A Modified Look-Up Table Based Algorithm with a Self-Posed Scheme for Fine-Mode Aerosol Microphysical Properties Inversion by Multi-Wavelength Lidar
<p>Process of the LUT element matching algorithm based on RF. (<b>a</b>) Process of obtaining the final solution from the LUT. The blue cubes represent the elements of the LUT, yellow cubes represent the reduced solution space obtained by the k-NN algorithm, red cubes represent the possible solutions after processing by the RF algorithm, and the green circle represents the final solution after averaging the possible solutions. The three cubes belong to the same data set. The circle indicates that it generally does not correspond to any LUT element. (<b>b</b>) Workflow of the RF algorithm. Using the “bagging” strategy to extract several permutations from the full permutation to generate decision trees. Each tree prunes optical parameters according to its permutation. The orange circles represent the elements retained during each pruning, light blue circles represent the excluded parts, and arrows indicate different directions in different dimensions. The red circle is the output of a single decision tree, i.e., a possible solution. After averaging all possible solutions, the final solution is obtained, where the yellow part corresponds to the reduced solution space in (<b>a</b>), and the green part corresponds to the final solution. (<b>c</b>) Pruning process of a single decision tree. For each pruning, the optical parameter distances are first sorted. In the first step, for example, <math display="inline"><semantics> <mrow> <msup> <mrow> <mi>G</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> is selected, which means sorting based on the distance of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>B</mi> </mrow> <mrow> <mn>355</mn> </mrow> </msub> </mrow> </semantics></math> and retaining the top <math display="inline"><semantics> <mrow> <mi>ω</mi> </mrow> </semantics></math> portion with the smallest distances. In the second step, <math display="inline"><semantics> <mrow> <msup> <mrow> <mi>G</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math> is selected, and the remaining part is sorted and pruned based on the distance of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>B</mi> </mrow> <mrow> <mn>1064</mn> </mrow> </msub> </mrow> </semantics></math>. This process continues until the last pruning, where the remaining part is output as a possible solution.</p> "> Figure 2
<p>Process diagram of the modified algorithm. It includes two inversion iterations, where the solid lines depict the process of the first inversion and the dashed lines represent the process of the second inversion. The parts highlighted in orange indicate the additional aspects introduced by the modified algorithm compared to the basic algorithm.</p> "> Figure 3
<p>Example of the decision tree pruning process. (<b>a</b>) Distances between all elements in the reduced solution space and the input optical parameter set on the 11 optical parameters. The horizontal axis represents different optical parameters, and the vertical axis represents the magnitude of the distance. The shaded area in the graph indicates the distribution of the data. Optical parameters corresponding to 1–11 are explained on the right side. (<b>b</b>) Operation’s mapping on the sixth optical parameter when pruning the second optical parameter in (<b>a</b>). The red-shaded area represents the data retained after pruning. (<b>c</b>) Operation’s mapping on the second optical parameter when pruning the sixth optical parameter in (<b>a</b>).</p> "> Figure 4
<p>Flowchart of generating the reduced solution space and the constraint window. The blue portion represents the generation process of the reduced solution space and the green portion represents the generation process of the constraint window.</p> "> Figure 5
<p>Aircraft trajectory maps in California on (<b>a</b>) 30 January and (<b>b</b>) 31 January. The blue trace represents the track of the B-200 and the green trace represents that of the P-3B.</p> "> Figure 6
