Related Experiment Video
Updated: Jun 15, 2026

11:34
Scattering And Absorption of Light in Planetary Regoliths
Published on: July 1, 2019
Summary
This study models multiple radiation scattering in 3-D clouds using probabilistic bundle distribution. It presents a new radiation diffusivity expression for non-isotropic scattering, aiding cloud radiation transfer analysis.
Area of Science:
- Atmospheric physics
- Radiative transfer theory
Background:
- Multiple radiation scattering is crucial for understanding energy transfer in clouds.
- Accurate modeling of scattering is complex due to cloud heterogeneity.
Purpose of the Study:
- To develop a theoretical framework for multiple radiation scattering in 3-D clouds.
- To derive probabilistic expressions for scattered energy bundle distribution.
- To present an equation for radiation diffusivity in non-isotropic scattering scenarios.
Main Methods:
- Modeling radiation as energy bundles interacting with cloud particles.
- Developing probabilistic expressions to describe bundle distribution after scattering.
- Formulating an analytical expression for radiation diffusivity.
Main Results:
- Probabilistic expressions for energy bundle distribution were successfully developed.
- A novel expression for radiation diffusivity, accounting for non-isotropic scattering, was derived.
- The theory's applicability was demonstrated through two numerical examples.
Conclusions:
- The developed theory provides a robust method for analyzing multiple radiation scattering in 3-D clouds.
- The new diffusivity expression enhances understanding of radiative transfer in complex cloud structures.
- The findings have implications for climate modeling and remote sensing applications.
More Related Videos
Related Concept Videos
Application of Linearization and Approximation
A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
Linear Approximations
For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
Maxwell-Boltzmann Distribution: Problem Solving
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Propagation of Uncertainty from Random Error
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
Propagation of Uncertainty from Systematic Error
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
Precipitation Processes
The experimental conditions in a gravimetric analysis should be optimized to maximize the particle size and purity of the obtained precipitate. Ideally, the concentration of the precipitating reagent should be low with effective stirring to maintain low relative supersaturation for the growth of large crystals. In homogeneous precipitation, the precipitant is slowly generated by a chemical reaction in the solution to avoid local reagent excesses. For example, urea decomposes gradually to...

