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Related Concept Videos

Linear Approximations01:23

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...
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Difference from Background: Limit of Detection01:05

Difference from Background: Limit of Detection

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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

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Concentration estimation from differential absorption lidar using nonstationary Wiener filtering.

R E Warren

    Applied Optics
    |June 18, 2010
    PubMed
    Summary

    This study introduces a new filtering method for differential absorption lidar (DIAL) data. The technique smooths concentration estimates while accounting for local data uncertainty, improving accuracy.

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    Area of Science:

    • Atmospheric Science
    • Optical Remote Sensing
    • Signal Processing

    Background:

    • Range-resolved differential absorption lidar (DIAL) systems provide valuable atmospheric concentration data.
    • Estimates from DIAL can be noisy and require effective smoothing and differentiation techniques.
    • Existing methods may not adequately address the local uncertainty inherent in lidar measurements.

    Purpose of the Study:

    • To present a novel approach for smoothing and differentiating path-integrated concentration estimates from DIAL.
    • To develop a method that accounts for local uncertainty in the input lidar data.
    • To demonstrate the efficacy of the proposed method using both synthetic and real-world data.

    Main Methods:

    • Implementation of a nonstationary Wiener-Kolmogorov filtering theory.
    • Application of the filtering technique to path-integrated concentration estimates.
    • Validation using simulated and actual range-resolved differential absorption lidar data.

    Main Results:

    • The developed method effectively smooths DIAL concentration estimates.
    • The filtering approach adapts to local variations in data uncertainty.
    • Demonstrated successful application on both synthetic and actual lidar datasets.

    Conclusions:

    • The nonstationary Wiener-Kolmogorov filtering approach offers an improved method for DIAL data processing.
    • This technique enhances the reliability of atmospheric concentration measurements by considering local data uncertainty.
    • The method provides a robust tool for analyzing lidar-derived atmospheric data.