Related Experiment Video
Updated: Jun 15, 2026
06:49
In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation
Published on: March 2, 2021
Approximation to the Lorentzian coefficient for efficient calculation of transmittance profiles
Applied Optics
|March 4, 2010
Summary
This study introduces an efficient method for calculating atmospheric transmittance by approximating the Lorentzian coefficient. This significantly reduces computational time while maintaining high accuracy for atmospheric modeling.
Area of Science:
- Atmospheric science
- Radiative transfer modeling
- Computational physics
Background:
- Calculating atmospheric transmittance line-by-line is computationally intensive.
- The Lorentzian coefficient evaluation is a major bottleneck, requiring extensive calculations for each gas, wavenumber, line, temperature, and pressure.
Purpose of the Study:
- To develop a computationally efficient method for calculating atmospheric transmittance.
- To reduce the excessive computational time associated with the Lorentzian coefficient evaluation.
Main Methods:
- Utilized an approximating function to factor out temperature and pressure-dependent quantities from wavenumber-dependent terms.
- Implemented a numerical procedure to handle cases near the line center, beyond the approximation's direct applicability.
- Applied the method to H(2)O, CO(2), N(2)O, and CO in a 33-level atmosphere for specific Nimbus 6 frequencies.
Main Results:
- Achieved a significant reduction in arithmetic operations compared to exact coefficient calculations.
- Demonstrated a computational time reduction by a factor of over 9.
- Yielded transmittance values with numerical accuracy of four significant figures or better.
Conclusions:
- The proposed approximation method offers a substantial improvement in computational efficiency for atmospheric transmittance calculations.
- This approach enables faster and accurate atmospheric modeling, crucial for climate and remote sensing applications.
- The method is validated for key atmospheric gases in a multi-level atmosphere.
Related Concept Videos
01:09UV–Vis Spectroscopy: Beer–Lambert Law
The Beer-Lambert law describes the relationship between absorbance and concentration, which combines the principles established by scientists Johann Heinrich Lambert and August Beer. Lambert's law states that when light passes through a medium, the loss in intensity is directly proportional to the original intensity and the path length of the light. Beer's law proposed that the transmittance of a solution remains constant if the product of concentration and path length is constant. The modern...
01:28Debye–Huckel–Onsager Conductance Equation
The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
01:28Simpson's Rule II
In warehouse roofing applications, corrugated or curved metal sheets are commonly used to improve structural strength, water drainage, and ventilation efficiency. To accurately estimate material requirements and optimize design parameters, engineers must determine the curved surface area of these sheets. Because the sheet profiles often repeat smoothly along their length, they can be effectively approximated by parabolic curves, enabling the use of numerical integration techniques for area...
01:23Linear 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...
01:05Absorption of Radiation
The rate of heat transfer by emitted radiation is described by the Stefan-Boltzmann law of radiation:
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...