<p>Data processing and comparison process between the two aircraft. The blue annotations indicate important parameters and results during the process. HSRL optical data undergoes screening for depolarization ratio (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>δ</mi> </mrow> <mrow> <mn>532</mn> </mrow> </msub> </mrow> </semantics></math>) and Ångström exponent (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mi>α</mi> </mrow> </msub> <mo>(</mo> <mn>355</mn> <mo>−</mo> <mn>532</mn> <mo>)</mo> </mrow> </semantics></math>), followed by inversion to obtain CRI and APSD, and then the calculation of <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>S</mi> <mi>A</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mi mathvariant="normal">t</mi> </mrow> </msub> </mrow> </semantics></math> products. P-3B data were screened based on <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mi mathvariant="normal">t</mi> </mrow> </msub> </mrow> </semantics></math>, and APSD, environmental scattering coefficient, and dry absorption coefficient were obtained from measurements by UHSAS, nephelometer, and PSAP, respectively. Finally, <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>S</mi> <mi>A</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mi mathvariant="normal">t</mi> </mrow> </msub> </mrow> </semantics></math> are computed. The conditions for mutual comparison of the products obtained from both aircraft are within the spirals of P-3B, where validation of the aerosol vertical profile information can be performed.</p> "> Figure 7
<p>Average retrieval errors and computation time for the microphysical parameters under the 3<span class="html-italic">β</span> + 2<span class="html-italic">α</span> and 3<span class="html-italic">β</span> + 1<span class="html-italic">α</span> configurations. (<b>a</b>–<b>f</b>) The retrieval errors and consumed time for 3<span class="html-italic">β</span> + 2<span class="html-italic">α</span>. (<b>g</b>–<b>l</b>) The retrieval errors and consumed time for 3<span class="html-italic">β</span> + 1<span class="html-italic">α</span>. The blue bars represent the results of the basic algorithm, while the red bars represent the results of the modified algorithm. The test data are divided into two categories: grid points and non−grid points.</p> "> Figure 8
<p>Average retrieval errors and computation time for the microphysical parameters under the 2<span class="html-italic">β</span> + 1<span class="html-italic">α</span> and 3<span class="html-italic">β</span> configurations. (<b>a</b>–<b>f</b>) The retrieval errors and consumed time for 2<span class="html-italic">β</span> + 1<span class="html-italic">α</span>. (<b>g</b>–<b>l</b>) The retrieval errors and consumed time for 3<span class="html-italic">β</span>. The results are marked similarly to those in <a href="#remotesensing-16-02265-f007" class="html-fig">Figure 7</a>.</p> "> Figure 9
<p>Stability testing results for the retrieval algorithms under the 3<span class="html-italic">β</span> + 2<span class="html-italic">α</span> and 3<span class="html-italic">β</span> + 1<span class="html-italic">α</span> configurations. (<b>a</b>–<b>e</b>) Box plots for retrieval errors of aerosol microphysical properties under 3<span class="html-italic">β</span> + 2<span class="html-italic">α.</span> (<b>f</b>–<b>j</b>) Box plots for retrieval errors of aerosol microphysical properties under 3<span class="html-italic">β</span> + 1<span class="html-italic">α.</span> The box plots are generated according to the IQR strategy. The blue box plots represent the basic algorithm and the red plots represent the modified algorithm. The wavy−shaded areas on the <span class="html-italic">y</span>−axis indicate truncation and jumps for visualization purposes.</p> "> Figure 10
<p>Stability testing results for the retrieval algorithms under the 2<span class="html-italic">β</span> + 1<span class="html-italic">α</span> and 3<span class="html-italic">β</span> configurations. (<b>a</b>–<b>e</b>) Box plots for retrieval errors of aerosol microphysical properties under 2<span class="html-italic">β</span> + 1<span class="html-italic">α.</span> (<b>f</b>–<b>j</b>) Box plots for retrieval errors of aerosol microphysical properties under 3<span class="html-italic">β.</span> The meaning of the labels is consistent with <a href="#remotesensing-16-02265-f009" class="html-fig">Figure 9</a>.</p> "> Figure 11
<p>Function of inversion error versus fixed error when artificially distorting individual input optical properties. (<b>a</b>–<b>d</b>) Inversion errors of 3<span class="html-italic">β</span> + 2<span class="html-italic">α</span> (<b>a</b>), 3<span class="html-italic">β</span> + 1<span class="html-italic">α</span> (<b>b</b>), 2<span class="html-italic">β</span> + 1<span class="html-italic">α</span> (<b>c</b>) and 3<span class="html-italic">β</span> (<b>d</b>) configurations regarding <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mi mathvariant="normal">r</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>e</b>–<b>h</b>) Same as (<b>a</b>–<b>d</b>), but showing inversion errors regarding <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mi mathvariant="normal">i</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>i</b>–<b>l</b>) Same as (<b>a</b>–<b>d</b>), but showing inversion errors regarding <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>S</mi> <mi>A</mi> </mrow> </semantics></math>. (<b>m</b>–<b>p</b>) Same