing radiative intensity at the second step, is developed. The accuracy of the combined method is examined for model problems involving two multi-dimensional configurations of an anisotropically scattering medium. A detailed analysis is performed for a medium with scattering phase function described by a family of the Henyey–Greenstein functions. The accuracy of the two-step method is assessed by comparing the distribution of the radiative flux leaving the medium to that obtained by a reference complete Monte Carlo method. This study confirms the main results of previous papers on the errors of the two-step solution method. The combined method leads to a significant reduction in computational time as compared to the reference method, by at least 1 order of magnitude. Finally, possible applications of the combined method are briefly discussed.


2018 ◽  
Vol 9 (1) ◽  
pp. 48 ◽  
Author(s):  
Peng Chen ◽  
Delu Pan ◽  
Zhihua Mao ◽  
Hang Liu

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.


2021 ◽  
Author(s):  
Alex Innanen ◽  
Brittney Cooper ◽  
Charissa Campbell ◽  
Scott Guzewich ◽  
Jacob Kloos ◽  
...  

<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>


2012 ◽  
Vol 32 (9) ◽  
pp. 0901001
Author(s):  
孟祥谦 Meng Xiangqian ◽  
胡顺星 Hu Shunxing ◽  
王英俭 Wang Yingjian ◽  
胡欢陵 Hu Huanling

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