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Related Concept Videos

Application of Linearization and Approximation01:29

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...
Application of Nonlinear Inequalities01:29

Application of Nonlinear Inequalities

A nonlinear inequality describes a comparison involving an expression that curves or behaves more complexly than a straight line. These inequalities often appear in forms that include squares, products, or variables in the denominator.To solve such an inequality, one starts by rewriting it so that zero appears on one side. For example, the inequality:  can be factored as: This form makes it easier to identify the values that cause the expression to equal zero. In this case, the key values are 3...
Derivatives of Inverse Trigonometric Functions01:30

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A ship tracking an approaching aircraft relies on geometric measurements to find out the aircraft’s position relative to the observer. By measuring the slant distance to the aircraft and the angle of elevation, the horizontal and vertical components of the distance can be obtained using trigonometric relationships. This geometric approach provides a basis for analyzing how the observed angle changes as the aircraft moves closer to the ship.To examine the mathematical behavior of the angle of...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Linear Approximation in Frequency Domain

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Related Experiment Video

Updated: Jun 24, 2026

Applying X-ray Imaging Crystal Spectroscopy for Use as a High Temperature Plasma Diagnostic
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Published on: August 25, 2016

Efficient nonlinear inversion for atmospheric sounding and other applications.

Richard Lynch1, Jean-Luc Moncet, Xu Liu

  • 1Atmospheric and Environmental Research, Inc., 131 Hartwell Avenue, Lexington, Massachusetts 02421-3126, USA. rlynch@aer.com

Applied Optics
|April 3, 2009
PubMed
Summary
This summary is machine-generated.

A new method, DRAD, efficiently retrieves atmospheric variables from remote sensing data, even with highly nonlinear problems and uncertain initial guesses. This technique improves upon existing methods like Levenberg-Marquardt for atmospheric profile retrieval.

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Area of Science:

  • Atmospheric Science
  • Remote Sensing
  • Data Assimilation

Background:

  • Retrieving atmospheric and surface variables from remote observations commonly requires minimizing nonlinear cost functions.
  • The success of minimization methods heavily depends on the nonlinearity of the cost function and the accuracy of the initial guess.
  • Existing methods may struggle with highly nonlinear problems or limited prior information.

Purpose of the Study:

  • To introduce and evaluate a novel minimization method, DRAD (iterative), for atmospheric state variable retrieval.
  • To demonstrate DRAD's applicability to highly nonlinear cost functions and scenarios with minimal a priori information.
  • To assess the efficiency of DRAD across a range of initial guess errors.

Main Methods:

  • Development and application of the DRAD minimization method.
  • Retrieval of water vapor and temperature profiles using simulated Atmospheric Infrared Sounder (AIRS) observations.
  • Comparative analysis with the Levenberg-Marquardt method for retrieval efficiency.

Main Results:

  • DRAD demonstrates effectiveness in retrieving atmospheric profiles under conditions of high nonlinearity.
  • The method shows efficiency across a wide spectrum of initial guess errors, outperforming comparisons in challenging cases.
  • Simulated AIRS data retrieval confirms DRAD's capability for water vapor and temperature profile estimation.

Conclusions:

  • DRAD offers a robust and efficient solution for atmospheric retrieval problems characterized by significant nonlinearity.
  • The method's performance across varying initial guess errors highlights its practical utility in remote sensing applications.
  • DRAD represents a valuable advancement for improving the accuracy and reliability of atmospheric state variable retrieval.