Related Experiment Video
Updated: Jun 6, 2026
08:52
Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere
Published on: April 30, 2018
Finite-element algorithm for radiative transfer in vertically inhomogeneous media: numerical scheme and applications
Applied Optics
|November 12, 2010
Summary
A new finite-element method accurately calculates radiative transfer, including multiple scattering and bidirectional reflectivity in atmospheres. This computational tool enhances understanding of solar radiation interactions across UV, visible, and near-infrared spectrums.
Area of Science:
- Atmospheric physics and radiative transfer modeling.
- Computational electromagnetics and numerical methods.
Background:
- Accurate modeling of radiative transfer is crucial for understanding atmospheric phenomena and solar energy applications.
- Previous methods often simplified or neglected azimuthal dependence and complex boundary interactions.
Purpose of the Study:
- To extend a finite-element method (FEM) for solving the radiative transfer equation (RTE).
- To incorporate full azimuthal dependence, multiple scattering, and bidirectional reflectivity.
- To apply the method to vertically inhomogeneous plane-parallel atmospheres.
Main Methods:
- Developed a finite-element method (FEM) for the radiative transfer equation (RTE).
- Included algorithms for multiple scattering and bottom boundary bidirectional reflectivity.
- Applied the method to simulate incident solar radiation (UV, visible, near-infrared).
Main Results:
- The extended FEM accurately computes the full azimuthal dependence of radiance.
- The method demonstrates high accuracy even with a reduced number of grid points.
- Successful applications to realistic atmospheric models were performed.
Conclusions:
- The developed FEM provides an accurate and efficient tool for radiative transfer simulations.
- The code is available for researchers studying atmospheric radiation.
- Enhances understanding of light propagation in complex atmospheric environments.
Related Concept Videos
01:26Transmission-Line Differential Equations
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
01:09Radiation Pressure: Problem Solving
The radiation pressure applied by an electromagnetic wave on a perfectly absorbing surface equals the energy density of the wave. The wave's momentum also gets transferred to the surface when an electromagnetic wave is entirely absorbed by it. The rate at which momentum is transmitted to an absorbing surface perpendicular to the propagation direction equals the force on the surface.
The average value of the rate of momentum transfer divided by the absorbing area represents the average force per...
The average value of the rate of momentum transfer divided by the absorbing area represents the average force per...
01:05Absorption of Radiation
The rate of heat transfer by emitted radiation is described by the Stefan-Boltzmann law of radiation:
01:17Radiation: Applications
The average temperature of Earth is the subject of much current discussion. Earth is in radiative contact with both the Sun and dark space; it receives almost all its energy from the radiation of the Sun and reflects some of it into outer space. Dark space is very cold, about 3 K, so Earth radiates energy into it. For instance, heat transfer occurs from soil and grasses, the rate of which can be so rapid that frost can occur on clear summer evenings, even in warm latitudes.
The average...
The average...
01:20Conduction, Convection and Radiation: Problem Solving
There are three methods by which heat transfer can take place: conduction, convection, and radiation. Each method has unique and interesting characteristics, but all three have two things in common: they transfer heat solely because of a temperature difference; and the greater the temperature difference, the faster the heat transfer.
In order to solve a problem related to heat transfer, first of all, the situation needs to be examined to determine the type of heat transfer involved. This could...
In order to solve a problem related to heat transfer, first of all, the situation needs to be examined to determine the type of heat transfer involved. This could...
01:20Maxwell-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