as (<b>a</b>–<b>d</b>), but showing inversion errors regarding <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>q</b>–<b>t</b>) Same as (<b>a</b>–<b>d</b>), but showing inversion errors regarding <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mi mathvariant="normal">t</mi> </mrow> </msub> </mrow> </semantics></math>. The horizontal axis represents the value of the fixed error, while the vertical axis represents the inversion error, with the zero−error line highlighted by a dashed line. For different optical parameters, lines with different colors and markers represent <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>β</mi> </mrow> <mrow> <mn>355</mn> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>β</mi> </mrow> <mrow> <mn>532</mn> </mrow> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>β</mi> </mrow> <mrow> <mn>1064</mn> </mrow> </msub> </mrow> </semantics></math> with blue hexagons, orange circles, and yellow stars, respectively, while <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>355</mn> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>532</mn> </mrow> </msub> </mrow> </semantics></math> are represented by purple diamonds and green squares, respectively.</p> "> Figure 12
<p>Inversion errors after applying random Gaussian noise disturbance to the input data at error levels of 10% and 20%. (<b>a</b>–<b>d</b>) Inversion errors of 3<span class="html-italic">β</span> + 2<span class="html-italic">α</span> (<b>a</b>), 3<span class="html-italic">β</span> + 1<span class="html-italic">α</span> (<b>b</b>), 2<span class="html-italic">β</span> + 1<span class="html-italic">α</span> (<b>c</b>) and 3<span class="html-italic">β</span> (<b>d</b>) configurations regarding <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mi mathvariant="normal">r</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>e</b>–<b>h</b>) Same as (<b>a</b>–<b>d</b>), but showing inversion errors regarding <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mi mathvariant="normal">i</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>i</b>–<b>l</b>) Same as (<b>a</b>–<b>d</b>), but showing inversion errors regarding <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>S</mi> <mi>A</mi> </mrow> </semantics></math>. (<b>m</b>–<b>p</b>) Same as (<b>a</b>–<b>d</b>), but showing inversion errors regarding <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>q</b>–<b>t</b>) Same as (<b>a</b>–<b>d</b>), but showing inversion errors regarding <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mi mathvariant="normal">t</mi> </mrow> </msub> </mrow> </semantics></math>. The error levels of 10% and 20% are represented by blue and orange images, respectively. The results are presented in the form of violin plots, which are an enhanced version of box plots that provide more detailed information about the distribution of the data. In each violin plot, the vertical gray bars correspond to the ends of the box plot whiskers, representing the maximum and minimum values of the statistical distribution. The shaded area corresponds to the interquartile range of 25% and 75% of the box plot. Horizontally, the shaded area represents the probability density function of the data distribution, showing the frequency of data distribution in each interval. The white points indicate the position of zero, and the horizontal green bars represent the mean values.</p> "> Figure 13
<p>Original optical data from the HSRL collected during the DISCOVER−AQ field campaign in California on 30 and 31 January 2013. The horizontal axis represents UTC time, and the vertical axis represents altitude above sea level. The data for the two days are shown in the left and right columns, respectively. (<b>a</b>,<b>b</b>) Profile s of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>β</mi> </mrow> <mrow> <mn>355</mn> </mrow> </msub> </mrow> </semantics></math> on the two days. (<b>c</b>,<b>d</b>) Profile s of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>β</mi> </mrow> <mrow> <mn>532</mn> </mrow> </msub> </mrow> </semantics></math> on the two days. (<b>e</b>,<b>f</b>) Profile s of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>β</mi> </mrow> <mrow> <mn>1064</mn> </mrow> </msub> </mrow> </semantics></math> on the two days. (<b>g</b>,<b>h</b>) Profile s of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>355</mn> </mrow> </msub> </mrow> </semantics></math> on the two days. (<b>i</b>,<b>j</b>) Profile s of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mn>532</mn> </mrow> </msub> </mrow> </semantics></math> on the two days. (<b>k</b>,<b>l</b>) Profile s of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>γ</mi> </mrow> <mrow> <mi>α</mi> </mrow> </msub> <mo> </mo> <mo>(</mo> <mn>355</mn> <mo>−</mo> <mn>532</mn> <mo>)</mo> </mrow> </semantics></math> on the two days.</p> "> Figure 14
