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Keywords = Hapke two-layer medium model

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19 pages, 7790 KiB  
Article
Spectral Simulation and Error Analysis of Dusty Leaves by Fusing the Hapke Two-Layer Medium Model and the Linear Spectral Mixing Model
by Baodong Ma, Xiangru Yang, Defu Che, Yang Shu, Quan Liu and Min Su
Remote Sens. 2023, 15(5), 1220; https://doi.org/10.3390/rs15051220 - 22 Feb 2023
Viewed by 1328
Abstract
The Hapke two-layer medium model is an efficient way of simulating the spectra of dusty leaves. However, the simulation accuracy is low when the amount of dustfall is small. To solve this problem, we introduced the dust coverage factor and the linear spectral [...] Read more.
The Hapke two-layer medium model is an efficient way of simulating the spectra of dusty leaves. However, the simulation accuracy is low when the amount of dustfall is small. To solve this problem, we introduced the dust coverage factor and the linear spectral mixing model, to improve the accuracy of the Hapke two-layer medium model. Firstly, based on the assumption of spherical dust particles, the arrangement and accumulation mode of the particles were set, and the coverage factor and accumulation thickness of particles in the leaf area were calculated. Then, the coverage factor was used as an abundance. Endmembers were the spectra of dust-free leaves (measured) and dust-covered leaves (simulated by model), and the final simulated spectra were calculated using linear spectral mixing theory. This study presents the following findings: (1) When the coverage factor was calculated using the exponential model, the maximum difference between the corrected simulated spectra and the measured spectra was 3.4%, and the maximum difference between the original simulated spectra and the measured spectra was 15.2%. The accuracy of the corrected spectra is much higher than that of the original simulated spectra. (2) In this study, the physical thickness and optical thickness calculated by the Hapke two-layer medium model are equivalent, which is quite different from the actual dust accumulation. When the linear spectral mixing model is introduced, to modify the simulation value when the number of dust particles accumulated is less than one layer, the spectral endmember value of the simulated dust leaf is replaced by the simulation spectrum when the number of dust particles accumulated is exactly one layer. The calculated cor-rection spectrum has high rationality and credibility. This finding may be beneficial for monitoring amounts of dustfall accurately using remote sensing in mining areas. Full article
(This article belongs to the Section Environmental Remote Sensing)
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Figure 1

Figure 1
<p>The main experimental procedure of this study.</p>
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<p>Device for measuring the spectrum of dusty leaves in the dust falling experiment. (<b>a</b>) is a photo of the experimental setup. (<b>b</b>) is a leaf covered with a certain amount of dust.</p>
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<p>Particle arrangement and accumulation mode: (<b>a</b>) is the arrangement and accumulation of dust particles on the leaves. (<b>b</b>) is a schematic of the calculation of the value of <span class="html-italic">a</span>.</p>
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<p>Spectral curves of leaves with different amounts of dustfall.</p>
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<p>The Hapke two-layer medium model simulates the spectral curves of leaves with different amounts of dustfall, the results were calculated using Equation (6).</p>
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<p>The difference between the simulated spectral value and the measured spectrum.</p>
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<p>The simulation spectrum results after error correction, and the results were calculated from Equations (21) and (22).</p>
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<p>The corrected simulated spectral reflectance was compared with the measured spectrum: (<b>a</b>) is the spectrum at a dustfall amount of 76 g/m<sup>2</sup>; (<b>b</b>) is the spectrum at a dustfall amount of 100 g/m<sup>2</sup>.</p>
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<p>The difference curve between the corrected simulated and the measured values.</p>
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<p>Two-dimensional surface diagram of the difference between the corrected and measured values of the Hapke two-layer medium model simulated spectra.</p>
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<p>Another arrangement and accumulation mode of dust particles.</p>
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<p>Error surface obtained based on the dust accumulation mode shown in <a href="#remotesensing-15-01220-f011" class="html-fig">Figure 11</a>.</p>
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<p>The coverage of linear and nonlinear computation with the amounts of dustfall.</p>
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<p>The difference between the corrected results and the measured values.</p>
Full article ">Figure 15
<p>The variation of the difference between the corrected spectrum and the measured value as a function of wavelength and dust magnitude is calculated by Equation (30).</p>
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