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.

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.

Radiative Transfer Modeling and Monte Carlo Simulating of a New Digital Airborne Camera

2011 ◽  
Vol 189-193 ◽  
pp. 1641-1646
Author(s):  
Lei Yan ◽  
Shi Hu Zhao ◽  
Yi Ni Duan
Keyword(s):  
Remote Sensing ◽  
Monte Carlo ◽  
Radiative Transfer ◽  
Digital Imaging ◽  
Geometric Model ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
Central Projection ◽  
Imaging Device ◽  
Radiative Model

Application of digital aerial camera was a milestone in the development of Photogrammetry and Remote Sensing. The new digital sensor leads to the changes of remote sensing imaging models. Generally, remote sensing imaging models have two kinds: geometric model and radiative model, in which radiative model mainly focus on the radiative quality of remote sensing images. In this paper, a new kind of airborne camera, namely Twice Imaging Digital Camera (TIDC), is introduced, which integrates the advantages of film airborne camera and digital one. It adopts twice imaging techniques to acquire large format, strict central projection images. The radiative transfer model of TIDC is built on the physical processing of digital imaging. The intermediate imaging device of TIDC influences digital images’ quality badly, such as luminous intensity distribution, decay and noise. For this reason, the approach of light tracing based on Monte Carlo is used to simulate radiative transfer in TIDC and test the performance of the intermediate imaging device. The importance of this work is: The Monte Carlo simulating experiment proposed by this paper can be widely applied in the simulation and modeling of other digital imaging systems, and has great practical value in the evaluation and optimization of image quality, the improvement of remote sending imaging system, as well as the estimate of image acquirement results.

A Combined P1 and Monte Carlo Model for Radiative Transfer in Multi-Dimensional Anisotropically Scattering Media

2010 ◽  
Author(s):  
Leonid Dombrovsky ◽  
Wojciech Lipin´ski
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Phase Function ◽  
Monte Carlo Model ◽  
Reference Method ◽  
Computational Time ◽  
Scattering Media ◽  
Combined Method ◽  
Scattering Phase ◽  
Scattering Phase Function

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.

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.

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