<p>Comparisons of retrieved microphysical parameter profiles from the HSRL on 30 January 2013, with P−3B in-situ measurements at six validation sites. (<b>a</b>–<b>g</b>) represent the results for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </msub> </mrow> </semantics></math>, while (<b>h</b>–<b>n</b>) represent the results for <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>S</mi> <mi>A</mi> </mrow> </semantics></math>. (<b>a</b>–<b>f</b>) and (<b>h</b>–<b>m</b>) show the profile information for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>S</mi> <mi>A</mi> </mrow> </semantics></math>, respectively, at the six sites. The results retrieved using the 3<span class="html-italic">β</span> + 2<span class="html-italic">α</span>, 3<span class="html-italic">β</span> + 1<span class="html-italic">α</span>, 2<span class="html-italic">β</span> + 1<span class="html-italic">α</span>, and 3<span class="html-italic">β</span> configurations are depicted with blue, orange, yellow, and purple lines and markers, respectively, while in-situ measurement data are represented by black lines and markers. The <span class="html-italic">x</span>-axis represents the values of the microphysical parameters, and the <span class="html-italic">y</span>-axis represents altitude. (<b>g</b>,<b>n</b>) show box plots of the retrieval errors for all data points at the six validation sites on that day, where the color scheme matches that of <a href="#remotesensing-16-02265-f009" class="html-fig">Figure 9</a>.</p> "> Figure 15
<p>Comparisons of retrieved microphysical parameter profiles from the HSRL on 31 January 2013, with P-3B in-situ measurements at six validation sites. (<b>a</b>–<b>g</b>) represent the results for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </msub> </mrow> </semantics></math>, while (<b>h</b>–<b>n</b>) represent the results for <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>S</mi> <mi>A</mi> </mrow> </semantics></math>. (<b>a</b>–<b>f</b>) and (<b>h</b>–<b>m</b>) show the profile information for <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>S</mi> <mi>A</mi> </mrow> </semantics></math>, respectively, at the six sites. The annotations in the figure correspond to those in <a href="#remotesensing-16-02265-f014" class="html-fig">Figure 14</a>.</p> ">
Abstract
:1. Introduction
2. Materials and Methods
2.1. Retrieval Algorithm for Fine-Mode Aerosol Microphysical Properties Based on LUT—Basic Algorithm: k-NN and RF
2.2. Retrieval Algorithm for Fine-Mode Aerosol Microphysical Properties Based on LUT—Modified Algorithm: Weighted “Bagging” Strategy and Self-Posed Scheme
2.3. Source and Processing of NASA DISCOVER-AQ Field Campaign Data
3. Results
3.1. Numerical Test of Simulated Error-Free Data
3.2. Sensitivity Study of Individual Input Optical Property
3.3. Study on Input Optical Properties with Random Gaussian Noise
3.4. DISCOVER-AQ Case Study
4. Discussion and Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Values | Interval |
---|---|---|
1.30–1.70 | 0.02 | |
0.00–0.05 | 0.001 | |
0.38–0.50 | 0.01 | |
(nm) | 50–500 | 10 |
Category | Parameter | Values |
---|---|---|
Grid | 1.3, 1.4, 1.5, 1.6 | |
0.001, 0.005, 0.01, 0.015, 0.020, 0.025, 0.035, 0.050 | ||
lnσ | 0.40 | |
(nm) | 70, 100, 140, 180, 240, 300 | |
Non-grid | 1.35, 1.45, 1.55, 1.65 | |
0.001, 0.005, 0.01, 0.015, 0.020, 0.025, 0.035, 0.050 | ||
0.40 | ||
(nm) | 75, 100, 140, 180, 225, 300 |
Spiral Points | Site1 | Site2 | Site3 | Site4 | Site5 | Site6 |
---|---|---|---|---|---|---|
Latitude (°) | 35.35 | 36.03 | 36.32 | 36.17 | 36.62 | 36.76 |
Longitude (°) | −118.98 | −119.03 | −119.67 | −120.10 | −120.40 | −119.78 |
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Zhou, Z.; Ma, Y.; Yin, Z.; Hu, Q.; Veselovskii, I.; Müller, D.; Gong, W. A Modified Look-Up Table Based Algorithm with a Self-Posed Scheme for Fine-Mode Aerosol Microphysical Properties Inversion by Multi-Wavelength Lidar. Remote Sens. 2024, 16, 2265. https://doi.org/10.3390/rs16132265
Zhou Z, Ma Y, Yin Z, Hu Q, Veselovskii I, Müller D, Gong W. A Modified Look-Up Table Based Algorithm with a Self-Posed Scheme for Fine-Mode Aerosol Microphysical Properties Inversion by Multi-Wavelength Lidar. Remote Sensing. 2024; 16(13):2265. https://doi.org/10.3390/rs16132265
Chicago/Turabian StyleZhou, Zeyu, Yingying Ma, Zhenping Yin, Qiaoyun Hu, Igor Veselovskii, Detlef Müller, and Wei Gong. 2024. "A Modified Look-Up Table Based Algorithm with a Self-Posed Scheme for Fine-Mode Aerosol Microphysical Properties Inversion by Multi-Wavelength Lidar" Remote Sensing 16, no. 13: 2265. https://doi.org/10.3390/rs16132265